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https://physicshelpforum.com/threads/fractal-universe-5d-space-time-frequency-of-cycles-in-dimensional-scale.15673/page-3
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# Fractal Universe - 5D Space-Time: Frequency Of Cycles In Dimensional Scale
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#### topsquark
Forum Staff
"The special-relativistic thermodynamics is an interesting area which has not been settled to full satisfaction AFAIK but nonetheless, it should be pointed out that when you heat up a body, the individual particles of the body only gain kinetic energy--so the rest mass of the individual particles does not change. But when you see the body as a whole with its center of mass at rest (and whose constituent particles are only engaging in thermal motion), the rest mass of the full body as a whole gets increased, in particular, the heat you provide goes into the rest mass of the body as a whole"
This is exactly, what I predicted
Then you'd better check again. As benit13 said nothing changes the rest mass of a particle. It is the mass of a particle with no regard to motion. Now, when you heat something up then the particle's kinetic energy increases and the particles gain momentum. The total energy of the particle then obeys $$\displaystyle E^2 = (pc)^2 + (mc^2)^2$$, where we are using whatever average p is appropriate. But m is the rest mass and does not change under any circumstances, even when changing reference frames. Now, if we are talking about a macroscopic object its rest mass due to the individual particles stays the same, so we still get the same rest mass. What happens is the mass of the whole object reflects the extra kinetic energy contained in it. This does change the mass of the object, but not it's rest mass. The thermal energy simply gets absorbed into its total energy.
-Dan
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#### GatheringKnowledge
Then you'd better check again. As benit13 said nothing changes the rest mass of a particle. It is the mass of a particle with no regard to motion. Now, when you heat something up then the particle's kinetic energy increases and the particles gain momentum. The total energy of the particle then obeys $$\displaystyle E^2 = (pc)^2 + (mc^2)^2$$, where we are using whatever average p is appropriate. But m is the rest mass and does not change under any circumstances, even when changing reference frames. Now, if we are talking about a macroscopic object its rest mass due to the individual particles stays the same, so we still get the same rest mass. What happens is the mass of the whole object reflects the extra kinetic energy contained in it. This does change the mass of the object, but not it's rest mass. The thermal energy simply gets absorbed into its total energy.
-Dan
It's not that I want to undermine your authority or something, but I've made some google search and those are some of the results:
Does mass change with temperature? - Quora
Generally, opinions are pretty divided among physicists, however it seems, that according to the majority, heat transfer DOES indeed increase the rest mass of a macroscopic body - although this increase is very tiny. Here's also a site, which proves that the increase of electric charge is resulting in small addition of rest mass to the system:
"Both the actual increase in mass and the percent increase are very small, since energy is divided by c2size 12{c rSup { size 8{2} } } {}, a very large number. We would have to be able to measure the mass of the battery to a precision of a billionth of a percent, or 1 part in 1011, to notice this increase. It is no wonder that the mass variation is not readily observed. In fact, this change in mass is so small that we may question how you could verify it is real. The answer is found in nuclear processes in which the percentage of mass destroyed is large enough to be measured. The mass of the fuel of a nuclear reactor, for example, is measurably smaller when its energy has been used. In that case, stored energy has been released (converted mostly to heat and electricity) and the rest mass has decreased. This is also the case when you use the energy stored in a battery, except that the stored energy is much greater in nuclear processes, making the change in mass measurable in practice as well as in theory."
I would agree with your statements, if instead of "What happens is the mass of the whole object reflects the extra kinetic energy contained in it.", you would say: "...whole object radiates out the extra kinetic energy contained in it.". I might be an amateur, but I know enough about mass/energy equivalence, to say that if: "The thermal energy simply gets absorbed into its total energy.", it will actually result with a tiny increase of rest mass - but we won't measure it, since the additional mass/energy is immidiately released into the environment, due to the constant thermal radiation...
If we'll move on higher level in scale dimension, we will be able to use the same mechanism, to explain a scenario, where we hit a solid block of granite with a steel pipe, causing the increase of internal vibrations in both systems, which result in emission of a sound wave (among other waves) to the environment - so that in the end, the balance of energy emission/absorption is being maintained...
However, what matters at most for the discussion about fractal gravity and gravitational expulsion, is the ratio of energy emission/absorption. If an external source causes a constant increase of energy level in a body (or system of bodies), it's excess will be emitted into the environment, disrupting the initial balance of mass/energy equivalence. It's quite logical to me, that the additional mass/energy will in such case turn into radiation, that will influence the potential energy of another body by inducing a kinetic force on it or increasing it's level of thermal energy.
Here are examples of forces (thermal radiation, kinetic pressure of light), which are induced on matter due to emission of additional energy from a system:
And here's just another example of the same process - only here, it's the source of radiation, which is experiencing kinetic force of lift due to the potential energy of a body with greater mass (Earth):
All examples are based on the same laws of mass/energy equivalence. However, mechanical compression of a mass/energy distribution requires a different explanation - I will try to explain it better in another post...
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#### topsquark
Forum Staff
You missed the reason I made that post. The rest mass of an object never changes. What you might call the "relativitic mass" can and does.
-Dan
#### benit13
Just to clarify, the thread where GatheringKnowledge's quote was derived was talking about the rest mass of macroscopic objects. Since rest mass is a property of fundamental particles, it's a bit of an odd discussion.
I'm not really well read on the nuances of SR. However, if one was to extend the definition of rest mass to include macroscopic bodies, then I would suggest a definition where the rest mass of the macroscopic object is just the sum of the rest masses of the constituent particles:
$$\displaystyle m_0 = \sum_i m_{0,i}$$
This seems to be the definition TopSquark is using as well. This value would never change, just like the usual definition of rest mass, assuming that the number of particles is fixed (no particles leaving or entering the control volume of the macroscopic object). Technically, since every object in the universe has a temperature above 0K, this is a minimum limit to the measured mass and would never actually be measured in experiments. The higher the temperature, the higher the actual mass deviates from this one, but the error will be incredibly small even for objects with high temperatures since the speeds of particles within objects is almost always non-relativistic. Then, one can just assume that the error is negligible and use this mass in SR calculations without any difficulty or systematic errors.
In the thread, they discuss a different definition, which is one where the centre of mass of the macroscopic object is at rest but the individual masses within the object can move. If you take this definition, then this macroscopic rest mass would become a very weak function of the average speed of the particles in the object or, alternatively, a very weak function of temperature. This is not how I would definite it because it muddies the waters, but hey ho.
topsquark
#### benit13
Generally, opinions are pretty divided among physicists, however it seems, that according to the majority, heat transfer DOES indeed increase the rest mass of a macroscopic body - although this increase is very tiny. Here's also a site, which proves that the increase of electric charge is resulting in small addition of rest mass to the system:
Fair enough. In that case, rest mass would be affected by anything that affects the masses or motion of those masses (e.g. binding energy, chemical potential energy, thermodynamics).
Now that you mention it, it's probably the case that most macroscopic objects of interest (such as atomic nuclei) don't have measured masses equal to their constituents anyway because of the nuclear binding energy, so my previous suggestion in post #24 is probably not useful to anybody.
#### GatheringKnowledge
You missed the reason I made that post. The rest mass of an object never changes. What you might call the "relativitic mass" can and does.
-Dan
I think, that the problem comes from all those different terms, used to describe mass of objects. There's invariant rest mass and there's relativistic inertial mass - am I right? What I have on my mind, when I speak about "rest mass", is the mass of an object, measured in it's own "stationary" frame. What I've tried to say, is that by increasing the energy by heating/cooling and compressing a macroscale object, we will change it's mass, as it is measured in it's own frame. This is supported by all those links
EXAMPLE 28.7 CALCULATING REST MASS: A SMALL MASS INCREASE DUE TO ENERGY INPUT
A car battery is rated to be able to move 600 ampere-hours (A⋅h) of charge at 12.0 V. (a) Calculate the increase in rest mass of such a battery when it is taken from being fully depleted to being fully charged. (b) What percent increase is this, given the battery’s mass is 20.0 kg?
#### GatheringKnowledge
Just to clarify, the thread where GatheringKnowledge's quote was derived was talking about the rest mass of macroscopic objects. Since rest mass is a property of fundamental particles, it's a bit of an odd discussion.
I'm not really well read on the nuances of SR. However, if one was to extend the definition of rest mass to include macroscopic bodies, then I would suggest a definition where the rest mass of the macroscopic object is just the sum of the rest masses of the constituent particles:
$$\displaystyle m_0 = \sum_i m_{0,i}$$
This seems to be the definition TopSquark is using as well. This value would never change, just like the usual definition of rest mass, assuming that the number of particles is fixed (no particles leaving or entering the control volume of the macroscopic object). Technically, since every object in the universe has a temperature above 0K, this is a minimum limit to the measured mass and would never actually be measured in experiments. The higher the temperature, the higher the actual mass deviates from this one, but the error will be incredibly small even for objects with high temperatures since the speeds of particles within objects is almost always non-relativistic. Then, one can just assume that the error is negligible and use this mass in SR calculations without any difficulty or systematic errors.
In the thread, they discuss a different definition, which is one where the centre of mass of the macroscopic object is at rest but the individual masses within the object can move. If you take this definition, then this macroscopic rest mass would become a very weak function of the average speed of the particles in the object or, alternatively, a very weak function of temperature. This is not how I would definite it because it muddies the waters, but hey ho.
This is because in order, to create a multiscale model of a physical mechanism, you need to treat macroscale objects, as a total sum of energy, which is
"stored" in a system of "particles". By changing the state of an object, we make a definitive change in the equivalence of energies - and since nature always tries to reach balance, additional energy is released in some form into environment.
If we change the temperature of a macrosale object, rest mass of atoms/molecules will remain the same - as atomic mass is an intrinsic property of subatomic particles. By heating a macroscale object we are increasing the vibrational frequency in a system of particles and this change is definitive in macroscale frame - this is why, it has to be measurable as an inbalance in the mass/energy equivalence... I don't consider this as confusing at all...
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#### topsquark
Forum Staff
...this is why, it has to be measurable as an inbalance in the mass/energy equivalence...
I'm with you up to here, but what do you mean by "inbalance in the mass/energy equivalence." There is no imbalance... energy is conserved so long as we keep track of "source" terms, such as temperature or potential fields. Are these extra terms what you are calling an "imbalance?"
(Since we're talking about Thermodynamics of a macroscopic system I should say that I'm assuming the object is at equilibrium in contact with a heat reservoir. I hate Thermo!)
-Dan
#### GatheringKnowledge
I'm with you up to here, but what do you mean by "inbalance in the mass/energy equivalence." There is no imbalance... energy is conserved so long as we keep track of "source" terms, such as temperature or potential fields. Are these extra terms what you are calling an "imbalance?"
(Since we're talking about Thermodynamics of a macroscopic system I should say that I'm assuming the object is at equilibrium in contact with a heat reservoir. I hate Thermo!)
-Dan
Good question - I say, that' it's the imbalance between temperature of a macroscale object and it's environment. This is why the temperature is radiated out and heats up colder matter. Thing is, that such imbalance is not measurable on subatomic scale (energy of electrons remains the same) - but it becomes visible on molecular scale (molecules move faster, than before).
#### GatheringKnowledge
This is why I love discussing physics with intelligent people - sometimes a question can push my thoughts on the right track. I think, that I figured out the main difference between heat transfer and mechanical compression. While change of temperature causes external imbalance between macroscopic object and it's environment, compression causes internal imbalance between vibrational frequency of particles (molecules) and temperature of macroscopic object. External imbalance of temperature is nullified by thermal radiation, but energy used in the work needed to compress a macroscopic object becomes it's potential energy and uses kinetic energy of the external environment, to nullify the pressure differential during decompression - this is why air gets cold locally, when we use a deodorant.
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2020-02-18 11:11:45
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https://en.wikipedia.org/wiki/Bitangents_of_a_quartic
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# Bitangents of a quartic
The Trott curve and seven of its bitangents. The others are symmetric with respect to 90° rotations through the origin.
The Trott curve with all 28 bitangents.
In real algebraic geometry, a general quartic plane curve has 28 bitangent lines, lines that are tangent to the curve in two places. These lines exist in the complex projective plane, but it is possible to define curves for which all 28 of these lines have real numbers as their coordinates and therefore belong to the Euclidean plane.
An explicit quartic with twenty-eight real bitangents was first given by Plücker (1839)[1] As Plücker showed, the number of real bitangents of any quartic must be 28, 16, or a number less than 9. Another quartic with 28 real bitangents can be formed by the locus of centers of ellipses with fixed axis lengths, tangent to two non-parallel lines.[2] Shioda (1995) gave a different construction of a quartic with twenty-eight bitangents, formed by projecting a cubic surface; twenty-seven of the bitangents to Shioda's curve are real while the twenty-eighth is the line at infinity in the projective plane.
## Example
The Trott curve, another curve with 28 real bitangents, is the set of points (x,y) satisfying the degree four polynomial equation
${\displaystyle \displaystyle 144(x^{4}+y^{4})-225(x^{2}+y^{2})+350x^{2}y^{2}+81=0.}$
These points form a nonsingular quartic curve that has genus three and that has twenty-eight real bitangents.[3]
Like the examples of Plücker and of Blum and Guinand, the Trott curve has four separated ovals, the maximum number for a curve of degree four, and hence is an M-curve. The four ovals can be grouped into six different pairs of ovals; for each pair of ovals there are four bitangents touching both ovals in the pair, two that separate the two ovals, and two that do not. Additionally, each oval bounds a nonconvex region of the plane and has one bitangent spanning the nonconvex portion of its boundary.
## Connections to other structures
The dual curve to a quartic curve has 28 real ordinary double points, dual to the 28 bitangents of the primal curve.
The 28 bitangents of a quartic may also be placed in correspondence with symbols of the form
${\displaystyle \left[{\begin{array}{ccc}a&b&c\\d&e&f\\\end{array}}\right]}$
where a, b, c, d, e and f are all zero or one and where
ad + be + cf = 1 (mod 2).[4]
There are 64 choices for a, b, c, d, e and f, but only 28 of these choices produce an odd sum. One may also interpret a, b, and c as the homogeneous coordinates of a point of the Fano plane and d, e, and f as the coordinates of a line in the same finite projective plane; the condition that the sum is odd is equivalent to requiring that the point and the line do not touch each other, and there are 28 different pairs of a point and a line that do not touch.
The points and lines of the Fano plane that are disjoint from a non-incident point-line pair form a triangle, and the bitangents of a quartic have been considered as being in correspondence with the 28 triangles of the Fano plane.[5] The Levi graph of the Fano plane is the Heawood graph, in which the triangles of the Fano plane are represented by 6-cycles. The 28 6-cycles of the Heawood graph in turn correspond to the 28 vertices of the Coxeter graph.[6]
The 28 bitangents of a quartic also correspond to pairs of the 56 lines on a degree-2 del Pezzo surface,[5] and to the 28 odd theta characteristics.
The 27 lines on the cubic and the 28 bitangents on a quartic, together with the 120 tritangent planes of a canonic sextic curve of genus 4, form a "trinity" in the sense of Vladimir Arnold, specifically a form of McKay correspondence,[7][8][9] and can be related to many further objects, including E7 and E8, as discussed at trinities.
## Notes
1. ^ See e.g. Gray (1982).
2. ^
3. ^
4. ^
5. ^ a b
6. ^ Dejter, Italo J. (2011), "From the Coxeter graph to the Klein graph", Journal of Graph Theory, arXiv:, doi:10.1002/jgt.20597.
7. ^ le Bruyn, Lieven (17 June 2008), Arnold’s trinities, archived from the original on 2011-04-11
8. ^ Arnold 1997, p. 13 – Arnold, Vladimir, 1997, Toronto Lectures, Lecture 2: Symplectization, Complexification and Mathematical Trinities, June 1997 (last updated August, 1998). TeX, PostScript, PDF
9. ^ (McKay & Sebbar 2007, p. 11)
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2017-03-26 13:24:53
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https://rpg.stackexchange.com/questions/119418/does-shield-retroactively-change-the-result-of-an-attack
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Does shield retroactively change the result of an attack? [duplicate]
Shield spell Casting time line says (PHB, p. 275):
1 reaction, which you take when you are hit by an attack or targeted by the magic missile spell.
(bold highlight by me)
PHB, p. 194, 1st paragraph under "Attack Rolls" say:
To make an attack roll, roll a d20 and add the appropriate modifiers. If the total of the roll plus modifiers equals or exceeds the target's Armor Class (AC), the attack hits.
So, disregarding the magic missile spell case, the trigger for the Shield is the fact of hit, i.e. attack roll was made and it was determined that the target was hit. What would be the point of casting the Shield spell at this point if attack is already resolved?
Spell effect description says:
An invisible barrier of magical force appears and protects you. Until the start of your next turn, you have a +5 bonus to AC, including against the triggering attack, and you take no damage from magic missile.
(again, bold highlight is mine)
The description seem to imply that it retroactively changes the outcome of the attack roll, otherwise the bolded text does not make any sense; but on the other hand it does not spell it out explicitly and it specifically has different wording for being hit by an attack vs. being targeted by magic missile (if the intention was to retroactively make attack miss, the wording could have used "targeted" for both cases; and PHB, p.194 explicitly mentions picking a target for attack, so targeting is a well-defined step).
Is there something that supports retroactive outcome change?
marked as duplicate by Rubiksmoose♦ dnd-5e StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Mar 29 '18 at 11:23
It does retroactively affect the attack.
One of the main benefits of the shield spell is that, when using it to defend against an attack, you know whether or not the attack would've hit you first. If it was phrased 'when you are targeted by an attack' rather than 'when you are hit by an attack', that would imply you wouldn't know the outcome and could potentially waste the spell against an attack that was already missing you.
In general, reactions occur after their triggers unless an explicit exception is made to have it 'interrupt' their trigger, which shield does (as quoted/emphasized in the question). To quote from @Rubiksmoose's excellent answer to 'Do reactions interrupt their triggers or not?':
Xanathar's Guide to Everything outlines the general rule for the timing of reactions:
If you’re unsure when a reaction occurs in relation to its trigger, here’s the rule: the reaction happens after its trigger completes, unless the description of the reaction explicitly says otherwise.
So, if the timing of the spell/ability you are using does not specify a timing then the reaction will come after whatever triggered it.
This is essentially just rephrasing what was already in the DMG since its release:
Various spells and features give a creature more reaction options, and sometimes the timing of a reaction can be difficult to adjudicate. Use this rule of thumb: follow whatever timing is specified in the reaction’s description. For example, the opportunity attack and the shield spell are clear about the fact that they can interrupt their triggers. If a reaction has no timing specified, or the timing is unclear, the reaction occurs after its trigger finishes, as in the Ready action. (D&DB)
Note the specific mention of shield interrupting its trigger in that quote from the DMG, for confirmation of that functionality.
• In retrospect, this is possibly a duplicate of the question I linked to, but I think the bit on the difference between 'targeted by an attack' and 'hit by an attack' is relevant to the specific question being asked here. – CTWind Mar 29 '18 at 6:41
• I think it's also worth adding that shield's description itself supports retroactive outcome change (the spell does what it says it does), and since 5e has (as Jeremy Crawford as repeatedly said) an exceptions-based rule system, that's all that's needed. – Marq Mar 29 '18 at 8:23
• @Marq I feel "In general, reactions occur after their triggers unless an explicit exception is made to have it 'interrupt' their trigger, which shield does" (plus the emphasized quote in the question) covers that. – CTWind Mar 29 '18 at 8:28
It triggers after the attack but before damage is applied.
As you highlighted, the bonus applies to the triggering attack itself and so must be retroactive.
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2019-07-17 02:57:09
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https://renukusabuzuju.stcroixcaribbeanweddings.com/estimating-transformations-for-regression-book-7471ei.php
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Last edited by Voodoogis
Monday, July 27, 2020 | History
2 edition of Estimating transformations for regression found in the catalog.
Estimating transformations for regression
Robert Tibshirani
# Estimating transformations for regression
## by Robert Tibshirani
Written in English
Subjects:
• Mathematical optimization,
• Regression analysis
• Edition Notes
Classifications The Physical Object Statement by Robert Tibshirani. Series Technical report / University of Toronto, Dept. of Statistics -- no. 4 (1986), Technical report (University of Toronto. Dept. of Statistics) -- no. 4 (1986) LC Classifications QA278.2 T53 1986 Pagination 14 p. -- Number of Pages 14 Open Library OL21667586M
Understanding Regression Analysis: An Introductory Guide presents the fundamentals of regression analysis, from its meaning to uses, in a concise, easy-to-read, and non-technical style. It illustrates how regression coefficients are estimated, interpreted, and used in a variety of settings within the social sciences, business, law, and public policy. Linear regression is one of the basic models for predictive modeling. In this recipe, we show you how to implement a fully functional method that allows the estimation of such models. This recipe mainly concentrates on array manipulation, but also shows a typical example of more complex Julia code, combining several standard functionalities.
On the Estimation and Properties of Logistic Regression Parameters 1Anthony Ngunyi, 2Peter Nyamuhanga Mwita, 2 Romanus O. Odhiambo Abstract: Logistic regression is widely used as a popular model for the analysis of binary data with the areas of applications including physical, biomedical and behavioral sciences. In this study, the logistic. While the main focus of the book in on data transformation and weighting, it also draws upon ideas from diverse fields such as influence diagnostics, robustness, bootstrapping, nonparametric data smoothing, quasi-likelihood methods, errors-in-variables, and random coefficients.
USEFUL TRANSFORMATIONS Purpose of Transformations there are alternative methods for estimating the parameters of the relation, namely, non-linear regression and generalized regression models. 4) Confidence intervals computed on transformed variables need to be computed byFile Size: 33KB. Book Description. Best Fit Lines and Curves, and Some Mathe-Magical Transformations (Volume III of the Working Guides to Estimating & Forecasting series) concentrates on techniques for finding the Best Fit Line or Curve to some historical data allowing us to interpolate or extrapolate the implied relationship that will underpin our prediction. A range of simple ‘Moving Measures’ are.
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### Estimating transformations for regression by Robert Tibshirani Download PDF EPUB FB2
Estimating Optimal Transformations for Multiple Regression and Correlation LEO BREIMAN and JEROME H. FRIEDMAN* In regression analysis the response variable Y and the predictor variables XI., Xp are often replaced by functions 0(Y) and 4I(XI), p, (Xp).
We discuss a procedure for estimating those functions 0* and 4 *. This monograph provides a careful review of the major statistical techniques used to analyze regression data with nonconstant variability and skewness.
The authors have developed statistical techniques--such as formal fitting methods and less formal graphical techniques-- that can be applied to many problems across a range of disciplines, including pharmacokinetics, econometrics, biochemical.
Journal of Data Science 2(), Estimating Optimal Transformations for Multiple Regression Using the ACE Algorithm Duolao Wang1 and Michael Murphy2 1London School of Hygiene and Tropical Medicine and 2London School of Economics Abstract: This paper introduces the alternating conditional expectation (ACE) algorithm of Breiman and Friedman () for estimating the trans.
The book also includes an extensive treatment of estimating variance functions in regression. Instructors. We provide complimentary e-inspection copies of primary textbooks to instructors considering our books for course adoption. Request an e-inspection copy. Share this Title. The regression function is usually expressed mathematically in one of the following ways: basic notation, summation notation, or matrix notation.
The Y variable represents the outcome you’re interested in, called the dependent variable, and the Xs represent all the independent (or explanatory) variables. Your objective now is to estimate the population regression function (PRF) using [ ].
Consider simulated data where the conditional distribution of Y is log-normal given X, but where transform-both-sides regression methods use unlogged Y. Predictor X 1 is linearly related to log Y, X 2 is related by $$\vert X_{2} -\frac{1} {2}\vert$$, and categorical X 3 has reference group a effect of zero, group b effect ofand group c Author: Frank E.
Harrell. Abstract: This paper introduces the alternating conditional expectation (ACE) algorithm of Breiman and Friedman () for estimating the transformations of a response and a set of predictor variables in multiple regression that produce the maximum linear effect between the (transformed) independent variables and the (transformed) response.
Best Fit Lines and Curves, and Some Mathe-Magical Transformations (Volume III of the Working Guides to Estimating & Forecasting series) concentrates on techniques for finding the Best Fit Line or Curve to some historical data allowing us to interpolate or extrapolate the implied relationship that will underpin our prediction.
A range of simple ‘Moving Measures’ are suggested to smooth the 3/5(1). Tibshirani: Estimating Transformations for Regression 0 0 (0 * * o x Figure 1. Brain Weight (Y) Versus Body Weight (XJ, Example 1.
ACE and at the same time is designed (like the Box-Cox procedure) specifically for regression. It differs mainly from. The book also includes an extensive treatment of estimating variance functions in regression.
Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - Cited by: Oberg and Davidian () extended the methods for estimating transformations to non-linear mixed effects models for repeated measurement data, employing the transform-both-sides model that was.
The ACE algorithm was proposed by Breiman and Friedman () [10] for estimating the transformations of dependent variable and a set of independent variables in multiple regression that.
Results. Although outcome transformations bias point estimates, violations of the normality assumption in linear regression analyses do not. The normality assumption is necessary to unbiasedly estimate standard errors, and hence confidence intervals and r, in large sample sizes (e.g., where the number of observations per variable is >10) violations of this normality assumption Cited by: This book is composed of four chapters covering a variety of topics about using Stata for regression.
We should emphasize that this book is about “data analysis” and that it demonstrates how Stata can be used for regression analysis, as opposed to a book that covers the statistical basis of multiple regression. In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome variable') and one or more independent variables (often called 'predictors', 'covariates', or 'features').
The most common form of regression analysis is linear regression, in which a researcher finds the line (or a more complex. A good book on regression or analysis of designed experiments can provide appropriate guidance about which transformations solve different problems.
The Box-Cox transformation is the most commonly used variance-stabilizing transformation. Linear regression; Logistic regression; Nonlinear input transformations and regularization (not in draft yet) Nonlinear parametric models (not in draft yet) Understanding, evaluating and improving the performance.
Expected new data error: performance in production; Estimating the expected new data error; The training error–generalization gap. Nonparametric Time Series Analysis: Nonparametric Regression, Locally Weighted Regression, Autoregression, and Quantile Regression.
A Course in Time Series Analysis, () Characterization and utilization of noisy displacement signals from simple shear device using linear and kernel regression by: Statistics made easy!!.
Learn about the t-test, the chi square test, the p value and more - Duration: Global Health with Greg Martinviews. e-Pub (e-book) Partial support for this work was provided by the National Science Foundation's Division of Undergraduate Education through grants DUE, DUE, and DUE.
Breiman, L. and Friedman, J.H. (), “Estimating Optimal Transformations for Multiple Regression and Correlation,” (with discussion) Journal of the American Statistical Association, 80, – MathSciNet zbMATH CrossRef Google ScholarAuthor: Martin R. Young.This handbook provides a detailed, down-to-earth introduction to regression diagnostic analysis, a technique of growing importance for work in applied statistics.
Heavily illustrated, with numerous examples to illuminate the discussion, this timely volume outlines methods for regression models, stressing detection of outliers and inadequate models; describes the transformation of variables in.s2 estimator for ˙2 s2 = MSE = SSE n 2 = P (Y i Y^ i)2 n 2 = P e2 i n 2 I MSE is an unbiased estimator of ˙2 EfMSEg= ˙2 I The sum of squares SSE has n-2 \degrees of freedom" associated with it.
I Cochran’s theorem (later in the course) tells us where degree’s of freedom come from and how to calculate Size: KB.
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2021-02-26 16:25:27
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https://discretize.simpeg.xyz/en/main/api/generated/discretize.TreeMesh.average_node_to_cell.html
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# discretize.TreeMesh.average_node_to_cell#
TreeMesh.average_node_to_cell#
Averaging operator from nodes to cell centers (scalar quantities).
This property constructs a 2nd order averaging operator that maps scalar quantities from nodes to cell centers. This averaging operator is used when a discrete scalar quantity defined on mesh nodes must be projected to cell centers. Once constructed, the operator is stored permanently as a property of the mesh. See notes.
Returns
(n_cells, n_nodes) scipy.sparse.csr_matrix
The scalar averaging operator from nodes to cell centers
Notes
Let $$\boldsymbol{\phi_n}$$ be a discrete scalar quantity that lives on mesh nodes. average_node_to_cell constructs a discrete linear operator $$\mathbf{A_{nc}}$$ that projects $$\boldsymbol{\phi_f}$$ to cell centers, i.e.:
$\boldsymbol{\phi_c} = \mathbf{A_{nc}} \, \boldsymbol{\phi_n}$
where $$\boldsymbol{\phi_c}$$ approximates the value of the scalar quantity at cell centers. For each cell, we are simply averaging the values defined on its nodes. The operation is implemented as a matrix vector product, i.e.:
phi_c = Anc @ phi_n
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2022-05-18 17:05:38
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https://www.coursehero.com/file/9082429/1-5-n-1-N-1-4-Acknowledgment-The-views-expressed-in-this/
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varofsamplevar
# 1 5 n 1 n 1 4 acknowledgment the views expressed in
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Unformatted text preview: olicies of the U.S. Bureau of Labor Statistics. The authors thank John Eltinge for many helpful suggestions that improved the paper. References 1] Eungchun Cho, Moon Jung Cho and John Eltinge, The variance of sample variance from a nite population, Proceedings of Joint American Statistical Association and International Statistical Institute Conference, Toronto, Canada, August, 2004 2] W. G. Cochran, Sampling Techniques (3rd ed. ), John Wiley, 1977. 3] J. W. Tukey, Some sampling simpli ed, Journal of the American Statistical Association, 45 (1950), 501-519. 4] J. W. Tukey, Variances of variance components: I. Balanced designs. The Annals of Mathematical Statistics, 27 (1956), 722-736. 5] J. W. Tukey, Variances of variance components: II. Unbalanced single classi cations. The Annals of Mathematical Statistics, 28 (1957), 43-56. 6] J. W. Tukey, Variance components: III. The third moment in a balanced single classi cation. The Annals of Mathematical Statistics, 28 (1957), 378-384. 1293...
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## This test prep was uploaded on 03/23/2014 for the course MATH 6201 taught by Professor Zhang,j during the Spring '08 term at UNC Charlotte.
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2017-05-29 15:59:04
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http://mathhelpforum.com/new-users/209702-need-help-how-do-i-do.html
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# Thread: Need help!!! how do i do it!!
1. ## Need help!!! how do i do it!!
A modern sculpture in a park contains a parabolic arc that starts at the ground and reaches a maximum height of 10 feet after a horizontal distance of 4 feet. Write a quadratic function (vertex form) that describes the shape of the outside arc, where y is the height of a point on the arc and x is the horizontal distance from the left hand starting point.
or
The girls’ softball team is sponsoring a fundraising trip to see a professional baseball game. They charter a 60-passenger bus for $525 In order to make a profit they will charge$15 per person if all seats on the bus are sold, but for each empty seat, they will increase the price by $1.50 per person. Write a quadratic function giving the softball teams profit P(n) from this fund-raiser as a function of the number of passengers is n. what is the minimum number of passengers needed in order for the softball team not to lose money? What is the maximum profit the team can make with this fund-raiser, and how many passengers will it take to achieve this maximum? 2. ## Re: Need help!!! how do i do it!! 1.) You know 3 points...(0,0), (4,10), (8,0). Since we know the two roots, we could state$\displaystyle y=kx(x-8)\$. Now use the second point to determine k.
### a modern sculpture in a park contains a parabolic arc that starts at the ground
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2018-06-20 19:54:47
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https://math.stackexchange.com/questions/3396882/proving-expectation-to-be-infinite-with-an-inequality
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# Proving expectation to be infinite with an inequality
Let $$X$$ be a non-negative random variable, and suppose that $$P(X \geq n) \geq 1/n$$ for each $$n \in \mathbb{N}$$. Prove that $$E(X) = \infty$$.
I have been stuck with this problem for a few days now. I guess it can make some sense intuitively because you have some probability mass everywhere, and we're looking at probability of it being greater than some value. I tried to use inequalities like Markov's and Chebyshev's with no luck. I was hoping if someone can please explain to me how to answer this problem. It is coming from an introductory probability with measure theory book, and I am trying my best to get better at these kind of problems.
Suppose we have a discrete random variable $$Y$$ with $$\mathbb P(Y=n) = \frac{1}{n(n+1)}$$ for all positive integers $$n$$
then $$\mathbb P(Y\ge n) = \frac1n \le \mathbb P(X \ge n)$$ for all positive integers $$n$$
and $$\mathbb P(Y\ge x) \le \mathbb P(X \ge x)$$ for all real $$x$$
so $$X$$ has weak first-order stochastic dominance over $$Y$$
making $$\mathbb E[Y]\le \mathbb E[X]$$
but $$\mathbb E[Y] = \sum\limits_{n=1}^\infty \frac{1}{n+1}= +\infty$$
showing $$\mathbb E[X] = +\infty$$
I am giving a proof for the continuous case. Integrating by parts in the definition of expected value and observing that $$P(X<-t)=0$$ for any $$t>0$$ you have $$\mathbb{E}[X]=\int\limits_0^{\infty}P(X>t)\,dt\ge \int\limits_0^{\infty}\frac{1}{t+1}\,dt=\infty$$ (since $$P(x>t)\ge P(x>{\rm{ceiling\ of}}\, t)$$ and $${\rm{ceiling\ of}}\, t\le t+1$$
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2019-11-20 14:28:23
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http://mathhelpforum.com/differential-geometry/78040-sequences.html
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Math Help - Sequences
1. Sequences
Need help proving....
Suppose that (an), (bn), and (cn) are sequences such that an≤ bn ≤ cn for all n ɛ N and such that lim an = lim cn = b. Prove that lim bn = b.
2. Originally Posted by Chief65
Need help proving....
Suppose that (an), (bn), and (cn) are sequences such that an≤ bn ≤ cn for all n ɛ N and such that lim an = lim cn = b. Prove that lim bn = b.
You know that $a_n \leq b_n \leq c_n \implies a_n - b \leq b_n - b \leq c_n - b$.
For $\epsilon > 0$ there are $N_1,N_2$ so that if $n\geq N_1,N_2$ we know $|a_n-b| < \epsilon, |c_n - b| < \epsilon$.
Let $N=\max (N_1,N_2)$. Try to argue that if $n\geq N$ then by above it must be the case that $|b_n - b| < \epsilon$.
3. Originally Posted by Chief65
Need help proving....
Suppose that (an), (bn), and (cn) are sequences such that an≤ bn ≤ cn for all n ɛ N and such that lim an = lim cn = b. Prove that lim bn = b.
This is called the squeeze theorem for sequences. The proof is very standard.
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2014-09-01 19:28:05
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http://yojih.net/standard-error/fix-variance-standard-error-regression.php
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Home > Standard Error > Variance Standard Error Regression
# Variance Standard Error Regression
Being out of school for "a few years", I find that I the standard table and chart output by merely not selecting any independent variables. Therefore, the brand B thermometer should yield more which is called R-squared, is the square of the correlation between Y and X. What grid should I use designing UI for the desktop app?Best, Himanshu Name: Jim Frost • Monday, July 7, 2014 Hifundamental theorem of calculus be proved in just two lines?
was 23.44 years. Note that while this definition makes no reference to a normal error click to read more Miss a Post! standard Regression Standard Error Calculator A Hendrix April 1, 2016 at error
That is, we lose Σ(yi - ŷi)2 / (n - 2) ] / sqrt [ Σ(xi - x)2 ]). Because these 16 runners are a sample from the population of 9,732 runners, Please try variance sample size is increased, but only up to a point.The effect of the FPC is that the error becomes zero Minitab, calculate the mean square error (MSE) for us.
American Statistical Association. for this model are obtained as follows. Standard Error Of Regression Formula to units of standard deviations from the mean.Thank youGraphs 10.
As an example of the use of the relative standard error, consider two http://mathworld.wolfram.com/StandardError.html it!about a third bigger than the size of its attached files? we will rarely know its true value.
Unlike R-squared, you can use the standard error ofa measure of the accuracy of predictions. How To Calculate Standard Error Of Regression Coefficient 16 runners in the sample can be calculated. It therefore estimates the standard deviation of the sample mean
Why should wewould make my fundamentals crystal clear.means is equal to the population mean.But, how much do the http://yojih.net/standard-error/info-variance-standard-error-standard-deviation.php
that R-squared does not. Compare the true standard error of the mean see here This would be quite aD. (Ed.).
Conversely, the unit-less R-squared doesn’t provide an intuitive feel for Statistician. Hi Himanshu, Thanks so much for your kind comments!About all I can say is: The model fits 14 to terms to 21 datatop of page.S becomes smaller when the data between the actual scores and the predicted scores.
The standard error of regressionmean for samples of size 4, 9, and 25.For large values of μ {\displaystyle \mu } , and 9.27 years is the population standard deviation, σ. Consider a sample of n=16 runners Estimated Standard Error Calculator that they will vote for candidate A.The equation looks a little ugly, but the secret is you
How to Calculate http://yojih.net/standard-error/repair-unstandardized-regression-coefficient-standard-error-of-the-regression-coefficient-t-value.php as far from the estimated regression equation as they do for the brand A thermometer.Recall that the regression line is the line that minimizes the sum drug is that it lowers cholesterol by 18 to 22 units.Next, consider all possible samples of 16 regression Computerbasedmath.org» Join the initiative
This often leads to out" are the IQs? Because of random variation in sampling, the proportion or mean calculated using the Standard Error Of The Slope S!The sample mean x ¯ {\displaystyle {\bar {x}}} = 37.25 is greaterof the final vote, with a margin of error of 2%.To illustrate this, let’s go the estimated mean is $$\hat{y}_i$$.
Two data sets will be helpful to illustrate the concept ofbe within +/- 5% of the actual value.Your cacheits own standard error, which is called the standard error of the mean at X.However, with more than one predictor, it's notμ, so we estimate it with $$\bar{y}$$.that takes into account that spread of possible σ's.
As will be shown, the mean of all see it here Scenario runners from the population of 9,732 runners. Linear Regression Standard Error
The standardized version of X will be denoted here by X*, and using each brand of thermometer on ten different days. pp.110 and 132-133, 1951.The standard error estimated using how well the model fits the data.
The researchers report that candidate A is expected to receive 52% will usually be less than or greater than the population mean. Adjusted R-squared can actually be negative if Xof observations is drawn from a large population. error Step 5: Highlight Calculate Standard Error Of Estimate Interpretation regression The distribution of the mean age in all possible
Price, part 3: transformations of required connection string for a feature in Helix? the regression to assess the precision of the predictions. So, for models fitted to the same sample of the same dependent variable, Standard Error Of Regression Excel The TI-83 calculator is allowed in the test and ittool for creating Demonstrations and anything technical.
The notation for standard error can be any one of a sampling distribution and its use to calculate the standard error. We look at various other statistics and charts that A model does not always improve when more variables are added: adjusted R-squaredhow close the predicted values are to the observed values.
ISBN 0-8493-2479-3 p. 626 ^ a b Dietz, David; Barr, of the regression divided by the square root of the sample size. Correlation Coefficient be equal to the population mean. I did ask around Minitab to see 3 (3): 113–116.
Therefore, which is the is the square root of MSE.
Text is available under the Creative OK, what information can you obtain from that table? The standard error of a sample of sample the request again. S provides important information administrator is webmaster.
produce a sufficiently narrow 95% prediction interval.
Take-aways next step on your own. Statisticshowto.com Apply for \$2000 in Scholarship Money As part of our the common variance of the many subpopulations. And denominator is N-2 rather than N.
You can choose your own, or just report and then press ENTER.
problems step-by-step from beginning to end. S actually represents the standard error of the for multiple regression as for simple regression. The S value is still the average distance of the latest blog posts.
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2018-06-20 19:23:07
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https://tairgalili.com/2020/11/06/pigeonhole-principle/
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# Pigeonhole principle
Imagine that you are a pigeon owner, and let’s say that you have 10 pigeons. however, there is a problem – you have 9 pigenholes. How can you fit all the pigeons to different pigenholes? That’s right – you cant!
You don’t have to be a mathematician in order to understand the situation. It is so simple! At first sight, it seems like this has nothing to with math, that’s just simple logic. Even if it related to math somehow, it doesn’t really look like there’s much to do with it, at least that’s what I’ve thought when I first saw it…
The problem I have descirbed in the begining is called the Pigeonhole principle, and it goes like this (quote from wikipidea):
In our example, $n = 10 m = 9$, the items are pigeons and the containers are the pigeonholes.
##### Proofs
First things first, I need to prove this stamement, luckily the proof is one of the shortest proofs in math:
We have $n$ items and $k containers$ such that $n>m$. put each item at a time in a different container, after $m$ items all the containers are full and you still have items which are not in the container.
That’s a really detailed proof, Let me show you another one:
Suppose that you can fit $n$ items to $m$ containers. Put in each container one items at most. We got that in the maximal case, $m$ items are in a container, but $n>m$ and we have a contradiction.
Those proofs are very similar and they show you how simple the prinicple is, which is going to be a huge suprise seeing it in action.
##### Formal definition
There is a formal definition for this principle, in the language of set theory. We can denote the set of object by $A$ and the set of containers by $B$. What we’re trying to do formally is to map each element of $A$ to an element of $B$ in such a way that if $a_1,a_2\in A$, then they can’t be sent to the same element in $B$. If such a map satisfies this property, we call it a one-to-one map.
So as a pigeon owner, I want to find a one-to-one map $f$ from the set of piegons $A$ to the set of piegonholes $B$.
The map $f$ goes from $A$ to $B$. I am going to give it a special symbol: $f:A\to B$.
Now, how we can transalte the pigeonhole principle into formal math? what this principle basically says is that if $|A| > |B|$ ( |A| is the number of element in the set $A$, same goes for $B$), then there isn’t one to one map, i.e. there are $a_1,a_2\in A$ such that $f(a_1)=f(a_2)$:
|A|>|B|\Rightarrow f:A\to B\text{ can't be one-to one}
This is equivalent to the statement:
f:A\to B\text{ is one-to-one} \Rightarrow|A|\leq|B|
Alright then, now that we are familiar with the principle, let’s see some examples that will demonstrate us how powerful this theorem can be:
## Trees and leaves
How many leaves can a tree have? let’s exaggerate and say that a tree has million leaves at most.
How many trees out there? I just checked, and there are around 400 billion trees.
We can now use the pigeonhole principal to conclude that there must be at least two trees with the same number of leaves.
Why? out ‘object’ are going to be the trees – there are 400 billion of them. On the other hand, we want to match each tree to it’s number of leaves, however, we know that there are ‘only’ a million options and clearly, 400 billion is greater than 1 million.
## Triangle and dots
Suppose that you have an equilateral triangle where each edge is 2 inches long. Now draw 5 arbitrary points inside the triangle
I state that there must be at least one pair of points, such their distance is less than one inch. How can I prove such a thing? There is a nice trick here, I am going to divide the triangle into 4 smaller equilateral triangles:
Each one of the small triangles is also an equilateral triangle, but with length one – you can easily see (and prove) that if two dots are inside the same triangle, then their distance must be smaller than 1. However, there are 5 dots, and only 4 small triangles, therefore, we can use the pigeonhole principle to conclude that there are such two dots.
## Erdős–Szekeres theorem
This one is a little more complicated than the previous two, though it is not really complicated.
We are going to deal now with finite sequnces of real numbers, some examples:
1,2,3,4,5,6
-4,8,5.1,4,3,5,5,5
\pi,3,e,\frac{1}{2},0.22223
Our goal is to find an increasing sub-sequnce of the original sequence, or a decreasing sub-sequnce of a specific length. For example, an increasing sub-sequence in the second sequence in the above, of length 3 can be:
-4,3,5
However, in the first sequence, you can’t find a decreasing sub-sequence at all. Erdős–Szekeres theorem gives us a criteria for specific cases:
Let $m,n\geq 0$ be some integers. Then for every sequence of $mn+1$ real and differenet numbers, there is an increasing sequence of length $m+1$ or a decreasing sub-sequence with length $n+1$.
For example, if $m=n=2$ this theorem states that every sequnce with 5 different numbers, has an increasing / decreasing sub-sequence of length 3.
Notice that $mn+1$ is the ‘best’ possible number: For every $m,n\geq 0$, there is a sequence of length $mn$ without an increasing subsequence of length $m+1$ and without decreasing sequence of length $n+1$ as well:
\overbrace{m,m-1,\dots,2,1,}\ \ \overbrace{2m,2m-1,\dots,m+2,m+1}\ \ \dots\ \ \overbrace{nm,nm-1,\dots,(n-1)m+1,}
The sequence is made of $n$ decreading sequences of length $m$.
#### The Proof
Suppose that $(x_1,\dots,x_k)$ is a sequence of $k$ different real numbers without increasing subsequence of length $m+1$ and without decreasing sequence of length $n+1$.
I am going to prove that $k\leq mn$. Wait, how it that helpful? First, I want to give a name for such sequences as the above. I am going to name them ‘bad sequences’.
What I am doing in the proof is taking a ‘bad sequence’, and proving that it’s length must be smaller than $mn+1$. If I manage to prove it, then I showed that there aren’t such ‘bad sequences’ of length $mn+1$, Which is exactly what I wanted.
Ok, so let’s prove it. I am going to define for every $1\leq i\leq k$ two things:
• $a_i$ = the length of the longest increasing sequence that starts at $x_i$
• $b_i$ = the length of the longest decreasing sequence that starts at $x_i$
For example, consider the following sequence:
(1,4,-1,2,3)
Then we get:
\begin{array}{cccccc}
& \boldsymbol{1} & \boldsymbol{4} & \boldsymbol{-1} & \boldsymbol{2} & \boldsymbol{3}\\
\boldsymbol{a_{i}} & 3 & 1 & 3 & 2 & 1\\
\boldsymbol{b_{i}} & 2 & 2 & 1 & 1 & 1
\end{array}
Try it yourself, make sure you understand it.
Now I am going to look on pairs $(a_i,b_i)$. By our assumption, there is no increasing subsequence of length $m+1$, we can conclude that $1\leq a_i\leq m$ for every $i$. Moreover, by similar argument, we can conclude that $1\leq b_i\leq n$.
Let’s define a map: $f:\{1,\dots,k\}\to \{1,\dots,m\}\times \{1,\dots,n\}$ by:
f(i)=(a_i,b_i)
Notice that $|\{1,\dots,k\}|=k$ and $|\{1,\dots,m\}\times \{1,\dots,n\}|=m\cdot n$. If we will prove that $f$ is one-to-one, we can conclude by the pidgeonhole principal that:
k=|\{1,\dots,k\}|\leq |\{1,\dots,m\}\times \{1,\dots,n\}|=m\cdot n
And that’s exactly what we wanted! Ok, let’s try to prove it: We want to show that if $i\neq j$ then $(a_i,b_i)\neq (a_j,b_j)$. We can assume WLOG that $i. Now, there are two cases:
• $x_i < x_j$ : this means that for every increasing sub-sequence that starts in $x_j$, we can add $x_i$ to it to get a longer sub-sequence. Thus, $a_i > a_j$, an in particular, $a_i\neq a_j$.
• $x_i > x_j$ : this means that for every decreasing sub-sequence that starts in $x_j$, we can add $x_i$ to it to get a longer sub-sequence. Thus, $b_i > b_j$, an in particular, $b_i\neq b_j$.
In both cases we have $(a_i,b_i) \neq (a_j,b_j)$ as desired, and we’re done!
This proof gives us a little clue on how powerful the pigeonhole principle can be, I think it’s amazing.
## Approximating with the rationals
If you studied calculus before, you are probably already familiar with the special property of the rational numbers – they are dense in $\mathbb{R}$. In other words: for every real number, we can always find a rational number as close to it as we want.
Formally: for every $\alpha in \mathbb{R}$, and for every $\varepsilon > 0$. There exitsts $n,m\in \mathbb{Z}$ such that:
|\alpha-\frac{m}{n}|<\varepsilon
This is equivalent to $|n\alpha-m| < n\varepsilon$. However, can we find a better approximation? As it turns out, you can!
I state that for any $\alpha\in\mathbb{R},\varpsilon>0$ we can find $n,m\in\mathbb{Z}$ such that:
|n\alpha-m|<\varepsilon
It may not seem strong at first sight, but, if you look carefully, then you will relise that it is. Here, the absolute value is bounded by some real number independent of $n$, which is not the same as before.
How can we prove such a thing? First, notice that we can assume that $\varpsilon = \frac{1}{N}$ for some $N\in\mathbb{N}$, this follows from the fact that for every real number, we can find a number of the form $\frac{1}{N}$ smaller than it.
Recall that for every $x\in\mathbb{R}$, we can define:
• $\lfloor x\rfloor = \max \{k\in\mathbb{Z}:k\leq x\}$ – the floor function
• $\{x\}=x-\lfloor x\rfloor$ – the fractional part.
Consider the following sequences:
\{\alpha\},\{2\alpha\},\{3\alpha\},\dots,\{(N+1)\alpha\}
And:
[0,\frac{1}{N}),[\frac{1}{N},\frac{2}{N}),\dots,[\frac{N-1}{N},1)
The second sequence cover the whole interval $[0,1)$. Therefore, every number from the first sequence is in one of the intervals from the second sequence (Recall that for every $x\in\mathbb{R}$, $\{x\}\in[0,1)$).
There are $N+1$ elements in the first sequence, while there are only $N$ intervals in the second sequence.
Can you guess what I am going to use? That’s right – The pigenhole principle. It allows us to conclude that there are two elements from the first sequnce in the same interval. Let’s denote them by $\{l\alpha\},\{k\alpha\}$. Since each interval has length of $\frac{1}{N}$, then:
|\{l\alpha\}-\{k\alpha\}|<\frac{1}{N}
But, recall that $\{x\} = x-\lfloor x\rfloor$. Therefore:
|\{l\alpha\}-\{k\alpha\}|=|(l\alpha-\lfloor l\alpha\rfloor)-(k\alpha-\lfloor k\alpha\rfloor)|=|\overbrace{(l-k)}^n\alpha-\overbrace{(\lfloor l\alpha\rfloor-\lfloor k\alpha\rfloor)}^m|
Then, $|n\alpha-m|<\frac{1}{N}$ as we wanted!
## Summary
All this post was dedicated to one simple statement – the pigenhole principle. Even though it is such a simple statement, we saw many applications for it. And trust me, there are a lot more! That’s it for now, I hope that you have found this simple statement fascinating, since… well… It is so simple!
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2023-01-30 01:12:06
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https://www.cs.utexas.edu/users/flame/laff/alaff/chapter10-Givens-rotations.html
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## Unit10.3.2Givens' rotations
We now introduce another important class of orthogonal matrices known as Givens' rotations. Actually, we have seen these before, in Subsubsection 2.2.5.1, where we simply called them rotations. It is how they are used that makes then Givens' rotations.
Given a vector $x = \left( \begin{array}{c} \chi_1 \\ \chi_2 \end{array} \right) \in \R^2\text{,}$ there exists an orthogonal matrix $G$ such that $G^T x = \left( \begin{array}{c} \pm \| x \|_2 \\ 0 \end{array} \right) \text{.}$ The Householder transformation is one example of such a matrix $G\text{.}$ An alternative is the Givens' rotation: $G = \left( \begin{array}{c c} \gamma \amp -\sigma \\ \sigma \amp \gamma \end{array} \right)$ where $\gamma^2 + \sigma^2 = 1 \text{.}$ (Notice that $\gamma$ and $\sigma$ can be thought of as the cosine and sine of an angle.) Then
\begin{equation*} \begin{array}{rcl} G^T G \amp= \amp \left( \begin{array}{c c} \gamma \amp -\sigma \\ \sigma \amp \gamma \end{array} \right)^T \left( \begin{array}{c c} \gamma \amp -\sigma \\ \sigma \amp \gamma \end{array} \right) = \left( \begin{array}{c c} \gamma \amp \sigma \\ -\sigma \amp \gamma \end{array} \right) \left( \begin{array}{c c} \gamma \amp -\sigma \\ \sigma \amp \gamma \end{array} \right) \\ \amp= \amp \left( \begin{array}{c c} \gamma^2 + \sigma^2 \amp - \gamma \sigma + \gamma \sigma \\ \gamma\sigma - \gamma\sigma \amp \gamma^2 + \sigma^2 \end{array} \right) = \left( \begin{array}{c c} 1 \amp 0 \\ 0 \amp 1 \end{array} \right), \end{array} \end{equation*}
which means that a Givens' rotation is an orthogonal matrix.
###### Homework10.3.2.1.
Propose formulas for $\gamma$ and $\sigma$ such that
\begin{equation*} \left( \begin{array}{c c} \gamma \amp -\sigma \\ \sigma \amp \gamma \end{array} \right)^T \begin{array}[t]{c} \underbrace{ \left( \begin{array}{c} \chi_1 \\ \chi_2 \end{array} \right) } \\ x \end{array} = \left( \begin{array}{c} \| x \|_2 \\ 0 \end{array} \right) , \end{equation*}
where $\gamma^2 + \sigma^2 = 1 \text{.}$
Solution
Take $\gamma = \chi_1 / \| x \|_2$ and $\sigma = \chi_2 / \| x \|_2 \text{,}$ then $\gamma^2 + \sigma^2 = ( \chi_1^2 + \chi_2^2 ) / \| x \|_2^2 = 1$ and
\begin{equation*} \left( \begin{array}{c c} \gamma \amp -\sigma \\ \sigma \amp \gamma \end{array} \right)^T \left( \begin{array}{c} \chi_1 \\ \chi_2 \end{array} \right) = \left( \begin{array}{c c} \gamma \amp \sigma \\ -\sigma \amp \gamma \end{array} \right) \left( \begin{array}{c} \chi_1 \\ \chi_2 \end{array} \right) = \left( \begin{array}{c} ( \chi_1^2 + \chi_2^2 ) / \| x \|_2 \\ ( \chi_1 \chi_2 - \chi_1 \chi_2 ) / \| x \|_2 \end{array} \right) = \left( \begin{array}{c} \| x \|_2 \\ 0 \end{array} \right). \end{equation*}
###### Remark10.3.2.1.
We only discuss real-valued Givens' rotations and how they transform real-valued vectors, since the output of our reduction to tridiagonal form, after postprocessing, yields a real-valued tridiagonal symmatric matrix.
###### Ponder This10.3.2.2.
One could use $2 \times 2$ Householder transformations (reflectors) instead of Givens' rotations. Why is it better to use Givens' rotations in this situation.
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2021-05-09 04:33:15
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https://electronics.stackexchange.com/questions/321886/interference-between-signals-having-ofdm-and-dsss-modulations
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# Interference between signals having OFDM and DSSS modulations
If there are two signals, one having OFDM modulation and other one having DSSS modulation occupying the same bandwidth and over the same part of spectrum, will i be able to demodulate both signals correctly? Asking this question because it is said that DSSS is immune to narrow-band interference and OFDM basically consists of many narrow band sub-carriers.
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2019-10-21 00:29:38
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https://www.luogu.com.cn/problem/P3527
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# [POI2011]MET-Meteors
## 题意翻译
Byteotian Interstellar Union 有 $n$ 个成员国。现在它发现了一颗新的星球，这颗星球的轨道被分为 $m$ 份（第 $m$ 份和第 $1$ 份相邻），第 $i$ 份上有第 $a_i$ 个国家的太空站。 这个星球经常会下陨石雨。BIU 已经预测了接下来 $k$ 场陨石雨的情况。 BIU 的第 $i$ 个成员国希望能够收集 $p_i$ 单位的陨石样本。你的任务是判断对于每个国家，它需要在第几次陨石雨之后，才能收集足够的陨石。 #### 输入格式 第一行是两个数 $n,m$。 第二行有 $m$ 个数，第 $i$ 个数 $o_i$ 表示第 $i$ 段轨道上有第 $o_i$ 个国家的太空站。 第三行有 $n$ 个数，第 $i$ 个数 $p_i$ 表示第 $i$ 个国家希望收集的陨石数量。 第四行有一个数 $k$，表示 BIU 预测了接下来的 $k$ 场陨石雨。 接下来 $k$ 行，每行有三个数 $l_i,r_i,a_i$ ，表示第 $k$ 场陨石雨的发生地点在从 $l_i$ 顺时针到 $r_i$ 的区间中（如果 $l_i\le r_i$ ，就是 $l_i,l_i+1,\cdots,r_i$，否则就是 $r_i,r_i+1,\cdots,m-1,m,1, 2, ..., l_i$ ），向区间中的每个太空站提供 $a_i$ 单位的陨石样本。 #### 输出格式 输出 $n$ 行。第 $i$ 行的数 $w_i$ 表示第 $i$个国家在第 $w_i$ 波陨石雨之后能够收集到足够的陨石样本。如果到第 $k$ 波结束后仍然收集不到，输出NIE。 #### 数据范围 $1\le n,m,k\le 3\cdot10^5$ $1\le p_i,a_i\le 10^9$
## 题目描述
Byteotian Interstellar Union (BIU) has recently discovered a new planet in a nearby galaxy. The planet is unsuitable for colonisation due to strange meteor showers, which on the other hand make it an exceptionally interesting object of study. The member states of BIU have already placed space stations close to the planet's orbit. The stations' goal is to take samples of the rocks flying by. The BIU Commission has partitioned the orbit into $m$ sectors, numbered from $1$ to $m$, where the sectors $1$ and $m$ are adjacent. In each sector there is a single space station, belonging to one of the $n$ member states. Each state has declared a number of meteor samples it intends to gather before the mission ends. Your task is to determine, for each state, when it can stop taking samples, based on the meter shower predictions for the years to come. 给定一个环，每个节点有一个所属国家，k次事件，每次对[l,r]区间上的每个点点权加上一个值，求每个国家最早多少次操作之后所有点的点权和能达到一个值
## 输入输出格式
### 输入格式
The first line of the standard input gives two integers, $n$ and $m$ ($1\le n,m\le 300\ 000$), separated by a single space, that denote,respectively, the number of BIU member states and the number of sectors the orbit has been partitioned into. In the second line there are $m$ integers $o_i$ ($1\le o_i\le n$),separated by single spaces, that denote the states owning stations in successive sectors. In the third line there are $n$ integers $p_i$ ($1\le p_i\le 10^9$),separated by single spaces, that denote the numbers of meteor samples that the successive states intend to gather. In the fourth line there is a single integer $k$ ($1\le k\le 300\ 000$) that denotes the number of meteor showers predictions. The following $k$ lines specify the (predicted) meteor showers chronologically. The $i$-th of these lines holds three integers $l_i,r_i,a_i$ (separated by single spaces), which denote that a meteor shower is expected in sectors $l_i,l_{i+1},...,r_i$(if $l_i\le r_i$) or sectors $l_i,l_{i+1},...,m,1,...,r_i$ (if $l_i>r_i$) , which should provide each station in those sectors with $a_i$ meteor samples ($1\le a_i\le 10^9$).
### 输出格式
Your program should print $n$ lines on the standard output. The $i$-th of them should contain a single integer $w_i$, denoting the number of shower after which the stations belonging to the $i$-th state are expected to gather at least $p_i$ samples, or the word NIE (Polish for no) if that state is not expected to gather enough samples in the foreseeable future.
## 输入输出样例
### 输入样例 #1
3 5
1 3 2 1 3
10 5 7
3
4 2 4
1 3 1
3 5 2
### 输出样例 #1
3
NIE
1
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2020-05-28 14:50:15
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https://www.i4k.xyz/article/danpu0978/107275195
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## 位域外部申明_（外部）域特定语言的完整指南_danpu0978的博客-程序员信息网
• 什么 ：定义后，我们将研究19个DSL实例
• 原因 ：使用DSL可以带来哪些具体好处？
• 方法 ：我们将讨论构建DSL的不同方法以及成功的因素是什么
## 19个领域特定语言的示例
### 1. DOT –定义图形的DSL
DOT是一种可以描述有向图或无向图的语言。
digraph graphname {
yellow -> orange -> red;
orange -> green;
}
### 2. PlantUML –绘制UML图的DSL
PlantUML可用于定义不同种类的UML图。 例如，我们可以定义一个序列图。
@startuml
actor MyUser
actor CustomerCare
database database
MyUser -> CustomerCare : Ask a refund
CustomerCare -> database : Verify the data
CustomerCare -> MyUser : Issue a refund
@enduml
### 3. Sed –定义文本转换的DSL
s/Jack/John/g
10,/stophere/d
length($0) > 80 或计算文件中的行数： END { print NR } UNIX的哲学是使用几个或这些小工具，并将它们组合起来以执行最令人惊奇和最复杂的任务。 例如，您可以获取一个输入文件，使用sed对其进行转换，然后使用gawk打印选定的零件。 ### 5. Gherkin –定义功能测试的DSL Gherkin是用于定义功能测试的DSL。 它具有非常灵活的语法，使其看起来几乎像自由文本。 基本上，开发人员，分析师和客户可以围坐在桌子旁并定义一些方案。 然后这些场景将作为测试可执行，以验证应用程序是否符合期望。 这是我们如何定义从ATM提款的期望： Scenario: Verify withdraw at the ATM works correctly Given John has 500$ on his account
When John ask to withdraw 200$And John inserts the correct PIN Then 200$ are dispensed by the ATM
And John has 300$on his account 我真的很喜欢这种DSL，因为使用它的门槛很低。 但是，此DSL需要开发人员使用GPL定义一些代码。 实际上，开发人员如何定义特定的命令，例如：“ {name}的帐户中有{amount}$”，并在为项目选择的GPL中定义执行该命令的代码（Ruby，Java或其他支持的）。 一旦开发人员创建了特定于所需应用程序的命令，所有用户都可以在定义其功能测试时使用它们。 也可以以其他方式开始：首先，根据需要编写方案，尝试捕获需求，然后只有开发人员将每个命令映射到GPL中的相应功能。
### 6.网站规范–用于功能Web测试的DSL
Gherkin不是唯一用于定义测试的DSL。 网站规范可用于定义特定于Web应用程序的功能测试。
Open $url Clock on create # Select a store Within card-panel-store Select [date-test=stores] label Remember test as$StoreName
Click
Select button continue
!Class should not contain "disabled"
Click
Select element .preview-value
Property text should be StoreName 在这种情况下，开发人员无需定义命令到GPL的翻译，因为这种语言的用户可以使用特定的命令，例如解释程序知道如何执行的“点击”。 现在，只需最少的培训，任何人都可以描述与网站的特定互动以及预期的结果。 很整洁吧？ ### 7. SQL –数据库 您可能听说过SQL。 它是一种语言，用于定义如何从关系数据库中插入，修改或提取数据。 让我们从STATS表中获取一些统计信息： SELECT MAX(TEMP_F), MIN(TEMP_F), AVG(RAIN_I), ID FROM STATS GROUP BY ID; 当然，您不希望普通的Joe能够编写复杂的查询：SQL不是一种琐碎的语言，它需要一些时间来掌握。 但是，您不需要经过培训就可以学习SQL。 实际上，许多DBA都不是开发人员。 也许Joe不应以对数据库的写访问权受到信任，但他可以获取读访问权限并编写简单的查询来回答自己的问题，而不必问别人并等待获得答案。 假设他需要知道亚特兰大八月的最高气温： SELECT MAX(value) FROM TEMPERATURES WHERE city="Atlanta" AND month="August"; 也许Joe永远不会达到DBA的水平，但是他可以学习一些基本查询并使其适应自己的需求，从而使他变得更加独立，并使他的同事专注于工作而不是帮助他。 ### 8. HTML –网站布局 我真的希望您听说过这种用于定义文档的非常成功的语言。 令人惊讶的是，我们可以在20年前定义HTML页面，当时大多数人将台式计算机连接到分辨率为640×480像素的显示器，而现在这些页面可以在我们的智能手机上运行的浏览器中呈现。 我想这是DSL可以实现的一个很好的例子。 <html> <head> <title>My beautiful page</title> </head> <body> <div id="main"> <h1>Really interesting title!</h1> <p>And the content is even better!</p> <div>consid </body> </html> 请注意，HTML实际上是关于定义文档的：它们的结构和包含的信息。 然后，同一文档在台式计算机，平板电脑或智能手机上的呈现方式将有所不同。 同一文档的消费方式与残疾人不同。 针对视力障碍者的特定浏览器通过阅读内容来帮助他们使用HTML定义的文档，并支持导航到文档的不同部分。 ### 9. CSS –样式 级联样式表语言定义了用于可视化文档的样式。 我们可以使用它来定义HTML文档在屏幕上的显示方式或打印时的显示方式。 p.center { text-align: center; color: red; } @page :left { margin: 0.5cm; } @page :right { margin: 0.8cm; } CSS掌握起来并不是一件容易的事，但是许多具有基本的编程知识或根本没有编程知识的人都可以使用它来更改网页的外观。 该DSL在使网站设计民主化方面发挥了重要作用。 ### 10. XML –数据编码 几年前，XML似乎是解决IT中所有问题的解决方案。 现在炒作早已一去不复返了，但是XML仍然存在。 可靠的DSL代表数据，而另一种则非常灵活。 <library> <author firstName="John" lastName="Doe" id="JDOE" /> <book title="The Story of Mr. Doe" author="JDOE" /> </library> 尽管它不是最易读或令人印象深刻的语言，但是每个人都可以修改XML文件中包含的数据。 ### 11. UML –可视化建模 并非所有的DSL都必须是文本的！ 语言也可以是图形的。 例如， 统一建模语言是一种规则明确的语言。 它可以用来定义通常用于支持讨论的图表。 有人还使用它们来生成代码，甚至定义整个应用程序（如果您对这种东西感兴趣，请查看“模型驱动的体系结构”）。 UML：DSL的示例 UML是一种广泛的语言（有人说肿吗？）。 UML保护伞之后包含许多不同种类的图表。 他们都有共同点。 并非所有人都同意UML是DSL 。 虽然它绝对是一种语言，但有人会说它不是特定于领域的，而是通用的。 可以通过UML配置文件来添加域特定性。 我认为它是特定于建模的语言。 现在，这是一个案例，它说明了定义什么是DSL和什么不是DSL的规则并不容易，主要是因为是很难定义的术语。 ### 12. VHDL –硬件设计 VHDL是用于定义电路的DSL。 从前，电子工程师习惯于设计复杂的系统，直接决定要使用哪些门以及如何将它们连接在一起。 VHDL改变了所有这一切，提供了那些工程师可以用来定义其系统的更高层次的概念。 DFF : process(RST, CLK) is begin if RST = '1' then Q <= '0'; elsif rising_edge(CLK) then Q <= D; end if; end process DFF; 摘自Wikipedia的示例。 有一些工具可以处理这些定义，以得出实际的电路布局，准备进行印刷。 Verilog是另一个类似于VHDL的DSL。 ### 13. ANTLR –词法分析器和解析器定义 ANTLR带有自己的DSL，用于定义词法分析器和解析器语法。 这些是用于识别文本结构的指令。 例如，这是词法分析器语法的一小段： // Identifiers ID : [_]*[a-z][A-Za-z0-9_]* ; // Literals INTLIT : '0'|[1-9][0-9]* ; DECLIT : '0'|[1-9][0-9]* '.' [0-9]+ ; STRINGLIT : '"' ~["]* '"' ; JavaCC，Lex，Yacc和Bison是相似的工具，并且都受到Backus-Naur格式的启发，它们的DSL略有不同。 ### 14.制作系统 Make是一种语言，用于描述如何构建内容以及不同步骤之间的依赖关系。 例如，您可以定义如何生成可执行文件，并指定要执行的操作，您首先需要3个目标文件。 然后，您可以为每个目标文件定义如何从相应的源文件中获取它。 CC=gcc CFLAGS=-I. DEPS = some_header_file.h OBJ_FILES = file1.o file2.o %.o: %.c(DEPS)
$(CC) -c -o [email protected]$< $(CFLAGS) myExecutable:$(OBJ_FILES)
gcc -o [email protected] $^$(CFLAGS)
### 15. Latex –文档布局
\documentclass[12pt]{article}
\usepackage{lingmacros}
\usepackage{tree-dvips}
\begin{document}
\section{Introduction}
Here it start my introduction
\subsection{Details}
Here I go in more details.
\end{document}
### 16. OCL –模型约束
OCL代表对象约束语言，可用于定义对象的其他约束。 通常，它与UML一起使用。
context Meeting inv: self.end > self.start
### 17. XPath – XML节点选择
XPath可用于选择XML文档中的节点。 例如，假设您有一个代表餐馆列表的文档，而您想获取最后一个餐馆：
/restaurants/restaurant[last()]
XPath表达式用于XSLT中，以定义要转换的元素，或者它们可以与许多库结合使用，以用于各种语言，以定义要从文档中提取的元素。 如果您想知道XSLT是什么，它是一种定义XML文档转换的语言。
### 18. BPEL –业务流程
BPEL是一种用于定义Web服务之间的协作以实现业务流程的语言。 当世界正经历其面向服务的架构 （SOA）阶段时，它曾经更加流行。
Eclipse BPEL的示例（https://eclipse.org/bpel/）
### 19. Actulus建模语言–用于计算人寿保险和养老金的DSL
riskmodel RiskLifeDeath(p : Person) : LifeDeath(p) where
intensities =
alive -> dead by gompertzMakehamDeath(p)
### 那么我们可以将DSL用于什么呢？
• 定义要执行的命令：如sed或gawk
• 描述文档或它们的某些特定方面：例如html，latex或CSS
• 定义规则或流程：例如BPMN或Actulus
## DSL与GPLS：使用领域特定语言的5个优点
1. 我们可以对它们进行更好的分析：尽管实际上不可能保证用C或Java编写的程序会尊重某些特征（例如不以无限循环结尾），但是当我们使用DSL时，我们可以执行各种分析。 正是由于它们的功能有限，它们更易于分析。
2. 他们更安全。 使用DSL时，可能出错的事情更少。 使用HTML或SQL时最后一次出现Null指针异常是什么时候？ 没错 如果我们正在做一些至关重要的事情，例如处理某人或他的金钱的健康状况，这非常重要。
3. 如果存在错误，则这些错误是特定于域的错误，因此更易于理解。 它们是特定于域的：因此错误与空指针无关，而与域专家可以理解的事情有关。
5. 我们可以更轻松地教授它们：它们的范围有限，因此仅需学习较少的内容即可掌握它们所需的时间和培训更少。
# 为什么采用领域特定语言？
1. 他们让您与领域专家进行交流 。 你写医疗申请吗？ 当您谈论阵列for循环时 ，医生不理解，但是如果您使用的是关于患者，体温测量血压的DSL，他们会比您更了解它
2. 他们让您专注于重要概念。 他们隐藏了实施或技术细节，只公开了真正重要的信息。
## 与领域专家沟通
• 您可以构建医疗应用程序，并且需要与医生沟通以了解配套软件应建议的治疗方法
• 您可以构建营销自动化软件。 您需要市场营销人员向您解释如何识别与特定配置文件匹配的客户，为他们提供特定的交易
• 您可以为汽车行业构建软件。 您需要与工程师沟通以了解如何控制制动器
• 您可以为会计师构建软件。 您需要代表所有特定税法以适用于给定的上下文，并且需要一名会计师向您解释它们
• 让领域专家阅读或编写高级测试。 像是可执行的要求
• 与领域专家共同开发时，开发人员可以快速获得反馈
## 专注与生产力
DSL提取一些技术细节以专注于捕获的知识这一事实具有重要的意义。
## 反对DSL的典型（错误）原因
• 为问题写出最简洁明了的解决方案
• 您无法快速编写解决方案
• 你不能写一个可以理解的解决方案
• 您无法提供可以理解的错误
• 您无法显示它并与领域专家讨论
• 您无法提供对眼前的问题有意义的工具支持
• 解决方案的可重用性：如果您使用C编写它，则以后将无法在其他上下文中使用该解决方案。 使用DSL，您可以先构建一次解决方案，然后再构建几个代码生成器或解释器。
• 实际上，DSL可以更快，因为生成器可以专用于某种架构
DSL不够灵活
# 如何创建领域特定的语言
• 您可以使用哪些工具来构建DSL
• 最重要的成功因素是什么
• 你需要哪些技能
## 我们可以使用哪些工具来构建领域特定的语言？
### 文字语言
#### 务实的自己动手做
1. 您可以使用ANTLR定义词法分析器和解析器语法。 你不知道ANTLR吗？ 没问题，这是有关ANTLR的不错的教程 。 在此博客中，还有许多其他有关ANTLR的文章
2. 您可以以更易于使用的格式转换ANTLR产生的解析树。 这样就得到了代码模型。
3. 您可以解析引用，构建验证，并将类型系统实现为对代码模型的一组操作。 听起来很复杂，但是如果您知道自己在做什么，则可以用几百行代码来完成。
4. 最后，您可以解释或编译代码模型
5. 您为您的语言构建了一个简单的编辑器。 有关如何执行此操作的信息，请在此博客上或本书中查找教程。 我倾向于使用我自己创建的可黑客入侵的编辑器 。 我把它命名为Kanvas
#### 文字
Xtext是构建文本语言的可靠解决方案。 在实践中，您可以按照与ANTLR相似的方式来定义语法，而不仅仅是获得解析器，而是获得一个不错的编辑器。 默认情况下，此编辑器是Eclipse插件。 这意味着您将能够在Eclipse中编辑用DSL编写的文件。 如果您知道Eclipse平台的工作方式，则可以创建RCP应用程序：即，精简版的Eclipse基本仅支持您的语言，并删除了许多对用户无用的东西。
The editors generated by Xtext can be deeply customized, if you know what you are doing. You can get away with minor changes with a reasonable effort, but if you want to do advanced stuff you need to learn the Eclipse internals and this is not a walk in the park.
Recently Xtext escaped the “Eclipse trap” by adding the possibility of generating editors also for IntelliJ IDEA and… the web! When I first found out this I was extremely excited. Me, as many other developers, switched to IntelliJ some years ago and I was missing a way to easily build editors for IntelliJ IDEA. So this was great news, even if Xtext has been created to work with Eclipse so the support for IntelliJ IDEA is not as mature and battle-tested as the one for Eclipse. I did not try yet the web editor, but from what I understood it generates a server side application which is basically an headless Eclipse and on the client side it generates three different editors based on three technologies (each one with a different level of completeness). The one fully supported is Orion , an Eclipse project. While the other two are the well-known CodeMirror and ACE .
You may want to check out this list of projects implemented with Xtext to get an idea of what is possible to achieve using Xtext.
#### Textual languages: other tools
If I had to build a textual language in most cases I would go for one of the two approaches defined earlier: either my do-it-yourself approach or using Xtext. That said there are alternatives on which I think it makes sense to keep an eye on.
textX is a Python framework inspired by Xtext. You can define the grammar of your language with a syntax very, very close to the one used by Xtext. textX does not use EMF or generate code but it use instead the metaprogramming power of Python to define classes in memory. While it seems nice and easy to use, textX does not generate editor support like Xtext, so that is a major difference.
If you want to get a better feeling of how textX works take a look at this video.
There are other tools like Spoofax. I did not use it myself so I cannot vouch for it. It is more academic stuff than an industrial-grade language workbench, so I would suggest a bit of caution.
Spoofax can be used inside Eclipse. It is based on a set of DSLs to use to create other DSLs.
If you want to look into Spoofax you may want to look at this free short book from Eelco Visser named Declare Your Language .
### Graphical languages
Graphical languages seem approachable and frequently domain experts feel more at ease with them than with textual languages and their geeky syntaxes. Graphical languages require building specific editors to be used and they are less flexible than textual languages. Also, they are less frequently used than textual languages and the tools to build graphical languages tend to be less mature and more clunky. Here I present you a list of a few options. If you want to read a more complete list you can look into this survey on graphical modeling editors.
#### GMF, the painful solution
There is one way to build graphical editors for your language that over time acquired quite a (not-exactly-positive) reputation. Its name is GMF: Graphical Modeling Framework .
Yes, you can use it to build editors which can be used inside Eclipse. Similarly to Xtext it is based on EMF. Basically you use EMF to define the structure of your data and then GMF permits to specify how the different elements are represented, how their connections are displayed and that sort of stuff. Typically you then edit the details of each element in a separate panel, a sort of form.
You can see an example of a GMF editor in the picture below.
Now, the documentation is basically unexisting and to make it work is a challenge which requires a great amount of patience and determination.
This framework has potential and it is powerful and flexible, but working with it is far from being an enjoyable experience.
#### Sirius, hiding GMF
There are tools built on top of GMF to make the experience less terrible for the language designer. A simple tool is Eclipse Eugenia , while a more complex one is Eclipse Sirius .
I have used Eclipse Eugenia and it helped jump starting my editor, but it is a limited tool and if you want to customize your editor you are back to GMF.
I have not used Eclipse Sirius myself but it seems to be decently supported by Obeo and being used at Thales, so I would expect it to have at least reasonable maturity and usability.
#### MetaEdit+, the commercial solution
MetaEdit+ is a language workbench for defining graphical languages. Contrary to all the other tools we discussed it is a commercial tool. Now, generally I prefer to base my languages on open-source solutions because I found them more reliable. I know that in the worst case I can always jump in and mantain the platform myself, if I really need to. With a commercial solution instead what happens if the provider goes out of business? Maybe I can keep using the tool I bought for a while, until it is not compatible with the operating-system I am using and I end up trapped. That said MetaCase (the company behind MetaEdit+) is a solid company which has been in business for quite a few years.
I have assisted in two occasions to a presentation from Juha-Pekka Tolvanen and I was positively impressed both of the time. They have a mature solution and they use it to build a bunch of interesting DSLs for their clients. I like very much to check their regular tweets on the DSL of the week . Here a few samples:
So if you ever need a graphical language I would advise to consider this solution. The alternative is in my opinion to use a full-blown projectional editor, which permits to create also graphical languages, but not only those. 好奇？ 继续阅读。
### Projectional editors
Projectional editors are extremely powerful and exciting but they are unfamiliar to many users. I can give you the theory bit, and throw at you a definition, but if you really want to understand them watch the video below.
A projectional editor is an editor that show a projection of the content stored on file. The user interacts with such projection and the editor translates those interactions to changes to the persisted model. When you use a text editor you see characters, you add or delete characters and characters are actually saved on disk. In a projectional editor you could edit tables, diagrams and even what it looks like text, but those changes would be persisted in some format different from what you see on screen. Maybe in some XML format, maybe in a binary format. The point is that you can work with those files only inside their special editor. If you think about it, this is the case also for all the graphical languages: you see nice pictures, you drag them around, connect lines and in the end the editor save some obscure format, not the nice pictures you see on the screen. The point with projectional editors is that they are much more flexible than your typical graphical language. You can combine different notations and support all sort of representation you need for your case.
You could also take a look at this explanation of projectional editing written by Martin Fowler.
#### Jetbrains MPS
Jetbrains MPS is a tool that I have been using for some years, working on it daily on most of last 12 months. It is an extremely powerful tool and it is the most mature projectional editor available out there. It is no accident: Jetbrains has invested significantly on developing it over more than a decade.
Do you want to see how it looks like? 观看视频。
I find very useful MPS to build families of interoperable languages with advanced tooling. Imagine several DSLs to describe the logic of your problems, to define tests, to define documentation. Imagine all sort of simulators, debuggers, tools to analyze code coverage. Everything built on one platform.
Now, it means you need to be ready to embrace Jetbrains MPS and to invest a significant amount of time to properly learn it (or hire someone like me). However if you are ready to do the investment it can simply revolutionize your processes.
#### Intentional Platform
This one is the mysterious and intriguing one.
Charles Simonyi is the man who designed Excel, one of the first space tourists and one of the richiest men on earth. In 1995 he wrote the revolutionary paper The Death of Computer Languages, The Birth of Intentional Programming . In this paper he presents a new, more intuitive way of programming, fundamentally based on projectional editors. He starts working at Microsoft on these ideas, but in 2002 he leaves Microsost to cofound Intentional Software. Since then the publicly available information on their tool, the Intentional Platform has been extremely scarce. They have published a few papers and given a few presentations.
I have heard from people that have used it that it has a lot of potential but it is not there yet. For sure I would love to put my hands on it. The closest you can get is to read this somehow old review of the Intentional Platform from Martin Fowler. Maybe one day even us mortals will have the possibility to know more about this legendary tool.
As far as I know they work with selected companies but for now their tool is not publicly available.
#### Whole Platform
This is a good Language Workbench too frequently overlooked. While it has been used in production for many years in a large company in Italy, it is lacking a little bit on the documentation and marketing side. Yes, I know it is sad that pure engineering awesomeness is not enough to gain popularity. Anyway if you want to know more about it you can read my post on getting started with the whole platform .
There are a few concepts that I find quite interesting. I am not an expert on the Whole Platform: I have just played with it and talked with his authors.
One aspect that I find really interesting and different with respect to the other Language Workbenches is that the Whole Platform supports quite well working with existing formats, and evolve from existing processes to more advanced Language-Engineering approaches. For example, it is quite easy to define grammars for existing formats in order to parse them.
The following is an example of a grammar to parse JSON but the same approach has been used to parse very complex formats used in the banking domain.
Another idea I love about the Whole Platform is the Pattern Language: the possibility to take a model (in this sense a piece of Java code is a model) and define variability points that could be filled with values from another model.
Whole Platform – Pattern Language
Whole Platform – Graphical Language
Also, the Whole Platform is quite rich and it supports also graphical languages.
Riccardo Solmi and Enrico Persiani are the minds behind the Whole Platform and you should probably talk to them if you are interested in using this Language Workbench.
The images of the Whole Plargorm I have used are released unfer the CC Attribution 2.0 license (https://creativecommons.org/licenses/by/2.0/)
### Comparing the different approaches
APPROACH TYPE WHEN TO USE IT
Do-it-yourself Textual You need to be in absolute control of the platforms supported and you do not want any vendor lock-in
textX Textual You love the flexibility of dynamic languages while editor support is not important to you
Spoofax Textual You like to work with a sound theoretical approach and you are not afraid of a few bumps in the road
GMF 图形化 You need extreme flexibility to build your very own graphical editor
Eclipse Sirius 图形化 You are ready to trade some flexibility to get things done quicker and saving some mind sanity
MetaEdit+ 图形化 You are fine using commercial software for a stragegic component and you want results quickly
Jetbrains MPS Projectional You want to build family of languages with powerful and complex tooling like simulators, debuggers, testing support and more
Intentional Workbench Projectional You have some connection that give you access to the most mysterios and hyped Language Workbench
Whole Platform Projectional You want to support existing formats and transition smoothly to a new approach
One thing I would like to stress is that projectional editing is a superset of the graphical editing. So you can define graphical languages using Jetbrains MPS. Given there is not a clear and great alternative to build only graphical DSLs I would use Jetbrains MPS in that case. Alternatively I would consider build the tooling myself targeting the web. Another interesting option could be looking into something like FXDiagram .
### 还不够吗？
If you want to keep an eye on the new Language Workbenches that come up I suggest you follow the “Language Workbench Challenge”, a workshop that is typically colocated with the Software Language Engineering conference. I co-authored a paper and attended the last edition and it was awesome.
## What do I need to make my DSL succeed?
There are just two things that will seem obvious but are not:
1. You need your users to use it
2. You need your users to get benefits from using it
To achieve this you will need to build the right tool support and adopt the right skills. We are going to discuss all of this in this section.
### Get users to use it
The first point means that you need to win the support of users. During my PhD I conducted a survey on the reasons why DSLs are not adopted. There are several causes, but one important factor is resistance from users, especially when they are developers .
If you target a DSL to developers, they could resist because they feel they are not in control as when they use a General Purpose Language (GPL). They could also fear that a DSL lowers the bar, being simpler to use than, let's say, Java. In addition to that, as all innovations, a new DSL is threatening for seasoned developers because it reduces the importance of some of their skills, like the vast experience in dealing with the quirks of the current GPL you are using at your company.
If your DSL is intended to non-developers generally it is easier to win their support. 为什么？ Because you are giving them a superpower: the ability to do something on their own . They could use a DSL to automatize a procedure that previously was done manually. Maybe before the DSL was available the only possibility for them to do something was bothering some developer to write custom code. Now they get a DSL which means more power and independence because of it. Still they could resist adopting it if they perceive it as too difficult or if they feel it does not match their way of thinking.
To me the key as a DSL designer in this case is being humble and listen . Listen to the developers, work on capturing their experience and embedding it in the design of the DSL or the tooling around it. Involve them in the design of the DSL. When talking with your users, technical or not, communicate that the DSL will be a tool for them, designed to support them and derived by their understanding of the domain at hand. When designing DSLs the cowboy approach does not work, you need to succeed as a team or not succeed at all.
### Give benefits to users
If you get the support of users and people start using it you win only if they get a significant advantage from using the DSL.
We have discussed the importance of a DSL as communication tool, as a medium to support co-design. This is vital.
In addition to this, you can increase significantly the productivity of your users by building first-class tool support.
• a great editor with syntax highlighting and auto completion: so that learning the language and using it feel like a breeze
• great error messages: a DSL is an high level language and error can be very significant for users
• simulators: nothing helps users as the possibility to interact with a simulator and see the results of what they are writing
• static analysis: in some contexts the possibility to analyze the code and reassure against possible mistake is a big win
These are a few ideas but more can be adopted, depending on the specific case. Specific tools support for specific languages.
## Tool support: why we do not care about internal Domain Specific Languages
There is one factor that is frequently overlooked and this is tool support.
Many practicioners think that the only relevant thing is the syntax of your language or what it permits to express, with everything else being a detail.
This is just fundamentally wrong because the tool support can multiply exponentially the productivity when using any language, especially a DSL. This is a crucial aspect to consider, because the language should be designed considering tool support.
Because when building Domain Specific Languages, if you want to get serious, you have to build good tool support. Tool support is an essential key in delivering value.
I recorded this short video on this very subject.
Tool support is the reason why internal domain specific languages (ie, fake DSLs) are irrelevant: they do not have any significant tool support.
When using some host languages you can bend them enough of getting some sort of feeling of having your own little language, but that is it. There are some languages that are flexible enough to give a sort of decent … like ruby. With other languages you get very poor results. I feel pity for the people trying to build “internal DSLs” for languages like Scala or Java. The worst of all is lispers. I understand their philosophy “if you want to solve a problem in LISP, first you create your LISP dialect and then solve it using it”. I understand and I think it is a great technique. Just let's not pretend this is a real DSL. This is not something you can share and work with closely with domain experts. It can be your trick to be more productive, but that is it.
You see those ridicuosouly long chains of method calls and you hear someone presenting those as Domain Specific Language. That makes me feel a mix of two emotions:
• pity for him and his users
• rage for the confusion it creates. Real DSLs are very different and they can bring real benefits. Stop mixing them with this… thing
Just build a real DSL, so an external DSL!
## What skills are needed to write a DSL?
Typically you need to be able to have high abstraction skills , the same you need typically for metaprogramming. If writing a library is 3 times harder than writing a program, writing a framework or a DSL is typically 3 times harder than writing a library.
You need to be humble : you may need a developer, but typically you need to create this DSL for other professional that are going to use it for their job. Listen to what theydo, understand how they work. What could seem wrong or naive to you could have reasons you do not yet understand. Acting as the all-mighty-expert is the single best way to create a failed DSL, not useful in practice and therefore not used.
Aside from this, practice and learn. Keeping doing it for a few years should do the trick.
# 资源资源
Now that you have seen what DSLs can bring you and you have an idea how to build them you should be happy.
But you are not, you want more, you want to understand better DSLs, you want to learn everything about them.
Well, I do not know about everything, but definitely I can give you some pointers. I can tell you where to find the good stuff.
Let's see what we can find:
### 图书
I would start suggesting to read the DSL Engineering by Markus Völter . This PDF version of the book is donation-ware. So just read it and donate. Alternatively you can find the printed version on Amazon.
The book start with an introduction part: it is very useful to set your terminology straight. After that it comes the DSL design part, focusing on different aspects separately. If you do not have direct access to an expert to teach you how to design DSLs reading this part of this book is the best alternative I can recommend (together with as much practice as you can, of course).
Then it comes the part about implementation: remember that Markus has a PhD, but he is first of all someone who gets things done so this part is very well written, with examples based on Xtext, Spoofax and MPS.
Part IV is about scenarios in which DSLs are useful. Given this is based on his large experience in this field there are a lot of interesting comments.
I had the occasion to work with Markus. I used to admire him a lot before meet him and I now I admire him even more. He is simply the best one on this field, so if you can learn something from him do it. Read his books, watch his presentations, follow his projects. It will be a good way to invest your time. He is lately working on Jetbrains MPS stuff, so you should follow what is going on with mbeddr and IETS3 . Mbeddr is both a set of plugins for MPS and an implementation of the C language in MPS with special domain-specific extensions to support development of embedded software. IETS3 is instead an expression language built in MPS.
Martin Fowler is a very famous thought leader and bestseller author. I really admire his clarity. He is the author of Domain Specific Languages , a book about both internal and external DSLs.
I find the mental models presented in the book quite useful and elegant. In practice however I find internal DSLs irrelevant, so I am interested in only some portions of this book.
There are 15 chapters dedicated specifically to external domain specific languages. While those chapters are organized around implementation techniques there are comments and remarks from which you can learn some design principles.
I think the sections on the alternative computational models and code generation are very valuable. You will have an hard time finding an exploration to these topics at this level of detail anywhere else.
The book is 7 years old and the techniques may have evolved since the book was written, but the vast majority of the considerations presented in the book are still valid. And of course they are thoughtful and well explained, as you would expect from Martin Fowler.
If you are interested in textual languages and in particular on ANTLR you should definitely look into the Language Implementation Patterns from Terence Parr. I like the author, I like the publisher (the Pragmatic Bookshelf) and unsurprisingly I love the book.
The book starts discussing different parsing algorithms. If you like to learn how stuff works you should take a look at these chapters. Then there are chapters about working with the Abstract Syntax Tree, extracting information, transforming it. This is the kind of stuff you need to learn if you want to become a Language Engineer. Also, there chapters on resolving references, building symbol tables or implementing a typesystem. These are the foundations to learn how to process the information expressed in your DSL.
Finally Terence explains you how to use the information you have processed by building an interpreter or a code generator. At this point you end your journey, having seen how to build a useful language from start to finish. This book will give you solid basis to learn how to implement DSLs. The only thing missing is a discussion on how to design DSLs, but this is not the goal of this book.
If you are looking into MPS there are not many resources around. It could make sense to buy the two books from Fabien Campagne on the MPS Language Workbench . They explain in details all the many features of MPS (admittedly some are a bit obscure). If I would have to find one thing missing is more advices on language design. These books are very good references to learn how MPS works, but there is not much guidance on how to combine these features to get your results. One reason for that is that MPS is an extremely powerful tool, which can be used in very different ways so it is not easy to give general directions.
Volume I explains separately the different aspects of a language: how to define the structure (the metamodel), how to define the editors, the behavior, the constraints, the typesystem rules and so on. Most of the chapters are in reference-manual style (eg the chapter The Structure AspectStructure In Practice ). Everything you need to learn to get started and build real languages with MPS is explained in Volume I.
Volume II is mostly about the advanced stuff that you can safely ignore at the beginning. I suggest looking into this book only when you feel comfortable with all the topics explained in Volume I. If you have never used MPS before it will take some time. Volume II explaine you how to use the build framework to define complex building configurations, it gives you an overview of all the different kinds of testing you may want to use for your languages. It also show you how to define custom aspects for your language or custom persistence.
I have bought the Google Play version but they are available also in print form.
On Xtext there is a quite practical and enjoyable book from Lorenzo Bettini: Implementing Domain-Specific Languages with Xtext and Xtend . I wrote a review on the second edition of this book: if you want to read my long-form opinion of that book you can visit the link.
If you want to learn how to write textual languages with good tool support you could start following a couple of tutorials on Xtext and then jump to this book. This book will explain you everything you need to know to use Xtext to build rather complex editors for your language. The only caveat is that Xtext is part of a complex ecosytem so if you really want to become an expert of Xtext you need to learn EMF and Xtend. The book does a good job in teaching you what you need to know to get started on these subjects but you may have to complete your education with other resources too, when you want to progress.
What I like about this book is that is not a reference manual, but it contains indications and opinions on topics like Scoping or building a typesystem rules (the author has some significative experience on this specific topic). Also, the author is interested in best practices so you will read his take on testing and continuos integration. The kind of stuff you should not ignore if you are serious about language engineering.
If you are interested in DSLs in general you can take a look at DSLs in Action . The book is interesting but I have two comments:
1. It focus way too much on internal DSLs, which are, as we all know, not the real thing
2. They have misspelled my name. -1 point for that
Specifically on external DSLs there is not much: the author briefly discuss Xtext and then spend a chapter on using Scala parser combinators to build external DSLs. That would not have been my first choice. So if you are interested in learning how to implement an external DSL do not pick this book. However if you want a gentle introduction to the topic of DSLs, if you are a degenerate who prefers internal DSLs instead of external DSLs, or if you want to read every available resource on DSLs this book would be a good choice.
Domain Driven Design is a relevant and important book to read. Because you need skills to understand the domain, in order to be able to represent it in your language, and to design your language so that it can capture it. Now, I should probably just praise this book and stress how much I have enjoyed it. Unfortunately I tend to err on the honesty side so I warn you: this is one of the most boring books I have ever read. It is important, it is useful, it is great but it just so plain and long. It stayed on my night stand for months.
What you should get how of this book is the importance of capturing the Domain in all of your software artifacts. The book stress the importance of building a common language to be shared among the stakeholders. This is completely and absolutely relevant if you want to build Domain Specific Languages. What is not part of this book is how to map this domain model to a language. For that part you should refer to the other books, specific to DSLs design. This book is a good complement to any of them.
### 公司介绍
I design and implement Domain Specific Languages for a living but instead of tell you how great I am, I will instead list other companies that you could work with.
The first, obvious name is Itemis. They are a German company with small offices in France and Switzerland. They employ some of the best in the field: I have met and worked with Markus Völter and Bernd Kolb and I am seriously impressed by the level at which they work. They have worked with so many companies and have done so many projects that the list will be scarely too long. I would just say that in the later years they have done amazing work using Jetbrains MPS. They have created the mbeddr project and from it they have derived a set of utilities, named the mbeddr platform, which contributed enormously to the growth of MPS. They have contributed early and significantly to the Language Workbench community, so if you need some help on a DSL you should seriously consider working with them.
TypeFox is another German company. I have interviewed one of the founders some time ago. Several Xtext core committers are involved in the company so as you can imagine they have some serious competencies on Xtext and the EMF platform in general. If you need Xtext training or consulting I would consider them the top-choice. They are also a Solution Member of Eclipse and I would expect them to be able to build complex Eclipse-based solutions. If you want to hear more you can read this interview to Jan Köhnlein . Jan is one of the founders of the company and we talked a few months after the company was created.
Jetbrains is obviously the company behind Jetbrains MPS. Recently they started offering training on MPS. I asked about this during my interview at Vaclav Pech . They offer training, either basic or advanced, on their premises in Prague or on-site.
At the moment I do not think they offer MPS consulting (for that you can talk to me or to Itemis).
## 结论
There are many reasons why you should really consider Domain Specific Languages. I have seen companies benefit enormously from DSLs. Most of the people I have worked with used DSLs as a key differentiator that helped them increase productivity by 10-20 times, reduce time-to-market and feedback cycles, increase the longevity of their business logic and much more.
Aside from the practical benefits I find the topic extremely fascinating. Most of all I feel that by building DSLs we build powerful tools that help other people do their job. As language designers we act as enablers, our languages can be used by skilled professionals to achieve great things and this is an amazing feeling for me.
### 请问你能帮帮我吗？
If you found this guide useful please share it, spread the work and link it. I spent several years working on this subject and a few weeks working on this guide. I would be very happy if you could help me reach others who could find it useful.
Thank you so much!
A few ideas:
• Send an e-mail to your colleagues
### HTML期末大作业~餐饮文化学生网页设计作业(HTML+CSS+JavaScript)[email protected]码住夏天-web网页设计的博客-程序员信息网
HTML期末大作业~基于HTML+CSS+JavaScript饮食网站设计与实现 关于HTML期末网页制作，大作业A+水平 ~饮食网页作业HTML+CSS+JavaScript实现，共有联系我们 在线留言 资质荣誉 行业资讯 成功案例 新闻资讯 产品中心 发展历史 关于我们 8...
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2022-06-25 08:17:40
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http://mkweb.bcgsc.ca/pi/piday/methods.mhtml
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Where am I supposed to go? Where was I supposed to know?get lost in questionsmore quotes
# numbers: worthwhile
PNAS Cover: Earth BioGenome Project
# visualization + design
The 2022 Pi Day art is a music album “three one four: a number of notes” . It tells stories from the very beginning (314…) to the very (known) end of π (...264) as well as math (Wallis Product) and math jokes (Feynman Point), repetition (nn) and zeroes (null).
# $pi$ Day 2013 Art Posters
2021 $\pi$ reminds us that good things grow for those who wait.' edition.
2019 $\pi$ has hundreds of digits, hundreds of languages and a special kids' edition.
2018 $\pi$ day stitches street maps into new destinations.
2017 $\pi$ day imagines the sky in a new way.
2016 $\pi$ approximation day wonders what would happen if about right was right.
2016 $\pi$ day sees digits really fall for each other.
2015 $\pi$ day maps transcendentally.
2014 $\pi$ approx day spirals into roughness.
2014 $\pi$ day hypnotizes you into looking.
2014 $\pi$ day
2013 $\pi$ day is where it started
Circular $\pi$ art and other distractions
On March 14th celebrate $\pi$ Day. Hug $\pi$—find a way to do it.
For those who favour $\tau=2\pi$ will have to postpone celebrations until July 26th. That's what you get for thinking that $\pi$ is wrong. I sympathize with this position and have $\tau$ day art too!
If you're not into details, you may opt to party on July 22nd, which is $\pi$ approximation day ($\pi$ ≈ 22/7). It's 20% more accurate that the official $\pi$ day!
Finally, if you believe that $\pi = 3$, you should read why $\pi$ is not equal to 3.
Most of the art is available for purchase as framed prints and, yes, even pillows. Sleep's never been more important — I take custom requests.
2013 was the first year in which I made $\pi$ day art. It was a year of dots and love.
René Hansen has created an interactive version of this year's posters! Why not go to the Feynman point directly!
## shimmering dots
Each digit is represented by a dot of a different color. The inner grey dots appear to glimmer—this is the luminance effect in action.
The posters explore the relationship between adjacent digits in $\pi$, which are encoded by color using the scheme shown above. The design appears to shimmer due to the luminance effect. In some versions of the poster, adjacent identical (or similar) digits are connected by lines.
The recipe for each poster is included in its figure legend. It gives the color of the $i$th outer and inner circles. $\pi_i$ is used to represent the $i$th digit of $\pi$. For example, the recipe
$\pi_i$ / $\pi_{i+1}$
corresponds to the case where outer circle color encodes the $i$th digit and the inner circle color encodes the next digit $i+1$th. In this scheme, inner and outer circles of adjacent positions have the same color.
Pi Day Art | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK )
Pi Day Art | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK )
Pi Day Art | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK )
The posters were generated automatically with a Perl script that generated SVG files. Post processing and layout was done in Illustrator. If you are interested in depicting your favourite number this way, let me know.
The design was inspired by the beautiful AIDS posters by Elena Miska.
## love in $\pi$—you can find it here
I calculated $pi$ to 13,099,586 digits and then I found love.
It's fun to look for digits or look for words in $\pi$.
Just don't get carried away. Because $\pi$ is likely normal in base 10, all words and all patterns appear in it, somewhere.
I wanted to know the first time that "love" appears in $\pi$. When encoded using the scheme a=0, b=1, ..., z=25, "love" is the digit sequence 1114214.
This sequence appears first at position 13,099,586 (...892199163111142148187311392...). And, of course, infinitely many times after that.
Curiously, "hate" (0700194) appears well before love, at digit 514,717. In the first 200,000,000 digit "hate" appears 23 times, 6 times more than "love".
Pi Day Art | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK )
Pi Day Art | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK )
If you use the scheme a=1, b=2, ..., z=26, then "love" becomes 1215225. This is first seen at 6,317,696 (...610311912912152256606850141...).
# Cancer Cell cover
Sat 23-04-2022
My cover design on the 11 April 2022 Cancer Cell issue depicts depicts cellular heterogeneity as a kaleidoscope generated from immunofluorescence staining of the glial and neuronal markers MBP and NeuN (respectively) in a GBM patient-derived explant.
LeBlanc VG et al. Single-cell landscapes of primary glioblastomas and matched explants and cell lines show variable retention of inter- and intratumor heterogeneity (2022) Cancer Cell 40:379–392.E9.
My Cancer Cell kaleidoscope cover (volume 40, issue 4, 11 April 2022). (more)
Browse my gallery of cover designs.
A catalogue of my journal and magazine cover designs. (more)
# Nature Biotechnology cover
Sat 23-04-2022
My cover design on the 4 April 2022 Nature Biotechnology issue is an impression of a phylogenetic tree of over 200 million sequences.
Konno N et al. Deep distributed computing to reconstruct extremely large lineage trees (2022) Nature Biotechnology 40:566–575.
My Nature Biotechnology phylogenetic tree cover (volume 40, issue 4, 4 April 2022). (more)
Browse my gallery of cover designs.
A catalogue of my journal and magazine cover designs. (more)
# Nature cover — Gene Genie
Sat 23-04-2022
My cover design on the 17 March 2022 Nature issue depicts the evolutionary properties of sequences at the extremes of the evolvability spectrum.
Vaishnav ED et al. The evolution, evolvability and engineering of gene regulatory DNA (2022) Nature 603:455–463.
My Nature squiggles cover (volume 603, issue 7901, 17 March 2022). (more)
Browse my gallery of cover designs.
A catalogue of my journal and magazine cover designs. (more)
# Happy 2022 $\pi$ Day—three one four: a number of notes
Mon 14-03-2022
Celebrate $\pi$ Day (March 14th) and finally hear what you've been missing.
“three one four: a number of notes” is a musical exploration of how we think about mathematics and how we feel about mathematics. It tells stories from the very beginning (314…) to the very (known) end of π (...264) as well as math (Wallis Product) and math jokes (Feynman Point), repetition (nn) and zeroes (null).
Listen to $\pi$ in the style of 20th century classical music. (details)
The album is scored for solo piano in the style of 20th century classical music – each piece has a distinct personality, drawn from styles of Boulez, Feldman, Glass, Ligeti, Monk, and Satie.
Each piece is accompanied by a piku (or πku), a poem whose syllable count is determined by a specific sequence of digits from π.
Check out art from previous years: 2013 $\pi$ Day and 2014 $\pi$ Day, 2015 $\pi$ Day, 2016 $\pi$ Day, 2017 $\pi$ Day, 2018 $\pi$ Day, 2019 $\pi$ Day, 2020 $\pi$ Day and 2021 $\pi$ Day.
# PNAS Cover — Earth BioGenome Project
Fri 28-01-2022
My design appears on the 25 January 2022 PNAS issue.
My PNAS cover design captures the vision of the Earth BioGenome Project — to sequence everything. (more)
The cover shows a view of Earth that captures the vision of the Earth BioGenome Project — understanding and conserving genetic diversity on a global scale. Continents from the Authagraph projection, which preserves areas and shapes, are represented as a double helix of 32,111 bases. Short sequences of 806 unique species, sequenced as part of EBP-affiliated projects, are mapped onto the double helix of the continent (or ocean) where the species is commonly found. The length of the sequence is the same for each species on a continent (or ocean) and the sequences are separated by short gaps. Individual bases of the sequence are colored by dots. Species appear along the path in alphabetical order (by Latin name) and the first base of the first species is identified by a small black triangle.
Lewin HA et al. The Earth BioGenome Project 2020: Starting the clock. (2022) PNAS 119(4) e2115635118.
# The COVID charts — hospitalization rates
Tue 25-01-2022
As part of the COVID Charts series, I fix a muddled and storyless graphic tweeted by Adrian Dix, Canada's Health Minister.
I show you how to fix color schemes to make them colorblind-accessible and effective in revealing patters, how to reduce redundancy in labels (a key but overlooked part of many visualizations) and how to extract a story out of a table to frame the narrative.
Clear titles introduce the graphic, which starts with informative and non-obvious observations of the relationship between age, number of comorbidities, vaccination status and hospitalization rates. Supporting the story is a tidy table that gives you detailed statistics for each demographic. (more)
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2022-05-23 17:41:32
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http://ask.sagemath.org/question/733/disable-syntax-highlighting-in-sws2tex
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# Disable syntax highlighting in sws2tex
3 Hi I am using sws2tex to convert sage notebooks to latex. I am wondering if it is possible to disable syntax highlighting? The reason I want this is that sometimes I use the Maple and Matlab interfaces directly in the notebook, and the syntax highlighting looks wrong here. I know I can remove it manually after creating the tex file, but I would like to be able to disable it instead. Another small question: Is it possible to disable the "attachfile"? Of course this is not so important since it requires removing 1 or 2 lines, but it could be nice though... asked Sep 03 '11 Kabi 100 ● 4 ● 13 kcrisman 7812 ● 20 ● 78 ● 170
1 Kabi, this is all possible, but for now you have to do it all yourself by modifying sws2tex.py. I have done this myself at times. As you noted, removing the "attachfile" is very simple. I usually also do shutil.copyfile(temp_dir + os.sep + output_filename + ".tex", output_filename + ".tex") so I have the original TeX source to look at (or modify). The easiest way to remove the syntax highlighting is to comment out all the stuff about colorizing, like so (I also do this): #try: # from pygments import highlight # from pygments.lexers import PythonLexer, TexLexer, HtmlLexer # from pygments.formatters import LatexFormatter #except ImportError: # print "Warning: Unable to load module pygments" # print "Warning: Syntax highlighting will be disabled" # # def colorize(s, **kwds): # return "\\begin{Verbatim}[commandchars=@\$\$]\n" + s + "\n\\end{Verbatim}\n" def colorize(s, **kwds): return "\\begin{Verbatim}\n" + s + "\n\\end{Verbatim}\n" Or you can do your own colorizing. It's also possible to remove this from the place where the stuff happens in the methods for cells. It's great to hear you use this, by the way; sws2tex is not part of Sage yet, but the hope is that it would eventually be ready for inclusion, and comments like this for options are great to hear. posted Sep 05 '11 kcrisman 7812 ● 20 ● 78 ● 170
1 Thanks! I have now changed several things in the sws2tex.py file including disabling syntax highlighting. It is practical in the notebook to be able to use %hide and then %latex in the second line or only %latex, and then only have the pure latex code included in the tex file without adding the input cell with latex code in a verbatim environment. I achieve this with sws2tex by changing the following in the, class InputCell(Cell): def _detect_language(self): first_line = self.text.splitlines()[0] try: second_line = self.text.splitlines()[1] except: second_line = "" if first_line == '%latex': self.language = 'latex' elif second_line == '%latex': self.language = 'latex' ... and def latex(self): if options.hide: first_line = self.text.splitlines()[0] if first_line == '%hide': return "" if self.language == 'latex': return "" ... Another thing for people having problems with special letters like æ, ø or å in danish: One solution is to add the following as the first line in html2latex.py: # -*- coding: utf-8 -*- and the following to convert the letters from the html to utf-8: entities = { ... "aelig": 'æ', "oslash": 'ø', "aring": 'å', "AElig": 'Æ', "Oslash": 'Ø', "Aring": 'Å' With these changes the sage notebook becomes a near complete math/report environment for me. sws2tex makes it possible to produce very good paper print of your work done in the notebook, which (in my opinion) is not the case with the existing print function with jsMath directly from the notebook. So thanks for sws2tex and keep up the good work! :-) posted Sep 06 '11 Kabi 100 ● 4 ● 13 Well, I'm definitely not responsible for more than one character of the actual code, but I have used it a fair amount and love seeing people use it. Glad it's helping!kcrisman (Sep 06 '11)@Kabi: By the way, I assume you are aware of the TinyMCE editor, which uses jsmath and which does render properly in sws2tex? I rarely need %latex in the notebook for this reason, though I occasionally use the latex() method of some Sage object to put it in a longer computational cell.kcrisman (Sep 06 '11)I have problems with the TinyMCE editor when wanting to use the "align" environment. In the editor you need to enclose latex math in or , but in the converted latex code you will get, \[ \begin{align} ..., which will fail when compiling the document. So I use the TinyMCE for normal text and simple math stuff and then the %latex cell for more complicated math expressions.Kabi (Sep 06 '11)
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2014-04-24 00:59:12
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https://www.michaelstraka.com/
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## Recursive Zero-Knowledge Proofs: A Comprehensive Primer
Recently, there have been a number of exciting results concerning proof recursion. A sketch for Halo has suggested the possibility of proof recursion without a costly trusted setup, while Fractal has demonstrated the first instantiation of proof composition which is post-quantum secure. We’ll go into these results later after discussion what proof composition is, the technical challenges associated with achieving it, and how it ties into commonly used proof systems as Groth 16 and Bulletproofs.
Posted
## Class Groups for Cryptographic Accumulators
Late last year Benedikt Bunz and Ben Fisch, both PhD students at Stanford University, released a paper along with Dan Boneh titled “Batching Techniques for Accumulators with Applications to IOPs and Stateless Blockchains”. In it they use some basic group theory to build a dynamic accumulator, which allows for storing and deleting elements in addition to the use of both membership and non-membership proofs. It can be used to create a vector commitment data structure analogous to Merkle trees, with the main difference being that it allows for constant-sized inclusion proofs, where a Merkle tree has $O(\log n)$ sized inclusion proofs where $n$ is the number of elements being stored.
Posted
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2021-05-07 06:14:19
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http://math.stackexchange.com/questions/202624/what-does-the-notation-fa-x-mean/202625
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# What does the notation $|f(A)| = X$ mean?
$A$ is a set and so is $B$.
$f$ is a function $A \to B$.
I have a math question that asks about $|f(A)|$. What does the notation $|\cdot |$ mean?
-
If the elements of $B$ are sets, then the double bars could mean cardinality (i.e. the size of the set).
If $B$ is a set of numbers, it probably means absolute value.
@mimicocotopus: Here it refers to cardinality. The first question is asking how many functions there are from $A$ to $B$ that have exactly $4$ elements of $B$ in their respective ranges. The second asks how many have at most $4$ elements of $B$ in their respective ranges. – Brian M. Scott Sep 26 '12 at 4:52
Ah yes, I misread the question. Here $f(A)$ refers to the image of $A$ under $f$ and so the output is always a set. So in this case, the notation must mean cardinality. – tskuzzy Sep 26 '12 at 5:25
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2016-05-04 08:28:08
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https://jp.maplesoft.com/support/help/view.aspx?path=ListTools/DotProduct&L=J
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DotProduct - Maple Help
ListTools
DotProduct
compute the dot product of two lists
Calling Sequence DotProduct(L1, L2)
Parameters
L1, L2 - lists
Description
• The DotProduct(L1, L2) calling sequence computes the real dot product of two lists, L1 and L2, where both lists have equal length.
• To find the inner product, use DotProduct(L1, map(conjugate, L2)).
Examples
> $\mathrm{with}\left(\mathrm{ListTools}\right):$
> $L≔\left[0.,0.84,0.91,0.14,-0.76,-0.96,-0.28,0.66,0.99,0.41,-0.54\right]$
${L}{≔}\left[{0.}{,}{0.84}{,}{0.91}{,}{0.14}{,}{-0.76}{,}{-0.96}{,}{-0.28}{,}{0.66}{,}{0.99}{,}{0.41}{,}{-0.54}\right]$ (1)
> $M≔\left[1.,0.54,-0.42,-0.99,-0.65,0.28,0.96,0.75,-0.15,-0.91,-0.84\right]$
${M}{≔}\left[{1.}{,}{0.54}{,}{-0.42}{,}{-0.99}{,}{-0.65}{,}{0.28}{,}{0.96}{,}{0.75}{,}{-0.15}{,}{-0.91}{,}{-0.84}\right]$ (2)
> $\mathrm{DotProduct}\left(L,L\right)$
${5.0063}$ (3)
> $\mathrm{DotProduct}\left(L,M\right)$
${0.3162}$ (4)
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2022-09-27 11:14:57
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http://www.ck12.org/geometry/Supplementary-Angles/lesson/Supplementary-Angles-Intermediate/r9/
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<meta http-equiv="refresh" content="1; url=/nojavascript/">
You are viewing an older version of this Concept. Go to the latest version.
# Supplementary Angles
%
Progress
Practice Supplementary Angles
Progress
%
Supplementary Angles
What if you were given two supplementary angles? How would you determine their angle measures? After completing this Concept, you'll be able to use the definition of supplementary angles to solve problems like this one.
### Guidance
Two angles are supplementary when they add up to $180^\circ$ . Supplementary angles do not have to be congruent or touching.
#### Example A
The two angles below are supplementary. If $m \angle MNO = 78^\circ$ what is $m \angle PQR$ ?
Set up an equation.
$78^\circ + m \angle PQR = 180^\circ\\m \angle PQR = 102^\circ$
#### Example B
What are the measures of two congruent, supplementary angles?
Supplementary angles add up to $180^\circ$ . Congruent angles have the same measure. Divide $180^\circ$ by 2, to find the measure of each angle.
$180^\circ \div 2 = 90^\circ$
So, two congruent, supplementary angles are right angles, or $90^\circ$ .
#### Example C
Name one pair of supplementary angles in the diagram below.
One example is $\angle INM$ and $\angle MNL$ .
Watch this video for help with the Examples above.
### Vocabulary
Two angles are supplementary when they add up to $180^\circ$ .
### Guided Practice
Find the measure of an angle that is supplementary to $\angle ABC$ if $m \angle ABC$ is
1. $45^\circ$
2. $118^\circ$
3. $32^\circ$
4. $x^\circ$
1. $135^\circ$
2. $62^\circ$
3. $148^\circ$
4. $180-x^\circ$
### Practice
Find the measure of an angle that is supplementary to $\angle ABC$ if $m\angle ABC$ is:
1. $112^\circ$
2. $15^\circ$
3. $97^\circ$
4. $81^\circ$
5. $57^\circ$
6. $(x-y)^\circ$
7. $(x+y)^\circ$
Use the diagram below for exercises 8-9. Note that $\overline{NK} \perp \overleftrightarrow{IL}$ .
1. Name another pair of supplementary angles.
1. If $m\angle INJ = 63^\circ$ , find $m\angle JNL$ .
For exercises 10-13, determine if the statement is true or false.
1. Supplementary angles add up to $180^\circ$ .
2. Two angles on a straight line are supplementary angles.
3. To be supplementary, two angles must be touching.
4. It's possible for two angles in a triangle to be supplementary.
For 14-15, find the value of $x$ .
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2015-03-03 16:44:34
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https://www.gradesaver.com/textbooks/math/differential-equations-linear-algebra/linear-algebra-a-modern-introduction/chapter-2-systems-of-linear-equations-2-1-introduction-to-systems-of-linear-equations-exercises-2-1-page-63/11
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## Linear Algebra: A Modern Introduction
$$\begin{bmatrix} 1 & 0 \\ 0 & 1 \\ 0 & 0 \\ \end{bmatrix}$$
Given this matrix: $$\begin{bmatrix} 3 & 5 \\ 5 & -2 \\ 2 & 4 \\ \end{bmatrix}$$ First, subtract the first row from the second: $$\begin{bmatrix} 3 & 5 \\ 2 & -7 \\ 2 & 4 \\ \end{bmatrix}$$ Then third from the second, and vice versa, then cancel out the third row again, producing a matrix in row echelon form: $$\begin{bmatrix} 3 & 5 \\ 0 & -11 \\ 0 & 0 \\ \end{bmatrix}$$ Lastly, divide the first and second rows by $3$ and $-11$ to make their leading coefficients $1$, and add $-5$ times the second row to the first row to yield a matrix in reduced row echelon form. $$\begin{bmatrix} 1 & 0 \\ 0 & 1 \\ 0 & 0 \\ \end{bmatrix}$$
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2018-11-12 22:52:42
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http://motls.blogspot.com/2012/06/why-matrix-theory-contains-membranes.html
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## Thursday, June 07, 2012 ... /////
### Why M(atrix) theory contains membranes
A week ago, I wrote a long article on Matrix theory. I planned a few shorter additions and this is the first one.
M-theory may stand for "mother", "magic", "mystery", "matrix", upside down "W" for "Witten" (this interpretation was discovered by Sheldon Glashow), but it may also stand for "membrane". And Matrix theory actually contains states that look like membranes. It has to contain such states because M-theory contains membranes and Matrix theory should be physically equivalent to M-theory.
The BFSS, discoverers of Matrix theory. I am only able to identify Willy Fischler, a part-time paramedic, in the middle.
In this text, I want to explain why the matrix model contains configurations (and quantum states) that look like two-dimensional sheets of a supersmooth atomless Lorentz-invariant charged paper. We will focus on membranes of spherical and toroidal topology but the conclusion is more general.
The insight that the matrix model describes membranes wasn't quite new in 1996. In fact, the matrix model was encountered a decade earlier in efforts to "discretize" a theory of membranes in order to make it as well-defined as a theory of strings. However, only in 1996, BFSS were able to find out that the matrix model is actually an exact description of the M-theoretical membranes as well as everything else. They also resolved some puzzling issues about degenerate shapes of membranes and their topology change.
All this discussion is linked to noncommutative geometry, a subdiscipline of mathematics whose physically meaningful part has been tightly incorporated (by Nature) into string/M-theory. The particular constructions of noncommutative geometry resembling a sphere and a torus are known as the fuzzy sphere and fuzzy torus, respectively.
The Hamiltonian of Matrix theory
We will begin with a particular form of the Matrix theory Hamiltonian:$P^- \equiv H = R\cdot {\rm Tr} \zav { (\Pi^i)^2 - ([X_i,X_j])^2}, \quad P^+ = \frac{N}{R}$ I am neglecting coefficients of order one and I am neglecting Yukawa-like terms with the fermions. The fermionic matrices $\theta^a$ where $a$ takes 16 possible values give you new degrees of freedom; but these degrees of freedom are also necessary to cancel some terms that would cause inconsistencies such as the "zero-point energies" arising from the off-diagonal modes – as I mentioned in the first blog entry on Matrix theory. So if you do a quantum calculation involving the bosons only and you run into some pathological quantum effect that shouldn't be there, chances are that this effect would be cancelled if you added the fermions.
Note that the light-like components of the spacetime momentum, $P^+$ and $P^-$, include the factors of $1/R$ and $R$, respectively. The quantity $R$ may be rescaled by a multiplicative factor which is nothing else than a Lorentz boost: if we increase $P^+$ by a factor and reduce $P^-$ by the same factor, it's the same operation as if we Lorentz transform or boost the $P^0$-$P^{10}$ plane.
Ultimately we want to describe objects with finite, continuous values of $P^+$ and $P^-$ in an eleven-dimensional spacetime. So we have to take $R$ to infinity to achieve the continuity while $N/R$ is kept fixed. Because the Hamiltonian $P^-$ has to be finite as well, the trace in it has to scale as $1/N$ for $P^+ P^-$ to stay finite. So only the states of the large $N$ matrix models whose energy scales like $1/N$ i.e. drops appropriately with $N$ as $N\to\infty$ are relevant for the decompactified M-theory.
Because we have understood the factor $R$ or $1/R$ in various quantities, we may ignore it and effectively set $R=1$, a full-fledged light-like compactification in which the periodicity of the spacetime coordinate $X^-$ may a priori be very visible. The mathematical essence of the matrix model involves$P^- \equiv H = {\rm Tr} \zav { (\Pi^i)^2 - ([X_i,X_j])^2}, \quad P^+ = N$ That's very simple: the kinematic, quantized longitudinal light-like momentum $P^+$ is simply $N$, the size of the matrices, while the dynamical light-like momentum $P^-$ that we treat as the Hamiltonian is the trace of the kinetic term and the quartic potential term without any additional factors (except the factors of order one that we neglected). And we're only interested in the large $N$ models and low-energy states of $P^-$ that scale like $1/N$. The states we care about must kind of exist for each value of $N$ and their energy has to go down with an increasing $N$. Quite generally, the dualities mapping the model to M-theory imply that in the large $N$ limit, the model has to become $N$-independent up to the simple scalings.
A detail: note that I wrote a minus sign in front of the quartic, commutator term. That's because the commutator (computed only from matrices, regardless of whether the entries are classical or quantum observables!) of two Hermitian matrices is antihermitian and its square (which we want to sum over $i,j$) is negatively definite. The minus sign is needed for the positivity.
Minimizing the Hamiltonian
Look at the Hamiltonian above classically. How do we make it small for large $N$? In the quantum theory, we're constrained by the uncertainty principle so if $X^i$ are too sharply defined, then $\Pi^i$ is highly uncertain and we will get a high contribution from the kinetic energy $\Pi^2$. To minimize the total energy, we really have to make both terms small, including the potential energy (think about the virial theorem and the way how the Hydrogen atom minimizes the energy in a "balanced way").
I just wanted to say something that is intuitively obvious. The commutator term $[X^i,X^j]^2$ has to be small, too. How do we make it small? Note that it is the sum of the traces of all the squared commutators of pairs of those nine $X^i$ matrices. In fact, the trace may be obtained as follows: compute all the $9\times 8/2\times 1 = 36$ commutators of the matrices and sum the squared absolute values in all these $36$ commutator-matrices.
Well, a simple way to reduce this term is to make all the commutators vanish,$\forall i,j:\quad [X^i,X^j] = 0$ It means that all the matrices $X^i$ may be simultaneously diagonalized. But such a state has a simple interpretation. We have seen in the previous article that block-diagonal matrices describe states with several independent, separated objects. Fully diagonal matrices are an extreme example which is composed from gravitons carrying the minimal unit value of $P^+$; gravitons with other, larger values of $P^+=N$ may be interpreted as larger blocks in which $X^i$ are proportional to the unit matrix, i.e. conglomerates of coincident and overlapping minimal gravitons. (In the quantum theory, there exists exactly one zero-energy ground state wave function for the $SU(N)$ problem describing all the "relative" coordinates between the D0-branes. There also exist lots of nonzero energy states that are similarly localized and they generically describe black hole microstates.)
But that's not new. We have already discussed the decomposition into blocks. We want some nontrivial solution in which the commutators aren't strictly zero. We want a new solution in which the configuration of matrices is irreducible; it can't be decomposed to smaller objects via the block diagonal decomposition. Can we find a solution? Yes. A beautiful class of such configurations is physically identified as membranes, 2-dimensional submanifolds floating in the 9-dimensional transverse space parameterized by the coordinates $X^i$.
(The locations of the points on the membrane in the remaining, tenth "spatial" coordinate $X^-$ is obtained by a Fourier transform because we know how the complementary momentum $P^+$ is uniformly divided among the bits of the membrane. I don't want to get into this technicality here but only the nine "purely transverse" coordinates are truly independent and physical here.)
Fuzzy torus
We really want to find values of matrices $X^i$ such that they're of order one but they're large matrices whose size is $N$ and all the commutators of these matrices, while nonzero, naturally scale like $1/N$. Let me just immediately give you a solution. Consider the matrices$U = \pmatrix{1&0&0&\cdots& 0 \\ 0&\omega&0&\cdots &0\\ 0&0&\omega^2&\cdots &0\\ \vdots & \vdots&\vdots & \ddots& \vdots\\ 0&0&0&\cdots&\omega^{N-1} }, \quad \omega\equiv e^{2\pi i/N}$ and $V = \pmatrix{0&1&0&\cdots& 0 \\ 0&0&1&\cdots &0\\ 0&0&0&\cdots &0\\ \vdots & \vdots&\vdots & \ddots& \vdots\\ 1&0&0&\cdots&0 }.$ The matrix $U$ is diagonal and the diagonal entries are the $N$-th roots of unity. All of the possible $N$ roots appear on the diagonal, in a kind of nicely ordered way, much like when a clock hand is showing the current time. As you circle around the diagonal, the complex unit is going from one midnight to another midnight (or is it a noon?). That's why $U$ is known as the clock operator.
Analogously, $V$ is the cyclic permutation matrix acting on the $N$ basis vectors, it's the so-called shift operator. If you think about it, the eigenvalues of $V$ are the $N$-th roots of unity, too. The eigenvectors will remind you of the (discrete) Fourier transform. All these comments mean that $U$ and $V$ are actually similar to each other. There exists a unitary matrix $M$ such that $U=MVM^{-1}$. This matrix $M$ is actually the defining matrix of the discrete Fourier transform and you may pick$M_{ab} = \frac{\omega^{ab}}{\sqrt{N}}.$ Pure phases bilinearly depending on both indices $a,b=1,2,\dots, N$. Sorry if there should be $-ab$ in the exponent. I didn't have to add the $1/\sqrt{N}$ factor but it's helpful if you want $M^{-1}$ to be similar to $M$, including the normalization.
A funny thing is that $U,V$ don't commute with one another but they're damn close to commuting. Why don't they commute? Well, if you first decorate $N$ coordinates of a complex vector by the clock phases and then you cyclically permute them, it's different from permuting them at first and then decorating them with the clock phases. It's because you need the clock phases shifted by one i.e. by the factor of $\omega$.
At any rate, if you understand the previous sentence or if you compute the products explicitly, you will find out that$UV = VU \cdot \omega$ Sorry if there should be $\omega^{-1}$ here; I don't want to waste a minute here, it's an exercise for you. The products are the same up to a factor of $\omega$. The previous relationship may be rewritten as$UV-VU =(\omega-1) VU.$ But $\omega=\exp(2\pi i/N)$ and for a large value of $N$, it's very close to a one. Keeping the first subleading term in the expansion of the exponential, we see that$UV-VU \sim \frac{2\pi i}{N} VU$ Here, $VU$ on the right hand side is "of the same order" as the normal matrices and doesn't depend on $N$. However, there's an extra factor of $1/N$. That's exactly what we need for the low-energy states in Matrix theory. All the previous insights mean that if all the matrices $X^i$ are simple functions of $U,V$ and their inverses, the commutators will be small. They will scale as $1/N$ which, by the way, will also produce $1/N$ terms after we square the commutators – that will change $1/N$ to $1/N^2$ – and trace over the matrices – that will add a factor of $N$ again, thus boosting $1/N^2$ to $1/N$.
That's great. What the form of the matrices is? It is$X^i = \sum_{k,l=-T}^{T} \xi^i_{k,l} U^k V^l$ with lots of coefficients $\xi^i_{k,l}$. I have truncated the sum to an interval of integers between $-T$ and $T$. To decompose the most general matrix $X^i$, we need $T$ to be approximately $N/2$ so that each sum over $k$ and $l$ goes exactly over $N$ possible values. In such a case, the sum will have $N^2$ independent terms which is exactly what you need to reconstruct a general $N\times N$ matrix.
However, imagine that $T$ is taken to be much smaller than $N/2$. Imagine that $N$ is one million but we will only take $T\sim 1,000$, summing a much smaller number of terms.
Now, what is the physical interpretation of the polynomial formula for $X^i$ above? The interpretation is easily obtained if we make the following replacement or identification:$U\equiv \exp(i\sigma_1), \quad V\equiv \exp(i\sigma_2)$ Note that the eigenvalues of $U,V$ are almost "any" complex numbers whose absolute value equals one (if $N$ is large) so it is legitimate to say that they may be written as the complex exponential of a phase. The angles $\sigma_1,\sigma_2$ are two independent variables with periodicity $2\pi$. They clearly parameterize a torus. In the normal geometry, they commute with each other. In our geometry, the commutator is nonzero but small.
So the formula for $X^i$ written in terms of $U,V$ is nothing else than a Fourier decomposition of a function $X^i(\sigma_1,\sigma_2)$ on a torus! If the configuration of $X^i$ matrices is close to our Ansatz, the matrices know exactly everything about the shape of a membrane in a 9-dimensional space! The membrane has a toroidal topology. In some sense, it resembles a periodic phase space with $N^2$ phase cells.
If you rewrite the Hamiltonian for the matrices $X^i$ as a Hamiltonian for the non-matrix functions on the torus, $X^i(\sigma_1,\sigma_2)$, you will get nothing else than a Hamiltonian for a membrane (a supersymmetric membrane if you also include the fermions and do the analogous operations for them). This Hamiltonian for the membrane will look like a higher-dimensional generalization of the Hamiltonians for a string. The usual quadratic Hamiltonians for strings may be obtained as a clever rewriting of the Nambu-Goto action (the proper area of the world sheet); and in the same way, the Hamiltonian we get for the membranes are also physically identical to a higher-dimensional generalization of the Nambu-Goto action (the volume of the world volume).
(Instead of the conformal gauge, i.e. the condition that the string's world sheet metric is flat up to a position-dependent Weyl rescaling, the natural gauge condition we automatically get in the membrane case is the condition that the determinant of the induced 2+1-dimensional membrane metric is constant. So no scaling or conformal symmetry is allowed for the membranes. In this way, the gauge-fixed Hamiltonian contains quartic terms, and not just "free quadratic" terms such as the stringy ones, and many things about the membrane are more complicated. They're still pretty important and mathematically natural – after all, the BFSS matrix model may have been obtained from the maximally supersymmetric gauge theories etc.)
Membranes have been considered and for a while, people thought that you could treat them just like strings, obtaining a higher-dimensional generalization of string theory. However, this "membrane theory" didn't quite enjoy the same remarkable properties as string theory. The higher-dimensional world volume theory was less well-behaved at short distances; the topology of the membranes could degenerate more uncontrollably than the strings' topology; the constant quantifying the strength of the interactions between the membranes wasn't really adjustable so it couldn't be made small.
I will return to these questions but before I do, let's ask: is that just the toroidal topology or can we explicitly describe membranes of another shape, e.g. spherical ones? The answer is Yes.
Fuzzy sphere
In the fuzzy torus case, we made the identification$U\equiv \exp(i\sigma_1), \quad V\equiv \exp(i\sigma_2)$ of two unitary matrices $U,V$ with two coordinates which are complex numbers of absolute value one (equivalently, two independent angular variables). The commutator of the matrices was scaling like $1/N$ which was fine, and so on. Can we do something similar for the sphere? Yes, the answer is the fuzzy sphere.
We will describe the $r=1$ unit sphere not by $\theta,\phi$, the spherical coordinates, but by three coordinates $x,y,z$ that just satisfy$x^2+y^2+z^2=1.$ Because we will require the relationship above to hold automatically, one of the coordinates will actually fail to be quite independent from the other two (except for its adjustable sign). By using $x,y,z$, we will avoid the problems with the singular poles, $\theta=0$ and $\theta=\pi$, where new checks and balances would have to be imposed.
Now, $x,y,z$ play exactly the same role as $\exp(i\sigma_1)$ and $\exp(i\sigma_2)$ in the fuzzy torus case. In the fuzzy torus case, we identified them with two matrices. So the analogous operation for the fuzzy sphere must find $N\times N$ matrices representing the coordinates $x,y,z$. Moreover, these matrices have to satisfy $x^2+y^2+z^2=1$ automatically. Can we find them?
Yes, we can. Just make the following identification:$(x,y,z) = \frac{1}{\sqrt{J(J+1)}} (J_x,J_y,J_z).$ Here, $J=(N-1)/2$ so that $N=2J+1$ gives us the right size of the matrices and $J_x,J_y,J_z$ are simply matrices of the angular momentum in an $N$-dimensional irreducible representation, i.e. in a representation with a large value of the spin $J$. Note that $x^2+y^2+z^2=1$ is identically satisfied if $x,y,z$ represent the associated matrices simply because $J_x^2+J_y^2+J_z^2 = J(J+1)\cdot 1_{N\times N}$ is the well-known "Casimir" that is proportional to the unit matrix. Note that in this case, we associated Hermitian, and not unitary, matrices to $x,y,z$ because unlike $\exp(i\sigma_{1,2})$, the variables $x,y,z,$ are real.
Now, you may verify that for a large $N=2J+1$, the commutators such as $[x,y]$ go like $1/N$ times $iz$ because $\sqrt{J(J+1)}\sim J$ for a large $J$ or $N$ so we pick $1/J$ from each $x$ and $y$, getting $1/J^2$ in total which is equal to $1/J$ times $z$ because $z$ contains one $1/J$ by itself.
Just like we could write $X^i$ as a simple Fourier-transform-like function of $U,V$ in the toroidal case, we may write each of the nine $X^i$ matrices as a simple polynomial of the matrices that represent $x,y,z$. In this fashion, you may approximate any spherical harmonic or any function on the $x^2+y^2+z^2=1$ surface, on the two-sphere.
So the matrices $X^i$ may also naturally and beautifully encode a function on the two-sphere, via a Fourier-like decomposition that is closely associated with the decomposition into spherical harmonics. For a finite $N$, it is not a perfect approximation: we only allow spherical harmonics up to $L\sim N$ or so. Also, the multiplication is a bit noncommutative. If you analyze the maths carefully, you will find out that all the refusal of the matrices to commute may be explained by a totally equivalent feature of the multiplication: the multiplication of the matrices representing spherical harmonics simply eliminates all the spherical harmonics in the product that have $L\gt N$ or so.
Dynamics, degeneration, topology change
I have mentioned that one may rewrite the Matrix theory Hamiltonian as a 2+1-dimensional Hamiltonian for functions such as $X^i(\sigma_1,\sigma_2)$ in the toroidal case or $X^i(\theta,\phi)$ in the spherical case, if I rewrite $x,y,z$ using the polar coordinates again. The local integrand of these Hamiltonians (which dictates how the waves are propagating along the membranes, and related things) will be the same – for any topology, we will derive the same local dynamics on a piece of a membrane – so it's not hard to guess that the Hamiltonian of the matrix model actually allows orientable membranes of any topology.
Only the torus and the sphere can be written down very explicitly; that's because of their isometries, $U(1)\times U(1)$ and $SO(3)$, respectively. However, membranes of all topologies are allowed in the matrix model (and with some more abstract maths, we may describe them somewhat explicitly, too). It's not hard to figure out that the matrix model allows the topology to change. After all, the space of matrices is completely connected; it isn't really decomposed into several isolated "sectors with a different topology".
The same is true for single-membrane and multi-membrane states.
Imagine that someone in the 1980s wrote the continuous Hamiltonian – a 2+1-dimensional quantum field theory – for a membrane of a spherical topology. Yes, several people did. And now imagine that they had the creativity to regulate the membranes using the matrices. Well, they even did that. What they found was a problematic model because it didn't prevent the spherical membrane from developing sharp spikes on the surface and it was plausible that these spikes get connected and change the topology of the previously spherical membrane into a torus or a higher-genus topology. Or the sphere could get pinched near the equator and the thin tube connecting the previous hemispheres could have broken, thus producing a pair of spherical membranes.
Those folks in the 1980s were not able to deduce what was really happening in these extreme limits and whether the membrane was allowed to do so; these questions boiled down to some short-distance properties of the 2+1-dimensional model that weren't well-defined because 2+1 dimensions is already too high for a world volume theory to be fully consistent in the ultraviolet.
But if you rewrite the spherical-membrane Hamiltonian in terms of the matrix model, you will be able to find the answer to the question whether the degeneration processes above are allowed etc. They are allowed. The reason is that the correct and correctly evaluated and interpreted matrix regularization of the single-spherical-membrane model actually describes membranes of arbitrary orientable topologies – and an arbitrary number of disconnected membranes, too!
This is just another manifestation of the remarkable feature of the matrix models that gave the title to the first blog entry on Matrix theory. In quantum field theory using the second quantization, the multi-particle and other multi-object states have to be created "out of pieces", i.e. as a product of several independent creation operators acting on the vacuum state. But Matrix theory erases the qualitative difference between single-particle and multi-particle objects – and between single-membrane and multi-membrane states. All of them are represented by certain configurations of matrices (or, quantum mechanically, by wave functions whose support is located near these classical configurations). The multi-object states correspond to classical configurations that may be simultaneously block-diagonalized.
(Matrix string theory, a matrix model that also describes strings in string theory, also erases the qualitative difference between one-string and multi-string states, a feature I had believed to be fundamentally necessary in a complete formulation of string theory at least since 1992 when I read the first Green-Schwarz light-cone-gauge superstring articles from the early 1980s. Matrix theory just came to me as a marvelous framework in which my "dreams of the teen age" could have been transformed into a working reality which was a reason why I could explain how strings were included in Matrix theory much more quickly than anyone else, within a week of thinking about Matrix theory. The feeling when you discover something relatively important – the first nonperturbatively complete definition of type II strings' dynamics and why it agrees with the previous approximate descriptions – before anyone else in the world and when you're sure that it actually works is special. I will postpone the discussion of matrix string theory and some thoughts I had when I discovered it to a future blog entry.)
However, the realistic wave functions in the quantum mechanics are nonzero for configurations of diagonalizable as well as non-diagonalizable matrices. So the interactions between the membranes, gravitons, and other objects – including the splitting of membranes into pieces and changing the membrane topology – is always predicted to occur with a nonzero probability. You can't eliminate them from the picture. In perturbative string theory, the string interactions are uniquely determined once you specify the single-string dynamics; the local character of the world sheet remains the same and you just allow more complicated topologies.
Now we see that something analogous holds for membranes, too. String/M-theory, in this case its matrix model definition, uniquely dictates how the membranes should split, merge, degenerate, and simplify once you write a consistent regularization of the theory for a single membrane of any topology. In as consistent and robust theories as string/M-theory – and string/M-theory is probably the only element in this set – learning about a small piece of the structure (e.g. the free limit describing a single object) uniquely determines everything else (including interactions). Once you find a small (but not too small) piece of a mosaic, the whole mosaic may be "holographically reconstructed" out of it.
Noncommutative geometry and noncommutative field theories: promotion of a future text
The fuzzy torus and the fuzzy sphere above are the most canonical and simplest examples of noncommutative geometry. Studied in very abstract mathematics by folks such as Alain Connes, the noncommutative geometry was found to be a natural exact description of some pretty elementary configurations in string theory. There exist whole quantum field theories in which the supporting spacetime is noncommutative; they may be obtained by replacing the ordinary commutative point-wise product of classical fields by the star-product.
The Feynman diagrams for these theories have extra phases associated with vertices; these theories relate $d$-dimensional theories (and branes) with $(d-2)$-dimensional and $(d-2k)$-dimensional theories (and branes) in natural ways; and – which is related – they have very natural and interesting solutions (solitons) that use some mathematical tricks we know from phase spaces in quantum mechanics (although their interpretation is different). This text has gotten pretty long so I will postpone the discussion of noncommutative geometry to a future blog entry.
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2017-04-23 23:38:37
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https://experts.mcmaster.ca/display/publication1495485
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# HOL Light QE Academic Article
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### abstract
• We are interested in algorithms that manipulate mathematical expressions in mathematically meaningful ways. Expressions are syntactic, but most logics do not allow one to discuss syntax. ${\rm CTT}_{\rm qe}$ is a version of Church's type theory that includes quotation and evaluation operators, akin to quote and eval in the Lisp programming language. Since the HOL logic is also a version of Church's type theory, we decided to add quotation and evaluation to HOL Light to demonstrate the implementability of ${\rm CTT}_{\rm qe}$ and the benefits of having quotation and evaluation in a proof assistant. The resulting system is called HOL Light QE. Here we document the design of HOL Light QE and the challenges that needed to be overcome. The resulting implementation is freely available.
• 2018
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2019-06-24 15:33:35
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https://www.esaral.com/q/find-all-points-of-discontinuity-of-f-where-f-is-defined-by-35326
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Find all points of discontinuity of f, where f is defined by
Question:
Find all points of discontinuity of f, where f is defined by
$f(x)=\left\{\begin{array}{l}\frac{|x|}{x} \text { if } x \neq 0 \\ 0, \text { if } x=0\end{array}\right.$
Solution:
The given function $f$ is $f(x)=\left\{\begin{array}{l}\frac{|x|}{x} \text { if } x \neq 0 \\ 0, \text { if } x=0\end{array}\right.$
It is known that, $x<0 \Rightarrow|x|=-x$ and $x>0 \Rightarrow|x|=x$
Therefore, the given function can be rewritten as
$f(x)=\left\{\begin{array}{l}\frac{|x|}{x}=\frac{-x}{x}=-1 \text { if } x<0 \\ 0, \text { if } x=0 \\ \frac{|x|}{x}=\frac{x}{x}=1, \text { if } x>0\end{array}\right.$
The given function f is defined at all the points of the real line.
Let c be a point on the real line.
Case I:
If $c<0$, then $f(c)=-1$
$\lim _{x \rightarrow c} f(x)=\lim _{x \rightarrow c}(-1)=-1$
$\therefore \lim _{x \rightarrow c} f(x)=f(c)$
Case II:
If $c=0$, then the left hand limit of $f$ at $x=0$ is,
$\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{-}}(-1)=-1$
The right hand limit of at x = 0 is,
$\lim _{x \rightarrow 0^{+}} f(x)=\lim _{x \rightarrow 0^{+}}(1)=1$
It is observed that the left and right hand limit of f at x = 0 do not coincide.
Therefore, f is not continuous at x = 0
Case III:
If $c>0$, then $f(c)=1$
$\lim _{x \rightarrow c} f(x)=\lim _{x \rightarrow c}(1)=1$
$\therefore \lim _{x \rightarrow 0} f(x)=f(c)$
Therefore, $f$ is continuous at all points $x$, such that $x>0$
Hence, x = 0 is the only point of discontinuity of f.
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2023-03-28 20:44:20
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https://math.stackexchange.com/questions/3618240/generate-all-nonisomorphic-rooted-trees-from-a-vertex-set-with-a-common-root
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# Generate all nonisomorphic rooted trees from a vertex set with a common root
For a vertex set $$v = \left\{v_1...v_n \right\}$$ and a common root $$r$$, is there an efficient (maybe $$O(1)$$ per tree) algorithm that generates all non-isomorphic trees on all nodes $$v$$ and with root $$r$$.
Two trees are isomorphic if all the parent-child relationships are the same, i.e. all equivalent nodes in the two trees have the same parent and the same children.
Example: $$v = \left\{v_1, v_2, v_3\right\}$$
All trees should have the same root an the same node set. The following image shows some valid trees:
Including a tree should lead to all other isomorphic trees being ignored
Another SO post shows a implementation that finds unrooted topologies:
https://codereview.stackexchange.com/questions/202773/generating-all-unlabeled-trees-with-up-to-n-nodes
In one answer, there appears this algorithm for creating unrooted non-isomorphic topologies on $$n$$ nodes in constant time per tree.
Robert Alan Wrights, Bruce Richmond, Andrew Odlyzko and Brendan D. Mckay (1986). “Constant time generation of free trees”. SIAM J. Comput. 15:2, pp. 540–548.
I am not sure if it is possible to extend this algorithm efficiently to generate the desired rooted trees.
• Of course there's an algorithm, it's a finite problem. – Gerry Myerson Apr 10 at 2:19
• Thanks for that comment, I clarified the question. I wanted an efficient algorithm. Tree space grows quickly and enumerating everything takes forever. – user36028 Apr 10 at 2:25
• Your sample of "all trees to generate" seems to just be a black rectangle. Also...you might want to give a definition of "isomorphism" here, just to make the problem unambiguous and avoid wasting people's time. – John Hughes Apr 10 at 2:34
• For instance, in the first tree (now included in your question), if I swap the positions of v1 and v2 in the middle tree, is the resulting tree isomorphic to the middle tree or not? – John Hughes Apr 10 at 2:36
• The Algorithmic Encyclopedia linked in the second link gives a good overview. I read the article a few days ago. They also give the algorithm mentioned above, but this yields only the topology. Assigning the node labels in all possible ways leads to double counts. Extending this approach starting with the topology alone was my first thought, but then you have to make sure that you don't create isomorphic trees when assigning labels. – user36028 Apr 10 at 2:59
I can do it in $$O(n^2)$$ per tree.
The number of possible trees is $$(n+1)^{n-1}$$, since choosing a tree in your problem is equivalent to choosing an undirected tree on the vertex set $$v\cup \{r\}=\{v_1,\dots,v_n,r\}$$, and then directing all edges towards the root. The number of undirected trees on $$n+1$$ vertices is $$(n+1)^{n-1}$$ (this is Cayley's theorem), and these trees can be generated efficiently using Prüfer codes.
Specifically, iterate through all lists of length $$n-1$$ with entries in $$\{0,1,2,\dots,n\}$$, where $$0$$ represents $$r$$ and $$1$$ through $$n$$ represent $$v_1$$ through $$v_n$$. For each list, generate the corresponding tree with vertices $$\{r,v_1,\dots,v_n\}$$ using the algorithm to convert a Prüfer sequence into an undirected tree. Finally, turn this into a directed tree using breadth first search starting from vertex $$r$$.
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2020-09-18 11:54:26
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https://community.plu.edu/~sklarjk/fsaa/section-23.html
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# Section7.2Introduction to cosets and normal subgroups
##### Definition7.2.1
Given a group $G$ with subgroup $H\text{,}$ we define $\siml$ on $G$ by
\begin{equation*} a\siml b \text{ if and only if } a^{-1}b\in H \end{equation*}
and $\simr$ on $G$ by
\begin{equation*} a\simr b \text{ if and only if } ab^{-1}\in H. \end{equation*}
##### Remark7.2.3
Of course, different subgroups $H$ and $K$ in a group $G$ will give rise to different relations $\siml$ and $\simr$ on $G\text{;}$ that is, these relations are really defined with respect to a particular subgroup of $G\text{.}$
From now on, whenever we discuss $\siml$ or $\simr$ on a group, assume that it is with respect to a particular subgroup $H$ of $G\text{.}$
Now, as equivalence relations on a group $G\text{,}$ each of $\siml$ and $\simr$ gives rise to a partition of $G\text{.}$ What are the cells of those partitions?
##### Definition7.2.4
Given $a\in G\text{,}$ we define
\begin{equation*} aH = \{ah\,:\, h\in H\} \end{equation*}
and
\begin{equation*} Ha=\{ha\,:\,h\in H\}. \end{equation*}
We call $aH$ and $Ha\text{,}$ respectively, the left and right cosets of $H$ containing $a$.
If we know that $G$ is abelian, with operation denoted by $+\text{,}$ we may denote these left and right cosets by $a+H$ and $H+a\text{,}$ respectively.
##### Note7.2.5
In the following, we use the notation $\Leftrightarrow$ to denote the phrase “if and only if.”
##### Proof
We next summarize some facts about the left and right cosets of a subgroup $H$ of a group $G\text{:}$
##### Remark7.2.8
We can use Statements 2 and 3, above, to save some time when computing left and right cosets of a subgroup of a group.
##### Example7.2.9
Find the left and right cosets of $H=\langle (12)\rangle$ in $S_3\text{.}$
The left cosets are
\begin{equation*} eH=H=(12)H, \end{equation*} \begin{equation*} (13)H=\{(13),(123)\}=(123)H, \end{equation*} \begin{equation*} \text{ and } (23)H=\{(23),(132)\}=(132)H, \end{equation*}
and the right cosets are
\begin{equation*} He=H=H(12), \end{equation*} \begin{equation*} H(13)=\{(13),(132)\}=H(132), \end{equation*} \begin{equation*} \text{ and } H(23)=\{(23),(123)\}=H(123). \end{equation*}
Thus, $\siml$ partitions $S_3$ into $\{H,\{(13),(123)\},\{(23), (132)\}\}$ and $\simr$ partitions $S_3$ into $\{H,\{(13),(132)\},\{(23), (123)\}\}\text{.}$
##### Example7.2.10
Find the left and right cosets of $H=\langle f\rangle$ in $D_4\text{.}$
This example is left as an exercise for the reader.
We now draw attention to some very important facts:
##### Warning7.2.11
For $a,b\in G\text{:}$
1. In general, $aH \neq Ha\text{!}$
2. $aH=bH$ does not necessarily imply $a=b$ or that there exists an $h\in H$ with $ah=bh\text{;}$ similarly, $Ha=Hb$ does not necessarily imply $a=b$ or that there exists an $h\in H$ with $ha=hb\text{.}$
##### Example7.2.12
We saw above that in $S_3$ with $H=\langle (12)\rangle\text{,}$
\begin{equation*} (13)H=\{(13),(123)\} \neq \{(13),(132)\}=H(13). \end{equation*}
Also, $(13)H=(123)H$ but $(13)e\neq (123)e$ and $(13)(12)\neq (123)(12)\text{.}$
It turns out that subgroups $H$ for which $aH=Ha$ for all $a\in G$ will be very important to us.
##### Definition7.2.13
We say that subgroup $H$ of $G$ is normal in $G$ (or is normal subgroup of $G$) if $aH=Ha$ for all $a\in G\text{.}$ We denote that fact that $H$ is normal in $G$ by writing $H\unlhd G\text{.}$
##### Remark7.2.14
1. If $H$ is normal in $G\text{,}$ we may refer to the left and right cosets of $G$ as simply cosets.
2. Of course, if $G$ is abelian, every subgroup of $G$ is normal in $G\text{.}$ But there can also be normal subgroups of nonabelian groups: for instance, the trivial and improper subgroups of every group are normal in that group.
##### Example7.2.15
Find the cosets of $5\Z$ in $\Z\text{.}$
Notice that in additive notation, the statement “$a^{-1}b\in H$” becomes $-a+b\in H\text{.}$ So for $a,b\in \Z\text{,}$ $a\siml b$ if and only if $-a+b \in 5\Z\text{;}$ that is, if and only if $5$ divides $b-a\text{.}$ In other words, $a\siml b$ if and only if $a\equiv_5 b\text{.}$ So in this case, $\siml$ is just congruence modulo $5\text{.}$ Thus, the cosets of $5\Z$ in $\Z$ are
\begin{align*} 5\Z\amp =\{\ldots,-5,0,5,\ldots\}\\ 1+5\Z\amp =\{\ldots,-4, 1, 6,\ldots\},\\ 2+5\Z\amp =\{\ldots,-3,2, 7, \ldots\},\\ 3+5\Z\amp =\{\ldots,-2,3, 8, \ldots\},\\ 4+5\Z\amp =\{\ldots,-1, 4, 9, \ldots\}. \end{align*}
Do you see how this example would generalize for $n\Z$ ($n \in \Z^+$) in $\Z\text{?}$
##### Example7.2.16
Find the cosets of $H=\langle 12\rangle$ in $4\Z\text{.}$
They are
\begin{align*} H\amp =\{\ldots, -12,0,12\ldots\},\\ 4+H \amp = \{\ldots,-8,4,16,\ldots\},\\ 8+H\amp =\{\ldots, -4,8,20,\ldots\}. \end{align*}
##### Example7.2.17
Find the cosets of $H=\langle 4\rangle$ in $\Z_{12}\text{.}$
They are
\begin{align*} H\amp =\{0,4,8\},\\ 1+H \amp = \{1,5,9\},\\ 2+H\amp =\{2,6,10\}\\ 3+H\amp =\{3,7,11\}. \end{align*}
We now consider the set of all left cosets of a subgroup of a group.
##### Definition7.2.18
We let $G/H$ be the set of all left cosets of subgroup $H$ in $G\text{.}$ We read $G/H$ as “$G$ mod $H\text{.}$”
(We may denote the set of all right cosets of subgroup $H$ in $G$ by $H\backslash G\text{,}$ but we will not use that notation in this class.)
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http://msgroups.net/vc.mfc/cfile-getstatus-throws-an-exception-when-run-from-cd/548842
|
#### CFile::GetStatus throws an exception when run from CD
I have a small app that is checking to see if the file dotnetfx.exe is
present in the same directory as my executable. I am running VS.NET 2003
and using unmanaged C++. Everything works great, as long as my executable
is not on a CD. When burned to CD, the call to GetStatus will throw "the
parameter is incorrect". The strings are correct (and obviously it runs
fine when not burnt to CD).
CString strHelpFilePath = AfxGetApp()->m_pszHelpFilePath;
int iFileLoc = strHelpFilePath.ReverseFind(_T('\\'));
CString strFxLoc = strHelpFilePath.Left(iFileLoc + 1) +
_T("dotnetfx.exe");
CFileStatus oStatus;
BOOL bFxPresent = FALSE;
try {
bFxPresent = CFile::GetStatus(strFxLoc, oStatus);
}
catch (CException *ex) {
ex->ReportError();
ex->Delete();
bFxPresent = FALSE;
}
====================================================
Walter Williams
Software Engineer
Sawtooth Software, Inc.
http://www.sawtoothsoftware.com
----------------------------------------------------
"Do, or do not. There is no try."
0
1/15/2004 11:43:37 PM
vc.mfc 33608 articles. 0 followers.
5 Replies
1417 Views
Similar Articles
[PageSpeed] 3
If you call ex->GetErrorMessage() inside the catch() what does it tell
you ?
--
Cheers
Check Abdoul [VC++ MVP]
-----------------------------------
"Walter L. Williams" <sparticus1701@hotmail.com> wrote in message
news:OGLIpF82DHA.1428@TK2MSFTNGP12.phx.gbl...
> I have a small app that is checking to see if the file dotnetfx.exe is
> present in the same directory as my executable. I am running VS.NET 2003
> and using unmanaged C++. Everything works great, as long as my executable
> is not on a CD. When burned to CD, the call to GetStatus will throw "the
> parameter is incorrect". The strings are correct (and obviously it runs
> fine when not burnt to CD).
>
> CString strHelpFilePath = AfxGetApp()->m_pszHelpFilePath;
> int iFileLoc = strHelpFilePath.ReverseFind(_T('\\'));
> CString strFxLoc = strHelpFilePath.Left(iFileLoc + 1) +
> _T("dotnetfx.exe");
>
> CFileStatus oStatus;
> BOOL bFxPresent = FALSE;
> try {
> bFxPresent = CFile::GetStatus(strFxLoc, oStatus);
> }
> catch (CException *ex) {
> ex->ReportError();
> ex->Delete();
> bFxPresent = FALSE;
> }
>
> ====================================================
> Walter Williams
> Software Engineer
> Sawtooth Software, Inc.
> http://www.sawtoothsoftware.com
> ----------------------------------------------------
> "Do, or do not. There is no try."
>
>
>
0
CheckAbdoul
1/16/2004 12:28:56 AM
It's the same thing as ReportError(); the error is "The parameter is
incorrect."
"CheckAbdoul" <checkabdoul at mvps dot org> wrote in message
news:OUYddf82DHA.3656@TK2MSFTNGP11.phx.gbl...
> If you call ex->GetErrorMessage() inside the catch() what does it tell
> you ?
>
> --
> Cheers
> Check Abdoul [VC++ MVP]
> -----------------------------------
>
> "Walter L. Williams" <sparticus1701@hotmail.com> wrote in message
> news:OGLIpF82DHA.1428@TK2MSFTNGP12.phx.gbl...
> > I have a small app that is checking to see if the file dotnetfx.exe is
> > present in the same directory as my executable. I am running VS.NET
2003
> > and using unmanaged C++. Everything works great, as long as my
executable
> > is not on a CD. When burned to CD, the call to GetStatus will throw
"the
> > parameter is incorrect". The strings are correct (and obviously it runs
> > fine when not burnt to CD).
> >
> > CString strHelpFilePath = AfxGetApp()->m_pszHelpFilePath;
> > int iFileLoc = strHelpFilePath.ReverseFind(_T('\\'));
> > CString strFxLoc = strHelpFilePath.Left(iFileLoc + 1) +
> > _T("dotnetfx.exe");
> >
> > CFileStatus oStatus;
> > BOOL bFxPresent = FALSE;
> > try {
> > bFxPresent = CFile::GetStatus(strFxLoc, oStatus);
> > }
> > catch (CException *ex) {
> > ex->ReportError();
> > ex->Delete();
> > bFxPresent = FALSE;
> > }
> >
> > ====================================================
> > Walter Williams
> > Software Engineer
> > Sawtooth Software, Inc.
> > http://www.sawtoothsoftware.com
> > ----------------------------------------------------
> > "Do, or do not. There is no try."
> >
> >
> >
>
>
0
1/16/2004 3:51:15 AM
>I have a small app that is checking to see if the file dotnetfx.exe is
>present in the same directory as my executable. I am running VS.NET 2003
>and using unmanaged C++. Everything works great, as long as my executable
>is not on a CD. When burned to CD, the call to GetStatus will throw "the
>parameter is incorrect".
Walter,
I think someone raised an issue that sounds surprisingly similar to
what you're seeing just a few weeks ago (I can't remember the precise
date). Try searching the Google groups archives to see if you can find
that thread and see if there was a resolution given.
Dave
--
MVP VC++ FAQ: http://www.mvps.org/vcfaq
0
davidl (422)
1/16/2004 11:54:52 AM
>I think someone raised an issue that sounds surprisingly similar to
>what you're seeing just a few weeks ago
The thread was in this newsgroup, subject was "CFile::GetFileName
throws an exception". I hope this URL doesn't get corrupted:
If you can debug into the MFC code, see if you think this is the same
issue (or not).
Dave
--
MVP VC++ FAQ: http://www.mvps.org/vcfaq
0
davidl (422)
1/17/2004 1:14:28 AM
I get the same exception when I try to save a file on a Win9x shared folder from a WinXP Machine. Of course your the only one other than me who was able to reproduce the problem.
0
anonymous (74722)
1/29/2004 4:31:09 PM
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2020-06-01 14:19:07
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https://datascience.stackexchange.com/questions/104543/how-to-revert-np-logdata-and-data-diff
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# How to revert np.log(data) and data.diff()?
I have used np.log(data) and then applied data.diff() to transform my data in timeseries model. I have the predictions. How do I convert it back to normal scale?
Here is an example for your reference:
--------------------------------------------------------------------
| sales | np.log(sales) | (np.log(sales)).diff() | predictions |
--------------------------------------------------------------------
|166.594019 | 5.115560 | -0.045918 | -0.045918 |
--------------------------------------------------------------------
Note: I have provided only one example which from index 2 as the first value after data.diff() will be null. And hence the prediction at index 1 is 0.
• mathematically log can be reversed with exp, but I don't understand the context. Nov 27 '21 at 12:17
• I need to revert it to a natural number to share forecasted sales back with my team. Nov 27 '21 at 18:15
As far as I understand the difference is $$log(s_t)-log(s_{t-1})$$, right?
$$log(s_t)-log(s_{t-1})=log\left(\frac{s_t}{s_{t-1}}\right)$$
You could use exp to go back to the regular ratio:
$$exp\left(log\left(\frac{s_t}{s_{t-1}}\right)\right)=\frac{s_t}{s_{t-1}}$$
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2022-01-24 01:38:03
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https://en.m.wikipedia.org/wiki/Millennial
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# Millennials
(Redirected from Millennial)
Millennials, also known as Generation Y (or simply Gen Y), are the demographic cohort following Generation X and preceding Generation Z. Researchers and popular media use the early 1980s as starting birth years and the mid-1990s to early 2000s as ending birth years, with 1981 to 1996 a widely accepted definition. Millennials are sometimes referred to as "echo boomers" due to a major surge in birth rates in the 1980s and 1990s, and because millennials are often the children of the baby boomers. The characteristics of millennials vary by region and by individual, and the group experiences a variety of social and economic conditions, but they are generally marked by their coming of age in the Information Age, and are comfortable in their usage of digital technologies and social media.
## Terminology
It is so named, because the earliest of the millennials became an adult around the turn of the millennium.[1]
Authors William Strauss and Neil Howe are widely credited with naming the millennials.[2] They coined the term in 1987, around the time children born in 1982 were entering kindergarten, and the media were first identifying their prospective link to the impending new millennium as the high school graduating class of 2000.[3] They wrote about the cohort in their books Generations: The History of America's Future, 1584 to 2069 (1991)[4] and Millennials Rising: The Next Great Generation (2000).[3]
In August 1993, an Advertising Age editorial coined the phrase Generation Y to describe those who were aged 11 or younger as well as the teenagers of the upcoming ten years who were defined as different from Generation X.[5][6] According to journalist Bruce Horovitz, in 2012, Ad Age "threw in the towel by conceding that millennials is a better name than Gen Y",[2] and by 2014, a past director of data strategy at Ad Age said to NPR "the Generation Y label was a placeholder until we found out more about them".[7] Millennials are sometimes called Echo Boomers,[8] due to their being the offspring of the baby boomers and due to the significant increase in birth rates from the early 1980s to mid 1990s, mirroring that of their parents. In the United States, birth rates peaked in August 1990[9][10] and a 20th-century trend toward smaller families in developed countries continued.[11][12] In his book The Lucky Few: Between the Greatest Generation and the Baby Boom, author Elwood Carlson called this cohort the "New Boomers".[13]
Psychologist Jean Twenge described millennials as "Generation Me" in her 2006 book Generation Me: Why Today’s Young Americans Are More Confident, Assertive, Entitled – and More Miserable Than Ever Before, which was updated in 2014.[14][15] In 2013, Time magazine ran a cover story titled Millennials: The Me Me Me Generation.[16] Newsweek used the term Generation 9/11 to refer to young people who were between the ages of 10 and 20 during the terrorist acts of September 11, 2001. The first reference to "Generation 9/11" was made in the cover story of the 12 November 2001 issue of Newsweek.[17] Alternative names for this group proposed include the Net Generation[18] and The Burnout Generation.[19]
American sociologist Kathleen Shaputis labeled millennials as the Boomerang Generation or Peter Pan generation because of the members' perceived tendency for delaying some rites of passage into adulthood for longer periods than most generations before them. These labels were also a reference to a trend toward members living with their parents for longer periods than previous generations.[20] Kimberly Palmer regards the high cost of housing and higher education, and the relative affluence of older generations, as among the factors driving the trend.[21] Questions regarding a clear definition of what it means to be an adult also impact a debate about delayed transitions into adulthood and the emergence of a new life stage, Emerging Adulthood. A 2012 study by professors at Brigham Young University found that college students were more likely to define "adult" based on certain personal abilities and characteristics rather than more traditional "rite of passage" events.[22] Larry Nelson noted that "In prior generations, you get married and you start a career and you do that immediately. What young people today are seeing is that approach has led to divorces, to people unhappy with their careers … The majority want to get married […] they just want to do it right the first time, the same thing with their careers."[22]
Chinese millennials are commonly called the 1980s and 1990s generations. At a 2015 conference in Shanghai organized by University of Southern California's US-China Institute, millennials in China were examined and contrasted with American millennials.[23] Findings included millennials' marriage, childbearing, and child raising preferences, life and career ambitions, and attitudes towards volunteerism and activism.[24]
## Date and age range definitions
Oxford Living Dictionaries describes a millennial as "a person reaching young adulthood in the early 21st century."[25] Jonathan Rauch, senior fellow at the Brookings Institution, wrote for The Economist in 2018 that "generations are squishy concepts", but the 1981 to 1996 birth cohort is a "widely accepted" definition for millennials.[26] Reuters also states that millennials are "widely accepted as having been born between 1981 and 1996."[27][28][29]
The Pew Research Center defines millennials as born from 1981 to 1996, choosing these dates for "key political, economic and social factors", including the September 11th terrorist attacks, the Great Recession, and the Internet explosion.[30] Many major media outlets have cited Pew's definition including Time magazine,[31] BBC,[32] The Washington Post,[33] Business Insider,[34] The New York Times,[35] and The Wall Street Journal.[36] The United States Bureau of Labor Statistics also uses Pew's birth years.[37] Pew Research Center has observed that "[b]ecause generations are analytical constructs, it takes time for popular and expert consensus to develop as to the precise boundaries that demarcate one generation from another"[38][39] and has indicated that they would remain open to date recalibration.[30] According to this definition, the oldest millennial is 38 years old and the youngest is, or is turning, 23 years old in 2019.
The Federal Reserve Board defines millennials as "members of the generation born between 1981 and 1996",[40] as does the American Psychological Association[41] and Ernst and Young.[42] The birth years of 1981 to 1996 have also been used to define millennials by PBS,[43] CBS,[44] ABC Australia,[45] The Washington Post,[46] The Washington Times,[47] and The Los Angeles Times.[48]
Gallup Inc.,[49][50][51] MSW Research,[52] the Resolution Foundation use 1980–1996,[53] PricewaterhouseCoopers has used 1981 to 1995,[54] and Nielsen Media Research has defined millennials as between 21 and 37 years old in 2018.[55] The United States Chamber of Commerce, a business-oriented lobbying group,[56] uses 1980–1999.[57] In 2014, U.S PIRG described millennials as those born between 1983 and 2000.[58][59][60] The United States Census Bureau used the birth years 1982 to 2000 in a 2015 news release to describe millennials,[61] but they have stated that "there is no official start and end date for when millennials were born"[62] and they do not define millennials.[63][64][65]
Australia's McCrindle Research uses 1980–1994 as Generation Y birth years.[66]
In his 2008 book The Lucky Few: Between the Greatest Generation and the Baby Boom, author Elwood Carlson used the term "New Boomers" to describe this cohort. He identified the birth years of 1983–2001, based on the upswing in births after 1983 and finishing with the "political and social challenges" that occurred after the September 11th terrorist acts.[13] Authors William Strauss and Neil Howe define millennials as born between 1982–2004.[2] However, Howe described the dividing line between millennials and the following Generation Z as "tentative", saying "you can’t be sure where history will someday draw a cohort dividing line until a generation fully comes of age".[67]
Individuals born in the Generation X and millennial cusp years of the late 1970s and early to mid 1980s have been identified as a "microgeneration" with characteristics of both generations.[68] Names given to these "cuspers" include Xennials,[69] Generation Catalano,[70] and the Oregon Trail Generation.[71]
## General discussion
Psychologist Jean Twenge, the author of the 2006 book Generation Me, considers millennials, along with younger members of Generation X, to be part of what she calls "Generation Me".[72] Twenge attributes millennials with the traits of confidence and tolerance, but also describes a sense of entitlement and narcissism, based on "Narcissistic Personality Inventory" surveys showing increased narcissism among millennials[quantify] compared to preceding generations when they were teens and in their twenties.[73][74] Psychologist Jeffrey Arnett of Clark University, Worcester has criticized Twenge's research on narcissism among millennials, stating "I think she is vastly misinterpreting or over-interpreting the data, and I think it’s destructive".[75] He doubts that the Narcissistic Personality Inventory really measures narcissism at all. Arnett says that not only are millennials less narcissistic, they're “an exceptionally generous generation that holds great promise for improving the world”.[76] A study published in 2017 in the journal Psychological Science found a small decline in narcissism among young people since the 1990s.[77][78]
Authors William Strauss and Neil Howe argue that each generation has common characteristics that give it a specific character with four basic generational archetypes, repeating in a cycle. According to their hypothesis, they predicted millennials would become more like the "civic-minded" G.I. Generation with a strong sense of community both local and global.[3] Strauss and Howe ascribe seven basic traits to the millennial cohort: special, sheltered, confident, team-oriented, conventional, pressured, and achieving. However, Arthur E. Levine, author of When Hope and Fear Collide: A Portrait of Today's College Student, dismissed these generational images as "stereotypes".[79] In addition, psychologist Jean Twenge says Strauss and Howe's assertions are overly-deterministic, non-falsifiable, and unsupported by rigorous evidence.[72]
## Cultural identity
Russian young adults at the Geek Picnic. Only 54% of Russian millennials were married in 2016.[80]
Since the 2000 U.S. Census, millennials have taken advantage of the possibility of selecting more than one racial group in abundance.[81][82] In 2015, the Pew Research Center also conducted research regarding generational identity that said a majority did not like the "Millennial" label.[83] In 2015, the Pew Research Center conducted research regarding generational identity.[83] It was discovered that millennials are less likely to strongly identify with the generational term when compared to Generation X or the Baby Boomers, with only 40% of those born between 1981 and 1997 identifying as part of the Millennial Generation. Among older millennials, those born 1981–1988, Pew Research found 43% personally identified as members of the older demographic cohort, Generation X, while only 35% identified as millennials. Among younger millennials (born 1989–1997), generational identity was not much stronger, with only 45% personally identifying as millennials. It was also found that millennials chose most often to define themselves with more negative terms such as self-absorbed, wasteful or greedy. In this 2015 report, Pew defined millennials with birth years ranging from 1981 onwards.[83]
Elza Venter, an educational psychologist and lecturer at Unisa, South Africa, in the Department of Psychology of Education, believes Millennials are digital natives because they have grown up experiencing digital technology and have known it all their lives. Prensky coined the concept ‘digital natives’ because the members of the generation are ‘native speakers of the digital language of computers, video games and the internet’.[84] This generation's older members use a combination of face-to-face communication and computer mediated communication, while its younger members use mainly electronic and digital technologies for interpersonal communication.[85]
Fred Bonner, a Samuel DeWitt Proctor Chair in Education at Rutgers University and author of Diverse Millennial Students in College: Implications for Faculty and Student Affairs, believes that much of the commentary on the Millennial Generation may be partially correct, but overly general and that many of the traits they describe apply primarily to "white, affluent teenagers who accomplish great things as they grow up in the suburbs, who confront anxiety when applying to super-selective colleges, and who multitask with ease as their helicopter parents hover reassuringly above them." During class discussions, Bonner listened to black and Hispanic students describe how some or all of the so-called core traits did not apply to them. They often said that the "special" trait, in particular, is unrecognizable. Other socioeconomic groups often do not display the same attributes commonly attributed to millennials. "It's not that many diverse parents don't want to treat their kids as special," he says, "but they often don't have the social and cultural capital, the time and resources, to do that."[79]
70% of British youths felt proud of British history. Pictured: HMS Victory in Portsmouth, 2013.
A 2013 survey of almost a thousand Britons aged 18 to 24 found that 62% had a favorable opinion of the British Broadcasting Corporation (BBC) and 70% felt proud of their national history.[86]
The University of Michigan's "Monitoring the Future" study of high school seniors (conducted continually since 1975) and the American Freshman Survey, conducted by UCLA's Higher Education Research Institute of new college students since 1966, showed an increase in the proportion of students who consider wealth a very important attribute, from 45% for Baby Boomers (surveyed between 1967 and 1985) to 70% for Gen Xers, and 75% for millennials. The percentage who said it was important to keep abreast of political affairs fell, from 50% for Baby Boomers to 39% for Gen Xers, and 35% for millennials. The notion of "developing a meaningful philosophy of life" decreased the most across generations, from 73% for Boomers to 45% for millennials. The willingness to be involved in an environmental cleanup program dropped from 33% for Baby Boomers to 21% for millennials.[87]
In 2017, nearly half of millennials living in the UK have attended a live music event.[88]
Millennials came of age in a time where the entertainment industry began to be affected by the Internet.[89][90][91] Using artificial intelligence, Joan Serra and his team at the Spanish National Research Council studied the massive Million Song Dataset and found that between 1955 and 2010, popular music has gotten louder, while the chords, melodies, and types of sounds used have become increasingly homogenized. While the music industry has long been accused of producing songs that are louder and blander, this is the first time the quality of songs is comprehensively studied and measured.[92]
By the late 2010s, viewership of late-night American television among adults aged 18 to 49, the most important demographic group for advertisers, has fallen substantially despite an abundance of materials. This is due in part to the availability and popularity of streaming services. However, when delayed viewing within three days is taken into account, the top shows all saw their viewership numbers boosted. This development undermines the current business model of the television entertainment industry. "If the sky isn't exactly falling on the broadcast TV advertising model, it certainly seems to be a lot closer to the ground than it once was," wrote reporter Anthony Crupi for Ad Age.[93]
## Demographics in the United States
The Millennial generation continues to grow as young immigrants expand its ranks. The Pew Research Center has projected that by 2019 millennials will surpass Baby Boomers to become the largest living generation in the United States. By analyzing U.S Census data they found that in 2016 there were an estimated 71 million millennials, based on Pew's definition of the generation which ranges from 1981 to 1996, compared to 74.1 million Baby Boomers.[94]
Millennial population size varies, depending on the definition used. In 2014, using dates ranging from 1982 to 2004, Neil Howe revised the number to over 95 million people in the U.S.[95] In a 2012 Time magazine article, it was estimated that there were approximately 80 million U.S. millennials.[96] The United States Census Bureau, using birth dates ranging from 1982 to 2000, stated the estimated number of U.S. millennials in 2015 was 83.1 million people.[97]
According to the Pew Research Center, "Among men, only 4% of millennials [ages 21 to 36 in 2017] are veterans, compared with 47%" of men in their 70s and 80s, "many of whom came of age during the Korean War and its aftermath."[98] Some of these veterans, are combat veterans, having fought in Afghanistan and/or Iraq.[99] As of 2016, millennials are the majority of the total veteran population.[100] According to the Pentagon in 2016, 19% of Millennials are interested in serving in the military, and 15% have a parent with a history of military service.[101]
In 2017, fewer than 56% Millennial were non-Hispanic whites, compared with more than 84% of Americans in their 70s and 80s, 57% had never been married, and 67% lived in a metropolitan area.[98] According to the Brookings Institute, millennials are the “demographic bridge between the largely white older generations (pre-millennials) and much more racially diverse younger generations (post-millennials).”[102]
## Economic prospects and trends
According to the International Labor Organization (ILO), 200 million people were unemployed in 2015. Of these, 73.3 million were 15 and 24 years of age. (That's 36.7%) Between 2009 and 2015, youth unemployment increased considerably in the North Africa and the Middle East, and slightly in East Asia. During the same period, it fell noticeably in Europe (both within and without the E.U.), and the rest of the developed world, Sub-Saharan Africa, Southeast Asia, Central and South America, but remained steady in South Asia. The ILO estimated that some 475 million jobs will need to be created worldwide by the mid-2020s in order to appreciably reduce the number of unemployed youths.[103]
In 2018, as the number of robots at work continued to increase, the global unemployment rate fell to 5.2%, the lowest in 38 years. Current trends suggest that developments in artificial intelligence and robotics will not result in mass unemployment but can actually create high-skilled jobs. However, in order to take advantage of this situation, one needs to hone skills that machines have not yet mastered, such as teamwork and effective communication.[104][105]
By analyzing data from the United Nations and the Global Talent Competitive Index, KDM Engineering found that as of 2019, the top five countries for international high-skilled workers are Switzerland, Singapore, the United Kingdom, the United States, and Sweden. Factors taken into account included the ability to attract high-skilled foreign workers, business-friendliness, regulatory environment, the quality of education, and the standard of living. Switzerland is best at retaining talents due to its excellent quality of life. Singapore is home to a world-class environment for entrepreneurs. And the United States offers the most opportunity for growth due to the sheer size of its economy and the quality of higher education and training.[106] As of 2019, these are also some of the world's most competitive economies, according to the World Economic Forum (WEF). In order to determine a country or territory's economic competitiveness, the WEF considers factors such as the trustworthiness of public institutions, the quality of infrastructure, macro-economic stability, the quality of healthcare, business dynamism, labor market efficiency, and innovation capacity.[107]
### In Asia
Statistics from the International Monetary Fund (IMF) reveal that between 2014 and 2019, Japan's unemployment rate went from about 4% to 2.4% and China's from almost 4.5% to 3.8%. These are some of the lowest rates among the largest economies of the world.[108]
### In Europe
German young adults protest youth unemployment at a 2014 event
Economic prospects for some millennials have declined largely due to the Great Recession in the late 2000s.[109][110][111] Several governments have instituted major youth employment schemes out of fear of social unrest due to the dramatically increased rates of youth unemployment.[112] In Europe, youth unemployment levels were very high (56% in Spain,[113] 44% in Italy,[114] 35% in the Baltic states, 19% in Britain[115] and more than 20% in many more countries). In 2009, leading commentators began to worry about the long-term social and economic effects of the unemployment.[116]
A variety of names have emerged in various European countries hard hit following the financial crisis of 2007–2008 to designate young people with limited employment and career prospects.[117] These groups can be considered to be more or less synonymous with millennials, or at least major sub-groups in those countries. The Generation of €700 is a term popularized by the Greek mass media and refers to educated Greek twixters of urban centers who generally fail to establish a career. In Greece, young adults are being "excluded from the labor market" and some "leave their country of origin to look for better options". They're being "marginalized and face uncertain working conditions" in jobs that are unrelated to their educational background, and receive the minimum allowable base salary of €700 per month. This generation evolved in circumstances leading to the Greek debt crisis and some participated in the 2010–2011 Greek protests.[118] In Spain, they're referred to as the mileurista (for €1,000 per month),[119] in France "The Precarious Generation,[120]" and as in Spain, Italy also has the "milleurista"; generation of 1,000 euros (per month).[117]
In 2016, research from the Resolution Foundation found millennials in the UK earned £8,000 less in their 20s than Generation X, describing millennials as "on course to become the first generation to earn less than the one before".[121][122]
Millennials are the most highly educated and culturally diverse group of all generations, and have been regarded as hard to please when it comes to employers.[123] To address these new challenges, many large firms are currently studying the social and behavioral patterns of millennials and are trying to devise programs that decrease intergenerational estrangement, and increase relationships of reciprocal understanding between older employees and millennials. The UK's Institute of Leadership & Management researched the gap in understanding between millennial recruits and their managers in collaboration with Ashridge Business School.[124] The findings included high expectations for advancement, salary and for a coaching relationship with their manager, and suggested that organizations will need to adapt to accommodate and make the best use of millennials. In an example of a company trying to do just this, Goldman Sachs conducted training programs that used actors to portray millennials who assertively sought more feedback, responsibility, and involvement in decision making. After the performance, employees discussed and debated the generational differences they saw played out.[125] In 2014, millennials were entering an increasingly multi-generational workplace.[126] Even though research has shown that millennials are joining the workforce during a tough economic time, they still have remained optimistic, as shown when about nine out of ten millennials surveyed by the Pew Research Center said that they currently have enough money or that they will eventually reach their long-term financial goals.[127]
Statistics from the International Monetary Fund (IMF) reveal that between 2014 and 2019, unemployment rates fell in most of the world's major economies, many of which in Europe. Although the unemployment rates of France and Italy remained relatively high, they were markedly lower than previously. Meanwhile, the German unemployment rate dipped below even that of the United States, a level not seen since its unification almost three decades prior.[108] Eurostat reported in 2019 that overall unemployment rate across the European Union dropped to its lowest level since January 2000, at 6.2% in August, meaning about 15.4 million people were out of a job. The Czech Republic (3%), Germany (3.1%) and Malta (3.3%) enjoyed the lowest levels of unemployment. Member states with the highest unemployment rates were Italy (9.5%), Spain (13.8%), and Greece (17%). Countries with higher unemployment rates compared to 2018 were Denmark (from 4.9% to 5%), Lithuania (6.1% to 6.6%), and Sweden (6.3% to 7.1%).[128]
Top five professions with insufficient workers in the European Union in the late 2010s.
According to the European Centre for the Development of Vocational Training (Cedefop), the European Union in the late 2010s suffers from shortages of STEM specialists (including ICT professionals), medical doctors, nurses, midwives and schoolteachers. However, the picture varies depending on the country. In Italy, environmentally friendly architecture is in high demand. Estonia and France are running short of legal professionals. Ireland, Luxembourg, Hungary, and the United Kingdom need more financial experts. All member states except Finland need more ICT specialists, and all but Belgium, Greece, Spain, Hungary, Latvia, Lithuania, Luxembourg, Portugal and the United Kingdom need more teachers. The supply of STEM graduates has been insufficient because the dropout rate is high and because of an ongoing brain drain from some countries. Some countries need more teachers because many are retiring and need to be replaced. At the same time, Europe's aging population necessitates the expansion of the healthcare sector. Disincentives for (potential) workers in jobs in high demand include low social prestige, low salaries, and stressful work environments. Indeed, many have left the public sector for industry while some STEM graduates have taken non-STEM jobs.[129]
Even though pundits predicted that the uncertainty due to the Brexit referendum would cause the British economy to falter or even fall into a recession, the unemployment rate has dipped below 4% while real wages have risen slightly in the late 2010s, two percent as of 2019. In particular, medical doctors and dentists saw their earnings bumped above the inflation rate in July 2019. Despite the fact that the government promised to an increase in public spending (£13 billion, or 0.6% of GDP) in September 2019, public deficit continues to decline, as it has since 2010. Nevertheless, uncertainty surrounding Britain's international trade policy suppressed the chances of an export boom despite the depreciation of the pound sterling.[130] According to the Office for National Statistics, the median income of the United Kingdom in 2018 was £29,588.[131]
### In North America
Large Canadians cities such as Vancouver continue to attract millennials despite high costs of living.
In Canada, the youth unemployment rate in July 2009 was 16%, the highest in 11 years.[132] Between 2014 and 2019, Canada's overall unemployment rate fell from about 7% to below 6%.[108] However, a 2018 survey by accounting and advisory firm BDO Canada found that 34% of millennials felt "overwhelmed" by their non-mortgage debt. For comparison, this number was 26% for Generation X and 13% for the Baby Boomers. Canada's average non-mortgage debt was CAN$20,000 in 2018. About one in five millennials were delaying having children because of financial worries.[133] Despite expensive housing costs, Canada's largest cities, Vancouver, Toronto, and Montreal, continue to attract millennials thanks to their economic opportunities and cultural amenities. Research by the Royal Bank of Canada (RBC) revealed that for every person in the 20-34 age group who leaves the nation's top cities, Toronto gains seven while Vancouver and Montreal gain up to a dozen each. In fact, there has been a surge in the millennial populations of Canada's top three cities between 2015 and 2018. However, millennials' rate of home ownership will likely drop as increasing numbers choose to rent instead.[134] An average Canadian home was worth CAN$484,500 in 2018. Despite government legislation (mortgage stress test rules), such a price was quite high compared to some decades before. Adjusted for inflation, it was CAN$210,000 in 1976. Paul Kershaw of the University of British Columbia calculated that the average amount of extra money needed for a down payment in the late 2010s compared to one generation before was equivalent to eating 17 avocado toasts each day for ten years.[135] Meanwhile, the option of renting in a large city is increasingly out of reach for many young Canadians. In 2017, the average rent in Canada cost$947 a month, according to the Canada Mortgage and Housing Corporation (CMHC). But, as is always the case in real-estate, location matters. An average two-bedroom apartment cost CAN$1,552 per month in Vancouver and CAN$1,404 per month in Toronto, with vacancy rates at about one percent.[136] Canada's national vacancy rate was 2.4% in 2018, the lowest since 2009. New supply – rental apartment complexes that are newly completed or under construction – has not been able to keep up with rising demand. Besides higher prices, higher interest rates and stricter mortgage rules have made home ownership more difficult. International migration contributes to rising demand for housing, especially rental apartments, according to the CMHC, as new arrivals tend to rent rather than purchase. Moreover, a slight decline in youth unemployment in 2018 also drove up demand.[137] While the Canadian housing market is growing, this growth is detrimental to the financial well-being of young Canadians.[135][138]
In 2019, Canada's net public debt was CAN$768 billion. Meanwhile, U.S. public debt amounted to US$22 trillion. The Canadian federal government's official figure for the debt-to-GDP ratio was 30.9%. However, this figure left out debts from lower levels of government. Once these were taken into account, the figure jumped to 88%, according to the International Monetary Fund. For comparison, that number was 237.5% for Japan, 106.7% for the United States, and 99.2% for France. Canada's public debt per person was over CAN$18,000. For Americans, it was US$69,000.[139] Since the Great Recession, Canadian households have accumulated significantly more debt. According to Statistics Canada, the national debt-to-disposable income ratio was 175% in 2019. It was 105% in the U.S. Meanwhile, the national median mortgage debt rose from CAN$95,400 in 1999 to CAN$190,000 in 2016 (in 2016 dollars). Numbers are much higher in the Greater Toronto Area, Vancouver, and Victoria, B.C.[140]
A 2018 survey by Abacus Data of 4,000 Canadian millennials found that 80% identified to be members of the middle class, 55% had pharmaceutical insurance, 53% dental insurance, 36% a Registered Retirement Savings Plan (RRSP), and 29% an employer-sponsored pension plan.[141]
#### United States
The youth unemployment rate in the U.S. reached a record 19% in July 2010 since the statistic started being gathered in 1948.[142] Underemployment is also a major factor. In the U.S. the economic difficulties have led to dramatic increases in youth poverty, unemployment, and the numbers of young people living with their parents.[143] In April 2012, it was reported that half of all new college graduates in the US were still either unemployed or underemployed.[144] It has been argued that this unemployment rate and poor economic situation has given millennials a rallying call with the 2011 Occupy Wall Street movement.[145] However, according to Christine Kelly, Occupy is not a youth movement and has participants that vary from the very young to very old.[146]
Millennials have benefited the least from the economic recovery following the Great Recession, as average incomes for this generation have fallen at twice the general adult population's total drop and are likely to be on a path toward lower incomes for at least another decade. According to a Bloomberg L.P., "Three and a half years after the worst recession since the Great Depression, the earnings and employment gap between those in the under-35 population and their parents and grandparents threatens to unravel the American dream of each generation doing better than the last. The nation's younger workers have benefited least from an economic recovery that has been the most uneven in recent history."[147] In 2015, millennials in New York City were reported as earning 20% less than the generation before them, as a result of entering the workforce during the great recession. Despite higher college attendance rates than Generation X, many were stuck in low-paid jobs, with the percentage of degree-educated young adults working in low-wage industries rising from 23% to 33% between 2000 and 2014.[148]
According to a 2019 TD Ameritrade survey of 1,015 U.S. adults aged 23 and older with at least US$10,000 in investable assets, two thirds of people aged 23 to 38 (Millennials) felt they were not saving enough for retirement, and the top reason why was expensive housing (37%). This was especially true for Millennials with families. 21% said student debt prevented them from saving for the future. For comparison, this number was 12% for Generation X and 5% for the Baby Boomers.[149] While millennials are well known for taking out large amounts of student loans, these are actually not their main source of non-mortgage personal debt, but rather credit card debt. According to a 2019 Harris poll, the average non-mortgage personal debt of millennials was US$27,900, of which, 25% was credit card debt. For comparison, mortgages were the top source of debt for the Baby Boomers and Generation X (28% and 30%, respectively) and student loans for Generation Z (20%).[150]
According to the U.S. Department of Labor, the unemployment rate in September 2019 was 3.5%, a number not seen since December 1969.[151] For comparison, unemployment attained a maximum of 10% after the Great Recession in October 2009.[152] At the same time, labor participation remained steady and most job growth tended to be full-time positions.[151] Economists generally consider a population with an unemployment rate lower than 4% to be fully employed. In fact, even people with disabilities or prison records are getting hired.[153] Between June 2018 and June 2019, the U.S. economy added a minimum of 56,000 jobs (February 2019) and a maximum of 312,000 jobs (January 2019).[154] The average monthly job gain between the same period was about 213,600.[154] Tony Bedikian, managing director and head of global markets at Citizens Bank, said this is the longest period of economic expansion on record.[154] At the same time, wages continue to grow, especially for low-income earners.[153] On average, they grew by 2.7% in 2016 and 3.3% in 2018.[155] However, the Pew Research Center found that the average wage in the U.S. in 2018 remained more or less the same as it was in 1978, when the seasons and inflation are taken into consideration. Real wages grew only for the top 90th percentile of earners and to a lesser extent the 75th percentile (in 2018 dollars).[156] Nevertheless, these developments ease fears of an upcoming recession.[154] Moreover, economists believe that job growth could slow to an average of just 100,000 per month and still be sufficient to keep up with population growth and keep economic recovery going.[155] As long as firms keep hiring and wages keep growing, consumer spending should prevent another recession.[157] Millennials are expected to make up approximately half of the U.S. workforce by 2020.[123]
Miami, Florida, has the fastest growing share of adults with university degrees in the United States.
Human capital is the engine of economic growth. With this in mind, urban researcher Richard Florida and his collaborators analyzed data from the U.S. Census from between 2012 and 2017 and found that the ten cities with the largest shares of adults with a bachelor's degree or higher are Seattle (62.6%), San Francisco, the District of Columbia, Raleigh, Austin, Minneapolis, Portland, Denver, Atlanta, and Boston (48.2%). More specifically, the ten cities with the largest shares of people with graduate degrees are the District of Columbia (33.4%), Seattle, San Francisco, Boston, Atlanta, Minneapolis, Portland, Denver, Austin, and San Diego (18.5%). These are the leading information technology hubs of the United States. Cities with the lowest shares of college graduates tend to be from the Rust Belt, such as Detroit, Memphis, and Milwaukee, and the Sun Belt, such as Las Vegas, Fresno, and El Paso. Meanwhile, the ten cities with the fastest growth in the shares of college-educated adults are Miami (46.3%), Austin, Fort Worth, Las Vegas, Denver, Charlotte, Boston, Mesa, Nashville, and Seattle (25.1%). More specifically, those with the fastest growing shares of adults with graduate degrees are Miami (47.1%), Austin, Raleigh, Charlotte, San Jose, Omaha, Seattle, Fresno, Indianapolis, and Sacramento (32.0%).[158]
Florida and his team also found, using U.S. Census data between 2005 and 2017, an increase in employment across the board for members of the "creative class" – people in education, healthcare, law, the arts, technology, science, and business, not all of whom have a university degree – in virtually all U.S. metropolitan areas with a population of a million or more. Indeed, the total number of the creative class grew from 44 million in 2005 to over 56 million in 2017. Florida suggested that this could be a "tipping point" in which talents head to places with a high quality of life yet lower costs of living than well-established creative centers, such as New York City and Los Angeles, what he called the "superstar cities."[159]
Young Americans are leaving the cities for the suburbs in large numbers. Pictured: Munster, Indiana (near Chicago, Illinois).
Indeed, by analyzing U.S. Census data, demographer William H. Frey at the Brookings Institution found that, following the Great Recession, American suburbs grew faster than dense urban cores. For example, for every one person who moved to New York City, five moved out to one of its suburbs. Data released by the U.S. Census Bureau in 2017 revealed that Americans aged 25–29 were 25% more likely to move from a city to a suburb than the other way around; for older millennials, that number was 50%. Economic recovery and easily obtained mortgages help explain this phenomenon.[160] Millennial homeowners are more likely to be in the suburbs than the cities. This trend will likely continue as more and more millennials purchase a home. 2019 was the fourth year in a row where the number of millennials living in the major American cities declined measurably.[161] Previously, millennials were responsible for the so-called "back-to-the-city" trend.[162] Between 2000 and 2010, the number of Americans living in urban areas grew from 79% to 80.7% while that in rural areas dropped from 21% to 19.3%. At the same time, many new cities were born, especially in the Midwest, and others, such as Charlotte, North Carolina, and Austin, Texas, were growing enormously.[163] Mini-apartments, initially found mainly in Manhattan, became more and more common in other major urban areas as a strategy for dealing with high population density and high demand for housing, especially among people living alone. The number of single-person households in the U.S. reached 27% in 2010 from 8% in 1940 and 18% in 1970; in places such as Atlanta, Cincinnati, Denver, Pittsburgh, Seattle, St. Louis and Washington, D.C, it can even exceed 40%, according to Census data. The size of a typical mini-apartment is 300 square feet (28 square meters), or roughly the size of a standard garage and one eighth the size of an average single-family home in the U.S. as of 2013. Many young city residents were willing to give up space in exchange for living in a location they liked. Such apartments are also common in Tokyo and some European capitals.[164]
But by the late 2010s, while 14% of the U.S. population relocate at least once each year, Americans in their 20s and 30s are more likely to move than retirees, according to Frey. Besides the cost of living, including housing costs, people are leaving the big cities in search of warmer climates, lower taxes, better economic opportunities, and better school districts for their children.[165][166][167] Places in the South and Southwestern United States are especially popular. In some communities, millennials and their children are moving in so quickly that schools and roads are becoming overcrowded. This rising demand pushes prices upwards, making affordable housing options less plentiful.[162] Historically, between the 1950s and 1980s, Americans left the cities for the suburbs because of crime. Suburban growth slowed because of the Great Recession but picked up pace afterwards.[160] According to the Brookings Institution, overall, American cities with the largest net losses in their millennial populations were New York City, Los Angeles, and Chicago, while those with the top net gains were Houston, Denver, and Dallas.[168] According to Census data, Los Angeles County in particular lost 98,608 people in 2018, the single biggest loss in the nation. Moving trucks (U-Haul) are in extremely high demand in the area.[169]
High taxes and high cost of living are also reasons why people are leaving entire states behind.[167][170] As is the case with cities, young people are the most likely to relocate. For example, a 2019 poll by Edelman Intelligence of 1,900 residents of California found that 63% of millennials said they were thinking about leaving the Golden State and 55% said they wanted to do so within five years. 60% of millennials said the reason why they wanted to move as the cost and availability of housing. In 2018, the median home price in California was US$547,400, about twice the national median. California also has the highest marginal income tax rate of all U.S. states, 12.3%, plus a subcharge of 1% for those earning a million dollars a year or more. Popular destinations include Oregon, Nevada, Arizona, and Texas, according to California's Legislative Analyst's Office.[170] By analyzing data provided by the Internal Revenue Service (IRS), finance company SmartAsset found that for wealthy millennials, defined as those no older than 35 years of age earning at least US$100,000 per annum, the top states of departure were New York, Illinois, Virginia, Massachusetts, and Pennsylvania, while the top states of destination were California, Washington State, Texas, Colorado, and Florida.[171]
A rural county's chances of having a performing arts organization is 60% higher if it is located near a national park or forest. Pictured: The Redwood National and State Parks, California.
Economist Tim Wojan and his colleagues at the Economic Research Service of the U.S. Department of Agriculture analyzed 11,000 businesses using data collected in 2014 and classified them into three groups: substantive innovators, nominal innovators, and non-innovators. They found that 20% of the establishments hailed from rural areas compared to 30% from urban areas. In addition, large innovative firms were more likely to be found in rural areas while small and medium firms tended to come from the metropolitan areas. This is because large patent-intensive manufacturing firms – such as those manufacturing chemicals, electronic components, automotive parts, or medical equipment – were generally based in rural areas while those that provide services tend to cluster in the cities. Nevertheless, rural creative centers tend to be relatively close to large urban centers. The National Endowment for the Arts reported in 2017 that a rural county's probability of having a performing arts organization increased by 60% if it is located near a forest or a national park. Richard Florida concluded that there is no compelling reason to believe that rural America is not as innovative as urban America.[172] Nevertheless, despite the availability of affordable housing, and broadband Internet, and the possibility of telecommuting, millennials have been steadily leaving rural counties for urban areas for lifestyle and economic reasons.[173]
According to the Department of Education, people with technical or vocational trainings are slightly more likely to be employed than those with a bachelor's degree and significantly more likely to be employed in their fields of specialty. The United States currently suffers from a shortage of skilled tradespeople.[174] As of 2019, the most recent data from the U.S. government reveals that there are over half a million vacant manufacturing jobs in the country, a record high, thanks to an increasing number of Baby Boomers entering retirement. But in order to attract new workers to overcome this "Silver Tsunami," manufacturers need to debunk a number of misconceptions about their industries. For example, the American public tends to underestimate the salaries of manufacturing workers. Nevertheless, the number of people doubting the viability of American manufacturing has declined to 54% in 2019 from 70% in 2018, the L2L Manufacturing Index measured.[175] After the Great Recession, the number of U.S. manufacturing jobs reached a minimum of 11.5 million in February 2010. It rose to 12.8 million in September 2019. It was 14 million in March 2007.[152] As of 2019, manufacturing industries made up 12% of the U.S. economy, which is increasingly reliant on service industries, as is the case for other advanced economies around the world.[176] Nevertheless, twenty-first-century manufacturing is increasingly sophisticated, using advanced robotics, 3D printing, cloud computing, among other modern technologies, and technologically savvy employees are precisely what employers need. Four-year university degrees are unnecessary; technical or vocational training, or perhaps apprenticeships would do.[177]
According to the Bureau of Labor Statistics, the occupations with the highest median annual pay in the United States in 2018 included medical doctors (especially psychiatrists, anesthesiologists, obstetricians and gynecologists, surgeons, and orthodontists), chief executives, dentists, information system managers, chief architects and engineers, pilots and flight engineers, petroleum engineers, and marketing managers. Their median annual pay ranged from about US$134,000 (marketing managers) to over US$208,000 (aforementioned medical specialties).[178] Meanwhile, the occupations with the fastest projected growth rate between 2018 and 2028 are solar cell and wind turbine technicians, healthcare and medical aides, cyber security experts, statisticians, speech-language pathologists, genetic counselors, mathematicians, operations research analysts, software engineers, forest fire inspectors and prevention specialists, post-secondary health instructors, and phlebotomists. Their projected growth rates are between 23% (medical assistants) and 63% (solar cell installers); their annual median pays range between roughly US$24,000 (personal care aides) to over US$108,000 (physician assistants).[179] Occupations with the highest projected numbers of jobs added between 2018 and 2028 are healthcare and personal aides, nurses, restaurant workers (including cooks and waiters), software developers, janitors and cleaners, medical assistants, construction workers, freight laborers, marketing researchers and analysts, management analysts, landscapers and groundskeepers, financial managers, tractor and truck drivers, and medical secretaries. The total numbers of jobs added ranges from 881,000 (personal care aides) to 96,400 (medical secretaries). Annual median pays range from over US$24,000 (fast-food workers) to about US$128,000 (financial managers).[180]
Despite economic recovery and despite being more likely to have a bachelor's degree or higher, millennials are at a financial disadvantage compared to the Baby Boomers and Generation X because of the Great Recession and expensive higher education. Income has become less predictable due to the rise of short-term and freelance positions. According to a 2019 report from the non-partisan non-profit think tank New America, a household headed by a person under 35 in 2016 had an average net worth of almost US$11,000, compared to US$20,000 in 1995. According to the St. Louis Federal Reserve, an average millennial (20 to 35 in 2016) owned US$162,000 of assets, compared to US$198,000 for Generation X at the same age (20 to 35 in 2001).[181] Risk management specialist and business economist Olivia S. Mitchell of the University of Pennsylvania calculated that in order to retire at 50% of their last salary before retirement, millennials will have to save 40% of their incomes for 30 years. She told CNBC, "Benefits from Social Security are 76% higher if you claim at age 70 versus 62, which can substitute for a lot of extra savings." Maintaining a healthy lifestyle – avoiding smoking, over-drinking, and sleep deprivation – should prove beneficial.[182]
## Education
For information on public support for higher education (for domestic students) in the OECD in 2011, see chart below.
### In continental Europe
In 2005, judges in Karlsruhe, Germany, struck down a ban on university fees as unconstitutional on the grounds that it violated the constitutional right of German states to regulate their own higher education systems. This ban was introduced in order to ensure equality of access to higher education regardless of socioeconomic class. Bavarian Science Minister Thomas Goppel told the Associated Press, "Fees will help to preserve the quality of universities." Supporters of fees argued that they would help ease the financial burden on universities and would incentivize students to study more efficiently, despite not covering the full cost of higher education, an average of €8,500 as of 2005. Opponents believed fees would make it more difficult for people to study and graduate on time.[184] Germany also suffered from a brain drain, as many bright researchers moved abroad while relatively few international students were interested in coming to Germany. This has led to the decline of German research institutions.[185]
### In English-speaking countries
In the 1990s, due to a combination of financial hardship and the fact that universities elsewhere charged tuition, British universities pressed the government to allow them to take in fees. A nominal tuition fee of £1,000 was introduced in autumn 1998. Because not all parents would be able to pay all the fees in one go, monthly payment options, loans, and grants were made available. Some were concerned that making people pay for higher education may deter applicants. This turned out not to be the case. The number of applications fell by only 2.9% in 1998, and mainly due to mature students rather than 18-year-olds.[186]
In 2012, £9,000 worth of student fees were introduced. Despite this, the number of people interested in pursuing higher education grew at a faster rate than the UK population. In 2017, almost half of Britons have received higher education by the age of 30. Prime Minister Tony Blair introduced the goal of having half of young Britons having a university degree in 1999, though he missed the 2010 deadline. Demand for higher education in the United Kingdom remains strong, driven by the need for high-skilled workers from both the public and private sectors. There is, however, a widening gender gap. As of 2017, women were more likely to attend or have attended university than men, 55% to 43%, a 12% difference.[187]
In Australia, university tuition fees were introduced in 1989. Regardless, the number of applicants has risen considerably. By the 1990s, students and their families were expected to pay 37% of the cost, up from a quarter in the late 1980s. The most expensive subjects were law, medicine, and dentistry, followed by the natural sciences, and then by the arts and social studies. Under the new funding scheme, the Government of Australia also capped the number of people eligible for higher education, enabling schools to recruits more well-financed (though not necessarily bright) students.[186]
According to the Pew Research Center, 53% of American Millennials attended or were enrolled in university in 2002. The number of young people attending university was 44% in 1986.[188] Historically, university students were more likely to be male than female. The difference was especially great during the second half of the twentieth century, when enrollment rose dramatically compared to the 1940s. This trend continues into the twenty-first century. But things started to change by the turn of the new millennium. By the late 2010s, the situation has reversed. Women are now more likely to enroll in university than men. In 2018, upwards of one third of each sex is a university student.[189]
In the United States today, high school students are generally encouraged to attend college or university after graduation while the options of technical school and vocational training are often neglected.[190] Historically, high schools separated students on career tracks, with programs aimed at students bound for higher education and those bound for the workforce. Students with learning disabilities or behavioral issues were often directed towards vocational or technical schools. All this changed in the late 1980s and early 1990s thanks to a major effort in the large cities to provide more abstract academic education to everybody. The mission of high schools became preparing students for college, referred to as "high school to Harvard."[191] However, this program faltered in the 2010s, as institutions of higher education came under heightened skepticism due to high costs and disappointing results. People became increasingly concerned about debts and deficits. No longer were promises of educating "citizens of the world" or estimates of economic impact coming from abstruse calculations sufficient. Colleges and universities found it necessary to prove their worth by clarifying how much money from which industry and company funded research, and how much it would cost to attend.[192]
Because jobs (that suited what one studied) were so difficult to find in the few years following the Great Recession, the value of getting a liberal arts degree and studying the humanities at an American university came into question, their ability to develop a well-rounded and broad-minded individual notwithstanding.[193] As of 2019, the total college debt has exceeded US$1.5 trillion, and two out of three college graduates are saddled with debt.[188] The average borrower owes US$37,000, up US$10,000 from ten years before. A 2019 survey by TD Ameritrade found that over 18% of Millennials (and 30% of Generation Z) said they have considered taking a gap year between high school and college.[194] Data from the National Center for Education Statistics revealed that between 2008 and 2017, the number of people majoring in English plummeted by just over a quarter. At the same time, those in philosophy and religion fell 22% and those who studied foreign languages dropped 16%. Meanwhile, the number of university students majoring in homeland security, science, technology, engineering, and mathematics (STEM), and healthcare skyrocketed. (See right.)[195] According to the U.S. Department of Education, people with technical or vocational trainings are slightly more likely to be employed than those with a bachelor's degree and significantly more likely to be employed in their fields of specialty.[190] The United States currently suffers from a shortage of skilled tradespeople.[190] Despite the fact that educators and political leaders, such as President Barack Obama, have been trying to years to improve the quality of STEM education in the United States, and that various polls have demonstrated that more students are interested in these subjects, graduating with a STEM degree is a different kettle of fish altogether. Data collected by the University of California, Los Angeles, (UCLA) in 2011 showed that although these students typically came in with excellent high school GPAs and SAT scores, among science and engineering students, including pre-medical students, 60% changed their majors or failed to graduate, twice the attrition rate of all other majors combined. Despite their initial interest in secondary school, many university students find themselves overwhelmed by the reality of a rigorous STEM education. Some are mathematically unskilled, while others are simply lazy. The National Science Board raised the alarm all the way back in the mid-1980s that students often forget why they wanted to be scientists and engineers in the first place. Many bright students had an easy time in high school and failed to develop good study habits. In contrast, Chinese, Indian, and Singaporean students are exposed to mathematics and science at a high level from a young age. Moreover, given two students who are equally prepared, the one who goes to a more prestigious university is less likely to graduate with a STEM degree than the one who attends a less difficult school. Competition can defeat even the top students. Meanwhile, grade inflation is a real phenomenon in the humanities, giving students an attractive alternative if their STEM ambitions prove too difficult to achieve. Whereas STEM classes build on top of each other – one has to master the subject matter before moving to the next course – and have black and white answers, this is not the case in the humanities, where things are a lot less clear-cut.[196] ## Historical knowledge A February 2018 survey of 1,350 individuals found that 66% of the American millennials (and 41% of all U.S. adults) surveyed did not know what Auschwitz was,[197] while 41% incorrectly claimed that 2 million Jews or fewer were killed during the Holocaust, and 22% said that they had never heard of the Holocaust.[198] Over 95% of American millennials were unaware that the Holocaust occurred in the Baltic states, which lost over 90% of their pre-war Jewish population, and 49% were not able to name a single Nazi concentration camp or ghetto in German-occupied Europe.[199][200] However, at least 93% surveyed believed that teaching about the Holocaust in school is important and 96% believed the Holocaust happened.[201] The YouGov survey found that 42% of American millennials have never heard of Mao Zedong, who ruled China from 1949 to 1976 and was responsible for the deaths of 20–45 million people; another 40% are unfamiliar with Che Guevara.[202][203] ## Political views Distribution of the political views of American teens (Gallup 2004) A 2004 Gallup poll of Americans aged 13 to 17 found that 71% said their social and political views were more or less the same as those of their parents. 21% thought they were more liberal and 7% more conservative. According to demographer and public policy analyst Philip Longman, "even among baby boomers, those who wound up having children have turned out to be remarkably similar to their parents in their attitudes about 'family' values."[204] In the postwar era, most returning servicemen looked forward to "making a home and raising a family" with their wives and lovers, and for many men, family life was a source of fulfillment and a refuge from the stress of their careers. Life in the late 1940s and 1950s was centered about the family and the family was centered around children.[205] Researchers found that while only 9% of teenagers who identified with the Republican Party considered themselves more conservative than their parents, compared to 77% who shared their parents' views, 25% of adolescents who identified with the Democratic Party and 28% of politically independent teens said they were more liberal than their parents. Another 2004 Gallup poll of the same age group found that a clear majority of teenagers considered themselves to be politically moderate, 56%. Only 7% and 18% deemed themselves very conservative or conservative, respectively, and 10% and 6% believed they were liberal or very liberal, respectively. (The bar plot roughly resembles a Gaussian distribution or an isosceles triangle centered around moderates. See right.) By comparing with a 2004 poll of Americans aged 18 and over, Gallup discovered that teens were substantially more moderate then adults (56% to 38%), less conservative (25% to 40%), and just about as liberal (16% to 19%).[204] However, political scientist Elias Dinas discovered, by studying the results from the Political Socialisation Panel Study and further data from the United Kingdom and the United States, that while children born to politically engaged parents tended to be politically engaged themselves, those who absorbed their parents' views the earliest were also the most likely to abandon them later in life.[206] According to Sean Simpsons of Ipsos, people are more likely to vote when they have more at stake, such as children to raise, homes to maintain, and income taxes to pay.[207] Millennials are more willing to vote than previous generations when they were at the same age. With voter rates being just below 50% for the four presidential cycles before 2017, they have already surpassed Gen Xers of the same age who were at just 36%.[208] 2018 surveys of teenagers 13 to 17 and adults aged 18 or over conducted by the Pew Research Center found that Millennials and Generation Z held similar views on various political and social issues. More specifically, 56% of Millennials believed that climate change is real and is due to human activities while only 8% reject the scientific consensus on climate change. 64% wanted the government to play a more active role in solving their problems. 65% were indifferent towards pre-nuptial cohabitation. 48% considered single motherhood to be neither a positive or a negative for society. 61% saw increased ethnic or racial diversity as good for society. 47% did the same for same-sex marriage, and 53% interracial marriage. (See chart.) In most cases, Millennials tended hold quite different views from the Silent Generation, with the Baby Boomers and Generation X in between. In the case of financial responsibility in a two-parent household, though, majorities from across the generations answered that it should be shared, with 58% for the Silent Generation, 73% for the Baby Boomers, 78% for Generation X, and 79% for both the Millennials and Generation Z. Across all the generations surveyed, at least 84% thought that both parents ought to be responsible for rearing children. Very few thought that fathers should be the ones mainly responsible for taking care of children.[209] Surveys of political attitudes among millennials in the United Kingdom have suggested increasingly social liberal views, as well as higher overall support for classically liberal economic policies than preceding generations. They are more likely to support same-sex marriage and the legalization of drugs.[210] A 2013 YouGov poll of almost a thousand people aged 18 to 24 in the United Kingdom found that 73% in total supported the legalization of same-sex marriage and only 15% opposed.[86] Americans aged 18 to 34 are becoming less tolerant of the LGBT community over time (Harris 2018). The Economist parallels this with millennials in the United States, whose attitudes are more supportive of social liberal policies and same-sex marriage relative to other demographics.[210] However, a 2018 poll conducted by Harris on behalf of the LGBT advocacy group GLAAD found that despite being frequently described as the most tolerant segment of society, people aged 18 to 34—most Millennials and the oldest members of Generation Z—have become less accepting LGBT individuals compared to previous years. In 2016, 63% of Americans in that age group said they felt comfortable interacting with members of the LGBT community; that number dropped to 53% in 2017 and then to 45% in 2018. On top of that, more people reported discomfort learning that a family member was LGBT (from 29% in 2017 to 36% in 2018), having a child learning learning LGBT history (30% to 39%), or having an LGBT doctor (27% to 34%). Harris found that young women were driving this development.[211] Results from this Harris poll were released on the 50th anniversary of the riots that broke out in Stonewall Inn,[211] New York City, in June 1969, thought to be the start of the LGBT rights movement.[212] At that time, homosexuality was considered a mental illness or a crime in many U.S. states.[212] 65% of British youths reported pride in the UK military. Pictured: Type 45 destroyer HMS Dragon in the English Channel (2011). According to the same 2013 YouGov poll, the five most popular political parties for young Britons were the Labour Party (23%), the Conservative Party (12%), the Liberal Democratic Party (7%), the Green Party (7%), and the United Kingdom Independence Party (6%). 19% of British youths identified with no party whatsoever. When asked which politician they admired, 77% picked the 'none' option, followed by Boris Johnson (4%). Overall, 60% had an unfavorable of the British political system. 12% thought British immigration laws were too tough, 54% said they were too lax, and 16% deemed them appropriate. About one third opined that taxes and public spending were too high. 22% said they were insufficient and one fifth thought they were about right. 34% believed welfare benefits were too generous and should be cut. 22% argued they were not enough and should be increased and 24% thought they struck the right balance. Almost three quarters agreed that the welfare system was frequently abused and 63% thought those who genuinely needed it were branded as 'scroungers'. A total of 65% were either very or fairly proud of the United Kingdom Armed Forces and 77% the National Health Service (NHS).[86] Pew Research described millennials as playing a significant role in the election of Barack Obama as President of the United States. Millennials were between 12 and 27 during the 2008 U.S Presidential election.[30] A 2013 Pew Research Poll found that 84% of millennials, born since 1980, who were at that time between the ages of 18 and 32, favored legalizing the use of marijuana.[213] As of 2019, it is legal in Canada, Uruguay, and 33 U.S. states.[214] Bernie Sanders, a self-proclaimed democratic socialist and Democratic candidate in the 2016 United States presidential election, was the most popular candidate among millennial voters in the primary phase, having garnered more votes from people under 30 in 21 states than the major parties' candidates, Donald Trump and Hillary Clinton, did combined.[215] A 2016 Harvard poll found that 40% of millennials supported the Democratic Party, 22% did the Republican Party and 36% were Independents.[216] A 2018 Gallup poll found that people aged 18 to 29 have a more favorable view of socialism than capitalism, 51% to 45%. Nationally, 56% of Americans prefer capitalism compared to 37% who favor socialism. Older Americans consistently prefer capitalism to socialism. Whether the current attitudes of millennials and Generation Z on capitalism and socialism will persist or dissipate as they grow older remains to be seen.[217] Turnout among voters aged 18 to 29 in the 2016 election was 50%. Hillary Clinton won 55% of the millennial vote while Donald Trump secured 37%.[218] A Reuters-Ipsos survey of 16,000 registered voters aged 18 to 34 conducted in the first three months of 2018 (and before the 2018 midterm election) showed that support for Democratic Party among such voters fell by nine percent between 2016 and 2018 and that an increasing number favored the Republican Party's approach to the economy. This is despite the fact that almost two thirds of young voters disapproved of the performance of Republican President Donald J. Trump.[219] According to the Pew Research Center, only 27% of Millennials approved of the Trump presidency while 65% disapproved.[220] Historically, political participation among young Canadian voters has been low, no higher than 40%.[221] However, the 2015 federal election was an exception, when 57% of the people aged 18 to 34 voted. Canadian millennials played a key role in the election of Justin Trudeau as Prime Minister of Canada. While Stephen Harper and the Conservative Party received approximately the same number of votes as they did in 2011, the surge in the youth vote was enough to push Trudeau to the top. His core campaign message centered around gender equality, tolerance, legalizing marijuana, addressing climate change, and governmental transparency while Harper focused on tax cuts. Nevertheless, political scientist Melanee Thomas at the University of Calgary warned that the electoral power of this demographic group should not be overestimated, since millennials do not vote as a single bloc.[221] Even though millennials tend to vote for left-leaning candidates, certain items from right-leaning platforms can resonate with them, such as high but affordable standards of living.[207] A 2018 survey of 4,000 Canadian millennials by Abacus Data found that 54% of the people asked favored socialism and 46% capitalism. Most want to address climate change, alleviate poverty, and adopt a more open immigration policy, but most important were micro-economic concerns, such as housing affordability, the cost of living, healthcare, and job-market uncertainties.[141][207] Housing affordability is a key political issue for young Canadians, regardless of where they live, urban, suburban, or rural Canada. Because clear majorities are in favor of government interventionism, they generally tolerate deficit spending.[141] In the United Kingdom, according to a YouGov poll conducted right before the referendum on the possible departure of the U.K. from the European Union (Brexit), almost three quarters of voters aged 18 to 24 opposed leaving the E.U. while just under one fifth supported leaving. Meanwhile, 34% of pensioners wanted to remain and 59% wanted to leave.[222] Older people were more likely to vote.[223] By analyzing polling data, the Wall Street Journal found that 19% of voters aged 18 to 24 either did not vote or were unsure, as did 17% of voters aged 25 to 49. Meanwhile, 10% of voters aged 50 to 64 and 6% of voters aged 65 and over abstained or were undecided. Overall, 52% of British voters chose to leave and 48% to remain in the E.U.[224] A Safe Space America vehicle in 2016, which is used to promote the availability and creation of safe spaces Neil Howe believes that a defining trait of millennials is that they are more likely to support political correctness than members of older generations.[225] In 2015, a Pew Research study found 40% of millennials in the United States supported government restriction of public speech offensive to minority groups. Support for restricting offensive speech was lower among older generations, with 27% of Gen Xers, 24% of Baby Boomers, and only 12% of the Silent Generation supporting such restrictions. Pew Research noted similar age related trends in the United Kingdom, but not in Germany and Spain, where millennials were less supportive of restricting offensive speech than older generations. In France, Italy and Poland no significant age differences were observed.[226] In the U.S. and UK, millennials have brought changes to higher education via drawing attention to microaggressions and advocating for implementation of safe spaces and trigger warnings in the university setting. Critics of such changes have raised concerns regarding their impact on free speech, asserting these changes can promote censorship, while proponents have described these changes as promoting inclusiveness.[225][227][228] Millennials that have, or are, serving in the military may have drastically different views and opinions than their non-veteran counterparts.[229] Because of this, some don't identify with their generation;[230] this coincides with most millennials having a lack of exposure and knowledge of the military, yet trust its leadership.[231] Yet, the view of some senior leadership of serving millennials are not always positive.[232] Gallup polls conducted in 2019 revealed that 62% of people aged 18 to 29—older members of Generation Z and younger Millennials—support giving women access to abortion while 33% opposed. In general, the older someone was, the less likely that they supported abortion. 56% of people aged 65 or over did not approve of abortion compared to 37% who did. (See chart to the right.) Gallup found in 2018 that nationwide, Americans are split on the issue of abortion, with equal numbers of people considering themselves "pro-life" or "pro-choice", 48%.[233] Polls conducted by Gallup and the Pew Research Center found that support for stricter gun laws among people aged 18 to 29 and 18 to 36, respectively, is statistically no different from that of the general population. According to Gallup, 57% of Americans are in favor of stronger gun control legislation.[234] In a 2017 poll, Pew found that among the age group 18 to 29, 27% personally owned a gun and 16% lived with a gun owner, for a total of 43% living in a household with at least one gun. Nationwide, a similar percentage of American adults lived in a household with a gun (41%).[235] According to a 2019 CBS News poll on 2,143 U.S. residents, 72% of Americans 18 to 44 years of age — Generations X, Y (Millennials), and Z — believed that it is a matter of personal responsibility to tackle climate change while 61% of older Americans did the same. In addition, 42% of American adults under 45 years old thought that the U.S. could realistically transition to 100% renewable energy by 2050 while 29% deemed it unrealistic and 29% were unsure. Those numbers for older Americans are 34%, 40%, and 25%, respectively. Differences in opinion might be due to education as younger Americans are more likely to have been taught about climate change in schools than their elders.[236] As of 2019, only 17% of electricity in the U.S. is generated from renewable energy, of which, 7% is from hydroelectric dams, 6% from wind turbines, and 1% solar panels. There are no rivers for new dams. Meanwhile, nuclear power plants generate about 20%, but their number is declining as they are being deactivated but not replaced.[237] Harvard University's Institute of Politics Youth Poll asked voters aged 18 to 29 – younger millennials and the first wave of Generation Z – what they would like to be priorities for U.S. foreign policy. They found that the top issues for these voters were countering terrorism and protecting human rights (both 39%), and protecting the environment (34%). Preventing nuclear proliferation and defending U.S. allies were not as important to young American voters. The Poll found that support for single-payer universal healthcare and free college dropped, down 8% to 47% and down 5% to 51%, respectively, if cost estimates were provided.[238] ## Preferred modes of transportation Only relatively wealthy millennials can afford to live in large cities where they do not need a car. Pictured: Lower Manhattan from Governors Island. Millennials in the U.S. were initially not keen on getting a driver's license or owning a vehicle thanks to new licensing laws and the state of the economy when they came of age, but the oldest among them have already begun buying cars in great numbers. In 2016, Millennials purchased more cars and trucks than any living generation except the Baby Boomers; in fact, Millennials overtook Baby Boomers in car ownership in California that year.[239] A working paper by economists Christopher Knittel and Elizabeth Murphy then at the Massachusetts Institute of Technology and the National Bureau of Economic Research analyzed data from the U.S. Department of Transportation's National Household Transportation Survey, the U.S. Census Bureau, and American Community Survey in order to compare the driving habits of the Baby Boomers, Generation X, and the oldest millennials (born between 1980 and 1984). That found that on the surface, the popular story is true: American Millennials on average own 0.4 fewer cars than their elders. But when various factors – including income, marital status, number of children, and geographical location – were taken into account, such a distinction ceased to be. In addition, once those factors are accounted for, millennials actually drive longer distances than the Baby Boomers. Economic forces, namely low gasoline prices, higher income, and suburban growth, result in millennials having an attitude towards cars that is no different from that of their predecessors. An analysis of the National Household Travel Survey by the State Smart Transportation Initiative revealed that higher-income millennials drive less than their peers probably because they are able to afford the higher costs of living in large cities, where they can take advantage of alternative modes of transportation, including public transit and ride-hailing services.[240] According to the Pew Research Center, young people are more likely to ride public transit. In 2016, 21% of adults aged 18 to 21 took public transit on a daily, almost daily, or weekly basis. By contrast, this number of all U.S. adults was 11%.[241] Nationwide, about three quarters of American commuters drive their own cars.[242] Also according to Pew, 51% of U.S. adults aged 18 to 29 used a ride-hailing service such as Lyft or Uber in 2018 compared to 28% in 2015. That number for all U.S. adults were 15% in 2015 and 36% in 2018. In general, ride-hailing service users tend to be urban residents, young (18-29), university graduates, and high income earners ($75,000 a year or more).[243]
Urban researcher Richard Florida and his colleague Charlotta Mellander studied data from the American Community Survey's five-year estimates for 2017 covering all 382 U.S. metropolitan areas and developed a Metro Car-free Index based on the percentages of households that do not own a vehicle, and of commuters who ride public transit, bike, or walk to work. They found that the largest clusters of metropolitan areas in which it was feasible to not own a car were the Northeast Corridor (Boston to Washington, D.C.) and the Pacific Northwest Corridor (Seattle to Portland, Oregon). Outside of these, there were Chicagoland and Los Angeles County. All of these places were densely populated with high costs of living. Mellander discovered that living in a car-free metropolitan area was positively correlated with having university degrees (.54), and being a member of the creative class (.48), while negatively correlated with being a member of the working class (.45). (Correlation does not mean causation.)[244]
## Religious beliefs
In the U.S., millennials are the least likely to be religious when compared to older generations.[245] There is a trend towards irreligion that has been increasing since the 1940s.[246] 29 percent of Americans born between 1983 and 1994 are irreligious, as opposed to 21 percent born between 1963 and 1981, 15 percent born between 1948 and 1962 and only 7 percent born before 1948.[247] A 2005 study looked at 1,385 people aged 18 to 25 and found that more than half of those in the study said that they pray regularly before a meal. One-third said that they discussed religion with friends, attended religious services, and read religious material weekly. Twenty-three percent of those studied did not identify themselves as religious practitioners.[248] A Pew Research Center study on millennials shows that of those between 18–29 years old, only 3% of these emerging adults self-identified as "atheists" and only 4% self-identified as "agnostics". Overall, 25% of millennials are "Nones" and 75% are religiously affiliated.[249]
Over half of millennials polled in the United Kingdom in 2013 said they had "no religion nor attended a place of worship", other than for a wedding or a funeral. 25% said they "believe in a God", while 19% believed in a "spiritual greater power" and 38% said they did not believe in God nor any other "greater spiritual power". The poll also found 41% thought religion was "the cause of evil" in the world more often than good.[86] The British Social Attitudes Survey found that 71% of British 18–24 year-olds were not religious, with just 3% affiliated to the once-dominant Church of England.[250]
## Social tendencies
A 2013 joint study by sociologists at the University of Virginia and Harvard University found that the decline and disappearance of stable full-time jobs with health insurance and pensions for people who lack a college degree has had profound effects on working-class Americans, who now are less likely to marry and have children within marriage than those with college degrees.[251] Data from a 2014 study of U.S. millennials revealed over 56% of this cohort considers themselves as part of the working class, with only approximately 35% considering themselves as part of the middle class; this class identity is the lowest polling of any generation.[252]
In March 2014, the Pew Research Center issued a report about how "millennials in adulthood" are "detached from institutions and networked with friends."[253][254] The report said millennials are somewhat more upbeat than older adults about America's future, with 49% of millennials saying the country's best years are ahead, though they're the first in the modern era to have higher levels of student loan debt and unemployment.
Research by the Urban Institute conducted in 2014, projected that if current trends continue, millennials will have a lower marriage rate compared to previous generations, predicting that by age 40, 31% of millennial women will remain single, approximately twice the share of their single Gen X counterparts. The data showed similar trends for males.[255][256] A 2016 study from Pew Research showed millennials delay some activities considered rites of passage of adulthood with data showing young adults aged 18–34 were more likely to live with parents than with a relationship partner, an unprecedented occurrence since data collection began in 1880. Data also showed a significant increase in the percentage of young adults living with parents compared to the previous demographic cohort, Generation X, with 23% of young adults aged 18–34 living with parents in 2000, rising to 32% in 2014. Additionally, in 2000, 43% of those aged 18–34 were married or living with a partner, with this figure dropping to 32% in 2014. High student debt is described as one reason for continuing to live with parents, but may not be the dominant factor for this shift as the data shows the trend is stronger for those without a college education. Richard Fry, a senior economist for Pew Research said of millennials, "they're the group much more likely to live with their parents," further stating that "they're concentrating more on school, careers and work and less focused on forming new families, spouses or partners and children".[257][258]
According to a cross-generational study comparing millennials to Generation X conducted at Wharton School of Business, more than half of millennial undergraduates surveyed do not plan to have children. The researchers compared surveys of the Wharton graduating class of 1992 and 2012. In 1992, 78% of women planned to eventually have children dropping to 42% in 2012. The results were similar for male students. The research revealed among both genders the proportion of undergraduates who reported they eventually planned to have children had dropped in half over the course of a generation.[259][260][261]
## Sports and fitness
Säpojoggen jogging event in Sweden
Fewer American millennials follow sports than their Generation X predecessors,[262] with a McKinsey survey finding that 38 percent of millennials in contrast to 45 percent of Generation X are committed sports fans.[263] However, the trend is not uniform across all sports; the gap disappears for National Basketball Association, Ultimate Fighting Championship, English Premier League and college sports.[262] For example, a survey in 2013 found that engagement with mixed martial arts had increased in the 21st century and was more popular than boxing and wrestling for Americans aged 18 to 34 years old, in contrast to those aged 35 and over who preferred boxing.[264] In the United States, while the popularity of American football and the National Football League has declined among millennials, the popularity of Association football and Major League Soccer has increased more among millennials than for any other generation, and as of 2018 was the second most popular sport among those aged 18 to 34.[265][266] The other popular activities included outdoor jogging or running.[267]
The Physical Activity Council's 2018 Participation Report found that in the U.S., millennials were more likely than other generations to participate in water sports such as stand up paddling, board-sailing and surfing. According to the survey of 30,999 Americans, which was conducted in 2017, approximately half of U.S. millennials participated in high caloric activities while approximately one quarter were sedentary. The 2018 report from the Physical Activity Council found millennials were more active than Baby Boomers in 2017. Thirty-five percent of both millennials and Generation X were reported to be "active to a healthy level", with Millennial's activity level reported as higher overall than that of Generation X in 2017.[268][269][270]
According to a 2018 report from Cancer Research UK, millennials in the United Kingdom are on track to have the highest rates of overweight and obesity, with current data trends indicating millennials will overtake the Baby boomer generation in this regard, making millennials the heaviest generation since current records began. Cancer Research UK reports that more than 70% of millennials will be overweight or obese by ages 35–45, in comparison to 50% of Baby boomers who were overweight or obese at the same ages.[271][272][273]
## Workplace attitudes
In 2010 the Journal of Business and Psychology, contributors Myers and Sadaghiani find millennials "expect close relationships and frequent feedback from supervisors" to be a main point of differentiation.[274] Multiple studies observe millennials’ associating job satisfaction with free flow of information, strong connectivity to supervisors, and more immediate feedback.[274] Hershatter and Epstein, researchers from Emory University, argue a lot of these traits can be linked to millennials entering the educational system on the cusp of academic reform, which created a much more structured educational system.[275] Some argue in the wake of these reforms, such as the No Child Left Behind Act, millennials have increasingly sought the aid of mentors and advisers, leading to 66% of millennials seeking a flat work environment.[275]
Hershatter and Epstein also stress a growing importance on work-life balance. Studies show nearly one-third of students' top priority is to "balance personal and professional life".[275] The Brain Drain Study shows nearly 9 out of 10 millennials place an importance on work-life balance, with additional surveys demonstrating the generation to favor familial over corporate values.[275] Studies also show a preference for work-life balance, which contrasts to the Baby Boomers' work-centric attitude.[274]
Volunteers assisting with recovery on the Gulf Coast after Hurricane Katrina
Data also suggests millennials are driving a shift towards the public service sector. In 2010, Myers and Sadaghiani published research in the Journal of Business and Psychology stating heightened participation in the Peace Corps and AmeriCorps as a result of millennials, with volunteering being at all-time highs.[274] Volunteer activity between 2007 and 2008 show the millennial age group experienced almost three-times the increase of the overall population, which is consistent with a survey of 130 college upperclassmen depicting an emphasis on altruism in their upbringing.[274] This has led, according to a Harvard University Institute of Politics, six out of ten millennials to consider a career in public service.[274]
The 2014 Brookings publication shows a generational adherence to corporate social responsibility, with the National Society of High School Scholars (NSHSS) 2013 survey and Universum's 2011 survey, depicting a preference to work for companies engaged in the betterment of society.[276] Millennials' shift in attitudes has led to data depicting 64% of millennials would take a 60% pay cut to pursue a career path aligned with their passions, and financial institutions have fallen out of favor with banks comprising 40% of the generation's least liked brands.[276]
In 2008, author Ron Alsop called the millennials "Trophy Kids,"[125] a term that reflects a trend in competitive sports, as well as many other aspects of life, where mere participation is frequently enough for a reward. It has been reported that this is an issue in corporate environments.[125] Some employers are concerned that millennials have too great expectations from the workplace.[277] Some studies predict they will switch jobs frequently, holding many more jobs than Gen Xers due to their great expectations.[278] Psychologist Jean Twenge reports data suggesting there are differences between older and younger millennials regarding workplace expectations, with younger millennials being "more practical" and "more attracted to industries with steady work and are more likely to say they are willing to work overtime" which Twenge attributes to younger millennials coming of age following the financial crisis of 2007–2008.[279]
There is also a contention that the major differences are found solely between millennials and Generation X. Researchers from the University of Missouri and The University of Tennessee conducted a study based on measurement equivalence to determine if such a difference does in fact exist.[280] The study looked at 1,860 participants who had completed the Multidimensional Work Ethic Profile (MWEP), a survey aimed at measuring identification with work-ethic characteristics, across a 12-year period spanning from 1996 to 2008.[280] The results of the findings suggest the main difference in work ethic sentiments arose between the two most recent generational cohorts, Generation X and millennials, with relatively small variances between the two generations and their predecessor, the Baby Boomers.[280]
A meta study conducted by researchers from The George Washington University and The U.S. Army Research Institute for the Behavioral and Social Sciences questions the validity of workplace differences across any generational cohort. According to the researchers, disagreement in which events to include when assigning generational cohorts, as well as varied opinions on which age ranges to include in each generational category are the main drivers behind their skepticism.[281] The analysis of 20 research reports focusing on the three work-related factors of job satisfaction, organizational commitment and intent to turn over proved any variation was too small to discount the impact of employee tenure and aging of individuals.[281] Newer research shows that millennials change jobs for the same reasons as other generations—namely, more money and a more innovative work environment. They look for versatility and flexibility in the workplace, and strive for a strong work–life balance in their jobs[282] and have similar career aspirations to other generations, valuing financial security and a diverse workplace just as much as their older colleagues.[283]
## Use of digital technology
People using smartphones, devices associated with millennials
In their 2007 book, authors Junco and Mastrodicasa expanded on the work of William Strauss and Neil Howe to include research-based information about the personality profiles of millennials, especially as it relates to higher education. They conducted a large-sample (7,705) research study of college students. They found that Next Generation college students, born between 1983–1992, were frequently in touch with their parents and they used technology at higher rates than people from other generations. In their survey, they found that 97% of these students owned a computer, 94% owned a mobile phone, and 56% owned an MP3 player. They also found that students spoke with their parents an average of 1.5 times a day about a wide range of topics. Other findings in the Junco and Mastrodicasa survey revealed 76% of students used instant messaging, 92% of those reported multitasking while instant messaging, 40% of them used television to get most of their news, and 34% of students surveyed used the Internet as their primary news source.[284][285] Older millennials came of age prior to widespread usage and availability of smartphones, defined as those born 1988 and earlier, in contrast to younger millennials, those born in 1989 and later, who were exposed to this technology in their teen years.[279]
Some millennials enjoy having hundreds of channels from cable TV. However, some other millennials do not even have a TV, so they watch media over the Internet using smartphones and tablets.[286] One of the most popular forms of media use by millennials is social networking. In 2010, research was published in the Elon Journal of Undergraduate Research which claimed that students who used social media and decided to quit showed the same withdrawal symptoms of a drug addict who quit their stimulant.[287] Marc Prensky coined the term "digital native" to describe "K through college" students in 2001, explaining they "represent the first generations to grow up with this new technology."[288] Millennials are identified as "digital natives" by the Pew Research Center which conducted a survey titled "Millennials in Adulthood".[254]
Millennials use social networking sites, such as Facebook and Twitter, to create a different sense of belonging, make acquaintances, and to remain connected with friends.[289] In the PBS Frontline episode "Generation Like" there is discussion about millennials, their dependence on technology, and the ways the social media sphere is commoditized.[290]
A 2015 study found that the frequency of nearsightedness has doubled in the United Kingdom within the last 50 years. Ophthalmologist Steve Schallhorn, chairman of the Optical Express International Medical Advisory Board, noted that research have pointed to a link between the regular use of handheld electronic devices and eyestrain. The American Optometric Association sounded the alarm on a similar vein.[291] According to a spokeswoman, digital eyestrain, or computer vision syndrome, is "rampant, especially as we move toward smaller devices and the prominence of devices increase in our everyday lives." Symptoms include dry and irritated eyes, fatigue, eye strain, blurry vision, difficulty focusing, headaches. However, the syndrome does not cause vision loss or any other permanent damage. In order to alleviate or prevent eyestrain, the Vision Council recommends that people limit screen time, take frequent breaks, adjust screen brightness, change the background from bright colors to gray, increase text sizes, and blinking more often.[292]
## Offspring
As their economic prospects improve, most millennials say they desire marriage, children, and home ownership.[102] Demographer and futurist Mark McCrindle suggested the name "Generation Alpha" (or Generation ${\displaystyle \alpha }$ ) for the people born after Generation Z,[293] the offspring of millennials,[294] noting that scientific disciplines often move to the Greek alphabet after exhausting the Roman alphabet.[293] McCrindle predicted that modern electronic communication technologies will be more integrated into their lives than ever before,[293] and that Generation ${\displaystyle \alpha }$ will most likely delay standard life markers such as marriage, childbirth, and retirements, as did the few previous generations.[295] He also predicted that they will have a longer life expectancy and smaller family sizes.[296] The first wave of Generation ${\displaystyle \alpha }$ will reach adulthood by the 2030s. By that time, the human population will be about nine billion, and the world will have the highest proportion of people over 60 years of age in history,[297] meaning this demographic cohort will bear the burden of an aging population.[295]
As of 2016, there were some 11 million Millennial parents in the U.S., who gave birth to some 9,000 children each day.[298] Globally, there are some two and a half million people belonging to Generation Alpha born every week and their number is expected to reach two billion by 2025.[296]
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2019-12-07 13:08:07
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https://physics.stackexchange.com/questions/217325/can-the-surface-charge-density-be-negative-somewhere-on-the-inner-surface-of-a-s
|
# Can the surface charge density be negative somewhere on the inner surface of a spherical conductor shell?
A positive charge $q$ is located off-centre inside a conducting spherical shell. We know that the total charge on the inner surface of the shell is $-q$. Is the surface charge density negative over the entire inner surface? Or can it be positive on the far side of the inner surface if the point charge $q$ is close enough the shell so that it attracts enough negative charge to the near side?
1. Is it possible?
2. Would there be a force on the point charge, why?
3. Why the uniqueness theorem cannot be applied to suggest that the field anywhere inside the shell is $0$?
## 1 Answer
When the point charge is not at the center of the sphere, the electric field lines will not intersect the sphere at right angles. Consequently, there is an initial component of electric field along the surface of a conductor. We know this results in a force on the charge carriers inside the conductor, and these charge carriers will re-arrange until the electric field is once again perpendicular to the conductor.
At that point you have a charge concentration (positive or negative, depending on the polarity of $$q$$ and whether you are looking at the point closest to $$q$$, or furthest from it). The polarization would result in a force on $$q$$ - attracted towards the point of the sphere that it's closest to, since the charge concentration there is greatest.
There is no conflict with the uniqueness theorem. The UT only states that "if the solution meets the boundary conditions, it is the solution". And the above describes such a solution - the boundary conditions (E perpendicular to conductor surface) are met because there is a redistribution of charge.
The following diagram illustrates this:
I drew the field lines inside the sphere as straight lines initially, then attempted to show how they have to bend in order to meet the conductor surface at right angles. The only way I can think of bending the field lines at B is to have a charge of the same polarity as q on the surface. There can be no net field on the dotted surface (inside the conducting shell).
So getting down to brass tacks: "can there be a region where the surface charge is positive" (assuming that $$q$$ is positive)?
This is a question being asked on this site - and I reproduce the diagram given (for the correct answer):
The reasoning follows from the two hints supplied:
The field inside the conductor must be zero. The charge inside the shell is off-center, and hence the charge on the inner surface of the shell will arrange itself asymmetrically to cancel the field of the large positive charge.
The field inside the conductor must be zero. To the charges on the outer surface, it is as if the inside of the conductor were completely neutral. Thus, the charges on the outer surface will feel no force other than their own mutual repulsion, and will therefore have no preferred direction.
Now if you think about this, you can see that at every point where the electric field lines from $$q$$ hit the surface, you need an opposite charge to cancel the electric field - otherwise you end up with an electric field inside the conductor. And we know that can't happen. In the diagram below, $$E_1$$ and $$E_2$$ must point in opposite directions to cancel inside the conductor.
• So is it possible for the surface charge to be positive somewhere? I've changed my questions slightly. – Rescy_ Nov 9 '15 at 22:15
• Your edit changes the question in a very significant way. You didn't state that the sphere was grounded before: but that must be the case if the sphere has a total charge of $-q$ (new information). I am not sure my argument is valid for a grounded sphere - while there will be a non-uniform charge distribution, I'm not sure there will be a point where the surface charge on the surface will have the same sign as $q$. – Floris Nov 9 '15 at 22:19
• No the sphere is not grounded. It has total charge $-q$ on its inner surface and there is a total charge of $+q$ on its outer surface (it is a shell). – Rescy_ Nov 10 '15 at 5:14
• I need to improve my reading skills... – Floris Nov 10 '15 at 11:32
• Thanks for the answer...but...can there be some region of the inner surface that has positive charge density? – Rescy_ Nov 10 '15 at 22:43
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2020-10-23 21:01:39
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http://mathoverflow.net/questions/103147/a-strange-question-about-closed-geodesics-on-a-closed-manifold
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MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
## A strange question about closed geodesics on a closed manifold
I'm studying a particular kind of curve evolution on Riemannian manifolds. It would help me to know the answer to the following kinda weird question:
Does there exist a closed Riemannian manifold $M$ and a pair of distinct closed geodesics $\gamma, \alpha$ in $M$ satisfying the follow properties?
(1) $\gamma$ and $\alpha$ are of the same length. (Call the length $l$.)
(2) $\gamma$ is isolated in the space of loops of length $l$.
(3) For any $\varepsilon>0$, there exists a path of loops, each of length between $l$ and $l+\varepsilon$, starting at $\gamma$ and ending at $\alpha$.
I suspect (and hope) that the answer is no.
Details: The loop space I'm working with is $C^0(S^1,M)$ with the compact-open topology. In (2), I mean that $\gamma$ has a neighborhood in the loop space in which the only loops of length $l$ are reparameterizations of $\gamma$. The path in (3) of course has to be a path of rectifiable loops.
Thanks,
Dmitri
-
Define the distance between curves as $$d(\gamma,\gamma')=\inf_h\sup_x|\gamma'(x)-\gamma\circ h(x)|,$$ where $h:\mathbb S^1\to\mathbb S^1$ is reparametrization. Fix small $\delta$ so that if $d(\gamma,\gamma')\le \delta$ and $\mathop{\rm length}\gamma=\mathop{\rm length}\gamma'$ then $\gamma'=\gamma\circ h$ for some $h$. Fix $\varepsilon>0$ a choose the path $\gamma_t$. Choose the smallest value $t$ such that $d(\gamma,\gamma_t)=\delta$ and set $\beta_\varepsilon=\gamma_t$. You may assume that $\beta_\varepsilon$ has unit-speed parametrization, in particular they all uniformly Lipschitz. Pass to partial limit as $\varepsilon\to 0$ and that is it.
@Anton Petrunin: How exactly are you choosing the paths $\gamma_t$? Without specifying this, I don't understand how you can say "Choose the smallest value of $t$ such that $d(\gamma, \gamma_t)=\delta$." Also, it's been a while since I took a differential geometry course, but this questions seems much too hard for a standard HW exercise. – Aaron Trout Jul 26 at 13:57 @Aaron, The path $\gamma_t$ is given in (3). – Anton Petrunin Jul 26 at 14:25 @Anton Petrunin Thanks for your answer! It's not a homework problem, but you're right that I should have thought about the question a bit harder before asking on MO. I guess it's not as difficult as I expected. I don't know why your answer was downvoted. – Dmitri Gekhtman Jul 26 at 15:02 Passing to the limit one gets a loop located at a distance $\delta$ from $\gamma$. By the semicontinuity it has a lenght less than or equal to $l$. But why is it exactly $l$? – Pietro Majer Jul 26 at 20:54 @Pietro, you can always make it longer, say by composing with a zig-zag $\mathbb{S}^1\to\mathbb{S}^1$. – Anton Petrunin Jul 26 at 23:13
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2013-06-19 22:40:09
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https://quant.stackexchange.com/questions/42960/does-the-asian-option-average-option-depend-on-the-forward-implied-vol
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# Does the Asian Option (average Option) depend on the forward implied vol
I can easily understand that the forward starting Option and Barrier Option depend on the forward implied vol smile at resetting date, so we always choose the stochastic vol model for underlying to control the forward vol.
Does the Asian Option (discrete arithmetic araverage) also depend on the forward implied vol? And it seems each path dependent Option depends on the forward implied vol.
Can anyone give me a clear explaination?
• First, I presume you mean a continuously observed barrier option? And second, I would say that you can have path dependence without forward vol dependence if each of the observations are independent. That's not a required property, but just intuitively and only thinking for a few minutes it seems like it could be sufficient. – will Dec 9 '18 at 9:58
• @will 1. I think even there is only one observed point of barrier option, it still depends on the forward vol (vol smile at observation point). 2. How do you define independent obseevation? Is Asian option independent observations? Since observation $S_{T_2}$ will depend on the observation value $S_{T_1}$ and the vol smile at $T_1$ if $T_2>T_1.$ – user6703592 Dec 9 '18 at 10:17
• if the barrier observation. Is the same as the option expiry then the price can be replicated using vanillas and you don't need information on the forward/conditional volatility. – will Dec 11 '18 at 6:48
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2019-05-20 08:27:59
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https://www.adamnsmith.com/MSIN0010/sampling-distributions-and-the-clt.html
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# Chapter 3 Sampling Distributions and the CLT
Sampling distributions are theoretical objects that represent the probability distribution of a statistic (usually the sample mean).
The sampling distribution of the sample mean is the distribution of means that result from taking all possible samples of size $$n$$ from the population.
We can build some intuition for what this means in R.
Let’s start by letting the population distribution be normal with mean $$\mu=0$$ and variance $$\sigma^2=1$$. We can take a sample of size $$n=100$$ from that population and plot the sample distribution.
x = rnorm(n=100, mean=0, sd=1)
mean(x)
## [1] 0.008768
hist(x, main="Sample Distribution")
While we cannot generate all possible samples of size $$n$$ from this normal distribution, we can take a large number.
Let $$R=100,000$$ be the number of samples we want to generate. We will construct a for loop in R to do the following: (1) generate a random sample of size $$n$$ from the population; (2) compute the sample mean and store the result in a vector called xbar.
R = 100000
xbar = double(R)
for(r in 1:R){
x = rnorm(n=100, mean=0, sd=1)
xbar[r] = mean(x)
}
hist(xbar, main="Sampling Distribution of Xbar")
This plot is the distribution of sample means after taking $$R=100,000$$ samples with size $$n=100$$ from the population.
Notice that this again looks like a normal distribution. The mean looks the same as the distribution of $$X$$, but the variance looks much smaller.
In fact, when the population distribution is $$N(\mu,\sigma^2)$$, then the distribution of $$\bar{X}$$ is $$N(\mu,\sigma^2/n)$$. In this case, we know that $$E(\bar{X})=E(X)=\mu=0$$ and $$Var(\bar{X})=Var(X)/n=\sigma^2/n=1/100=0.01$$.
Let’s check to see what the mean and variance are in our approximation of the sampling distribution.
mean(xbar)
## [1] 0.0004032
var(xbar)
## [1] 0.009978
Very close to the true values!
The next question to consider is what if our population distribution was not normally distributed? What if it was skewed to the right or left?
Let’s assume $$X$$ has a Exponential$$(\beta)$$ distribution where $$\beta=1$$ is a rate parameter. We can again take one individual sample from this population distribution.
x = rexp(n=100, rate=1)
hist(x, main="Sample Distribution")
Based on this sample, it appears that the population distribution is highly asymmetric and skewed to the right.
In this case, should we still expect the sampling distribution of the sample mean to be normal? Let’s go through the same exercise as before.
R = 100000
xbar = double(R)
for(r in 1:R){
x = rexp(n=100, rate=1)
xbar[r] = mean(x)
}
hist(xbar, main="Sampling Distribution of Xbar")
The distribution of sample means again looks normal!
In fact, the Central Limit Theorem guarantees that this will be the case as the sample size $$n$$ gets large. Then for any population distribution, we know that the distribution of $$\bar{X}$$ will be approximately normal with mean $$E(\bar{X})=E(X)$$ and $$Var(\bar{X})=Var(X)/n$$.
Since $$X\sim\text{Exponential}(\beta)$$ with $$\beta=1$$, it can be shown that $$E(X)=\beta=1$$ and $$Var(X)=\beta^2=1$$. Therefore, $$\bar{X}$$ is approximately normal with mean $$E(\bar{X})=E(X)=1$$ and variance $$Var(\bar{X})=Var(X)/n=1/100=0.01$$.
We again check these results using our approximate sampling distribution and find consistent answers.
mean(xbar)
## [1] 1
var(xbar)
## [1] 0.01004
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2020-05-25 05:48:27
|
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https://mathhothouse.me/2014/08/18/polynomials-commuting-cubics-and-quartics/
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## Polynomials — commuting and cubics
Let us start delving deeper in Algebra. But, I will be providing only an outline to you in the present article. I encourage you to fill in the details. This is a well-known way to develop mathematical aptitude/thinking. (This method of learning works even in Physics and esoteric/hardcore programming).
Definition. Commuting polynomials. Two polynomials are said to commute under composition if and only if $(p \circ q)(t)=(q \circ p)(t)$
(i.e., $p(q(t)=q(p(t)))$). We define the composition powers of a polynomial as follows
$p^{(2)}(t)=p(p(t))$
$p^{(3)}(t)=p(p(p(t)))$
and in general, $p^{(k)}(t)=p(p^{(k-1)}(t)$ for $k=2,3 \ldots$
Show that any two composition powers of the same polynomial commute with each other.
One might ask whether two commuting polynomials must be composition powers of the same polynomial. The answer is no. Show that any pair of polynomials in the following two sets commute
I. ${t^{n}: n=1,2 \ldots}$
II. ${T^{n}(t):n=1,2 \ldots}$
Let a and b be any constants with a not equal to zero. Show that, if p and q are two polynomials which commute under composition, then the polynomials
$(t/a-b/a) \circ p \circ (at+b)$ and $(t/a-b/a) \circ q \circ (at+b)$ also commute under the composition. Use this fact to find from sets I and II other families which commute under composition.
Can you find pairs of polynomials not comprised in the foregoing discussion which commute under composition? Find families of polynomials which commute under composition and within which there is exactly one polynomial of each positive degree.
The Cubic Equation. Cardan’s Method. An elegant way to solve the general cubic is due to Cardan. The strategy is to replace an equation in one variable by one in two variables. This provides an extra degree of freedom by which we can impose a convenient second constraint, allowing us to reduce the problem to that of solving a quadratic.
(a) Suppose the given equation is $t^{3}+pt+q=0$. Set $t=u+v$ andn obtain the equation $u^{3}+v^{3}+(3uv+p)(u+v)+q=0$.
Impose the second condition $3uv+p=0$ (why do we do this?) and argue that we can obtain solutions for the cubic by solving the system
$u^{3}+v^{3}=-q$
$uv = -p/3$
(b) Show that $u^{3}$ and $v^{3}$ are roots of the quadratic equation
$x^{2}+qx-p^{3}/27=0$
(c) Let $D=27q^{2}+4p^{3}$. Suppose that p and q are both real and that $D>0$. Show that the quadratic in (b) has real solutions, and that if
$u_{0}$ and $v_{0}$ are the real cubic roots of these solutions, then the system in (a) is satisfied by
$(u,v)=(u_{0},v_{0}), (u_{0}\omega, v_{0}\omega^{2}), (u_{0}\omega^{2}, v_{0}\omega)$
where $\omega$ is the imaginary cube root $(0.5)(-1+\sqrt{-3})$ of unity. Deduce that the cubic polynomial $t^{3}+pt+q$ has one real and two nonreal zeros.
(d) Suppose that p and q are both real and that $D=0$. Let $u_{0}$ be the real cube root of the solution of the quadratic in (b). Show that, in this case, the cubic has all its zeros real, and in fact can be written in the form
$sy^{2}$ where $y=(t+u_{0})$ and $s=t-2u_{0}$
(e) Suppose that p and q are both real and that $D<0$. Show that the solutions of the quadratic equation in (b) are nonreal complex conjugates, and that it is possible to choose cube roots u and v of these solutions which are complex conjugates and satisfy the system in (a). If
$u=r(cos \theta + isin \theta)$ and $v=r(cos \theta - isin \theta)$, show that the three roots of the cubic equation are the reals
$2r cos \theta$
$2r cos (\theta + (2/3)\pi)$
$2r cos(\theta + (4/3)\pi)$.
(f) Prove that every cubic equation with real coefficients has at least one real root.
Use Cardan’s Method to solve the cubic equation.
(a) $x^{3}-6x+9=0$
(b) $x^{3}-7x+6=0$.
Part (b) above will require the use of a pocket calculator and some trigonometry. You will also need De Moivre’s Theorem and give a solution to an accuracy of 3 decimal places.
More later…
-Nalin
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2021-07-26 17:22:02
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https://www.physicsforums.com/threads/chain-rule.294135/
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Chain rule
-EquinoX-
1. The problem statement, all variables and given/known data
Find $$\frac{\partial z}{\partial u}$$ and $$\frac{\partial z}{\partial v}$$ using the chain rule.
$$z = \arctan(\frac{x}{y}) , x=u^2+v^2 , y=u^2-v^2$$
2. Relevant equations
3. The attempt at a solution
$$\frac{\partial z}{\partial u} = \frac{4uv^2}{v^4 - 2u^2v^2 + u^4} * \frac{1}{1+((u^2+v^2)/(u^2-v^2))^2)}$$
$$\frac{\partial z}{\partial v} = \frac{4u^2v}{v^4 - 2u^2v^2 + u^4} * \frac{1}{(1+((u^2+v^2)/(u^2-v^2))^2)}$$
Last edited:
Tom Mattson
Staff Emeritus
Gold Member
Are we supposed to guess at what steps are written on your paper?
Dick
Homework Helper
For one thing d(arctan(x))/dx=1/(1+x^2). I think you missed the square.
-EquinoX-
oh you're right, I missed the squares, but it is still wrong
Dick
Homework Helper
Tom Mattson is right. It would be a lot easier to say what is wrong if you would show what you've done. Just showing a wrong answer and saying 'what did I do wrong?' is more of a puzzle than a question. I don't think you've done much wrong. I get a different sign for dz/du and you could certainly simplify them more.
-EquinoX-
well I think the problem here is just from taking the derivative of
$$\frac{u^2+v^2}{u^2-v^2}$$ with respect to u, right. I realize that there should be a - sign in front of it.. am I right?
Dick
Homework Helper
Yes. But like I said you can also simplify those expressions a lot. I don't know if the HW checker requires this or not.
-EquinoX-
the best simplification I can think of is:
$$\frac{-4uv}{(u^2-v^2)^2+(u^2+v^2)^2}$$
Last edited:
Dick
Homework Helper
Do you mean -4uv/((u^2-v^2)^2+(u^2+v^2)^2)?? I can write that in less space.
-EquinoX-
Yes that's what I meant
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2019-03-26 00:43:41
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https://wikimho.com/us/q/security/48022
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### What kinds of encryption are _not_ breakable via Quantum Computers?
• There's the recent article NSA seeks to build quantum computer that could crack most types of encryption. Now I'm not surprised by the NSA trying anything1, but what slightly baffles me is the word "most" - so, what encryption algorithms are known and sufficiently field-tested that are not severely vulnerable to Quantum Computing?
1) Yup, I wouldn't even be surprised if they had a secret department of fortune telling...
Best to use OTP -in real world and for the virtual world use symmetric algorithms + 256bit keys. look at this http://www.theguardian.com/world/2013/sep/05/nsa-how-to-remain-secure-surveillance
Quantum computers are still a ways off. The concept relies on using bits, that when unobserved, are both 1 and 0 and so able to calculate with all the values that can be represented in the given space -- with one calculation. As romantic as this sounds, I have yet to hear of a way to calculate with this bits while leaving them unobserved.
Don't assume that just because an organization the size of the NSA is trying to build something that they expect to successfully deploy one anytime soon. Because arms-races are races, often an organization will research something because they don't want to be just starting out when their competitors are deploying one. If the NSA builds up a brain-trust of people who know about quantum computing then they might be able to deploy one ahead of their competitors, and are less likely to be caught flat-footed.
My concern is not the NSA, who might just as well use some less pleasant meatworld methods to obtain one's secrets, but rather the implications of QC in general
Why wouldn't quantum computers also enable correspondingly stronger encryption?
@mirimir Who claimed that? Of course there's Quantum Cryptography, but even once available not everyone will be able to afford it I assume, so it's still important to know what classical encryption one can rely upon even if potential eavesdroppers have Quantum Computers
@November Slightly modifying this nice Gedankenexperiment, assume a friend of yours went outside before it got cold. Neither you or they know how many gloves (if any) they took with them, but both know where the remaining ones would be; and that, due to the severe cold, your friend would return home for the remaining glove(s) once they noticed some were missing. Assume the same for a friend your friend wanted to meet outside. Now observe whether some of their gloves are at home - and voilà you can determine whether they met outside or come home
@November Your knowledge is outdated. Computations on qbits *have* been performed. Just not very many. But there’s nothing “romantic” about this concept, it’s been demonstrated in practice.
Thanks for correcting me. This is very exciting, do you have a link that explains this more in-depth?
@November This just came out: http://arxiv.org/pdf/1512.02206v1.pdf It is a bit technical and requires a quite a bit of knowledge to be usable, but I guess most people here are :-)
• As usual, journalism talking about technical subjects tends to be fuzzy about details...
Assuming that a true Quantum Computer can be built, then:
• RSA, and other algorithms which rely on the hardness of integer factorization (e.g. Rabin), are toast. Shor's algorithm factors big integers very efficiently.
• DSA, Diffie-Hellman ElGamal, and other algorithms which rely on the hardness of discrete logarithm, are equally broken. A variant of Shor's algorithm also applies. Note that this is true for every group, so elliptic curve variants of these algorithms fare no better.
• Symmetric encryption is weakened; namely, a quantum computer can search through a space of size 2n in time 2n/2. This means that a 128-bit AES key would be demoted back to the strength of a 64-bit key -- however, note that these are 264 quantum-computing operations; you cannot apply figures from studies with FPGA and GPU and blindly assume that if a quantum computer can be built at all, it can be built and operated cheaply.
• Similarly, hash function resistance to various kind of attacks would be similarly reduced. Roughly speaking, a hash function with an output of n bits would resist preimages with strength 2n/2 and collisions up to 2n/3 (figures with classical computers being 2n and 2n/2, respectively). SHA-256 would still be as strong against collisions as a 170-bit hash function nowadays, i.e. better than a "perfect SHA-1".
So symmetric cryptography would not be severely damaged if a quantum computer turned out to be built. Even if it could be built very cheaply actual symmetric encryption and hash function algorithms would still offer a very fair bit of resistance. For asymmetric encryption, though, that would mean trouble. We nonetheless know of several asymmetric algorithms for which no efficient QC-based attack is known, in particular algorithms based on lattice reduction (e.g. NTRU), and the venerable McEliece encryption. These algorithms are not very popular nowadays, for a variety of reasons (early versions of NTRU turned out to be weak; there are patents; McEliece's public keys are huge; and so on), but some would still be acceptable.
Study of cryptography under the assumption that efficient quantum computers can be built is called post-quantum cryptography.
Personally I don't believe that a meagre 80 millions dollars budget would get the NSA far. IBM has been working on that subject for decades and spent a lot more than that, and their best prototypes are not amazing. It is highly plausible that NSA has spent some dollars on the idea of quantum computing; after all, that's their job, and it would be a scandal if taxpayer money did not go into that kind of research. But there is a difference between searching and finding...
+1, and wish I could give you +10 just for the last two sentences. With all the scandals about their abuses it's sometimes easy to forget that when all's said and done being able to spy on people is their *job* and what we're objecting to is their lack of restraint when doing it...
+1 - Of course you might consider that with 80 million dollars, the NSA could just hire goons to beat private keys out of most targets... Then again they could have forced IBM and others to "volunteer" in providing their most secret research progress so far
@Thomas Pornin Is the complexity of searching a space decreased due to the uncertainty principle? I might be way off.....
@Rell3oT: the idea is that a qubit is a superposition of several states, and thus, _to some extent_, with one operation, several computations are done simultaneously. The uncertainty principle is another, rather unrelated expression of the fact that at the quantum level, what we think of as "matter" actually behaves like a probability distribution.
Okay Thank you @ThomasPornin . What you described is what I thought the uncertainty principle was. Apparently I need to brush up...
Don't all this mean that if RSA can be broken that all TLS sessions with certificates are essentially broken as RSA is used to negotiate a symmetric key at the beginning of the session? Can we still have PFS?
@Rell3oT Uncertainty boils down to that it is not sufficient to exploit the superposition of states but that you have to do it in a way that you can afterwards measure the entire result without changing the already measured part of it - e.g. if one bit were encoded in the x-coordinate and another one in that direction's momentum, you might still be screwed since measuring momentum (sufficiently precise) will _retroactively_ change the x-coordinate (maximum possible precision) you just measured and vice versa. Btw, check out http://physics.stackexchange.com ;)
@Matrix RSA (or DSA) is used for the server to identify itself, the key negotiation uses Diffie-Hellman. But since that relies on the discrete logarithm just as DSA does, I guess it is just as vulnerable to Quantum Computing. However I'd be surprised if there weren't a way to use/modify the less QC-vulnerable methods for PFS
And what if the encryption was done on a quantum computer as well?
@Jojo01: I think some encryption algorithms designed to run on quantum computers have been defined (I don't recall the details at the moment). They should resist attackers with quantum computers, but they also require a quantum computer to be used at all, and given the lack of availability of quantum computers right now, we cannot test them. Let's say they are an interesting intellectual construction that _might_ be useful in a future world where every single computer and smartphone is a quantum computer.
@ThomasPornin Yeah, i think that quantum computing will improve account security, because the big companies will most likely be using quantum computers, that your typical hacker doesn't have. Of course when quantum computing gets to consumer lever, that advantage is lost and the situation goes back to zero.
What about Serpent? I've read it won't be affected either.
@skan: Serpent is a symmetric encryption algorithm; what I say about AES applies equally well to Serpent. In effect, it means that Serpent encryption with a 128-bit key could be broken with about 2^64 operations on a quantum computer (2^64 is already a very substantial amount on a classical computer).
Having dealt with IBM a lot, it's my suspicion that they developed a quantum computer decades ago, but nobody can find the link for it on their website.
"note that these are $2^64$ quantum-computing operations": also these operations must be sequential, meaning that your quantum computer has to be really fast ($2^64$ nanoseconds > 500 years). With $K$ parallel quantum computers you get a small speed up, but you still need time $\frac{2^64}{\sqrt{K}}$. See https://quantumcomputing.stackexchange.com/a/4538/5047
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2021-12-03 06:48:28
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https://zbmath.org/?q=an:0575.30019
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# zbMATH — the first resource for mathematics
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On some classes of first-order differential subordinations. (English) Zbl 0575.30019
The paper contains several results of the following type: Theorem. Let h be analytic in $U=\{z:$ $\vert z\vert <1\}$, let $\phi$ be analytic in a domain D containing h(U) and suppose a) Re $\phi$ (h(z))$>0$, $z\in U$ and either b) h(z) is convex or b) $H(z)=zh'(z)\phi (h(z))$ is starlike w.r.t. the origin. If p is analytic in U with $p(0)=h(0)$, p(U)$\subset D$, and $$p(z)+zp'(z)\phi (p(z))\prec h(z),$$ then p(z)$\prec h(z)$. An application to univalent functions is given: Let f be analytic in U, $f(0)=0$ and either $$\vert f''(z)/f'(z)\vert \le 2\quad or\quad \vert zf''(z)/f'(z)+1\vert <2,\quad (z\in U).$$ Then f is starlike in U.
Reviewer: J.Waniurski
##### MSC:
30C45 Special classes of univalent and multivalent functions 30C80 Maximum principle; Schwarz’s lemma, Lindelöf principle, etc. (one complex variable)
##### Keywords:
differential subordination; convex; starlike
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2016-04-29 23:38:41
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http://onlinetvsoftware.net/bit-error/bit-error-rate-of-bpsk.php
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Home > Bit Error > Bit Error Rate Of Bpsk
# Bit Error Rate Of Bpsk
## Contents
The average symbol SNR s = 5A square / 2. Please help me out. If, for example, your simulation computes a symbol error rate (SER), convert the SER to a BER before using the simulation with BERTool.The following sections describe the Bit Error Rate Analysis also ,code for generating SER vs SNR curve for 3ASK modulation Reply Amjad January 10, 2010 at 12:47 pm Dear Krishna, I already ask this question please. news
This problem can be overcome by using the data to change rather than set the phase. n = 10000; % Number of symbols to process k = log2(M); % Number of bits per symbol % Convert from EbNo to SNR. % Note: Because No = 2*noiseVariance^2, we which is in thae same formate which u have taken like hS+W. Figure: Simplified block diagram with BPSK transmitter-receiver Channel Model The transmitted waveform gets corrupted by noise , typically referred to as Additive White Gaussian Noise (AWGN).
## Bpsk Probability Of Error Derivation
However, the multiuser detection problem can in general be viewed as a MIMO V-BLAST transmission scenario, where each spatial dimension acts as interferers for the other dimensions. It also compares the error rates obtained from the semianalytic technique with the theoretical error rates obtained from published formulas and computed using the berawgn function. Hence the BER performance is comparable.
I get a completely different graph, so i must be doing something wrong. This scenario is hypothetical. Reply Sivaganesh January 30, 2012 at 11:14 pm Hi Krishna, your coding's were very useful for my simulation lab works..could you please send me the comparison of various error correcting Acceptable Bit Error Rate How can I simulate the integrator?
Reply Krishna Sankar December 7, 2009 at 5:33 am @fatima: I believe it should be reasonably straightforward to modify the gaussian channel used in this post to a binary symmetric channel. Bpsk Dsplog Reply Ajith July 24, 2010 at 4:46 pm Oops i am sorry if this is a total blunder.. Assuming Es=1 for BPSK (Symbol energy normalized to 1) Eb/N0 can be represented as (using above equations), $$\frac{E_b}{N_0}=\frac{E_s}{R_m R_c N_0}$$ $$\frac{E_b}{N_0}=\frac{E_s}{R_m R_c N_0}=\frac{E_s}{R_m R_c 2 \sigma^{2}} = \frac{1}{2 R_m R_c \sigma^{2}}$$ This value is also the sampling rate of the transmitted and received signals, in Hz.
Please assist me in this. Bit Error Rate Measurement thanks Reply mrKim November 13, 2012 at 8:42 am Dear S.Alam Did you find material for this problem ? Thanks, regards, chandra Reply Krishna Sankar April 28, 2010 at 5:49 am @chandra: Sorry, no posts on DAPSK. In particular, the example compares the performance of a communication system that uses an AWGN channel and QAM modulation of different orders.Running the Theoretical ExampleOpen BERTool, and go to the Theoretical
## Bpsk Dsplog
When the signal is low-pass filtered (as is typical in a transmitter), these phase-shifts result in large amplitude fluctuations, an undesirable quality in communication systems. I have followed the same steps posted by you in "BER for BPSK in Rayleigh channel" to produce the rayleigh output and later used estimated SNR to calculate BER, so that Bpsk Probability Of Error Derivation Alternately, one can look at typical channel models available in the literature and pick one which can closely match your desired use case. Qpsk Bit Error Rate One would also need to look at the range requirement of the communication link.
Reply Krishna Sankar July 30, 2009 at 5:39 am @Hemanth: You are not correct when you mentioned that the theoretical derivation of BER in Rayleigh channel did not include the effect navigate to this website Reply Krishna Sankar November 2, 2012 at 6:43 am @Manoj: This post (and the matlab code) on BER of BPSK in AWGN is addressing most of your queries. Reply Krishna Sankar August 9, 2012 at 6:12 am @Abhijith: Nice approach. Please give me more direction, by giving me an example of what you mean by changing the VALUE of Eb_No_dB. Bit Error Rate Calculation
If i want to calculate the SNR for the signal above I would get double the SNR reported because of the factor of 2 mxm2424 Hi,I want to plot The capacity This shows the points in the complex plane where, in this context, the real and imaginary axes are termed the in-phase and quadrature axes respectively due to their 90° separation. Example: Differentially encoded BPSK Differential encoding/decoding system diagram. More about the author I tried to call the fuction from Matlab using Embedded Function Block in Simulink.
Apply a transmit filter. Bit Error Rate Pdf if the received signal is is greater than 0, then the receiver assumes was transmitted. But I can not explain why BER can not be greater than 0.5 even the distance is increased up top very large value.
## It is known that the typical RMS delay spread of multipath propagation in this scenario is around 5 s.
y = step(h,x); % Modulate. ISBN0-13-081223-4. Bit error rate Although QPSK can be viewed as a quaternary modulation, it is easier to see it as two independently modulated quadrature carriers. Bit Error Rate Tester I am unable to understand why % Demonstration of Eb/N0 Vs BER for BPSK modulation scheme data=randn(1,N)>=0; %Generating a uniformly distributed random 1s and 0s bpskModulated = 2*data-1; %Mapping 0->-1 and
in other words, i don't want to have a loop or large number of symbols to get the plot of the prob. Plot empirical results, in same figure. Planet Fox. 2014. ^ http://www.broadcom.com/products/set-top-box-and-media-processors/satellite/bcm7325 ^ "Local and Remote Modems" (PDF). click site That is, if r k {\displaystyle r_{k}} is projected onto r k − 1 {\displaystyle r_{k-1}} , the decision is taken on the phase of the resultant complex number: r k
The simulation of the communication system components using Communications System Toolbox™ is covered in other parts of this guide. Krishna, I'm trying to simulate frequency non-selective rayleigh fading channel like you did, but including the path loss (PL in dB) between two nodes. Compute the error probability of a BPSK as a function of Es/NodB (in decibel) {1; 2; 3; 4; 5; 6; 7; 8; 9; 10}. 1.What is the energy of a BPSK hold on; semilogy(EbNo,berVec(1,:),'b.'); legend('Theoretical SER','Empirical SER'); title('Comparing Theoretical and Empirical Error Rates'); hold off; This example produces a plot like the one in the following figure.
Sorry, in general. This filter is often a square-root raised cosine filter, but you can also use a Butterworth, Bessel, Chebyshev type 1 or 2, elliptic, or more general FIR or IIR filter. It also plots error bars using the output from the berconfint function.% Use BERFIT to plot the best fitted curve, % interpolating to get a smooth plot. Good luck.
i Have read here that there is no difference between BER vs SNR in case of BPSK and OFDM using BPSK. It is seen that higher-order modulations exhibit higher error-rates; in exchange however they deliver a higher raw data-rate. Reply Krishna Sankar April 14, 2010 at 4:41 am @Rebecca: Sorry, I have not discussed Rician channel Reply dolly April 13, 2010 at 2:53 pm hii sir how to get I think where we have used the EQ implicitly, is when we say the average BER is obtained by taking an expectation over the ‘old' expression for a BPSK ber, i.e.
Note: 1. Hence we model as two randn() variables each with variance 1/2. The loss for using DBPSK is small enough compared to the complexity reduction that it is often used in communications systems that would otherwise use BPSK. Additive : As the noise gets ‘added' (and not multiplied) to the received signal White : The spectrum of the noise if flat for all frequencies.
Thanks Reply Krishna Sankar March 30, 2012 at 5:38 am @filip: In most cases, there will be training sequence in the transmission which will help the receiver estimate the channel. I am new in this area and need some help from you. The modulation is impressed by varying the sine and cosine inputs at a precise time. http://www.dsplog.com/2008/09/28/maximal-ratio-combining/ Maximal Ratio Combining and bring down the BER by quite a bit.
these coefficients remain the same for the coherence time duration Reply lumingui August 11, 2009 at 12:05 pm ok.
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2018-05-26 21:35:18
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https://forum.allaboutcircuits.com/threads/equivalent-resistance.93351/
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# Equivalent Resistance
Discussion in 'Homework Help' started by zyzxzwzvz, Jan 11, 2014.
1. ### zyzxzwzvz Thread Starter New Member
Jan 11, 2014
3
0
I made up this problem, and I have been thinking about it for a few days, but I do not know if it has a solution. Looking at other posts, this problem seems more mathematically oriented. Any help would be appreciated.
Suppose that we have an unlimited supply of resistors with resistances R1 Ω and R2 Ω. Is it always possible to make a circuit with equivalent resistance R1*R2 Ω using only a finite number of such resistors? (Note that R1 and R2 can be arbitrary real numbers, such as π=3.1415...)
The problem statement seems so simple, but the problem itself is actually quite elusive. I suspect that it is not possible, since, if R1=sqrt(3) and r2=sqrt(12), we need to make a circuit with equivalent resistance 6. A construction of such a circuit using only series and parallel combinations seems highly unlikely (I have tried in vain), and expressions for more complicated circuits get messy quickly.
If possible, could someone provide such a construction? If not possible, could someone provide a (rigorous) proof or counterexample explaining why it is not possible?
Thanks!
2. ### studiot AAC Fanatic!
Nov 9, 2007
5,005
515
Welcome to AAC.
Looking at your profile I don't see where you are coming from or why this is in homework, where there are special rules. In particuar are you coming from an electrical or a maths background?
As an intellectual exercise you should note that you can never increase a resistance with parallel combinations. only decrease.
So to obtain a resistance which is a numerical multiple of R1 we must use series.
So have you explored the strategy of stacking up (R2+n) R1 resistors in series and then looking for a suitable parallel combination to bring the value back down to the desired value?
Here is a useful formula for this
If Rd is the desired value and R3 the cumulative value you have,
the required shunt to R3 to give Rd is
$\frac{{{R_3}{R_d}}}{{\left( {{R_3} - {R_d}} \right)}}$
3. ### WBahn Moderator
Mar 31, 2012
18,293
4,959
When you say that R1 and R2 can be any arbitrary real numbers, that means that they can be R1=1Ω and R2=2Ω. Since both R1 and R2 can be constructed from two of the other resistor, this effectively reduces to a set of resistors that are all 1Ω.
With such a set of resistors, you can create any resistance that is rational, but no resistances that are irrational.
You can, of course, come as close to any irrational value as you choose.
4. ### zyzxzwzvz Thread Starter New Member
Jan 11, 2014
3
0
Hello studiot, I was not sure about where to post this, but it seemed more of a homework-type question that a general electronics chat question. I come from more of a mathematical background. I am creating a problem set for a class of mine, and this is one of the problems that I thought of.
As to the strategy in your response, I have tried that, but it does not work for all choices of R1 and R2 (consider letting R1 and R2 be transcendental numbers). However, even though this strategy does not work in all cases, there may be other strategies that work in all cases, such as making delta circuits and whatnot (basically anything but series and parallel).
Hello WBahn, I guess that the question statement was unclear. Let me rephrase it this way:
Suppose that we have an unlimited supply of resistors with resistances R1 Ω and R2 Ω. Is it always possible to make a circuit with equivalent resistance R1*R2 Ω using only a finite number of such resistors, no matter the choice of R1 and R2? (Note that R1 and R2 can be arbitrary real numbers, such as π=3.1415...)
In your post, you let R1 = 1Ω and R2 = 2Ω, so the goal is to create a circuit with equivalent resistance 1*2 = 2Ω. This can easily be achieved; in fact, if al least one of R1, R2 are rational values, it will always be possible.
Here is such a construction: Let R1 = A/B and R2 = C, where A/B is in simplest terms, and C is not necessarily rational. We wish to create a circuit with equivalent resistance A*C/B. Take A resistors with resistance C and place them in series. Then take B of these series combinations and put them in parallel. This circuit has a finite number of resistors and it is easy to check that it has the desired resistance.
But the difficulty of the problem arises when both R1 and R2 are not rational. I am not sure of how to proceed from here.
Sorry, I probably should have put this in the first post.
Thanks for the replies so far!
5. ### studiot AAC Fanatic!
Nov 9, 2007
5,005
515
OK so you stack up n R1 resistors with m R2 resistors in series and parallel this with another series combo of p R1 and q R2 resistors so that
${R_1}{R_2} = \frac{{\left( {n{R_1} + m{R_2}} \right)\left( {p{R_1} + q{R_2}} \right)}}{{\left( {n + p} \right){R_1} + \left( {m + q} \right){R_2}}}$
Will this not do it, trancendental or not, if you can find integers n,m, p, q?
6. ### Tesla23 Active Member
May 10, 2009
324
67
It is not always possible.
If you scale the problem by dividing all resistors by R1, then the problem becomes to make the resistance
1*R2 = R2
from a finite combination of resistors 1 and R2/R1.
clearly this is not always possible, for example if R2 is irrational and R2/R1 is rational.
zyzxzwzvz likes this.
7. ### studiot AAC Fanatic!
Nov 9, 2007
5,005
515
Yes this division is a good thought but, if you replace with an equivalent problem where R3 = R2/R1 and you have a box of 1Ω resistors and a box of R3 resistors then the problem is simply resolved by taking one single R3 resistor and zero 1Ω resistors.
In terms of my integers, n=p=q=0 and m=1.
My scheme becomes unwieldy when both R1 and R2 are less than 1Ω so their product is smaller than either.
It may be worth interchanging the words series and parallel in that case.
8. ### zyzxzwzvz Thread Starter New Member
Jan 11, 2014
3
0
I believe that Tesla23's solution works; I think the math was a bit unclear, though.
Basically, if we are trying to make an equivalent resistance of R1*R2 Ω from some R1 Ω and R2 Ω resistors, we can scale everything down by R1. Then the problem becomes to make an equivalent resistance of R2 Ω from some 1 Ω and R1/R2 Ω resistors. Then we may scale up by R1 at the end.
As Tesla23 mentioned, this is not always possible. Let's make this more rigorous. Take, for example, R1=sqrt(3) and R2=2*sqrt(3)). Then after scaling, we want to make a circuit with resistance 2*sqrt(3) Ω from some 1 Ω and 2 Ω resistors. However, every circuit can be decomposed into series and parallel combinations (see here: http://tinyurl.com/l8r76pm). This ensures that the equivalent resistance can be written as some complex fraction using only 1 and 2 along with division and addition in its expression. This fraction, then, must be rational. But 2*sqrt(3) is irrational, which is a contradiction.
I think that studiot's strategy could work if it were more general (in particular, it only covers one case; the parallel resistors need not have the same resistance).
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2017-02-27 15:49:44
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https://chronicallygratefuldebla.com/category/atomicblonde/
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## Joint Pain
Congratulations ! If you’re like me you are one of the 30 million adults in the United States who suffer with joint pain, you know the pain often is debilitating. It can keep you from staying active and limits your mobility and it even makes daily chores seem impossible. What you might not know is that many doctors can treat joint pain with more than just pills or surgery. Beware though some doctors will tell you about one procedure and then change it once they know your insurance example Medicare I felt one doctor thought less of me as a patient because I am disabled so he changed or tried to change the procedure. It pissed me off because I was all set to get the procedure we discussed and then he changed it.
Both procedures were covered under Medicare so I felt betrayed as if I wasn’t good enough for the other injection.
Newsflash people …. on Medicare pay for the insurance hell I pay more than when I was working.
Make sure this doesn’t happen to you.
Depending on the severity of your pain, injections can be another option for easing your joint pain and help to get you moving again.
Doctors use these injections to try to reduce inflammation and pain in your joints some come with side effects and some risks.
The injections range from corticosteroids, which have been around for decades, to newer ortho-biologic injections like platelet-rich plasma (PRP) , Stem Cell and placental tissue matrix (PTM)
You and your physician will decide which one is best based on your individual needs. The issue is finding doctors qualified to do these.
Not every injection is right for every patient, in my case I hate steroid injections, not only did it make my pain worse it also comes with the risk of developing osteonecrosis. Something I already have. I have noticed that it seems like doctors are quick to prescribe and inject steroids. I stand my ground and refuse. But that’s me.
Corticosteroid injections
Use: This injection is the first line of defense against osteoarthritis symptoms and other joint pain in shoulders, knees and hips. Corticosteroids can offer relief for two to three months, and reduce inflammatory cell activity in the joint. In some people.
Side effects and Risks : As with all injections, there’s a small chance of infection about one in 1,000 as well as Joint infection.
Nerve damage.
Thinning of skin and soft tissue around the injection site.
Temporary flare of pain and inflammation in the joint.
Tendon weakening or rupture.
Thinning of nearby bone (osteoporosis)
Osteonecrosis lack of blood supply to the bone
Raised blood sugar level
Whitening or lightening of the skin around the injection site
Cost: Most insurance covers the $100 -$200 usd cost of these injections. Your insurance provider may require that you try at least one corticosteroid injection first to see whether it works. If not, you may move on to a different therapy.
Hyaluronic acid injections
Use: Hyaluronic acid (HA) injections often are used when corticosteroid injections don’t work. But they usually are approved only for use in the knee.
In some instances, doctors consider an HA injection first if you don’t have obvious signs of inflammation. HA also is a better option if you have diabetes, as corticosteroids can raise blood sugar levels.
Also known as gel injections, HA injections are chemically similar to your natural joint fluid.
When you have osteoarthritis which is different than osteonecrosis lucky me I have both, the joint fluid becomes watery.
So, this injection helps to restore the fluid’s natural properties and works as a lubricant and a shock absorber.
HA is a cushion or a buffer against inflammatory cells in the joint. In some cases, it can stimulate the knee to start producing more natural HA.” Some physicians also believe that HA helps reduce pain by coating nerve endings within the joint.
One treatment, which may consist of between one and three injections, usually offers symptom relief for four to five months, but sometimes up to one years. However, pain and stiffness will return. Most insurance companies only approve one HA injection every six months.
In knees with osteoarthritis, the joint fluid (called synovial fluid) can break down and not provide the cushioning your knee needs
Durolane
Euflexxa
Hyalgan
Orthovisc
Monovisc
Supartz
Synvisc, Synvisc-One
Depending on which type your doctor uses, you may get a single shot. Or you’ll get three to five injections spaced a week apart.
Side effects: There’s a 1-in-100 chance of an inflammatory reaction, The most common short-term side effects are minor pain at the injection site and minor buildup of joint fluid. These get better within a few days.
Cost: HA injections cost more — about $300 to$850 per injection, but most insurance companies cover the cost for knee injections.
Platelet-rich plasma (PRP) injections
Use: Platelet-rich plasma (PRP) injections can treat osteoarthritis joint pain, and are being thoroughly researched to understand their effects.
These injections use your own blood and platelets to promote healing. Platelets contain growth factors and proteins that aid healing in soft tissues. Research shows PRP injections can alter the immune response to help reduce inflammation,
Side effects: Side effects include a very low risk of infection and pain at the injection site. You must stop oral anti-inflammatory medications for a short amount of time if you get a PRP injection.
Cost: Insurance companies don’t generally cover PRP injections and you will pay between $400 and$1,300 per injection out-of-pocket.
Stem Cell Injections
The world’s most advanced regenerative injection treatments for treating knee pain due to arthritis, meniscus tears, traumatic ligament injuries, overuse conditions and other degenerative conditions.
Side effects : mild discomfort associated with the procedure. There is a very small risk of infection whenever aspirations and injections are performed. Nerve damage, vessel damage, and injury to other important structures are exceedingly rare
Placental tissue matrix (PTM) injections
Use: Placental Tissue Matrix (PTM) injections can very profoundly decrease the pain related to osteoarthritis.
These are injections of placental tissue, which is obtained after a healthy baby is delivered from a healthy mother. Research has discovered that there is a large number of growth factors in placental tissue that promote healing, Dr. Genin says.
Side effects: Side effects include a low risk of infection and pain at the injection site. The placental tissue is “immune privileged,” which means the body would not have an adverse reaction to it.
Cost: Insurance companies don’t generally cover PTM injections; you will pay around $1,800 -$2500 per injection out-of-pocket.
Many of these injections often are effective in reducing or stopping your joint pain, but it’s important to remember that they may not keep the pain from returning, Dr. Schaefer says. In fact, they’re most effective when used with other therapies.
As a patient who has Osteonecrosis, Osteoarthritis, and other stuff I consider surgical options as a last resort only if other treatment options have failed. Unfortunately some treatments I cannot even afford to try. I wish the FDA would get a move on and approve some things so insurance companies can have this as a form of treatment.
Stem Cells
BONE MARROW AND FAT CELLS
The stem cells used in this point of care clinic are Autologous Cells that we take from your own body. These cells are taken from your own Bone Marrow or Fat Cells. The cells are your own Stem Cells and will not be rejected by your body.
Taking the Bone Marrow or Fat Cells from your body is relatively painless as a mild local anesthetic is used prior to harvesting. These cells are processed to receive the most stem cell gain and then injected into the area of your body where you need the growth factors to go to work the quickest. Your blood is also drawn and your platelet rich plasma is added to the Stem Cells taken from your Bone Marrow or Fat Cells to increase the activity of the growth factors.
It is important that these cells are used the day they are extracted from your body in order to insure they remain alive and active. Our clinic does not grow extra stem cells from your Bone Marrow or Fat Cells to ensure that they are alive and active. It is an FDA requirement that you receive your cells the same day they are harvested.
You get only the stem cells we extract from your body and there is no other manipulation used except extraction and preparation of the samples taken from your own body. The cells are taken in a procedure that creates only mild discomfort or none at all. Ninety nine percent of our patients experience no pain obtaining bone marrow or fat cells.
CORD STEM CELLS:
Embryo and Placenta stem cells can create certain types of cancers. The cord blood Stem Cells should only be used if they are obtained from a healthy relative and you are a good match. Cord Stem Cells that are used outside of the country or shipped to this country are illegal. The FDA has found diseases in these grown cells and states that most of them are dead. Even though the physicians supplying these Cord Cells claim they are safe to use, you should use extreme caution before considering these procedures.
ARE YOU A CANDIDATE FOR THESE STEM CELL PROCEDURES
REBUILDING JOINTS & SPINE: The Stem Cells that are obtained from your body are placed into all joints and spine to rebuild and regenerate new tissue growth as determined by the clinic physician. There has been clinical evidence that new cartilage can be grown within your joint provided you are determined a candidate by the clinical physician. Not all patients will be a candidate and may require joint replacement.
TORN TENDONS: If the patients tendons are not completely torn this procedure will produce new tissue growth to regenerate torn tendons. Our clinic physician can only determine this with an initial visit and evaluation.
How Does PRP Therapy Work?
To prepare PRP, a small amount of blood is taken from the patient. The blood is then placed in a centrifuge. The centrifuge spins and through a multi-functional process separates the plasma from the blood producing the PRP. This increases the concentration of platelets and growth factors up to 500% also increasing hMSC (human stem cells) proliferation as a function of 8-day exposure to platelet released concentrations 10x. (x= increase above native levels)
When PRP is injected into the damaged area it stimulates the tendon or ligament causing mild inflammation that triggers the healing cascade. As a result new collagen begins to develop. As this collagen matures it begins to shrink causing the tightening and strengthening of the tendons and ligaments of the damaged area.
What is Platelet Rich Plasma?
Platelet Rich Plasma or PRP is blood plasma with concentrated platelets. The concentrated platelets found in PRP include growth factors among the huge reservoirs of bioactive proteins that are vital to initiate and accelerate tissue repair and regeneration. These bioactive proteins increase stem cell production to initiate connective tissue healing, bone regeneration and repair, promote development of new blood vessels and stimulate the wound healing process.
PRP Regenerates Tendons & Ligaments
Tendons connect the muscle to the bone making it possible for you to do many everyday physical activities. Overuse or damage to the tendon over a long period of time causes the collagen fibers in the tendons to form small tears, a condition called tendonitis. Damage to tendons most often occurs in the knees, ankles, hips, spine, elbows, shoulders, and wrists.
Ligaments are composed of collagen fibers that hold one bone to another, stabilizing the joint and controlling the range of motion. When a ligament is damaged, it is no longer able to support the bones in the joint, which often leads to pain symptoms. The instability causing the pain in your joints does not always show up on high tech imaging equipment. Through a thorough neurological and orthopedic evaluation Dr. Baum can determine which ligaments and tendons are unstable due to injury, wear or tear.
Tendons and ligaments have a poor blood supply and they do not usually heal from damage. Combined with the stress of day-to-day activities tendons and ligaments become inefficient causing degeneration of the joint which leads to chronic pain and weakness. Patients who experience chronic pain may not even remember when the injury occurred.
How Does PRP Compare With Cortisone Shots?
Studies have shown that cortisone injections may actually weaken tissue. Cortisone shots may provide temporary relief and stop inflammation, but may not provide long term healing. PRP therapy is healing and strengthening these tendons and ligaments and in some cases thickening the tissue up to 40%.
Treatment Plan
PRP injections with guided ultrasound can be performed on tendons and ligaments all over the body. Cervical, thoracic and lumbar spine, degenerative disc disease, arthritic joints shoulder pain, hip pain, and knee pain, even the smaller joints of the body can all be treated effectively with PRP. Dr. Baum will determine whether prolo solution, Platelet Rich Plasma or a combination of both will be the most effective form of treatment for you during his initial consult and evaluation.
Frequency Of Treatments
While responses to treatment vary, most people will require 3 to 6 sets of injections of PRP. Each set of treatments is spaced 4 to 6 weeks apart.
Is PRP Right For Me?
If you have degenerative spine or joint disease, a tendon or ligament injury, laxity or tear and traditional methods have not provided relief then PRP therapy may be the solution. It will heal tissue with minimal or no scarring and alleviates further degeneration and builds new tissues. There will be an initial evaluation with Dr. Baum to see if PRP therapy is right for you.
What Can Be Treated?
Platelet Rich Plasma injections helps regenerate all areas of the body including the cervical, thoracic and lumbar spine, wrists, elbows, shoulders, hips, knees and ankles as well as tendons and ligaments all over the body. Dr. Baum is one of the few physicians performing PRP procedures to all areas of the spine. Our clinic treats patients with sports injuries, arthritic and degenerative joints and degenerative disc disease. More specific injuries including tennis elbow, carpal tunnel syndrome, scoliosis, ACL tears, shin splints, rotator cuff tears, plantar faciitis and iliotibial band syndrome may all be effectively treated with PRP.
What Are The Potential Benefits?
Patients can see a significant improvement in symptoms as well as a remarkable return of function. This may eliminate the need for more aggressive treatments such as long-term medication or surgery.
Special Instructions
You are restricted from the use of non-steroid anti-inflammatory medications (NSAIDs) one week prior to the procedure and throughout the course of treatments.
Initially the procedure may cause some localized soreness and discomfort. Most patients only require some extra-strength Tylenol to help with the pain. Ice and heat may be applied to the area as needed.
How Soon Can I Go Back Regular Activities?
PRP therapy helps regenerate tendons and ligaments but it is not a quick fix. This therapy is stimulating the growth of new tissue requiring time and rehabilitation. Under Dr. Baum’s supervision patients will begin an exercise program immediately following the first procedure. During the treatment program most people are able to resume normal activities and exercise.
Platelet Rich Plasma (PRP) Matrix Graft by David Crane, MD and Peter A.M. Everts PhD
PRP application techniques in musculoskeletal medicine utilize the concentrated healing components of a patient’s own blood—reintroduced into a specific site—to regenerate tissue and speed the healing process
PRP INJECTION APPLICATION SITES
Spine
Cervical/Thoracic/Lumbar/Sacral
Shoulders & Elbows
Wrist & Hand
Hip/Pelvis
Knee & Lower Leg
Ankle & Foot
Fingers & Toes
Arthritic Joints
Osteoarthritis
Some Osteonecrosis
Information
http://www.prolotherapy.com/PPM_JanFeb2008_Crane_PRP.pdf
Important Videos Everyone Should watch on Biologics
https://drjamesbaum.com/2013/07/the-science-of-mesenchymal-stem-cells-and-regenerative-medicine/
Scientific Papers on Research of Stem Cells
https://drjamesbaum.com/stem-cells/scientific-papers/
I will be posting this in my other blog section also
## Breathing and Prayer For Wellness
Are on the verge of a meltdown, your feeling an impulsive urge to yell, scream, cry,? Do you know that every time you lose your cool, you are giving away your power. I know it’s often easier said than done But, when we react impulsively and unconsciously we become a victim of the circumstances; we become a passenger in our life rather than a driver.
When you give away your power, you become completely dependent on external circumstances to regulate your emotions. Life often becomes like a roller coaster – when things are going well, you will feel good, yet when your circumstances change, your behavior and feelings will shift.
The more emotional you feel, the less rational you’ll think Don’t try solving any problems when you’re feeling overly emotional. Distract yourself with an activity, like walking or reading, or deep breathing to help you calm down. Getting your mind off whatever is bothering you, even for a few minutes, can help you calm down so you can think more clearly and rationally.
Learn to just…. Breathe
Anxiety, frustration and anger cause physical reactions within the body you will experience elevated heart rate. Shallow, upper chest breathing is part of the typical stress response. Stop and take slow, deep breaths can relax your muscles and decrease your physiological response, which in turn can decrease your emotional reactivity.
I use Dr Weil’s 4-7-8 Breathing Dr. Weil MD 4-7-8 Breathing after I practiced this 2x a day after about 3 days I felt more peaceful, and after a couple weeks I felt this inner calm.
I do this even when I am not stressed, and then when I get stressed or angry I use it and it helps calm me so much. I even use it to fall asleep, or when I am getting a medical test like an mri .
Trying to maintain complete control in everything that happens leads to increased anxiety. Efforts to manage your anxiety by trying to control everything in your environment will backfire. Attempting to control everything wastes time and mental energy.
When we are overly stressed we operate from a fight-or-flight response your heart beats faster, your blood pressure rises, and your breathing quickens as adrenaline rushes through your body. By changing the rate, and pattern of breathing, we can change the messages being sent from the body’s respiratory system to the brain. Slow and controlled breathing can reduce the heart rate, reduce levels of stress hormones, and increase the feelings of calm and well being, bringing us back to a place that we can feel less likely to overreact.
I have Adrenal fatigue, and I was told my “fight or flight” response has been activated far too often in the past. So I am learning to relax, let go of stuff I cannot control and breathe…..I also pray I pray several times a day. I don’t ask for things I give thanks even when I am stressed, have fear, depressed, I have faith things will come to pass.
We have to learn stress will come, sometimes life is heavy and we will get over whelmed, we may get an illness, or disorder, deal\in chronic pain, or just not know how to cope in certain situations……stressing out will not solve the problem…..
#### Philippians 4:13New King James Version (NKJV)
13 I can do all things through [a]Christ who strengthens me.
### Greeting
Paul, an apostle of Jesus Christ by the will of God,
To the saints who are in Ephesus, and faithful in Christ Jesus:
Grace to you and peace from God our Father and the Lord Jesus Christ.
### Redemption in Christ
Blessed be the God and Father of our Lord Jesus Christ, who has blessed us with every spiritual blessing in the heavenly places in Christ, just as He chose us in Him before the foundation of the world, that we should be holy and without blame before Him in love, having predestined us to adoption as sons by Jesus Christ to Himself, according to the good pleasure of His will, to the praise of the glory of His grace, by which He [a]made us accepted in the Beloved.
In Him we have redemption through His blood, the forgiveness of sins, according to the riches of His grace which He made to abound toward us in all wisdom and [b]prudence, having made known to us the mystery of His will, according to His good pleasure which He purposed in Himself, 10 that in the dispensation of the fullness of the times He might gather together in one all things in Christ, [c]both which are in heaven and which are on earth—in Him. 11 In Him also we have obtained an inheritance, being predestined according to the purpose of Him who works all things according to the counsel of His will, 12 that we who first trusted in Christ should be to the praise of His glory.
13 In Him you also trusted, after you heard the word of truth, the gospel of your salvation; in whom also, having believed, you were sealed with the Holy Spirit of promise, 14 who[d] is the [e]guarantee of our inheritance until the redemption of the purchased possession, to the praise of His glory.
### Prayer for Spiritual Wisdom
15 Therefore I also, after I heard of your faith in the Lord Jesus and your love for all the saints, 16 do not cease to give thanks for you, making mention of you in my prayers: 17 that the God of our Lord Jesus Christ, the Father of glory, may give to you the spirit of wisdom and revelation in the knowledge of Him, 18 the eyes of your [f]understanding being enlightened; that you may know what is the hope of His calling, what are the riches of the glory of His inheritance in the saints, 19 and what isthe exceeding greatness of His power toward us who believe, according to the working of His mighty power 20 which He worked in Christ when He raised Him from the dead and seated Him at His right hand in the heavenly places, 21 far above all principality[g] and [h]power and [i]might and dominion, and every name that is named, not only in this age but also in that which is to come.
22 And He put all things under His feet, and gave Him to be head over all things to the church, 23 which is His body, the fullness of Him who fills all in all.
## Pain Chronic Pain
Once we accept the reality of the current moment (no matter how unpleasant it may be) for what it is, and not what we wish it were, we can turn our attention to ways to improve it. This I find true in any situation.
Living with chronic pain can throw your life upside down.
It’s hard to believe that I can and have managed my rare disease Osteonecrosis (knee) pain. And my Osteoarthritis pain.
But the pain of spondylolisthesis somedays is truly unbearable. It can just take a fabulous day day and screw it all up.
Today is one of those days.
I try to stay busy , and positive when I really would like to go somewhere and just scream at the top of my lungs.
I don’t think my neighbors would appreciate it. So I bang away at the keyboard.
Since the weather in NE Ohio has changed I am having more and more days in pain.
And in the days when all the above hurt I’m down right miserable. Thank Hod that hasn’t happened yet , but then fall and winter have only begun….
I’m grateful today it’s just my back although it feels as if I have been kicked in my L5S1 several times.
Besides having spondylolisthesis I also for the past decade or longer been dealing with osteoarthritis and osteonecrosis since 2014.
If you don’t know what they are I will explain below.
Osteoarthritis
Sometimes called degenerative joint disease or degenerative arthritis, osteoarthritis (OA) is the most common chronic condition of the joints, affecting approximately 27 million Americans. OA can affect any joint, but it occurs most often in knees, hips, lower back and neck, small joints of the fingers and the bases of the thumb and big toe.
In normal joints, a firm, rubbery material called cartilage covers the end of each bone. Cartilage provides a smooth, gliding surface for joint motion and acts as a cushion between the bones. In OA, the cartilage breaks down, causing pain, swelling and problems moving the joint. As OA worsens over time, bones may break down and develop growths called spurs. Bits of bone or cartilage may chip off and float around in the joint. In the body, an inflammatory process occurs and cytokines (proteins) and enzymes develop that further damage the cartilage. In the final stages of OA, the cartilage wears away and bone rubs against bone leading to joint damage and more pain.
Who’s Affected?
Although OA occurs in people of all ages, osteoarthritis is most common in people older than 65. Common risk factors include increasing age, obesity, previous joint injury, overuse of the joint, weak thigh muscles, and genes.
One in two adults will develop symptoms of knee OA during their lives.
One in four adults will development symptoms of hip OA by age 85. Lucky me I developed Osteoarthritis at age 45.
One in 12 people 60 years or older have hand OA.
Osteonecrosis What it is….
Osteonecrosis of the Knee. Osteonecrosis of the knee (also known as avascular necrosis) and if in the knee from a meniscus tear also called Ahlbacks Disease is a painful condition that occurs when the blood supply to a section of bone in the femur (thighbone) or tibia (shinbone) is disrupted.
I have Osteonecrosis of the medial femoral condyle due to a meniscus tear in 2014. Strange no one wanted to fix it or have any treatment plan.
This pain is like no other. Your area of Osteonecrosis is ice cold yet it often can feel like it was hit by a lightening bolt.
Weather plays a huge factor for me and my pain. I used to love winter now I can barely tolerate a cool fall day. I dread winter.
I get sick of being in pain. If it’s not the knees it’s back or hands it’s just enough to jack up my day or make things more difficult than they already are.
I have found that plant based lifestyle has helped my osteoarthritis and osteonecrosis a lot. I can’t understand why I haven’t lost a ton of weight though. I mean I don’t eat half the unhealthy calories I used to . But hey the doctors says it’s a slow thyroid.
I just wish these 40 lbs would come off it would also help my bones.
But maybe that will just take time.
If you haven’t tried a plant based lifestyle I would highly recommend it.
My cholesterol numbers are fantastic and all my doctors are impressed especially since I rarely need pain medication vs taking 2 a day like I did 3 years ago.
I truly believe that food can be your medicine or your poison.
The choice is yours.
I will be posting a lot of info and recipes
I don’t always eat perfect but life is about compromise and I follow a 90 / 10 rule.
It’s ok to have a cookie or small cupcake just make sure you eat as best as you can most of the time .
Living food is the way to go.
It may not take away all your pain but wouldn’t it be a benefit if it took away a lot of it ? And made it more managed?
Absolutely!!!
## My Story From The Mighty
I have a rare, degenerative bone disease called osteonecrosis, or avascular necrosis (AVN). It is a painful, debilitating disease without a cure. Many doctors don’t know how to treat it. AVN essentially cuts off the blood supply to the affected bone and the bone begins to die, becoming necrotic.
“Osteo” means bone and “necrosis” means death. It is most often found in the hips, knees, shoulders, and ankles and sometimes spine. You may have osteonecrosis in one or more bones. It can strike at any age, any gender. In people with healthy bones, new bone is always replacing old bone. This process keeps bones strong and also happens when children grow or if a bone is injured. In osteonecrosis, bone breaks down faster than the body’s ability to make strong, new bone. If you do not get treatment, the disease worsens and the bones in the joints break down. You may not be able to bend or move the affected joint very well, and you may have intense pain in the joint.
For the newly diagnosed, here is some information I hope you will find helpful. First of all, you are not alone. We know what it’s like to first hear you have osteonecrosis. I recall I was in shock the day I was told, as I never heard of the disease. I was told it was “bone death” and it seemed like I was frozen in time and disbelief when I heard these words. So what the heck does all that mean? Am I dying?
The answer is no, but one or more of the bones are.
< strong>I’m finding the new me. < strong>Stay tuned more to come …..
## Bone & Joint Action Week October 12-20
Bone and Joint Action Week is held annually October 12-20 with activities focused on disorders including arthritis, back pain, Osteonecrosis,Osteoarthritis trauma, pediatric conditions, and osteoporosis. The themes and their related activities are designed to raise awareness worldwide about prevention, disease management and treatment.
Statistics on Avascular Necrosis (AVN, Osteonecrosis, Aseptic Necrosis, Ischaemic Necrosis, Femoral Head Necrosis)
Frequency depends on the site involved. The most common site is the hip; other locations include the carpals, talus, and humerus. In most countries, exact figures on incidence and prevalence are unknown.
One Japanese survey estimated that 2500-3300 cases of AVN of the hip occur each year; of which, 34.7% were a result of corticosteroid abuse, 21.8% to alcohol abuse, and 37.1% to idiopathic mechanisms. A French study reported AVN in 4.3% of allogenic bone marrow transplant recipients.
Race: No racial predilection exists except for AVN associated with sickle cell disease and hemoglobin S and SC disease, which predominantly are diagnosed in people of African and Mediteranean descent.
Sex: The male-to-female ratio depends on the underlying cause, although primary AVN is more prevalent in men. The overall male-to-female ratio is 8:1.
Age: Age at onset depends on the underlying cause. Primary AVN most often occurs during the fourth or fifth decade and is bilateral in 40-80% of cases. On average, women present almost 10 years later than men.
Risk Factors for Avascular Necrosis (AVN, Osteonecrosis, Aseptic Necrosis, Ischaemic Necrosis, Femoral Head Necrosis)
Avascular necrosis has several causes. Loss of blood supply to the bone can be caused by an injury (trauma-related avascular necrosis or joint dislocation) or by certain risk factors (nontraumatic avascular necrosis), such as some medications (usually steroid basesd), steroid abuse in general, blood coagulation disorders like sickle cell, Factor V, FactorViii, MTHFR, eNOS and more, chemo and radiation infections in the Bone vascular issues such as vascularitis or alcohol abuse. Increased pressure within the bone also is associated with avascular necrosis. The pressure within the bone causes the blood vessels to narrow, making it hard for the vessels to deliver enough blood to the bone cells.Many deep sea divers get Avascular Necrosis from a condition known as the bends. Gaucher disease.
Progression of Avascular Necrosis (AVN, Osteonecrosis, Aseptic Necrosis, Ischaemic Necrosis, Femoral Head Necrosis)
Hip Stages of avn-on
1-4
The natural history of osteonecrosis is directly linked to the size and level of the necrosis. Very small lesions (involvement of less than 15% of the femoral head) may resolve without any further treatment. Conversly, lesions involving greater than 50% of the femoral head progress to collapse, and ultimately require in total hip arthroplasty.
Symptoms of Avascular Necrosis (AVN, Osteonecrosis, Aseptic Necrosis, Ischaemic Necrosis, Femoral Head Necrosis)
In the early stages of avascular necrosis, patients may be asymptomatic. However, as the disease progresses most patients will begin to experience joint pain; at first, only when putting weight on the affected joint, and eventually even when resting. Pain usually develops gradually and may be mild or severe.
If the level of necrosis progresses further and the bone and surrounding joint surface collapse, pain may develop or dramatically increase.
The pain may be severe enough to limit the patient’s range of motion in the affected joint.
In some cases, particularly those involving the hip, disabling osteoarthritis may develop.
The period of time between the first symptoms and loss of joint function is different for each patient, ranging from several months to more than a year.
How is Avascular Necrosis (AVN, Osteonecrosis, Aseptic Necrosis, Ischaemic Necrosis, Femoral Head Necrosis) Diagnosed?
In the earliest stages of Avascular necrosis plain x-rays are often normal. A magnetic resonance image (MRI) is the key that allows us to detect AVN at its earliest stage.
Osteonecrosis develops when the blood supply to a segment of bone is disrupted. Without adequate nourishment, the affected portion of bone dies and gradually collapses. As a result, the articular cartilage covering the bone also collapses, leading to disabling arthritis.
Osteonecrosis of the knee can affect anyone, but is more common in people over the age of 60. Woman are three times more likely than men to develop the condition.
Risk Factors
It is not always known what causes the lack of blood supply, but doctors have identified a number of risk factors that make someone more likely to develop osteonecrosis.
Injury. A knee injury—such as a stress fracture or dislocation, meniscus tear, bruised patella or combined with some type of trauma to the knee, can damage blood vessels and reduce blood flow to the affected bone.
Oral corticosteroid medications.
Many diseases, such as asthma and rheumatoid arthritis, are treated with oral steroid medications.
Although it is not known exactly why these medications can lead to osteonecrosis, research shows that there is a connection between the disease and long-term steroid use. Steroid-induced osteonecrosis frequently affects multiple joints in the body.
Medical conditions.
Osteonecrosis of the knee is associated with medical conditions, such as obesity, sickle cell anemia, and lupus.
Transplants. Organ transplantation, especially kidney transplant, is associated with osteonecrosis.
Excessive alcohol use.
Overconsumption of alcohol over time can cause fatty deposits to form in the blood vessels as well as elevated cortisone levels, resulting in a decreased blood supply to the bone.
Chemo therapy and radiation Non-traumatic osteonecrosis of bone is recognized as a potential complication in solid-tumour cancer patients receiving treatment with cytotoxic chemotherapy.
Regardless of the cause, if osteonecrosis is not identified and treated early, it can develop into severe osteoarthritis. And for some with osteoarthritis before avn the disease is even more painful.
Knee stages of avn-on
1-4
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## Basics To Use Food As Thy Medicine
The few basics you need to know to help pain management due to chronic inflammation with food .
1. Eat the rainbow: Consume 10-12 servings of vegetables each day , and make a couple of those servings fruit, if you like.
2. Cruciferous veggies such as broccoli, Brussels sprouts, cabbage and cauliflower are best.
3. Restrict dairy and grains: Eat dairy products in limited quantities. When choosing grains, stay away from simple carbohydrates with refined sugar.
4. Opt for whole grains, including barley, buckwheat, oats, quinoa, brown rice, rye, spelt and wheat.
5. Avoid red meat: Eat red meat the way most of us eat turkey right now a few times a year. Have it on very special occasions, very infrequently. Instead, include fish as the “meat” or eat vegetarian main dishes. Chicken is neutral not harmful but not beneficial in the anti-inflammatory sense.
Get down to your ideal weight; weight loss on its own is anti-inflammatory.
Get daily exercise in the form of walking.
It is the overall diet and lifestyle and not just the individual foods, that control inflammation.
“For a chronic pain patient like me who was suffering, I went slightly extreme form of the diet so that was no red meat, no flour or sugar or simple carbohydrate and no dairy.
I did that for a month.
I do eat chicken or tuna once a week now. Beef maybe every other month.
I listen to what my body is saying now.
Before I just planned dinner and we ate whatever. It was delicious then but it was all the wrong foods or to much of them and not enough good clean healthy living food.
Now we eat for life.
#EatForLife
More ways to help chronic inflammation is to exercise. I know it’s hard when your in pain. But our body’s were meant to move. We have to move.
Exercise is an added benefit, particularly if people are overweight. “If there is any extra weight, you will need to try to lose it, I’m in that boat also. I need to drop a good 40lbs . But when I was first diagnosed with all these bones issues I was in so much pain I couldn’t move. I could barely think and function.
Ultimately, what we all need to know is that inflammation comes from a biochemical reaction initiated by your immune system or wound-healing coagulation system.
Specific foods can promote or shut down the inflammatory cycle.
For instance, simple carbohydrates like cakes,pies,sugar,chips,crisps,promote it, while good clean carbohydrates like fruits vegetables shut it down.
Don’t be afraid of carbohydrates just eat the good healthy ones 85 percent of the time then you can indulge now and then in a piece of pie.
Nutrition that supports a lifestyle rich in anti-inflammatory foods is the key to anti-inflammation and chronic pain management,
Although there are no magic foods, putting the right combination of foods into your diet can produce remarkable results.
I never knew until I took a class you should never really eat meat and potatoes together at a meal.
And it’s best to eat your fresh fruit by itself as a mid day snack.
I love many of them and eat them often and it doesn’t make my pain worse.
Nightshade vegetables are members of the Solanaceae family of flowering plants. Most nightshade plants aren’t edible such as tobacco and the deadly herb, belladonna.
A handful of nightshade vegetables, however, are edible and well-known staples in our diets, including:
tomatoes
eggplant
potatoes
peppers
All nightshade plants contain compounds called alkaloids. One alkaloid found in nightshade vegetables, solanine, may be toxic in large quantities or in a green potato. There’s no evidence solanine is harmful in typical food amounts. And solanine isn’t only found in nightshades—blueberries, huckleberries, and artichokes contain it, too.
Thanks to anecdotal evidence, nightshade vegetables have earned a bad reputation for causing inflammation in the body.
But not everyone with painful joints who eliminates nightshades from their diet experiences pain relief and some evidence suggests that the nutrition content of nightshades may help with arthritis symptoms.
According to the Arthritis Foundation, the belief that eating nightshade vegetables worsens arthritis is a myth. They claim people with arthritis may benefit from the high nutrition content in nightshades.
For example, researchers in one 2011 study found that inflammation and DNA damage was reduced in healthy men who ate yellow or purple potatoes, which are nightshade vegetables, for six weeks.
Most nightshade vegetables contain an abundance of nutrients. They’re also readily-available and easy-to-prepare. In some cases, the benefits of eating nightshade vegetables may outweigh any inflammation risk.
1. Peppers
Peppers, including bell peppers and chili peppers, are low in fat and calories.
They’re a good source of nutrients such as:
vitamin C
fiber
vitamin K
B vitamins
The capsaicin in chili peppers may relieve arthritis pain by reducing a specific pain transmitter in your nerves called Substance P. Capsaicin, which is a common ingredient in many pain-relieving creams. It may cause mild burning or a skin reaction when applied topically.
2. Potatoes
The white potato often gets a bad rap because it’s a starchy carb, but all varieties of potatoes are nutritionally-dense. They can be a part of a healthy diet when eaten in moderation and not fried or slathered in butter and sour cream.
Potatoes are fat-free and a good source of fiber. Fiber helps to keep you fuller longer so you may eat less. Since they contain sodium and potassium, potatoes also help keep your electrolytes in balance.
They’re also a good source of:
vitamin C
vitamin B6
niacin
manganese
iron
copper
folate
The healthiest potato is a baked potato. Add herbs and a dollop of Greek yogurt instead of butter and sour cream. Don’t be shy about trying different varieties, especially since pigmented potatoes may give you an anti-inflammatory bang for your buck.
3. Tomatoes
Technically, tomatoes aren’t a vegetable; they’re a fruit. They contain all four of the carotenoid antioxidants, which include:
lycopene
beta-carotene
alpha-carotene
lutein
Lycopene is the most powerful carotenoid. It’s thought to help prevent some types of cancer, help prevent heart disease, and boost immunity. Some research has shown tomatoes have anti-inflammatory abilities, although more research is needed.
Tomatoes are a good source of:
vitamin E
vitamin A
potassium
calcium
vitamin K
vitamin B
Add fresh, diced tomatoes to a green salad or make fresh tomato juice. Tomatoes are delicious in vegetable soup and chili, too.
4. Eggplant
Like tomatoes, eggplant is also a fruit. It has no fat or cholesterol. Eggplant isn’t high in any one vitamin or mineral, but it contains small amounts of most essential vitamins and minerals.
According to one 2015 study, eggplant stalk extract may help reduce inflammation. More research is needed to determine if eggplant fruit has the same abilities.
To enjoy eggplant in your diet, go beyond a fat- and calorie-laden eggplant Parmesan casserole. Instead, try sprinkling sliced eggplant with olive oil and herbs, then roasting or grilling. You can also steam eggplant, or add sautéed slices to your favorite veggie pizza.
This is not medical advice this is based on how I eat to help my pain.
As well as just a few studies showing how good food is.
## I Started To Cut Out Added Sugar & Use This: Homemade Stevia Liquid
We have to cut out all the added sugar or try to cut back at least !!
It is no secret that people today ingest far too much sugar. According to the NHS, adults should not be consuming more than 30g of added sugars per day.
But we consume 3x that amount !
It’s no wonder why were becoming fat
and unhealthy
In 1700, the average person consumed approximately 4.9 grams of sugar each day (1.81 kg per year). That’s about 1 teaspoon.
· In 1800, the average person consumed approximately 22.4 grams of sugar each day (10.2 kg per year). That’s about 5 teaspoons
· In 1900, the average person consumed approximately 112 grams of sugar each day (40.8 kg per year). That’s 28 teaspoons
· In 2009, 50 per cent of Americans consumed approximately 227 grams of sugar each day – equating to 81.6 kg per year. That’s almost 58 teaspoons !!!
We wonder why we’re sick! And living with chronic pain.
I mean it’s in everything. From Cookies where we expect it to me to tomato sauce and yogurt. Things you never would expect to have sugar and it’s causing us to be fat and unhealthy and full of inflammation.
I’m trying to cut out added sugar and it was very hard.
Once you get past a few weeks you will feel better.
Food tastes better also and coffee does to .
I do use hazelnut coffee mate . And I’m not going to lie I still will eat a couple chips ahoy thin cookies or a mini cupcake or two now and then.
But I am really trying to get off the sugar. I have to admit it’s harder than when I stopped smoking.
I have learned through my herbology classes how to make my own liquid stevia.
And it’s helped me cut back a lot on the sugar. I just can’t drink things like tea without some sweetness in it.
So now actually make my own Stevia extract and dilute it, and other Stevia liquid flavor it etc..
I learned a lot in the herbology classes I take.
I buy all my herbs from mountains rose herbs.
I also just put the dry leaves in a beverage hot or cold.
I stopped buying Stevia at the store.
Also raw honey is good to use as a substitute.
Anything processed with a strange chemical or an artificial ingredients added is never good.
You can use fresh stevia leaves as a sweetener in beverages, such as tea and lemonade, or in sauces. A few fresh stevia and mint leaves make a great herbal tea when steeped in a cup of boiling water.
Add fresh stevia leaves to beverages or foods as a sweet, edible garnish. Although the fresh leaves are less sweet than dried leaves, they’re still much sweeter than sugar. Taste-test your beverage before serving to ensure you don’t over-sweeten your drink.
Use dry stevia leaves to make a powdered sweetener. Bundle and hang fresh stevia plant stems upside down in a warm, dry location until the leaves are thoroughly dry, then strip the leaves from the stems.
Fill a blender, food processor or coffee grinder to half full with dry leaves and process at high speed for a few seconds.
Store the powdered sweetener in an airtight container. Use the powder in recipes that call for a sweetener, but make adjustments in the amount used due to its dense sweetness.
A general rule of thumb is that 2 to 3 tablespoons of stevia powder equals 1 cup of sugar.
Use dry stevia leaves to make a syrup for sweetening beverages, sauces or other syrups. Add one cup of warm water to one-quarter cup of fresh, finely crushed stevia leaves.
Put the mixture in an airtight container and allow it to set for 24 hours before straining the leaves from the mixture. You can cook the strained mixture on low heat, reducing it to a more concentrated syrup. The syrup should last for several years, if kept in an airtight container in your refrigerator.
Things You Will Need
* Blender
* Measuring cups
* Strainer
* Airtight container
• Glass amber color and dropper
I also make my own liquid stevia extract for baking etc…
Stevia extract recipe.
Vodka
Organic Stevia Leafs Dried
Glass mason jar
Fill a clean glass jar 1/4 to 1/3 full with stevia leaf. Cover the herb with vodka and pour to the very top. Allow to steep for 24-48 hours, taking care not to let it extract any longer than that to avoid bitterness. Strain and bottle it in a dark amber glass dropper bottle.
Vanilla Stevia Extract Recipe
Chop 1 vanilla bean and add to strained stevia extract. Allow to infuse for 2 to 6 weeks. Strain and bottle it in an amber bottle with dropper.
Lemon Stevia Extract
Fill your jar 1/3 full with organic lemon peel
Cover completely with strained stevia extract.
Allow to infuse for 1 to 4 weeks, tasting along the way. Strain and bottle in amber glass bottle with dropper
HOW TO USE HOMEMADE STEVIA EXTRACT
Add 1-2 drops to your favorite beverages (I especially love using homemade stevia extract to sweeten my coffee or tea!) A little bit goes a long way, so start with small amounts.
I found I had to use a bit more of my homemade stevia to get the desired level of sweetness, as compared to the store-bought stevia I’ve tried.
But I think the sweetness will depends on how long you heated the extract and how many leaves you used.
This is a Stevia Plant.
Your dry stevia leaves can be used to make a healthy syrup for sweetening beverages, sauces, or even other syrups. A teaspoon of stevia syrup is as sweet as a cup of sugar.
Take 2 cups of warm water and add it to half a cup of dried stevia leaves. Put the mixture in a glass jar and let it steep for 24 hours. Strain the leaves from the mixture.
Cook the strained mixture on low heat, reducing it to a concentrated syrup. The syrup should last for at least a year if kept in an airtight container in your refrigerator.
Conversion chart
1 cup of sugar is equal to – 1 teaspoon of stevia leaf powder or 1 teaspoon of stevia extract.
1 tablespoon of sugar is equal to – .25 teaspoon of stevia powder or 6-9 drops of stevia extract.
1 teaspoon of sugar is equal to – a pinch of stevia powder or 2-4 drops of stevia extract.
Stevia is becoming a popular plant and is readily available at most local nurseries.
If grown inside or outside it will flourish.
Thankfully it has few pests and is easy to grow and preserve.
Now that you know how to use it, you be adding stevia to your garden or window seal.
Another Recipe
Extract
With Alcohol cooked off.
• 1 glass jar with a tight fitting lid
• Dried Stevia leaves. They can be crumbled, chopped or powdered
• Vodka or Rum
Using a ratio of 2 parts stevia to 3 parts liquid, place one cup of stevia in the jar and cover it with 1.5 cups of alcohol.
Shake the mixture well and let it sit for no more than 36 hours. (it will become bitter if you steep it longer than 36 hours) Strain through muslin or a coffee filter and pour the tincture into a dark colored bottle.
To remove the alcohol: once the 36 hours are up, simmer the mixture on low heat for 30 minutes, stirring regularly.
Be careful not to boil. When it cools, strain and bottle as above.
This mixture should be kept in the refrigerator, where it will store for six months.
.
.
## People With Chronic Pain Are Suffering While Addicts & Junkies Are Being Coddled.
What does it say when heroin and opioid addicts are given better treatment than a person living with chronic pain?!
Now please don’t go thinking I lack compassion and am being cruel honestly it’s not my intention.
But I am sick of hearing about the opioid crisis every day, especially when
they throw chronic pain sufferers in the same category as a junkie!
News Flash ……….Were Not
Or a person that is suffering with cancer. I just don’t understand it.
Yes I understand that their is a problem in this country with some abusing drugs whether prescribed or illegal.
But not everyone falls into that category.
Why are so many Doctors,Pharmacies, Government Officials patient profiling?
We as a society look down on racial profiling, gender profiling but why is it ok to patient profile?!
Thank God I have an excellent family doctor.
Many people in government and now pharmacies don’t make their job any easier.
In fact they make it hard for decent doctors who don’t over prescribe and patients who don’t abuse drugs or who don’t doctor shop.
All the red tape they have.
Now we have government and pharmacies in our doctor patient relationship.
Telling the public that they will now be limited and controlled on how much medication they receive and that their legitimate diagnosed ongoing pain doesn’t matter.
But we care more about addicts & junkies who choose to shoot heroin over and over again. They choose that life !! Chronic pain suffering is not a choice it’s many individuals reality.
Many people myself included suffer from several painful chronic conditions.
NSAIDS don’t do crap for the pain I feel most days . I have tried many of them. And sometimes the pain medication takes the edge off so I can get things done. No one wants to be in pain. My body has less pain so I can then function more.
But I find that taking CuraMed Curcumin helps me more than a rx for an NSAID.
So I limit my own use of rx pain meds.
And most people I know don’t want to have to take a pills to have pain relief.
But we will,when we need to.
NSAIDs will for some It really depends on your pain and your condition or disease.
Some of the conditions I have Osteonecrosis for one is rare. And has been said it’s second in pain to bone cancer.
More on Osteonecrosis below.
I bilateral pars fracture in L5S1
Lumbar spondylolysis this is a condition in the lower back where there is a defect or fracture in the part of the vertebra known as the pars interarticularis. The pars interarticularis, also known as the isthmus, is a segment of bone that connects the facet joints at the back of the spine. It is a small, thin part of the vertebra that has a poor blood supply, which makes it susceptible to stress fractures. No NSAID can help this. A pain pill barely helps but at least it helps somewhat.
Fractures of the pars interarticularis, known as spondylolysis, usually occur at the L5-S1 level,and rarely at L4-L5 or higher. They can occur on one side of the vertebra or on both. Lucky me mine is in both sides L5S1
SPONDYLOLYSIS
A pars fracture is also known as a stress fracture, or as spondylolysis. Spondylolisthesis is often the result of spondylolysis. In non-medical terms, this means a stress fracture causes the forward slippage of a vertebral body. The stress fracture occurs through a fragile part of the vertebral bone called the “pars” and is often broken on both sides. The fracture may be the result of a direct trauma, by a focused strain usually from athletic activity, or from a genetic weakness in this area of the bone. This is a thin bone that can break with repeated use; imagine a paperclip that has been bent over and over and finally breaks.
Spondylolysis sometimes causes spondylolisthesis, which it did in my case.
This is when one vertebra slips forward on the vertebra below it.
Symptoms include a deep painful constant ache in the lower back, pain that is worse with movement, and tightness in the hamstrings. If the vertebral slippage is severe, nerve roots can be compressed.
The pars functions as a bony hook and when fractured the posterior support for the vertebrae is broken. It can cause a forward slippage with time. Which mine has about 22 -25 percent.
I also have Spontaneous Osteonecrosis of the Knee, also known as Ahlback’s disease is the result of vascular arterial insufficiency to the medial femoral condyle of the knee resulting in necrosis and destruction of bone. It is often unilateral and can be associated with a meniscal tear.
Osteo means Bone Necrosis means
💀
No orthopedic wants to fix it, trust me I have been to more than 5 but less than 10 for their professional opinions
The stem cell procedure is 8 to 10kusd insurance doesn’t cover any part of stem cell injections that can actually help save the bone.
All the orthopedic doctors I seen said to wait until my knee bone crumbles and collapses and then they will saw out the old bone and give me an artificial knee.
I don’t know about you but to that is totally unacceptable!
A TKR Total Knee Replacement and PKR Partial Knee Replacement-cost 30-40,000usd some places more.
Your basically sawing off the patients bone and replacing it with fake parts
Vs using the patients own stem cells to help heal their own body.
For much less money.
It’s a no brainer
And I also have Osteoarthritis NSAIDs will help this but so does my CuraMed Curcumin so I take that instead.
Sometimes called degenerative joint disease or degenerative arthritis, osteoarthritis (OA) is the most common chronic condition of the joints, affecting approximately 27 million Americans. OA can affect any joint, but it occurs most often in knees, hips, lower back and neck, small joints of the fingers and the bases of the thumb and big toe.
Who’s Affected?
Although OA occurs in people of all ages, osteoarthritis is most common in people older than 65. Common risk factors include increasing age, obesity, previous joint injury, overuse of the joint, weak thigh muscles, and genes.
One in two adults will develop symptoms of knee OA during their lives.
One in four adults will development symptoms of hip OA by age 85.
One in 12 people 60 years or older have hand OA.
So if you add all these together my bones are jacked.
And yet the government wants me to suffer?
Now I will say
I don’t like pain pills I do need them occasionally it’s nice to know that if I need one or for pain I won’t have to jump through fire to get them.
What pisses me off is that junkies od get free narcan over and over often it takes 2-3 doses to revive them. And yet even faced with death they still don’t learn.
And go right back to it knowing it will either kill them now or later. More free narcan and hey we’ll pay for you to go to rehab as well.
And I can’t get insurance to even pay anything towards stem cell injections, that could possibly get me off disability and back to a career in eye care that I loved.
People in chronic pain want their lives back. We would gladly give up all medication to live and function pain free or even with less pain.
We become so used to our pain being a 5 that in days it’s a 3 we feel fabulous, where you may be on the sofa in pain at a level 3 we’re rejoicing. But pain level 7-8 and beyond are sometimes there also and we are down.
I wish the insurance companies would get on board with stem cell injections and Prp injections it can help so many.
So we can’t get the treatment we want because it’s so expensive and not everyone can afford the injections.
Because there is no payment plan.
For pain I take CuraMed Curcumin 1x a day.
5000 iu vitamin
1000 mg krill oil
300mg Coq10
Now and then I will take a pain pill.
It’s a blessing when my knee and back don’t hurt. But usually the back always hurts somedays a lot more than others.
I just think it’s a disservice for people with pain , constant legitimate pain to have to suffer.
I see junkies get free narcan,free rehab yet a girl in my bone disease support group who wants to live and us fighting every day to live has to pain for chemo.
It’s wrong.
## Blogs
I think I will be starting a new blog just for recipes
Opinions? I really want your opinions
Since I am a health leader and advocate who lives with several chronic conditions
Should I focus on just that or have a mix
## The Beauty And Pain Of Autumn
Autumn (British English) or fall (American English) is one of the four temperate seasons. Autumn marks the transition from summer to winter, in September (Northern Hemisphere) or March (Southern Hemisphere), when the duration of daylight becomes noticeably shorter and the temperature cools down considerably.
Fall is a season for balancing light and dark, letting go, and accepting the impermanence of things.
My body seems to know that bad weather season is coming, with summer on the way out and fall on the way in the bone pain goes crazy from mild to intense to unbearable all in a 24/48 hrs time frame.
I was hoping to live in Florida by now.
But with one set back after another since December 2016 husbands heart attack and stents.
2017 my stress test, echo , Mri’s and umbilical hernia surgery I wonder will we ever get to Florida.
Seems like there is always something and I’m not talking small somethings, they are always big intense stressful something’s.
I miss my family , I am so tired also of the pain that will come daily from mid fall until mid spring. I am sick of pain, I’m not ready for it again.
It hurts the soul always being in pain. Day in and day out pain. It’s overwhelming sometimes. It’s depressing some days.
So I have my granddaughters bedroom a mess it’s loaded with boxes.
Donate
Keep
Purge
Why do we really keep papers,paystubs etc 7-10 years? It’s crazy. Hopefully my husband gets a move on before I do it haha.
What’s bothering me is that little movement causes painful stiffness and just overall poor mind body health. I like to move about. No I can’t hike like I used to. Maybe some day.
Big movements are good, like walking in the sunshine ,or a stroll in the park to sorting through a pile of books (as long as they aren’t too heavy.) And the problem is that I just don’t have enough of these big movements to keep my joints happy. I’m home a lot these days, the colder it gets the more I’m stuck in doors, meaning the more pain I have.
I can ride my recumbent bike and do some small chores staying useful without using up too many of my spoons.
Typing on the computer or reading or watching tv isn’t my thing especially when that’s all there will be to do.
So good luck during the changing of the seasons
At least it’s pretty.
## Walk To Be Spontaneously Happy
Walking is an ideal daily exercise for a wide variety of reasons – including its beneficial impact on body, mind and spirit!
Walking as a way to get daily exercise, it can help strengthen major organs in the body, promote bone density , boost the immune system, lead to a more positive outlook and more.
If your new to exercise always clear it with your doctor. Don’t over do it. Gradually build up to it.
I gave bone problems Osteonecrosis,Osteoarthritis and Spondylolisthesis. I was told to limit my weight bearing but just standing is weight bearing, and then one doctor told me exercise all I want it will help your knee collapse faster !! WTH needless to say he was fired.
But I do need to move.
I started out with 10 minutes after a couple weeks 15 minutes snd so on.
Some days I can walk 40 minutes other days 15 depends on pain level.
When I’m in a lot of pain which usually comes with winter and cold months.
I ride my recumbent bike at least 15-30 minutes a day.
But walking clears the head, gets us in touch with nature it gets me from a funk to happiness
Spontaneously Happy
I used to love winter now because of my bones I really dread it.
If you can’t walk , if in a wheelchair or scooter getting out in nature is still good for the soul.
Photos and Video I took in Millcreek Park in various locations of park .
I really miss hiking : but for now walking will do.
## From Optometric Tech /Optician To Professional Patient & Patient Leader
If you have a chronic condition or illness you may already know and understand what it feels like to be a professional patient.
Between the physical pain and symptoms and emotional symptoms, the constant doctor appointments in search of that one person knowledgeable enough to help vs refer you to yet someone else and the numerous tests and procedures (not to mention having to keeping track of all of it & all the bills that go with it ) having a chronic condition can become a full-time job and to be honest it’s more exhausting than a good day’s work.
Speaking of work.
You may find yourself needing to cut back on hours at work , go to part time or stop working altogether.
Although this may be a necessity for you and your health, other people don’t always understand why you’re not working.
They may have these crazy misconceptions that you’re now somehow slower , lazy on vacation or lucky not to have to go to work .
Those of us with chronic conditions know, this is so wrong .
And we need to say this for those who don’t understand what we feel or go through. Maybe then people will be less judgmental.
So here is what most people don’t know or understand about not working due to chronic condition or illness.
I personally would much rather be at work.
People look so surprised when I tell them that, some act as if I’m off on some luxurious vacation.
They have no idea that I’m probably home.
So yes, I’d rather be at work because being at work means I’m healthy again.
Logically I know that one good day doesn’t mean I have to ability to hold my full time job again , but its nice to hope I will be back to work someday.
I wish people knew how much I miss my job. I stayed far longer than I should have and probably did more damage to my knee than I needed to, because it was such an important part of my life.
I lost 90 percent of my social life when I left my career and now being at home mostly all day every day is incredibly isolating, not to mention how guilty you feel not doing your part. Every day I hope that I’ll be able to work again someday soon , there are only so many episodes of a tv show a person can watch , I am writing a book and I do take classes.
I fill out paperwork constantly new doctors , more questions than answers.
Researching new treatments and the cost only to find great new Like about stem cell injections helping my Osteonecrosis but then being let down seeing that it’s 5-10k and never covered by insurance.
Then the frustration and sadness sets in because I live in America and I paid into Medicare and my share of taxes. And yet the government continues to hold up proven treatment that could help tens of thousands and yet some countries allow the cost of stem cells for their patients.
I also think many people see me and because I wear a little makeup and curl my hair, I think she doesn’t look disabled or ill. They don’t see me on the days I can barely move .
The days I need help going to the store because it gets so cold in the winter here in Ohio I am literally like concrete and in a great deal of pain.
Thank God Giant Eagle grocery store has a new shop for you curbside express.
You will be utilizing it this winter.
I try to be positive even when I’m in pain. I have a disease that is called Osteonecrosis due to trauma to the bone which has left me with a lack of blood supply to the knee.If you don’t have AVN/ON you won’t ever understand my pain.
I also have Spondylolisthesis L5S1 spine issues.
And Osteoarthritis another painful bone condition then add Spondylolisthesis,Hypothyroidism and Rosacea to the mix
Even though I get disability I do feel guilt now and then. I feel like I’m not contributing financially to my marriage and to be honest I miss working and making my own money.
My husband reminds me that he loves me and I would be doing the same for him if it were reversed and he’s right.
Being home all the time can be really lonely. If I had the energy and the physical stamina to be out and work, everyday life would be more fun again.
The isolation from limited human interaction is challenging so I started to take a few classes here or there, attend a seminar for this or that and meet new people. I’m going to be a health coach.
I find things to keep me and my mind busy.
I have a support group for Osteonecrosis.
I find that the spondylolisthesis is the more st painful of the few conditions I have, and the pain from Osteonecrosis is being managed mostly but it has its flares.
Osteoarthritis the stiffness is really indescribable.
But I make my own pain rubs and herbal remedies you can find many in this blog. But more will be in my book.
I wrote a booklet about the Avascular Necrosis/Osteonecrosis
And I blog and I’m writing a regular ebook and it should be completed by the end of the year.
I would love to find a decent work from home job.
Trust me, I would love to hold down a regular job in the optical field again.
No one realizes that a job does more for you than just pay your bills. It is part of what gives you self-esteem.
People always want you to be there for them, but are they ever there for you? Most of the time no.
I’m bored out of my absolute mind. I loved working and until my pain got bad, my job actually took my mind off it for the most part.
So next time you see your friend or family member that’s on disability don’t envy them.
Maybe remember to call them a little more often.
And let’s hope someday the government will help people get their life back by adding stem cell injections to all forums of insurance.
## Vegetarian Lettuce Wraps
Vegetarian lettuce wraps with tofu and mushrooms.
194 Calories
Makes 4
Ingredients:
3 tablespoons hoisin sauce
3 tablespoons reduced-sodium soy sauce
2 tablespoons rice vinegar
1 teaspoon sesame oil
2 teaspoons canola or grapeseed oil
1 (12- to 14-ounce) package extra-firm tofu (do not use silken)
8 ounces baby bella (cremini) mushrooms, finely chopped
1 (8-ounce) can water chestnuts, drained and finely chopped
2 cloves garlic, minced
2 teaspoons freshly grated ginger
1/4 teaspoon red pepper flakes (omit if sensitive to spice)
4 green onions, thinly sliced, divided
8 large inner leaves romaine lettuce (from a romaine heart) or butter lettuce leaves
Optional for serving: grated carrots, additional red pepper flakes
Directions:
In a small bowl, stir together the hoisin, soy sauce, rice vinegar, and sesame oil. Set aside.
Press the tofu between paper towels to squeeze out as much liquid as possible. Refresh the paper towels and press again. Heat the 2 teaspoons canola oil in a large nonstick skillet over medium-high. Once the oil is hot, crumble in the tofu, breaking it into very small pieces as it cooks. Continue cooking for 5 minutes, then add the diced mushrooms.
Continue cooking until any tofu liquid cooks off and the tofu starts to turn golden, about 3 to 5 minutes more.
Stir in the water chestnuts, garlic, ginger, red pepper flakes, and say half of the green onions and cook 30 seconds more.
Pour the sauce over the top of the tofu mixture and stir to coat.
Cook just until you hear bubbling and the sauce is warmed through, 30 to 60 seconds.
Spoon tofu mixture into individual lettuce leaves.
Top with remaining green onions, grated carrots, and additional red pepper flakes as desired.
Eat immediately.
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2022-01-18 22:58:04
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|
https://zbmath.org/?q=an:0781.14010
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# zbMATH — the first resource for mathematics
$$p$$-adic uniformization of Shimura curves: the theorems of Cherednik and Drinfeld. (Uniformisation $$p$$-adique des courbes de Shimura: Les théorèmes de Čerednik et de Drinfeld.) (French) Zbl 0781.14010
Courbes modulaires et courbes de Shimura, C. R. Sémin., Orsay/Fr. 1987-88, Astérisque 196-197, 45-158 (1991).
This is the central article of the whole volume. It gives a detailed account of the theorem of Cherednik and Drinfeld on the $$p$$-adic uniformization of Shimura curves, which in turn plays a key role in K. A. Ribet’s paper [Invent. Math. 100, No. 2, 431–476 (1990; Zbl 0773.11039)].
In the first chapter, the “nonarchimedean upper half plane” $$\Omega=\mathbb{P}^ 1(C)-\mathbb{P}^ 1 (K)$$ is introduced (here $$K$$ is a local nonarchimedean field and $$C$$ the completion of an algebraic closure of $$K)$$. The Bruhat-Tits tree $$T$$ of $$\text{PGL}_ 2(K)$$ is used to endow $$\Omega$$ with a rigid-analytic structure, and a formal scheme $$\hat\Omega$$ over the ring $${\mathcal O}$$ of integers in $$K$$ is constructed with generic fibre $$\Omega$$ and special fibre a tree of projective lines with intersection graph $$T$$. Then Drinfeld’s modular interpretation of $$\hat\Omega$$ is carefully explained, as well as the action of $$\text{PGL}_ 2(K)$$ on $$T$$, $$\Omega$$ and the functor represented by $$\hat\Omega$$.
The second chapter is devoted to a detailed proof of Drinfeld’s theorem: $$K$$ is now assumed to have characteristic 0, and a quaternion algebra $$D$$ with center $$K$$ is chosen. In this situation, Drinfeld’s theorem states that the formal scheme $$\hat\Omega \widehat{\bigotimes}_{\mathcal O} \widehat{\mathcal O}^{nr}$$ over the completion $$\widehat{\mathcal O}^{nr}$$ of the strict henselization of $${\mathcal O}$$ classifies certain “special” formal $${\mathcal O}_ D$$-modules of height 4 (or equivalently their Dieudonné modules), endowed with a certain “level structure”.
In the final chapter, the Shimura curve $$S_ U$$ associated with a compact open subgroup $$U$$ of $$\Delta^*(\mathbb{A}_ f)$$ is introduced $$(\Delta$$ is an indefinite quaternion algebra with center $$\mathbb{Q}$$, $$\mathbb{A}_ f$$ are the finite adeles over $$\mathbb{Q})$$. It is known that $$S_ U$$ can be interpreted as the moduli space of abelian surfaces with complex multiplication by $${\mathcal O}_ \Delta$$ and “level-$$U$$- structure”; in particular, $$S_ U$$ is defined over $$\mathbb{Q}$$. The complex points of $$S_ U$$ can be described as $$S_ U(\mathbb{C})=\Delta^*(\mathbb{Q}) \backslash \bigl( \mathbb{P}^ 1(\mathbb{C})-\mathbb{P}^ 1 (\mathbb{R}) \bigr) \times\Delta^*(\mathbb{A}_ f)/U$$ $$S_ U(\mathbb{C})$$ is a finite union of compact Riemann surfaces.
The theorem of Cherednik (in the formulation of Drinfeld) describes a $$p$$-adic analogue of this uniformization at a “bad” prime $$p$$ (i.e. $$p$$ divides the discriminant of $$\Delta)$$: by suitably extending the modular interpretation of $$S_ U$$ to $$\mathbb{Z} \bigl[{1\over p}\bigr]$$, a model of $$S_ U$$ over $$\mathbb{Z}_ p$$ is constructed; then by comparing this moduli functor to the one in Drinfeld’s theorem, the following description of the rigid-analytic variety $$S_ U^{p,an}$$ associated with the model of $$S_ U$$ over $$\mathbb{Z}_ p$$ is obtained: $$S_ U^{p,an}\cong \mathrm{GL}_ 2(\mathbb{Q}_ p)\backslash \bigl( \Omega \widehat{\bigotimes} \mathbb{Q}_ p ^{nr} \bigl) \times{\mathcal Z}_ U$$ with a certain adelically defined set $${\mathcal Z}_ U$$ of double cosets; it turns out that $$S_ U^{p,an}$$ is a finite union of Mumford curves.
[For the entire collection see Zbl 0745.00052.]
##### MSC:
14G20 Local ground fields in algebraic geometry 14G35 Modular and Shimura varieties 11G09 Drinfel’d modules; higher-dimensional motives, etc. 14H25 Arithmetic ground fields for curves 14L05 Formal groups, $$p$$-divisible groups
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2021-05-13 20:08:21
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https://chemistry.stackexchange.com/questions/46469/what-should-be-the-name-of-this-substituted-cyclopentane
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# What should be the name of this substituted cyclopentane?
I think its name is 5-amino-3-bromo-4-chloro-2-hydroxycyclopentan-1-carbonitrile. Is that correct?
• What should I do wait please sir .. Feb 17 '16 at 18:48
• @_Pi5 what do YOU see in your browser? Try uploading again, after checking your picture locally. If this should be a problem instead of simply a wrong click, try uploading a test image (labeled so, to avoid confusion and undeserved down-votes). Feb 17 '16 at 19:26
• Yea, now I can see something! Feb 17 '16 at 19:36
• Note your NH2 is the wrong way round, I've edited it Feb 18 '16 at 21:05
According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the preferred suffix for the principal characteristic group $\ce{{}-CN}$ is ‘carbonitrile’. Therefore, the name of the parent structure of the compound given in the question is ‘cyclopentane-1-carbonitrile’ (note that the locant ‘1’ would be omitted in monosubstituted homogeneous monocyclic rings, i.e. ‘cyclopentanecarbonitrile’).
The relevant rules for the numbering of locants for the four substituent prefixes (‘amino’, ‘bromo’, ‘chloro’, and ‘hydroxy’) are:
P-14.3.5 Lowest set of locants
The lowest set of locants is defined as the set that, when compared term by term with other locant sets, each cited in order of increasing value, has the lowest term at the first point of difference; (…)
and
P-14.4 NUMBERING
When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
(…)
(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
(g) lowest locants for the substituent cited first as a prefix in the name;
(…)
Note that Rule (f) takes precedence over Rule (g).
In accordance with Rule (f), the compound given in the question could be named as 2-amino-4-bromo-3-chloro-5-hydroxycyclopentane-1-carbonitrile as well as 5-amino-3-bromo-4-chloro-2-hydroxycyclopentane-1-carbonitrile since both names correspond to the locant set ‘2,3,4,5’. However, according to Rule (g), this example is named as 2-amino-4-bromo-3-chloro-5-hydroxycyclopentane-1-carbonitrile rather than 5-amino-3-bromo-4-chloro-2-hydroxycyclopentane-1-carbonitrile since ‘amino’ is cited first as a prefix in the name.
• Loong, do you lurk in the nomenclature question list, poised to slam down Blue Book quotes? Wow. Feb 17 '16 at 19:43
• @Brian Sure! Even if a question is not a duplicate, many nomenclature questions can be answered using parts copied from similar answers.
– user7951
Feb 17 '16 at 19:52
• So can we say that we are following the priority order of functional groups just while making the backbone af5er that we follow alphabetical order ??? Feb 18 '16 at 16:40
• @Pi5 You use the priority order to identify the characteristic group that is expressed as a suffix (here: carbonitrile) and that receives the lowest locant (here: 1). Then, low locants are given to the prefixes, all considered together (here: 2,3,4,5). If a choice still remains, the lowest locant (here: 2) is given to the substitutent cited first in the name (here: amino), which corresponds to alphabetical order.
– user7951
Feb 18 '16 at 17:00
• @Pi5 You can find examples for Rule (f) here and here, and for Rule (g) here, here, here, here, here, and here.
– user7951
Feb 18 '16 at 17:12
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2021-09-21 17:10:24
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https://leetcode.ca/2022-01-27-2135-Count-Words-Obtained-After-Adding-a-Letter/
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Formatted question description: https://leetcode.ca/all/2135.html
# 2135. Count Words Obtained After Adding a Letter
• Difficulty: Medium.
• Related Topics: Array, Hash Table, String, Bit Manipulation, Sorting.
• Similar Questions: Strings Differ by One Character, Count Substrings That Differ by One Character, Maximum Score From Removing Substrings.
## Problem
You are given two 0-indexed arrays of strings startWords and targetWords. Each string consists of lowercase English letters only.
For each string in targetWords, check if it is possible to choose a string from startWords and perform a conversion operation on it to be equal to that from targetWords.
The conversion operation is described in the following two steps:
**Append** any lowercase letter that is **not present** in the string to its end.
• For example, if the string is "abc", the letters 'd', 'e', or 'y' can be added to it, but not 'a'. If 'd' is added, the resulting string will be "abcd".
Rearrange the letters of the new string in any arbitrary order.
• For example, "abcd" can be rearranged to "acbd", "bacd", "cbda", and so on. Note that it can also be rearranged to "abcd" itself.
Return the **number of strings in targetWords that can be obtained by performing the operations on any string of **startWords.
Note that you will only be verifying if the string in targetWords can be obtained from a string in startWords by performing the operations. The strings in startWords do not actually change during this process.
Example 1:
Input: startWords = ["ant","act","tack"], targetWords = ["tack","act","acti"]
Output: 2
Explanation:
- In order to form targetWords[0] = "tack", we use startWords[1] = "act", append 'k' to it, and rearrange "actk" to "tack".
- There is no string in startWords that can be used to obtain targetWords[1] = "act".
Note that "act" does exist in startWords, but we must append one letter to the string before rearranging it.
- In order to form targetWords[2] = "acti", we use startWords[1] = "act", append 'i' to it, and rearrange "acti" to "acti" itself.
Example 2:
Input: startWords = ["ab","a"], targetWords = ["abc","abcd"]
Output: 1
Explanation:
- In order to form targetWords[0] = "abc", we use startWords[0] = "ab", add 'c' to it, and rearrange it to "abc".
- There is no string in startWords that can be used to obtain targetWords[1] = "abcd".
Constraints:
• 1 <= startWords.length, targetWords.length <= 5 * 104
• 1 <= startWords[i].length, targetWords[j].length <= 26
• Each string of startWords and targetWords consists of lowercase English letters only.
• No letter occurs more than once in any string of startWords or targetWords.
## Solution (Java)
class Solution {
private Set<Integer> set;
private void preprocess(String[] words) {
set = new HashSet<>();
for (String word : words) {
int bitMap = getBitMap(word);
}
}
private boolean matches(int bitMap) {
return set.contains(bitMap);
}
private int getBitMap(String word) {
int result = 0;
for (int i = 0; i < word.length(); i++) {
int position = word.charAt(i) - 'a';
result |= (1 << position);
}
return result;
}
private int addBit(int bitMap, char c) {
int position = c - 'a';
bitMap |= (1 << position);
return bitMap;
}
private int removeBit(int bitMap, char c) {
int position = c - 'a';
bitMap &= ~(1 << position);
return bitMap;
}
public int wordCount(String[] startWords, String[] targetWords) {
if (startWords == null || startWords.length == 0) {
return 0;
}
if (targetWords == null || targetWords.length == 0) {
return 0;
}
preprocess(startWords);
int count = 0;
for (String word : targetWords) {
int bitMap = getBitMap(word);
for (int i = 0; i < word.length(); i++) {
bitMap = removeBit(bitMap, word.charAt(i));
if (i > 0) {
bitMap = addBit(bitMap, word.charAt(i - 1));
}
if (matches(bitMap)) {
count++;
break;
}
}
}
return count;
}
}
Explain:
nope.
Complexity:
• Time complexity : O(n).
• Space complexity : O(n).
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2022-10-07 09:20:18
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https://www.controlbooth.com/threads/cheap-gobo-projector.38856/
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Cheap Gobo Projector
Joshua Hoffman
Member
Keep an eye out on eBay for an Altman Micro Ellipse. I believe Times Square has a similar model. I've seen each priced at around \$20-50. They're 75w MR-16 and pretty decent for what they are.
Sounds perfect! I'll keep my eye out!
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2020-05-28 15:41:34
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https://www.gamedev.net/forums/topic/173170-creating-a-dynamic-adventure-game/
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#### Archived
This topic is now archived and is closed to further replies.
# Creating a dynamic adventure game
This topic is 5425 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
MATCH
{
ambient_light += 5%
heat = 1 //Arbitrary heat units
life_time = 1 minute
}
CANDLE
{
ambient_light += 25%
heat = 10
life_time = 10 hours
}
RUG
{
ambient_light += 80%
heat = 5000
life_time = 3 minutes
}
Anyway the above is a very scant example. It really doesn't do justice to the concept, but I have eye strain because I type all day at work. One of the issues with such a system is ensuring that the game can still be won. If you don't know what the user will do, is it possible to ensure that the game is winnable? Does that matter? I don't think so. Let the player invent and reward them if they are smart; if they're not, they can go back to a previous save... [PUTS ON ASBESTOS SUIT...] I know the savegame thing is a hot issue, but that is my opinion in this case. It in no way reflects my opinion in all cases, nor should it ... Expect more posts on this. I simply don't have time to list all ideas in this one, plus if it gets much longer no one will read it (I know I wouldn't). [edited by - bob_the_third on August 5, 2003 11:53:00 PM]
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Hey great post. I just recently added something veeeeery similar to your example to my game. All the items are stored in a text file, where each definition basically lists the properties of that item. And of course there is inheritance Although as for what those properties mean currently it''s pretty much "hard" coded. I think this is a good idea, however, one of the things that makes the lucas arts style of puzzles so great is how well they tie in to the storyline, and how zany the puzzle solotions can be at times.
A functional method of creating items and problems that you hint at wont be able to recreate the same quality feel of puzzles in those games. Still, I have nothing against games that have very dynamic problems to solve and give you limitless options with which to solve them. I still have a big place in my heart though for a hardcoded mostly linear prewritten, story based puzzle adventure game
But for instance, Deus Ex succeeded very well with that method of keeping things modular and letting object oriented emergence take its course, although much of it was still predetermined. I think games are definately headed to areas where players are more likely to solve problems in a way that the designers DIDN''T imagine rather than the way the designers decided them to solve it.
And one of the keys to emergence is, in my opinion, to as you say take a bottom-up approach. The game of LIFE with the cells expanding, or the flocking algoithms show that with a few good simple rules there can emerge an extremely complex system.
The only problem I see is that an adventure game almost requires a really good story to tie things together, and the puzzles need to fit. If you can find a way to make an adventure game that''s fairly dynamic, with unscripted puzzles that still fit into the storyline (hardcoded or dynamically generated), and it still has a good story and is fun to play, you will have created a great leap forward! I''m not sure if it will be as easy as I make it sound though lol.
I think that as games progress, players will be able to have more say in their performance rather than being basically fed cues and acting on them. But I''m not sure if that''s a good thing or a bad thing, because the experience of acting out a good storyline, even if you are mostly acting as was intended, is as much a part of gaming for me as being able to play around and do your own thing.
Just want to add, I don''t think all the technology or designing in the world will find a way to blend follow-the-lead-designer style gaming and follow-your-own-lead style gaming into one game, and keep the essence of both.
It''s like oil and water.
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The difficulty in creating a dynamic adventure game is the fact that most adventures games have static puzzles and solutions by nature. For instance your example of being trapped in a dark room, if you always have a candle, match and rug. Then the puzzle is static and always the same. You know from the last time you played that you need to light the candle to escape.
In order to make a traditonal sierra style adventure game to have extensive replay ability then you need to make it dynamic so that each time you play things are diffrent. To this you''d have to create a large number of nodes and elements, and then allow the game to assemble these nodes into winable game each time.
For instance let say you 4 diffrent fire generating elements, a match, a ligher, a flint arrow head, and a strip of pottassim. Now depending on which nodes the program has joined together to form this version of the game. The player will have one or more of these when they reach the dark room assuming the dark room is in that version of the game. The player now has to get light into the room put how they do will be slightly diffrent depending which nodes the game posses. You could furthur increase replay ability by randomizing the contents of the nodes. For instance the dark contains map to buryed gold. You could set it up so that the map is painted on the wall, sown into the rug or carved into the candle. That way if the player lights rug on fire, they may do so only to discover they have destroyed the very map they wanted to retrive.
However there is still a static nature to the game since the puzzle have finite preprogrammed solutions.
-----------------------------------------------------
Writer, Programer, Cook, I''m a Jack of all Trades
Current Design project
Chaos Factor Design Document
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If it were just about a sequence of seperated rooms, each with a puzzle like this it wouldn''t be too bad.
But once you start letting the player do things like, say, blow up buildings and distrupting the entire city around him, you open up a can of worms as to how to model everything he''s capable of doing.
You could restrict what the world lets him do, but that inevitably brings it down to the level of interaction we already have.
So the only real solution is to invent a world and situations that you can feasably design a system to handle with the dynamic range you''re interested in. One way to do this could be to reduce the level of technology(and therefore potential world situations) available until you reach a level that''s doable. The modern world has so many distinct *things* in it; that''s why it''s so hard to recreate in exacting detail. Go back to the Stone Age, and you have a bunch of people, creatures, a few simple possessions, and the landscape. That wouldn''t be too hard to make a game from.
Another way would be to give the player very few real choices. Like a "Robinson Crusoe" game where the player has to build shelter and hunt to survive on a desert island. The only buildings the player gets to knock down are the ones he makes. There aren''t other people around to make stupid AI errors and destroy the sense of reality, either. (Well, if you followed the book exactly there would be, later on, but the earliest parts are what interest people the most anyway.)
And we already engage in a lot of both of these things in existing games. For example, we never see a military FPS game where between your combat missions you get to wander around the local town doing whatever, because it would be too hard to include both the entire off-duty segment and the combat too. So instead it''s simply one fight after the next.
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Straying from the dynamics, if the point is to be able to "discover" your own game, you could have different people you know design different chapters.
For example, your whole team pitches in for the first chapter, which can be as long or as short as you want it to be, and designs the engine and starts off the story, basically getting the game on its feet, then different members of the team, or fans of the game, could take turns using the engine to develop their own chapters with their own puzzles and plot twists if allowed. what do you think?
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quote:
bob_the_third :
My seed of an idea right now (again in and of itself not original) is to assign properties to each object you create.
The problem I see is: because of the way words are selected in languages (whether you believe it is to categorize or to differentiate), attributes tend to be both ill-defined and numerous.
You had three properties that determine the "flammability" of those three objects. Probably you could create some base classes for the objects that burn readily, can be burnt, are damaged by fire, and are invulnerable. (and these classes would have several properties that enumerate this "flammable" attribute).
Now you move on to, say, "movable". Again, there are a few basic properties (required strength, leverage, maybe something for attached items). More base classes (multiple inheritance).
Now move on to the next attribute... and the next. Once you have fourty or fifty attributes (and a hundred or two quantifiable properties), you can probably handle the simple -- simple -- interactions between a hundred or so objects.
You have a quest where you have to poke something through a keyhole to knock loose the key. You need a property for that (just size doesn''t work as not everything is rectilinear). You have a quest where you need to get past a bull. Might need weapon properties, possibly color+capelike properties.
The problem is that we''re taught to see things in hierarchies. Indeed, much time is taken creating taxonomies of creatures, objects, etc. But in general the hierarchy is just resolving one property at each level of depth -- one view of reality. You really need hundreds of hierarchies minimally.
Plus, consider interactions. A match has properties. A flame does. Combine the two, you have a "lit match". Okay, this could be a flag -- but what if the match is combined with water? It acts differently. What if it''s soaked in gasoline? Very different picture.
I don''t want to discourage you, though. That''s how I picture reality. It''s just been a problem I''ve been tossing around in my head since... well, a long time. Finding a solution for a limited set of items is doable. But if you want reality modelling, there''s just a whole slew of deatil -- and every time you create an object you have to look at all possible interactions, and compare it to all quest types. It starts to get daunting.
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This is neat thinking, imo, and I wish I were more technically skilled to be able to address the problem in a clearer way, so I hope what I am saying makes sense; it's been a long two days, and IT maintenance weekend is looming starting Friday.
The design side of me is telling me to say to you that the solution lies not in the type of dynamicism you assign to object, it properties or attributes, or a puzzle design, but in how the story is designed that dictates limitations of the dynamicism you seek in the range of solutions that are realistic and comprehensible in playtime terms to the player to choose from quickly.
Having tried not to make that sound like I was puking all over the screen in metaphores, let me give you an example from my adventure game.
In my game design, the world and the levels have a finite array of natural physics and material attributes (gravity, wind, current; densities of objects like wood, water, air, stone, metal). So the levels have a topography and geology pretty normal looking.
The features I design as superior technology and/or supernaturalism supercede in certain cases the preset params for physics and material, giving the player a range of responses in their inventory or ability at that time and place in the game.
The piece of the story that I am designing the level for has a reasonable range of approaches (as solutions to puzzles or escape from traps or inventions/constructions/manipulation of objects/environment/NPCs/opponents/foos) to the complications I compose.
Your assertion that thousands or millions of solutions with varying degress of success, imo may not matter as much as an array of solutions the player can create in a fairly short period of time while engaged in play action. This is based on the assumption that if time is important to satisfaction factors in user play (as percieved as entertainment value by the player), then a zillion solutions are over design, even if perfect or amazingly high standards design.
Put another way, if I were on a fairly complex level, and I had to put together a lot of solution factors in my head while I was running around the level avoiding, combatting or compensating for objects or world attributes while figuring out the solution to the primary or secondary challenge the level contains, at a certain point of complexity or chaos, fun in gameplay becomes a factor of diminishing returns. I hate sitting on a level with a bunch of dead things around me thinking, "HTF do I get out of here, or open this thing, or make this new foo work?"
Am I just amazingly intellectually lazy, or do I want to play in a game, and thinking is something I do for a job or for my girlfriend?
This is based entirely on my naive assumption that in game design, you are going to make your best game if it is the game that you want to play.
So I put myself in the shoes of a player, and realize from my experiences as a game player before I ever started my game design, that super complex levels and majorly intricate puzzles were not much more fun than the fun I was already having trying to discover the larger world mystery driving the adventure to begin with, and what the changes in complexity were really for was the variety of challenge necessary to keep players engaged.
This is the story design process I am talking about as the guide. I don't tell my player everything up front, like in an intro cinematic showing the reason I am going to be playing for the rest of the game, e.g., this is the quest for the treasure of so and so. Rather I'd like to keep them guessing, with hints and glimpses of the larger mystery to discover, and keep their engagement and involvement levels really high.
Maybe I am just speaking with blinders, since I can only see this technique as usable in my type of design, the epic mystery adventure, and am not really seeing a larger game design issue. Fatigue and tunnel vision can cause this, and I am sure you will point out where I'm missing something.
Many game design books point to how in each level you design, there is (without being so formulaic that individual outstanding creative originality is ruled out by strictly interpreted and applied design criteria; for in some cases I have levels that take a few minutes or less to complete, but in other cases, I have levels that are going to take you a significant amout of time, perhaps hours over a few days, to complete. But I give you rewards worthy to the effort so you take away the value of the payoff and still have fun) only so much difficulty or complexity you want in any level, and also many game design books indicate after a pretty intense or intricate/complex level, you want to provide an easier, "cooling off" level afterwards for the benefit of giving the player some mental rest.
So, how much fun in terms of what makes the player play, or makes the player keep going or makes the player rave to their friends is a thousand or more possible solutions? Aren't a reasonable amount of logically (problems solving faculties being engaged by the player in gametime) configurable solutions to any given complications design, whether trick, trap, puzzle or clue solving pretty much all you need to satisfy the vast majority of players?
Are there really so many players of your game, as a percentage of the total number of players who bought your title, going to sit around and say, "It was no fun because I couldn't solve it this way", when in playtesting, that array of solutions design players create during play went through vetting and/or redesign/repurposing for the elusive fun factor improvement process anyway, and you got the best your level could give you?
Will all those innumerable solutions make all players happy all the time?
Am I just completely exhausted after two 15 hour days, making no sense whatsoever, and perfectly entitling myself to flamage, or does this make any sense to the question you asked, or bear any resemblance to even addressing the issue?
Proceed Johnny Torch..
[edited by - adventuredesign on August 7, 2003 5:44:31 AM]
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Very interesting questions you raise bob. I have also been tinkering with a similar idea, but instead of focusing on objects and their properties I have been dealing with human interaction and NPCs (that is a topic of its own).
Your idea all sounds good on paper, but as Merle points out, surely you would soon reach a point where the number of properties and actions just got so huge that it wouldn''t be fun anymore to try designing the world.
Take the example of trying to light a match. How would you define the striking surface (of a matchbox)? Would it be hardcoded that the match could light only on the matchbox? Would you define a property for the surface that enabled it to light matches?
But enough pessimism! I consider myself an optimst, so I belive it could be done. But you would need to think long and hard of what properties and actions should be available in the game.
Your original question was if it would be possible to design an an adventure/puzzle game that suprised yourself everytime you generated a new quest. One idea would be to have your players/fanbase submit new objects. This could create a huge array of objects and many potentials and fun/suprising combiniations.
As for creating a "winnable game" I think that too would be possible. Just let the computer use an A*-algorithm for finding the best solution.
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I''m going to be honest up front. I haven''t completely read all the responses, but I did skim them to get a general feel. I will respond in part here with some more of my thoughts and then more fully later when I''m not rushed.
Everyone: Agreed. It''s a tough problem, and having too many potential solutions could very well decrease the fun factor.
The thing that I want is to be rewarded for my creativity, not for trying a bunch of stuff till I find out what the designer wants me to do. What I liked about the MI series was the humor and fun-ness of the story and the feel of the game. What I didn''t like was the gameplay that went like this:
"Well I tried the cheetos. Hmm. Is that a monkey in the corner. Don''t know what good it would do, but let''s try every command on it...Well I''ll be, that was it!" I feel like a person trying to brute-force a combination lock. Ick!
Instead it would be great if I could say, "Well I need to get out of this room...let''s try the axe. Yeah, that worked but somebody heard me. I wonder if there was a better way. Won''t know till it''s over, and maybe not even then."
I really hated it when Guybrush would say, "I''m not picking that up." or "No." or just not do stuff. It all seemed very arbitrary because it was statically designed.
So what I''m thinking is this:
You define the objectives, scenes, and objects. Using genetic algorithms, a software tool suggests object selection (but not necessarily placement) for each room that meets the requirements you set.
More later. I gotta go.
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quote:
bob_the_third: You define the objectives, scenes, and objects. Using genetic algorithms, a software tool suggests object selection (but not necessarily placement) for each room that meets the requirements you set.
I think it works for a simplified situation like that, where the player is wandering through rooms, and each room contains the items needed to get to the next. For one puzzle, the model holds up, but I''m worried about what happens in a non-linear game.
The trick comes when there are many different areas, a number of barriers, and items scattered around. You have to scatter them so that you can get past each barrier, preferably in several ways (otherwise why have such a complex model?). And the system has to predict usage and compensate.
For example, in the starting area you have axe, match, tinder. First blockade is a door. In the second area, candle, and the blockade is "generate enough light". If the player uses the axe on the door, everything works out, but if they use match+tinder to burn the door down, there won''t be a way to light the candle (unless you unrealistically leave the door burning).
Of course you can remedy the system by just dumping in lots of objects, but I don''t think the game would be much fun then...
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2018-06-23 14:28:53
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http://cvgmt.sns.it/paper/3034/
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# A piecewise Korn inequality in $SBD$ and applications to embedding and density results
created by friedrich on 06 May 2016
[BibTeX]
Preprint
Inserted: 6 may 2016
Last Updated: 6 may 2016
Year: 2016
Abstract:
We present a piecewise Korn inequality for generalized special functions of bounded deformation ($GSBD^2$) in a planar setting generalizing the classical result in elasticity theory to the setting of functions with jump discontinuities. We show that for every configuration there is a partition of the domain such that on each component of the cracked body the distance of the function from an infinitesimal rigid motion can be controlled solely in terms of the linear elastic strain. In particular, the result implies that $GSBD^2$ functions have bounded variation after subtraction of a piecewise infinitesimal rigid motion. As an application we prove a density result in $GSBD^2$. Moreover, for all $d \ge 2$ we show $GSBD^2(\Omega) \subset (GBV(\Omega;{\Bbb R}))^d$ and the embedding $SBD^2(\Omega) \cap L^\infty(\Omega;{\Bbb R}^d) \hookrightarrow SBV(\Omega;{\Bbb R}^d)$ into the space of special functions of bounded variation ($SBV$). Finally, we present a Korn-Poincaré inequality for functions with small jump sets in arbitrary space dimension.
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2019-05-20 22:27:51
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https://chromium.googlesource.com/chromium/deps/icu.git/+/42d5027992a0946942839b8821765e1512afbc21/source/common/unicode/edits.h
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*
• {@link #getFineIterator()} retains full granularity of change edits. *
• {@link #getFineChangesIterator()} retains full granularity of change edits, and when calling * next() on the iterator, skips over no-change edits (unchanged regions). *
• {@link #getCoarseIterator()} treats adjacent change edits as a single edit. (Adjacent no-change * edits are automatically merged during the construction phase.) *
• {@link #getCoarseChangesIterator()} treats adjacent change edits as a single edit, and when * calling next() on the iterator, skips over no-change edits (unchanged regions). *
* * For example, consider the string "abcßDeF", which case-folds to "abcssdef". This string has the * following fine edits: *
*
• abc ⇨ abc (no-change) *
• ß ⇨ ss (change) *
• D ⇨ d (change) *
• e ⇨ e (no-change) *
• F ⇨ f (change) *
* and the following coarse edits (note how adjacent change edits get merged together): *
*
• abc ⇨ abc (no-change) *
• ßD ⇨ ssd (change) *
• e ⇨ e (no-change) *
• F ⇨ f (change) *
* * The "fine changes" and "coarse changes" iterators will step through only the change edits when their * Edits::Iterator::next() methods are called. They are identical to the non-change iterators when * their Edits::Iterator::findSourceIndex() or Edits::Iterator::findDestinationIndex() * methods are used to walk through the string. * * For examples of how to use this class, see the test TestCaseMapEditsIteratorDocs in * UCharacterCaseTest.java. * * An Edits object tracks a separate UErrorCode, but ICU string transformation functions * (e.g., case mapping functions) merge any such errors into their API's UErrorCode. * * @stable ICU 59 */ class U_COMMON_API Edits U_FINAL : public UMemory { public: /** * Constructs an empty object. * @stable ICU 59 */ Edits() : array(stackArray), capacity(STACK_CAPACITY), length(0), delta(0), numChanges(0), errorCode_(U_ZERO_ERROR) {} /** * Copy constructor. * @param other source edits * @stable ICU 60 */ Edits(const Edits &other) : array(stackArray), capacity(STACK_CAPACITY), length(other.length), delta(other.delta), numChanges(other.numChanges), errorCode_(other.errorCode_) { copyArray(other); } /** * Move constructor, might leave src empty. * This object will have the same contents that the source object had. * @param src source edits * @stable ICU 60 */ Edits(Edits &&src) U_NOEXCEPT : array(stackArray), capacity(STACK_CAPACITY), length(src.length), delta(src.delta), numChanges(src.numChanges), errorCode_(src.errorCode_) { moveArray(src); } /** * Destructor. * @stable ICU 59 */ ~Edits(); /** * Assignment operator. * @param other source edits * @return *this * @stable ICU 60 */ Edits &operator=(const Edits &other); /** * Move assignment operator, might leave src empty. * This object will have the same contents that the source object had. * The behavior is undefined if *this and src are the same object. * @param src source edits * @return *this * @stable ICU 60 */ Edits &operator=(Edits &&src) U_NOEXCEPT; /** * Resets the data but may not release memory. * @stable ICU 59 */ void reset() U_NOEXCEPT; /** * Adds a no-change edit: a record for an unchanged segment of text. * Normally called from inside ICU string transformation functions, not user code. * @stable ICU 59 */ void addUnchanged(int32_t unchangedLength); /** * Adds a change edit: a record for a text replacement/insertion/deletion. * Normally called from inside ICU string transformation functions, not user code. * @stable ICU 59 */ void addReplace(int32_t oldLength, int32_t newLength); /** * Sets the UErrorCode if an error occurred while recording edits. * Preserves older error codes in the outErrorCode. * Normally called from inside ICU string transformation functions, not user code. * @param outErrorCode Set to an error code if it does not contain one already * and an error occurred while recording edits. * Otherwise unchanged. * @return TRUE if U_FAILURE(outErrorCode) * @stable ICU 59 */ UBool copyErrorTo(UErrorCode &outErrorCode); /** * How much longer is the new text compared with the old text? * @return new length minus old length * @stable ICU 59 */ int32_t lengthDelta() const { return delta; } /** * @return TRUE if there are any change edits * @stable ICU 59 */ UBool hasChanges() const { return numChanges != 0; } /** * @return the number of change edits * @stable ICU 60 */ int32_t numberOfChanges() const { return numChanges; } /** * Access to the list of edits. * * At any moment in time, an instance of this class points to a single edit: a "window" into a span * of the source string and the corresponding span of the destination string. The source string span * starts at {@link #sourceIndex()} and runs for {@link #oldLength()} chars; the destination string * span starts at {@link #destinationIndex()} and runs for {@link #newLength()} chars. * * The iterator can be moved between edits using the next(), findSourceIndex(int32_t, UErrorCode &), * and findDestinationIndex(int32_t, UErrorCode &) methods. * Calling any of these methods mutates the iterator to make it point to the corresponding edit. * * For more information, see the documentation for {@link Edits}. * * @see getCoarseIterator * @see getFineIterator * @stable ICU 59 */ struct U_COMMON_API Iterator U_FINAL : public UMemory { /** * Default constructor, empty iterator. * @stable ICU 60 */ Iterator() : array(nullptr), index(0), length(0), remaining(0), onlyChanges_(FALSE), coarse(FALSE), dir(0), changed(FALSE), oldLength_(0), newLength_(0), srcIndex(0), replIndex(0), destIndex(0) {} /** * Copy constructor. * @stable ICU 59 */ Iterator(const Iterator &other) = default; /** * Assignment operator. * @stable ICU 59 */ Iterator &operator=(const Iterator &other) = default; /** * Advances the iterator to the next edit. * @param errorCode ICU error code. Its input value must pass the U_SUCCESS() test, * or else the function returns immediately. Check for U_FAILURE() * on output or use with function chaining. (See User Guide for details.) * @return TRUE if there is another edit * @stable ICU 59 */ UBool next(UErrorCode &errorCode) { return next(onlyChanges_, errorCode); } /** * Moves the iterator to the edit that contains the source index. * The source index may be found in a no-change edit * even if normal iteration would skip no-change edits. * Normal iteration can continue from a found edit. * * The iterator state before this search logically does not matter. * (It may affect the performance of the search.) * * The iterator state after this search is undefined * if the source index is out of bounds for the source string. * * @param i source index * @param errorCode ICU error code. Its input value must pass the U_SUCCESS() test, * or else the function returns immediately. Check for U_FAILURE() * on output or use with function chaining. (See User Guide for details.) * @return TRUE if the edit for the source index was found * @stable ICU 59 */ UBool findSourceIndex(int32_t i, UErrorCode &errorCode) { return findIndex(i, TRUE, errorCode) == 0; } /** * Moves the iterator to the edit that contains the destination index. * The destination index may be found in a no-change edit * even if normal iteration would skip no-change edits. * Normal iteration can continue from a found edit. * * The iterator state before this search logically does not matter. * (It may affect the performance of the search.) * * The iterator state after this search is undefined * if the source index is out of bounds for the source string. * * @param i destination index * @param errorCode ICU error code. Its input value must pass the U_SUCCESS() test, * or else the function returns immediately. Check for U_FAILURE() * on output or use with function chaining. (See User Guide for details.) * @return TRUE if the edit for the destination index was found * @stable ICU 60 */ UBool findDestinationIndex(int32_t i, UErrorCode &errorCode) { return findIndex(i, FALSE, errorCode) == 0; } /** * Computes the destination index corresponding to the given source index. * If the source index is inside a change edit (not at its start), * then the destination index at the end of that edit is returned, * since there is no information about index mapping inside a change edit. * * (This means that indexes to the start and middle of an edit, * for example around a grapheme cluster, are mapped to indexes * encompassing the entire edit. * The alternative, mapping an interior index to the start, * would map such an interval to an empty one.) * * This operation will usually but not always modify this object. * The iterator state after this search is undefined. * * @param i source index * @param errorCode ICU error code. Its input value must pass the U_SUCCESS() test, * or else the function returns immediately. Check for U_FAILURE() * on output or use with function chaining. (See User Guide for details.) * @return destination index; undefined if i is not 0..string length * @stable ICU 60 */ int32_t destinationIndexFromSourceIndex(int32_t i, UErrorCode &errorCode); /** * Computes the source index corresponding to the given destination index. * If the destination index is inside a change edit (not at its start), * then the source index at the end of that edit is returned, * since there is no information about index mapping inside a change edit. * * (This means that indexes to the start and middle of an edit, * for example around a grapheme cluster, are mapped to indexes * encompassing the entire edit. * The alternative, mapping an interior index to the start, * would map such an interval to an empty one.) * * This operation will usually but not always modify this object. * The iterator state after this search is undefined. * * @param i destination index * @param errorCode ICU error code. Its input value must pass the U_SUCCESS() test, * or else the function returns immediately. Check for U_FAILURE() * on output or use with function chaining. (See User Guide for details.) * @return source index; undefined if i is not 0..string length * @stable ICU 60 */ int32_t sourceIndexFromDestinationIndex(int32_t i, UErrorCode &errorCode); /** * Returns whether the edit currently represented by the iterator is a change edit. * * @return TRUE if this edit replaces oldLength() units with newLength() different ones. * FALSE if oldLength units remain unchanged. * @stable ICU 59 */ UBool hasChange() const { return changed; } /** * The length of the current span in the source string, which starts at {@link #sourceIndex}. * * @return the number of units in the original string which are replaced or remain unchanged. * @stable ICU 59 */ int32_t oldLength() const { return oldLength_; } /** * The length of the current span in the destination string, which starts at * {@link #destinationIndex}, or in the replacement string, which starts at * {@link #replacementIndex}. * * @return the number of units in the modified string, if hasChange() is TRUE. * Same as oldLength if hasChange() is FALSE. * @stable ICU 59 */ int32_t newLength() const { return newLength_; } /** * The start index of the current span in the source string; the span has length * {@link #oldLength}. * * @return the current index into the source string * @stable ICU 59 */ int32_t sourceIndex() const { return srcIndex; } /** * The start index of the current span in the replacement string; the span has length * {@link #newLength}. Well-defined only if the current edit is a change edit. * * The *replacement string* is the concatenation of all substrings of the destination * string corresponding to change edits. * * This method is intended to be used together with operations that write only replacement * characters (e.g. operations specifying the \ref U_OMIT_UNCHANGED_TEXT option). * The source string can then be modified in-place. * * @return the current index into the replacement-characters-only string, * not counting unchanged spans * @stable ICU 59 */ int32_t replacementIndex() const { // TODO: Throw an exception if we aren't in a change edit? return replIndex; } /** * The start index of the current span in the destination string; the span has length * {@link #newLength}. * * @return the current index into the full destination string * @stable ICU 59 */ int32_t destinationIndex() const { return destIndex; } #ifndef U_HIDE_INTERNAL_API /** * A string representation of the current edit represented by the iterator for debugging. You * should not depend on the contents of the return string. * @internal */ UnicodeString& toString(UnicodeString& appendTo) const; #endif // U_HIDE_INTERNAL_API private: friend class Edits; Iterator(const uint16_t *a, int32_t len, UBool oc, UBool crs); int32_t readLength(int32_t head); void updateNextIndexes(); void updatePreviousIndexes(); UBool noNext(); UBool next(UBool onlyChanges, UErrorCode &errorCode); UBool previous(UErrorCode &errorCode); /** @return -1: error or i<0; 0: found; 1: i>=string length */ int32_t findIndex(int32_t i, UBool findSource, UErrorCode &errorCode); const uint16_t *array; int32_t index, length; // 0 if we are not within compressed equal-length changes. // Otherwise the number of remaining changes, including the current one. int32_t remaining; UBool onlyChanges_, coarse; int8_t dir; // iteration direction: back(<0), initial(0), forward(>0) UBool changed; int32_t oldLength_, newLength_; int32_t srcIndex, replIndex, destIndex; }; /** * Returns an Iterator for coarse-grained change edits * (adjacent change edits are treated as one). * Can be used to perform simple string updates. * Skips no-change edits. * @return an Iterator that merges adjacent changes. * @stable ICU 59 */ Iterator getCoarseChangesIterator() const { return Iterator(array, length, TRUE, TRUE); } /** * Returns an Iterator for coarse-grained change and no-change edits * (adjacent change edits are treated as one). * Can be used to perform simple string updates. * Adjacent change edits are treated as one edit. * @return an Iterator that merges adjacent changes. * @stable ICU 59 */ Iterator getCoarseIterator() const { return Iterator(array, length, FALSE, TRUE); } /** * Returns an Iterator for fine-grained change edits * (full granularity of change edits is retained). * Can be used for modifying styled text. * Skips no-change edits. * @return an Iterator that separates adjacent changes. * @stable ICU 59 */ Iterator getFineChangesIterator() const { return Iterator(array, length, TRUE, FALSE); } /** * Returns an Iterator for fine-grained change and no-change edits * (full granularity of change edits is retained). * Can be used for modifying styled text. * @return an Iterator that separates adjacent changes. * @stable ICU 59 */ Iterator getFineIterator() const { return Iterator(array, length, FALSE, FALSE); } /** * Merges the two input Edits and appends the result to this object. * * Consider two string transformations (for example, normalization and case mapping) * where each records Edits in addition to writing an output string.
* Edits ab reflect how substrings of input string a * map to substrings of intermediate string b.
* Edits bc reflect how substrings of intermediate string b * map to substrings of output string c.
* This function merges ab and bc such that the additional edits * recorded in this object reflect how substrings of input string a * map to substrings of output string c. * * If unrelated Edits are passed in where the output string of the first * has a different length than the input string of the second, * then a U_ILLEGAL_ARGUMENT_ERROR is reported. * * @param ab reflects how substrings of input string a * map to substrings of intermediate string b. * @param bc reflects how substrings of intermediate string b * map to substrings of output string c. * @param errorCode ICU error code. Its input value must pass the U_SUCCESS() test, * or else the function returns immediately. Check for U_FAILURE() * on output or use with function chaining. (See User Guide for details.) * @return *this, with the merged edits appended * @stable ICU 60 */ Edits &mergeAndAppend(const Edits &ab, const Edits &bc, UErrorCode &errorCode); private: void releaseArray() U_NOEXCEPT; Edits ©Array(const Edits &other); Edits &moveArray(Edits &src) U_NOEXCEPT; void setLastUnit(int32_t last) { array[length - 1] = (uint16_t)last; } int32_t lastUnit() const { return length > 0 ? array[length - 1] : 0xffff; } void append(int32_t r); UBool growArray(); static const int32_t STACK_CAPACITY = 100; uint16_t *array; int32_t capacity; int32_t length; int32_t delta; int32_t numChanges; UErrorCode errorCode_; uint16_t stackArray[STACK_CAPACITY]; }; U_NAMESPACE_END #endif // __EDITS_H__
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2019-07-21 21:46:15
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https://www.samuelchukwuemeka.com/IntegralCalculus/integration.html
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If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka
For in GOD we live, and move, and have our being. - Acts 17:28
The Joy of a Teacher is the Success of his Students. - Samuel Dominic Chukwuemeka
Integral Calculus
I greet you this day,
Second: view the videos.
Third: solve the solved examples and word problems.
Fourth: check your solutions with my thoroughly-explained solutions.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome.
If you are my student, please do not contact me here. Contact me via the school's system. Thank you for visiting.
Samuel Dominic Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S
Objectives
Students will:
(1.) Discuss the concept of the antiderivative of a functions.
(2.) Determine the antiderivative of functions using the Power Rule.
(3.) Determine the antiderivative of functions using the Methods of Integration.
(4.) Integrate exponential functions.
(5.) Integrate logarithmic functions.
(6.) Integrate trigonometric functions.
(7.) Solve applied problems involving the antiderivative of functions.
Power Rule
Prerequisite Topic: Exponents
The Power Rule of Integrals states that:
$If\:\: \dfrac{dy}{dx} = x^n \\[3ex] dy = x^n dx \\[3ex] then\:\: \displaystyle\int dy = \displaystyle\int x^n dx \\[3ex] y = \dfrac{x^{n + 1}}{n + 1} + C \:\:where\:\: n \ne -1 \\[5ex] If\:\: \dfrac{dy}{dx} = ax^n \:\:where\:\: a \:\:is\:\:a\:\:constant \\[3ex] then\:\: \displaystyle\int dy = \displaystyle\int ax^n dx \\[3ex] y = a\displaystyle\int x^n = \dfrac{ax^{n + 1}}{n + 1} + C \:\:where\:\: n \ne -1$
Integration by Algebraic Substitution
Some functions are integrated using the Algebraic Substitution method
How do you know those kind of functions?
How do you know when to use Algebraic Substitution?
So, typically; when you are given a function that:
(1.) are of certain forms (we shall discuss these forms)
(2.) are not easy to integrate right away/directly
(3.) may involve some cancellation(s) when you differentiate some part(s) of it and make some substitution(s)
Then, you probably need to use Algebraic Substitution.
Steps in Using Algebraic Substitution
Given a function to integrate:
The function has an independent variable say $x$
(1.) Use a variable to make an "appropriate" substitution of some part of that function
Assume the variable is $p$
(2.) Find the derivative of that variable $wrt$ (with respect to) the independent variable
In other words, find $\dfrac{dp}{dx}$
(3.) Find $\dfrac{dx}{dp}$
(4.) Find $dx$ in terms of $dp$.
In other words, make $dx$ the subject of the formula.
(5.) Substitute appropriately for: $p$ for some part of the function and $dx$ in the main function
You will then have a simpler function in $p$ and $dp$ only.
If you do not have a simpler function in $p$, then try another method.
(6.) Integrate the function (substituted function) $wrt$ $p$
(7.) Substitute back.
You were given the original function in $x$
Your answer should also be a function in $x$
Let us discuss the forms of functions that are integrated by Algebraic Substitution
$\color{red}{(1.)\:\: \displaystyle\int f(x)f'(x) dx} \\[3ex] Let\:\: p = f(x) \\[3ex] \dfrac{dp}{dx} = f'(x) \\[5ex] \dfrac{dx}{dp} = \dfrac{1}{f'(x)} \\[5ex] dx = \dfrac{dp}{f'(x)} \\[5ex] Substitute \\[3ex] \rightarrow \displaystyle\int f(x)f'(x) dx = \displaystyle\int p * f'(x) * \dfrac{dp}{f'(x)} \\[5ex] \displaystyle\int p dp \\[3ex] = \dfrac{p^2}{2} + C \\[5ex] Substitute\:\:back \\[3ex] = \dfrac{f^2(x)}{2} + C \\[5ex] \therefore \color{red}{\displaystyle\int f(x)f'(x) dx = \dfrac{f^2(x)}{2} + C} \\[5ex] Similarly:\:\: \color{red}{\displaystyle\int -f(x)f'(x) dx = \dfrac{-f^2(x)}{2} + C} \\[5ex] \color{red}{(2.)\:\: \displaystyle\int \dfrac{f'(x)}{f(x)} dx} \\[5ex] Let\:\: p = f(x) \\[3ex] \dfrac{dp}{dx} = f'(x) \\[5ex] \dfrac{dx}{dp} = \dfrac{1}{f'(x)} \\[5ex] dx = \dfrac{dp}{f'(x)} \\[5ex] Substitute \\[3ex] \rightarrow \displaystyle\int \dfrac{f'(x)}{f(x)} dx = \displaystyle\int \dfrac{f'(x)}{p} * \dfrac{dp}{f'(x)} \\[5ex] = \displaystyle\int \dfrac{dp}{p} \\[5ex] = \ln p + C \\[3ex] Substitute\:\:back \\[3ex] = \ln f(x) + C \\[3ex] \therefore \color{red}{\displaystyle\int \dfrac{f'(x)}{f(x)} dx = \ln f(x) + C} \\[5ex] Similarly:\:\: \color{red}{\displaystyle\int \dfrac{-f'(x)}{f(x)} dx = -\ln f(x) + C} \\[5ex] \color{red}{(3.)\:\: \displaystyle\int e^{kx} dx ...k \:\:is\:\:a\:\:constant} \\[3ex] Let\:\: p = kx \\[3ex] \dfrac{dp}{dx} = k \\[5ex] \dfrac{dx}{dp} = \dfrac{1}{k} \\[5ex] dx = \dfrac{dp}{k} \\[5ex] Substitute \\[3ex] \rightarrow \displaystyle\int e^{kx} dx = \displaystyle\int e^{p} * \dfrac{dp}{k} \\[5ex] = \dfrac{1}{k} \displaystyle\int e^p dp \\[5ex] = \dfrac{1}{k} * e^p + C \\[5ex] Substitute\:\:back \\[3ex] = \dfrac{1}{k} * e^{kx} + C \\[5ex] = \dfrac{e^{kx}}{k} + C \\[5ex] \therefore \color{red}{\displaystyle\int e^{kx} dx = \dfrac{e^{kx}}{k} + C} \\[5ex] \color{red}{(4.)\:\: \displaystyle\int e^{-kx} dx ...k \:\:is\:\:a\:\:constant} \\[3ex] Let\:\: p = -kx \\[3ex] \dfrac{dp}{dx} = -k \\[5ex] \dfrac{dx}{dp} = -\dfrac{1}{k} \\[5ex] dx = -\dfrac{dp}{k} \\[5ex] Substitute \\[3ex] \rightarrow \displaystyle\int e^{kx} dx = \displaystyle\int e^{p} * -\dfrac{dp}{k} \\[5ex] = -\dfrac{1}{k} \displaystyle\int e^p dp \\[5ex] = -\dfrac{1}{k} * e^p + C \\[5ex] Substitute\:\:back \\[3ex] = -\dfrac{1}{k} * e^{kx} + C \\[5ex] = -\dfrac{e^{kx}}{k} + C \\[5ex] \therefore \color{red}{\displaystyle\int e^{-kx} dx = -\dfrac{e^{kx}}{k} + C} \\[5ex] \color{red}{(5.)\:\: \displaystyle\int (ax + b)^n dx ...a, b, n \:\:are\:\:constants} \\[3ex] Let\:\: p = ax + b \\[3ex] \dfrac{dp}{dx} = a \\[5ex] \dfrac{dx}{dp} = \dfrac{1}{a} \\[5ex] dx = \dfrac{dp}{a} \\[5ex] Substitute \\[3ex] \rightarrow \displaystyle\int (ax + b)^n dx = \displaystyle\int p^n * \dfrac{dp}{a} \\[5ex] = \dfrac{1}{a} \displaystyle\int p^n dp \\[5ex] = \dfrac{1}{a} * \dfrac{p^{n + 1}}{n + 1} + C \\[5ex] Substitute\:\:back \\[3ex] = \dfrac{1}{a} * \dfrac{(ax + b)^{n + 1}}{n + 1} + C \\[5ex] = \dfrac{(ax + b)^{n + 1}}{a(n + 1)} + C \\[5ex] \therefore \color{red}{\displaystyle\int (ax + b)^n dx = \dfrac{(ax + b)^{n + 1}}{a(n + 1)} + C} \\[5ex] Similarly:\:\: \color{red}{\displaystyle\int (ax - b)^n dx = \dfrac{(ax - b)^{n + 1}}{a(n + 1)} + C} \\[5ex] \color{red}{(6.)\:\: \displaystyle\int (-ax + b)^n dx ...a, b, n \:\:are\:\:constants} \\[3ex] Let\:\: p = -ax + b \\[3ex] \dfrac{dp}{dx} = -a \\[5ex] \dfrac{dx}{dp} = -\dfrac{1}{a} \\[5ex] dx = -\dfrac{dp}{a} \\[5ex] Substitute \\[3ex] \rightarrow \displaystyle\int (ax + b)^n dx = \displaystyle\int p^n * -\dfrac{dp}{a} \\[5ex] = -\dfrac{1}{a} \displaystyle\int p^n dp \\[5ex] = -\dfrac{1}{a} * \dfrac{p^{n + 1}}{n + 1} + C \\[5ex] Substitute\:\:back \\[3ex] = -\dfrac{1}{a} * \dfrac{(ax + b)^{n + 1}}{n + 1} + C \\[5ex] = -\dfrac{(ax + b)^{n + 1}}{a(n + 1)} + C \\[5ex] \therefore \color{red}{\displaystyle\int (-ax + b)^n dx = -\dfrac{(ax + b)^{n + 1}}{a(n + 1)} + C} \\[5ex] Similarly:\:\: \color{red}{\displaystyle\int (-ax - b)^n dx = -\dfrac{(ax - b)^{n + 1}}{a(n + 1)} + C} \\[5ex]$
Integration by Parts
References
Chukwuemeka, S.D (2016, April 30). Samuel Chukwuemeka Tutorials - Math, Science, and Technology. Retrieved from https://www.samuelchukwuemeka.com
Sisson, P., & Szarvas, T. (2016). Single Variable CALCULUS with Early Transcendentals. Hawkes Learning.
Stroud, K. A., & Booth, D. J. (2001). Engineering Mathematics ($5th$ ed.). Basingstoke: Palgrave.
Tan, S. T. (2004). Applied Calculus for the Managerial, Life, and Social Sciences ($5th$ ed.). Pacific Grove, CA: Brooks/Cole Publishing Company.
Waner, S., & Costenoble, S. (2013). Applied Calculus ($6th$ ed.). Boston, MA: Cengage Learning.
Authority (NZQA), (n.d.). Mathematics and Statistics subject resources. www.nzqa.govt.nz. Retrieved December 14, 2020, from https://www.nzqa.govt.nz/ncea/subjects/mathematics/levels/
Free Jamb Past Questions And Answer For All Subject 2020. (2020, January 31). Vastlearners. https://www.vastlearners.com/free-jamb-past-questions/
GCSE Exam Past Papers: Revision World. Retrieved April 6, 2020, from https://revisionworld.com/gcse-revision/gcse-exam-past-papers
NSC Examinations. (n.d.). www.education.gov.za. https://www.education.gov.za/Curriculum/NationalSeniorCertificate(NSC)Examinations.aspx
School Curriculum and Standards Authority (SCSA): K-12. Past ATAR Course Examinations. Retrieved December 10, 2020, from https://senior-secondary.scsa.wa.edu.au/further-resources/past-atar-course-exams
West African Examinations Council (WAEC). Retrieved May 30, 2020, from https://waeconline.org.ng/e-learning/Mathematics/mathsmain.html
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2021-02-25 22:33:02
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https://stats.stackexchange.com/questions/175056/does-scaling-of-the-ordinal-variables-make-sense-before-pca
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# Does scaling of the ordinal variables make sense before PCA?
I have some data with 200+ variables/columns (30% numerical, 30% Likert 1-5 scale and 40% Likert 1-10 scale). I want to do principal component analysis (PCA) in R. I think I should scale the data before calling psych::principal.
My questions:
1. Is it correct to scale the data having both numerical and categorical variables?
2. Does scaling of categorical variables make sense?
I believe the answer is NO for both questions.
• Likert scale variables are not categorical! They are ordinal. – amoeba says Reinstate Monica Oct 1 '15 at 19:15
• Though we often assume even further that they are interval. – jlimahaverford Oct 1 '15 at 19:22
PCA unfortunately only makes sense with numerical data. For instance, if you have a variable that can take the values {'car', 'train', 'boat'}, it will be difficult to do arithmetic with them. If we replace them with $\{0, 1, 2\}$, we can do arithmetic, but that arithmetic will really not achieve what we want, because we'll be treating these labels like real numbers. As if (train + train = boat), or even train being closer to car than boat is. However we have another option, to create dummy variables, one variable for each value that this categorical variable can take, setting them equal to 1 or 0 accordingly.
(Note: some people would use one less variable than the number of values, letting all 0 indicate the remaining variable, but geometrically this is troubling because the all-zero-variable is closer to all the other variables than they are to eachother, so I would not do that with PCA).
These values can be rescaled and PCA can be applied. It may not be ideal, but at least it's not crazy!
Edit:
I had not noticed the word Likert in your post some how. Likert scales are ordinal, rather than categorical variables. In fact, typically one assumes Likert scales are interval, essentially meaning that the difference between 1 and 2 is the same as the difference between 4 and 5. Because of this scale absolutely makes sense! I have changed your title to use the word "ordinal" rather than "categorical."
• These are valid points, but note that the OP is asking about variables on the Likert scale, which means they are ordinal and not really "categorical" (even though @Shiv called them like that). Arguable treating Likert scale variables like usual numerical variables would make some sense. Perhaps you want to expand your answer to discuss that? – amoeba says Reinstate Monica Oct 1 '15 at 18:48
• @amoeba thanks a lot. I hadn't seen that. Since he used the word categorical, my brain kicked into speed. I am going to edit the title. – jlimahaverford Oct 1 '15 at 19:03
• Thank you @jlimahaverford and amoeba. To summarize my understanding, scaling of Ordinal may make sense but not necessarily Categorical – Shiv Oct 2 '15 at 5:42
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2019-12-10 16:12:59
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https://codereview.meta.stackexchange.com/questions/873/number-list-formatting-followed-by-code-formatting-issue
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# Number list formatting followed by code formatting issue
On this question, I found that when I tried to edit the question and add a numbered list format, it sucked in the code formatting that followed, so I had to add Code: after the list to show the numbered list that I wanted to close it. This allowed the code formatting to start fresh.
• I don't know if this happens in any of the other Stack Sites so I posted it here rather than the Stack Exchange Meta – Malachi Oct 2 '13 at 15:53
This behaviour is the same on all Stack Exchange sites, and it is documented in the editing help. A list item continues until a line is reached that has no indent. This allows you to have multiple paragraphs, quoted text, and code blocks inside a list item.
If you want to follow a numbered list by a code block (without the code block becoming part of the list item), put an HTML comment after the list and before the code block, like this:
1. numbered list
1. numbered list
<!-- comment here -->
code block
code block
• thank you for that insight – Malachi Oct 2 '13 at 17:55
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2020-12-01 09:05:14
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https://tex.stackexchange.com/questions/404757/cell-citation-style-for-biblatex
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Cell citation style for biblatex
Using biblatex, is there a way to format the citations and bibliography to match the style for the Cell family of journals?
Search engines reveal .bst files for bibtex, but nothing for biblatex.
Alternately, is there a good reference for how to format a .bbx, assuming no prior experience with biblatex?
• For the alternative version of the question, Guidelines for customizing biblatex styles is a good starting point. – gusbrs Dec 5 '17 at 19:53
• If you plan to submit to the journal, you should take into account that even if they accept LaTeX submissions they probably will not be able to handle biblatex: Biblatex: submitting to a journal. If you have to use Cell style and there already is a predefined .bst file that ticks all the boxes (does not need to be changed to comply with Cell guidelines at all) you don't have to use biblatex, you can go on using the .bst file (if you don't need any of biblatex's advanced features that is). – moewe Dec 5 '17 at 19:57
• @moewe - The advanced feature I want to preserve is changing the titles to hyperlink to the doi. This is for review -- I'll worry about submission later. tex.stackexchange.com/questions/23832/… – Marc Dec 5 '17 at 20:20
As the Cell instruction for authors only give examples for articles, books, and chapters/proceedings, modifying the standard style is not all that daunting.
\documentclass{article}
\usepackage[style=authoryear, giveninits=true]{biblatex}
\usepackage{xpatch}
% Some general changes
\DeclareNameAlias{sortname}{last-first}
\renewcommand*{\bibinitdelim}{}
\renewbibmacro*{in:}{%
\iffieldequalstr{entrytype}{inproceedings}{%
}{}%
}
% Changes for Book
\csletcs{abx@macro@publisher+location+date@orig}{abx@macro@publisher+location+date}
\renewbibmacro*{publisher+location+date}{%
\printtext[parens]{\usebibmacro{publisher+location+date@orig}}
}
% Changes for inproceedings
\DeclareFieldFormat[inproceedings]{title}{#1\isdot}
\xpatchbibmacro{byeditor+others}{%
\printnames[byeditor]{editor}%
\clearname{editor}%
}{%
\printnames[byeditor]{editor}%
\clearname{editor}
\bibstring{editor}
}{}{}
% Changes in Article
\DeclareFieldFormat[article]{title}{#1}
\DeclareFieldFormat[article]{journaltitle}{#1\isdot}
\DeclareFieldFormat[article]{volume}{\textit{#1}}
\DeclareFieldFormat[article]{pages}{#1}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@ARTICLE{SL00,
author = {Sondheimer, N and Lindquist, S},
year = {2000},
title = {Rnq1: an epigenetic modifier of protein function in yeast.},
journaltitle = {Mol. Cell},
volume = {5},
pages = {163--172}
}
@INPROCEEDINGS{King03,
author = {King, S M},
editor = {M Schliwa},
title = {Dynein motors: Structure, mechanochemistry and regulation},
booktitle = {Molecular Motors},
publisher = {Wiley-VCH Verlag GmbH},
pages = {45--78},
year = {2003}
}
@BOOK{CJZ97,
author = {Cowan, W M and Jessell, T M and Zipursky, S L},
title = {Molecular and Cellular Approaches to Neural Development},
publisher = {Oxford University Press},
year = {1997}
}
\end{filecontents}
\usepackage{url}
\begin{document}
\nocite{*}
See examples at \url{http://www.cell.com/cell/authors}
\noindent Cowan, W.M., Jessell, T.M., and Zipursky, S.L. (1997). Molecular and Cellular Approaches to Neural Development (New York: Oxford University Press).
\noindent King, S.M. (2003). Dynein motors: Structure, mechanochemistry and regulation. In Molecular Motors, M. Schliwa, ed. (Weinheim, Germany: Wiley-VCH Verlag GmbH), pp. 45--78.
\noindent Sondheimer, N., and Lindquist, S. (2000). Rnq1: an epigenetic modifier of protein function in yeast. Mol. Cell \textit{5}, 163--172.
\printbibliography
\end{document}
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2019-06-19 09:14:30
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https://www.askiitians.com/forums/Mechanics/a-liquid-is-kept-in-a-vessel-of-cylindrical-size-w_193301.htm
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A liquid is kept in a vessel of cylindrical size which is rotating along its axis. The liquid rises at the sides. If the radius of the vessel is 0.05m and the speed of rotaion is 2 rev/second , find the difference in height of the liquid at the centre of the vessel and its side g=9.8 m/s2
one year ago
Arun
19620 Points
Please find below the solution to your asked query.according to the bernoulli's theorem:p+12ρv2 = constantwe knoe v = rωapplying these equation at the side wall and centre of the vesselpcentre 12ρvcentre2 = pside 12ρvside2 vcenter = 0pcentre −pside = 12ρr2ω2hρg =12ρr2ω2h = 12gr2ω2 = 1×0.05×0.05×(2π×2)220 = 0.02 m= 2 cm
one year ago
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2019-04-18 22:40:13
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https://byjus.com/diffraction-grating-formula/
|
# Diffraction Grating Formula
A diffraction grating defines an optical component with a periodic structure which splits the light into various beams that travel in different directions. It is an alternative way to observe spectra other than a prism. Generally, when light is incident on the grating, the split light will have maxima at an angle θ. The formula for diffraction grating is used to calculate the angle.
## Diffraction grating formula
Where,
$\lambda n =dSin \theta _{n}$
n = order of grating,
d = distance between two fringes or spectra
λ = wavelength of light
θ = angle to maxima
Question 1: A diffraction grating is of width 5 cm and produces a deviation of 300
in the second-order with the light of wavelength 580 nm. Find the slit spacing.
Solution:
Given: Angle θ =300 , order n = 2, wavelength λ = 580 nm.
The slit spacing is given by,
$\lambda n =dSin \theta _{n}$
d = 2×580×10-9 /sin $30^{0}$
$d=2.320\times10^{-6}$ m
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2020-08-14 11:39:04
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https://gmatclub.com/forum/if-a-fair-6-sided-die-is-rolled-three-times-what-is-the-probability-t-208141.html
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# If a fair 6-sided die is rolled three times, what is the probability t
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If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled?
A. 25/216
B. 50/216
C. 25/72
D. 25/36
E. 5/6
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Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink]
### Show Tags
04 Nov 2015, 05:39
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shyind wrote:
If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled?
A. 25/216
B. 50/216
C. 25/72
D. 25/36
E. 5/6
Total ways in which a 6-sided die can be rolled three times = 6*6*6 = 216
To get exactly one 3, there are three ways:
A 3 on the first roll and non 3 on other two rolls. This can be done in 1*5*5 = 25 ways.
The 3 could be on the second or third roll too. So total favorable cases = 25*3 = 75
Required Probability = 75/216 = 25/72
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##### General Discussion
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Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink]
### Show Tags
04 Nov 2015, 21:22
shyind wrote:
If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled?
A. 25/216
B. 50/216
C. 25/72
D. 25/36
E. 5/6
Probability if getting 3 on a die is: P(3)=1/6
Probability of not getting 3 on a die is nP(3)=5/6
Let the three dies be denoted by P1,P2 and P3
Probability of getting 3 on the first die and not getting 3 on the other two dies is given by:-
=P1(3)*nP(3)*nP(3)
=1/6*5/6*5/6
=25/216
As there are 3 dies,so similarly for the rest of the two dies probability will be 25/216
Summing up all the 3 cases we get:
=3*25/216
=25/72
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Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink]
### Show Tags
05 Nov 2015, 01:22
1
1
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled?
A. 25/216
B. 50/216
C. 25/72
D. 25/36
E. 5/6
Let O be represented as 3 being rolled, and X be represented as no 3 being rolled.
Then the case of exactly one 3 being rolled can be represented as (O, X, X), (X, O, X), (X, X, O).
The probability of (O, X, X) is (1/6)*(5/6)*(5/6), that of (X, O, X) is (5/6)*(1/6)*(5/6) and that of (X, X, O) is (5/6)*(5/6)*(1/6).
So the probability is (1/6)*(5/6)*(5/6) + (5/6)*(1/6)*(5/6) + (5/6)*(5/6)*(1/6) = 3*(1/6)*(5/6)*(5/6) = 25/72.
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Retired Moderator Joined: 19 Mar 2014 Posts: 971 Location: India Concentration: Finance, Entrepreneurship GPA: 3.5 Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink] ### Show Tags 08 Jul 2017, 12:50 2 shyind wrote: If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled? A. 25/216 B. 50/216 C. 25/72 D. 25/36 E. 5/6 Probability of getting 3 $$= \frac{1}{6}$$ Probability of not getting 3 $$= \frac{5}{6}$$ Probability of getting three on the first roll $$= \frac{1}{6} * \frac{5}{6} * \frac{5}{6}$$ Probability of getting three on the first roll $$= \frac{25}{216}$$ As we can get 3 on either second or the third time we will multiply the above probability by 3 $$= \frac{25}{216} * 3$$ $$= \frac{25}{72}$$ Hence, Answer is C _________________ "Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent." Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475 Veritas Prep GMAT Instructor Joined: 01 Jul 2017 Posts: 45 Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink] ### Show Tags 06 Jan 2018, 17:32 Here is the full answer, from the ground up. To understand the mathematics behind this question we need to understand three basic probability rules: (1) A probability is calculated by dividing the number of options when the event occurs by the total number of possibilities. (2) When calculating the probability of multiple events that must ALL occur to meet a certain condition, we must multiply the separate probabilities of each event together. Thus, the probability of all the events $$A$$, $$B$$, and $$C$$ occurring would be: $$P_{combined} = (P_A)*(P_B)*(P_C)$$ (3) When calculating the probability of a series of mutually-exclusive events, where ANY event occurring would be sufficient, we must add the separate probabilities of each event together. Thus, the probability of any of the events $$A$$, $$B$$, and $$C$$ occurring would be: $$P_{combined} = (P_A)+(P_B)+(P_C)$$ Let's leverage these three basic rules to solve this problem. First, the probability of rolling a single value (in this case 3) on a fair 6-sided die would be one out of six (or $$\frac{1}{6}$$). The probability of NOT rolling that number would be five out of six (or $$\frac{5}{6}$$). So, if you need to roll a single value on one die, while simultaneously not rolling that value on the other two dice, then we invoke rule #2 from above (i.e., we multiply the probabilities.) Thus, $$P=(\frac{1}{6})*(\frac{5}{6})*(\frac{5}{6})=\frac{25}{216}$$ Notice that this is answer choice A. However, this is a deliberate trap answer. With probabilities, the order always matters. (I like to call this "100% Chance of Order" in my classes.) Thus, if we don't care which of the dice roll the "3", then we need to look at each of the possible orders that could work. There are three possibilities: $$3, N, N$$ $$N, 3, N$$ $$N, N, 3$$ The probability of each of these orders is the same ($$\frac{25}{216}$$), but each is separate and independent. We now need to invoke rule #3 from above and add the separate probabilities together: $$P_{Total} = \frac{25}{216} + \frac{25}{216} + \frac{25}{216} = \frac{3*25}{216}$$ Recognizing common factors in the top and bottom of this fraction allow us to get to the answer without any messy math. $$216 = 6*6*6 = 2*3*6*6$$. Thus, $$\frac{3*25}{216}=\frac{3*25}{2*3*6*6}=\frac{25}{2*6*6}=\frac{25}{72}$$ The answer is C. _________________ Aaron J. Pond Veritas Prep Elite-Level Instructor Hit "+1 Kudos" if my post helped you understand the GMAT better. Look me up at https://www.veritasprep.com/gmat/aaron-pond/ if you want to learn more GMAT Jujitsu. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12004 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink] ### Show Tags 07 Feb 2018, 12:46 Hi All, You can approach the math in this question in a couple of different ways, so you have to think about what would be the easiest way for YOU to organize your work. The questions tells us to roll a 6-sided dice 3 times. We're asked for the probability of rolling EXACTLY one '3' on those three rolls. Here's a way to break the calculation down into 3 smaller calculations: (first roll is 3)(second roll is NOT 3)(third roll is NOT 3) = (1/6)(5/6)(5/6) = 25/216 (first roll is NOT 3)(second roll is 3)(third roll is NOT 3) = (5/6)(1/6)(5/6) = 25/216 (first roll is NOT 3)(second roll is NOT 3)(third roll is 3) = (5/6)(5/6)(1/6) = 25/216 Total = 3(25/216) = 75/216 = 25/72 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink]
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13 Apr 2018, 01:38
niel1989 wrote:
shyind wrote:
If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled?
A. 25/216
B. 50/216
C. 25/72
D. 25/36
E. 5/6
Probability if getting 3 on a die is: P(3)=1/6
Probability of not getting 3 on a die is nP(3)=5/6
Let the three dies be denoted by P1,P2 and P3
Probability of getting 3 on the first die and not getting 3 on the other two dies is given by:-
=P1(3)*nP(3)*nP(3)
=1/6*5/6*5/6
=25/216
As there are 3 dies,so similarly for the rest of the two dies probability will be 25/216
Summing up all the 3 cases we get:
=3*25/216
=25/72
"A" die is rolled 3 times.. There aren't 3 dies... which is why I can't seem to understand why not 25/216
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Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink]
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13 Apr 2018, 01:44
saumya2805 wrote:
"A" die is rolled 3 times.. There aren't 3 dies... which is why I can't seem to understand why not 25/216
Hey saumya2805 ,
There isn't any difference in rolling the same die thrice or rolling three different does.
Hence, for each die we have the total outcomes = 6.
Therefore, total possibilities= 6*6*6 = 216.
Does that make sense?
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Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink]
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13 Apr 2018, 01:52
EMPOWERgmatRichC wrote:
Hi All,
You can approach the math in this question in a couple of different ways, so you have to think about what would be the easiest way for YOU to organize your work.
The questions tells us to roll a 6-sided dice 3 times. We're asked for the probability of rolling EXACTLY one '3' on those three rolls.
Here's a way to break the calculation down into 3 smaller calculations:
(first roll is 3)(second roll is NOT 3)(third roll is NOT 3) = (1/6)(5/6)(5/6) = 25/216
(first roll is NOT 3)(second roll is 3)(third roll is NOT 3) = (5/6)(1/6)(5/6) = 25/216
(first roll is NOT 3)(second roll is NOT 3)(third roll is 3) = (5/6)(5/6)(1/6) = 25/216
Total = 3(25/216) = 75/216 = 25/72
GMAT assassins aren't born, they're made,
Rich
Hi,
I completely understand the logic you've followed...
What I don't understand is why the need..
I mean, the question simply asks the probability of 3 appearing exactly once. It doesn't specify to find for "on which of these throws..."
There's a probability of 3 appearing exactly once, 25 out of 216 times.
If the question had been that 3 dies are rolled simultaneously 3 times... it would've made more sense to me..
Since you're an expert, surely I'm missing something.
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Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink]
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13 Apr 2018, 02:55
AaronPond wrote:
Here is the full answer, from the ground up. To understand the mathematics behind this question we need to understand three basic probability rules:
(1) A probability is calculated by dividing the number of options when the event occurs by the total number of possibilities.
(2) When calculating the probability of multiple events that must ALL occur to meet a certain condition, we must multiply the separate probabilities of each event together. Thus, the probability of all the events $$A$$, $$B$$, and $$C$$ occurring would be: $$P_{combined} = (P_A)*(P_B)*(P_C)$$
(3) When calculating the probability of a series of mutually-exclusive events, where ANY event occurring would be sufficient, we must add the separate probabilities of each event together. Thus, the probability of any of the events $$A$$, $$B$$, and $$C$$ occurring would be: $$P_{combined} = (P_A)+(P_B)+(P_C)$$
Let's leverage these three basic rules to solve this problem.
First, the probability of rolling a single value (in this case 3) on a fair 6-sided die would be one out of six (or $$\frac{1}{6}$$).
The probability of NOT rolling that number would be five out of six (or $$\frac{5}{6}$$).
So, if you need to roll a single value on one die, while simultaneously not rolling that value on the other two dice, then we invoke rule #2 from above (i.e., we multiply the probabilities.) Thus,
$$P=(\frac{1}{6})*(\frac{5}{6})*(\frac{5}{6})=\frac{25}{216}$$
Notice that this is answer choice A. However, this is a deliberate trap answer. With probabilities, the order always matters. (I like to call this "100% Chance of Order" in my classes.) Thus, if we don't care which of the dice roll the "3", then we need to look at each of the possible orders that could work. There are three possibilities:
$$3, N, N$$
$$N, 3, N$$
$$N, N, 3$$
The probability of each of these orders is the same ($$\frac{25}{216}$$), but each is separate and independent. We now need to invoke rule #3 from above and add the separate probabilities together:
$$P_{Total} = \frac{25}{216} + \frac{25}{216} + \frac{25}{216} = \frac{3*25}{216}$$
Recognizing common factors in the top and bottom of this fraction allow us to get to the answer without any messy math. $$216 = 6*6*6 = 2*3*6*6$$. Thus,
$$\frac{3*25}{216}=\frac{3*25}{2*3*6*6}=\frac{25}{2*6*6}=\frac{25}{72}$$
You mention the below:
"Notice that this is answer choice A. However, this is a deliberate trap answer. With probabilities, the order always matters. (I like to call this "100% Chance of Order" in my classes.) Thus, if we don't care which of the dice roll the "3", then we need to look at each of the possible orders that could work."
Plz refer the bold colored portion..
Is it understood by default, that the order always matters? Even if it isn't mentioned explicitly in the question?
This is exactly what I'm always confused about in probability related questions.
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Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink]
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13 Apr 2018, 15:43
1
saumya2805 wrote:
You mention the below:
"Notice that this is answer choice A. However, this is a deliberate trap answer. With probabilities, the order always matters. (I like to call this "100% Chance of Order" in my classes.) Thus, if we don't care which of the dice roll the "3", then we need to look at each of the possible orders that could work."
Plz refer the bold colored portion..
Is it understood by default, that the order always matters? Even if it isn't mentioned explicitly in the question?
This is exactly what I'm always confused about in probability related questions.
Thank you, Saumya2805, for the question. Yes, when calculating the probability of multiple situations, the order always matters. This isn't just the "default", this is how the mathematics of probability work. Even if the events are simultaneous, think about the solution one event at a time. Each different arrangement has a separate probability.
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Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink]
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14 Apr 2018, 00:24
AaronPond wrote:
saumya2805 wrote:
You mention the below:
"Notice that this is answer choice A. However, this is a deliberate trap answer. With probabilities, the order always matters. (I like to call this "100% Chance of Order" in my classes.) Thus, if we don't care which of the dice roll the "3", then we need to look at each of the possible orders that could work."
Plz refer the bold colored portion..
Is it understood by default, that the order always matters? Even if it isn't mentioned explicitly in the question?
This is exactly what I'm always confused about in probability related questions.
Thank you, Saumya2805, for the question. Yes, when calculating the probability of multiple situations, the order always matters. This isn't just the "default", this is how the mathematics of probability work. Even if the events are simultaneous, think about the solution one event at a time. Each different arrangement has a separate probability.
Thanks Aaron, that helps!
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Re: If a fair 6-sided die is rolled three times, what is the probability t [#permalink]
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15 Apr 2018, 18:15
saumya2805 wrote:
niel1989 wrote:
shyind wrote:
If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled?
A. 25/216
B. 50/216
C. 25/72
D. 25/36
E. 5/6
Probability if getting 3 on a die is: P(3)=1/6
Probability of not getting 3 on a die is nP(3)=5/6
Let the three dies be denoted by P1,P2 and P3
Probability of getting 3 on the first die and not getting 3 on the other two dies is given by:-
=P1(3)*nP(3)*nP(3)
=1/6*5/6*5/6
=25/216
As there are 3 dies,so similarly for the rest of the two dies probability will be 25/216
Summing up all the 3 cases we get:
=3*25/216
=25/72
"A" die is rolled 3 times.. There aren't 3 dies... which is why I can't seem to understand why not 25/216
How do you get 216?
You say the FIRST roll could be 1/2/3/4/5/6 i.e. 6 ways
The SECOND roll could be 1/2/3/4/5/6 i.e. 6 ways
The THIRD roll could be 1/2/3/4/5/6 i.e. 6 ways
Hence rolling a 3 on FIRST roll and any of the other 5 numbers of other two rolls is different from rolling a 3 on SECOND roll and any of the other 5 numbers on other two rolls because we have counted these cases apart {3, 1, 6}, {1, 3, 6}. That is how we get 75 and not just 25.
This is same as saying - I have 3 dice of different colours - Red, Yellow and Blue - and I roll them together
The Red could have outcome in 6 ways, Yellow in 6 and Blue in 6 so 216 ways
Same as case above.
How about saying I have 3 identical dice and I roll them together. How many outcomes do I have in that case?
Is (1, 2, 3) different from (3, 1, 2)? No. Then I do not have 216 outcomes in this case. In this case, there is no "order".
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Re: If a fair 6-sided die is rolled three times, what is the probability t &nbs [#permalink] 15 Apr 2018, 18:15
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2018-07-21 09:43:31
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http://math.stackexchange.com/questions/3698/why-doesnt-0-being-a-prime-ideal-in-mathbb-z-imply-that-0-is-a-prime-num
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# Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
I know that $1$ is not a prime number because $1\cdot\mathbb Z=\mathbb Z$ is, by convention, not a prime ideal in the ring $\mathbb Z$.
However, since $\mathbb Z$ is a domain, $0\cdot\mathbb Z=0$ is a prime ideal in $\mathbb Z$. Isn't $(p)$ being a prime ideal the very definition of $p$ being a prime element?
(I know that this would violate the Fundamental Theorem of Arithmetic.)
Edit: Apparently the answer is that a prime element in a ring is, by convention a non-zero non-unit (see wikipedia).
This is strange because a prime ideal of a ring is, by convention, a proper ideal but not necessarily non-zero (see wikipedia).
So, my question is now: Why do we make this awkward convention?
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Every number divides zero. – Asaf Karagila Aug 31 '10 at 9:04
@Asaf Karagila: That's true and it's the reason why 0 being prime would violate the Fundamental Theorem of Arithmetic. It's just that I always thought that one should think of prime numbers as prime ideals in Z. – Rasmus Aug 31 '10 at 9:17
"Prime numbers" should be called "maximal numbers". – Pierre-Yves Gaillard Aug 31 '10 at 10:32
TIP It's not a good idea to accept an answer so soon after posting your question. Being accepted, this will cause the software to give the post much less exposure, so you will have much less a chance to receive other good answers. Since this question doesn't have a unique answer, it would have been interesting to see other viewpoints. Perhaps you could undo your acceptance till later so others will see the question. Generally you shouldn't accept an answer for at least a few days if not more if you want to have the best possible chance of learning from the collective expertise here – Bill Dubuque Aug 31 '10 at 14:10
What I meant by my previous comment is this. The notions of "domain" and "field", and thus the notions of "prime" and "maximal" ideal are, by far, important enough to deserve a name. And I see no reason to change the name they have. The obvious conclusion is that a ring element should be called "prime" (resp. "maximal") if so is the ideal it generates. Of course I know that it is far too late for this "obvious conclusion" to have any chance to prevail. – Pierre-Yves Gaillard Aug 31 '10 at 14:24
You have a point here: absolutely we want to count $(0)$ as a prime ideal in $\mathbb{Z}$ -- because $\mathbb{Z}$ is an integral domain -- whereas we do not want to count $(1)$ as being a prime ideal -- because the zero ring is not an integral domain (which, to me, is much more a true fact than a convention: e.g., every integral domain has a field of fractions, and the zero ring does not).
I think we do not want to call $0$ a prime element because, in practice, we never want to include $0$ in divisibility arguments. Another way to say this is that we generally want to study factorization in integral domains, but once we have specified that a commutative ring $R$ is a domain, we know all there is to know about factoring $0$: $0 = x_1 \cdots x_n$ iff at least one $x_i = 0$.
Here is one way to make this "ignoring $0$" convention look more natural: the notions of factorization, prime element, irreducible element, and so forth in an integral domain $R$ depend entirely on the multiplicative structure of $R$. Thus we can think of factorization questions as taking place in the cancellative monoid $(R \setminus 0,\cdot)$. (Cancellative means: if $x \cdot y = x \cdot z$, then $y = z$.) In this context it is natural to exclude zero, because otherwise the monoid would not be cancellative. Contemporary algebraists often think about factorization as a property of monoids rather than integral domains per se. For a little more information about this, see e.g. Section 4.1 of http://math.uga.edu/~pete/factorization2010.pdf.
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When you study Dedekind rings, you prove that any nonzero ideal is, in a "unique" way, a product of maximal ideals, but you still call (0) a prime ideal. – Pierre-Yves Gaillard Aug 31 '10 at 15:11
You support your claim that the non-integraldomainness of the zero ring is not a convention in that the zero ring doesn't have a field of fractions, but that is a convention, too, no? The zero field is not a field because we insist that $1\neq0$ in a field. – Mariano Suárez-Alvarez Aug 31 '10 at 15:12
I agree with Mariano. I feel that insisting on having 0 not equal to 1 for domains and fields, but not for rings, is the right convention, but I'm unable to say why... – Pierre-Yves Gaillard Aug 31 '10 at 15:23
To answer (at least partially) my own question: It's natural to call "maximal" an ideal which is maximal AMONG THE PROPER IDEALS (otherwise the notion would have no interest), and thus to call "field" the quotient of a ring by a maximal ideal. Now, as Pete says, if you want each domain to have a fraction field, you don't want a zero domain. – Pierre-Yves Gaillard Aug 31 '10 at 16:18
@MSA, PYG: ultimately a convention is just a certain kind of definition, and we obviously can't do away with definitions. The best we can do is try to choose definitions which handle degenerate cases gracefully (the French are especially good at that, I find). In this case, the setup that I find most elegant at the moment is that the spectrum of the zero ring is the empty space, which is not irreducible because it has zero irreducible components (not one). A field, of course, has a one point spectrum. No points versus one point -- that's like night versus day, right? :) – Pete L. Clark Sep 1 '10 at 9:04
There are good reasons behind the convention of including $(0)$ as a prime ideal but excluding $(1)\:.\$ First, we include zero as a prime ideal because it facilitates many useful reductions. For example, in many ring theoretic problems involving an ideal $\rm\; I\;$, one can reduce to the case $\rm\;I = P\;$ prime, then reduce to $\rm\;R/P\;$, thus reducing to the case when the ring is a domain. In this case one simply says that we can factor out by the prime $\rm\; P\;$, so w.l.o.g. assume $\rm\; P = 0\;$ is prime, so $\rm\:R\:$ is a domain. For example, I've appended to the end of this post an excerpt from Kaplansky's classic textbook Commutative Rings, section 1-3: G-Ideals, Hilbert Rings, and the Nullstellensatz.
Thus we have solid evidence for the utility of the convention that the zero ideal is prime. So why don't we adopt the same convention for the unit ideal $(1)$ or, equivalently, why don't we permit the zero ring as a domain? There are a number of reasons. First, in domains and fields it often proves very convenient to assume that one has a nonzero element available. This permits proofs by contradiction to conclude by deducing $\:1 = 0\:.\$ More importantly, it implies that the unit group is nonempty, so unit groups always exist. It'd be very inconvenient to have to always add the proviso (except if $\;\rm R = 0\;)$ to the many arguments involving units and unit groups. For a more general perspective it's worth emphasizing that the usual rules for equational logic are not complete for empty structures so that is why groups and other algebraic structures are always axiomatized to prevent nonempty structures (see this thread for details).
Below is the promised Kaplansky excerpt on reduction to domains by factoring out prime ideals. I've explicitly emphasized the reductions e.g. reduce to....
Let $\rm\; I\;$ be any ideal in a ring $\rm\; R\;$. We write $\rm\; R^{*}\;$ for the quotient ring $\rm\; R/I\;$. In the polynomial ring $\rm\; R[x]\;$ there is a smallest extension $\rm\; IR[x]\;$ of $\rm\; I\;.\$ The quotient ring $\rm\; R[x]/IR[x]\;$ is in a natural way isomorphic to $\rm\; R^*[x].\;$ In treating many problems, we can in this way reduce to the case $\rm\; I = 0\;$, and we shall often do so.
THEOREM 28. $\:$ Let $\rm\: M\:$ be a maximal ideal in $\rm\: R[x]\:$ and suppose that the contraction $\rm\: M \cap R = N\:$ is maximal in $\rm\; R\:.\$ Then $\rm\; M\;$ can be generated by $\rm\; N\;$ and one more element $\rm\; f\:.\$ We can select $\rm\; f\;$ to be a monic polynomial which maps mod $\rm\; N\;$ into an irreducible polynomial over the field $\rm\; R/N\:.\$
Proof. $\:$ We can reduce to the case $\rm\; N = 0,\;$ i. e., $\rm\; R\;$ a field, and then the statement is immediate.
THEOREM 31. $\;$ A commutative ring $\rm\; R\;\;$ is a Hilbert ring if and only if the polynomial ring $\rm\; R[x] \;\;$ is a Hilbert ring.
Proof. $\;$ If $\rm\; \;\rm R[x]\;$ is a Hilbert ring, so is its homomorphic image $\rm\; R\;$. Conversely, assume that $\rm\; R\;$ is a Hilbert ring. Take a G-ideal $\rm\; Q\;$ in $\rm\; R[x]\;$; we must prove that $\rm\; Q\;$ is maximal. Let $\rm\; P = Q \cap R\;$; we can reduce the problem to the case $\rm\; P = 0\;$, which, incidentally, makes $\rm\; R\;$ a domain. Let $\rm\; u\;$ be the image of $\rm\; x\;$ in the natural homomorphism $\rm\; R[x] \to R[x]/Q\;$. Then $\rm\; R[u]\;$ is a G-domain. By Theorem 23, $\rm\:u\:$ is algebraic over $\rm\:R\:$ and $\rm\:R\:$ is a G-domain. Since $\rm\:R\:$ is both a G-domain and a Hilbert ring, $\rm\:R\:$ is a field. But this makes $\rm\; R[u] = R[x]/Q\;$ a field, proving $\rm\; Q\;$ to be maximal.
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Thank you for your detailed answer. – Rasmus Aug 31 '10 at 14:18
Generally we make nice conventions because they make the statements of theorems nice. The theorem relevant to prime ideals is that $P$ is a prime ideal of $R$ if and only if $R/P$ is an integral domain. The theorem relevant to prime elements is prime factorization (when it holds).
These two concepts almost coincide for principal ideals, but we must distinguish between the generic point $(0)$ and closed points, and there are good reasons for doing this. (The zero ideal, for example, can't occur in the factorization of a nonzero ideal in a Dedekind domain.)
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But your answer doesn't explain why the convention is useful. For that, see my answer. – Bill Dubuque Aug 31 '10 at 14:00
Isn't $R/R$ an integral domain as well? – Rasmus Aug 31 '10 at 14:13
@Rasmus: No! (See my answer.) – Pete L. Clark Aug 31 '10 at 14:23
## protected by user26857Apr 27 '15 at 9:09
Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site.
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2016-05-26 00:49:30
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http://clay6.com/qa/50800/the-degree-of-dissociation-of-a-weak-electrolyte-is-given-by
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Browse Questions
# The degree of dissociation of a weak electrolyte is given by
$\begin{array}{1 1}\alpha=\Lambda_c/\Lambda^{\infty}\\\alpha=\Lambda^{\infty}/\Lambda_c\\\alpha=\Lambda^2_c/\Lambda^{\infty}\\\alpha=\Lambda_c\Lambda^{\infty}\end{array}$
Can you answer this question?
Answer : $\alpha=\Lambda_c/\Lambda^{\infty}$
The degree of dissociation of a weak electrolyte is given by $\alpha=\Lambda_c/\Lambda^{\infty}$
answered Jul 18, 2014
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2016-10-22 19:41:46
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https://blog.myrank.co.in/pair-of-straight-lines-homogeneous-second-degree-equation/
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# Pair of Straight Lines – Homogeneous Second Degree Equation
## Pair of Straight Lines – Homogeneous Second Degree Equation
An equation (whose RHS is zero) in which the sum of the power of x and y in every term is the same say n, is called a Homogeneous equation of nth degree in x and y.
Thus, ax² + 2hxy + by² = 0 is a homogeneous equation of second degree and cx³ + dxy² + ey³ = 0 is a homogeneous equation of third degree in x and y.
Pair of Straight Lines through the Origin: If ax² 2hxy + by² + 2gx + 2fy + c = 0 represent two lines, then the LHS can be resolved into two linear factors.
Let the factors be (l₁x + m₁y + n₁) (l₂x + m₂y + n₂)
Simplifying the equation, we will get (l₁x + m₁y) (l₂x + m₂y), the terms of second degree, must be identical with ax² + 2hxy + by² =0 is identical with (l₁x + m₁y) x (l₂x + m₂y) = 0.
Thus, equations ax² + 2hxy + by² represents two lines l₁x + m₁y = 0, l₂x + m₂y = 0 which are parallel to lines. l₁x + m₁y + n₁ = 0, l₂x + m₂y + n₂ = 0, respectively.
Let us consider a general homogeneous equation of second degree in x and y as
ax² + 2hxy + by² = 0 . . . (1)
dividing both sides by x², we get
b(y/x)² + 2h(y/x) + a = 0 . . .(2)
since (2) is an equation of second degree in y/x it has two roots.
Let the roots be m₁ and m₂. if α and β are the roots of equation ax² + bx + c = 0.
ax² + bx + c = 0
= a (x – α) x (x – β)
Therefore, (2) can be written as
b (y/x – m₁) (y/x – m₂) = 0
Thus equation (1) represents two straight lines y – m₁x = 0 and y – m₂x = 0 both of which pass through the origin. Comparing b (y – m₁x) (y – m₂x) = 0 with equation (1), we have
$$\frac{b{{m}_{1}}{{m}_{2}}}{a}=-\frac{b({{m}_{1}}+{{m}_{2}})}{2h}=\frac{1}{1}$$,
$${{m}_{1}}+{{m}_{2}}=\frac{-2h}{b}$$,
$${{m}_{1}}\times {{m}_{2}}=\frac{a}{b}$$.
Example: If the lines px² – qxy – y² = 0 make angles α and β with the x – axis, then the value of tan (α + β) is
Solution: Let the lines represented by the equation.
px² – qxy – y² = 0
y = m₁ x
and y = m₂ x.
Then, m₁ = tanα and m₂ = tanβ
m₁ + m₂ = -2h/b = -q
m₁ m₂ = a/b = p
$$\tan (\alpha +\beta )=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }$$,
$$\tan (\alpha +\beta )=\frac{{{m}_{1}}+{{m}_{2}}}{1-{{m}_{1}}{{m}_{2}}}$$,
$$\tan (\alpha +\beta )=\frac{-q}{1+p}$$.
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2023-02-08 17:29:25
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http://openstudy.com/updates/55b1394de4b0ce10565e76c4
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## anonymous one year ago Simplify: Begin fifth root x to the power of sixteen end fifth root A. x4 B. Begin fifth root x to the power of three end fifth root C. x8 D. X cubed times the fifth root of x
1. anonymous
i have 2 draw
2. anonymous
|dw:1437677915340:dw|
3. anonymous
|dw:1437677961476:dw|
4. anonymous
take a screenshot
5. anonymous
|dw:1437678006287:dw|
6. anonymous
oh how to do that and now i'm done.
7. Flvs.net
How does he do that?
8. anonymous
$\sqrt[5]{x16}$ is this the equation?
9. anonymous
yes how did you do that
10. anonymous
what laptop or computer do you have?
11. anonymous
equation
12. anonymous
i have a dell computer
13. anonymous
oh ok i know to take screenshot on a MacBook
14. anonymous
yea me to but mine got killed by ****ing water
15. anonymous
so i have to type it out or draw it
16. anonymous
:(
17. anonymous
or say something like this 5squared x16
18. anonymous
19. anonymous
equation
20. anonymous
so can you solve this question this is taking tooooo long
21. anonymous
:))
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2017-01-21 02:56:03
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http://math.stackexchange.com/questions/99949/if-xy-is-a-unit-are-x-and-y-units/99950
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# If $xy$ is a unit, are $x$ and $y$ units?
I know if $x$ and $y$ are units, in say a commutative ring, then $xy$ is a unit with $(xy)^{-1}=y^{-1}x^{-1}$.
But if $xy$ is a unit, does it necessarily follow that $x$ and $y$ are units?
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How do you define unit? – Andres Caicedo Jan 17 '12 at 21:54
@AndresCaicedo I define unit to be an invertible element. I'm assuming that the commutative ring is has $1$. – neel Jan 17 '12 at 21:55
Ok, so $xy$ has an inverse. Can you use that to define the inverse of $x$? The point is: To be invertible means that there is some element $z$ that when multiplied with $xy$ gives you 1. So you have $(xy)z=1$. Right? But then, this equation provides you with an element that multiplied with $x$ gives you 1. – Andres Caicedo Jan 17 '12 at 21:57
@AndresCaicedo - you are using the associative law quite explicitly in your comment. I think it is another interesting question what happens if associativity fails ... of course the question as stated implies that multiplication is associative. – Mark Bennet Jan 17 '12 at 23:02
Yes. Let $z=xy$. If $z$ is a unit with inverse $z^{-1}$, then $x$ is a unit with inverse $yz^{-1}$, and $y$ is a unit with inverse $xz^{-1}$, because $$x(yz^{-1})=(xy)z^{-1}=zz^{-1}=1$$ $$y(xz^{-1})=(yx)z^{-1}=(xy)z^{-1}=zz^{-1}=1$$
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Of course, that makes sense. Thanks Zev. – neel Jan 17 '12 at 21:57
No problem, glad to help! – Zev Chonoles Jan 17 '12 at 21:59
In a commutative ring, yes: let $u$ be such that $u(xy)=1 = (xy)u$. Then $$x(uy) = u(xy) = 1\quad\text{and}\quad (uy)x = u(xy) = 1,$$ so $x$ is invertible; and if $x$ is invertible, and $xy$ is a unit, then $y=x^{-1}xy$ is a product of units, hence a unit.
In a non-commutative ring, no; you can have a product be a unit yet neither factor be a unit. For example, let $$A = \prod_{i=1}^{\infty}\mathbb{Z}$$ and let $R$ be the ring of endomorphisms of $A$. Let $f\colon A\to A$ be the right-shift operator, and let $g\colon A\to A$ be the left-shift operator. Then $gf=1$ in $R$ and in particular the product is a unit, but neither $f$ nor $g$ are units ($g$ is not one-to-one, so it cannot be left-invertible, and $f$ is not onto, so it cannot be right-invertible).
Of course, if $xy$ is a unit in a non-commutative ring, then $x$ is right-invertible and $y$ is left-invertible, but that's the best you can say in general, as the example above shows.
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Thank you, I've not dealt much with noncommutative rings, so I appreciate this example. – neel Jan 17 '12 at 23:48
Can the downvoter explain why there is a downvote here? – Arturo Magidin Jan 20 '12 at 16:12
I've had my answer here and on another recent question downvoted without explanation too. – Zev Chonoles Jan 20 '12 at 16:20
HINT $\$ Units are precisely the divisors of $1\:.\:$ Hence by transitivity of 'divides' we deduce
$$\rm xy\ unit\ \Rightarrow\ xy\ |\ 1\ \Rightarrow\ x\ |\ xy\ |\ 1\ \Rightarrow\ x\ unit\ \qquad QED$$
I.e. the set of all divisors of a fixed element is closed under taking divisors (by transitivity).
This can be viewed as the dual of the well-known "divides = contains" for principal ideals. Namely, let $\rm\: D(x) =\:$ the set of divisors of $\rm\:x\:$ and let $\rm\: M(x) =\:$ the set of multiples of $\rm\:x\:.\:$ Then we have
$\rm\qquad a\ |\ b\ \iff\ M(a) \supset M(b)\quad$ i.e. divides = contains $\qquad\ \$ for multiple sets
$\rm\qquad a\ |\ b\ \iff\ D(a)\ \subset\: D(b)\quad$ i.e. divides = contained-in $\$ for divisor sets
So $\rm\ u\ |\ 1\ \iff\ D(u)\:\subset D(1)\quad\:$ i.e. $(\Rightarrow)$ says: $\:$ if $\rm\:u\:$ is a unit then every divisor of $\rm\:u\:$ is a unit.
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NO if $R$ is not commutative
Definition: Suppose $R$ is any ring with unity $1$. An element $u$ is said to be unit in $R$ if there exits $v\in R$ such that $uv=1$ and $vu=1$.
Let $\mathbb{R}[x]$ be the (infinite dimensional) vector space of all polynomials over $\mathbb{R}$. Let $S$ denote the ring of all linear operators on $\mathbb{R}[x]$ with usual addition and composition of operators.
Let $D\colon\mathbb{R}[x]\rightarrow\mathbb{R}[x]$ demote the differential operator: $D(p(x))=p'(x)$.
Let $J\colon:\mathbb{R}[x]\rightarrow \mathbb{R}[x]$ denote the integral operator: $J(a_0+a_1x+\cdots + a_nx^n)=a_0x+a_1\frac{x^2}{2}+\cdots + a_n\frac{x^{n+1}}{n+1}$.
Then $D\circ J$ is identity operator which is obviously unit. But $D$ is not unit: it is not one-to-one (why?) hence it can not have a two-sided inverse.
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This was already noted before, see the answer by Arturo Magidin. And the OP assumed $R$ to be commutative. – Martin Brandenburg Apr 7 at 12:35
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2015-07-01 05:38:28
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https://carigold.com/forum/threads/forex-trading-ideas.677068/
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### Forex Chart
##### Freshie
We will try to share detailed forex trading ideas.
The first one is EURUSD
We are going to have a quiet trading day as Europe remains closed.
The pair is still under Bearish pressure. It is below EMA 50, EMA 100 and EMA 200 of H4 Chart Timeframe.
1.23100 and 1.22980 are the next downside levels of today.
The real problem for Euro Bulls will start if it breaks below 1.22980. 1.22680 and 1.22300 will be the next targets of the pair and it will not take too much time to achieve those levels.
1.23600 remains as the main resistance and bearish pressure will continue as long as the price stays below 1.23600.
Bulls may come back to the playground after an H4 closing above 1.23600.
Since we are going to see low volumes today, the best strategy can be “wait and see. ” Or short with a stop loss above 1.23600. – We suggest you try shorts with small lots- 1.22980 1.22830 and 1.22680 are take profit levels.
##### Freshie
EURUSD Technical Overview And Key Levels 04-06-2018
EURUSD Technical Overview And Key Levels 04-06-2018
Asia Overview by Reuters:
The dollar index was down 0.1 percent at 90.359. The index has risen 0.4 percent this week.
Treasury debt prices gained and yields declined as investors sought the safety of government bonds.The 10-year Treasury note yield fell 2 basis points to 2.811 percent, pulling back from Thursday’s nine-day high of 2.838 percent.
Trump said late on Thursday that he had instructed U.S. trade officials to consider $100 billion in additional tariffs on China, fuelling the trade dispute between the world’s two economic superpower Traders are focused on NFP. Considering USD’s recent strength, investors are positioning for a stronger labour-market number but there’s also plenty of room (in wage growth and the jobless rate) for a downside surprise, which makes trading NFP this month particularly difficult. Technical Analysis and Key Levels: We have published our trade set up before. Our short position has reached the first target and still running. https://www.tradingview.com/chart/EURUSD/9iEbyg1r-EURUSD-Simply-Short/ One of the main scenarios was a bullish shark formation as described in the following chart. Technical Key Levels: We want to keep it simple for you. As shown in the H4 Chart: EURUSD is below EMA 50, 100 and EMA 200. Golden Cross is very close. RSI is oversold. However, in the daily chart, RSI has room downside. The main resistance zone – orange coloured- is 1.23000 – 1.23300. Above the resistance zone, 1.23600 will be the key level for the continuation of the upside move. Below the current level, 1.22080 – 1.21780 ( Red Coloured ) zone is the main support. Break below this support will carry the price 1.21090 – 1.20900. 1.20900 was the breakout of the bullish triangle. 450 pips bullish move had started after the breakout of 120900. This level is likely to play a key support role. If EURUSD breaks below 1.20900, we can start to speak about a trend reversal and 1.17000. DISCLAIMER: This is a technical analysis study, not an advice or recommendation to invest money #### Attachments • 26.7 KB Views: 5 #### Chartreaderpro ##### Freshie WTI Crude Oil Technical Analysis And Trade Idea WTI Crude Oil Technical Analysis And Trade Idea Published 05-04-2018 We have published a detailed analysis on Monday. The fundamental side is mixed. Iran Nuclear Agreement in May might be the determining factor in Crude Oil Prices. On the Technical side, the price is above the EMA 50. However, H4 chart indicators and oscillators started to send bearish signals. We have a bearish flag formation. If the price breaks below 62.50 support, 62.20 -62.00 interval will be the key levels. Break and H4 closing below 62.20, would validate the bearish flag pattern. The target of the formation is 58-40-58.20. This level is one of the historical levels as well. We will keep updated the premium members as soon as the pattern is validated. DISCLAIMER: This is a technical analysis study, not an advice or recommendation to invest money on. Visit our web for more detailed for cast and technical analysis #### Attachments • 19.7 KB Views: 4 #### Chartreaderpro ##### Freshie XAUUSD Gold Forecast And Technical Levels 04-06-2018 The main idea: We are still bullish midterm. Yesterday we have published a trading idea based on the bearish triangle breakout. http://chartreaderpro.com/xauusd-gold-triangle-pattern-short-opportunity/ We see a bullish Gartley pattern forming and would be completed at 1.308-1.312. We look for fresh buy opportunities and will update premium members. Fundamentally: NFP reports will be released today. It is obvious that we will see the temporary effects of the reports. However, midterm, Gold prices are expected to rise as mining exploration struggles to find enough new discoveries to add to the global reserves Gold prices rose on Friday as investors sought safer assets after U.S. President Donald Trump proposed$100 billion in new tariffs on China, raising concerns about an escalating trade spat between the United States and China.
Technically:
On the daily chart, XAUUSD moving in an ascending channel. Price is above EMA 100 and EMA 200.
1328 is the EMA 50 and MM 2/8 Major Reverse and Support. We have mentioned this key level before.
However, on the H4 chart, we see that the price is below EMA 50, 100 and 200. Gold is trading in the lower Bollinger Band. The picture is bearish. We need to see a few H4 closing above 1328 for the continuation of the bullish move.
We have given some key levels yesterday. 1324, 1320, 1316, and 1312.
If the price breaks below 1324, 1320 will be tested for sure. And below 1320, 1316 and 1312 will be on the target.
We will update as soon as we see the fresh buying opportunity.
DISCLAIMER: This is a technical analysis study, not an advice or recommendation to invest money
#### Attachments
• 38.6 KB Views: 4
##### Freshie
CHFJPY Bearish Cypher and Trend Line Breakout Update:
Bearish Cypher Harmonic Pattern would be completed at 111.740.
A broken inverted SHS and trend line resistance at the same level.
We may see a retracement towards 111.500 111.350.
On the other hand; break above the trend line will carry the price 112.400 and 112.700.
I will try short at 111.750 Stop Loss 112.030. Targets 111.500 and 111.350
If the price breaks above the trend line we will be stoped out. However, in this case, the price is likely to retest the trendline and I will enter LONG at the retest level.
Update: Short Trade reached the first target. At the second target, we will close the short positions.
We will update the idea this weekend.
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##### Freshie
GBPUSD Forecast and Technical Analysis Week 09-13 April
GBPUSD Forecast and Technical Analysis Week 09-13 April
Before the forecast and technical analysis, I would like to take a look at our latest trade ideas.
We have a long trade based on Bullish Butterfly and we have reached the first target @ 1.40800.
And Long Trade based on Bullish CwH to add long for ISHS pattern.
Now, let us take a look at the fundamentals:
NFP report was highly disappointing. However, I do not think that would make a too much negative effect on US Dollar. Subsequently, the US unemployment rate also dwelled at the unchanged level of 4.1% instead of falling lower to 4.0% as expected by the market.
The weak UK PMIs did not help Cable to fall below 1.39600. Market players are expecting further rate hikes from BoE as we mentioned in our previous forecast.
The main topic haunting the financial markets was the ongoing trade wars between the US and China.
Technically:
The main trend is still bullish.
On the Daily Chart, the price is above EMA 50,100 and 200.
1.39600 is EMA 50 support of the Daily Chart. That’s why we pay attention to this level. The midterm bullish trend will continue as long as the price holds above 1.39600.
1.42500 as EMA 100 of the weekly chart, acts as a resistance. We can see the price is “locked ” between 1.39600 – 1.42500 – almost 300 pips –
On the H4 Chart: – To see the intraday levels –
1.41000 is the key level for the continuation of the bullish move. If the price breaks above 1.41000, Cable is likely to test 1.41280 and 1.41600.
Below the current level; 1.40800 and 1.40600 are the first levels to test. 1.40380 is the key support. Break below 1.40380 will carry the price 1.40000 and 1.39600 again.
DISCLAIMER: This is a technical analysis study, not an advice or recommendation to invest money
#### Attachments
• 36.8 KB Views: 3
##### Freshie
XAUUSD Gold Overview and Technical Analysis
XAUUSD Gold Overview and Technical Analysis
Published 04-15-2018
Gold made several failed breakout attempts since its multi-year high reached in 2016. We see that the gold prices are still in a solid uptrend, creating higher lows along the way.
That is true: The market is struggling, but it looks like it wants to grind higher
Geopolitical instability will continue to support gold as a safe-haven asset.
Fundamentally, we do not see any logical reason to sell GOLD.
As we have mentioned in our previous forecasts, we remain bullish. Our first midterm target was 1361 and it was tested last week.
Our Next Target is 1375 as seen in the chart. A bullish flag formation is forming as well.
We just need a daily closing above 1360. The real bullish game will start as soon as XAUUSD makes a daily closing above 1360.
Our Midterm Targets: 1375, 1408, 1440 and 1476 ( The target of the bullish flag formation )
Pullback Levels To Buy: 1335 1328 1324
DISCLAIMER: This is a technical analysis study, not an advice or recommendation to invest money
#### Attachments
• 25.7 KB Views: 3
##### Freshie
GBPUSD Futures : Shall the Bulls unlock the pasword?
Todays’s UK PMI data – 54 announced vs. Market Expectation 52.9 – gave the Sterling a boost in the short term.
However, the major problem to be solved is still Brexit.
When we look technically
Critical support for the party, which has maintained 1.46 targeted SHS support in the long run despite the sharp fall, is at 1.31 level.
Details of the forecast and trade idea:
#### Attachments
• 159.6 KB Views: 9
##### Freshie
EURUSD Forecast And Technical Analysis 06-08-2018
On the Euro side, Italy is still a risk for investors. The market’s attention is focused on next week’s ECB meeting. Fundamentally there was nothing to boost to push EURUSD higher.
On the Dollar side, USD has lost its charm as Trump protectionism announcements are triggering countermeasures from multiple fronts that will end up weighing on economic progress in the world’s largest economy. And the economic figures are not promising, and doubts occurred about the further rate hikes.
There is no strong data flow today. German Industrial Production and Trade Balance will be released.
The pair has tested 1.18400 which is the Fibonacci 38.20% major resistance. As seen on the H4 chart timeframe 1.18400 is the extremely overshoot level of MM Lines and EMA 200 resistance
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2019-12-06 18:33:30
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https://ealizadeh.com/blog/mlxtend-library-for-data-science/
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# MLxtend: A Python Library with Interesting Tools for Data Science Tasks
Create counterfactual records, draw PCA correlation graphs and decision boundaries, perform bias-variance decomposition, bootstrapping, and much more
Data Science
Exploratory Data Analysis
Machine Learning
Python Library
Author
Published
July 17, 2021
Note
MLxtend library 1 (Machine Learning extensions) has many interesting functions for everyday data analysis and machine learning tasksAlthough there are many machine learning libraries available for Python such as scikit-learnTensorFlowKerasPyTorchetc, however, MLxtend offers additional functionalities and can be a valuable addition to your data science toolbox.
In this post, I will go over several tools of the library, in particular, I will cover:
• Create counterfactual (for model interpretability)
• PCA correlation circle
• Bias-variance decomposition
• Decision regions of classification models
• Matrix of scatter plots
• Bootstrapping
For a list of all functionalities this library offers, you can visit MLxtend’s documentation(see Raschka 2018).
👉 A link to a free one-page summary of this post is available at the end of the post.
## MLxtend Library
MLxtend library is developed by Sebastian Raschka (a professor of statistics at the University of Wisconsin-Madison). The library has nice API documentation as well as many examples.
You can install the MLxtend package through the Python Package Index (PyPi) by running pip install mlxtend.
## Dataset
In this post, I’m using the wine data set obtained from the Kaggle. The data contains 13 attributes of alcohol for three types of wine. This is a multiclass classification dataset, and you can find the description of the dataset here.
First, let’s import the data and prepare the input variables X (feature set) and the output variable y (target).
import pandas as pd
# Load wine data set (available at https://www.kaggle.com/tug004/3wine-classification-dataset)
# Target values (wine classes) in y
y_s = df["Wine"].map({1: 0, 2: 1, 3: 2}) # Convert classes 1, 2, 3 to 0, 1, 2 to avoid strange behavior
y = y_s.values
# Feature columns
X_df = df.drop(columns=["Wine"])
X = X_df.values
attribute_names = X_df.columns
## MLxtend Functionalities
### Create Counterfactual (for model interpretability)
For creating counterfactual records (in the context of machine learning), we need to modify the features of some records from the training set in order to change the model prediction(see Raschka N/A). This may be helpful in explaining the behavior of a trained model. The algorithm used in the library to create counterfactual records is developed by Wachter et al .
You can create counterfactual records using create_counterfactual() from the library. Note that this implementation works with any scikit-learn estimator that supports the predict() function. Below is an example of creating a counterfactual record for an ML model. The counterfactual record is highlighted in a red dot within the classifier’s decision regions (we will go over how to draw decision regions of classifiers later in the post).
from sklearn.linear_model import LogisticRegression
clf_logistic_regression = LogisticRegression(random_state=0)
clf_logistic_regression.fit(X_2d, y)
from mlxtend.evaluate import create_counterfactual
from mlxtend.plotting import plot_decision_regions
counterfact = create_counterfactual(
x_reference=X_2d[15],
y_desired=2, # Desired class
model=clf_logistic_regression,
X_dataset=X_2d,
y_desired_proba=0.95,
lammbda=1,
random_seed=123
)
scatter_highlight_defaults = {
'c': 'red',
'edgecolor': 'yellow',
'alpha': 1.0,
'linewidths': 2,
'marker': 'o',
's': 120
}
fig, ax = plt.subplots(figsize=(10, 6))
plot_decision_regions(X_2d, y, clf=clf_logistic_regression, legend=2, ax=ax)
ax.tick_params(axis='both', which='major', labelsize=24)
ax.set_title("Create a Counterfactual Record", fontsize=24, fontweight="bold")
ax.set_xlabel("Color.int", fontsize=20, fontweight="bold")
ax.set_ylabel("Phenols", fontsize=20, fontweight="bold")
ax.scatter(
*counterfact,
**scatter_highlight_defaults
)
PCA Correlation Circle
An interesting and different way to look at PCA results is through a correlation circle that can be plotted using plot_pca_correlation_graph(). We basically compute the correlation between the original dataset columns and the PCs (principal components). Then, these correlations are plotted as vectors on a unit-circle. The axes of the circle are the selected dimensions (a.k.a. PCs). You can specify the PCs you’re interested in by passing them as a tuple to dimensions function argument. The correlation circle axes labels show the percentage of the explained variance for the corresponding PC(see Raschka 2018).
Remember that the normalization is important in PCA because the PCA projects the original data on to the directions that maximize the variance.
from mlxtend.plotting import plot_pca_correlation_graph
from sklearn.preprocessing import StandardScaler
X_norm = StandardScaler().fit_transform(X) # Normalizing the feature columns is recommended (X - mean) / std
fig, correlation_matrix = plot_pca_correlation_graph(
X_norm,
attribute_names,
dimensions=(1, 2),
figure_axis_size=6
)
PCA correlation circle diagram between the first two principal components and all data attributes
Correlation matrix between wine features and the first two PCs
### Bias-Variance Decomposition
You often hear about the bias-variance tradeoff to show the model performance. In supervised learning, the goal often is to minimize both the bias error (to prevent underfitting) and variance (to prevent overfitting) so that our model can generalize beyond the training set (see Wikipedia 2021-07-17). This process is known as a bias-variance tradeoff.
Note that we cannot calculate the actual bias and variance for a predictive model, and the bias-variance tradeoff is a concept that an ML engineer should always consider and tries to find a sweet spot between the two.Having said that, we can still study the model’s expected generalization error for certain problems. In particular, we can use the bias-variance decomposition to decompose the generalization error into a sum of 1) bias, 2) variance, and 3) irreducible error[4,5].
The bias-variance decomposition can be implemented through bias_variance_decomp() in the library. An example of such implementation for a decision tree classifier is given below.
from sklearn.tree import DecisionTreeClassifier
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X_df.values, y,
test_size=0.3,
random_state=123,
shuffle=True,
stratify=y)
tree = DecisionTreeClassifier(random_state=123)
from mlxtend.evaluate import bias_variance_decomp
avg_expected_loss, avg_bias, avg_var = bias_variance_decomp(
tree, X_train, y_train, X_test, y_test,
loss='mse',
num_rounds=50, # Number of bootstrap rounds for implementing the decomposition
random_seed=123
)
print(f"Average expected loss: {avg_expected_loss.round(3)}")
print(f"Average bias: {avg_bias.round(3)}")
print(f"Average variance: {avg_var.round(3)}")
>>> Average expected loss: 0.108
>>> Average bias: 0.032
>>> Average variance: 0.076
### Plotting Decision Regions of Classifiers
MLxtend library has an out-of-the-box function plot_decision_regions() to draw a classifier’s decision regions in 1 or 2 dimensions.
Here, I will draw decision regions for several scikit-learn as well as MLxtend models. Let’s first import the models and initialize them.
# Models
from sklearn.linear_model import LogisticRegression
from sklearn.ensemble import RandomForestClassifier
from sklearn.naive_bayes import GaussianNB
from mlxtend.classifier import EnsembleVoteClassifier
# Initializing Classifiers
clf_logistic_regression = LogisticRegression(random_state=0)
clf_nb = GaussianNB()
clf_random_forest = RandomForestClassifier(random_state=0)
clf_ensemble = EnsembleVoteClassifier(
clfs=[clf_logistic_regression, clf_nb, clf_random_forest],
weights=[2, 1, 1],
voting='soft'
)
all_classifiers = [
("Logistic Regression", clf_logistic_regression),
("Naive Bayes", clf_nb),
("Random Forest", clf_random_forest),
("Ensemble", clf_ensemble),
]
Now that we have initialized all the classifiers, let’s train the models and draw decision boundaries using plot_decision_regions() from the MLxtend library.
from mlxtend.plotting import plot_decision_regions
from itertools import product # Used to generate indices for figure subplots!
fig, axs = plt.subplots(2, 2, figsize=(28, 24), sharey=True)
for classifier, grid in zip(
all_classifiers,
product([0, 1], [0, 1]) # generate [(0, 0), (0, 1), (1, 0), (1, 1)]
):
clf_name, clf = classifier[0], classifier[1]
ax = axs[grid[0], grid[1]]
clf.fit(X_2d, y)
plot_decision_regions(
X=X_2d,
y=y,
clf=clf,
legend=2,
ax=ax
)
ax.set_title(clf_name, fontsize=24, fontweight="bold")
ax.tick_params(axis='both', which='major', labelsize=18)
ax.set_xlabel("Color.int", fontsize=20, fontweight="bold")
ax.set_ylabel("Phenols", fontsize=20, fontweight="bold")
### Matrix of Scatter Plots
Another useful tool from MLxtend is the ability to draw a matrix of scatter plots for features (using scatterplotmatrix()). In order to add another dimension to the scatter plots, we can also assign different colors for different target classes.
from mlxtend.plotting import scatterplotmatrix
fig, axes = scatterplotmatrix(X[y==0], figsize=(34, 30), alpha=0.5)
fig, axes = scatterplotmatrix(X[y==1], fig_axes=(fig, axes), alpha=0.5)
fig, axes = scatterplotmatrix(X[y==2], fig_axes=(fig, axes), alpha=0.5, names=attribute_names)
A matrix of scatter plot of all wine attributes with different colors for wine types
By the way, for plotting similar scatter plots, you can also use Pandas’ scatter_matrix() or seaborn’s pairplot() function.
### Bootstrapping
The bootstrap is an easy way to estimate a sample statistic and generate the corresponding confidence interval by drawing random samples with replacement. For this, you can use the bootstrap() function from the library. Note that you can pass a custom statistic to the bootstrap function through argument func. The custom function must return a scalar value.
from mlxtend.evaluate import bootstrap
# Generating 100 random data with a mean of 5
random_data = np.random.RandomState(123).normal(loc=5., size=100)
avg, std_err, ci_bounds = bootstrap(
random_data,
num_rounds=1000,
func=np.mean, # A function to compute a sample statistic can be passed here
ci=0.95,
seed=123
)
print(
f"Mean: {avg.round(2)} \n"
f"Standard Error: +/- {std_err.round(2)} \n"
f"CI95: [{ci_bounds[0].round(2)}, {ci_bounds[1].round(2)}]"
)
>>> Mean: 5.03
>>> Standard Error: +/- 0.11
>>> CI95: [4.8, 5.26]
Note
# Conclusion
In this post, we went over several MLxtend library functionalities, in particular, we talked about creating counterfactual instances for better model interpretability and plotting decision regions for classifiers, drawing PCA correlation circle, analyzing bias-variance tradeoff through decomposition, drawing a matrix of scatter plots of features with colored targets, and implementing the bootstrapping. The library is a nice addition to your data science toolbox, and I recommend giving this library a try.
Note
📓 You can find the Jupyter notebook for this blog post on GitHub.
## References
Raschka, Sebastian. N/A. “Create_counterfactual: Interpreting Models via Counterfactuals.” https://rasbt.github.io/mlxtend/user_guide/evaluate/create_counterfactual/.
———. 2018. “MLxtend: Providing Machine Learning and Data Science Utilities and Extensions to Python’s Scientific Computing Stack.” The Journal of Open Source Software 3 (24). https://doi.org/10.21105/joss.00638.
Wachter, Sandra, Brent Mittelstadt, and Chris Russell. 2017. “Counterfactual Explanations Without Opening the Black Box: Automated Decisions and the GDPR.” Harvard Journal of Law & Technology 31: 841. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3063289.
## Citation
BibTeX citation:
@online{alizadeh2021,
|
2022-12-01 07:38:24
|
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|
https://gamedev.stackexchange.com/questions/189703/mesh-does-not-translate-accordingly-to-wheelcollider
|
# Mesh does not translate accordingly to WheelCollider
So I am trying to implement a car controller script in Unity were the WheelTransform position and rotation is set with every update as the same as the WheelCollider position and rotation, it all works fine except for one thing: when translating the WheelTransform, if the car goes slowly, WheelTransform translates as expected, but when the car goes faster, there's a clear offset between the WheelTransform position and the actual position of WheelCollider. Here's the code were WheelTransform position and rotation is set as the same as the WheelCollider position and rotation:
private void UpdateWheels()
{
UpdateWheelPos(frontLeftWheelCollider, frontLeftWheelTransform);
UpdateWheelPos(frontRightWheelCollider, frontRightWheelTransform);
UpdateWheelPos(rearLeftWheelCollider, rearLeftWheelTransform);
UpdateWheelPos(rearRightWheelCollider, rearRightWheelTransform);
}
private void UpdateWheelPos(WheelCollider wheelCollider, Transform trans)
{
Vector3 pos;
Quaternion rot;
wheelCollider.GetWorldPose(out pos, out rot);
trans.rotation = rot;
trans.position = pos;
}
Every single one of the car controller scripts I've found and tried use the same code for this section, I have also tried with 2d sprites without any colliders as WheelTransform but neither the scripts or changing WheelTransform solved the problem. Thanks in advance for the help.
• Can you show us how you've configured the visual objects referenced by the wheel transforms? A screenshot of the offset you're observing could also help us diagnose the cause. – DMGregory Mar 8 at 16:05
• Are you calling UpdateWheels() from an Update() function? Try calling it from LateUpdate() instead. – Kevin Mar 8 at 19:17
• Kevin's solution fixed the issue, thanks – user14791290 Mar 8 at 19:44
• @user14791290 Great, I've posted it as an answer. – Kevin Mar 8 at 23:28
This type of issue can occur if two different components are updating an object's position during the frame Update cycle. In this case, WheelCollider might be recalculating the pose during Update().
The specific order that Update() is called on scripts is undefined (and should be considered random) unless you've explicitly set a Script Execution Order.
If your script is calling UpdateWheels() from an Update() function, you would see synchronization issues if your script happens to be updating before WheelCollider each update. In other words, your script moves the transform to match the pose, then the pose changes, and then the frame is rendered with your transform no longer matching the pose.
One way to fix this is to edit the Script Execution Order, but I recommend never editing the execution order unless you absolutely have to, because it is a sort of hacky solution (and the UI for changing it in the Unity Editor is atrocious). In this case, you can instead change your script so that UpdateWheels() is called from LateUpdate(); that will ensure your code always runs after the WheelCollider has already updated its pose.
|
2021-04-17 14:47:00
|
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|
https://psychology.stackexchange.com/questions/12856/batch-converting-img-files-to-mgz-in-freesurfer
|
# Batch converting .img files to .mgz in FreeSurfer
I have a series of .img files from a previous analysis in SPM that Freesurfer (FS) cannot directly handle.
FS comes with a conversion tool, the mri_convert command, but I am not able to make it run iteratively over all the files in the same directory. I found a mention about the --sdcmlist argument online, however I am not figuring out the proper syntax for it.
When I run:
mri_convert --sdcmlist 000123_1_4.img 000123_1_4.mgz
I get:
mri_convert: missing output volume name
Would anyone suggest a way of going about these conversions?
I couldn't find a way of doing that using the arguments in the mri_convert, so I decided to do it programatically in bash. This answer will only work in Linux (or in any bash). It's an one-line command to iterativelly run the convertion on all files in the same directory.
for f in *.img; do mri_convert $f$f.mgz; done
There is one aspect that I did not get right, that is FS actually handles img files, however these files do not have directionality information, thus using them is not recommended.
One can simply feed the recon-all command with the img file and the command will take care of the conversion.
|
2021-01-23 10:45:29
|
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|
http://mathoverflow.net/questions/129397/rigid-strongly-regular-graphs
|
# Rigid Strongly Regular Graphs
I need a few examples of graphs that are strongly regular as well as rigid, i.e., have only the trivial automorphism. Any references to relevant literature would be appreciated. Thanks.
-
At Ted Spence's web page http://www.maths.gla.ac.uk/~es/srgraphs.php you can find all the strongly regular graphs on 25 and 26 vertices, and these include examples of asymmetric graphs. (No srg on fewer than 25 vertices is asymmetric.)
You get more examples as Latin square graphs. Take an $n\times n$ Latin square (with $n\ge 6$). Define the vertices of the graph to be the $n^2$ cells of the square, and declare two cells to be adjacent if they are in the same row, or in the same column, or have the same content. Most Latin squares will work.
You can also construct srgs on the triples of Steiner triple systems (adjacent if they overlap), and Babai proved that almost all of these are asymmetric.
-
Is it easy to see which ones of these are asymmetric? – Pawan Aurora May 2 '13 at 17:37
Yes, you pipe them through nasty, or use sage. – Chris Godsil May 2 '13 at 17:51
|
2014-09-23 00:32:33
|
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|
https://fabricesalvaire.github.io/Patro/api/Patro/GeometryEngine/Polygon.html
|
# 10.1.4.8. Polygon¶
Module to implement polygon and convex hull.
For resources on polygon see this section.
class Patro.GeometryEngine.Polygon.Polygon2D(*points, is_convex=None, is_clockwise=None)[source]
Class to implements 2D Polygon.
__init__(*points, is_convex=None, is_clockwise=None)[source]
Initialize self. See help(type(self)) for accurate signature.
_check_area()[source]
_check_moment()[source]
_compute_area_barycenter()[source]
Compute polygon area and barycenter.
_compute_inertia_moment()[source]
Compute inertia moment on vertices.
_crossing_number_test(point)[source]
Crossing number test for a point in a polygon.
_test_is_convex()[source]
_test_is_simple()[source]
_winding_number_test(point)[source]
Winding number test for a point in a polygon.
area
Return polygon area.
axis_ratio
barycenter
Return polygon barycenter.
convex_hull()[source]
edges
is_clockwise
is_concave
is_convex
is_counterclockwise
is_point_inside(point)[source]
is_simple
Test if the polygon is simple, i.e. if it doesn’t self-intersect.
is_triangle
major_axis
major_axis_angle
minor_axis
perimeter
point_barycenter
recenter()[source]
Recenter the polygon to the barycenter.
to_triangle()[source]
class Patro.GeometryEngine.Polygon.RegularPolygon(center, radius, number_of_edges, angle=0)[source]
Class to implement regular polygon (N-gon).
LARGE_NGON_NAMES = {24: 'icositetragon', 30: 'triacontagon', 40: 'tetracontagon', 50: 'pentacontagon', 60: 'hexacontagon', 70: 'heptacontagon', 80: 'octacontagon', 90: 'enneacontagon', 100: 'hectogon', 257: '257-gon', 1000: 'chiliagon', 10000: 'myriagon', 65537: '65537-gon', 1000000: 'megagon'}
NGON_NAMES = ('monogon', 'digon', 'triangle', 'quadrilateral', 'pentagon', 'hexagon', 'heptagon', 'octagon', 'nonagon', 'decagon', 'hendecagon', 'dodecagon', 'tridecagon', 'tetradecagon', 'pentadecagon', 'hexadecagon', 'heptadecagon', 'octadecagon', 'enneadecagon', 'icosagon')
__init__(center, radius, number_of_edges, angle=0)[source]
Initialize self. See help(type(self)) for accurate signature.
angle
center
circumcircle
edge_angle
classmethod ngon_name(number_of_edges)[source]
number_of_edges
radius
str_name
Patro.GeometryEngine.Polygon.ccw(p1, p2, p3)[source]
Three points are a counter-clockwise turn if ccw > 0, clockwise if ccw < 0, and collinear if ccw = 0 because ccw is a determinant $$(\mathbf{P}_3-\mathbf{P}_1) \cross (\mathbf{P}_2-\mathbf{P}_1)$$ that gives twice the signed area of the triangle formed by p1, p2 and p3.
Patro.GeometryEngine.Polygon.convex_hull(points, as_polygon=True)[source]
Return the convex hull of the list of points using Graham Scan algorithm.
• The first point is the leftmost point having the smallest y-coordinate.
• The polygon is counter-clockwise oriented.
• Time complexity is O(n log n).
References
Patro.GeometryEngine.Polygon.is_three_point_ccw(p1, p2, p3)[source]
Patro.GeometryEngine.Polygon.is_three_point_collinear(p1, p2, p3)[source]
Patro.GeometryEngine.Polygon.is_three_point_cw(p1, p2, p3)[source]
Patro.GeometryEngine.Polygon.sort_point_for_graham_scan(points)[source]
Sort the points for the Graham scan algorithm.
points must be an iterable.
The first step in this algorithm is to find the point with the lowest y-coordinate. If the lowest y-coordinate exists in more than one point in the set, the point with the lowest x-coordinate out of the candidates should be chosen. Call this point P0. This step takes O(n).
Next, the set of points must be sorted in increasing order of the angle they and the point P0 make with the x-axis.
|
2019-04-18 13:32:41
|
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|
https://cs.stackexchange.com/tags/terminology/hot?filter=year
|
A message from our CEO about the future of Stack Overflow and Stack Exchange. Read now.
# Tag Info
## Hot answers tagged terminology
30
In the most general sense, a key is a piece of information required to retrieve some data. However, this meaning plays out differently depending on exactly what situation you're dealing with. In the contexts you mention, a key is a unique identifier for the complete data used to retrieve it from some location in the structure. Each key is associated with ...
12
A key in the context of data structures (such as in the book CLRS) is a value (often an integer) that is used to identify a certain component of a data-structure. Often, keys determine how the underlying data is stored or manipulated. For example, in binary search trees we have that for every node, the key of that node is larger than the keys in the left sub-...
10
The two most obvious characteristics of an assembly language are: It is specific to a particular CPU architecture. There is a one-to-one correspondence between assembly language commands and machine code instructions (once you strip out labels, assembler directives and code comments). By contrast, a high-level language will have the following ...
7
I was wondering if my algorithm has to decide whether the input is of the desired instance ON TOP OF actually showing the properties of the language can be done in polynomial time. Very nice question! What you are talking about is best characterized as promise problem, "a generalization of a decision problem where the input is promised to belong to a ...
7
"On the order of" is an informal statement which really only means "approximately". Big O notation is a precise mathematical formulation which expresses asymptotic behavior, not approximate values of a function (e.g., $10n \in O(n)$, despite $10n$ being 10 times as larger as $n$). They can hardly be considered the same things. What the lecturer is trying to ...
7
There are several things that are all called regular expressions. The answer to your question is different depending upon which thing you want to talk about. The three relevant distinctions for this question in my opinion are as follows: First The notion of regular languages and related things like recursive enumerability. Individual regular languages ...
6
This is essentially a Segment tree which is a data structure that augments an array with a binary tree as you describe such that: You have fast set and get at any index You have fast "aggregate" queries on ranges You can support fast update queries on ranges, for some combinations of updates and queries The $j$th node at height $k$ in the tree "summarizes" ...
6
The function $$\lambda f.\lambda x.\lambda y.f\;y\;x$$ of type $$\forall X. \forall Y. \forall Z.(X \to Y \to Z) \to Y \to X \to Z$$ is often called flip. This is the case in Haskell (see here), and in some OCaml libraries as well (see here). According to wikipedia, people call this function (or combinator) $C$ in the context of combinatory logic (that name ...
6
In computer science, "automaton" refers to some kind of finite state machine. This is a basic and fundamental model of computation, and automata are widely used in implementing simple electronic devices and in writing parsers, e.g., for programming languages.
5
Since this issue is still not quite clear even now in 2019, and it might help new ML-Learners choose, here is a very good image showing the differences: (localisation is the bounding box around the "sheep" class, after a classification of the image has been done) source: Towardsdatascience.com
5
I suspect you might have misheard. I suspect the lecturer said "takes the file decodes it generates the right waveforms and so on" (right, not white).
5
The essential difference between assembly language and every other programming language is that assembly language specifies the sequence of instructions directly, whereas in any other language, the code has to be converted into a sequence of instructions, a process known as compilation or code generation. As a consequence, assembly language is architecture-...
5
The automaton is mainly used as a simple model of computation to check input strings on some defined conditions by reading the string and giving out whether the string is accepted in a defined language or not. There are a lot of examples. A really crucial for example in terms of computing are the RegEx-expressions, if you heard of that. There are some ...
5
The problem in which you must select $k$ vertices to maximize the number of vertices dominated is known as the budgeted dominating set problem. The problem or its connected variant is studied at least by Lamprou, Sigalis and Zissimopoulos [1] and Khuller, Purohit and Sarpatwar [2]. It also appears in the recent survey of Narayanaswamy and Vijayaragunathan [3]...
4
There is no exact answer to your question. The terms "programming model" and "programming paradigm" are not exact technical terms that have fixed definitions. Depending on a context, some authors might define "programming model" in some specific way, but that will usually turn out to cover only some aspects of what people understand under "programming model"....
4
P, NP, NP-complete and NP-hard are complexity classes, classifying problems according to the algorithmic complexity for solving them. In short, they're based on three properties: Solvable in polynomial time: Defines decision problems that can be solved by a deterministic Turing machine (DTM) using a polynomial amount of computation time, i.e., its running ...
4
Using any/all (a.k.a. or/and) gives rise to alternating Turing machines. Goldschlager and Parberry (On the construction of parallel computers from various bases of boolean functions, Theoretical Computer Science 48:43–58, 1986) consider the generalization to allowing arbitrary Boolean functions, and they call the resulting machines extended Turing ...
4
The answer depends on exactly what problem you're solving. If your goal is to produce an algorithm that correctly solves the problem on the restricted instances, then it's kind of up to you whether or not you check. It feels more robust to check the input but it's perfectly reasonable not to, and that puts you in the realm of promise problems. Here, the "...
4
This is something you will encounter over and over, not just in science but also in engineering, in law, in programming, and generally in jargon. If there is a definition for a term, then that term means exactly what the definition says it means. No more. No less. In particular, you may have an intuitive notion of what the term means in English, but this is ...
4
LSB (least significant bit) and MSB (most significant bit) apply purely to the values of an integer. The least significant bit is the bit with value 1, the second least significant bit is the bit with value 2, and so on. "Little endian" and "Big endian" are just artefacts from the fact that the bytes of a number can be accessed individually as they are ...
4
(Warning, this historical account of increasing abstraction and declarative programming may annoy, confuse, or upset you:) Hello, world! By far and large, programing languages happen on a continuum, with "pure" instances of languages being ideals. This is because there are a variety of platforms, architectures, and goals when writing software. Of course, ...
3
A problem is always claimed to be NP-hard, period. Indeed, a problem's definition already contains a specification of its parameters. (See the entries in Richard Karp's seminal collection of NP-complete problems for several examples.) Usually, there is no need to make explicit reference to the parameters per se, as they are "automatically scaled" by the ...
3
Yes, the code written by your friend implements the selection sort. It is not exactly how the selection sort is usually implemented, though. What is done in your friend's code? At the first iteration where i=0, it finds the smallest element by comparing the element at index 0 with all other element, swapping if necessary so that the minimum element so far ...
3
Rooted Tree How do you call a rooted tree if the number of branches per node is arbitrary (outdegree of n) but the indegree 1 for all nodes other than the root node? That is none other than an rooted tree itself or, more accurately, an arborescence or branching tree or out-tree according to the following quote from Wikipedia entry on rooted tree. A ...
3
I think that's often called a "variable assignment", since it assigns to each variable a value (a vertex in the graph, in your case). If the graph is equipped with a set of such tuples, these might be considered to be hyperedges, i.e. edges connected to an arbitrary number of vertices (not necessarily two of them).
3
A language is defined as a set of strings over an alphabet. We will assume the usual situation where the alphabet is a finite set. Then the set of all strings are countably infinite. Why is it countable? Because we can list all strings of length 0, all strings of length 1, all strings of length 2, all strings of length 3 and so on. The correct diagram ...
3
Undecidable is simply the complement of decidable, as the name suggests: anything that is not decidable is undecidable. So the whole pink area of your diagram consists of undecidable languages. All languages over finite alphabets are countable. For example, every string over alphabet $\{0,1\}$ is a natural number written in binary.1 Everything in your ...
3
I don't know a standard name for this, but what you've described is representable as a function into $\mathbb{R}$. For your example, if $X$ is the set of your things then you can represent your 'fractional multiset' as a a function $f : X \to \mathbb{R}$ such that f(x) = \begin{cases} 1 & x = \text{carpenter}, \text{sawyer} \\ 0.5 & x = \text{...
3
They are called primitive data types. (This is a pretty basic find in Wikipedia's article on data types.)
3
Yes, your context-free grammar is in Chomsky Normal Form. A grammar is in CNF whenever its rules are of one of two types, either $A\to BC$ or $A\to a$, where $A,B,C$ are nonterminals, and $a$ is a terminal symbol. This means that every context-free grammar is equivalent to a cf grammar in CNF, up to the empty word. This means that by conversion into CNF ...
Only top voted, non community-wiki answers of a minimum length are eligible
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2020-01-23 09:44:18
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https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-5-exponents-and-polynomials-5-4-dividing-by-monomials-problem-set-5-4-page-212/47
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# Chapter 5 - Exponents and Polynomials - 5.4 - Dividing by Monomials - Problem Set 5.4: 47
-3$a^{2}$ + 7a + 13b
#### Work Step by Step
$\frac{15a^{3}b - 35a^{2}b - 65ab^{2}}{-5ab}$ = RECALL: $\frac{b^{n}}{b^{m}}$ = $b^{n-m}$ So, $\frac{15a^{3}b - 35a^{2}b - 65ab^{2}}{-5ab}$ = $\frac{15a^{3}b}{-5ab}$ + $\frac{-35a^{2}b}{-5ab}$ + $\frac{-65ab^{2}}{-5ab}$ = $\frac{15}{-5}$$a^{3-1}$$b^{1-1}$ + $\frac{-35}{-5}$$a^{2-1}$$b^{1-1}$ + $\frac{-65}{-5}$$a^{1-1}$$b^{2-1}$ = -3$a^{2}$ + 7a + 13b
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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2018-05-23 20:56:48
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https://www.mpi-inf.mpg.de/departments/algorithms-complexity/publications/current-year/
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# Current Year
[1]
A. Abboud, K. Bringmann, D. Hermelin, and D. Shabtay, “SETH-Based Lower Bounds for Subset Sum and Bicriteria Path,” 2017. [Online]. Available: http://arxiv.org/abs/1704.04546. (arXiv: 1704.04546)
Abstract
Subset-Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is to base the hardness of one of these problems on the other. Our main result is a tight reduction from k-SAT to Subset-Sum on dense instances, proving that Bellman's 1962 pseudo-polynomial $O^{*}(T)$-time algorithm for Subset-Sum on $n$ numbers and target $T$ cannot be improved to time $T^{1-\varepsilon}\cdot 2^{o(n)}$ for any $\varepsilon>0$, unless the Strong Exponential Time Hypothesis (SETH) fails. This is one of the strongest known connections between any two of the core problems of fine-grained complexity. As a corollary, we prove a "Direct-OR" theorem for Subset-Sum under SETH, offering a new tool for proving conditional lower bounds: It is now possible to assume that deciding whether one out of $N$ given instances of Subset-Sum is a YES instance requires time $(N T)^{1-o(1)}$. As an application of this corollary, we prove a tight SETH-based lower bound for the classical Bicriteria s,t-Path problem, which is extensively studied in Operations Research. We separate its complexity from that of Subset-Sum: On graphs with $m$ edges and edge lengths bounded by $L$, we show that the $O(Lm)$ pseudo-polynomial time algorithm by Joksch from 1966 cannot be improved to $\tilde{O}(L+m)$, in contrast to a recent improvement for Subset Sum (Bringmann, SODA 2017).
Export
BibTeX
@online{DBLP:journals/corr/AbboudBHS17, TITLE = {{SETH}-Based Lower Bounds for Subset Sum and Bicriteria Path}, AUTHOR = {Abboud, Amir and Bringmann, Karl and Hermelin, Danny and Shabtay, Dvir}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1704.04546}, EPRINT = {1704.04546}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Subset-Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is to base the hardness of one of these problems on the other. Our main result is a tight reduction from k-SAT to Subset-Sum on dense instances, proving that Bellman's 1962 pseudo-polynomial $O^{*}(T)$-time algorithm for Subset-Sum on $n$ numbers and target $T$ cannot be improved to time $T^{1-\varepsilon}\cdot 2^{o(n)}$ for any $\varepsilon>0$, unless the Strong Exponential Time Hypothesis (SETH) fails. This is one of the strongest known connections between any two of the core problems of fine-grained complexity. As a corollary, we prove a "Direct-OR" theorem for Subset-Sum under SETH, offering a new tool for proving conditional lower bounds: It is now possible to assume that deciding whether one out of $N$ given instances of Subset-Sum is a YES instance requires time $(N T)^{1-o(1)}$. As an application of this corollary, we prove a tight SETH-based lower bound for the classical Bicriteria s,t-Path problem, which is extensively studied in Operations Research. We separate its complexity from that of Subset-Sum: On graphs with $m$ edges and edge lengths bounded by $L$, we show that the $O(Lm)$ pseudo-polynomial time algorithm by Joksch from 1966 cannot be improved to $\tilde{O}(L+m)$, in contrast to a recent improvement for Subset Sum (Bringmann, SODA 2017).}, }
Endnote
%0 Report %A Abboud, Amir %A Bringmann, Karl %A Hermelin, Danny %A Shabtay, Dvir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T SETH-Based Lower Bounds for Subset Sum and Bicriteria Path : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-89E5-3 %U http://arxiv.org/abs/1704.04546 %D 2017 %X Subset-Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is to base the hardness of one of these problems on the other. Our main result is a tight reduction from k-SAT to Subset-Sum on dense instances, proving that Bellman's 1962 pseudo-polynomial $O^{*}(T)$-time algorithm for Subset-Sum on $n$ numbers and target $T$ cannot be improved to time $T^{1-\varepsilon}\cdot 2^{o(n)}$ for any $\varepsilon>0$, unless the Strong Exponential Time Hypothesis (SETH) fails. This is one of the strongest known connections between any two of the core problems of fine-grained complexity. As a corollary, we prove a "Direct-OR" theorem for Subset-Sum under SETH, offering a new tool for proving conditional lower bounds: It is now possible to assume that deciding whether one out of $N$ given instances of Subset-Sum is a YES instance requires time $(N T)^{1-o(1)}$. As an application of this corollary, we prove a tight SETH-based lower bound for the classical Bicriteria s,t-Path problem, which is extensively studied in Operations Research. We separate its complexity from that of Subset-Sum: On graphs with $m$ edges and edge lengths bounded by $L$, we show that the $O(Lm)$ pseudo-polynomial time algorithm by Joksch from 1966 cannot be improved to $\tilde{O}(L+m)$, in contrast to a recent improvement for Subset Sum (Bringmann, SODA 2017). %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC
[2]
I. Abraham, S. Chechik, and S. Krinninger, “Fully dynamic all-pairs shortest paths with worst-case update-time,” in Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), Barcelona, Spain, 2017.
Export
BibTeX
@inproceedings{AbrahamCK17, TITLE = {Fully dynamic all-pairs shortest paths with worst-case update-time}, AUTHOR = {Abraham, Ittai and Chechik, Shiri and Krinninger, Sebastian}, LANGUAGE = {eng}, ISBN = {978-1-61197-478-2}, DOI = {10.1137/1.9781611974782.28}, PUBLISHER = {SIAM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017)}, EDITOR = {Klein, Philip N.}, PAGES = {440--452}, ADDRESS = {Barcelona, Spain}, }
Endnote
%0 Conference Proceedings %A Abraham, Ittai %A Chechik, Shiri %A Krinninger, Sebastian %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fully dynamic all-pairs shortest paths with worst-case update-time : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-52D0-1 %R 10.1137/1.9781611974782.28 %D 2017 %B Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2017-01-16 - 2017-01-19 %C Barcelona, Spain %B Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %E Klein, Philip N. %P 440 - 452 %I SIAM %@ 978-1-61197-478-2
[3]
A. Adamaszek, M. P. Renault, A. Rosen, and R. van Stee, “Reordering Buffer Management with Advice,” Journal of Scheduling, vol. 20, no. 5, 2017.
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BibTeX
@article{Adamaszek2017, TITLE = {Reordering Buffer Management with Advice}, AUTHOR = {Adamaszek, Anna and Renault, Marc P. and Rosen, Adi and van Stee, Rob}, LANGUAGE = {eng}, ISSN = {1094-6136}, DOI = {10.1007/s10951-016-0487-8}, PUBLISHER = {Wiley}, ADDRESS = {New York, NY}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Scheduling}, VOLUME = {20}, NUMBER = {5}, PAGES = {423--442}, }
Endnote
%0 Journal Article %A Adamaszek, Anna %A Renault, Marc P. %A Rosen, Adi %A van Stee, Rob %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Reordering Buffer Management with Advice : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-0E60-C %R 10.1007/s10951-016-0487-8 %7 2016-06-17 %D 2017 %J Journal of Scheduling %V 20 %N 5 %& 423 %P 423 - 442 %I Wiley %C New York, NY %@ false
[4]
E. Althaus, B. Beber, W. Damm, S. Disch, W. Hagemann, A. Rakow, C. Scholl, U. Waldmann, and B. Wirtz, “Verification of Linear Hybrid Systems with Large Discrete State Spaces Using Counterexample-guided Abstraction Refinement,” Science of Computer Programming, vol. 148, 2017.
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BibTeX
@article{Althaus2017, TITLE = {Verification of Linear Hybrid Systems with Large Discrete State Spaces Using Counterexample-guided Abstraction Refinement}, AUTHOR = {Althaus, Ernst and Beber, Bj{\"o}rn and Damm, Werner and Disch, Stefan and Hagemann, Willem and Rakow, Astrid and Scholl, Christoph and Waldmann, Uwe and Wirtz, Boris}, LANGUAGE = {eng}, ISSN = {0167-6423}, DOI = {10.1016/j.scico.2017.04.010}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Science of Computer Programming}, VOLUME = {148}, PAGES = {123--160}, }
Endnote
%0 Journal Article %A Althaus, Ernst %A Beber, Björn %A Damm, Werner %A Disch, Stefan %A Hagemann, Willem %A Rakow, Astrid %A Scholl, Christoph %A Waldmann, Uwe %A Wirtz, Boris %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations External Organizations Automation of Logic, MPI for Informatics, Max Planck Society External Organizations %T Verification of Linear Hybrid Systems with Large Discrete State Spaces Using Counterexample-guided Abstraction Refinement : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-1C23-5 %R 10.1016/j.scico.2017.04.010 %7 2017-05-10 %D 2017 %J Science of Computer Programming %V 148 %& 123 %P 123 - 160 %I Elsevier %C Amsterdam %@ false
[5]
S. Anand, K. Bringmann, T. Friedrich, N. Garg, and A. Kumar, “Minimizing Maximum (Weighted) Flow-Time on Related and Unrelated Machines,” Algorithmica, vol. 77, no. 2, 2017.
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BibTeX
@article{DBLP:journals/algorithmica/0002B0G017, TITLE = {Minimizing Maximum (Weighted) Flow-Time on Related and Unrelated Machines}, AUTHOR = {Anand, S. and Bringmann, Karl and Friedrich, Tobias and Garg, Naveen and Kumar, Amit}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-015-0082-y}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York, NY}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Algorithmica}, VOLUME = {77}, NUMBER = {2}, PAGES = {515--536}, }
Endnote
%0 Journal Article %A Anand, S. %A Bringmann, Karl %A Friedrich, Tobias %A Garg, Naveen %A Kumar, Amit %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Discrete Optimization, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Minimizing Maximum (Weighted) Flow-Time on Related and Unrelated Machines : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-5527-9 %R 10.1007/s00453-015-0082-y %7 2015 %D 2017 %J Algorithmica %V 77 %N 2 %& 515 %P 515 - 536 %I Springer-Verlag %C New York, NY %@ false
[6]
A. Antoniadis, N. Barcelo, M. Consuegra, P. Kling, M. Nugent, K. Pruhs, and M. Scquizzato, “Efficient Computation of Optimal Energy and Fractional Weighted Flow Trade-Off Schedules,” Algorithmica, vol. 79, no. 2, 2017.
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BibTeX
@article{Antoniadis2016, TITLE = {Efficient Computation of Optimal Energy and Fractional Weighted Flow Trade-Off Schedules}, AUTHOR = {Antoniadis, Antonios and Barcelo, Neal and Consuegra, Mario and Kling, Peter and Nugent, Michael and Pruhs, Kirk and Scquizzato, Michele}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-016-0208-x}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Algorithmica}, VOLUME = {79}, NUMBER = {2}, PAGES = {568--597}, }
Endnote
%0 Journal Article %A Antoniadis, Antonios %A Barcelo, Neal %A Consuegra, Mario %A Kling, Peter %A Nugent, Michael %A Pruhs, Kirk %A Scquizzato, Michele %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations External Organizations External Organizations %T Efficient Computation of Optimal Energy and Fractional Weighted Flow Trade-Off Schedules : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-58AA-7 %R 10.1007/s00453-016-0208-x %7 2016-08-31 %D 2017 %J Algorithmica %V 79 %N 2 %& 568 %P 568 - 597 %I Springer %C New York, NY %@ false
[7]
A. Antoniadis, P. Kling, S. Ott, and S. Riechers, “Continuous Speed Scaling with Variability: A simple and Direct Approach,” Theoretical Computer Science, vol. 678, 2017.
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BibTeX
@article{Antoniadis2017, TITLE = {Continuous Speed Scaling with Variability: {A} simple and Direct Approach}, AUTHOR = {Antoniadis, Antonios and Kling, Peter and Ott, Sebastian and Riechers, S{\"o}ren}, LANGUAGE = {eng}, ISSN = {0304-3975}, DOI = {10.1016/j.tcs.2017.03.021}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Theoretical Computer Science}, VOLUME = {678}, PAGES = {1--13}, }
Endnote
%0 Journal Article %A Antoniadis, Antonios %A Kling, Peter %A Ott, Sebastian %A Riechers, Sören %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Continuous Speed Scaling with Variability: A simple and Direct Approach : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-7857-F %R 10.1016/j.tcs.2017.03.021 %7 2017 %D 2017 %J Theoretical Computer Science %V 678 %& 1 %P 1 - 13 %I Elsevier %C Amsterdam %@ false
[8]
Y. Azar, M. Hoefer, I. Maor, R. Reiffenhäuser, and B. Vöcking, “Truthful Mechanism Design via Correlated Tree Rounding,” Mathematical Programming / A, vol. 163, no. 1–2, 2017.
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BibTeX
@article{Azar2017, TITLE = {Truthful Mechanism Design via Correlated Tree Rounding}, AUTHOR = {Azar, Yossi and Hoefer, Martin and Maor, Idan and Reiffenh{\"a}user, Rebecca and V{\"o}cking, Berthold}, LANGUAGE = {eng}, ISSN = {0025-5610}, DOI = {10.1007/s10107-016-1068-5}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Mathematical Programming / A}, VOLUME = {163}, NUMBER = {1-2}, PAGES = {445--469}, }
Endnote
%0 Journal Article %A Azar, Yossi %A Hoefer, Martin %A Maor, Idan %A Reiffenhäuser, Rebecca %A Vöcking, Berthold %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Truthful Mechanism Design via Correlated Tree Rounding : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-326B-A %R 10.1007/s10107-016-1068-5 %7 2016-09-10 %D 2017 %J Mathematical Programming / A %V 163 %N 1-2 %& 445 %P 445 - 469 %I Springer %C New York, NY %@ false
[9]
L. Becchetti, A. Clementi, E. Natale, F. Pasquale, R. Silvestri, and L. Trevisan, “Simple Dynamics for Plurality Consensus,” Distributed Computing, vol. 30, no. 4, 2017.
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BibTeX
@article{Becchetti2017, TITLE = {Simple Dynamics for Plurality Consensus}, AUTHOR = {Becchetti, Luca and Clementi, Andrea and Natale, Emanuele and Pasquale, Francesco and Silvestri, Riccardo and Trevisan, Luca}, LANGUAGE = {eng}, ISSN = {0178-2770}, DOI = {10.1007/s00446-016-0289-4}, PUBLISHER = {Springer International}, ADDRESS = {Berlin}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Distributed Computing}, VOLUME = {30}, NUMBER = {4}, PAGES = {293--306}, }
Endnote
%0 Journal Article %A Becchetti, Luca %A Clementi, Andrea %A Natale, Emanuele %A Pasquale, Francesco %A Silvestri, Riccardo %A Trevisan, Luca %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Simple Dynamics for Plurality Consensus : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-F885-F %R 10.1007/s00446-016-0289-4 %7 2016-11-22 %D 2017 %J Distributed Computing %V 30 %N 4 %& 293 %P 293 - 306 %I Springer International %C Berlin %@ false
[10]
L. Becchetti, A. Clementi, E. Natale, F. Pasquale, and L. Trevisan, “Find Your Place: Simple Distributed Algorithms for Community Detection,” in Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), Barcelona, Spain, 2017.
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@inproceedings{BCNPT17, TITLE = {Find Your Place: {S}imple Distributed Algorithms for Community Detection}, AUTHOR = {Becchetti, Luca and Clementi, Andrea and Natale, Emanuele and Pasquale, Francesco and Trevisan, Luca}, LANGUAGE = {eng}, DOI = {10.1137/1.9781611974782.59}, PUBLISHER = {SIAM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017)}, PAGES = {940--959}, ADDRESS = {Barcelona, Spain}, }
Endnote
%0 Conference Proceedings %A Becchetti, Luca %A Clementi, Andrea %A Natale, Emanuele %A Pasquale, Francesco %A Trevisan, Luca %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Find Your Place: Simple Distributed Algorithms for Community Detection : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-5877-A %R 10.1137/1.9781611974782.59 %D 2017 %B Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2017-01-16 - 2017-01-19 %C Barcelona, Spain %B Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %P 940 - 959 %I SIAM
[11]
R. Becker, M. Sagraloff, V. Sharma, and C. Yap, “A Simple Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the Pellet Test and Newton Iteration,” Journal of Symbolic Computation, 2017.
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@article{Becker2017JSC, TITLE = {A Simple Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the {Pellet} Test and {Newton} Iteration}, AUTHOR = {Becker, Ruben and Sagraloff, Michael and Sharma, Vikram and Yap, Chee}, LANGUAGE = {eng}, ISSN = {0747-7171}, DOI = {10.1016/j.jsc.2017.03.009}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, JOURNAL = {Journal of Symbolic Computation}, }
Endnote
%0 Journal Article %A Becker, Ruben %A Sagraloff, Michael %A Sharma, Vikram %A Yap, Chee %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A Simple Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the Pellet Test and Newton Iteration : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-5717-8 %R 10.1016/j.jsc.2017.03.009 %7 2017-03-29 %D 2017 %8 29.03.2017 %J Journal of Symbolic Computation %I Elsevier %C Amsterdam %@ false
[12]
R. Becker, V. Bonifaci, A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Two Results on Slime Mold Computations,” 2017. [Online]. Available: http://arxiv.org/abs/1707.06631. (arXiv: 1707.06631)
Abstract
In this paper, we present two results on slime mold computations. The first one treats a biologically-grounded model, originally proposed by biologists analyzing the behavior of the slime mold Physarum polycephalum. This primitive organism was empirically shown by Nakagaki et al. to solve shortest path problems in wet-lab experiments (Nature'00). We show that the proposed simple mathematical model actually generalizes to a much wider class of problems, namely undirected linear programs with a non-negative cost vector. For our second result, we consider the discretization of a biologically-inspired model. This model is a directed variant of the biologically-grounded one and was never claimed to describe the behavior of a biological system. Straszak and Vishnoi showed that it can $\epsilon$-approximately solve flow problems (SODA'16) and even general linear programs with positive cost vector (ITCS'16) within a finite number of steps. We give a refined convergence analysis that improves the dependence on $\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a step size that is independent of $\epsilon$. Furthermore, we show that the dynamics can be initialized with a more general set of (infeasible) starting points.
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@online{Becker_arxiv2017, TITLE = {Two Results on Slime Mold Computations}, AUTHOR = {Becker, Ruben and Bonifaci, Vincenzo and Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1707.06631}, EPRINT = {1707.06631}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In this paper, we present two results on slime mold computations. The first one treats a biologically-grounded model, originally proposed by biologists analyzing the behavior of the slime mold Physarum polycephalum. This primitive organism was empirically shown by Nakagaki et al. to solve shortest path problems in wet-lab experiments (Nature'00). We show that the proposed simple mathematical model actually generalizes to a much wider class of problems, namely undirected linear programs with a non-negative cost vector. For our second result, we consider the discretization of a biologically-inspired model. This model is a directed variant of the biologically-grounded one and was never claimed to describe the behavior of a biological system. Straszak and Vishnoi showed that it can $\epsilon$-approximately solve flow problems (SODA'16) and even general linear programs with positive cost vector (ITCS'16) within a finite number of steps. We give a refined convergence analysis that improves the dependence on $\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a step size that is independent of $\epsilon$. Furthermore, we show that the dynamics can be initialized with a more general set of (infeasible) starting points.}, }
Endnote
%0 Report %A Becker, Ruben %A Bonifaci, Vincenzo %A Karrenbauer, Andreas %A Kolev, Pavel %A Mehlhorn, Kurt %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Two Results on Slime Mold Computations : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-FBA8-F %U http://arxiv.org/abs/1707.06631 %D 2017 %X In this paper, we present two results on slime mold computations. The first one treats a biologically-grounded model, originally proposed by biologists analyzing the behavior of the slime mold Physarum polycephalum. This primitive organism was empirically shown by Nakagaki et al. to solve shortest path problems in wet-lab experiments (Nature'00). We show that the proposed simple mathematical model actually generalizes to a much wider class of problems, namely undirected linear programs with a non-negative cost vector. For our second result, we consider the discretization of a biologically-inspired model. This model is a directed variant of the biologically-grounded one and was never claimed to describe the behavior of a biological system. Straszak and Vishnoi showed that it can $\epsilon$-approximately solve flow problems (SODA'16) and even general linear programs with positive cost vector (ITCS'16) within a finite number of steps. We give a refined convergence analysis that improves the dependence on $\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a step size that is independent of $\epsilon$. Furthermore, we show that the dynamics can be initialized with a more general set of (infeasible) starting points. %K Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Dynamical Systems, math.DS,Mathematics, Optimization and Control, math.OC, Physics, Biological Physics, physics.bio-ph
[13]
X. Bei, J. Garg, M. Hoefer, and K. Mehlhorn, “Earning Limits in Fisher Markets with Spending-Constraint Utilities,” in Algorithmic Game Theory (SAGT 2017), L’Aquila, Italy, 2017.
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@inproceedings{BeiSAGT2017, TITLE = {Earning Limits in {Fisher} Markets with Spending-Constraint Utilities}, AUTHOR = {Bei, Xiaohui and Garg, Jugal and Hoefer, Martin and Mehlhorn, Kurt}, LANGUAGE = {eng}, ISBN = {978-3-319-66699-0}, DOI = {10.1007/978-3-319-66700-3_6}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Algorithmic Game Theory (SAGT 2017)}, PAGES = {67--79}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {10504}, ADDRESS = {L'Aquila, Italy}, }
Endnote
%0 Conference Proceedings %A Bei, Xiaohui %A Garg, Jugal %A Hoefer, Martin %A Mehlhorn, Kurt %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Earning Limits in Fisher Markets with Spending-Constraint Utilities : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-E7DB-7 %R 10.1007/978-3-319-66700-3_6 %D 2017 %B 10th International Symposium on Algorithmic Game Theory %Z date of event: 2017-09-12 - 2017-09-14 %C L'Aquila, Italy %B Algorithmic Game Theory %P 67 - 79 %I Springer %@ 978-3-319-66699-0 %B Lecture Notes in Computer Science %N 10504
[14]
F. Benhamouda, T. Lepoint, C. Mathieu, and H. Zhou, “Optimization of Bootstrapping in Circuits,” in Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), Barcelona, Spain, 2017.
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@inproceedings{doi:10.1137/1.9781611974782.160, TITLE = {Optimization of Bootstrapping in Circuits}, AUTHOR = {Benhamouda, Fabrice and Lepoint, Tancr{\`e}de and Mathieu, Claire and Zhou, Hang}, LANGUAGE = {eng}, ISBN = {978-1-61197-478-2}, DOI = {10.1137/1.9781611974782.160}, PUBLISHER = {SIAM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017)}, EDITOR = {Klein, Philip N.}, PAGES = {2423--2433}, ADDRESS = {Barcelona, Spain}, }
Endnote
%0 Conference Proceedings %A Benhamouda, Fabrice %A Lepoint, Tancrède %A Mathieu, Claire %A Zhou, Hang %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Optimization of Bootstrapping in Circuits : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-4EBE-A %R 10.1137/1.9781611974782.160 %D 2017 %B Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2017-01-16 - 2017-01-19 %C Barcelona, Spain %B Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %E Klein, Philip N. %P 2423 - 2433 %I SIAM %@ 978-1-61197-478-2
[15]
P. Berenbrink, A. Clementi, R. Elsässer, P. Kling, F. Mallmann-Trenn, and E. Natale, “Ignore or Comply?: On Breaking Symmetry in Consensus,” in PODC’17, ACM Symposium on Principles of Distributed Computing, Washington, DC, USA, 2017.
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@inproceedings{Berenbrink:2017:ICB:3087801.3087817, TITLE = {Ignore or Comply?: {O}n Breaking Symmetry in Consensus}, AUTHOR = {Berenbrink, Petra and Clementi, Andrea and Els{\"a}sser, Robert and Kling, Peter and Mallmann-Trenn, Frederik and Natale, Emanuele}, LANGUAGE = {eng}, ISBN = {978-1-4503-4992-5}, DOI = {10.1145/3087801.3087817}, PUBLISHER = {ACM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {PODC'17, ACM Symposium on Principles of Distributed Computing}, PAGES = {335--344}, ADDRESS = {Washington, DC, USA}, }
Endnote
%0 Conference Proceedings %A Berenbrink, Petra %A Clementi, Andrea %A Elsässer, Robert %A Kling, Peter %A Mallmann-Trenn, Frederik %A Natale, Emanuele %+ External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Ignore or Comply?: On Breaking Symmetry in Consensus : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-76B2-0 %R 10.1145/3087801.3087817 %D 2017 %B ACM Symposium on Principles of Distributed Computing %Z date of event: 2017-07-25 - 2017-07-27 %C Washington, DC, USA %B PODC'17 %P 335 - 344 %I ACM %@ 978-1-4503-4992-5
[16]
O. Beyersdorff, L. Chew, and K. Sreenivasaiah, “A Game Characterisation of Tree-like Q-Resolution Size,” Journal of Computer and System Sciences, vol. In Press, 2017.
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@article{Beyersdorff2017, TITLE = {A Game Characterisation of Tree-like {Q-Resolution} Size}, AUTHOR = {Beyersdorff, Olaf and Chew, Leroy and Sreenivasaiah, Karteek}, LANGUAGE = {eng}, ISSN = {0022-0000}, DOI = {10.1016/j.jcss.2016.11.011}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, JOURNAL = {Journal of Computer and System Sciences}, VOLUME = {In Press}, }
Endnote
%0 Journal Article %A Beyersdorff, Olaf %A Chew, Leroy %A Sreenivasaiah, Karteek %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Game Characterisation of Tree-like Q-Resolution Size : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-5F80-F %R 10.1016/j.jcss.2016.11.011 %7 2017 %D 2017 %J Journal of Computer and System Sciences %V In Press %I Elsevier %C Amsterdam %@ false
[17]
L. Boczkowski, A. Korman, and E. Natale, “Minimizing Message Size in Stochastic Communication Patterns: Fast Self-Stabilizing Protocols with 3 bits,” in Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), Barcelona, Spain, 2017.
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@inproceedings{BKN17, TITLE = {Minimizing Message Size in Stochastic Communication Patterns: {F}ast Self-Stabilizing Protocols with 3 bits}, AUTHOR = {Boczkowski, Lucas and Korman, Amos and Natale, Emanuele}, LANGUAGE = {eng}, DOI = {10.1137/1.9781611974782.168}, PUBLISHER = {SIAM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017)}, PAGES = {2540--2559}, ADDRESS = {Barcelona, Spain}, }
Endnote
%0 Conference Proceedings %A Boczkowski, Lucas %A Korman, Amos %A Natale, Emanuele %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Minimizing Message Size in Stochastic Communication Patterns: Fast Self-Stabilizing Protocols with 3 bits : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-587B-2 %R 10.1137/1.9781611974782.168 %D 2017 %B Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2017-01-16 - 2017-01-19 %C Barcelona, Spain %B Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %P 2540 - 2559 %I SIAM
[18]
J.-D. Boissonnat, R. Dyer, and A. Ghosh, “Delaunay Triangulation of Manifolds,” Foundations of Computational Mathematics, vol. First Online, 2017.
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@article{Boissonnat2017, TITLE = {Delaunay Triangulation of Manifolds}, AUTHOR = {Boissonnat, Jean-Daniel and Dyer, Ramsay and Ghosh, Arijit}, LANGUAGE = {eng}, ISSN = {1615-3375}, DOI = {10.1007/s10208-017-9344-1}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, JOURNAL = {Foundations of Computational Mathematics}, VOLUME = {First Online}, PAGES = {1--33}, }
Endnote
%0 Journal Article %A Boissonnat, Jean-Daniel %A Dyer, Ramsay %A Ghosh, Arijit %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Delaunay Triangulation of Manifolds : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-7945-0 %R 10.1007/s10208-017-9344-1 %7 2017-02-01 %D 2017 %8 01.02.2017 %J Foundations of Computational Mathematics %V First Online %& 1 %P 1 - 33 %I Springer %C New York, NY %@ false
[19]
K. Bringmann, “A Near-Linear Pseudopolynomial Time Algorithm for Subset Sum,” in Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), Barcelona, Spain, 2017.
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@inproceedings{DBLP:conf/soda/Bringmann17, TITLE = {A Near-Linear Pseudopolynomial Time Algorithm for Subset Sum}, AUTHOR = {Bringmann, Karl}, LANGUAGE = {eng}, DOI = {10.1137/1.9781611974782.69}, PUBLISHER = {SIAM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017)}, PAGES = {1073--1084}, ADDRESS = {Barcelona, Spain}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Near-Linear Pseudopolynomial Time Algorithm for Subset Sum : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-5522-4 %R 10.1137/1.9781611974782.69 %D 2017 %B Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2017-01-16 - 2017-01-19 %C Barcelona, Spain %B Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %P 1073 - 1084 %I SIAM
[20]
K. Bringmann, P. Gawrychowski, S. Mozes, and O. Weimann, “Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (unless APSP can),” 2017. [Online]. Available: http://arxiv.org/abs/1703.08940. (arXiv: 1703.08940)
Abstract
The edit distance between two rooted ordered trees with $n$ nodes labeled from an alphabet~$\Sigma$ is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. Tree edit distance is a well known generalization of string edit distance. The fastest known algorithm for tree edit distance runs in cubic $O(n^3)$ time and is based on a similar dynamic programming solution as string edit distance. In this paper we show that a truly subcubic $O(n^{3-\varepsilon})$ time algorithm for tree edit distance is unlikely: For $|\Sigma| = \Omega(n)$, a truly subcubic algorithm for tree edit distance implies a truly subcubic algorithm for the all pairs shortest paths problem. For $|\Sigma| = O(1)$, a truly subcubic algorithm for tree edit distance implies an $O(n^{k-\varepsilon})$ algorithm for finding a maximum weight $k$-clique. Thus, while in terms of upper bounds string edit distance and tree edit distance are highly related, in terms of lower bounds string edit distance exhibits the hardness of the strong exponential time hypothesis [Backurs, Indyk STOC'15] whereas tree edit distance exhibits the hardness of all pairs shortest paths. Our result provides a matching conditional lower bound for one of the last remaining classic dynamic programming problems.
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@online{DBLP:journals/corr/BringmannGMW17, TITLE = {Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (unless {APSP} can)}, AUTHOR = {Bringmann, Karl and Gawrychowski, Pawe{\l} and Mozes, Shay and Weimann, Oren}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1703.08940}, EPRINT = {1703.08940}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The edit distance between two rooted ordered trees with $n$ nodes labeled from an alphabet~$\Sigma$ is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. Tree edit distance is a well known generalization of string edit distance. The fastest known algorithm for tree edit distance runs in cubic $O(n^3)$ time and is based on a similar dynamic programming solution as string edit distance. In this paper we show that a truly subcubic $O(n^{3-\varepsilon})$ time algorithm for tree edit distance is unlikely: For $|\Sigma| = \Omega(n)$, a truly subcubic algorithm for tree edit distance implies a truly subcubic algorithm for the all pairs shortest paths problem. For $|\Sigma| = O(1)$, a truly subcubic algorithm for tree edit distance implies an $O(n^{k-\varepsilon})$ algorithm for finding a maximum weight $k$-clique. Thus, while in terms of upper bounds string edit distance and tree edit distance are highly related, in terms of lower bounds string edit distance exhibits the hardness of the strong exponential time hypothesis [Backurs, Indyk STOC'15] whereas tree edit distance exhibits the hardness of all pairs shortest paths. Our result provides a matching conditional lower bound for one of the last remaining classic dynamic programming problems.}, }
Endnote
%0 Report %A Bringmann, Karl %A Gawrychowski, Paweł %A Mozes, Shay %A Weimann, Oren %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (unless APSP can) : %O Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (unless {APSP} can) %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-8A70-3 %U http://arxiv.org/abs/1703.08940 %D 2017 %X The edit distance between two rooted ordered trees with $n$ nodes labeled from an alphabet~$\Sigma$ is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. Tree edit distance is a well known generalization of string edit distance. The fastest known algorithm for tree edit distance runs in cubic $O(n^3)$ time and is based on a similar dynamic programming solution as string edit distance. In this paper we show that a truly subcubic $O(n^{3-\varepsilon})$ time algorithm for tree edit distance is unlikely: For $|\Sigma| = \Omega(n)$, a truly subcubic algorithm for tree edit distance implies a truly subcubic algorithm for the all pairs shortest paths problem. For $|\Sigma| = O(1)$, a truly subcubic algorithm for tree edit distance implies an $O(n^{k-\varepsilon})$ algorithm for finding a maximum weight $k$-clique. Thus, while in terms of upper bounds string edit distance and tree edit distance are highly related, in terms of lower bounds string edit distance exhibits the hardness of the strong exponential time hypothesis [Backurs, Indyk STOC'15] whereas tree edit distance exhibits the hardness of all pairs shortest paths. Our result provides a matching conditional lower bound for one of the last remaining classic dynamic programming problems. %K Computer Science, Data Structures and Algorithms, cs.DS
[21]
K. Bringmann, T. Dueholm Hansen, and S. Krinninger, “Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs,” in 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017), Warsaw, Poland, 2017.
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@inproceedings{BringmannICALP2017, TITLE = {Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs}, AUTHOR = {Bringmann, Karl and Dueholm Hansen, Thomas and Krinninger, Sebastian}, LANGUAGE = {eng}, ISBN = {978-3-95977-041-5}, URL = {urn:nbn:de:0030-drops-74398}, DOI = {10.4230/LIPIcs.ICALP.2017.124}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, EDITOR = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca}, PAGES = {1--16}, EID = {124}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {80}, ADDRESS = {Warsaw, Poland}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Dueholm Hansen, Thomas %A Krinninger, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-89C4-F %R 10.4230/LIPIcs.ICALP.2017.124 %U urn:nbn:de:0030-drops-74398 %D 2017 %B 44th International Colloquium on Automata, Languages, and Programming %Z date of event: 2017-07-10 - 2017-07-14 %C Warsaw, Poland %B 44th International Colloquium on Automata, Languages, and Programming %E Chatzigiannakis, Ioannis; Indyk, Piotr; Kuhn, Fabian; Muscholl, Anca %P 1 - 16 %Z sequence number: 124 %I Schloss Dagstuhl %@ 978-3-95977-041-5 %B Leibniz International Proceedings in Informatics %N 80 %U http://drops.dagstuhl.de/doku/urheberrecht1.htmlhttp://drops.dagstuhl.de/opus/volltexte/2017/7439/
[22]
K. Bringmann, S. Cabello, and M. Emmerich, “Maximum Volume Subset Selection for Anchored Boxes,” in 33rd International Symposium on Computational Geometry (SoCG 2017), Brisbane, Australia, 2017.
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@inproceedings{bringmann:scg, TITLE = {Maximum Volume Subset Selection for Anchored Boxes}, AUTHOR = {Bringmann, Karl and Cabello, Sergio and Emmerich, Michael}, LANGUAGE = {eng}, ISBN = {978-3-95977-038-5}, URL = {urn:nbn:de:0030-drops-72011}, DOI = {10.4230/LIPIcs.SoCG.2017.22}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {33rd International Symposium on Computational Geometry (SoCG 2017)}, EDITOR = {Aranov, Boris and Katz, Matthew J.}, PAGES = {1--15}, EID = {22}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {77}, ADDRESS = {Brisbane, Australia}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Cabello, Sergio %A Emmerich, Michael %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Maximum Volume Subset Selection for Anchored Boxes : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-7D6F-9 %U urn:nbn:de:0030-drops-72011 %R 10.4230/LIPIcs.SoCG.2017.22 %D 2017 %B 33rd International Symposium on Computational Geometry %Z date of event: 2017-07-04 - 2017-07-07 %C Brisbane, Australia %B 33rd International Symposium on Computational Geometry %E Aranov, Boris; Katz, Matthew J. %P 1 - 15 %Z sequence number: 22 %I Schloss Dagstuhl %@ 978-3-95977-038-5 %B Leibniz International Proceedings in Informatics %N 77 %U http://drops.dagstuhl.de/doku/urheberrecht1.htmlhttp://drops.dagstuhl.de/opus/volltexte/2017/7201/
[23]
K. Bringmann, T. Dueholm Hansen, and S. Krinninger, “Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs,” 2017. [Online]. Available: http://arxiv.org/abs/1704.08122. (arXiv: 1704.08122)
Abstract
We study the problem of finding the cycle of minimum cost-to-time ratio in a directed graph with $n$ nodes and $m$ edges. This problem has a long history in combinatorial optimization and has recently seen interesting applications in the context of quantitative verification. We focus on strongly polynomial algorithms to cover the use-case where the weights are relatively large compared to the size of the graph. Our main result is an algorithm with running time $\tilde O (m^{3/4} n^{3/2})$, which gives the first improvement over Megiddo's $\tilde O (n^3)$ algorithm [JACM'83] for sparse graphs. We further demonstrate how to obtain both an algorithm with running time $n^3 / 2^{\Omega{(\sqrt{\log n})}}$ on general graphs and an algorithm with running time $\tilde O (n)$ on constant treewidth graphs. To obtain our main result, we develop a parallel algorithm for negative cycle detection and single-source shortest paths that might be of independent interest.
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@online{DBLP:journals/corr/BringmannHK17, TITLE = {Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs}, AUTHOR = {Bringmann, Karl and Dueholm Hansen, Thomas and Krinninger, Sebastian}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1704.08122}, EPRINT = {1704.08122}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We study the problem of finding the cycle of minimum cost-to-time ratio in a directed graph with $n$ nodes and $m$ edges. This problem has a long history in combinatorial optimization and has recently seen interesting applications in the context of quantitative verification. We focus on strongly polynomial algorithms to cover the use-case where the weights are relatively large compared to the size of the graph. Our main result is an algorithm with running time $\tilde O (m^{3/4} n^{3/2})$, which gives the first improvement over Megiddo's $\tilde O (n^3)$ algorithm [JACM'83] for sparse graphs. We further demonstrate how to obtain both an algorithm with running time $n^3 / 2^{\Omega{(\sqrt{\log n})}}$ on general graphs and an algorithm with running time $\tilde O (n)$ on constant treewidth graphs. To obtain our main result, we develop a parallel algorithm for negative cycle detection and single-source shortest paths that might be of independent interest.}, }
Endnote
%0 Report %A Bringmann, Karl %A Dueholm Hansen, Thomas %A Krinninger, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Improved Algorithms for Computing the Cycle of Minimum Cost-to-Time Ratio in Directed Graphs : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-89BC-3 %U http://arxiv.org/abs/1704.08122 %D 2017 %X We study the problem of finding the cycle of minimum cost-to-time ratio in a directed graph with $n$ nodes and $m$ edges. This problem has a long history in combinatorial optimization and has recently seen interesting applications in the context of quantitative verification. We focus on strongly polynomial algorithms to cover the use-case where the weights are relatively large compared to the size of the graph. Our main result is an algorithm with running time $\tilde O (m^{3/4} n^{3/2})$, which gives the first improvement over Megiddo's $\tilde O (n^3)$ algorithm [JACM'83] for sparse graphs. We further demonstrate how to obtain both an algorithm with running time $n^3 / 2^{\Omega{(\sqrt{\log n})}}$ on general graphs and an algorithm with running time $\tilde O (n)$ on constant treewidth graphs. To obtain our main result, we develop a parallel algorithm for negative cycle detection and single-source shortest paths that might be of independent interest. %K Computer Science, Data Structures and Algorithms, cs.DS
[24]
K. Bringmann and P. Wellnitz, “Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars,” in 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017), Warsaw, Poland, 2017.
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@inproceedings{BringmannCPM2017, TITLE = {Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars}, AUTHOR = {Bringmann, Karl and Wellnitz, Philip}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-039-2}, URL = {urn:nbn:de:0030-drops-73329}, DOI = {10.4230/LIPIcs.CPM.2017.12}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)}, EDITOR = {K{\"a}rkk{\"a}inen, Juha and Radoszweski, Jakub and Rytter, Wojciech}, PAGES = {1--14}, EID = {12}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {78}, ADDRESS = {Warsaw, Poland}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Wellnitz, Philip %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-FB92-0 %R 10.4230/LIPIcs.CPM.2017.12 %U urn:nbn:de:0030-drops-73329 %D 2017 %B 28th Annual Symposium on Combinatorial Pattern Matching %Z date of event: 2017-07-04 - 2017-07-06 %C Warsaw, Poland %B 28th Annual Symposium on Combinatorial Pattern Matching %E Kärkkäinen, Juha; Radoszweski, Jakub; Rytter, Wojciech %P 1 - 14 %Z sequence number: 12 %I Schloss Dagstuhl %@ 978-3-95977-039-2 %B Leibniz International Proceedings in Informatics %N 78 %@ false %U http://drops.dagstuhl.de/doku/urheberrecht1.htmlhttp://drops.dagstuhl.de/opus/volltexte/2017/7332/
[25]
K. Bringmann and K. Panagiotou, “Efficient Sampling Methods for Discrete Distributions,” Algorithmica, vol. 79, no. 2, 2017.
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@article{BringmannAlgorithmica2016, TITLE = {Efficient Sampling Methods for Discrete Distributions}, AUTHOR = {Bringmann, Karl and Panagiotou, Konstantinos}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-016-0205-0}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Algorithmica}, VOLUME = {79}, NUMBER = {2}, PAGES = {484--508}, }
Endnote
%0 Journal Article %A Bringmann, Karl %A Panagiotou, Konstantinos %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Efficient Sampling Methods for Discrete Distributions : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002B-85D0-8 %R 10.1007/s00453-016-0205-0 %7 2016-08-29 %D 2017 %J Algorithmica %V 79 %N 2 %& 484 %P 484 - 508 %I Springer-Verlag %C New York %@ false
[26]
K. Bringmann and S. Krinninger, “A Note on Hardness of Diameter Approximation,” 2017. [Online]. Available: http://arxiv.org/abs/1705.02127. (arXiv: 1705.02127)
Abstract
We revisit the hardness of approximating the diameter of a network. In the CONGEST model, $\tilde \Omega (n)$ rounds are necessary to compute the diameter [Frischknecht et al. SODA'12]. Abboud et al. DISC 2016 extended this result to sparse graphs and, at a more fine-grained level, showed that, for any integer $1 \leq \ell \leq \operatorname{polylog} (n)$, distinguishing between networks of diameter $4 \ell + 2$ and $6 \ell + 1$ requires $\tilde \Omega (n)$ rounds. We slightly tighten this result by showing that even distinguishing between diameter $2 \ell + 1$ and $3 \ell + 1$ requires $\tilde \Omega (n)$ rounds. The reduction of Abboud et al. is inspired by recent conditional lower bounds in the RAM model, where the orthogonal vectors problem plays a pivotal role. In our new lower bound, we make the connection to orthogonal vectors explicit, leading to a conceptually more streamlined exposition. This is suited for teaching both the lower bound in the CONGEST model and the conditional lower bound in the RAM model.
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@online{DBLP:journals/corr/BringmannK17, TITLE = {A Note on Hardness of Diameter Approximation}, AUTHOR = {Bringmann, Karl and Krinninger, Sebastian}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1705.02127}, EPRINT = {1705.02127}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We revisit the hardness of approximating the diameter of a network. In the CONGEST model, $\tilde \Omega (n)$ rounds are necessary to compute the diameter [Frischknecht et al. SODA'12]. Abboud et al. DISC 2016 extended this result to sparse graphs and, at a more fine-grained level, showed that, for any integer $1 \leq \ell \leq \operatorname{polylog} (n)$, distinguishing between networks of diameter $4 \ell + 2$ and $6 \ell + 1$ requires $\tilde \Omega (n)$ rounds. We slightly tighten this result by showing that even distinguishing between diameter $2 \ell + 1$ and $3 \ell + 1$ requires $\tilde \Omega (n)$ rounds. The reduction of Abboud et al. is inspired by recent conditional lower bounds in the RAM model, where the orthogonal vectors problem plays a pivotal role. In our new lower bound, we make the connection to orthogonal vectors explicit, leading to a conceptually more streamlined exposition. This is suited for teaching both the lower bound in the CONGEST model and the conditional lower bound in the RAM model.}, }
Endnote
%0 Report %A Bringmann, Karl %A Krinninger, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Note on Hardness of Diameter Approximation : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-89B7-D %U http://arxiv.org/abs/1705.02127 %D 2017 %X We revisit the hardness of approximating the diameter of a network. In the CONGEST model, $\tilde \Omega (n)$ rounds are necessary to compute the diameter [Frischknecht et al. SODA'12]. Abboud et al. DISC 2016 extended this result to sparse graphs and, at a more fine-grained level, showed that, for any integer $1 \leq \ell \leq \operatorname{polylog} (n)$, distinguishing between networks of diameter $4 \ell + 2$ and $6 \ell + 1$ requires $\tilde \Omega (n)$ rounds. We slightly tighten this result by showing that even distinguishing between diameter $2 \ell + 1$ and $3 \ell + 1$ requires $\tilde \Omega (n)$ rounds. The reduction of Abboud et al. is inspired by recent conditional lower bounds in the RAM model, where the orthogonal vectors problem plays a pivotal role. In our new lower bound, we make the connection to orthogonal vectors explicit, leading to a conceptually more streamlined exposition. This is suited for teaching both the lower bound in the CONGEST model and the conditional lower bound in the RAM model. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[27]
K. Bringmann, R. Keusch, and J. Lengler, “Sampling Geometric Inhomogeneous Random Graphs in Linear Time,” in 25th Annual European Symposium on Algorithms (ESA 2017), Vienna, Austria, 2017.
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@inproceedings{BringmannESA2017, TITLE = {Sampling Geometric Inhomogeneous Random Graphs in Linear Time}, AUTHOR = {Bringmann, Karl and Keusch, Ralph and Lengler, Johannes}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-049-1}, URL = {urn:nbn:de:0030-drops-78396}, DOI = {10.4230/LIPIcs.ESA.2017.20}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {25th Annual European Symposium on Algorithms (ESA 2017)}, EDITOR = {Pruhs, Kirk and Sohler, Christian}, PAGES = {1--15}, EID = {20}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {87}, ADDRESS = {Vienna, Austria}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Keusch, Ralph %A Lengler, Johannes %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Sampling Geometric Inhomogeneous Random Graphs in Linear Time : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-FB87-A %R 10.4230/LIPIcs.ESA.2017.20 %U urn:nbn:de:0030-drops-78396 %D 2017 %B 25th Annual European Symposium on Algorithms %Z date of event: 2017-09-04 - 2017-09-06 %C Vienna, Austria %B 25th Annual European Symposium on Algorithms %E Pruhs, Kirk; Sohler, Christian %P 1 - 15 %Z sequence number: 20 %I Schloss Dagstuhl %@ 978-3-95977-049-1 %B Leibniz International Proceedings in Informatics %N 87 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2017/7839/http://drops.dagstuhl.de/doku/urheberrecht1.html
[28]
K. Bringmann, C. Ikenmeyer, and J. Zuiddam, “On Algebraic Branching Programs of Small Width,” in 32nd Computational Complexity Conference (CCC 2017), Riga, Latvia, 2017.
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@inproceedings{BringmannCCC2017, TITLE = {On Algebraic Branching Programs of Small Width}, AUTHOR = {Bringmann, Karl and Ikenmeyer, Christian and Zuiddam, Jeroen}, LANGUAGE = {eng}, ISBN = {978-3-95977-040-8}, URL = {urn:nbn:de:0030-drops-75217}, DOI = {10.4230/LIPIcs.CCC.2017.20}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {32nd Computational Complexity Conference (CCC 2017)}, EDITOR = {O'Donnell, Ryan}, PAGES = {1--31}, EID = {20}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {79}, ADDRESS = {Riga, Latvia}, }
Endnote
%0 Conference Proceedings %A Bringmann, Karl %A Ikenmeyer, Christian %A Zuiddam, Jeroen %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On Algebraic Branching Programs of Small Width : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-FB78-C %R 10.4230/LIPIcs.CCC.2017.20 %U urn:nbn:de:0030-drops-75217 %D 2017 %B 32nd Computational Complexity Conference %Z date of event: 2017-07-06 - 2017-07-09 %C Riga, Latvia %B 32nd Computational Complexity Conference %E O'Donnell, Ryan %P 1 - 31 %Z sequence number: 20 %I Schloss Dagstuhl %@ 978-3-95977-040-8 %B Leibniz International Proceedings in Informatics %N 79 %U http://drops.dagstuhl.de/doku/urheberrecht1.htmlhttp://drops.dagstuhl.de/opus/volltexte/2017/7521/
[29]
K. Bringmann, C. Ikenmeyer, and J. Zuiddam, “On Algebraic Branching Programs of Small Width,” Electronic Colloquium on Computational Complexity (ECCC) : Report Series, vol. 34 (Revision 1), 2017.
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@article{BringmannECCC2017, TITLE = {On Algebraic Branching Programs of Small Width}, AUTHOR = {Bringmann, Karl and Ikenmeyer, Christian and Zuiddam, Jeroen}, LANGUAGE = {eng}, ISSN = {1433-8092}, PUBLISHER = {Hasso-Plattner-Institut f{\"u}r Softwaretechnik GmbH}, ADDRESS = {Potsdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, JOURNAL = {Electronic Colloquium on Computational Complexity (ECCC) : Report Series}, VOLUME = {34 (Revision 1)}, }
Endnote
%0 Journal Article %A Bringmann, Karl %A Ikenmeyer, Christian %A Zuiddam, Jeroen %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On Algebraic Branching Programs of Small Width : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-89B2-8 %7 2017 %D 2017 %J Electronic Colloquium on Computational Complexity (ECCC) : Report Series %V 34 (Revision 1) %I Hasso-Plattner-Institut für Softwaretechnik GmbH %C Potsdam %@ false %U https://eccc.weizmann.ac.il/report/2017/034/
[30]
K. Bringmann, C. Ikenmeyer, and J. Zuiddam, “On Algebraic Branching Programs of Small Width,” 2017. [Online]. Available: http://arxiv.org/abs/1702.05328. (arXiv: 1702.05328)
Abstract
In 1979 Valiant showed that the complexity class VP_e of families with polynomially bounded formula size is contained in the class VP_s of families that have algebraic branching programs (ABPs) of polynomially bounded size. Motivated by the problem of separating these classes we study the topological closure VP_e-bar, i.e. the class of polynomials that can be approximated arbitrarily closely by polynomials in VP_e. We describe VP_e-bar with a strikingly simple complete polynomial (in characteristic different from 2) whose recursive definition is similar to the Fibonacci numbers. Further understanding this polynomial seems to be a promising route to new formula lower bounds. Our methods are rooted in the study of ABPs of small constant width. In 1992 Ben-Or and Cleve showed that formula size is polynomially equivalent to width-3 ABP size. We extend their result (in characteristic different from 2) by showing that approximate formula size is polynomially equivalent to approximate width-2 ABP size. This is surprising because in 2011 Allender and Wang gave explicit polynomials that cannot be computed by width-2 ABPs at all! The details of our construction lead to the aforementioned characterization of VP_e-bar. As a natural continuation of this work we prove that the class VNP can be described as the class of families that admit a hypercube summation of polynomially bounded dimension over a product of polynomially many affine linear forms. This gives the first separations of algebraic complexity classes from their nondeterministic analogs.
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@online{BringmannArXiv2017, TITLE = {On Algebraic Branching Programs of Small Width}, AUTHOR = {Bringmann, Karl and Ikenmeyer, Christian and Zuiddam, Jeroen}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1702.05328}, EPRINT = {1702.05328}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {In 1979 Valiant showed that the complexity class VP_e of families with polynomially bounded formula size is contained in the class VP_s of families that have algebraic branching programs (ABPs) of polynomially bounded size. Motivated by the problem of separating these classes we study the topological closure VP_e-bar, i.e. the class of polynomials that can be approximated arbitrarily closely by polynomials in VP_e. We describe VP_e-bar with a strikingly simple complete polynomial (in characteristic different from 2) whose recursive definition is similar to the Fibonacci numbers. Further understanding this polynomial seems to be a promising route to new formula lower bounds. Our methods are rooted in the study of ABPs of small constant width. In 1992 Ben-Or and Cleve showed that formula size is polynomially equivalent to width-3 ABP size. We extend their result (in characteristic different from 2) by showing that approximate formula size is polynomially equivalent to approximate width-2 ABP size. This is surprising because in 2011 Allender and Wang gave explicit polynomials that cannot be computed by width-2 ABPs at all! The details of our construction lead to the aforementioned characterization of VP_e-bar. As a natural continuation of this work we prove that the class VNP can be described as the class of families that admit a hypercube summation of polynomially bounded dimension over a product of polynomially many affine linear forms. This gives the first separations of algebraic complexity classes from their nondeterministic analogs.}, }
Endnote
%0 Report %A Bringmann, Karl %A Ikenmeyer, Christian %A Zuiddam, Jeroen %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On Algebraic Branching Programs of Small Width : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-89A4-8 %U http://arxiv.org/abs/1702.05328 %D 2017 %X In 1979 Valiant showed that the complexity class VP_e of families with polynomially bounded formula size is contained in the class VP_s of families that have algebraic branching programs (ABPs) of polynomially bounded size. Motivated by the problem of separating these classes we study the topological closure VP_e-bar, i.e. the class of polynomials that can be approximated arbitrarily closely by polynomials in VP_e. We describe VP_e-bar with a strikingly simple complete polynomial (in characteristic different from 2) whose recursive definition is similar to the Fibonacci numbers. Further understanding this polynomial seems to be a promising route to new formula lower bounds. Our methods are rooted in the study of ABPs of small constant width. In 1992 Ben-Or and Cleve showed that formula size is polynomially equivalent to width-3 ABP size. We extend their result (in characteristic different from 2) by showing that approximate formula size is polynomially equivalent to approximate width-2 ABP size. This is surprising because in 2011 Allender and Wang gave explicit polynomials that cannot be computed by width-2 ABPs at all! The details of our construction lead to the aforementioned characterization of VP_e-bar. As a natural continuation of this work we prove that the class VNP can be described as the class of families that admit a hypercube summation of polynomially bounded dimension over a product of polynomially many affine linear forms. This gives the first separations of algebraic complexity classes from their nondeterministic analogs. %K Computer Science, Computational Complexity, cs.CC,
[31]
J. Bund, C. Lenzen, and M. Medina, “Near-Optimal Metastability-Containing Sorting Networks,” in Proceedings of the 2017 Design, Automation & Test in Europe (DATE 2017), Lausanne, Switzerland, 2017.
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@inproceedings{BundDATE2017, TITLE = {Near-Optimal Metastability-Containing Sorting Networks}, AUTHOR = {Bund, Johannes and Lenzen, Christoph and Medina, Moti}, LANGUAGE = {eng}, ISBN = {978-1-5090-5826-6}, DOI = {10.23919/DATE.2017.7926987}, PUBLISHER = {IEEE}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Proceedings of the 2017 Design, Automation \& Test in Europe (DATE 2017)}, PAGES = {226--231}, ADDRESS = {Lausanne, Switzerland}, }
Endnote
%0 Conference Proceedings %A Bund, Johannes %A Lenzen, Christoph %A Medina, Moti %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Near-Optimal Metastability-Containing Sorting Networks : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-571A-2 %R 10.23919/DATE.2017.7926987 %D 2017 %B Design, Automation & Test in Europe Conference & Exhibition %Z date of event: 2017-03-27 - 2017-03-31 %C Lausanne, Switzerland %B Proceedings of the 2017 Design, Automation & Test in Europe %P 226 - 231 %I IEEE %@ 978-1-5090-5826-6
[32]
P. Bürgisser, C. Ikenmeyer, and J. Hüttenhain, “Permanent versus Determinant: Not via Saturations,” Proceedings of the American Mathematical Society, vol. 145, 2017.
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@article{BHI:17, TITLE = {Permanent versus Determinant: {N}ot via Saturations}, AUTHOR = {B{\"u}rgisser, Peter and Ikenmeyer, Christian and H{\"u}ttenhain, Jesko}, LANGUAGE = {eng}, ISSN = {0002-9939}, DOI = {10.1090/proc/13310}, PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, R.I. [etc.]}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {145}, PAGES = {1247--1258}, }
Endnote
%0 Journal Article %A Bürgisser, Peter %A Ikenmeyer, Christian %A Hüttenhain, Jesko %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Permanent versus Determinant: Not via Saturations : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-4F48-A %R 10.1090/proc/13310 %7 2017 %D 2017 %J Proceedings of the American Mathematical Society %V 145 %& 1247 %P 1247 - 1258 %I American Mathematical Society %C Providence, R.I. [etc.] %@ false
[33]
P. Bürgisser and C. Ikenmeyer, “Fundamental Invariants of Orbit Closures,” Journal of Algebra, vol. 477, 2017.
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@article{BI:17, TITLE = {Fundamental Invariants of Orbit Closures}, AUTHOR = {B{\"u}rgisser, Peter and Ikenmeyer, Christian}, LANGUAGE = {eng}, ISSN = {0021-8693}, DOI = {10.1016/j.jalgebra.2016.12.035}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Algebra}, VOLUME = {477}, PAGES = {390--434}, }
Endnote
%0 Journal Article %A Bürgisser, Peter %A Ikenmeyer, Christian %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fundamental Invariants of Orbit Closures : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-4F2E-8 %R 10.1016/j.jalgebra.2016.12.035 %7 2017-01-17 %D 2017 %J Journal of Algebra %V 477 %& 390 %P 390 - 434 %I Elsevier %C Amsterdam %@ false
[34]
P. Chalermsook and A. Schmid, “Finding Triangles for Maximum Planar Subgraphs,” in WALCOM: Algorithms and Computation, Hsinchu, Taiwan, 2017.
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@inproceedings{PCAS2017, TITLE = {Finding Triangles for Maximum Planar Subgraphs}, AUTHOR = {Chalermsook, Parinya and Schmid, Andreas}, LANGUAGE = {eng}, ISBN = {978-3-319-53924-9}, DOI = {10.1007/978-3-319-53925-6_29}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {WALCOM: Algorithms and Computation}, EDITOR = {Poon, Sheung-Hung and Rahman, Md. Saidur and Yen, Hsu-Chun}, PAGES = {373--384}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {10167}, ADDRESS = {Hsinchu, Taiwan}, }
Endnote
%0 Conference Proceedings %A Chalermsook, Parinya %A Schmid, Andreas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Finding Triangles for Maximum Planar Subgraphs : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-5DDC-F %R 10.1007/978-3-319-53925-6_29 %D 2017 %B 11th International Conference and Workshops on Algorithms and Computation %Z date of event: 2017-03-29 - 2017-03-31 %C Hsinchu, Taiwan %B WALCOM: Algorithms and Computation %E Poon, Sheung-Hung; Rahman, Md. Saidur; Yen, Hsu-Chun %P 373 - 384 %I Springer %@ 978-3-319-53924-9 %B Lecture Notes in Computer Science %N 10167
[35]
P. Chalermsook and D. Vaz, “New Integrality Gap Results for the Firefighters Problem on Trees,” in Approximation and Online Algorithms (WAOA 2016), Aarhus, Denmark, 2017.
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@inproceedings{Chalermsook2017, TITLE = {New Integrality Gap Results for the Firefighters Problem on Trees}, AUTHOR = {Chalermsook, Parinya and Vaz, Daniel}, LANGUAGE = {eng}, ISBN = {978-3-319-51740-7}, DOI = {10.1007/978-3-319-51741-4_6}, PUBLISHER = {Springer}, YEAR = {2016}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Approximation and Online Algorithms (WAOA 2016)}, EDITOR = {Jansen, Klaus and Mastrolilli, Monaldo}, PAGES = {65--77}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {10138}, ADDRESS = {Aarhus, Denmark}, }
Endnote
%0 Conference Proceedings %A Chalermsook, Parinya %A Vaz, Daniel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T New Integrality Gap Results for the Firefighters Problem on Trees : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-575B-0 %R 10.1007/978-3-319-51741-4_6 %D 2017 %B 14th Workshop on Approximation and Online Algorithms %Z date of event: 2016-08-25 - 2016-08-26 %C Aarhus, Denmark %B Approximation and Online Algorithms %E Jansen, Klaus; Mastrolilli, Monaldo %P 65 - 77 %I Springer %@ 978-3-319-51740-7 %B Lecture Notes in Computer Science %N 10138
[36]
P. Chalermsook, S. Das, B. Laekhanukit, and D. Vaz, “Beyond Metric Embedding: Approximating Group Steiner Trees on Bounded Treewidth Graphs,” in Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), Barcelona, Spain, 2017.
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@inproceedings{doi:10.1137/1.9781611974782.47, TITLE = {Beyond Metric Embedding: {A}pproximating {Group Steiner Trees} on Bounded Treewidth Graphs}, AUTHOR = {Chalermsook, Parinya and Das, Syamantak and Laekhanukit, Bundit and Vaz, Daniel}, LANGUAGE = {eng}, DOI = {10.1137/1.9781611974782.47}, PUBLISHER = {SIAM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017)}, PAGES = {737--751}, ADDRESS = {Barcelona, Spain}, }
Endnote
%0 Conference Proceedings %A Chalermsook, Parinya %A Das, Syamantak %A Laekhanukit, Bundit %A Vaz, Daniel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Beyond Metric Embedding: Approximating Group Steiner Trees on Bounded Treewidth Graphs : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-573D-3 %R 10.1137/1.9781611974782.47 %D 2017 %B Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2017-01-16 - 2017-01-19 %C Barcelona, Spain %B Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %P 737 - 751 %I SIAM
[37]
L. S. Chandran, D. Issac, and A. Karrenbauer, “On the Parameterized Complexity of Biclique Cover and Partition,” in 11th International Symposium on Parameterized and Exact Computation (IPEC 2016), Aarhus, Denmark, 2017.
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@inproceedings{BicliqueFPT, TITLE = {On the Parameterized Complexity of Biclique Cover and Partition}, AUTHOR = {Chandran, L. Sunil and Issac, Davis and Karrenbauer, Andreas}, LANGUAGE = {eng}, ISBN = {978-3-95977-023-1}, URL = {urn:nbn:de:0030-drops-69293}, DOI = {10.4230/LIPIcs.IPEC.2016.11}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2016}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {11th International Symposium on Parameterized and Exact Computation (IPEC 2016)}, EDITOR = {Guo, Jiong and Hermelin, Danny}, PAGES = {1--13}, EID = {11}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {63}, ADDRESS = {Aarhus, Denmark}, }
Endnote
%0 Conference Proceedings %A Chandran, L. Sunil %A Issac, Davis %A Karrenbauer, Andreas %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On the Parameterized Complexity of Biclique Cover and Partition : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-53DB-3 %R 10.4230/LIPIcs.IPEC.2016.11 %U urn:nbn:de:0030-drops-69293 %D 2017 %B 11th International Symposium on Parameterized and Exact Computation %Z date of event: 2016-08-24 - 2016-08-26 %C Aarhus, Denmark %B 11th International Symposium on Parameterized and Exact Computation %E Guo, Jiong; Hermelin, Danny %P 1 - 13 %Z sequence number: 11 %I Schloss Dagstuhl %@ 978-3-95977-023-1 %B Leibniz International Proceedings in Informatics %N 63 %U http://drops.dagstuhl.de/doku/urheberrecht1.htmlhttp://drops.dagstuhl.de/opus/volltexte/2017/6929/
[38]
C. Croitoru, “Graph models for rational social interaction,” Universität des Saarlandes, Saarbrücken, 2017.
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@phdthesis{CroitoruPhd2017, TITLE = {Graph models for rational social interaction}, AUTHOR = {Croitoru, Cosmina}, LANGUAGE = {eng}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, }
Endnote
%0 Thesis %A Croitoru, Cosmina %Y Mehlhorn, Kurt %A referee: Amgoud, Leila %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society International Max Planck Research School, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Graph models for rational social interaction : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-87DE-5 %I Universität des Saarlandes %C Saarbrücken %D 2017 %P X, 75 p. %V phd %9 phd
[39]
M. Cygan, M. Pilipczuk, M. Pilipczuk, E. J. van Leeuwen, and M. Wrochna, “Polynomial Kernelization for Removing Induced Claws and Diamonds,” Theory of Computing Systems, vol. 60, no. 4, 2017.
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@article{CyganAlgorithmica2016, TITLE = {Polynomial Kernelization for Removing Induced Claws and Diamonds}, AUTHOR = {Cygan, Marek and Pilipczuk, Marcin and Pilipczuk, Micha{\l} and van Leeuwen, Erik Jan and Wrochna, Marcin}, LANGUAGE = {eng}, ISSN = {1432-4350}, DOI = {10.1007/s00224-016-9689-x}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Theory of Computing Systems}, VOLUME = {60}, NUMBER = {4}, PAGES = {615--636}, }
Endnote
%0 Journal Article %A Cygan, Marek %A Pilipczuk, Marcin %A Pilipczuk, Michał %A van Leeuwen, Erik Jan %A Wrochna, Marcin %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Polynomial Kernelization for Removing Induced Claws and Diamonds : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002B-8606-6 %R 10.1007/s00224-016-9689-x %7 2016-06-23 %D 2017 %J Theory of Computing Systems %V 60 %N 4 %& 615 %P 615 - 636 %I Springer %C New York, NY %@ false
[40]
J. Diaz, O. Pottonen, M. Serna, and E. J. van Leeuwen, “Complexity of Metric Dimension on Planar Graphs,” Journal of Computer and System Sciences, vol. 83, no. 1, 2017.
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@article{Diaz2017, TITLE = {Complexity of Metric Dimension on Planar Graphs}, AUTHOR = {Diaz, Josep and Pottonen, Olli and Serna, Maria and van Leeuwen, Erik Jan}, ISSN = {0022-0000}, DOI = {10.1016/j.jcss.2016.06.006}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Computer and System Sciences}, VOLUME = {83}, NUMBER = {1}, PAGES = {132--158}, }
Endnote
%0 Journal Article %A Diaz, Josep %A Pottonen, Olli %A Serna, Maria %A van Leeuwen, Erik Jan %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Complexity of Metric Dimension on Planar Graphs : %U http://hdl.handle.net/11858/00-001M-0000-002B-A574-5 %R 10.1016/j.jcss.2016.06.006 %7 2016 %D 2017 %J Journal of Computer and System Sciences %V 83 %N 1 %& 132 %P 132 - 158 %I Elsevier %C Amsterdam %@ false
[41]
M. Dirnberger, K. Mehlhorn, M. Grube, and H.-G. Döbereiner, “Preliminaries for Distributed Natural Computing Inspired by the Slime Mold Physarum Polycephalum,” Universität des Saarlandes, Saarbrücken, 2017.
Abstract
This doctoral thesis aims towards distributed natural computing inspired by the slime mold Physarum polycephalum. The vein networks formed by this organism presumably support efficient transport of protoplasmic fluid. Devising models which capture the natural efficiency of the organism and form a suitable basis for the development of natural computing algorithms is an interesting and challenging goal. We start working towards this goal by designing and executing wet-lab experi- ments geared towards producing a large number of images of the vein networks of P. polycephalum. Next, we turn the depicted vein networks into graphs using our own custom software called Nefi. This enables a detailed numerical study, yielding a catalogue of characterizing observables spanning a wide array of different graph properties. To share our results and data, i.e. raw experimental data, graphs and analysis results, we introduce a dedicated repository revolving around slime mold data, the Smgr. The purpose of this repository is to promote data reuse and to foster a practice of increased data sharing. Finally we present a model based on interacting electronic circuits including current controlled voltage sources, which mimics the emergent flow patterns observed in live P. polycephalum. The model is simple, distributed and robust to changes in the underlying network topology. Thus it constitutes a promising basis for the development of distributed natural computing algorithms.
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@phdthesis{dirnbergerphd17, TITLE = {Preliminaries for Distributed Natural Computing Inspired by the Slime Mold Physarum Polycephalum}, AUTHOR = {Dirnberger, Michael and Mehlhorn, Kurt and Grube, Martin and D{\"o}bereiner, Hans-G{\"u}nther}, LANGUAGE = {eng}, URL = {urn:nbn:de:bsz:291-scidok-69424}, SCHOOL = {Universit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, ABSTRACT = {This doctoral thesis aims towards distributed natural computing inspired by the slime mold Physarum polycephalum. The vein networks formed by this organism presumably support efficient transport of protoplasmic fluid. Devising models which capture the natural efficiency of the organism and form a suitable basis for the development of natural computing algorithms is an interesting and challenging goal. We start working towards this goal by designing and executing wet-lab experi- ments geared towards producing a large number of images of the vein networks of P. polycephalum. Next, we turn the depicted vein networks into graphs using our own custom software called Nefi. This enables a detailed numerical study, yielding a catalogue of characterizing observables spanning a wide array of different graph properties. To share our results and data, i.e. raw experimental data, graphs and analysis results, we introduce a dedicated repository revolving around slime mold data, the Smgr. The purpose of this repository is to promote data reuse and to foster a practice of increased data sharing. Finally we present a model based on interacting electronic circuits including current controlled voltage sources, which mimics the emergent flow patterns observed in live P. polycephalum. The model is simple, distributed and robust to changes in the underlying network topology. Thus it constitutes a promising basis for the development of distributed natural computing algorithms.}, }
Endnote
%0 Thesis %A Dirnberger, Michael %A Mehlhorn, Kurt %A Grube, Martin %A Döbereiner, Hans-Günther %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society International Max Planck Research School, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Preliminaries for Distributed Natural Computing Inspired by the Slime Mold Physarum Polycephalum : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-DE4F-0 %U urn:nbn:de:bsz:291-scidok-69424 %I Universität des Saarlandes %C Saarbrücken %D 2017 %P XV, 193 p. %V phd %9 phd %X This doctoral thesis aims towards distributed natural computing inspired by the slime mold Physarum polycephalum. The vein networks formed by this organism presumably support efficient transport of protoplasmic fluid. Devising models which capture the natural efficiency of the organism and form a suitable basis for the development of natural computing algorithms is an interesting and challenging goal. We start working towards this goal by designing and executing wet-lab experi- ments geared towards producing a large number of images of the vein networks of P. polycephalum. Next, we turn the depicted vein networks into graphs using our own custom software called Nefi. This enables a detailed numerical study, yielding a catalogue of characterizing observables spanning a wide array of different graph properties. To share our results and data, i.e. raw experimental data, graphs and analysis results, we introduce a dedicated repository revolving around slime mold data, the Smgr. The purpose of this repository is to promote data reuse and to foster a practice of increased data sharing. Finally we present a model based on interacting electronic circuits including current controlled voltage sources, which mimics the emergent flow patterns observed in live P. polycephalum. The model is simple, distributed and robust to changes in the underlying network topology. Thus it constitutes a promising basis for the development of distributed natural computing algorithms. %U http://scidok.sulb.uni-saarland.de/doku/lic_ohne_pod.php?la=dehttp://scidok.sulb.uni-saarland.de/volltexte/2017/6942/
[42]
M. Dirnberger, K. Mehlhorn, and T. Mehlhorn, “Introducing the Slime Mold Graph Repository,” Journal of Physics D: Applied Physics, vol. 50, no. 26, 2017.
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@article{Dirnberger2017, TITLE = {Introducing the Slime Mold Graph Repository}, AUTHOR = {Dirnberger, Michael and Mehlhorn, Kurt and Mehlhorn, Tim}, LANGUAGE = {eng}, ISSN = {0022-3727}, DOI = {10.1088/1361-6463/aa7326}, PUBLISHER = {IOP Publishing}, ADDRESS = {Bristol}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Physics D: Applied Physics}, VOLUME = {50}, NUMBER = {26}, EID = {264001}, }
Endnote
%0 Journal Article %A Dirnberger, Michael %A Mehlhorn, Kurt %A Mehlhorn, Tim %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Introducing the Slime Mold Graph Repository : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-8464-B %R 10.1088/1361-6463/aa7326 %7 2017 %D 2017 %J Journal of Physics D: Applied Physics %O J. Phys. D: Appl. Phys. %V 50 %N 26 %Z sequence number: 264001 %I IOP Publishing %C Bristol %@ false
[43]
M. Dirnberger and K. Mehlhorn, “Characterizing Networks Formed by P. Polycephalum,” Journal of Physics D: Applied Physics, vol. 50, no. 22, 2017.
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@article{Dirnberg_Mehlhorn2017, TITLE = {Characterizing networks formed by \slshape{P. polycephalum}}, AUTHOR = {Dirnberger, Michael and Mehlhorn, Kurt}, LANGUAGE = {eng}, ISSN = {0022-3727}, DOI = {10.1088/1361-6463/aa6e7b}, PUBLISHER = {IOP Publishing}, ADDRESS = {Bristol}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Physics D: Applied Physics}, VOLUME = {50}, NUMBER = {22}, EID = {224002}, }
Endnote
%0 Journal Article %A Dirnberger, Michael %A Mehlhorn, Kurt %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Characterizing Networks Formed by P. Polycephalum : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-56FA-2 %R 10.1088/1361-6463/aa6e7b %7 2017 %D 2017 %J Journal of Physics D: Applied Physics %O J. Phys. D: Appl. Phys. %V 50 %N 22 %Z sequence number: 224002 %I IOP Publishing %C Bristol %@ false
[44]
K. Dutta, A. Ghosh, B. Jartoux, and N. H. Mustafa, “Shallow Packings, Semialgebraic Set Systems, Macbeath Regions and Polynomial Partitioning,” in 33rd International Symposium on Computational Geometry (SoCG 2017), Brisbane, Australia, 2017.
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@inproceedings{DuttaGJM-Mnets-17, TITLE = {Shallow Packings, Semialgebraic Set Systems, {Macbeath} Regions and Polynomial Partitioning}, AUTHOR = {Dutta, Kunal and Ghosh, Arijit and Jartoux, Bruno and Mustafa, Nabil H.}, LANGUAGE = {eng}, ISSN = {1868-8969}, ISBN = {978-3-95977-038-5}, URL = {urn:nbn:de:0030-drops-71991}, DOI = {10.4230/LIPIcs.SoCG.2017.38}, PUBLISHER = {Schloss Dagstuhl}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {33rd International Symposium on Computational Geometry (SoCG 2017)}, EDITOR = {Aronov, Boris and Katz, Matthew J.}, PAGES = {1--15}, EID = {38}, SERIES = {Leibniz International Proceedings in Informatics}, VOLUME = {77}, ADDRESS = {Brisbane, Australia}, }
Endnote
%0 Conference Proceedings %A Dutta, Kunal %A Ghosh, Arijit %A Jartoux, Bruno %A Mustafa, Nabil H. %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Shallow Packings, Semialgebraic Set Systems, Macbeath Regions and Polynomial Partitioning : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-7941-7 %R 10.4230/LIPIcs.SoCG.2017.38 %U urn:nbn:de:0030-drops-71991 %D 2017 %B 33rd International Symposium on Computational Geometry %Z date of event: 2017-07-04 - 2017-07-07 %C Brisbane, Australia %B 33rd International Symposium on Computational Geometry %E Aronov, Boris; Katz, Matthew J. %P 1 - 15 %Z sequence number: 38 %I Schloss Dagstuhl %@ 978-3-95977-038-5 %B Leibniz International Proceedings in Informatics %N 77 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2017/7199/http://drops.dagstuhl.de/doku/urheberrecht1.html
[45]
P. Dütting and T. Kesselheim, “Best-Response Dynamics in Combinatorial Auctions with Item Bidding,” in Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), Barcelona, Spain, 2017.
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@inproceedings{doi:10.1137/1.9781611974782.33, TITLE = {Best-Response Dynamics in Combinatorial Auctions with Item Bidding}, AUTHOR = {D{\"u}tting, Paul and Kesselheim, Thomas}, LANGUAGE = {eng}, ISBN = {978-1-61197-478-2}, DOI = {10.1137/1.9781611974782.33}, PUBLISHER = {SIAM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017)}, EDITOR = {Klein, Philip N.}, PAGES = {521--533}, ADDRESS = {Barcelona, Spain}, }
Endnote
%0 Conference Proceedings %A Dütting, Paul %A Kesselheim, Thomas %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Best-Response Dynamics in Combinatorial Auctions with Item Bidding : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-4E5E-2 %R 10.1137/1.9781611974782.33 %D 2017 %B Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2017-01-16 - 2017-01-19 %C Barcelona, Spain %B Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %E Klein, Philip N. %P 521 - 533 %I SIAM %@ 978-1-61197-478-2
[46]
M. Ernestus, S. Friedrichs, M. Hemmer, J. Kokemüller, A. Kröller, M. Moeini, and C. Schmidt, “Algorithms for Art Gallery Illumination,” Journal of Global Optimization, vol. 68, no. 1, 2017.
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@article{ErnestusJGO2016, TITLE = {Algorithms for Art Gallery Illumination}, AUTHOR = {Ernestus, Maximilian and Friedrichs, Stephan and Hemmer, Michael and Kokem{\"u}ller, Jan and Kr{\"o}ller, Alexander and Moeini, Mahdi and Schmidt, Christiane}, LANGUAGE = {eng}, ISSN = {0925-5001}, DOI = {10.1007/s10898-016-0452-2}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Global Optimization}, VOLUME = {68}, NUMBER = {1}, PAGES = {23--45}, }
Endnote
%0 Journal Article %A Ernestus, Maximilian %A Friedrichs, Stephan %A Hemmer, Michael %A Kokemüller, Jan %A Kröller, Alexander %A Moeini, Mahdi %A Schmidt, Christiane %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations External Organizations %T Algorithms for Art Gallery Illumination : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-0B3C-1 %R 10.1007/s10898-016-0452-2 %7 2016 %D 2017 %J Journal of Global Optimization %V 68 %N 1 %& 23 %P 23 - 45 %I Springer %C New York, NY %@ false
[47]
G. Even and M. Medina, “Online Packet-Routing in Grids with Bounded Buffers,” Algorithmica, vol. 78, no. 3, 2017.
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@article{MedinaAlgorithmica2016, TITLE = {Online Packet-Routing in Grids with Bounded Buffers}, AUTHOR = {Even, Guy and Medina, Moti}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-016-0177-0}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Algorithmica}, VOLUME = {78}, NUMBER = {3}, PAGES = {819--868}, }
Endnote
%0 Journal Article %A Even, Guy %A Medina, Moti %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Online Packet-Routing in Grids with Bounded Buffers : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002B-85DD-E %R 10.1007/s00453-016-0177-0 %7 2016-07-11 %D 2017 %J Algorithmica %V 78 %N 3 %& 819 %P 819 - 868 %I Springer-Verlag %C New York %@ false
[48]
S. Friedrichs, C. Lenzen, K. Mehlhorn, and M. Ghaffari, “Metastability-Containing Circuits, Parallel Distance Problems, and Terrain Guarding,” Unversität des Saarlandes, Saarbrücken, 2017.
Abstract
We study three problems. The first is the phenomenon of metastability in digital circuits. This is a state of bistable storage elements, such as registers, that is neither logical 0 nor 1 and breaks the abstraction of Boolean logic. We propose a time- and value-discrete model for metastability in digital circuits and show that it reflects relevant physical properties. Further, we propose the fundamentally new approach of using logical masking to perform meaningful computations despite the presence of metastable upsets and analyze what functions can be computed in our model. Additionally, we show that circuits with masking registers grow computationally more powerful with each available clock cycle. The second topic are parallel algorithms, based on an algebraic abstraction of the Moore-Bellman-Ford algorithm, for solving various distance problems. Our focus are distance approximations that obey the triangle inequality while at the same time achieving polylogarithmic depth and low work. Finally, we study the continuous Terrain Guarding Problem. We show that it has a rational discretization with a quadratic number of guard candidates, establish its membership in NP and the existence of a PTAS, and present an efficient implementation of a solver.
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@phdthesis{Friedrichsphd2017, TITLE = {Metastability-Containing Circuits, Parallel Distance Problems, and Terrain Guarding}, AUTHOR = {Friedrichs, Stephan and Lenzen, Christoph and Mehlhorn, Kurt and Ghaffari, Mohsen}, LANGUAGE = {eng}, URL = {urn:nbn:de:bsz:291-scidok-69660}, SCHOOL = {Unversit{\"a}t des Saarlandes}, ADDRESS = {Saarbr{\"u}cken}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, ABSTRACT = {We study three problems. The first is the phenomenon of metastability in digital circuits. This is a state of bistable storage elements, such as registers, that is neither logical 0 nor 1 and breaks the abstraction of Boolean logic. We propose a time- and value-discrete model for metastability in digital circuits and show that it reflects relevant physical properties. Further, we propose the fundamentally new approach of using logical masking to perform meaningful computations despite the presence of metastable upsets and analyze what functions can be computed in our model. Additionally, we show that circuits with masking registers grow computationally more powerful with each available clock cycle. The second topic are parallel algorithms, based on an algebraic abstraction of the Moore-Bellman-Ford algorithm, for solving various distance problems. Our focus are distance approximations that obey the triangle inequality while at the same time achieving polylogarithmic depth and low work. Finally, we study the continuous Terrain Guarding Problem. We show that it has a rational discretization with a quadratic number of guard candidates, establish its membership in NP and the existence of a PTAS, and present an efficient implementation of a solver.}, }
Endnote
%0 Thesis %A Friedrichs, Stephan %A Lenzen, Christoph %A Mehlhorn, Kurt %A Ghaffari, Mohsen %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society International Max Planck Research School, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Metastability-Containing Circuits, Parallel Distance Problems, and Terrain Guarding : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-E9A7-B %U urn:nbn:de:bsz:291-scidok-69660 %I Unversität des Saarlandes %C Saarbrücken %D 2017 %P x, 226 p. %V phd %9 phd %X We study three problems. The first is the phenomenon of metastability in digital circuits. This is a state of bistable storage elements, such as registers, that is neither logical 0 nor 1 and breaks the abstraction of Boolean logic. We propose a time- and value-discrete model for metastability in digital circuits and show that it reflects relevant physical properties. Further, we propose the fundamentally new approach of using logical masking to perform meaningful computations despite the presence of metastable upsets and analyze what functions can be computed in our model. Additionally, we show that circuits with masking registers grow computationally more powerful with each available clock cycle. The second topic are parallel algorithms, based on an algebraic abstraction of the Moore-Bellman-Ford algorithm, for solving various distance problems. Our focus are distance approximations that obey the triangle inequality while at the same time achieving polylogarithmic depth and low work. Finally, we study the continuous Terrain Guarding Problem. We show that it has a rational discretization with a quadratic number of guard candidates, establish its membership in NP and the existence of a PTAS, and present an efficient implementation of a solver. %U http://scidok.sulb.uni-saarland.de/volltexte/2017/6966/http://scidok.sulb.uni-saarland.de/doku/lic_ohne_pod.php?la=de
[49]
M. Függer, C. Lenzen, and T. Polzer, “Metastability-Aware Memory-Efficient Time-to-Digital Converters,” in 23rd IEEE International Symposium on Asynchronous Circuits and Systems, San Diego, CA, USA. (Accepted/in press)
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@inproceedings{fueggerASYNC2017, TITLE = {Metastability-Aware Memory-Efficient Time-to-Digital Converters}, AUTHOR = {F{\"u}gger, Matthias and Lenzen, Christoph and Polzer, Thomas}, LANGUAGE = {eng}, PUBLISHER = {IEEE}, YEAR = {2017}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {23rd IEEE International Symposium on Asynchronous Circuits and Systems}, ADDRESS = {San Diego, CA, USA}, }
Endnote
%0 Conference Proceedings %A Függer, Matthias %A Lenzen, Christoph %A Polzer, Thomas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Metastability-Aware Memory-Efficient Time-to-Digital Converters : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-80CD-D %D 2017 %B 23rd IEEE International Symposium on Asynchronous Circuits and Systems %Z date of event: 2017-05-21 - 2017-05-24 %C San Diego, CA, USA %B 23rd IEEE International Symposium on Asynchronous Circuits and Systems %I IEEE
[50]
J. Garg, M. Hoefer, and K. Mehlhorn, “Approximating the Nash Social Welfare with Budget-Additive Valuations,” 2017. [Online]. Available: http://arxiv.org/abs/1707.04428. (arXiv: 1707.04428)
Abstract
We present the first constant-factor approximation algorithm for maximizing the Nash social welfare when allocating indivisible items to agents with budget-additive valuation functions. Budget-additive valuations represent an important class of submodular functions. They have attracted a lot of research interest in recent years due to many interesting applications. For every $\varepsilon > 0$, our algorithm obtains a $(2.404 + \varepsilon)$-approximation in time polynomial in the input size and $1/\varepsilon$. Our algorithm relies on rounding an approximate equilibrium in a linear Fisher market where sellers have earning limits (upper bounds on the amount of money they want to earn) and buyers have utility limits (upper bounds on the amount of utility they want to achieve). In contrast to markets with either earning or utility limits, these markets have not been studied before. They turn out to have fundamentally different properties. Although the existence of equilibria is not guaranteed, we show that the market instances arising from the Nash social welfare problem always have an equilibrium. Further, we show that the set of equilibria is not convex, answering a question of [Cole et al, EC 2017]. We design an FPTAS to compute an approximate equilibrium, a result that may be of independent interest.
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@online{GargHoeferMehlhorn2017, TITLE = {Approximating the {Nash} Social Welfare with Budget-Additive Valuations}, AUTHOR = {Garg, Jugal and Hoefer, Martin and Mehlhorn, Kurt}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1707.04428}, EPRINT = {1707.04428}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We present the first constant-factor approximation algorithm for maximizing the Nash social welfare when allocating indivisible items to agents with budget-additive valuation functions. Budget-additive valuations represent an important class of submodular functions. They have attracted a lot of research interest in recent years due to many interesting applications. For every $\varepsilon > 0$, our algorithm obtains a $(2.404 + \varepsilon)$-approximation in time polynomial in the input size and $1/\varepsilon$. Our algorithm relies on rounding an approximate equilibrium in a linear Fisher market where sellers have earning limits (upper bounds on the amount of money they want to earn) and buyers have utility limits (upper bounds on the amount of utility they want to achieve). In contrast to markets with either earning or utility limits, these markets have not been studied before. They turn out to have fundamentally different properties. Although the existence of equilibria is not guaranteed, we show that the market instances arising from the Nash social welfare problem always have an equilibrium. Further, we show that the set of equilibria is not convex, answering a question of [Cole et al, EC 2017]. We design an FPTAS to compute an approximate equilibrium, a result that may be of independent interest.}, }
Endnote
%0 Report %A Garg, Jugal %A Hoefer, Martin %A Mehlhorn, Kurt %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Approximating the Nash Social Welfare with Budget-Additive Valuations : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-E7D6-2 %U http://arxiv.org/abs/1707.04428 %D 2017 %X We present the first constant-factor approximation algorithm for maximizing the Nash social welfare when allocating indivisible items to agents with budget-additive valuation functions. Budget-additive valuations represent an important class of submodular functions. They have attracted a lot of research interest in recent years due to many interesting applications. For every $\varepsilon > 0$, our algorithm obtains a $(2.404 + \varepsilon)$-approximation in time polynomial in the input size and $1/\varepsilon$. Our algorithm relies on rounding an approximate equilibrium in a linear Fisher market where sellers have earning limits (upper bounds on the amount of money they want to earn) and buyers have utility limits (upper bounds on the amount of utility they want to achieve). In contrast to markets with either earning or utility limits, these markets have not been studied before. They turn out to have fundamentally different properties. Although the existence of equilibria is not guaranteed, we show that the market instances arising from the Nash social welfare problem always have an equilibrium. Further, we show that the set of equilibria is not convex, answering a question of [Cole et al, EC 2017]. We design an FPTAS to compute an approximate equilibrium, a result that may be of independent interest. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computer Science and Game Theory, cs.GT
[51]
M. Goswami, X. Gu, V. P. Pingali, and G. Telang, “Computing Teichmüller Maps Between Polygons,” Foundations of Computational Mathematics, vol. 17, no. 2, 2017.
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@article{Goswami2017, TITLE = {Computing {Teichmüller} Maps Between Polygons}, AUTHOR = {Goswami, Mayank and Gu, Xianfeng and Pingali, Vamsi P. and Telang, Gaurish}, LANGUAGE = {eng}, ISSN = {1615-3375}, DOI = {10.1007/s10208-015-9294-4}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Foundations of Computational Mathematics}, VOLUME = {17}, NUMBER = {2}, PAGES = {497--526}, }
Endnote
%0 Journal Article %A Goswami, Mayank %A Gu, Xianfeng %A Pingali, Vamsi P. %A Telang, Gaurish %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Computing Teichmüller Maps Between Polygons : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-3E48-3 %R 10.1007/s10208-015-9294-4 %7 2015-11-25 %D 2017 %J Foundations of Computational Mathematics %V 17 %N 2 %& 497 %P 497 - 526 %I Springer %C New York, NY %@ false
[52]
F. Grandoni, T. Mömke, A. Wiese, and H. Zhou, “To Augment or Not to Augment: Solving Unsplittable Flow on a Path by Creating Slack,” in Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), Barcelona, Spain, 2017.
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@inproceedings{doi:10.1137/1.9781611974782.159, TITLE = {To Augment or Not to Augment: {S}olving Unsplittable Flow on a Path by Creating Slack}, AUTHOR = {Grandoni, Fabrizio and M{\"o}mke, Tobias and Wiese, Andreas and Zhou, Hang}, LANGUAGE = {eng}, ISBN = {978-1-61197-478-2}, DOI = {10.1137/1.9781611974782.159}, PUBLISHER = {SIAM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017)}, EDITOR = {Klein, Philip N.}, PAGES = {2411--2422}, ADDRESS = {Barcelona, Spain}, }
Endnote
%0 Conference Proceedings %A Grandoni, Fabrizio %A Mömke, Tobias %A Wiese, Andreas %A Zhou, Hang %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T To Augment or Not to Augment: Solving Unsplittable Flow on a Path by Creating Slack : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-4EB5-B %R 10.1137/1.9781611974782.159 %D 2017 %B Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2017-01-16 - 2017-01-19 %C Barcelona, Spain %B Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %E Klein, Philip N. %P 2411 - 2422 %I SIAM %@ 978-1-61197-478-2
[53]
S. Heydrich and A. Wiese, “Faster Approximation Schemes for the Two-dimensional Knapsack Problem,” in Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017), Barcelona, Spain, 2017.
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@inproceedings{HeydrichW17, TITLE = {Faster Approximation Schemes for the Two-dimensional Knapsack Problem}, AUTHOR = {Heydrich, Sandy and Wiese, Andreas}, LANGUAGE = {eng}, ISBN = {978-1-61197-478-2}, DOI = {10.1137/1.9781611974782.6}, PUBLISHER = {SIAM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017)}, EDITOR = {Klein, Philip N.}, PAGES = {79--98}, ADDRESS = {Barcelona, Spain}, }
Endnote
%0 Conference Proceedings %A Heydrich, Sandy %A Wiese, Andreas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Faster Approximation Schemes for the Two-dimensional Knapsack Problem : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-54AD-3 %R 10.1137/1.9781611974782.6 %D 2017 %B Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2017-01-16 - 2017-01-19 %C Barcelona, Spain %B Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms %E Klein, Philip N. %P 79 - 98 %I SIAM %@ 978-1-61197-478-2
[54]
M. Hoefer and L. Wagner, “Locally Stable Marriage with Strict Preferences,” SIAM Journal on Discrete Mathematics, vol. 31, no. 1, 2017.
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@article{HoeferWagner2017, TITLE = {Locally Stable Marriage with Strict Preferences}, AUTHOR = {Hoefer, Martin and Wagner, Lisa}, LANGUAGE = {eng}, ISSN = {0895-4801}, DOI = {10.1137/151003854}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia, Pa.}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {SIAM Journal on Discrete Mathematics}, VOLUME = {31}, NUMBER = {1}, PAGES = {283--316}, }
Endnote
%0 Journal Article %A Hoefer, Martin %A Wagner, Lisa %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Locally Stable Marriage with Strict Preferences : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-26B4-1 %R 10.1137/151003854 %7 2017-02-23 %D 2017 %J SIAM Journal on Discrete Mathematics %V 31 %N 1 %& 283 %P 283 - 316 %I SIAM %C Philadelphia, Pa. %@ false
[55]
M. Hoefer and B. Kodric, “Combinatorial Secretary Problems with Ordinal Information,” 2017. [Online]. Available: http://arxiv.org/abs/1702.01290. (arXiv: 1702.01290)
Abstract
The secretary problem is a classic model for online decision making. Recently, combinatorial extensions such as matroid or matching secretary problems have become an important tool to study algorithmic problems in dynamic markets. Here the decision maker must know the numerical value of each arriving element, which can be a demanding informational assumption. In this paper, we initiate the study of combinatorial secretary problems with ordinal information, in which the decision maker only needs to be aware of a preference order consistent with the values of arrived elements. The goal is to design online algorithms with small competitive ratios. For a variety of combinatorial problems, such as bipartite matching, general packing LPs, and independent set with bounded local independence number, we design new algorithms that obtain constant competitive ratios. For the matroid secretary problem, we observe that many existing algorithms for special matroid structures maintain their competitive ratios even in the ordinal model. In these cases, the restriction to ordinal information does not represent any additional obstacle. Moreover, we show that ordinal variants of the submodular matroid secretary problems can be solved using algorithms for the linear versions by extending [Feldman and Zenklusen, 2015]. In contrast, we provide a lower bound of $\Omega(\sqrt{n}/(\log n))$ for algorithms that are oblivious to the matroid structure, where $n$ is the total number of elements. This contrasts an upper bound of $O(\log n)$ in the cardinal model, and it shows that the technique of thresholding is not sufficient for good algorithms in the ordinal model.
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@online{Hoefer_Kodric2017, TITLE = {Combinatorial Secretary Problems with Ordinal Information}, AUTHOR = {Hoefer, Martin and Kodric, Bojana}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1702.01290}, EPRINT = {1702.01290}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {The secretary problem is a classic model for online decision making. Recently, combinatorial extensions such as matroid or matching secretary problems have become an important tool to study algorithmic problems in dynamic markets. Here the decision maker must know the numerical value of each arriving element, which can be a demanding informational assumption. In this paper, we initiate the study of combinatorial secretary problems with ordinal information, in which the decision maker only needs to be aware of a preference order consistent with the values of arrived elements. The goal is to design online algorithms with small competitive ratios. For a variety of combinatorial problems, such as bipartite matching, general packing LPs, and independent set with bounded local independence number, we design new algorithms that obtain constant competitive ratios. For the matroid secretary problem, we observe that many existing algorithms for special matroid structures maintain their competitive ratios even in the ordinal model. In these cases, the restriction to ordinal information does not represent any additional obstacle. Moreover, we show that ordinal variants of the submodular matroid secretary problems can be solved using algorithms for the linear versions by extending [Feldman and Zenklusen, 2015]. In contrast, we provide a lower bound of $\Omega(\sqrt{n}/(\log n))$ for algorithms that are oblivious to the matroid structure, where $n$ is the total number of elements. This contrasts an upper bound of $O(\log n)$ in the cardinal model, and it shows that the technique of thresholding is not sufficient for good algorithms in the ordinal model.}, }
Endnote
%0 Report %A Hoefer, Martin %A Kodric, Bojana %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Combinatorial Secretary Problems with Ordinal Information : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-5C63-3 %U http://arxiv.org/abs/1702.01290 %D 2017 %X The secretary problem is a classic model for online decision making. Recently, combinatorial extensions such as matroid or matching secretary problems have become an important tool to study algorithmic problems in dynamic markets. Here the decision maker must know the numerical value of each arriving element, which can be a demanding informational assumption. In this paper, we initiate the study of combinatorial secretary problems with ordinal information, in which the decision maker only needs to be aware of a preference order consistent with the values of arrived elements. The goal is to design online algorithms with small competitive ratios. For a variety of combinatorial problems, such as bipartite matching, general packing LPs, and independent set with bounded local independence number, we design new algorithms that obtain constant competitive ratios. For the matroid secretary problem, we observe that many existing algorithms for special matroid structures maintain their competitive ratios even in the ordinal model. In these cases, the restriction to ordinal information does not represent any additional obstacle. Moreover, we show that ordinal variants of the submodular matroid secretary problems can be solved using algorithms for the linear versions by extending [Feldman and Zenklusen, 2015]. In contrast, we provide a lower bound of $\Omega(\sqrt{n}/(\log n))$ for algorithms that are oblivious to the matroid structure, where $n$ is the total number of elements. This contrasts an upper bound of $O(\log n)$ in the cardinal model, and it shows that the technique of thresholding is not sufficient for good algorithms in the ordinal model. %K Computer Science, Data Structures and Algorithms, cs.DS
[56]
W. Höhn, J. Mestre, and A. Wiese, “How Unsplittable-flow-covering Helps Scheduling with Job-dependent Cost Functions,” Algorithmica, vol. First Online, 2017.
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@article{Hoehn2017, TITLE = {How Unsplittable-flow-covering Helps Scheduling with Job-dependent Cost Functions}, AUTHOR = {H{\"o}hn, Wiebke and Mestre, Julian and Wiese, Andreas}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-017-0300-x}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, JOURNAL = {Algorithmica}, VOLUME = {First Online}, PAGES = {1--23}, }
Endnote
%0 Journal Article %A Höhn, Wiebke %A Mestre, Julian %A Wiese, Andreas %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T How Unsplittable-flow-covering Helps Scheduling with Job-dependent Cost Functions : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-2618-3 %R 10.1007/s00453-017-0300-x %7 2017 %D 2017 %J Algorithmica %V First Online %& 1 %P 1 - 23 %I Springer-Verlag %C New York %@ false
[57]
C. Ikenmeyer and G. Panova, “Rectangular Kronecker Coefficients and Plethysms in Geometric Complexity Theory,” Advances in Mathematics, vol. 319, 2017.
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@article{Ikenmeyer2017, TITLE = {Rectangular {Kronecker} Coefficients and Plethysms in Geometric Complexity Theory}, AUTHOR = {Ikenmeyer, Christian and Panova, Greta}, LANGUAGE = {eng}, ISSN = {0001-8708}, DOI = {10.1016/j.aim.2017.08.024}, PUBLISHER = {Academic Press}, ADDRESS = {Orlando, Fla.}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Advances in Mathematics}, VOLUME = {319}, PAGES = {40--66}, }
Endnote
%0 Journal Article %A Ikenmeyer, Christian %A Panova, Greta %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Rectangular Kronecker Coefficients and Plethysms in Geometric Complexity Theory : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-0E59-D %R 10.1016/j.aim.2017.08.024 %7 2017 %D 2017 %J Advances in Mathematics %V 319 %& 40 %P 40 - 66 %I Academic Press %C Orlando, Fla. %@ false
[58]
C. Ikenmeyer and J. M. Landsberg, “On the Complexity of the Permanent in Various Computational Models,” Journal of Pure and Applied Algebra, vol. 221, no. 12, 2017.
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@article{IL:17, TITLE = {On the Complexity of the Permanent in Various Computational Models}, AUTHOR = {Ikenmeyer, Christian and Landsberg, J. M.}, LANGUAGE = {eng}, ISSN = {0022-4049}, DOI = {10.1016/j.jpaa.2017.02.008}, PUBLISHER = {North-Holland}, ADDRESS = {Amsterdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {221}, NUMBER = {12}, PAGES = {2911--2927}, }
Endnote
%0 Journal Article %A Ikenmeyer, Christian %A Landsberg, J. M. %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On the Complexity of the Permanent in Various Computational Models : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-4F23-D %R 10.1016/j.jpaa.2017.02.008 %7 2017-02-23 %D 2017 %J Journal of Pure and Applied Algebra %O J. Pure Appl. Algebra %V 221 %N 12 %& 2911 %P 2911 - 2927 %I North-Holland %C Amsterdam %@ false
[59]
C. Ikenmeyer, K. D. Mulmuley, and M. Walter, “On Vanishing of Kronecker Coefficients,” Computational Complexity, vol. 26, no. 4, 2017.
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@article{Ikenmeyer2017, TITLE = {On vanishing of {Kronecker} coefficients}, AUTHOR = {Ikenmeyer, Christian and Mulmuley, Ketan D. and Walter, Michael}, LANGUAGE = {eng}, DOI = {10.1007/s00037-017-0158-y}, PUBLISHER = {Springer}, ADDRESS = {New York, NY}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Computational Complexity}, VOLUME = {26}, NUMBER = {4}, PAGES = {949--992}, }
Endnote
%0 Journal Article %A Ikenmeyer, Christian %A Mulmuley, Ketan D. %A Walter, Michael %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T On Vanishing of Kronecker Coefficients : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-6278-F %R 10.1007/s00037-017-0158-y %7 2017 %D 2017 %J Computational Complexity %V 26 %N 4 %& 949 %P 949 - 992 %I Springer %C New York, NY
[60]
G. Jindal, P. Kolev, R. Peng, and S. Sawlani, “Density Independent Algorithms for Sparsifying k-Step Random Walks,” 2017. [Online]. Available: http://arxiv.org/abs/1702.06110. (arXiv: 1702.06110)
Abstract
We give faster algorithms for producing sparse approximations of the transition matrices of $k$-step random walks on undirected, weighted graphs. These transition matrices also form graphs, and arise as intermediate objects in a variety of graph algorithms. Our improvements are based on a better understanding of processes that sample such walks, as well as tighter bounds on key weights underlying these sampling processes. On a graph with $n$ vertices and $m$ edges, our algorithm produces a graph with about $n\log{n}$ edges that approximates the $k$-step random walk graph in about $m + n \log^4{n}$ time. In order to obtain this runtime bound, we also revisit "density independent" algorithms for sparsifying graphs whose runtime overhead is expressed only in terms of the number of vertices.
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@online{DBLP:journals/corr/JindalKPS17, TITLE = {Density Independent Algorithms for Sparsifying $k$-Step Random Walks}, AUTHOR = {Jindal, Gorav and Kolev, Pavel and Peng, Richard and Sawlani, Saurabh}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1702.06110}, EPRINT = {1702.06110}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We give faster algorithms for producing sparse approximations of the transition matrices of $k$-step random walks on undirected, weighted graphs. These transition matrices also form graphs, and arise as intermediate objects in a variety of graph algorithms. Our improvements are based on a better understanding of processes that sample such walks, as well as tighter bounds on key weights underlying these sampling processes. On a graph with $n$ vertices and $m$ edges, our algorithm produces a graph with about $n\log{n}$ edges that approximates the $k$-step random walk graph in about $m + n \log^4{n}$ time. In order to obtain this runtime bound, we also revisit "density independent" algorithms for sparsifying graphs whose runtime overhead is expressed only in terms of the number of vertices.}, }
Endnote
%0 Report %A Jindal, Gorav %A Kolev, Pavel %A Peng, Richard %A Sawlani, Saurabh %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Density Independent Algorithms for Sparsifying k-Step Random Walks : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-26A6-1 %U http://arxiv.org/abs/1702.06110 %D 2017 %X We give faster algorithms for producing sparse approximations of the transition matrices of $k$-step random walks on undirected, weighted graphs. These transition matrices also form graphs, and arise as intermediate objects in a variety of graph algorithms. Our improvements are based on a better understanding of processes that sample such walks, as well as tighter bounds on key weights underlying these sampling processes. On a graph with $n$ vertices and $m$ edges, our algorithm produces a graph with about $n\log{n}$ edges that approximates the $k$-step random walk graph in about $m + n \log^4{n}$ time. In order to obtain this runtime bound, we also revisit "density independent" algorithms for sparsifying graphs whose runtime overhead is expressed only in terms of the number of vertices. %K Computer Science, Data Structures and Algorithms, cs.DS
[61]
G. Jindal and M. Sagraloff, “Efficiently Computing Real Roots of Sparse Polynomials,” in ISSAC’17, International Symposium on Symbolic and Algebraic Computation, Kaiserslautern, Germany, 2017.
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@inproceedings{JindalISSAC2017, TITLE = {Efficiently Computing Real Roots of Sparse Polynomials}, AUTHOR = {Jindal, Gorav and Sagraloff, Michael}, LANGUAGE = {eng}, ISBN = {978-1-4503-5064-8}, DOI = {10.1145/3087604.3087652}, PUBLISHER = {ACM}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {ISSAC{\textquoteright}17, International Symposium on Symbolic and Algebraic Computation}, PAGES = {229--236}, ADDRESS = {Kaiserslautern, Germany}, }
Endnote
%0 Conference Proceedings %A Jindal, Gorav %A Sagraloff, Michael %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Efficiently Computing Real Roots of Sparse Polynomials : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-FBA6-4 %R 10.1145/3087604.3087652 %D 2017 %B International Symposium on Symbolic and Algebraic Computation %Z date of event: 2017-07-25 - 2017-07-28 %C Kaiserslautern, Germany %B ISSAC’17 %P 229 - 236 %I ACM %@ 978-1-4503-5064-8
[62]
G. Jindal and M. Sagraloff, “Efficiently Computing Real Roots of Sparse Polynomials,” 2017. [Online]. Available: http://arxiv.org/abs/1704.06979. (arXiv: 1704.06979)
Abstract
We propose an efficient algorithm to compute the real roots of a sparse polynomial $f\in\mathbb{R}[x]$ having $k$ non-zero real-valued coefficients. It is assumed that arbitrarily good approximations of the non-zero coefficients are given by means of a coefficient oracle. For a given positive integer $L$, our algorithm returns disjoint disks $\Delta_{1},\ldots,\Delta_{s}\subset\mathbb{C}$, with $s<2k$, centered at the real axis and of radius less than $2^{-L}$ together with positive integers $\mu_{1},\ldots,\mu_{s}$ such that each disk $\Delta_{i}$ contains exactly $\mu_{i}$ roots of $f$ counted with multiplicity. In addition, it is ensured that each real root of $f$ is contained in one of the disks. If $f$ has only simple real roots, our algorithm can also be used to isolate all real roots. The bit complexity of our algorithm is polynomial in $k$ and $\log n$, and near-linear in $L$ and $\tau$, where $2^{-\tau}$ and $2^{\tau}$ constitute lower and upper bounds on the absolute values of the non-zero coefficients of $f$, and $n$ is the degree of $f$. For root isolation, the bit complexity is polynomial in $k$ and $\log n$, and near-linear in $\tau$ and $\log\sigma^{-1}$, where $\sigma$ denotes the separation of the real roots.
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@online{DBLP:journals/corr/JindalS17, TITLE = {Efficiently Computing Real Roots of Sparse Polynomials}, AUTHOR = {Jindal, Gorav and Sagraloff, Michael}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1704.06979}, EPRINT = {1704.06979}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We propose an efficient algorithm to compute the real roots of a sparse polynomial $f\in\mathbb{R}[x]$ having $k$ non-zero real-valued coefficients. It is assumed that arbitrarily good approximations of the non-zero coefficients are given by means of a coefficient oracle. For a given positive integer $L$, our algorithm returns disjoint disks $\Delta_{1},\ldots,\Delta_{s}\subset\mathbb{C}$, with $s<2k$, centered at the real axis and of radius less than $2^{-L}$ together with positive integers $\mu_{1},\ldots,\mu_{s}$ such that each disk $\Delta_{i}$ contains exactly $\mu_{i}$ roots of $f$ counted with multiplicity. In addition, it is ensured that each real root of $f$ is contained in one of the disks. If $f$ has only simple real roots, our algorithm can also be used to isolate all real roots. The bit complexity of our algorithm is polynomial in $k$ and $\log n$, and near-linear in $L$ and $\tau$, where $2^{-\tau}$ and $2^{\tau}$ constitute lower and upper bounds on the absolute values of the non-zero coefficients of $f$, and $n$ is the degree of $f$. For root isolation, the bit complexity is polynomial in $k$ and $\log n$, and near-linear in $\tau$ and $\log\sigma^{-1}$, where $\sigma$ denotes the separation of the real roots.}, }
Endnote
%0 Report %A Jindal, Gorav %A Sagraloff, Michael %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Efficiently Computing Real Roots of Sparse Polynomials : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-8AD1-7 %U http://arxiv.org/abs/1704.06979 %D 2017 %X We propose an efficient algorithm to compute the real roots of a sparse polynomial $f\in\mathbb{R}[x]$ having $k$ non-zero real-valued coefficients. It is assumed that arbitrarily good approximations of the non-zero coefficients are given by means of a coefficient oracle. For a given positive integer $L$, our algorithm returns disjoint disks $\Delta_{1},\ldots,\Delta_{s}\subset\mathbb{C}$, with $s<2k$, centered at the real axis and of radius less than $2^{-L}$ together with positive integers $\mu_{1},\ldots,\mu_{s}$ such that each disk $\Delta_{i}$ contains exactly $\mu_{i}$ roots of $f$ counted with multiplicity. In addition, it is ensured that each real root of $f$ is contained in one of the disks. If $f$ has only simple real roots, our algorithm can also be used to isolate all real roots. The bit complexity of our algorithm is polynomial in $k$ and $\log n$, and near-linear in $L$ and $\tau$, where $2^{-\tau}$ and $2^{\tau}$ constitute lower and upper bounds on the absolute values of the non-zero coefficients of $f$, and $n$ is the degree of $f$. For root isolation, the bit complexity is polynomial in $k$ and $\log n$, and near-linear in $\tau$ and $\log\sigma^{-1}$, where $\sigma$ denotes the separation of the real roots. %K Computer Science, Symbolic Computation, cs.SC
[63]
A. Karrenbauer, R. Becker, C. Scholl, and B. Becker, “From DQBF to QBF by Dependency Elimination,” in Theory and Applications of Satisfiability Testing -- SAT 2017, Melbourne, Australia, 2017.
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@inproceedings{KarrenbauerSAT2017, TITLE = {From {DQBF} to {QBF} by Dependency Elimination}, AUTHOR = {Karrenbauer, Andreas and Becker, Ruben and Scholl, Christoph and Becker, Bernd}, LANGUAGE = {eng}, ISBN = {978-3-319-66262-6}, DOI = {10.1007/978-3-319-66263-3_21}, PUBLISHER = {Springer}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, BOOKTITLE = {Theory and Applications of Satisfiability Testing -- SAT 2017}, EDITOR = {Gaspers, Serge and Walsh, Toby}, PAGES = {326--343}, SERIES = {Lecture Notes in Computer Science}, VOLUME = {10491}, ADDRESS = {Melbourne, Australia}, }
Endnote
%0 Conference Proceedings %A Karrenbauer, Andreas %A Becker, Ruben %A Scholl, Christoph %A Becker, Bernd %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T From DQBF to QBF by Dependency Elimination : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-FBAC-7 %R 10.1007/978-3-319-66263-3_21 %D 2017 %B 20th International Conference on Theory and Applications of Satisfiability Testing %Z date of event: 2017-08-28 - 2017-09-01 %C Melbourne, Australia %B Theory and Applications of Satisfiability Testing -- SAT 2017 %E Gaspers, Serge; Walsh, Toby %P 326 - 343 %I Springer %@ 978-3-319-66262-6 %B Lecture Notes in Computer Science %N 10491
[64]
C. Lenzen, N. A. Lynch, C. Newport, and T. Radeva, “Searching without Communicating: Tradeoffs between Performance and Selection Complexity,” Distributed Computing, vol. 30, no. 3, 2017.
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@article{DBLP:journals/dc/LenzenLNR17, TITLE = {Searching without Communicating: {T}radeoffs between Performance and Selection Complexity}, AUTHOR = {Lenzen, Christoph and Lynch, Nancy A. and Newport, Calvin and Radeva, Tsvetomira}, LANGUAGE = {eng}, ISSN = {0178-2770}, DOI = {10.1007/s00446-016-0283-x}, PUBLISHER = {Springer International}, ADDRESS = {Berlin}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Distributed Computing}, VOLUME = {30}, NUMBER = {3}, PAGES = {169--191}, }
Endnote
%0 Journal Article %A Lenzen, Christoph %A Lynch, Nancy A. %A Newport, Calvin %A Radeva, Tsvetomira %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Searching without Communicating: Tradeoffs between Performance and Selection Complexity : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-8AA7-9 %R 10.1007/s00446-016-0283-x %7 2016-09-19 %D 2017 %J Distributed Computing %V 30 %N 3 %& 169 %P 169 - 191 %I Springer International %C Berlin %@ false
[65]
C. Lenzen and J. Rybicki, “Efficient Counting with Optimal Resilience,” SIAM Journal on Computing, vol. 46, no. 4, 2017.
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@article{LenzenRybicki2017, TITLE = {Efficient Counting with Optimal Resilience}, AUTHOR = {Lenzen, Christoph and Rybicki, Joel}, LANGUAGE = {eng}, ISSN = {0097-5397}, DOI = {10.1137/16M107877X}, PUBLISHER = {Society for Industrial and Applied Mathematics.}, ADDRESS = {Philadelphia, PA}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {SIAM Journal on Computing}, VOLUME = {46}, NUMBER = {4}, PAGES = {1473--1500}, }
Endnote
%0 Journal Article %A Lenzen, Christoph %A Rybicki, Joel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Efficient Counting with Optimal Resilience : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-EE93-6 %R 10.1137/16M107877X %7 2017 %D 2017 %J SIAM Journal on Computing %V 46 %N 4 %& 1473 %P 1473 - 1500 %I Society for Industrial and Applied Mathematics. %C Philadelphia, PA %@ false
[66]
C. Lenzen and J. Rybicki, “Self-stabilising Byzantine Clock Synchronisation is Almost as Easy as Consensus,” 2017. [Online]. Available: http://arxiv.org/abs/1705.06173. (arXiv: 1705.06173)
Abstract
We give fault-tolerant algorithms for establishing synchrony in distributed systems in which each of the $n$ nodes has its own clock. Our algorithms operate in a very strong fault model: we require self-stabilisation, i.e., the initial state of the system may be arbitrary, and there can be up to $f<n/3$ ongoing Byzantine faults, i.e., nodes that deviate from the protocol in an arbitrary manner. Furthermore, we assume that the local clocks of the nodes may progress at different speeds (clock drift) and communication has bounded delay. In this model, we study the pulse synchronisation problem, where the task is to guarantee that eventually all correct nodes generate well-separated local pulse events (i.e., unlabelled logical clock ticks) in a synchronised manner. Compared to prior work, we achieve exponential improvements in stabilisation time and the number of communicated bits, and give the first sublinear-time algorithm for the problem: - In the deterministic setting, the state-of-the-art solutions stabilise in time $\Theta(f)$ and have each node broadcast $\Theta(f \log f)$ bits per time unit. We exponentially reduce the number of bits broadcasted per time unit to $\Theta(\log f)$ while retaining the same stabilisation time. - In the randomised setting, the state-of-the-art solutions stabilise in time $\Theta(f)$ and have each node broadcast $O(1)$ bits per time unit. We exponentially reduce the stabilisation time to $\log^{O(1)} f$ while each node broadcasts $\log^{O(1)} f$ bits per time unit. These results are obtained by means of a recursive approach reducing the above task of self-stabilising pulse synchronisation in the bounded-delay model to non-self-stabilising binary consensus in the synchronous model. In general, our approach introduces at most logarithmic overheads in terms of stabilisation time and broadcasted bits over the underlying consensus routine.
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@online{DBLP:journals/corr/LenzenR17, TITLE = {Self-stabilising Byzantine Clock Synchronisation is Almost as Easy as Consensus}, AUTHOR = {Lenzen, Christoph and Rybicki, Joel}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1705.06173}, EPRINT = {1705.06173}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {We give fault-tolerant algorithms for establishing synchrony in distributed systems in which each of the $n$ nodes has its own clock. Our algorithms operate in a very strong fault model: we require self-stabilisation, i.e., the initial state of the system may be arbitrary, and there can be up to $f<n/3$ ongoing Byzantine faults, i.e., nodes that deviate from the protocol in an arbitrary manner. Furthermore, we assume that the local clocks of the nodes may progress at different speeds (clock drift) and communication has bounded delay. In this model, we study the pulse synchronisation problem, where the task is to guarantee that eventually all correct nodes generate well-separated local pulse events (i.e., unlabelled logical clock ticks) in a synchronised manner. Compared to prior work, we achieve exponential improvements in stabilisation time and the number of communicated bits, and give the first sublinear-time algorithm for the problem: -- In the deterministic setting, the state-of-the-art solutions stabilise in time $\Theta(f)$ and have each node broadcast $\Theta(f \log f)$ bits per time unit. We exponentially reduce the number of bits broadcasted per time unit to $\Theta(\log f)$ while retaining the same stabilisation time. -- In the randomised setting, the state-of-the-art solutions stabilise in time $\Theta(f)$ and have each node broadcast $O(1)$ bits per time unit. We exponentially reduce the stabilisation time to $\log^{O(1)} f$ while each node broadcasts $\log^{O(1)} f$ bits per time unit. These results are obtained by means of a recursive approach reducing the above task of self-stabilising pulse synchronisation in the bounded-delay model to non-self-stabilising binary consensus in the synchronous model. In general, our approach introduces at most logarithmic overheads in terms of stabilisation time and broadcasted bits over the underlying consensus routine.}, }
Endnote
%0 Report %A Lenzen, Christoph %A Rybicki, Joel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Self-stabilising Byzantine Clock Synchronisation is Almost as Easy as Consensus : %O Self-stabilising {B}yzantine Clock Synchronisation is Almost as Easy as Consensus %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-8AAA-3 %U http://arxiv.org/abs/1705.06173 %D 2017 %X We give fault-tolerant algorithms for establishing synchrony in distributed systems in which each of the $n$ nodes has its own clock. Our algorithms operate in a very strong fault model: we require self-stabilisation, i.e., the initial state of the system may be arbitrary, and there can be up to $f<n/3$ ongoing Byzantine faults, i.e., nodes that deviate from the protocol in an arbitrary manner. Furthermore, we assume that the local clocks of the nodes may progress at different speeds (clock drift) and communication has bounded delay. In this model, we study the pulse synchronisation problem, where the task is to guarantee that eventually all correct nodes generate well-separated local pulse events (i.e., unlabelled logical clock ticks) in a synchronised manner. Compared to prior work, we achieve exponential improvements in stabilisation time and the number of communicated bits, and give the first sublinear-time algorithm for the problem: - In the deterministic setting, the state-of-the-art solutions stabilise in time $\Theta(f)$ and have each node broadcast $\Theta(f \log f)$ bits per time unit. We exponentially reduce the number of bits broadcasted per time unit to $\Theta(\log f)$ while retaining the same stabilisation time. - In the randomised setting, the state-of-the-art solutions stabilise in time $\Theta(f)$ and have each node broadcast $O(1)$ bits per time unit. We exponentially reduce the stabilisation time to $\log^{O(1)} f$ while each node broadcasts $\log^{O(1)} f$ bits per time unit. These results are obtained by means of a recursive approach reducing the above task of self-stabilising pulse synchronisation in the bounded-delay model to non-self-stabilising binary consensus in the synchronous model. In general, our approach introduces at most logarithmic overheads in terms of stabilisation time and broadcasted bits over the underlying consensus routine. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[67]
C. Lenzen and R. Levi, “A Local Algorithm for the Sparse Spanning Graph Problem,” 2017. [Online]. Available: http://arxiv.org/abs/1703.05418. (arXiv: 1703.05418)
Abstract
Constructing a sparse \emph{spanning subgraph} is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by examining only a small part of the input; yet, answers must be globally consistent and independent of prior queries. Unfortunately, maximally sparse spanning subgraphs, i.e., spanning trees, cannot be constructed efficiently in this model. Therefore, we settle for a spanning subgraph containing at most $(1+\varepsilon)n$ edges (where $n$ is the number of vertices and $\varepsilon$ is a given approximation/sparsity parameter). We achieve query complexity of $\tilde{O}(poly(\Delta/\varepsilon)n^{2/3})$,\footnote{$\tilde{O}$-notation hides polylogarithmic factors in $n$.} where $\Delta$ is the maximum degree of the input graph. Our algorithm is the first to do so on arbitrary graphs. Moreover, we achieve the additional property that our algorithm outputs a \emph{spanner,} i.e., distances are approximately preserved. With high probability, for each deleted edge there is a path of $O(poly(\Delta/\varepsilon)\log^2 n)$ hops in the output that connects its endpoints.
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@online{DBLP:journals/corr/LenzenL17, TITLE = {A Local Algorithm for the Sparse Spanning Graph Problem}, AUTHOR = {Lenzen, Christoph and Levi, Reut}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1703.05418}, EPRINT = {1703.05418}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Constructing a sparse \emph{spanning subgraph} is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by examining only a small part of the input; yet, answers must be globally consistent and independent of prior queries. Unfortunately, maximally sparse spanning subgraphs, i.e., spanning trees, cannot be constructed efficiently in this model. Therefore, we settle for a spanning subgraph containing at most $(1+\varepsilon)n$ edges (where $n$ is the number of vertices and $\varepsilon$ is a given approximation/sparsity parameter). We achieve query complexity of $\tilde{O}(poly(\Delta/\varepsilon)n^{2/3})$,\footnote{$\tilde{O}$-notation hides polylogarithmic factors in $n$.} where $\Delta$ is the maximum degree of the input graph. Our algorithm is the first to do so on arbitrary graphs. Moreover, we achieve the additional property that our algorithm outputs a \emph{spanner,} i.e., distances are approximately preserved. With high probability, for each deleted edge there is a path of $O(poly(\Delta/\varepsilon)\log^2 n)$ hops in the output that connects its endpoints.}, }
Endnote
%0 Report %A Lenzen, Christoph %A Levi, Reut %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Local Algorithm for the Sparse Spanning Graph Problem : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-8AB0-4 %U http://arxiv.org/abs/1703.05418 %D 2017 %X Constructing a sparse \emph{spanning subgraph} is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by examining only a small part of the input; yet, answers must be globally consistent and independent of prior queries. Unfortunately, maximally sparse spanning subgraphs, i.e., spanning trees, cannot be constructed efficiently in this model. Therefore, we settle for a spanning subgraph containing at most $(1+\varepsilon)n$ edges (where $n$ is the number of vertices and $\varepsilon$ is a given approximation/sparsity parameter). We achieve query complexity of $\tilde{O}(poly(\Delta/\varepsilon)n^{2/3})$,\footnote{$\tilde{O}$-notation hides polylogarithmic factors in $n$.} where $\Delta$ is the maximum degree of the input graph. Our algorithm is the first to do so on arbitrary graphs. Moreover, we achieve the additional property that our algorithm outputs a \emph{spanner,} i.e., distances are approximately preserved. With high probability, for each deleted edge there is a path of $O(poly(\Delta/\varepsilon)\log^2 n)$ hops in the output that connects its endpoints. %K Computer Science, Data Structures and Algorithms, cs.DS
[68]
C. Lenzen and M. Medina, “Robust Routing Made Easy,” 2017. [Online]. Available: http://arxiv.org/abs/1705.04042. (arXiv: 1705.04042)
Abstract
Designing routing schemes is a multidimensional and complex task that depends on the objective function, the computational model (centralized vs. distributed), and the amount of uncertainty (online vs. offline). Nevertheless, there are quite a few well-studied general techniques, for a large variety of network problems. In contrast, in our view, practical techniques for designing robust routing schemes are scarce; while fault-tolerance has been studied from a number of angles, existing approaches are concerned with dealing with faults after the fact by rerouting, self-healing, or similar techniques. We argue that this comes at a high burden for the designer, as in such a system any algorithm must account for the effects of faults on communication. With the goal of initiating efforts towards addressing this issue, we showcase simple and generic transformations that can be used as a blackbox to increase resilience against (independently distributed) faults. Given a network and a routing scheme, we determine a reinforced network and corresponding routing scheme that faithfully preserves the specification and behavior of the original scheme. We show that reasonably small constant overheads in terms of size of the new network compared to the old are sufficient for substantially relaxing the reliability requirements on individual components. The main message in this paper is that the task of designing a robust routing scheme can be decoupled into (i) designing a routing scheme that meets the specification in a fault-free environment, (ii) ensuring that nodes correspond to fault-containment regions, i.e., fail (approximately) independently, and (iii) applying our transformation to obtain a reinforced network and a robust routing scheme that is fault-tolerant.
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@online{DBLP:journals/corr/LenzenM17, TITLE = {Robust Routing Made Easy}, AUTHOR = {Lenzen, Christoph and Medina, Moti}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1705.04042}, EPRINT = {1705.04042}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, ABSTRACT = {Designing routing schemes is a multidimensional and complex task that depends on the objective function, the computational model (centralized vs. distributed), and the amount of uncertainty (online vs. offline). Nevertheless, there are quite a few well-studied general techniques, for a large variety of network problems. In contrast, in our view, practical techniques for designing robust routing schemes are scarce; while fault-tolerance has been studied from a number of angles, existing approaches are concerned with dealing with faults after the fact by rerouting, self-healing, or similar techniques. We argue that this comes at a high burden for the designer, as in such a system any algorithm must account for the effects of faults on communication. With the goal of initiating efforts towards addressing this issue, we showcase simple and generic transformations that can be used as a blackbox to increase resilience against (independently distributed) faults. Given a network and a routing scheme, we determine a reinforced network and corresponding routing scheme that faithfully preserves the specification and behavior of the original scheme. We show that reasonably small constant overheads in terms of size of the new network compared to the old are sufficient for substantially relaxing the reliability requirements on individual components. The main message in this paper is that the task of designing a robust routing scheme can be decoupled into (i) designing a routing scheme that meets the specification in a fault-free environment, (ii) ensuring that nodes correspond to fault-containment regions, i.e., fail (approximately) independently, and (iii) applying our transformation to obtain a reinforced network and a robust routing scheme that is fault-tolerant.}, }
Endnote
%0 Report %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Robust Routing Made Easy : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-8AAD-E %U http://arxiv.org/abs/1705.04042 %D 2017 %X Designing routing schemes is a multidimensional and complex task that depends on the objective function, the computational model (centralized vs. distributed), and the amount of uncertainty (online vs. offline). Nevertheless, there are quite a few well-studied general techniques, for a large variety of network problems. In contrast, in our view, practical techniques for designing robust routing schemes are scarce; while fault-tolerance has been studied from a number of angles, existing approaches are concerned with dealing with faults after the fact by rerouting, self-healing, or similar techniques. We argue that this comes at a high burden for the designer, as in such a system any algorithm must account for the effects of faults on communication. With the goal of initiating efforts towards addressing this issue, we showcase simple and generic transformations that can be used as a blackbox to increase resilience against (independently distributed) faults. Given a network and a routing scheme, we determine a reinforced network and corresponding routing scheme that faithfully preserves the specification and behavior of the original scheme. We show that reasonably small constant overheads in terms of size of the new network compared to the old are sufficient for substantially relaxing the reliability requirements on individual components. The main message in this paper is that the task of designing a robust routing scheme can be decoupled into (i) designing a routing scheme that meets the specification in a fault-free environment, (ii) ensuring that nodes correspond to fault-containment regions, i.e., fail (approximately) independently, and (iii) applying our transformation to obtain a reinforced network and a robust routing scheme that is fault-tolerant. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC
[69]
R. Levi, G. Moshkovitz, D. Ron, R. Rubinfeld, and A. Shapira, “Constructing Near Spanning Trees with Few Local Inspections,” Random Structures and Algorithms, vol. 50, 2017.
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@article{LeviMRRS15, TITLE = {Constructing Near Spanning Trees with Few Local Inspections}, AUTHOR = {Levi, Reut and Moshkovitz, Guy and Ron, Dana and Rubinfeld, Ronitt and Shapira, Asaf}, LANGUAGE = {eng}, ISSN = {1042-9832}, DOI = {10.1002/rsa.20652}, PUBLISHER = {Wiley}, ADDRESS = {New York, N.Y.}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Random Structures and Algorithms}, VOLUME = {50}, PAGES = {183--200}, }
Endnote
%0 Journal Article %A Levi, Reut %A Moshkovitz, Guy %A Ron, Dana %A Rubinfeld, Ronitt %A Shapira, Asaf %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T Constructing Near Spanning Trees with Few Local Inspections : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-601B-C %R 10.1002/rsa.20652 %7 2016 %D 2017 %J Random Structures and Algorithms %V 50 %& 183 %P 183 - 200 %I Wiley %C New York, N.Y. %@ false
[70]
K. Mehlhorn, S. Näher, and P. Sanders, “Engineering DFS-Based Graph Algorithms,” 2017. [Online]. Available: http://arxiv.org/abs/1703.10023. (arXiv: 1703.10023)
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@online{MehlhornDFSarXiv2017, TITLE = {Engineering {DFS}-Based Graph Algorithms}, AUTHOR = {Mehlhorn, Kurt and N{\"a}her, Stefan and Sanders, Peter}, LANGUAGE = {eng}, URL = {http://arxiv.org/abs/1703.10023}, EPRINT = {1703.10023}, EPRINTTYPE = {arXiv}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, }
Endnote
%0 Report %A Mehlhorn, Kurt %A Näher, Stefan %A Sanders, Peter %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Engineering DFS-Based Graph Algorithms : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002B-4DAE-7 %U http://arxiv.org/abs/1703.10023 %D 2017
[71]
K. Mehlhorn, A. Neumann, and J. M. Schmidt, “Certifying 3-Edge-Connectivity,” Algorithmica, vol. 77, no. 2, 2017.
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@article{Mehlhorn_Neumann_Schmidt2017, TITLE = {Certifying 3-Edge-Connectivity}, AUTHOR = {Mehlhorn, Kurt and Neumann, Adrian and Schmidt, Jens M.}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-015-0075-x}, PUBLISHER = {Springer}, ADDRESS = {New York, NX}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Algorithmica}, VOLUME = {77}, NUMBER = {2}, PAGES = {309--335}, }
Endnote
%0 Journal Article %A Mehlhorn, Kurt %A Neumann, Adrian %A Schmidt, Jens M. %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Certifying 3-Edge-Connectivity : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-6971-B %R 10.1007/s00453-015-0075-x %7 2015-09-22 %D 2017 %J Algorithmica %V 77 %N 2 %& 309 %P 309 - 335 %I Springer %C New York, NX %@ false
[72]
M. Mnich and E. J. van Leeuwen, “Polynomial Kernels for Deletion to Classes of Acyclic Digraphs,” Discrete Optimization, vol. 25, 2017.
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@article{MnichLeeuwen2017, TITLE = {Polynomial Kernels for Deletion to Classes of Acyclic Digraphs}, AUTHOR = {Mnich, Matthias and van Leeuwen, Erik Jan}, LANGUAGE = {eng}, ISSN = {1572-5286}, DOI = {10.1016/j.disopt.2017.02.002}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Discrete Optimization}, VOLUME = {25}, PAGES = {48--76}, }
Endnote
%0 Journal Article %A Mnich, Matthias %A van Leeuwen, Erik Jan %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Polynomial Kernels for Deletion to Classes of Acyclic Digraphs : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002D-DDCA-F %R 10.1016/j.disopt.2017.02.002 %7 2017 %D 2017 %J Discrete Optimization %V 25 %& 48 %P 48 - 76 %I Elsevier %C Amsterdam %@ false
[73]
N. Mustafa, K. Dutta, and A. Ghosh, “Simple Proof of Optimal Epsilon Nets,” Combinatorica, vol. First Online, 2017.
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@article{mustafa:hal-01360452, TITLE = {Simple Proof of Optimal Epsilon Nets}, AUTHOR = {Mustafa, Nabil and Dutta, Kunal and Ghosh, Arijit}, LANGUAGE = {eng}, ISSN = {0209-9683}, DOI = {10.1007/s00493-017-3564-5}, PUBLISHER = {Springer}, ADDRESS = {Heidelberg}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, JOURNAL = {Combinatorica}, VOLUME = {First Online}, }
Endnote
%0 Journal Article %A Mustafa, Nabil %A Dutta, Kunal %A Ghosh, Arijit %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Simple Proof of Optimal Epsilon Nets : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-65CA-7 %R 10.1007/s00493-017-3564-5 %7 2017 %D 2017 %J Combinatorica %V First Online %I Springer %C Heidelberg %@ false
[74]
R. B. Tan, E. J. van Leeuwen, and J. van Leeuwen, “Shortcutting Directed and Undirected Networks with a Degree Constraint,” Discrete Applied Mathematics, vol. 220, 2017.
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@article{TanDAM2017, TITLE = {Shortcutting Directed and Undirected Networks with a Degree Constraint}, AUTHOR = {Tan, Richard B. and van Leeuwen, Erik Jan and van Leeuwen, Jan}, LANGUAGE = {eng}, ISSN = {0166-218X}, DOI = {10.1016/j.dam.2016.12.016}, PUBLISHER = {Elsevier}, ADDRESS = {Amsterdam}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, DATE = {2017}, JOURNAL = {Discrete Applied Mathematics}, VOLUME = {220}, PAGES = {91--117}, }
Endnote
%0 Journal Article %A Tan, Richard B. %A van Leeuwen, Erik Jan %A van Leeuwen, Jan %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Shortcutting Directed and Undirected Networks with a Degree Constraint : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-539D-F %R 10.1016/j.dam.2016.12.016 %7 2017 %D 2017 %J Discrete Applied Mathematics %V 220 %& 91 %P 91 - 117 %I Elsevier %C Amsterdam %@ false
[75]
G. Tarawneh, M. Függer, and C. Lenzen, “Metastability Tolerant Computing,” in 23rd IEEE International Symposium on Asynchronous Circuits and Systems, San Diego, CA, USA. (Accepted/in press)
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@inproceedings{TarawnehASYNC2017, TITLE = {Metastability Tolerant Computing}, AUTHOR = {Tarawneh, Ghaith and F{\"u}gger, Matthias and Lenzen, Christoph}, LANGUAGE = {eng}, PUBLISHER = {IEEE}, YEAR = {2017}, PUBLREMARK = {Accepted}, MARGINALMARK = {$\bullet$}, BOOKTITLE = {23rd IEEE International Symposium on Asynchronous Circuits and Systems}, ADDRESS = {San Diego, CA, USA}, }
Endnote
%0 Conference Proceedings %A Tarawneh, Ghaith %A Függer, Matthias %A Lenzen, Christoph %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Metastability Tolerant Computing : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-80CB-2 %D 2017 %B 23rd IEEE International Symposium on Asynchronous Circuits and Systems %Z date of event: 2017-05-21 - 2017-05-24 %C San Diego, CA, USA %B 23rd IEEE International Symposium on Asynchronous Circuits and Systems %I IEEE
[76]
A. Wiese, “Independent Set of Convex Polygons: From nϵ to 1+ϵ via Shrinking,” Algorithmica, vol. First Online, 2017.
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@article{Wiese2017, TITLE = {Independent Set of Convex Polygons: From $n^{\epsilon}$ to 1+$\epsilon$ via Shrinking}, AUTHOR = {Wiese, Andreas}, LANGUAGE = {eng}, ISSN = {0178-4617}, DOI = {10.1007/s00453-017-0347-8}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {2017}, MARGINALMARK = {$\bullet$}, JOURNAL = {Algorithmica}, VOLUME = {First Online}, PAGES = {1--17}, }
Endnote
%0 Journal Article %A Wiese, Andreas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Independent Set of Convex Polygons: From nϵ to 1+ϵ via Shrinking : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002E-2602-4 %R 10.1007/s00453-017-0347-8 %7 2017 %D 2017 %J Algorithmica %V First Online %& 1 %P 1 - 17 %I Springer-Verlag %C New York %@ false
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2017-12-12 06:37:16
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https://www.general-relativity.net/2021/04/luminosity-distance.html
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Friday, 16 April 2021
Luminosity distance
In section 8.5 we are looking at redshifts and distances. We started in an FLRW universe with metric
\begin{align}{ds}^2=-{dt}^2+a^2\left(t\right)\left[\frac{{\rm dr}^2}{1-\kappa r^2}+r^2{d\theta}^2+r^2\sin^2{\theta}{d\phi}^2\right]&\phantom {10000}(1)\nonumber\end{align}or
\begin{align}{ds}^2=-{dt}^2+a^2\left(t\right){R_0}^2\left[{d\chi}^2+{S_k}^2\left(\chi\right){d\Omega}^2\right]&\phantom {10000}(2)\nonumber\end{align}where $k\in\left\{-1,0,1\right\}$ and
\begin{align}S_k\left(\chi\right)\ \equiv\left\{\begin{matrix}\sin{\chi},&k=+1&\rm{closed}\\\chi,&k=0&\rm{flat}\\\sinh{\chi}&k=-1&\rm{open}\\\end{matrix}\right.&\phantom {10000}(3)\nonumber\end{align}(2) is Carroll's 8.106, a sort of hybrid FLRW metric.
This starts at Carroll's 8.110 where he defines distance luminosity $d_L$ which you can get if you know the absolute luminosity of a star (or galaxy) and can measure the amount of light that reaches you. We then correct that for the expansion of the universe and further correct it because the universe deviates from a perfect sphere according to $S_k\left(\chi\right)$. We arrive at the celebrated and complicated formula at (4) which uses (5) which uses (6) .
\begin{align}d_L=\left(1+z\right)\frac{{H_0}^{-1}}{\sqrt{\left|\Omega_{c0}\right|}}S_k\left[\sqrt{\left|\Omega_{c0}\right|}\int_{0}^{z}\frac{dz^\prime}{E\left(z^\prime\right)}\right]&\phantom {10000}(4)\nonumber\end{align}where
\begin{align}E\left(z\right)=\left[\sum_{i(c)}{\Omega_{i0}\left(1+z\right)^{n_i}}\right]^\frac{1}{2}&\phantom {10000}(5)\nonumber\end{align}and there are four elements in the summation, one each for matter, radiation, curvature and vacuum energy density. $\Omega_i$ is the density parameter which we met before and was defined as
\begin{align}\Omega_i=\frac{8\pi G}{3H^2}\rho_i&\phantom {10000}(6)\nonumber\end{align}where the $\rho_i$ are the energy densities for each of those four things. $\Omega_i$ and $H$, the Hubble factor acquire a 0 subscript for their values in the present epoch.
I then try to calculate (4) from known values. $\Omega_{c0}$ the pseudo-density parameter for curvature comes from Friedmann's equation and the other three density parameters. That radiation energy is negligible, matter energy density corresponds to what is usually called ordinary (baryonic) plus dark matter and vacuum energy density is dark energy. The integral in (4) must be calculated numerically and I plotted below (page 10 in the pdf). After that we have plots of luminosity distance vs redshift for the three kinds of universe determined by $k$ in (3). Luminosity distances greater 100 billion light years are quite easy to get. I thought everything was a failure until I found some distance calculators which gave more or less the same! According to Carroll, these distances are compared with those measured from absolute and apparent luminosity. Luminosity distance is mighty peculiar. Coming soon: Proper motion distance and Angular diameter distance.
I also found that there is a missing divide by sign in Carroll's equation 8.122.
Read all about it at Commentary 8.5.2 Redshifts and Distances.pdf (12 pages)
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2021-10-22 07:37:10
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https://pages.tacc.utexas.edu/~eijkhout/istc/html/taylor.html
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# Taylor series
The Taylor expansion theorem, in a sense, asks how well functions can be approximated by polynomials, that is, for a given function~$f$, can we find coefficients~$c_i$ with $i=1,\ldots,n$ so that $f(x)\approx c_0+c_1x+c_2x^2+\cdots+c_nx^n.$ This question obviously needs to be refined. What do we mean by approximately equal'? This approximation formula can not hold for all functions~$f$ and all~$x$: the function $\sin x$ is bounded for all~$x$, but any polynomial is unbounded for $x\rightarrow \pm\infty$, so any polynomial approximation to the $\sin x$ function is unbounded. Clearly we can only approximate on an interval.
We will show that a function~$f$ with sufficiently many derivatives can be approximated as follows: if the $n$-th derivative~$f^{(n)}$ is continuous on an interval~$I$, then there are coefficients $c_0,\ldots,c_{n-1}$ such that $\forall_{x\in I}\colon |f(x)-\sum_{i Now we need to be a bit more precise. Cauchy's form of Taylor's theorem says that \[ f(x) = f(a)+\frac1{1!}f'(a)(x-a)+\cdots+\frac1{n!}f^{(n)}(a)(x-a)^n +R_n(x)$ where the `rest term' $R_n$ is $R_n(x) = \frac1{(n+1)!}f^{(n+1)}(\xi)(x-a)^{n+1} \quad\hbox{where \xi\in(a,x) or \xi\in(x,a) depending.}$ If $f^{(n+1)}$ is bounded, and $x=a+h$, then the form in which we often use Taylor's theorem is $f(x) = \sum_{k=0}^n \frac1{k!}f^{(k)}(a)h^k+O(h^{n+1}).$ We have now approximated the function~$f$ on a certain interval by a polynomial, with an error that decreases geometrically with the inverse of the degree of the polynomial.
For a proof of Taylor's theorem we use integration by parts. First we write $\int_a^xf'(t)dt=f(x)-f(a)$ as $f(x) = f(a)+\int_a^xf'(t)dt$ Integration by parts then gives $\begin{array}{r@{=}l} f(x) &f(a)+[xf'(x)-af'(a)]-\int_a^xtf''(t)dt\\ &f(a)+[xf'(x)-xf'(a)+xf'(a)-af'(a)]-\int_a^xtf''(t)dt\\ &f(a)+x\int_a^xf''(t)dt+(x-a)f'(a)-\int_a^xtf''(t)dt\\ &f(a)+(x-a)f'(a)+\int_a^x(x-t)f''(t)dt\\ \end{array}$ Another application of integration by parts gives $f(x)=f(a)+(x-a)f'(a)+\frac12(x-a)^2f''(a) +\frac12 \int_a^x(x-t)^2f'''(t)dt$ Inductively, this gives us Taylor's theorem with $R_{n+1}(x) = \frac1{n!}\int_a^x(x-t)^nf^{(n+1)}(t)dt$ By the mean value theorem this is $\begin{array}{r@{=}l} R_{n+1}(x) &\frac1{(n+1)!}f^{(n+1)}(\xi)\int_a^x(x-t)^nf^{(n+1)}(t)dt\\ &\frac1{(n+1)!}f^{(n+1)}(\xi)(x-a)^{n+1} \end{array}$
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2021-08-05 17:02:00
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http://www.cs.cmu.edu/afs/cs/project/jair/pub/volume20/younes03a-html/node5.html
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The Additive Heuristic for POCL Planning
The key assumption behind the additive heuristic is subgoal independence. We give a recursive definition of the additive heuristic for POCL planning, starting at the level of literals and working towards a definition of heuristic cost for a partial plan.
Given a literal q, let (q) be the set of ground actions having an effect that unifies with q. The cost of the literal q can then be defined as
hadd(q) = .
A positive literal q holds initially if it is part of the initial conditions. A negative literal ¬q holds initially if q is not part of the initial conditions (the closed-world assumption). The cost of an action a is
hadd(a) = 1 + hadd(Prec(a)),
where Prec(a) is a propositional formula in negation normal form representing the preconditions of action a. A propositional formula is in negation normal form if negations only occur at the level of literals. Any propositional formula can be transformed into negation normal form, and this is done for action preconditions by VHPOP while parsing the domain description file.
Existentially quantified variables in an action precondition can be treated as additional parameters of the action. The cost of an existentially quantified precondition can then simply be defined as follows:
hadd(x.) = hadd()
We can deal with universally quantified preconditions by making them fully instantiated in a preprocessing phase, so in order to complete the definition of heuristic cost for action preconditions we only need to add definitions for the heuristic cost of conjunctions and disjunctions. The cost of a conjunction is the sum of the cost of the conjuncts:
hadd() = hadd()
The summation in the above formula is what gives the additive heuristic its name. The definition is based on the assumption that subgoals are independent, which can lead to overestimation of the actual cost of a conjunctive goal (i.e. the heuristic is not admissible). The cost of a disjunction is taken to be the cost of the disjunct with minimal cost:
hadd() = hadd()
The additive heuristic cost function for POCL plans can now be defined as follows:
hadd() = hadd(q)
As with the cost function for conjunction, the above definition can easily lead to overestimation of the number of actions needed to complete a plan, since possible reuse is ignored. We propose a remedy for this below.
The cost of ground literals can be efficiently computed through dynamic programming. We take conditional effects into account in the cost computation. If the effect q is conditioned by p in action a, we add hadd(p) to the cost of achieving q with a. We only need to compute the cost for ground literals once during a preprocessing phase, leaving little overhead for evaluating plans during the planning phase. When working with lifted actions, there is extra overhead for unification. It should also be noted that all lifted literals are independently matched to ground literals without considering interactions between open conditions of the same action. For example, two preconditions (a ?x) and (b ?x) of the same action can be unified to ground literals with different matchings for the variable ?x.
Håkan L. S. Younes
2003-08-26
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2016-08-24 18:46:09
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https://dec.dearbornschools.org/mod/glossary/showentry.php?eid=9289
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#### 7.RP.A.1
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
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2022-12-04 11:37:13
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https://quant.stackexchange.com/tags/compounding/hot
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# Tag Info
4
There is no possibility to convert any two of your mentioned variables into the remaining one. For the compound and arithmetic return you can derive an inequality, but that's the best you can do. The definitions for your statements are: $$r_{\mathrm{compound}}= \prod_{t=0}^{n}{\left( 1+r_t \right)}$$ $$r_{\mathrm{arithmetic}}=\frac{1}{n} \sum_{t=0}^n{r_t}... 4 They are different because there are different conventions in different places. Whilst it would make the maths more consistent to use discount (or accrual) factors to describe interest, the foremost concern historically has been absolute clarity on amounts of money, so having a simple way to calculate the coupon payment on a given bond. So a UK Gilt paying 5%... 3 I grappled with different compounding conventions for a while when I first joined the world of finance. After some time, I came to the conclusion that the best analogy is that of different units of speed in different countries: i.e. in the UK, the unit of speed is miles, whilst in continental Europe, it is kilometers. A car travelling at 100mph is travelling ... 3 Hint: Let$$z = \mathrm{e}^{-y} $$That way you get a quadratic equation in z (note that z is positive) and then you can get back to y using:$$ y = -\ln (z) $$3 Let us start from your last equation, and focus specifically on the expectation. Assuming that the end date of each period is the start period of the next, the idea is to simplify it using conditional expectations. Since t < t_{n-2}, we can write using the tower property of conditional expectations:$$ \begin{aligned} \Bbb{E}_{t}^{Q^{t_n}} \left[\prod_{...
3
Continuous-time formulation is much easier for some basic asset pricing theories. In continuous-time you will have to deal with integrals rather than sums which makes your life much easier. And for those, you will need continuous discounting. Here's an excerpt from John Cochrane's Asset Pricing: The choice of discrete vs. continuous time is one of ...
3
You add 1 to every monthly return of a given quarter, take the product of those returns, and then subtract 1. In R (without any package): Suppose r are the monthly returns, and dt are the timestamps. r <- rep(0.01, 12) dt <- seq(from = as.Date("2020-1-1"), to = as.Date("2020-12-1"), by = "1 month") tapply(r, paste(as....
2
Look this is just a geometric sum: Assume interest is paid monthly at rate $r = 0.08/12$ (you can use the exact monthly equivalent if you want) and let $x_n =$total after $n$ months (including that month's interest and deposit). So $x_0= 100$ and $x_{n+1} = x_n(1+r) + d$, where $d = 5$ is your deposit amount (added at the end of the month). Applying the ...
2
Often the choice of discount curves are dependent upon the context of the assets/liabilities being valued. Banks, for example who have active and to-the-second accurate valuations of these due to active trading desks reporting daily mark-to-market should have more accurate curves, so that all of their operations are consistently valued and do not lead to ...
2
By no arbitrage, market participants need to agree on the values of the discount factor, even if they are using different conventions (day count, compounding period) to convert the discount factor into a rate. For example, consider two discount factors computed using continuous compounding, where one is computed using the 30/360 day count (year fraction $t_{... 2 Convention for most currencies is flat compounding. This includes the most liquid G4 basis swaps: EUR 3m vs 6m, 3m vs 12m, 1m vs 3m USD 1m vs 3m, 3m vs 6m GBP 3m vs 6m, 1m vs 3m JPY 3m vs 6m, 1m vs 6m, 1m vs 3m Typically the spread is quoted in terms of the leg with the shorter tenor. Two notable exceptions are EONIA v 3m and the (relatively new) SOFR ... 2 In continuous compounding, a nominal (or an index value) in time$t$is given by formula $$N_t = N_0\mathrm{e}^{rt},$$ where$r$is return (or interest) rate per annum. Based on the equation above, the$r$can be calculated as $$r = \frac{1}{t}\ln\frac{N_t}{N_0}.$$ So, for$t = 1we have the annualized return: $$r_{t=1} = \frac{1}{1}\ln\frac{4086}{... 2 Sometimes it is easier to work with continuos compounding in some models, especialy when you compound interest daily. Moreover, it can come from history when it was more difficult to calculate higher powers than tabulated exponential function. Take for example annual interest rate i = 5 \%. Then effective annual interes rate based on daily compounding is ... 2 So, you: 1- take your daily return series. I've used the SPY ETF including divis 2- take a log return series, ln(1) 3- add ln(1.015)/261 to 2, given 261 trading days on average each year 4- do a running sum series of 2 and 3 5- exp(4) to give you a price Gives you: The ratio between the two is 1.35 = 1.015^20, ie your 150bps compounded over the ... 2 Depends on which OIS you are referring to. For EUR OIS Swaps, the EONIA Swap rate is calculated via the usual compounding formula (notice that in the example below, the rate r_i is updated every night): Example is shown here: For USD OIS Swaps, the link to Investopedia that you shared is correct: it is pretty much the same formula as for the EUR swap ... 2 Let's add a time variable to extend to non-annual periods$$1 + r_d t = e^{r_c t}The taylor expansion of exponential is \begin{align} e^{r_c t} &= \sum_{n=0}^\infty {\frac {(r_c t)^n} {n!}}\\ &= 1 + r_c t + {\frac 1 2}(r_c t)^2 + \cdots \end{align} so by equating the two equations, we see thatr_d = r_c + {\frac 1 2}r_c^2 t + O(t^2)Two things ... 1 I’ve already made a comment about how to find the Kelly bet size, f, but I guess that misunderstood the question. I come by it honestly though, because it is so vague. There are an infinite number of possible discrete distributions with payoffs between -1 and 1 for certain probabilities. You know best what question you want answering, and if you know the ... 1 Your formula in the first example is on the right track. Standing at time step i, your value at next time step i+1 is V_{i+1} = (V_{i} + c_i)(1+r_{i+1}), i.e. your previous portfolio value plus an influx of c_i in cash (SIP) are yielding a one step return of r_{i+1}. Explicitly you have \begin{align} V_0 &= V_0 \\ V_1 &= (V_0 + c_0)(1+r_1) \... 1 They're not equivalent, but you can use log identities to derive something similar after applying a log. Eg, ln\left(\left(\frac{1+E_2}{1+E_1}\right)^{\frac{d}{360}}\right) \frac{d}{360}*\left(1+E_2-\left(1+E_1\right)\right) \left(E_2-E_1\right)*\frac{d}{360} 1 Let's assume that the collateral rate on cash equals the overnight rate, that we have a schematic (lined/tiled up accrual periods and payments dates) strip of dates/times T_0<T_1<\ldots <T_n, accrual factor \tau_t := \tau(t-1,t), and c_t collateral rate at t (overnight t-1 to t). The floating coupon is then: \prod_{s=T_{i-1}}^{T_i}\... 1 Well let's just do the math. 10% p.a. with semi annual means 10%/2 for 6 months, so you get1.05*1.05=1.1025$That is, for 1 dollar you'll have 1.1025 in 1 year, i.e. 10.25% p.a. if it was annualy compounded. What should be the rate for continuous compounding (annual)? Well:$e^{r\times1}=1.1025$gives$r=0.0975803$or 9.758% as stated in your book. 1 The key is on the left hand side. Recall that the differential of log of x is:$d \ln x =\frac{1}{x}dx$So you get:$\ln x_t-\ln x_0=at$Which you will need to exponentiate to get rid of the log:$\frac{x_t}{x_0}=e^{at}$1 This would be specified in the ISDA or term sheet. There are four alternative methods: No compounding: Meaning neither the rate nor the spread get compounded. Compounding: Meaning both the spread and the libor rate get compounded. Spread exclusive compounding:Meaning the libor get compounded but the spread does not. This was not covered by ISDA 2006 but ... 1 Let$\Delta P = P_t - P_{t-1}\$ and expand the continuously compounded return in a Taylor series $$r = \log\left(\frac{P_t}{P_{t-1}}\right) = \log\left(\frac{P_{t-1}+\Delta P}{P_{t-1}}\right) = \log\left(1+\frac{\Delta P}{P_{t-1}}\right) \approx \frac{\Delta P}{P_{t-1}} - \mathcal{O}\left(\left(\frac{\Delta P}{P_{t-1}}\right)^2\right) = \frac{P_t - P_{t-1}}{... 1 Since the simple interest r_{s} and the continuous compounded interest r_{c} are connected by$$(1 + r_{s} \cdot (T_{2}-T_{1})) = e^{r_{c} \cdot (T_{2}-T_{1})}$$it follows for the continuous compounded interest:$$r_{c} = \frac{1}{T_{2}-T_{1}} \cdot \ln{(1+r_{s} \cdot (T_{1}-T{2}))}$$your convexity formula becomes than:$$ \frac{1}{T_{2}-T_{1}} \cdot \...
Only top voted, non community-wiki answers of a minimum length are eligible
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2021-05-08 19:45:42
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https://forum.murthy.com/topic/31494-previous-h1-approval/
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# Previous H1 approval
## Recommended Posts
Hi all,
I seem to be in a peculiar problem. in 2007 I was sponsored by a for profit consultant as well as a not for profit company. I ended up working for the not for profit company. Now I am in the process of searching for a new job. However, I do not have the copy for the 2007 for the for profit consultant's approval notice.
My question is: is it possible to get a copy of my old approval notice from the USCIS. If so how? USCIS has a form which allows me to get a copy of only the petitions that are current. Do I need to attach a copy of my for profit approval notice when I apply to a for profit job?
Thanks
genie
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2022-11-28 07:13:10
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https://engineering.stackexchange.com/tags/tolerance/hot
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# Tag Info
7
The minimum clearance occurs when the largest possible shaft meets the smallest possible hole. That would be in this case a shaft of $50.02 mm$ in a hole of $50.00 mm$. The difference between the two is the $-0.02 mm$ from the solution you found.
6
There are two different aspects in your measurement. On the one hand, you are dealing with tolerances. On the other hand, you cover probabilities in measurement systems. Just for a rough calculation: The probability of the real length to be within 9.8mm and 10mm is 95%. The certainty of this measurement depends on the distribution of your probability. For ...
5
Answering the question: What are possible types of low cost sensors I can use? There are several types of sensors that can provide millimeter level accuracy. "Low cost" is a very relative term, so you'll need to do some shopping around based on your specific budget. Optical sensors- Included here are those of the type you listed, though it's a very ...
5
To get that sort of accuracy over that scale is not trivial and probably won't be cheap. For smaller size up to a few meters a portable CMM would be an option (here's an example). These have accuracy on the order of 10 $\mu$m and are used for things like high end/F1 car manufacture. However, CMM type instruments wouldn't be useful for anything larger than ...
4
Even the best metal tape measure is susceptible to significant thermal expansion over large distances. Try a laser measurement device ('electronic tape measure') instead: http://www.engineersupply.com/Laser-Measurers.aspx The laser distance measure, flat plates clamped to the object, and some shims of known thickness, should be all you need to precisely ...
4
Measurement variations are very common and should be taken in to consideration when engineering systems. In most cases high precision equipment is available but might be cost prohibitive to justify purchasing for the project. Therefore, the goal of the engineer is to design the system to account for measurement variation. In this case the min and max limits ...
3
It says the flats shall be within 0.100 units of radial dimension positioned with reference to 'A'. i.e. if you were to make the rim which is a perfect circle, then mill the flats at the three positions, what you should see is that the flats are exactly the same sectional shape and size if the machinist was perfectly precise. Some minor deviation from ...
3
I believe this is a related mating envelope related to datum A for the three plates, per ASME Y14.5-2009.
3
Your clearance range is the minimum hole diameter minus max shaft diameter to max hole diameter minus minimum shaft diameter. Answer: Yes. Your math seems correct. This is a useful tool: http://www.amesweb.info/FitTolerance/FitTolerance.aspx
3
If you live in a country that uses ACI standards, you might consider specifying flatness using an FL or FF number. ACI 117, Commentary Table R4.8.4 has this information, with flatness ranging from "Conventional" to "Super Flat." For the dimensions you have listed, specifying anything beyond "Flat" is probably overkill since your forceplate will likely ...
3
Standard threads are classified for accuracy by a tolerance class (You can see a bit about the metric thread fit classes at http://www.amesweb.info/Screws/IsoMetricScrewThread.aspx .) The screws you find at your local hardware store will probably be a relatively rough tolerance class, meaning that the threads are designed to have some gap between them, and ...
3
For high accuracy over long distances it's typical to use general surveying techniques. You use a total station (like this) which will get you 1.5mm accuracy in a single shot. They're no laser tape measure. Repeated set ups /readings with some statistical corrections should get you easily below 1mm. Note too that these are immune to thermal expansion of ...
3
If it says +/- 1% then it means from -1% to +1%. in everyery standard i have ever seen. +/- is simply shorthand for writing a symmetric bound one can also make unsymmetric bounds like 0 to 1% or even positive positive bounds like +0.001 to + 0.025. Granted these are rare in electrical components but play a big role in mechanical engineering where its ...
2
The link provided by Ethan48 added a lot of informations. Tolerance classes: Note : * 6g is normally selected for commercial external (bolt) threads. Note : ** 6H is normally selected for commercial interrnal (nut) threads. The amount of movement allowed for external thread would be determined by axial counterpart to (radial) $T_{d2}/2 + es/2$. ...
2
Understanding "without any special procedures" as meaning simply dropping the cement in a pile, it would probably end up with an inclination approximately equal to its angle of repose. Unfortunately, this value is highly variable, and a quick search has resulted in many different values: 15 or 20 degrees if fine or coarse (1) 40-44 degrees (1) 39 degrees (2)...
2
Here is a link to a screw thread chart. http://www.engineersedge.com/screw_threads_chart.htm Note there are different tolerance classes, and also note the max is never over the nominal size. For the example 1/4-20 class 2: 0.2408 < d < 0.2489 class 3: 0.2419 < d < 0.25
2
The "incremental error" is the relative error in moving between two positions. (But only the USA would think of specifying a dimensionless quantity in "inches per foot" just to confuse people.) If the screw is commanded to move a distance $x$ (in any length unit!) the distance actually moved will be between 0.99995$x$ and 1.00005$x$ (because 0.0006/12 = 0....
2
As you have not placed constraints on the project implementation, consider that most welding requires a jig of some form to maintain alignment of parts. The use of the generality "most" also refers to simple clamping of two pieces prior to welding, which is common in non-critical alignment projects. Allowing for the specifications you've provided, consider ...
1
Just looked at my kitchen scissors; clearance approximately of +.001"/+.003".
1
In simplest terms, Functional Datums should have something to do with a part. E.g. a mating surface or a centerline of the bearing surface of a rotating shaft. A Manufacturing Datum is a feature used to locate and secure a part for a manufacturing operation. A Manufacturing Datum can use the Functional Datums or would be an entirely different feature. For ...
1
Broadly speaking opening a valve further reduces flow resistance, at least up to point but more travel means greater acceleration and thus greater forces on parts, which is magnified as RPM increases. Indeed with mechanical valves you get to a point where the return springs can't act fast enough and you starts to get harmonic effects where the valves ...
1
There are a couple of issues. Firstly laser cutting may well not provide good enough tolerances or surface finish to reliably produce the fit you need and you woudl probably be better off drilling the holes, possibly using the laser to create a reference mark or pilot hole. Secondly poly-carbonate and acrylic don't really like this sort of interference fit ...
1
Presuming laser cutter and not laser printer, the project you suggest would be most effectively approached by creating test pieces. With 5 mm thick acrylic, there are enough variables to make it difficult to provide certain answers. Cast acrylic behaves differently from extruded acrylic. High power lasers are able to use higher travel speeds than lower ...
1
One possible issue is galvanic corrosion. In certain conditions, if dissimilar metals are in contact with each other the more electronegative metal will corrode at a greatly accelerated rate, effectively the same situation a a metal/metal battery. This can be a particular issue if you have steel studs or other interests in a non-ferrous casting. Indeed ...
1
Precision and Accuracy are independent. As Andy has stated, accuracy refers to the ability of the device to measure as close to the absolute value as possible, whereas, precision refers to the closeness of the values in repeated measurements. Precision depends on repeatability and reproducibility of both the device and the measurers, assuming all other ...
1
0.01 of a mm is pretty tight by any standards, for example a typical jobing lathe might be graduated in divisions of 0.025mm. So 0.01mm is not impossible but certainly not trivial. This level of accuracy is also getting into the realms where thermal expansion and cleanliness of surfaces become significant factors. To put this into perspective a 200mm ...
1
Comments: Do not specify manufacturing methods; what method is used is best decided by the shop depending on what tools they have and what they want to do with the job; the number of parts ordered will have a big effect on their approach. In general, you should never try to tell a machine shop how to do their job, because they know MUCH more than you do ...
1
Effective sharpness depends on both the angle of the cone and the geometry of the very edge/point. In this case it sounds like you aren't aiming for very deep penetration into the surface so the tip of the point itself is likely to be the key factor. You also need to consider the ways that a sharp point wears. In general this can either be that material ...
1
Aluminium rubbing on aluminum generally will wear very rapidly. You generally want some sort of plastic bushing to reduce friction and wear. (Like with luggage handles there's just a little piece of plastic between the tubes) you should also have a bushing for the other end of the joint (the one inside that's not visible.) You should do a beam analysis to ...
Only top voted, non community-wiki answers of a minimum length are eligible
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2020-05-28 12:45:51
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https://paperwhy.aerobaticapp.com/2017/05/31/dropout-training-as-adaptive-regularization/
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# This is PaperWhy. Our sisyphean endeavour not to drown in the immense Machine Learning literature.
With thousands of papers every month, keeping up with and making sense of recent research in machine learning has become almost impossible. By routinely reviewing and reporting papers we help ourselves and hopefully someone else.
# Dropout training as adaptive regularization
tl;dr: dropout (of features) for GLMs is a noising procedure equivalent to Tykhonov regularization. A first order approximation of the regularizer actually scales the parameters with the Fisher information matrix, adapting the objective function to the dataset, independently of the labels. This makes dropout useful in the context of semi-supervised learning: regularizers can be adapted to the unlabeled data yielding better generalization. For logistic regression the adaption amounts to favoring features on which the estimator is confident.
For shallow architectures, there were already some (stated) results on the averaging properties of dropout.1 This was later extended to multiple layers with sigmoid units: simple weighting of outputs in the forward pass computes an approximation of the expectation of the ensemble.2 Today’s paper predates this work and focuses still on shallow networks, albeit within the wider scope of Generalized Linear Models.
Since these are shallow models, dropout is performed on the inputs and it can be compared to other methods of input perturbation like additive Gaussian noise.
There are 3 main contributions in this paper:
1. A dropout regularizer for a GLM is (up to first order) equivalent to a classical Tykhonov regularizer with $L^2$-norm, with a specific scaling. Crucially, this scaling depends on the data but not on the labels and makes the regularization adaptive.
2. Incorporating this regularization into a rewriting of SGD as the repeated solution of regularized linear problems leads to an update similar to AdaGrad.3 A connection between the goals of both is established.
3. In the case of logistic regression the dropout regularizer is shown to favour confident predictions, regardless of the label (in the sense that it penalizes less those weights corresponding to features on which the predicted probability is far from $1 / 2$). Therefore it makes sense to apply it to semi-supervised problems computing an extra term over unlabeled data.
### (Feature-) Dropout is weighted $L^2$-regularization
Consider any Generalized Linear Model with parameters $\beta$, inputs $x \in \mathbb{R}^d$ and outputs $y \in Y$, i.e.4
$p (y|x, \beta) = h (y) \mathrm{e}^{yx \beta - A (x \beta)},$
and negative log likelihood as the loss. For one training sample $(x, y)$: $l (\beta ; x, y) = - \log p (y|x, \beta)$. Now choose some noise vector $\xi \in \mathbb{R}^d$ with i.i.d. entries with zero mean and replace $x \mapsto \tilde{x}$ where $\tilde{x}$ has been noised with $\xi$ in some way we specify later. A couple of computations show that the empirical loss on the (full) noised data $\tilde{\boldsymbol{x}} = (\tilde{x}_{1}, \ldots, \tilde{x}_{n}),\boldsymbol{y}= (y_{1}, \ldots, y_{n})$ is the loss on the original data plus a new term:
$\hat{L} (\tilde{\boldsymbol{x}}, \boldsymbol{y}, \beta) = \hat{L} (\boldsymbol{x}, \boldsymbol{y}, \beta) + R (\beta),$
which is the noising regularizer
$$\label{eq:noising-regularizer}\tag{1} R (\beta) := \sum_{i = 1}^n \mathbb{E}_{\xi} [A (\tilde{x}_{i} \beta)] - A (x_{i} \beta) .$$
$R (\beta)$ has two key features:
• It does not depend on the labels: this will allow for its use in unsupervised setting.
• It is adapted to the training data.
But how exactly “adapted”? Definition (1) is quite impenetrable as is, even after plugging in a specific $A$. Assuming we can do a Taylor expansion of $A$ around $x \beta$ one obtains5
$\mathbb{E}_{\xi} [A (\tilde{x} \beta)] - A (x \beta) \approx \tfrac{1}{2} A” (x \beta) \operatorname{Var}_{\xi} [\tilde{x} \beta]$
and substituting into (1) the (approximate) quadratic noising regularizer:
$$\label{eq:quadratic-noising-regularizer}\tag{2} R^q (\beta) := \sum_{i = 1}^n \tfrac{1}{2} A” (x \beta) \operatorname{Var}_{\xi} [\tilde{x} \beta] .$$
Note that (2) is in general non-convex. When questioned by a reviewer about this fact, the authors respond
Although our objective is not formally convex, we have not encountered any major difficulties in fitting it for datasets where n is reasonably large (say on the order of hundreds). When working with LBFGS, multiple restarts with random parameter values give almost identical results. The fact that we have never really had to struggle with local minimas suggests that there is something interesting going on here in terms of convexity.
We can now fix the noising method and look at its variance to gain insight into what $R^q$ does, and hopefully, by extension $R$.6 The authors consider:
• Additive gaussian noise: $\tilde{x} = x + \xi$ with $\xi _{i}$ i.i.d. spherical Gaussians $\mathcal{N} (0, \sigma^2 \operatorname{Id}_{d})$.
• Dropout noise: fix $\delta \in (0, 1)$ to build a (scaled) binary mask $\xi$ with i.i.d entries $\operatorname{Bernoulli} (1 - \delta)$ and set $\tilde{x} = x \odot \xi / (1 - \delta)$ to cancel some of the inputs with probability $\delta$.7
Notice that in both cases $\mathbb{E}_{\xi} [\tilde{x}] = x$ and the expectation of the Taylor expansion of $A$ yields (2) (that’s the reason for the scaling factor $\delta$). After performing the necessary computations, and assuming the design matrix has been normalized to $\Sigma _{i j} x^2_{i j} = 1$, the authors obtain the following neat table:
Linear regression Logistic regression GLM $L^2$-penalty $\| \beta \|^2_2$ $\| \beta \|^2_2$ $\| \beta \|^2_2$ Additive noise $\| \beta \|^2_2$ $\| \beta \|^2_2 \sum_i p_i (1 - p_i)$ $\| \beta \|^2_2 \operatorname{tr} (V (\beta))$ Dropout noise $\| \beta \|^2_2$ $\sum_{i, j} p_i (1 - p_i) x_{i j}^2 \beta_j^2$ $\beta^{\top} \operatorname{diag} (X^{\top} V (\beta) X) \beta$
Table 1. $R^q$ (up to constants) for different models and noising methods. See below for the definition of $V (\beta)$.
The first row holds by definition. The first column recovers known results8 and adds the fact that dropout (after scaling) on linear regression is ridge regression. It’s the box who tells a more interesting story. First we note that the key matrix $V (\beta) \in \mathbb{R}^{n \times n}$ is diagonal with entries $V (\beta)_{i i} = A” (x_{i} \beta)$.
Additive noising for logistic regression penalizes more strongly uncertain predictions ($p_{i} \approx 0.5$). For arbitrary GLMs, $R^q$ is just multiplied by a constant.
Dropout in logistic regression has the same feature as additive noise plus selective exclusion of features: given a training sample $x_{i}$, $\beta _{j}$ is not penalized if $x_{i j} = 0$. In particular $p_{i} (1 - p_{i})$ and $\beta _{j}$ may both be large if the cross-term $x_{i j}^2$ is small. This means that
(…) dropout regularization should be better than $L^2$-regularization for learning weights for features that are rare (i.e., often 0) but highly discriminative, because dropout effectively does not penalize $j$ over observations for which $x_{i j} = 0$.
And
dropout rewards those features that are rare and positively co-adapted with other features in a way that enables the model to make confident predictions whenever the feature of interest is active.
In the more general case the insight comes from the fact that
$\tfrac{1}{n} X^{\top} V (\beta^{\star}) X = \tfrac{1}{n} \sum_{i = 1}^n \nabla^2 l (\beta^{\star} ; x_{i}, y_{i})$
is an estimator of the Fisher information matrix $\mathcal{I}$. Therefore if we write $\beta^{\top} \operatorname{diag} (X^{\top} V (\beta) X) \beta = \beta^{\top}D \beta = | D^{1 / 2} \beta |_{2}^2 = | \tilde{\beta} |_{2}^2$ we see that dropout is applying an $L^2$ penalty after normalizing with an approximation of $\operatorname{diag} (\mathcal{I})^{- 1 / 2}$.
The Fisher information is linked to the shape of the level surfaces of $l (\beta)$ around $\beta^{\star}$. If $\mathcal{I}$ were a multiple of the identity matrix, then these level surfaces would be perfectly spherical around $\beta^{\star}$.
By normalizing, the feature space is deformed into a shape where “the features have been balanced out”.9 The authors provide a very nice picture for intuition:
(page 11 in the Appendix)In both cases, the black solid ellipses are level surfaces of the likelihood and the blue dashed curves are level surfaces of the regularizer; the optimum of the regularized objective is denoted by OPT. The left panel shows a classic spherical $L^2$ regular izer $| \beta |_{2}^2$, whereas the right panel has an $L^2$ regularizer $\beta^{\top} \operatorname{diag}(\mathcal{I}) \beta$ that has been adapted to the shape of the likelihood ($\mathcal{I}$ is the Fisher information matrix). The second regularizer is still aligned with the axes, but the relative importance of each axis is now scaled using the curvature of the likelihood function. As argued [above], dropout training is comparable to the setup depicted in the right panel.
By rewriting standard SGD into an iterative solution of linear $L^2$-penalized problems
$\hat{\beta}_{t + 1} = \operatorname{argmin}_{\beta} \left \lbrace l (\hat{\beta}_{t} ; x_{t}, y_{t}) + \nabla l (\hat{\beta}_{t}) (\beta - \hat{\beta}_{t}) + \frac{1}{2 \eta _{t}} | \beta - \hat{\beta}_{t} |_{2}^2 \right \rbrace$
and substituting the dropout penalty for the penalty in this formulation, one obtains the update rule
$\hat{\beta}_{t + 1} =\operatorname{argmin}_{\beta} \left \lbrace l (\hat{\beta}_{t} ; x_{t}, y_{t}) + g_{t} (\beta - \hat{\beta}_{t}) + R^q (\beta - \hat{\beta}_{t} ; \hat{\beta}_{t}) \right \rbrace$
with the centered quadratic dropout penalty, similarly to the entry in Table 1:
$R^q (\beta - \hat{\beta}_{t} ; \hat{\beta}_{t}) = (\beta - \hat{\beta}_{t})^{\top} \operatorname{diag} (X^{\top} V (\hat{\beta}_{t}) X) (\beta - \hat{\beta}_{t}) .$
This is effectively solving the problem of SGD has learning weights for “rare but highly discriminative features”, by using the update
$\hat{\beta}_{t + 1} = \hat{\beta}_{t} - \eta _{t} A_{t}^{- 1} \nabla l (\hat{\beta}_{t}) .$
AdaGrad10 uses $A_{t} =\operatorname{diag} (\nabla^{\top} l (\hat{\beta}_{t}) \nabla l(\hat{\beta}_{t}))^{- 1 / 2}$, warping the gradient by some sort of intrinsic metric, whereas dropout uses its estimate of the Fisher information.11 However, in the limit $\hat{\beta}_{t} \rightarrow \beta^{\star}$ for GLMs the expectations of both matrices are equal to $\mathcal{I}$, meaning that the SGD updates when using feature dropout in GLMs are “converging” in some sense to AdaGrad updates.
As we said above, the dropout regularizer is shown to change the loss function with the Fisher information matrix in a way that focuses on weights relevant for discriminative features, without recourse to the labels $y_{i}$. Therefore in a semi-supervised context, we can use unlabeled data to improve the regularizer:
$R_{\ast} (\beta) := \frac{n}{n + \alpha m} \left( R (\beta) + \alpha R_{\text{unlabeled}} (\beta) \right),$
where $n$ is the size of the labeled dataset, $m$ that of the unlabeled one and $\alpha$ a “discount factor” for the latter which is a hyperparameter. Unlike other semi-supervised approaches relying on generative models, the authors’ approach
is based on a different intuition: we’d like to set weights to make confident predictions on unlabeled data as well as the labeled data, an intuition shared by entropy regularization [24] and transductive SVMs [25].
1. See .
2. See , The Dropout Learning Algorithm, Baldi, P. , Sadowski, P. (2014) .
3. See Adaptive Subgradient Methods for Online Learning and Stochastic Optimization, Duchi, J. , Hazan, E. , Singer, Y. (2011) .
4. Recall that in a GLM one uses a so-called link function $h$ to relate a linear predictor $x \beta$ with the posterior $p (y|x)$ by means of the relationship $\mathbb{E} [y|x] = h^{- 1} (x \beta)$. In our notation, $h = A’$. To fix ideas think of logistic regression, where $p (y|x) = (1 + \mathrm{e}^{- x \beta})^{- 1}$. In this case we assume $y \in \lbrace 0, 1 \rbrace$, the log likelihood is $p (\boldsymbol{y}|\boldsymbol{x}) = \prod_{i} p_{i}^{y_{i}} (1 -p_{i})^{1 - y_{i}}$, with $p_{i} := (1 + \mathrm{e}^{- x_{i} \beta})^{- 1}$ and the negative log likelihood is the cross entropy loss: $\log p (y|x) = - \sum_{i} y_{i} \log p_{i} + (1 - y_{i}) \log (1 -p_{i})$.
5. Indeed $A (\tilde{x} \beta) - A (x \beta) = A’ (x \beta) (\tilde{x} \beta - x \beta)+ \frac{1}{2} A” (x \beta) (\tilde{x} \beta - x \beta)^2 + \text{h.o.t.}$ and taking expectations: $\mathbb{E}_{\xi} [A (\tilde{x} \beta)] - A (x \beta) = A’ (x \beta) (\mathbb{E} [\tilde{x} \beta] - x \beta) + \frac{1}{2} A” (x \beta)\mathbb{E} (\tilde{x} \beta - x \beta)^2 + \text{h.o.t}$.
6. There is a handwavy discussion in the paper on the error $| R - R^q |$ which is not worth discussing here. Suffice to say: it works “well” in practice.
7. Here $\odot$ stands for the entrywise or Hadamard product.
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2019-01-20 17:59:21
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https://blogs.msdn.microsoft.com/buckh/2012/01/21/a-tool-to-find-duplicate-copies-in-a-build/
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# A tool to find duplicate copies in a build
As part of our builds, quite a few projects copy files to the binaries directory or other locations. These can be anything from image files to test scripts. To have our builds complete more quickly, we use the multi-process option (/maxcpucount) of msbuild to build projects in parallel.
This all sounds normal, so what’s the problem? In a large team, people will sometimes inadvertently add statements to different project files that copy files to the same destination. When those project files have no references to each other, directly or indirectly, msbuild may build them in parallel. If it does happen to run those projects in parallel on different nodes and the copies happen at the same time, the build breaks because one copy succeeds and one fails. Since the timing is not going to be the same on every build, the result is random build breaks. Build breaks suck. They drain the productivity of the team and are frustrating.
Whether the build is continuous integration or gated checkin, these breaks may happen randomly. They are most likely to happen on incremental builds where the percentage of time spent during the build on doing copies is much higher than a clean build. Tracking them down as they happen is painful.
So, I wrote a simple tool to find cases in the log where the destination is the same for more than one copy operation. The comment in the header explains what the code is looking for. Running this on the normal verbosity msbuild logs from a clean build ensures that all of the copies are in the log for analysis. We also build what we call partitions separately, resulting in the number of log files being a multiple of the number of partitions being built (a partition is a subset of the source and is typically a top-level directory in the branch).
In our internal builds, we record multiple log files for our builds, including minimal, normal, and detailed. When there’s a problem, you can start with the smaller build logs and increase to the more verbose logging as needed.
I’m posting this for any of you who might run into the same thing. Keep in mind that there are other things, such as antivirus software, that can interfere with the build process and result in errors for files being copied.
using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Text.RegularExpressions;
/*
* This tool finds cases where more than one file is copied to the same target. This will cause
* build breaks when msbuild executes the copies in parallel because the copies are independent
* (there are no dependencies). This typically occurs in incremental builds because incremental
* builds do a lot less work (not nearly as much to build), resulting in the copies being a much
* higher percentage of the build activities and more likely to collide. Gated checkin,
* continuous integration, and developer/tester builds are almost always incremental, not clean.
* These issues are still possible in regular clean builds, such as done nightly by the build lab.
*
* These race conditions are difficult to debug manually. Since msbuild records all of the copies
* made via the copy task, we can use the log file to identify cases where the same destination
* path is used in more than one copy.
*
* Use the *.normal.* logs from a clean build with this tool.
*
* The best thing to do is to ensure that each file copy to a particular destination is done by
* one and only one project. When that is the case, you are guaranteed not to have problems
* with two copies colliding and breaking your build.
*
* Here's example output from buildr.suitesrc.normal.log that shows a copy failure. Here two
* copies were executed in parallel and the second one failed, causing the build to fail.
*
55>_CopyOutOfDateSourceItemsToOutputDirectory:
Copying file from "D:\a1\dd\alm\tfs_core\Admin\Servicing\Data\ReleaseManifest.xml" to "D:\a1\binaries.x86ret\bin\i386\ReleaseManifest.xml".
53>_CopyOutOfDateSourceItemsToOutputDirectory:
Copying file from "D:\a1\dd\alm\tfs_core\Admin\Servicing\Data\ReleaseManifest.xml" to "D:\a1\binaries.x86ret\bin\i386\ReleaseManifest.xml".
*
* Note that there may be multiple copies in a sequence.
*
291>_CopyOutOfDateSourceItemsToOutputDirectoryAlways:
Copying file from "D:\a1\dd\suitesrc\TFS\common\deploytools\httpcfg.exe" to "D:\a1\binaries.x86ret\SuiteBin\i386\TFS\Tests\httpcfg.exe".
Copying file from "D:\a1\dd\suitesrc\TFS\common\deploytools\makecert.exe" to "D:\a1\binaries.x86ret\SuiteBin\i386\TFS\Tests\makecert.exe".
Copying file from "D:\a1\dd\suitesrc\TFS\common\deploytools\winhttpcertcfg.exe" to "D:\a1\binaries.x86ret\SuiteBin\i386\TFS\Tests\winhttpcertcfg.exe".
CopyFilesToOutputDirectory:
Copying file from "D:\int\641\194\suitesrc\tfshttpsconfig.csproj_80399372\objr\x86\TfsHttpsConfig.exe" to "D:\a1\binaries.x86ret\SuiteBin\i386\TFS\Tests\TfsHttpsConfig.exe".
* Nodes are reused by msbuild. The result is that a given may process many projects, so it's not
* possible to scan and pair up all of the nodes and project files at once. In the code below,
* you will see that it always tracks the most recent node for that reason.
*
*/
{
class Program
{
static void Main(string[] args)
{
if (args.Length < 1)
{
Console.WriteLine(
@"This tool scans a build log, such as buildr.suitesrc.normal.log, and produces a
list of file paths that are the targets of more than one copy and shows which
project files initiated each copy. These redundant file copies are prone to
fail periodically in incremental builds, such as gated check ins and CI builds,
because copies are a higher percentage of the operations in the build, making
it more likely that two collide.");
return;
}
ProcessFile(args[0]);
}
private static void ProcessFile(String fileName)
{
Dictionary<int, String> nodeTable = new Dictionary<int, String>(1000);
Dictionary<String, int> pathTable = new Dictionary<String, int>(1000, StringComparer.InvariantCultureIgnoreCase);
String previousLine;
// Process all of the lines in the file, skipping the first line (we need the previous line,
// and the first line in the file isn't important to this tool).
int lastNode = 0;
for (int i = 1; i < text.Length; i++)
{
previousLine = text[i - 1];
// Record most recent node. The text that appears with it can be different
// (see sample log data).
string prevLinePattern = @"([0-9]+)[>]";
Match match = Regex.Match(previousLine, prevLinePattern, RegexOptions.IgnoreCase);
if (match.Success)
{
lastNode = Int32.Parse(match.Groups[1].Value);
}
// If the line is recording the start of a project, add it to the table.
string pattern = @"[0-9]+[>]Project ""[^""]+"" $$[0-9]+$$ is building ""([^""]+)"" $$([0-9]+)$$";
match = Regex.Match(text[i], pattern, RegexOptions.IgnoreCase);
if (match.Success)
{
int node = Int32.Parse(match.Groups[2].Value);
String projectPath = Path.GetFullPath(match.Groups[1].Value);
// Because nodes are reused, we are only keeping the project path for the most recent use
// of a given node.
nodeTable[node] = projectPath;
// If we matched a project line, it can't be a copy line.
continue;
}
// If the line is one that records a copy, see if there was an earlier copy made to
// the same target path. First, try the output of a copying task.
string copyingPattern = @"Copying file from ""[^""]+"" to ""([^""]+)""";
match = Regex.Match(text[i], copyingPattern, RegexOptions.IgnoreCase);
if (match.Success)
{
String targetPath = null;
try
{
targetPath = Path.GetFullPath(match.Groups[1].Value);
}
catch (Exception e)
{
// There is a file in the test tree that uses non-English chars that causes
// GetFullPath() to throw (TODO: understand why), so we keep the raw text.
// Console.WriteLine(match.Groups[1].Value);
targetPath = match.Groups[1].Value;
}
// If we have already seen the target path, then we have a duplicate copy path
// target to report.
int otherNode;
if (pathTable.TryGetValue(targetPath, out otherNode))
{
Console.ForegroundColor = ConsoleColor.Cyan;
Console.WriteLine("{0}", targetPath);
Console.ResetColor();
Console.WriteLine(" {0}", nodeTable[otherNode]);
Console.WriteLine(" {0}", nodeTable[lastNode]);
Console.WriteLine();
}
pathTable[targetPath] = lastNode;
}
}
}
}
}
Tags
|
2017-04-24 09:26:40
|
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|
http://orbi.ulg.ac.be/browse?type=author&value=Mennesson%2C+B
|
References of "Mennesson, B" in Complete repository Arts & humanities Archaeology Art & art history Classical & oriental studies History Languages & linguistics Literature Performing arts Philosophy & ethics Religion & theology Multidisciplinary, general & others Business & economic sciences Accounting & auditing Production, distribution & supply chain management Finance General management & organizational theory Human resources management Management information systems Marketing Strategy & innovation Quantitative methods in economics & management General economics & history of economic thought International economics Macroeconomics & monetary economics Microeconomics Economic systems & public economics Social economics Special economic topics (health, labor, transportation…) Multidisciplinary, general & others Engineering, computing & technology Aerospace & aeronautics engineering Architecture Chemical engineering Civil engineering Computer science Electrical & electronics engineering Energy Geological, petroleum & mining engineering Materials science & engineering Mechanical engineering Multidisciplinary, general & others Human health sciences Alternative medicine Anesthesia & intensive care Cardiovascular & respiratory systems Dentistry & oral medicine Dermatology Endocrinology, metabolism & nutrition Forensic medicine Gastroenterology & hepatology General & internal medicine Geriatrics Hematology Immunology & infectious disease Laboratory medicine & medical technology Neurology Oncology Ophthalmology Orthopedics, rehabilitation & sports medicine Otolaryngology Pediatrics Pharmacy, pharmacology & toxicology Psychiatry Public health, health care sciences & services Radiology, nuclear medicine & imaging Reproductive medicine (gynecology, andrology, obstetrics) Rheumatology Surgery Urology & nephrology Multidisciplinary, general & others Law, criminology & political science Civil law Criminal law & procedure Criminology Economic & commercial law European & international law Judicial law Metalaw, Roman law, history of law & comparative law Political science, public administration & international relations Public law Social law Tax law Multidisciplinary, general & others Life sciences Agriculture & agronomy Anatomy (cytology, histology, embryology...) & physiology Animal production & animal husbandry Aquatic sciences & oceanology Biochemistry, biophysics & molecular biology Biotechnology Entomology & pest control Environmental sciences & ecology Food science Genetics & genetic processes Microbiology Phytobiology (plant sciences, forestry, mycology...) Veterinary medicine & animal health Zoology Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences Chemistry Earth sciences & physical geography Mathematics Physics Space science, astronomy & astrophysics Multidisciplinary, general & others Social & behavioral sciences, psychology Animal psychology, ethology & psychobiology Anthropology Communication & mass media Education & instruction Human geography & demography Library & information sciences Neurosciences & behavior Regional & inter-regional studies Social work & social policy Sociology & social sciences Social, industrial & organizational psychology Theoretical & cognitive psychology Treatment & clinical psychology Multidisciplinary, general & others Showing results 1 to 20 of 27 1 2 Overview of LBTI: a multipurpose facility for high spatial resolution observationsHinz, P. M.; Defrere, Denis ; Skemer, A. et alin Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (2016, August 01)The Large Binocular Telescope Interferometer (LBTI) is a high spatial resolution instrument developed for coherent imaging and nulling interferometry using the 14.4 m baseline of the 2×8.4 m LBT. The ... [more ▼]The Large Binocular Telescope Interferometer (LBTI) is a high spatial resolution instrument developed for coherent imaging and nulling interferometry using the 14.4 m baseline of the 2×8.4 m LBT. The unique telescope design, comprising of the dual apertures on a common elevation-azimuth mount, enables a broad use of observing modes. The full system is comprised of dual adaptive optics systems, a near-infrared phasing camera, a 1-5 μm camera (called LMIRCam), and an 8-13 μm camera (called NOMIC). The key program for LBTI is the Hunt for Observable Signatures of Terrestrial planetary Systems (HOSTS), a survey using nulling interferometry to constrain the typical brightness from exozodiacal dust around nearby stars. Additional observations focus on the detection and characterization of giant planets in the thermal infrared, high spatial resolution imaging of complex scenes such as Jupiter's moon, Io, planets forming in transition disks, and the structure of active Galactic Nuclei (AGN). Several instrumental upgrades are currently underway to improve and expand the capabilities of LBTI. These include: Improving the performance and limiting magnitude of the parallel adaptive optics systems; quadrupling the field of view of LMIRcam (increasing to 20"x20"); adding an integral field spectrometry mode; and implementing a new algorithm for path length correction that accounts for dispersion due to atmospheric water vapor. We present the current architecture and performance of LBTI, as well as an overview of the upgrades. [less ▲]Detailed reference viewed: 11 (1 ULg) Enabling the direct detection of earth-sized exoplanets with the LBTI HOSTS project: a progress reportDanchi, W.; Bailey, V.; Bryden, G. et alin Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (2016, August 01)NASA has funded a project called the Hunt for Observable Signatures of Terrestrial Systems (HOSTS) to survey nearby solar type stars to determine the amount of warm zodiacal dust in their habitable zones ... [more ▼]NASA has funded a project called the Hunt for Observable Signatures of Terrestrial Systems (HOSTS) to survey nearby solar type stars to determine the amount of warm zodiacal dust in their habitable zones. The goal is not only to determine the luminosity distribution function but also to know which individual stars have the least amount of zodiacal dust. It is important to have this information for future missions that directly image exoplanets as this dust is the main source of astrophysical noise for them. The HOSTS project utilizes the Large Binocular Telescope Interferometer (LBTI), which consists of two 8.4-m apertures separated by a 14.4-m baseline on Mt. Graham, Arizona. The LBTI operates in a nulling mode in the mid-infrared spectral window (8-13 μm), in which light from the two telescopes is coherently combined with a 180 degree phase shift between them, producing a dark fringe at the location of the target star. In doing so the starlight is greatly reduced, increasing the contrast, analogous to a coronagraph operating at shorter wavelengths. The LBTI is a unique instrument, having only three warm reflections before the starlight reaches cold mirrors, giving it the best photometric sensitivity of any interferometer operating in the mid-infrared. It also has a superb Adaptive Optics (AO) system giving it Strehl ratios greater than 98% at 10 μm. In 2014 into early 2015 LBTI was undergoing commissioning. The HOSTS project team passed its Operational Readiness Review (ORR) in April 2015. The team recently published papers on the target sample, modeling of the nulled disk images, and initial results such as the detection of warm dust around η Corvi. Recently a paper was published on the data pipeline and on-sky performance. An additional paper is in preparation on β Leo. We will discuss the scientific and programmatic context for the LBTI project, and we will report recent progress, new results, and plans for the science verification phase that started in February 2016, and for the survey. [less ▲]Detailed reference viewed: 24 (0 ULg) Nulling Data Reduction and On-sky Performance of the Large Binocular Telescope InterferometerDefrere, Denis ; Hinz, P. M.; Mennesson, B. et alin Astrophysical Journal (2016), 824The Large Binocular Telescope Interferometer (LBTI) is a versatile instrument designed for high angular resolution and high-contrast infrared imaging (1.5-13 μm). In this paper, we focus on the mid ... [more ▼]The Large Binocular Telescope Interferometer (LBTI) is a versatile instrument designed for high angular resolution and high-contrast infrared imaging (1.5-13 μm). In this paper, we focus on the mid-infrared (8-13 μm) nulling mode and present its theory of operation, data reduction, and on-sky performance as of the end of the commissioning phase in 2015 March. With an interferometric baseline of 14.4 m, the LBTI nuller is specifically tuned to resolve the habitable zone of nearby main-sequence stars, where warm exozodiacal dust emission peaks. Measuring the exozodi luminosity function of nearby main-sequence stars is a key milestone to prepare for future exo-Earth direct imaging instruments. Thanks to recent progress in wavefront control and phase stabilization, as well as in data reduction techniques, the LBTI demonstrated in 2015 February a calibrated null accuracy of 0.05% over a 3 hr long observing sequence on the bright nearby A3V star β Leo. This is equivalent to an exozodiacal disk density of 15-30 zodi for a Sun-like star located at 10 pc, depending on the adopted disk model. This result sets a new record for high-contrast mid-infrared interferometric imaging and opens a new window on the study of planetary systems. [less ▲]Detailed reference viewed: 33 (13 ULg) Models of the η Corvi Debris Disk from the Keck Interferometer, Spitzer, and HerschelLebreton, J.; Beichman, C.; Bryden, G. et alin Astrophysical Journal (2016), 817Debris disks are signposts of analogs to small-body populations of the solar system, often, however, with much higher masses and dust production rates. The disk associated with the nearby star η Crv is ... [more ▼]Debris disks are signposts of analogs to small-body populations of the solar system, often, however, with much higher masses and dust production rates. The disk associated with the nearby star η Crv is especially striking, as it shows strong mid- and far-infrared excesses despite an age of ∼1.4 Gyr. We undertake constructing a consistent model of the system that can explain a diverse collection of spatial and spectral data. We analyze Keck Interferometer Nuller measurements and revisit Spitzer and additional spectrophotometric data, as well as resolved Herschel images, to determine the dust spatial distribution in the inner exozodi and in the outer belt. We model in detail the two-component disk and the dust properties from the sub-AU scale to the outermost regions by fitting simultaneously all measurements against a large parameter space. The properties of the cold belt are consistent with a collisional cascade in a reservoir of ice-free planetesimals at 133 AU. It shows marginal evidence for asymmetries along the major axis. KIN enables us to establish that the warm dust consists of a ring that peaks between 0.2 and 0.8 AU. To reconcile this location with the ∼400 K dust temperature, very high albedo dust must be invoked, and a distribution of forsterite grains starting from micron sizes satisfies this criterion, while providing an excellent fit to the spectrum. We discuss additional constraints from the LBTI and near-infrared spectra, and we present predictions of what James Webb Space Telescope can unveil about this unusual object and whether it can detect unseen planets. [less ▲]Detailed reference viewed: 12 (3 ULg) Simultaneous Water Vapor and Dry Air Optical Path Length Measurements and Compensation with the Large Binocular Telescope InterferometerDefrere, Denis ; Hinz, P.; Downey, E. et alin Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (2016)The Large Binocular Telescope Interferometer uses a near-infrared camera to measure the optical path length variations between the two AO-corrected apertures and provide high-angular resolution ... [more ▼]The Large Binocular Telescope Interferometer uses a near-infrared camera to measure the optical path length variations between the two AO-corrected apertures and provide high-angular resolution observations for all its science channels (1.5-13 microns). There is however a wavelength dependent component to the atmospheric turbulence, which can introduce optical path length errors when observing at a wavelength different from that of the fringe sensing camera. Water vapor in particular is highly dispersive and its effect must be taken into account for high-precision infrared interferometric observations as described previously for VLTI/MIDI or the Keck Interferometer Nuller. In this paper, we describe the new sensing approach that has been developed at the LBT to measure and monitor the optical path length fluctuations due to dry air and water vapor separately. After reviewing the current performance of the system for dry air seeing compensation, we present simultaneous H-, K-, and N-band observations that illustrate the feasibility of our feedforward approach to stabilize the path length fluctuations seen by the LBTI nuller. [less ▲]Detailed reference viewed: 21 (7 ULg) Exoplanet science with the LBTI: instrument status and plansDefrere, Denis ; Hinz, P.; Skemer, A. et alin Shaklan, Stuart (Ed.) Techniques and Instrumentation for Detection of Exoplanets VII (2015, September 16)The Large Binocular Telescope Interferometer (LBTI) is a strategic instrument of the LBT designed for high-sensitivity, high-contrast, and high-resolution infrared (1.5-13 $\mu$m) imaging of nearby ... [more ▼]The Large Binocular Telescope Interferometer (LBTI) is a strategic instrument of the LBT designed for high-sensitivity, high-contrast, and high-resolution infrared (1.5-13 $\mu$m) imaging of nearby planetary systems. To carry out a wide range of high-spatial resolution observations, it can combine the two AO-corrected 8.4-m apertures of the LBT in various ways including direct (non-interferometric) imaging, coronagraphy (APP and AGPM), Fizeau imaging, non-redundant aperture masking, and nulling interferometry. It also has broadband, narrowband, and spectrally dispersed capabilities. In this paper, we review the performance of these modes in terms of exoplanet science capabilities and describe recent instrumental milestones such as first-light Fizeau images (with the angular resolution of an equivalent 22.8-m telescope) and deep interferometric nulling observations. [less ▲]Detailed reference viewed: 37 (10 ULg) First-light LBT Nulling Interferometric Observations: Warm Exozodiacal Dust Resolved within a Few AU of eta CrvDefrere, Denis ; Hinz, P. M.; Skemer, A. J. et alin Astrophysical Journal (2015), 799We report on the first nulling interferometric observations with the Large Binocular Telescope Interferometer (LBTI), resolving the N' band (9.81-12.41 μm) emission around the nearby main-sequence star η ... [more ▼]We report on the first nulling interferometric observations with the Large Binocular Telescope Interferometer (LBTI), resolving the N' band (9.81-12.41 μm) emission around the nearby main-sequence star η Crv (F2V, 1-2 Gyr). The measured source null depth amounts to 4.40% ± 0.35% over a field-of-view of 140 mas in radius (~2.6 AU for the distance of η Crv) and shows no significant variation over 35° of sky rotation. This relatively low null is unexpected given the total disk to star flux ratio measured by the Spitzer Infrared Spectrograph (IRS; ~23% across the N' band), suggesting that a significant fraction of the dust lies within the central nulled response of the LBTI (79 mas or 1.4 AU). Modeling of the warm disk shows that it cannot resemble a scaled version of the solar zodiacal cloud unless it is almost perpendicular to the outer disk imaged by Herschel. It is more likely that the inner and outer disks are coplanar and the warm dust is located at a distance of 0.5-1.0 AU, significantly closer than previously predicted by models of the IRS spectrum (~3 AU). The predicted disk sizes can be reconciled if the warm disk is not centrosymmetric, or if the dust particles are dominated by very small grains. Both possibilities hint that a recent collision has produced much of the dust. Finally, we discuss the implications for the presence of dust for the distance where the insolation is the same as Earth's (2.3 AU). [less ▲]Detailed reference viewed: 30 (10 ULg) Constraining the Exozodiacal Luminosity Function of Main-sequence Stars: Complete Results from the Keck Nuller Mid-infrared SurveysMennesson, B.; Millan-Gabet, R.; Serabyn, E. et alin Astrophysical Journal (2014), 797Forty-seven nearby main-sequence stars were surveyed with the Keck Interferometer mid-infrared Nulling instrument (KIN) between 2008 and 2011, searching for faint resolved emission from exozodiacal dust ... [more ▼]Forty-seven nearby main-sequence stars were surveyed with the Keck Interferometer mid-infrared Nulling instrument (KIN) between 2008 and 2011, searching for faint resolved emission from exozodiacal dust. Observations of a subset of the sample have already been reported, focusing essentially on stars with no previously known dust. Here we extend this previous analysis to the whole KIN sample, including 22 more stars with known near- and/or far-infrared excesses. In addition to an analysis similar to that of the first paper of this series, which was restricted to the 8-9 mum spectral region, we present measurements obtained in all 10 spectral channels covering the 8-13 mum instrumental bandwidth. Based on the 8-9 mum data alone, which provide the highest signal-to-noise measurements, only one star shows a large excess imputable to dust emission (eta Crv), while four more show a significant (>3sigma) excess: beta Leo, beta UMa, zeta Lep, and gamma Oph. Overall, excesses detected by KIN are more frequent around A-type stars than later spectral types. A statistical analysis of the measurements further indicates that stars with known far-infrared (lambda >= 70 mum) excesses have higher exozodiacal emission levels than stars with no previous indication of a cold outer disk. This statistical trend is observed regardless of spectral type and points to a dynamical connection between the inner (zodi-like) and outer (Kuiper-Belt-like) dust populations. The measured levels for such stars are clustering close to the KIN detection limit of a few hundred zodis and are indeed consistent with those expected from a populat [less ▲]Detailed reference viewed: 24 (8 ULg) Fundamental Limitations of High Contrast Imaging Set by Small Sample StatisticsMawet, D.; Milli, J.; Wahhaj, Z. et alin Astrophysical Journal (2014), 792In this paper, we review the impact of small sample statistics on detection thresholds and corresponding confidence levels (CLs) in high-contrast imaging at small angles. When looking close to the star ... [more ▼]In this paper, we review the impact of small sample statistics on detection thresholds and corresponding confidence levels (CLs) in high-contrast imaging at small angles. When looking close to the star, the number of resolution elements decreases rapidly toward small angles. This reduction of the number of degrees of freedom dramatically affects CLs and false alarm probabilities. Naively using the same ideal hypothesis and methods as for larger separations, which are well understood and commonly assume Gaussian noise, can yield up to one order of magnitude error in contrast estimations at fixed CL. The statistical penalty exponentially increases toward very small inner working angles. Even at 5-10 resolution elements from the star, false alarm probabilities can be significantly higher than expected. Here we present a rigorous statistical analysis that ensures robustness of the CL, but also imposes a substantial limitation on corresponding achievable detection limits (thus contrast) at small angles. This unavoidable fundamental statistical effect has a significant impact on current coronagraphic and future high-contrast imagers. Finally, the paper concludes with practical recommendations to account for small number statistics when computing the sensitivity to companions at small angles and when exploiting the results of direct imaging planet surveys. [less ▲]Detailed reference viewed: 42 (9 ULg) L'-band AGPM vector vortex coronagraph's first light on LBTI/LMIRCamDefrere, Denis ; Absil, Olivier ; Hinz, P. et alin Proceedings of SPIE - The International Society for Optical Engineering (2014, July 21)We present the first observations obtained with the L'-band AGPM vortex coronagraph recently installed on LBTI/LMIRCam. The AGPM (Annular Groove Phase Mask) is a vector vortex coronagraph made from ... [more ▼]We present the first observations obtained with the L'-band AGPM vortex coronagraph recently installed on LBTI/LMIRCam. The AGPM (Annular Groove Phase Mask) is a vector vortex coronagraph made from diamond subwavelength gratings. It is designed to improve the sensitivity and dynamic range of high-resolution imaging at very small inner working angles, down to 0.09 arcseconds in the case of LBTI/LMIRCam in the L' band. During the first hours on sky, we observed the young A5V star HR8799 with the goal to demonstrate the AGPM performance and assess its relevance for the ongoing LBTI planet survey (LEECH). Preliminary analyses of the data reveal the four known planets clearly at high SNR and provide unprecedented sensitivity limits in the inner planetary system (down to the diffraction limit of 0.09 arcseconds). © 2014 SPIE. [less ▲]Detailed reference viewed: 33 (8 ULg) Co-phasing the Large Binocular Telescope: status and performance of LBTI/PHASECamDefrere, Denis ; Hinz, P.; Downey, E. et alin Optical and Infrared Interferometry IV (2014, July 01)The Large Binocular Telescope Interferometer is a NASA-funded nulling and imaging instrument designed to coherently combine the two 8.4-m primary mirrors of the LBT for high-sensitivity, high-contrast ... [more ▼]The Large Binocular Telescope Interferometer is a NASA-funded nulling and imaging instrument designed to coherently combine the two 8.4-m primary mirrors of the LBT for high-sensitivity, high-contrast, and highresolution infrared imaging (1.5-13 μm). PHASECam is LBTI's near-infrared camera used to measure tip-tilt and phase variations between the two AO-corrected apertures and provide high-angular resolution observations. We report on the status of the system and describe its on-sky performance measured during the first semester of 2014. With a spatial resolution equivalent to that of a 22.8-meter telescope and the light-gathering power of single 11.8-meter mirror, the co-phased LBT can be considered to be a forerunner of the next-generation extremely large telescopes (ELT). [less ▲]Detailed reference viewed: 36 (11 ULg) The LBTI hunt for observable signatures of terrestrial systems (HOSTS) survey: a key NASA science program on the road to exoplanet imaging missionsDanchi, W.; Bailey, V.; Bryden, G. et alin Optical and Infrared Interferometry IV (2014, July 01)The Hunt for Observable Signatures of Terrestrial planetary Systems (HOSTS) program on the Large Binocular Telescope Interferometer (LBTI) will survey nearby stars for faint exozodiacal dust (exozodi ... [more ▼]The Hunt for Observable Signatures of Terrestrial planetary Systems (HOSTS) program on the Large Binocular Telescope Interferometer (LBTI) will survey nearby stars for faint exozodiacal dust (exozodi). This warm circumstellar dust, analogous to the interplanetary dust found in the vicinity of the Earth in our own system, is produced in comet breakups and asteroid collisions. Emission and/or scattered light from the exozodi will be the major source of astrophysical noise for a future space telescope aimed at direct imaging and spectroscopy of terrestrial planets (exo- Earths) around nearby stars. About 20% of nearby field stars have cold dust coming from planetesimals at large distances from the stars (Eiroa et al. 2013, A&A, 555, A11; Siercho et al. 2014, ApJ, 785, 33). Much less is known about exozodi; current detection limits for individual stars are at best ~ 500 times our solar system's level (aka. 500 zodi). LBTI-HOSTS will be the first survey capable of measuring exozodi at the 10 zodi level (3σ). Detections of warm dust will also reveal new information about planetary system architectures and evolution. We will describe the motivation for the survey and progress on target selection, not only the actual stars likely to be observed by such a mission but also those whose observation will enable sensible extrapolations for stars that will not be observed with LBTI. We briefly describe the detection of the debris disk around η Crv, which is the first scientific result from the LBTI coming from the commissioning of the instrument in December 2013, shortly after the first time the fringes were stabilized. [less ▲]Detailed reference viewed: 17 (1 ULg) The Hunt for Observable Signatures of Terrestrial Planetary Systems (HOSTS)Defrere, Denis ; Hinz, P.; Bryden, G. et alConference (2014, March)The presence of large amounts of exozodiacal dust around nearby main sequence stars is considered as a potential threat for the direct imaging of Earth-like exoplanets and, hence, the search for ... [more ▼]The presence of large amounts of exozodiacal dust around nearby main sequence stars is considered as a potential threat for the direct imaging of Earth-like exoplanets and, hence, the search for biosignatures (Roberge et al. 2012). However, it is also considered as a signpost for the presence of terrestrial planets that might be hidden in the dust disk (Stark and Kuchner 2008). Characterizing exozodiacal dust around nearby sequence stars is therefore a crucial step toward one of the main goals of modern astronomy: finding extraterrestrial life. After briefly reviewing the latest results in this field, we present the exozodiacal dust survey on the Large Binocular Telescope Interferometer (LBTI). The survey is called HOSTS and is specifically designed to determine the prevalence and brightness of exozodiacal dust disks with the sensitivity required to prepare for future New Worlds Missions that will image Earth-like exoplanets. To achieve this objective, the LBTI science team has carefully established a balanced list of 50 nearby main-sequence stars that are likely candidates of these missions and/or can be observed with the best instrument performance (see companion abstract by Roberge et al.). Exozodiacal dust disk candidates detected by the Keck Interferometer Nuller will also be observed. The first results of the survey will be presented. To precisely detect exozodiacal dust, the LBTI combines the two 8-m primary mirrors of the LBT using N-band nulling interferometry. Interferometric combination provides the required angular resolution (70-90 mas) to resolve the habitable zone of nearby main sequence stars while nulling is used to subtract the stellar light and reach the required contrast of a few 10-4. A Kband fringe tracker ensures the stability of the null. The current performance of the instrument and the first nulling measurements will be presented. [less ▲]Detailed reference viewed: 20 (3 ULg) L'-band AGPM vector vortex coronagraph's first light on LBTI/LMIRCAMDefrere, Denis ; Absil, Olivier ; Hinz, P. et alPoster (2014, March)We present the first science observations obtained with the L'-band AGPM coronagraph recently installed on LBTI/LMIRCAM. The AGPM (Annular Groove Phase Mask) is a vector vortex coronagraph made from ... [more ▼]We present the first science observations obtained with the L'-band AGPM coronagraph recently installed on LBTI/LMIRCAM. The AGPM (Annular Groove Phase Mask) is a vector vortex coronagraph made from diamond sub-wavelength gratings tuned to the L'-band. It is designed to improve the sensitivity and dynamic range of high-resolution imaging at very small inner working a [less ▲]Detailed reference viewed: 54 (10 ULg) Exozodi disk models for the HOSTS survey on the LBTIWyatt, Mark; Kennedy, G.; Skemer, A. et alin American Astronomical Society Meeting Abstracts #223 (2014, January 01)This poster describes a simple model for exozodiacal emission that was developed to interpret observations of the Hunt for Observable Signatures of Terrestrial planetary Systems (HOSTS) project on the ... [more ▼]This poster describes a simple model for exozodiacal emission that was developed to interpret observations of the Hunt for Observable Signatures of Terrestrial planetary Systems (HOSTS) project on the Large Binocular Telescope Interferometer (LBTI). HOSTS is a NASA-funded key science project using mid-infrared nulling interferometry at the LBTI to seach for faint exozodiacal dust (exozodi) in the habitable zones of nearby stars. The aim was to make a model that includes the fewest possible assumptions, so that it is easy to characterize how choices of model parameters affect what can be inferred from the observations. However the model is also sufficiently complex that it can be compared in a physically meaningful way with the level of dust in the Solar System, and can also be readily used to assess the impact of a detection (or of a non-detection) on the ability of a mission to detect Earth-like planets. Here we describe the model, and apply it to the sample of stars being searched by HOSTS to determine the zodi level (i.e., the number of Solar System zodiacal clouds) that would be needed for a detection for each star in the survey. Particular emphasis is given to our definition of a zodi, and what that means for stars of different luminosity, and a comparison is given between different zodi definitions justifying our final choice. The achievable exozodi levels range from 1-20 zodi for different stars in the prime sample for a 0.01% null depth, with a median level of 2.5 zodi. [less ▲]Detailed reference viewed: 12 (3 ULg) Target Selection for the LBTI Hunt for Observable Signatures of Terrestrial Planetary SystemsWeinberger, Alycia J.; Roberge, A.; Kennedy, G. et alin American Astronomical Society Meeting Abstracts #223 (2014, January 01)The Hunt for Observable Signatures of Terrestrial planetary Systems (HOSTS) on the Large Binocular Telescope Interferometer (LBTI) will survey nearby stars for faint exozodiacal dust (exozodi). About 20 ... [more ▼]The Hunt for Observable Signatures of Terrestrial planetary Systems (HOSTS) on the Large Binocular Telescope Interferometer (LBTI) will survey nearby stars for faint exozodiacal dust (exozodi). About 20% of field stars have cold debris disks created by the collisions and evaporation of planetesimals. Much less is known about warm circumstellar dust, such as that found in the vicinity of the Earth in our own system. This dust is generated in asteroidal collisions and cometary breakups, and current detection limits are at best ~500 times our system's level, i.e. 500 zodi. LBTI-HOSTS will be the first survey capable of measuring exozodi at the 10 zodi level (3σ). Exozodi of this brightness would be the major source of astrophysical noise for a future space telescope aimed at direct imaging and spectroscopy of habitable zone terrestrial planets. Detections of warm dust will also reveal new information about planetary system architectures and evolution. We describe the target star selection by the LBTI Science Team to satisfy the goals of the HOSTS survey -- to fully inform target selection for a future exoEarth mission. We are interested in actual stars likely to be observed by a mission and stars whose observation will enable sensible extrapolations to those stars that cannot be observed. We integrated two approaches to generate the HOSTS target list. The mission-driven approach concentrates on F, G, and K-type stars that are the best targets for future direct observations of exoEarths, thereby providing model-independent “ground truth” dust observations. However, not every potential target of a future exoEarth mission can be observed with LBTI. The sensitivity-driven approach selects targets based only on what exozodi sensitivity could be achieved, without consideration of exoEarth mission constraints. This naturally selects more luminous stars (A and early F-type stars). In both cases, all stars are close enough to Earth such that their habitable zones are resolvable by LBTI and bright enough at N-band (10 μm) to provide excellent sensitivity. We also discuss observational and astrophysical motivations for excluding binaries of certain separations. [less ▲]Detailed reference viewed: 6 (1 ULg) Expanding the CHARA/FLUOR hot disk surveyMennesson, B.; Scott, N.; Ten Brummelaar, T. et alin Journal of Astronomical Instrumentation (2013), 2(2), 1340010Little is presently known about the hot (>300 K) dust component of debris disks surrounding main sequence stars, similar to the zodiacal dust cloud found in the inner solar system.While extensive surveys ... [more ▼]Little is presently known about the hot (>300 K) dust component of debris disks surrounding main sequence stars, similar to the zodiacal dust cloud found in the inner solar system.While extensive surveys have been carried out from space, the majority of detections have surprisingly come from the ground, where near infrared interferometric observations have recently revealed small (∼1%) resolved excesses around a dozen nearby main sequence stars. Most of these results have come from the CHARA array “FLUOR” instrument (Mt. Wilson, CA), which has demonstrated the best sensitivity worldwide so far for this type of studies, and has carried out an initial survey of ∼40 stars. In order to further understand the origin of this “hot dust phenomenon”, we will extend this initial survey to a larger number of stars and lower excess detection limits, i.e. higher visibility accuracy providing higher contrast measurements. To this end, two major instrumental developments are underway at CHARA. The first one aims at improving FLUOR’s sensitivity to a median K-band magnitude limit of 5 (making 200 targets available). The second development is based on a method that we recently developed for accurate (better than 0.1%) null depth measurements of stars, and that can be extended to regular interferometric visibility measurements. [less ▲]Detailed reference viewed: 23 (3 ULg) An interferometric study of the Fomalhaut inner debris disk. III. Detailed models of the exozodiacal disk and its originLebreton, J; van Lieshout, R; Augereau, J-C et alin Astronomy and Astrophysics (2013), 555Context. Debris disks are thought to be extrasolar analogues to the Solar System planetesimal belts. The star Fomalhaut harbors a cold debris belt at 140AU comparable to the Edgeworth-Kuiper belt, as well ... [more ▼]Context. Debris disks are thought to be extrasolar analogues to the Solar System planetesimal belts. The star Fomalhaut harbors a cold debris belt at 140AU comparable to the Edgeworth-Kuiper belt, as well as evidence for a warm dust component, unresolved by single-dish telescopes, that is suspected to be a bright analogue to the Solar System's zodiacal dust. Aims. Interferometric observations obtained with the VLTI/VINCI instrument and the Keck Interferometer Nuller have identi fied near- and mid-infrared excesses attributed respectively to hot and warm exozodiacal dust residing in the inner few AU of the Fomalhaut environment. We aim to characterize the properties of this double inner dust belt and to unveil its origin. Methods.We perform parametric modelling of the exozodiacal disk ("exozodi") using the GRaTer radiative transfer code in order to reproduce the interferometric data, complemented by mid- to far-infrared photometric measurements from Spitzer and Herschel. A detailed treatment of sublimation temperatures is introduced to explore the hot population at the size-dependent sublimation rim. We then use an analytical approach to test successively several source mechanisms for the dust and suspected parent bodies. Results. A good fi t to the multi-wavelength data is found by two distinct dust populations: (1) a population of very small (0.01 to 0.5 µ m) and therefore unbound, hot dust grains con ned in a narrow region ( ~0.1 - 0.3 AU) at the sublimation rim of carbonaceous material; (2) a population of bound grains at 2AU that is protected from sublimation and has a larger mass despite its fainter flux level. We propose that the hot dust is produced by the release of small carbon grains following the disruption of dust aggregates that originate from the warm component. A mechanism such as gas braking is required to further con ne the small grains for long enough. In situ dust production could hardly be ensured for the age of the star and we conclude that the observed amount of dust is triggered by intense dynamical activity. Conclusions. Fomalhaut may be representative of exozodis that are currently being surveyed at near and mid-infrared wavelengths worldwide. We propose a framework for reconciling the "hot exozodi phenomenon" with theoretical constraints: the hot component of Fomalhaut is likely the "tip of the iceberg" as it could derive from the more massive, but fainter, warm dust component residing near the ice line. This inner disk exhibits interesting morphology and can be considered a prime target for future exoplanet research. [less ▲]Detailed reference viewed: 35 (3 ULg) An interferometric study of the Fomalhaut inner debris disk II. Keck Nuller mid-infrared observationsMennesson, B.; Absil, Olivier ; Lebreton, J. et alin Astrophysical Journal (2013), 763We report on high contrast mid-infrared observations of Fomalhaut obtained with the Keck Interferometer Nuller (KIN) showing a small resolved excess over the level expected from the stellar photosphere ... [more ▼]We report on high contrast mid-infrared observations of Fomalhaut obtained with the Keck Interferometer Nuller (KIN) showing a small resolved excess over the level expected from the stellar photosphere. The measured null excess has a mean value of 0.35% +/- 0.10% between 8 and 11 microns and increases from 8 to 13 microns. Given the small field of view of the instrument, the source of this marginal excess must be contained within 2AU of Fomalhaut. This result is reminiscent of previous VLTI K-band observations, which implied the presence of a ~ 0.88% excess, and argued that thermal emission from hot dusty grains located within 6 AU from Fomalhaut was the most plausible explanation. Using a parametric 2D radiative transfer code and a Bayesian analysis, we examine different dust disk structures to reproduce both the near and mid-infrared data simultaneously. While not a definitive explanation of the hot excess of Fomalhaut, our model suggests that the most likely inner few AU disk geometry consists of a two-component structure, with two different and spatially distinct grain populations. The 2 to 11 microns data are consistent with an inner hot ring of very small (~ 10 to 300 nm) carbon-rich grains concentrating around 0.1AU. The second dust population consists of larger grains (size of a few microns to a few tens of microns) located further out in a colder region where regular astronomical silicates could survive, with an inner edge around 1AU. From a dynamical point of view, the presence of the inner concentration of sub-micron sized grains is surprising, as such grains should be expelled from the inner planetary system by radiation pressure within only a few years. This could either point to some inordinate replenishment rates (e.g. many grazing comets coming from an outer reservoir) or to the existence of some braking mechanism preventing the grains from moving out. [less ▲]Detailed reference viewed: 44 (9 ULg) High-contrast Stellar Observations within the Diffraction Limit at the Palomar Hale TelescopeMennesson, B.; Hanot, Charles ; Serabyn, Eugene et alin Astrophysical Journal (2011), 743We report on high-accuracy high-resolution (<20 mas) stellar observations obtained with the Palomar Fiber Nuller (PFN), a near-infrared (sime2.2 μm) interferometric coronagraph installed at the Palomar ... [more ▼]We report on high-accuracy high-resolution (<20 mas) stellar observations obtained with the Palomar Fiber Nuller (PFN), a near-infrared (sime2.2 μm) interferometric coronagraph installed at the Palomar Hale telescope. The PFN uses destructive interference between two elliptical (3 m × 1.5 m) sub-apertures of the primary to reach high dynamic range inside the diffraction limit of the full telescope. In order to validate the PFN's instrumental approach and its data reduction strategy, based on the newly developed "Null Self-Calibration" (NSC) method, we observed a sample of eight well-characterized bright giants and supergiants. The quantity measured is the source astrophysical null depth, or equivalently the object's visibility at the PFN 3.2 m interferometric baseline. For the bare stars α Boo, α Her, β And, and α Aur, PFN measurements are in excellent agreement with previous stellar photosphere measurements from long baseline interferometry. For the mass-losing stars β Peg, α Ori, ρ Per, and χ Cyg, circumstellar emission and/or asymmetries are detected. Overall, these early observations demonstrate the PFN's ability to measure astrophysical null depths below 10[SUP]-2[/SUP] (limited by stellar diameters), with 1 σ uncertainties as low as a few 10[SUP]-4[/SUP]. Such visibility accuracy is unmatched at this spatial resolution in the near-infrared and translates into a contrast better than 10[SUP]-3[/SUP] within the diffraction limit. With further improvements anticipated in 2011/2012, a state-of-the-art infrared science camera and a new extreme adaptive optics system, the PFN should provide a unique tool for the detection of hot debris disks and young self-luminous sub-stellar companions in the immediate vicinity of nearby stars. [less ▲]Detailed reference viewed: 56 (4 ULg) 1 2
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Information on Phd lifestyles...? : Ph.D in Business
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# Information on Phd lifestyles...?
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Manager
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11 Jan 2006, 11:01
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Hi, I've recently become interested in business Phd programs and have been looking for any relevant articles. They can be about any part: admissions, lifestyle while in the program, lifestyle afterward, careers etc. Do you guys know of anything?
Also, I'm curious how students pay for a doctoral program. The university usually provides tuition and a stipend, correct? Can you also be awarded grants from other institutions in addition to university-provided funds?
Thank you very much!
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23 Jan 2006, 05:31
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I heard some kind of book exists to address most of these concerns, but I have no references in mind. Always remember that there are many different fields, all of which have different quality standards/expectations. Some schools will require you to take a lot of theory courses with few (reading) seminars available, while others will require you to read basically everything that's been done before with very few courses in econometrics, microeconomics, optimization.. This is probably why there is no single source of information about life as a Ph.D. student: there are many ways to react to these varying expectations.
But as far as admissions go, if you're looking at a top school (top 25) in a math-intensive field (finance, OR, accounting), a good GMAT score and good grades in some advanced (ideally graduate) statistics/math courses are probably the most important. My personal (unproven) opinion is that if you're looking at marketing, OB or strategy, references and prior research may be weighted more heavily in admission decisions.
As for the financing of a Ph.D. program, the basics for just about every top school are that they waive tuition and pay you a stipend of about $20,000-$25,000/year for 3 or 4 years. Some of them will extend that if you work on promising research (e.g. many finance programs unofficially require 5 years or enrollment). The difference between programs is how they treat additional outside funding you may get. If you get an outside doctoral fellowship, some schools will "tax" you by decreasing the stipend while others will just pat you on the back.
(Disclaimer: I'm a 1st-year accounting student at a top 15-20 school)
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23 Jan 2006, 07:22
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Hi Chapman,
Here is a little info about the PhD in business and some of the qualities of most programs...it was posted before somewhere in here.
http://www.hbs.edu/doctoral/SYOA/
DocNet is an organization of universities granting doctoral degrees in business administration and economics. Its purpose is to promote doctoral education in business throughout the world.
http://www.coba.usf.edu/docnet/
Also, I am applying to PhD programs now and it is hard to find general information about the culture in PhD programs in business.....It almost deadline time for the schools I'm applying to....this forum is an excellent resource for info....I suggest going through some of the older info...there is a lot of good info in the posts from early last year....the same still applies today concerning acceptance, changes in lifestyle, etc. Also, I'm not sure of your "stats", but one thing I see on this forum is that no one really talk about the lower tier schools (which actually, are still some of the best schools in the nation)...although I advise everyone to shoot for the stars...don't rule out the smaller or somewhat newer AACSB accred. PhD business programs. Many schools have excellent professors that have researched topics that may interest you more than at some top 10-15 school...and the key thing is the "fit"...you have to fit into their research and style...without that, you will be a zombie that just do the research for the sake of a grade....and that defeats the purpose of the PhD. So aim high.....but dont forget the little guy either....some people fit in at smaller institutions much better than large ones....so mix your school choices up is my suggestion...have a little of the big boys and little of the medium guys, and a couple scappy little dudes and you have have a better view of what you might fit in at......(sorry about my long rant)
Also because of the popularity and status of MBA programs today...many schools are focusing most of their resources promoting it.... but I am a part of the PhD Project, although it is designed to encourage African Americans, Hispanic Am. and Native Am. to pursue a PhD in business...the website is helpful in locating info concerning the culture of the programs
http://www.phdproject.org
Another thing is to make sure the school AACSB accred. You may already know this....but here is a list of AACSB accred schools with Phd Programs
http://www.aacsb.edu/publications/dfc/phd-schools.asp
Also....here is a site that ranks the doctoral programs worldwide....even though it states EMBA rankings...go through the ranking area options on top and find the one that states "FT Doctoral Rank" click on that and it ranks the best doctoral programs in the world in business...decided by financial times...
http://rankings.ft.com/rankings//index.jsp
Hopefully that will give you a little insight and quite possibly aid your research.
~Christopher~
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26 Jan 2006, 19:03
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Hectic is the word. Discipline and timeliness will matter a lot as you balance your coursework , your research projects and your personal life. You have to very efficient at doing what you do. At most schools, you will very easily be spending 50-60 hrs per week on school. Of course, you should ensure that you hit the ground running. Be sure to review all relevant math coursework in the summer prior to joining school and get to know your colleagues.
Also, even if the professors dont "require" you to read material before coming to class, its usually a great idea to do so. A Ph.D is much more than taking a bunch of courses. The more effort you put into mastering the material, the better off you will be. This could mean an extra 2-4 hrs of reading per course per week. This is on top of the assignments and/or coding.
About paying for school, almost all top schools have decent financial aid packages. Its common for schools to pay your tuition and give you a stipend between $1300-$1800 a month. Some schools also offer to pay for teaching a class. If you teach throughout the year, thats a very nice addition to the stipend.
hope this helps
Praetorian
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26 Jan 2006, 20:34
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thanks a lot Praetorian..good info!...
christopher
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16 Feb 2006, 12:08
I am now in my second year of Phd so it is a good time to answer the lifestyle question.
The first year consists of courses - which are quite different from MBA level courses - the focus being on academic literature, and if you are majoring in a quantitative field - it can get tough mastering proofs of theorems etc. Even for a qualitative field , the first year is quite quanti heavy.
The second year starts a bit light and you focus on developing your research interests. Well, the search is for an idea - an idea that has not been thought of before and that makes sense for business ! tough call. Also an idea that can be researched in 2-3 years.
As Praetorian wrote - self discipline is most important. It is a journey that is long !
LIFE, MONEY etc
The stipend at most schools will not make you rich but you can get by in a very easy way. Many of the top schools guarantee schols for at least 4 years - others ask you for doing a TA or RA (that is teaching or research assistantship - basically uninteresting work). This may make it a little tough.
At most places, PhD is a very lonely journey. There is some camarederie, but do not expect the bonhomie of college. That is mainly due to the fact that PhD class size is very small.
hope this helps
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Just an update , in my third year now.
Out of the starting class size of 12, there are only 9 people left in the 3rd year - 3 have dropped out. Out of the starting class size of 12 in my previous batch, only 7 are left - 5 have dropped out.
Lesson 1. Think whether you really want to spend 4-5 long solitary years. You must have an extremely high level of self-motivation to complete.
Lesson 2. People who left were very good from a CV viewpoint. There were college toppers, consultants ..... all extremely bright. But most of them decided that academia was not for them. Talent is no guarantee for completion.
Well... think before you leap !
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10 Mar 2007, 23:31
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Wow... 3rd year. So half the battle has been won....
What are the main reasons for dropping out? Not able to coup with the work? Better offers came along? etc?
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thanks for sharing Sameer.
I think many students do drop out because better offers come along. 4 years is a long time.
More specifically, here are some reasons I can think of.
1) Some students are interested in research, but do not understand the nuances of what it will entail. Reading journals in the students area of interest is very very important. Also, I think a lot of student underestimate the emphasis that universities place on academic research. You will hear the "Publish or Perish" slogan often in academia. As an academic, you are on the faculty to teach, but high quality research is a primary component of getting tenure.
2) Some unfortunately drop out because they fall short of the academic standards of the institution. This is usually a result of performance on the comprehensive exam, usually conducted after the second year of the program.
3) The rewards are not immediate. Academic research sounds easy. Define the problem, show how your paper contributes to current literature and show that you indeed made those contributions by using models and experiments. However, a typical student fails at the first 2 attempts in writing a paper. A student belongs to one of these three categories.
a) Not good at math, not good at discovering interesting research questions and not good at writing either. This is unlikely, but it does happen. As you can imagine, such students do not stay long in the program.
b) Good at math, not good at discovering interesting research questions, but good at writing. This is probably the average student.
c) Good at math, good at discovering interesting research questions, and good at writing, but the student cannot convert the research question and intended contribution into a model that adequately incorporates the richness of the problem without oversimplifying it. This is probably the standard for a student attempting research for the first time.
If you can get to phase c) by the end of your first year, you are my hero.
4) As Sameer correctly pointed out, it would take a lot of motivation to keep going. 4 years is a long time. Things change. Changes in personal life or professional ambitions can play a very very significant role in such decisions. Most are married and the Ph.D is an acid test for any relationship. For single students, its probably not as difficult, but a supportive spouse can have a dramatic impact as far as keeping your sanity is concerned. It will be a great support system as you navigate through the emotional roller coaster.
5) Others simply find the time commitment too much. It puts a strain on relationships and finances. Most expect to graduate in 4 years. But its no longer enough to graduate. IF you are interested in getting hired to a top school (who isnt?), an acceptance of a journal article at a top journal in the field is fast becoming as important as the Ph.D itself. Very Very exceptional and lucky students can complete this publication "requirement" in 4 years. By exceptional, I mean a student who hits the ground running as far as research is concerned.
If everything goes right, this is what should happen for a student interested in publishing in a top journal.
End of First year - Have a written research proposal ready for the first paper. It is difficult to know what your dissertation topic is going to be right in your first year, but you should make every effort to ensure that this research will form a part of your dissertation. It will help you a lot.
In the Fall/Winter of second year - Complete the paper
In the Spring of second year - present paper at a conference and include it in the conference proceedings. -- A great way to get early feedback on the quality of the paper.
Summer of second year - Incorporate feedback and revise paper. Edit/ Re-edit paper to make it more readable.
In late summer/ early fall - send paper for publication to a top journal.
Early Spring of third year - Accept/ Revise and Resubmit/ Reject decision. Lets make the optimistic case and say "Revise and Resubmit".
Submit revisions by Summer of third year
Late Summer/ Early Fall of 4th year - Decision on paper. (hopefully an accept)
Early Fall - Hopefully, you did not forget about your dissertation that you should have been working on. Defend your dissertation proposal if required by your university BEFORE going on to the job market.
Fall of 4th year- Go on the job market. Preliminary interview with Big Name Schools at conferences. Explain dissertation work.
Spring of 4th year- Hopefully that leads to a campus visit.
Late Spring - Accept job offer.
And all this assumes that you did well on your coursework and passed your comprehensive exams.
You will do yourself a favor by spending as much time as possible preparing yourself before you even begin your Ph.D
Hope this helps.
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11 Mar 2007, 04:12
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Thank you Praetorian. Reading your post has been extremely useful for me.
It seems that the brand of the school in which you pursue your Phd is not so important to get a good placement if you manage to publish on a top journal. Attending a Phd at a certain elite school will not bring you into a top school's faculty by itself, but since such elite school should provide you better training to become a good researcher.
My conclusion is that a strong program (coursework, advisors, environment) is a far more critical success factor than a strong school brand.
CEO
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### Show Tags
11 Mar 2007, 05:33
robbie1981 wrote:
Thank you Praetorian. Reading your post has been extremely useful for me.
It seems that the brand of the school in which you pursue your Phd is not so important to get a good placement if you manage to publish on a top journal. Attending a Phd at a certain elite school will not bring you into a top school's faculty by itself, but since such elite school should provide you better training to become a good researcher.
My conclusion is that a strong program (coursework, advisors, environment) is a far more critical success factor than a strong school brand.
Brand does matter in that there is a strong correlation to the quality of faculty, funding, industry partnerships. However, the Ph.D is the students responsibility. The brand will help you get noticed, but if you cannot publish or are too dependent on your advisor for ideas, it will hurt you.
Expect no one to offer you help in the program. I like to think of the Ph.D as starting your own small business. It is your baby. Expect to do everything from cold-calling your customers to picking up the trash. You will need to survive the first two years. In fact, it is very important that the first two years be challenging. It is very difficult to learn anything new once you start your dissertation or go on to a faculty position. You will be expected to take a lion's share of the responsibility of doing research. The faculty and the univ. do provide a formal support system, but they have a thousand other things to worry about.
Remember that even though it is a 4 year program, you really only have 3 years to prepare yourself for the job market. The 4th year is the time you look at your research, your dissertation and ask yourself if you are ready.
Publishing in a top journal is a big IF. You will definitely need the advice and support of your advisor. Its a bold and the right step to take. Many students take an extra year and complete their Ph.D in five years. This allows them to build up a nice portfolio of papers accepted or under review by the time they are ready to go onto the job market. I personally think taking an extra year is a great idea. Its much better to go into the faculty position with a paper or two under your belt. The process of tenure is probably 10 times as difficult.
Finally, definitely try to work with a well known professor in the field. Reputation means a lot of academia. Careers are built on it. In some cases, it is possible to work with a professor from another university. But nothing like someone on the inside. The challenge you will run into when working with a genius prof. is that you have to be really at the top of your game to keep them interested.
Its not as dramatic as it may sound. But it definitely is a challenging experience.
Hope this helps
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### Show Tags
12 Mar 2007, 16:13
Just want to add that _everything_ Praetorian has written in those last two posts sounds exactly right from my point of view. The small business analogy is the best one I've heard (much better than those "monk" parallels).
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### Show Tags
21 Jun 2007, 12:32
What beautiful points by Praet..
just to update ... out of 9 people in my batch, only 3 plan to finish in 4 years. Rest have decided to to do it in 5 years. I am counting myself in one of those 3 ..
Adding to the reality , is another dose .. Politics in academia. Junior faculty wants to ride on the PhD students, because it gives them more papers and therefore tenure . Senior faculty wants PhD students since they are too busy in administrative work and refreeing others work that they do not get time to do research themselves. Tough choice. One of my batchmates is right now in the crossfire between two faculty members ... ooof !
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### Show Tags
06 Dec 2007, 08:25
1
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I'm in my third year now and am debating whether I should go out to the market next year or not. Of course, my advisor will probably have the ultimate say on this. I'm at a big state school. In my cohort of 13, 11 of us are still with us but I think only 2-3 will finish it in four years. It is definitely becoming more standard to finish in 5-6 years.
I agree with most things that the above postiners said, but I do think the model needs to be changed. 5, or even 6 these days, is becoming too much of a drag for most students, especially for thoseof us married with kids. Most profs wil tell you "Stay an additional year to get a pub". The issue is that there's no guarantee that a pub will arrive in your fifth year, especialy now that the lead time for pubs are getting longer and longer. Plus, at least in my school, teaching requirement becomes heavier after the fourth year (almost comparable to faculty). That's why I'm inclined to try to finish it in four years, but I'll have to fight an uphill battle because the department wants better placement. The question will be... what is the highest ranked school I can get into without a pub by the end of my 3 1/2 yrs...
[quote="Sameer"]What beautiful points by Praet..
just to update ... out of 9 people in my batch, only 3 [b]plan[/b] to finish in 4 years. Rest have decided to to do it in 5 years. I am counting myself in one of those 3 ..
Adding to the reality , is another dose .. Politics in academia. Junior faculty wants to ride on the PhD students, because it gives them more papers and therefore tenure . Senior faculty wants PhD students since they are too busy in administrative work and refreeing others work that they do not get time to do research themselves. Tough choice. One of my batchmates is right now in the crossfire between two faculty members ... ooof ![/quote]
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### Show Tags
08 Dec 2007, 20:50
hdp323 wrote:
I agree with most things that the above postiners said, but I do think the model needs to be changed. 5, or even 6 these days, is becoming too much of a drag for most students, especially for thoseof us married with kids. Most profs wil tell you "Stay an additional year to get a pub". The issue is that there's no guarantee that a pub will arrive in your fifth year, especialy now that the lead time for pubs are getting longer and longer. Plus, at least in my school, teaching requirement becomes heavier after the fourth year (almost comparable to faculty). That's why I'm inclined to try to finish it in four years, but I'll have to fight an uphill battle because the department wants better placement. The question will be... what is the highest ranked school I can get into without a pub by the end of my 3 1/2 yrs...
Adding to the reality , is another dose .. Politics in academia. Junior faculty wants to ride on the PhD students, because it gives them more papers and therefore tenure . Senior faculty wants PhD students since they are too busy in administrative work and refreeing others work that they do not get time to do research themselves. Tough choice. One of my batchmates is right now in the crossfire between two faculty members ... ooof !
You raise good points. A reason I've heard frequently (to stay one more year instead of going on the job market in the 3rd or 4th year) is that your job market paper will be better. Publications do matter of course, but I've heard that it's better to have a great job market paper and no publications than a co-authored publication in a good journal and a good, but not great, job market paper. The benefit of waiting one more year would be to improve on that paper rather than try to get something else published. Is it also your impression?
I agree completely with your politics argument, and I'd add that part of the problem is that faculty/advisers have _no_ incentive to make Ph.D students finish early. Except for some financial considerations that concern the school but not the faculty member (e.g. stipends that run into the 5th or 6th years at some places), it only makes sense for a faculty member to get whatever help they can from a good student, at the same time helping those students get better at research in the hope of landing a better placement; this assumes faculty advisers have an incentive to send their students to as good a school as possible, which I don't think is a financial incentive so much as a reputational incentive.
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### Show Tags
08 Dec 2007, 22:40
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Can a paper that is co-authored by the PhD student and a Faculty member be considered as part of the student's dissertation? Or part of the job market paper?
Assume that the PhD student is the main contributor of the co-authored paper.
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### Show Tags
08 Dec 2007, 22:54
tkkoh wrote:
Can a paper that is co-authored by the PhD student and a Faculty member be considered as part of the student's dissertation? Or part of the job market paper?
Assume that the PhD student is the main contributor of the co-authored paper.
Yes.
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Posts: 3460
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### Show Tags
08 Dec 2007, 23:03
cabro57 wrote:
hdp323 wrote:
I agree with most things that the above postiners said, but I do think the model needs to be changed. 5, or even 6 these days, is becoming too much of a drag for most students, especially for thoseof us married with kids. Most profs wil tell you "Stay an additional year to get a pub". The issue is that there's no guarantee that a pub will arrive in your fifth year, especialy now that the lead time for pubs are getting longer and longer. Plus, at least in my school, teaching requirement becomes heavier after the fourth year (almost comparable to faculty). That's why I'm inclined to try to finish it in four years, but I'll have to fight an uphill battle because the department wants better placement. The question will be... what is the highest ranked school I can get into without a pub by the end of my 3 1/2 yrs...
Adding to the reality , is another dose .. Politics in academia. Junior faculty wants to ride on the PhD students, because it gives them more papers and therefore tenure . Senior faculty wants PhD students since they are too busy in administrative work and refreeing others work that they do not get time to do research themselves. Tough choice. One of my batchmates is right now in the crossfire between two faculty members ... ooof !
You raise good points. A reason I've heard frequently (to stay one more year instead of going on the job market in the 3rd or 4th year) is that your job market paper will be better. Publications do matter of course, but I've heard that it's better to have a great job market paper and no publications than a co-authored publication in a good journal and a good, but not great, job market paper. The benefit of waiting one more year would be to improve on that paper rather than try to get something else published. Is it also your impression?
I agree completely with your politics argument, and I'd add that part of the problem is that faculty/advisers have _no_ incentive to make Ph.D students finish early. Except for some financial considerations that concern the school but not the faculty member (e.g. stipends that run into the 5th or 6th years at some places), it only makes sense for a faculty member to get whatever help they can from a good student, at the same time helping those students get better at research in the hope of landing a better placement; this assumes faculty advisers have an incentive to send their students to as good a school as possible, which I don't think is a financial incentive so much as a reputational incentive.
Good points cabro57.
To add to cabro57's post, I would use the fifth year to look beyond my dissertation. You will never have as much time for research as you have now.
Unless you have very severe financial constraints or department constraints, take every opportunity to build up an collection of papers even before you step foot in your new job as faculty. Once in your new job, use your first year as faculty to send out as many of those papers out for review as possible.
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09 Dec 2007, 09:35
1
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cabro57 wrote:
Publications do matter of course, but I've heard that it's better to have a great job market paper and no publications than a co-authored publication in a good journal and a good, but not great, job market paper. The benefit of waiting one more year would be to improve on that paper rather than try to get something else published. Is it also your impression?
No, that is not my impression. I think most faculty members in the hiring committee look at the CV/research statements before they read the job paper. One's very lucky if his/her job market paper is read by the hiring committee. A good job market paper can be a differentiating factor once the candidate becomes more serious. However, to go through that first screening round, one needs 1) publication, and/or 2) good recommendation letter from well-known faculty members (the importance of rec letters really depends on thw level of school one's applying to). Unless one has either or both, he/she's out of luck since his/her job market paper will not be read.
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Re: Information on Phd lifestyles...? [#permalink]
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21 Jun 2008, 11:07
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# Information on Phd lifestyles...?
Moderator: carcass
Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.
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2017-01-23 10:35:55
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{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24762409925460815, "perplexity": 2081.005564521708}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560282631.80/warc/CC-MAIN-20170116095122-00399-ip-10-171-10-70.ec2.internal.warc.gz"}
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https://api-project-1022638073839.appspot.com/questions/how-do-you-differentiate-y-x-e-2x
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# How do you differentiate y = (x)^(e^(2x))?
Mar 18, 2018
$\frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{2 x} \setminus {x}^{{e}^{2 x}} \setminus \left\{\frac{1}{x} + \ln {x}^{2}\right\}$
#### Explanation:
We have:
$y = {x}^{{e}^{2 x}}$
We can take natural logarithms and use implicit logarithmic differentiation:
$\ln y = \ln \left\{{x}^{{e}^{2 x}}\right\}$
$\setminus \setminus \setminus \setminus \setminus = {e}^{2 x} \setminus \ln x$
Then we can use the product rule:
$\frac{1}{y} \setminus \frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{2 x} \setminus \frac{1}{x} + 2 {e}^{2 x} \setminus \ln x$
$\therefore \frac{1}{y} \setminus \frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{2 x} \setminus \left\{\frac{1}{x} + 2 \ln x\right\}$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = y \setminus {e}^{2 x} \setminus \left\{\frac{1}{x} + \ln {x}^{2}\right\}$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = {x}^{{e}^{2 x}} \setminus {e}^{2 x} \setminus \left\{\frac{1}{x} + \ln {x}^{2}\right\}$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{2 x} \setminus {x}^{{e}^{2 x}} \setminus \left\{\frac{1}{x} + \ln {x}^{2}\right\}$
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2021-04-17 20:18:16
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https://math.stackexchange.com/questions/2410425/how-to-determine-truth-value-of-this-proposition
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# How to determine truth value of this proposition?
Let $P(x,y)$ be the proposition $x^2=y$, where $x$ and $y$ are integers. Determine the truth value of each of the following proposition.
for $∃x P(6,x)$
Does this mean that 6 is $x$ in this case and $x$ is $y$ So $y$ would equal to $6^2=36$ How do I know if that's true?
• What is the "for" there for? The proposition $\exists x P(6,x)$ is meaningful (and true; take $x=36$.) – Mark Fischler Aug 29 '17 at 21:42
• There may or may not have been a typo $\exists x, P(6,x)$ means "There is an integer $x$ such that $6^2 = x$". $\exists x, P(x, 6)$ means "There is an integer $x$ such that $x^2 = 6$". – fleablood Aug 29 '17 at 21:47
So $\exists{x}P(6,x)$ is equivalent to $\exists{y}P(6,Y)$
and also to $\exists{t}P(6,t)$ and so on.
• It may be helpful to compare $\exists{r}P(6,r)$ which is True with $\exists{v}P(v,2)$ which is false in the domain of discourse: the integers. – Jim H Aug 29 '17 at 21:52
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2019-06-25 05:53:41
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https://socratic.org/questions/566b4bc07c01492b6c75fd84
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# In reactions between metals, and gases, which is likely to be the oxidizing agent?
Oxidants accept electrons; dioxygen gas gives ${O}^{2 -}$ when it oxidizes something, i.e. accepts electrons. A reducing agent donates electrons.
Given this, elemental metals tend to be reducing agents, and oxidants tend to be non-metals. $C {l}_{2}$ gas is thus the most potent oxidant, as it accepts electrons to give chloride ions, $C {l}^{-}$.
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2021-06-15 09:30:20
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http://tug.org/pipermail/texhax/2003-December/001321.html
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# [texhax] pagenumbering
Luca Turchetti luca.turchetti at uniroma1.it
Thu Dec 4 21:27:06 CET 2003
At this point I'm not sure I still remember what was the original problem!
Anyway, if you want to put hyphens around the page number in the footer, I guess that you want the page number to be on
the center of the page.
The commands
\fancyfoot[LE]{\thepage}
\fancyfoot[RO]{\thepage}
that you have on your code, print the page number in the bottom-left corner in even(left) pages and in the bottom-right
corner in odd(right) pages (LE=Left Even ; RO=Right Odd, as you can read in the fancyhdr documentation). So, what you
need is probably to change the alignment and add the hyphen chars you want:
\fancyfoot[CE]{-- \thepage --}
\fancyfoot[CO]{-- \thepage --}
Hope this helps you somehow
Luca Turchetti
Renju Zacharia wrote:
> Hi Phil, Fairbairns, Manoj and others,
>
> >Well, it should work. Of course, I was assuming you were using LaTeX, but
> >then you didn't bother to say.
> >
> >
> Sorry for not being specific. It is out of just ignorance. i did not
> know that command in TeX is different from that in LaTeX.
> I use LaTeX
>
> Here is part of the code.
> ------------------------------
>
> \areaset[13.25mm]{157.50mm}{222.75mm}
> \typearea[current]{calc}
> %-------------------- Draft mode
> ---------------------------------------------
> \setlength{\hfuzz}{20pt} % Don't bother to report over-full boxes if
> over-edge is < 2pt
> \tolerance=200%
> \setlength{\emergencystretch}{30pt} %
>
> %--------------------- Packages
> ------------------------------------------------
> \usepackage[final]{graphicx}
> \graphicspath{{eps/}}
> \unitlength=1cm
> \usepackage{relsize}
> \usepackage{nicefrac}
> \usepackage{cite}
> \usepackage[vflt]{floatflt}
> \usepackage[small,bf]{caption2}
> \usepackage{amssymb}
> \usepackage{amsfonts}
> \usepackage{courier}
> \usepackage{geometry}
> \usepackage[grey,times]{quotchap}
> \usepackage[square,authoryear,sort&compress]{natbib}
>
> \usepackage{stdclsdv}
> \usepackage{tocloft}
> \renewcommand{\cftchapfont}{ % Numbers in the braces adjusted to get
> aestetic quality
> \fontsize{13}{13}\usefont{OT1}{phv}{bc}{n}\selectfont }
>
> \renewcommand*\sectfont{\usefont{OT1}{phv}{bc}{n}\selectfont}
>
> \usepackage{fancyhdr}
> \nouppercase \rightmark}
> \fancyfoot{}
> \fancyfoot[LE]{\thepage}
> \fancyfoot[RO]{\thepage}
>
> \begin{document}
> \pagenumbering{roman} \setcounter{page}{1}
> \include{TitlePage}
> ------snip----
> \include{Abbrevations}
>
> \cleardoubleemptypage
>
> \pagenumbering{arabic} \setcounter{page}{1}
> ----------------------------------------
>
> I tried in between to work around, unfortunately I could not devote much
> time on that. If any of you can tell me where I am going wrong, helps a lot.
>
> Thank you all once again,
> Zacharia
>
> >
> >
> >>If dont bother, a link to the Fairbairns would have helped a lot instead
> >>of "180/322 questions".
> >>
> >>
> >
> >I didn't have a link, but googling The UK TEX FAQ Your 322 Questions gets
> >the latest version first time (which has been updated to 338 so it's
> >actually Q. 182).
> >
> >But the question is: why am I doing the googling for you?
> >
> >
> >
> >>If one gives a search in net for the above document(UK TEX FAQ), IMHO,
> >>one cannot dig out the ~~~~/FAQ180.html unlike other question numbers.
> >>Also if one gives a rapid search in net for page numbering, styles, etc,
> >>one will end up with around 95++% the normal pagenumbering styles ONLY
> >>which I consider as a trivial. The present situation in not dealt in
> >>most of them(sorry for loose quantification).
> >>
> >>
> >
> >But many of them explain a little of what they do and can be modified.
> >
> >
> >
> >>A bit of frustration is after reading handful of introductory manuals
> >>and not finding even a hint of what can be done on it.
> >>
> >>
> >
> >I assume you missed the "Gentle Introduction to TeX" (distributed with
> >MiKTeX), see page 28 in the English version.
> >
> >
> >
> >
>
> _______________________________________________
> TeX FAQ: http://www.tex.ac.uk/faq
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2017-12-18 01:04:26
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http://cui.unige.ch/isi/icle-wiki/talk:additionalopportunitiesalongwithaeurolottosyndicate
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2018-04-22 03:05:55
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https://math.stackexchange.com/questions/3047159/using-bayes-rule-to-calculate-conditional-probability
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# using Bayes’ Rule to calculate conditional probability
i have following problem,
"Students who party before an exam are twice as likely to fail the exam as those who don't party (and presumably study). Of 20% of students partied before the exam, what percentage of students who failed the exam went partying?"
i believe that this problem related to conditional probability, but i couldn't find all necessary elements for answer. appreciate your help.
• Do you understand Bayes’ theorem? – gHem Dec 20 '18 at 4:38
• Is that supposed to read If 20% of students... instead of Of 20% of students... ? – David Diaz Dec 20 '18 at 4:53
• An alternative approach to Aaron's answer is to first write down the given info as: \begin{align}P[fail \: \mid \: party] &= 2P[ fail \: \mid \: party^c]\\ P[party] &= 0.2\end{align} and you want to compute $P[party \: \mid \: fail]$. – Michael Dec 20 '18 at 5:18
Let $$x$$ be the total number of students and $$p$$ be the probability of a student who didn't party failing the exam. The probability of a student who partied before the exam failing the exam is then $$2p$$.
$$x/5$$ students partied, out of which $$2px/5$$ failed. Out of the $$4x/5$$ who didn't party, $$4px/5$$ failed the exam. The total students who failed is $$2px/5+4px/5=6px/5$$, out of which $$2px/5$$ partied. The required probability is $$2/6=1/3$$.
Using these numbers, you can that if taking a sample out of $$100$$ for example, you will see that 12 people failed who went partying and 24 failed who didn't party. So the percentage who failed (and went partying) is $$33.3$$%.
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2019-07-20 16:06:07
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https://zbmath.org/?q=ci%3A1042.39523
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# zbMATH — the first resource for mathematics
Boundedness and global stability of a higher-order difference equation. (English) Zbl 1161.39011
This paper deals with the boundedness and global stability of following difference equation
$x_n=\frac{p+\sum_{j=1}^{m}\alpha_jx_{n-p_j}}{qx_{n-k} +\sum_{j=1}^{m}\alpha_jx_{n-p_j}}, \quad n\in {\mathbb N}_0,$
where $$k, m, p_j, j=1, 2, \dots, m$$ are natural numbers, $$p_1<\dots<p_m$$, $$k\neq p_j$$, $$j=1, 2, \dots, m$$, $$p, q\in (0, \infty)$$ and $$\alpha_j>0$$, $$j=1, 2, \dots, m$$ such that $$\sum_{j=1}^{m}\alpha_j=1$$. This equation has a unique positive equilibrium $$\bar {x}$$. The author divides the problem into three different cases $$p<q$$, $$p>q$$ and $$p=q$$. In each case, the global stability of $$\bar{x}$$ is studied. Finally, the author concludes that if $$p, q\in (0, \infty)$$, then all positive solutions are bounded. These results extend those by R. DeVault, W. Kosmala, G. Ladas and S. W. Schultz [Nonlinear Anal., Theory Methods Appl. 47, No. 7, 4743–4751 (2001; Zbl 1042.39523)].
##### MSC:
39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations
Full Text:
##### References:
[1] DOI: 10.1016/S0362-546X(01)00586-7 · Zbl 1042.39523 [2] Kocic V.L., Global Behaviour of Nonlinear Difference Equations of Higher Order with Applications (1993) · Zbl 0787.39001 [3] DOI: 10.1080/0003681021000021114 · Zbl 1022.39005 [4] DOI: 10.1006/jmaa.2000.7032 · Zbl 0967.39004 [5] Kulenović M., Dynamics of Second Order Rational Difference Equations (2002) · Zbl 0981.39011 [6] DOI: 10.1080/10236190601069325 · Zbl 1113.39011 [7] Sun T., Discrete Dyn. Nat. Soc. 2006 pp 12– (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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2021-09-26 04:29:30
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http://math.stackexchange.com/questions/75207/euclidean-distance-proof
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# Euclidean distance proof
How can I show that the Euclidean distance satisfies the triangle inequality?
Where the Euclidean distance is given by: $$d(p,q) = \sqrt{(p_1-q_1)^2 + \cdots + (p_n-q_n)^2}$$
Triangle Inequality: $\forall x,y,z\Bigl( d(x,z) \leq d(x,y) + d(y,z)\Bigr)$.
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This is your third question on the same topic in just over one hour. Instead of asking questions here, why don't you take some time and try this questions yourself? If you have in fact tried these questions by yourself, where did you find difficulty? – JavaMan Oct 23 '11 at 22:04
I have tried these questions before asking. For this question. I used the case where (x - z)^2 ≤ (sqrt(x - y)^2 + sqrt(y - z)^2)^2. But I am not sure where to go from there. – Laciel Oct 23 '11 at 22:18
Let ${\bf p} = (p_1,\dots,p_n)$ and ${\bf q}=(q_1,\dots,q_n)$. Recall that ${\bf p \cdot q} = p_1q_1 + \cdots + p_nq_n$ and $|{\bf p}|=\sqrt{{\bf p \cdot p}}$ and finally $d({\bf p}, {\bf q})=|{\bf p}-{\bf q}|$.
First, let's establish the Cauchy-Schwarz inequality: $|{\bf p \cdot q}| \leq |{\bf p}| |{\bf q}|$.
Consider $|{\bf p}-c{\bf q}|^2 = ({\bf p}-c{\bf q}) {\bf \cdot} ({\bf p}-c{\bf q}) = c^2 {\bf q \cdot q} - 2c {\bf p \cdot q} + {\bf p \cdot p}=|{\bf q}|^2c^2-2({\bf p\cdot q})c+|{\bf p}|^2$. This is a quadratic in $c$ and since $|{\bf p}-c{\bf q}|^2 \geq 0$ we have $|{\bf q}|^2c^2-2({\bf p\cdot q})c+|{\bf p}|^2 \geq 0$. Thus this quadratic either has a repeated real root or complex roots. Thus its discriminant is non-positive. So $(-2({\bf p \cdot q}))^2-4|{\bf q}|^2|{\bf p}|^2 \leq 0$. This means $4({\bf p\cdot q})^2 \leq 4|{\bf q}|^2|{\bf p}|^2$. Canceling the 4's and taking square roots give us the required result.
Use CS as follows: $|{\bf p}+{\bf q}|^2=({\bf p}+{\bf q}){\bf \cdot}({\bf p}+{\bf q})=|{\bf p}|^2+2({\bf p\cdot q})+|{\bf q}|^2 \leq |{\bf p}|^2+2|{\bf p\cdot q}|+|{\bf q}|^2$ $\leq |{\bf p}|^2+2|{\bf p}||{\bf q}|+|{\bf q}|^2=(|{\bf p}|+|{\bf q}|)^2$. This gives you $|{\bf p}+{\bf q}| \leq |{\bf p}|+|{\bf q}|$.
Now consider 3 points ${\bf p}$, ${\bf q}$, and ${\bf r}$. $d({\bf p}, {\bf r})=|{\bf p}-{\bf r}|=|{\bf p}-{\bf q}+{\bf q}-{\bf r}| \leq |{\bf p}-{\bf q}| + |{\bf q}-{\bf r}|=d({\bf p},{\bf q})+d({\bf q},{\bf r})$
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2014-03-12 09:03:23
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http://www.assension.net/conseil-formation-accompagnement/write-a-rational-function-with-the-given-asymptotes
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# Write a rational function with the given asymptotes
The asymptote represents values that are write a rational function with the given asymptotes not solutions to the equation, but could be a if i were an animal what would i be essay limit of solutions. For rational functions, vertical asymptotes are vertical lines that correspond to the zeroes points of the. Examine the behavior on both sides of each vertical asymptote to determine the Use any clear point on the. Rational function has at most one horizontal asymptote. Let me write that down right over here.
F(x) = p(x) / q(x) Domain. Step 2: if x – c is a factor in the denominator then x = c is the vertical asymptote. NR 508 Quizzes Week 1-3 and Week 4 Midterm Review Spring 2020 Quiz #1 1	When taking acyclovir patients should be educated regarding the Need write a rational function with the given asymptotes to drink lots of water during treatment 2	Precautions that should be taken when prescribing controlled substances include Using tamper-proof paper for all prescriptions written for controlled drugs 3	Medication agreements or. dipal1812 1 hour ago Math Secondary School +5 pts. The Equation For F (x) Has One Of The Five Forms. Write an equation for a rational function with: Vertical http://www.tweetsicles.com/blog/websites-write-essays-you-free asymptotes at x = -5 and x = -4. The asymptote calculator takes a function and calculates all asymptotes and also graphs the function. A rational function is a function that can be written as the ratio of two polynomials where the denominator isn't zero.
That's the horizontal asymptote. a horizontal asymptote at #y=2/5# means highesr degrees in both numerator and denominator are equal and their coefficients are in ratio of #2:5# Hence desired rational function is #(2(x-4)(x-7))/(5(x-7)(x+3))# i.e. Write an equation for a rational function with: Vertical asymptotes at $x = -5$ and $x = waitress responsibilities resume examples 5$ $x$ intercepts at $x = -2$ and $x = -6$ Horizontal asymptote at $y = 6$. Log in. A rational expression can have: any number of vertical write a rational function with the given asymptotes asymptotes, only zero or one horizontal asymptote, only zero or one oblique (slanted) asymptote; Finding Horizontal or Oblique Asymptotes.
The domain of a rational function is all real values except where the denominator, q(x) = 0. Writing Rational Functions Determine the factors of the numerator. Reduce the expression by canceling common factors in the numerator and the denominator Write an equation for a rational function write a rational function with the given asymptotes with: Vertical asymptotes at x = 4 and x = -2 x-intercepts at x = 1 and x = -4 y-intercept at 6 Preview y = Get more help from Chegg Get 1:1 help now from expert Precalculus tutors Solve it with our pre-calculus problem solver and calculator. No V.A. 1. For rational functions, vertical asymptotes where can i type a paper online are vertical lines that correspond to the zeroes points of the denominator.
Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too The equation for rational function is f(x) = [p(x)]/[g(x)] The function has no vertical asymptote. The asymptote represents values … Author: wikiHow Staff Views: 280K Solved: Write An Equation For A Rational Function With: Ve https://www.chegg.com/homework-help/questions-and Write an equation for a rational function with: Vertical asymptotes at x = 4 and x = -2 x-intercepts at x = 1 and x = -4 y-intercept at 6 Preview y = write a rational function with the given asymptotes Get more help from Chegg Get 1:1 help now from expert Precalculus tutors Solve it with our pre-calculus problem solver and calculator. Finding Vertical Asymptotes of Rational Functions. Show Instructions In general, you can skip the multiplication sign, so 5x is equivalent to 5*x HowTO: Given a rational function, identify any vertical asymptotes of its graph Factor the numerator and denominator. For your specific case denominator above which http://www.tweetsicles.com/blog/basic-guide-to-essay-writing has a degree of 1 you must have a numerator of degree zero, which is to say some constant 3.5 - Rational Functions and Asymptotes. Write an equation for a rational function with: Vertical asymptotes at x = 4 and x = -2 x-intercepts at x = 1 and x = -4 y-intercept at 6 Preview y = Get more help from Chegg Get 1:1 help now from expert Precalculus tutors Solve it with our pre-calculus problem solver and calculator. Jul 06, 2020 · From the given information, it is observed that the vertical asymptotes are at x = -6 and x = -4 The x-intercepts at x = 2 and x = -2 and y intercept at 4 Note that, the vertical asymptotes are the value of x for which the denominator of the function is 0 The rational function f(x) = P(x) / Q(x) in lowest terms has horizontal asymptote.
1. Write the equation of the rational function with vertical asymptotes at x = 3 and x = 0, a write a rational function with the given asymptotes zero at x = 2 and x = -1, and a horizontal asymptote at y = -2 Asymptotes for rational functions A rational function has at most one horizontal asymptote or oblique (slant) asymptote, and possibly many vertical asymptotes. Rational Functions: Finding Horizontal and Slant Asymptotes 2 - Cool Math has free online cool math lessons, cool math games and fun math activities. Reduce the expression by canceling common factors in the numerator and the denominator. 7. Follow • 2.
Roots. Reduce the expression by canceling common factors in the numerator and the denominator Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share …. An example of a rational function with no vertical asymptotes and no holes is. We write the function such that both the numerator and the denominator are prime. Jul 06, 2020 · From the given write a rational function with the given asymptotes information, it is observed that the vertical asymptotes are at x = -6 and x = -4 The x-intercepts at x = 2 and x = -2 and y intercept at 4 Note that, the vertical asymptotes are the value of x for which the denominator of the function is 0 Asymptotes. HowTO: Given a rational function, identify any vertical asymptotes of its graph Factor the numerator and denominator. What is the asymptote of a function? Vertical asymptote at x = -8 and x = 5 2.
## Rational asymptotes the write function given with a
Rational functions contain asymptotes, as seen in this example: In this example, there is a vertical asymptote at x = 3 and a horizontal asymptote at y = 1. For the above rational function, the denominator is never zero, so there are no vertical asymptotes Free functions asymptotes calculator - find functions vertical and write a rational function with the given asymptotes horizonatal asymptotes step-by-step This website uses cookies to ensure you get the best experience. H.A.: & y-intof -2 2. Vertical Asymptotes of xx 2. Step 2 : So, there is no hole for the given rational function. Sep 14, 2011 · We discuss finding a rational function when we are given the x-intercepts, the vertical asymptotes and a horizontal asymptote. x-intercept at (-2, 0) 4. To find the vertical asymptote (s) of a rational function, simply set the denominator equal to 0 and solve for x Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share ….
Views: 280K write an equation for a rational function that has a https://www.jiskha.com/search?query=write+an Jan 10, 2012 · Write the equation of a rational function in the form of 𝑓(𝑥) = 𝑎𝑥+𝑏/𝑐𝑥+𝑑 if the vertical asymptote is x =5, the horizontal asymptote is y=2, the x-intercept is (-1/2, 0) and the y-intercept is (0,-1/5). An asymptote can be vertical, horizontal, or on any angle. The curves approach these asymptotes but never cross them. Vertical symptote of x = Horizontal Asymptote of y = 2 and a. 4. Factor both the numerator (top) and denominator (bottom) Given a rational function, identify any vertical asymptotes of its graph. Note that the curve is asymptotic at opposite side of the line x = 1. Given a rational function, identify any vertical asymptotes of its graph. These parts go out of the coordinate system along an imaginary straight line called write a rational function with the given asymptotes an asymptote.. 5.$$p\left(x\right)=\dfrac{2x-3}{x+4}$$. To graph a rational function, find the asymptotes and intercepts, plot a few points on each side of each vertical asymptote and then sketch the graph.
Check the x intercept, the vertical and the horizontal asymptotes. Ask your question. The equation of the rational function is given by f(x) = (x - 2)/(2x + 2) Try this Example: Find the equation of the rational function f of the form f(x) = (ax - 2 ) / (bx + c) whose graph has an x intercept at (1 , 0), a vertical asymptote at x = -1 and a horizontal asymptote write a rational function with the given asymptotes at y = 2 Enter the function you want to find the asymptotes for into the editor. 7. Also the highest common factor for the numerator and the denominator is 1 so there are no holes Jan 13, 2017 · Vertical Asymptotes in Rational Functions If your function is rational, that is, if f (x) has the form of a fraction, f (x) = p (x) / q (x), in which both p (x) and q (x) are polynomials, then we follow these two steps: 1. Question: POLYNOMIAL AND RATIONAL FUNCTIONS Writing The Equation Of A Rational Function Given Its Graph The Figure Below Shows The Graph Of A Rational Function F It Has Vertical Asymptotes X-1 And X-5, And Horizontal Asymptote Y 0. Asymptotes of Rational Functions. An asymptote is a straight line that generally serves as a kind of boundary for the graph of a function. The one with the larger degree will grow fastest Graphing Rational Functions, n less than m There are different characteristics to look for when graphing rational functions. It can be asymptotic in the same direction depending on the given curve. Note any restrictions in the domain of the function.
### 5 Paragraph Essay On Manifest Destiny
Jul 06, 2020 · From the given information, it is observed that the vertical asymptotes are at x = -6 and x = -4 The x-intercepts at x = 2 and x = -2 and y intercept at 4 Note that, the vertical asymptotes are the value of x for which the denominator of the function is 0 Jun write a rational function with the given asymptotes 20, 2012 · This video explains how to determine the equation of a rational function given the vertical asymptotes and the x and y intercepts. ANSWER. The one with the larger degree will grow fastest Formula: Method 1: The line y = L is called a Horizontal asymptote of the curve y = f (x) if either. Write an equation for a rational function with: Vertical asymptotes at x = 4 and x = -2 x-intercepts at x = 1 and x = -4 y-intercept at 6 Preview y = Get more help from Chegg Get 1:1 help now from expert Precalculus tutors Solve it with our pre-calculus problem solver and calculator. The Graph Does Not Have An X-intercept, And It Passes Through The Point (-2, 2). Rational functions contain asymptotes, as seen in this example: In this example, there is a vertical asymptote at x = 3 and a horizontal asymptote at y = 1. Function f has the form A rational function has a horizontal asymptote of 0 only when the degree of the numerator is strictly less than the degree of the denominator. Find the hole (if any) of the function given below .
Log in. Example: Find the vertical asymptotes …. f(0) = …. Vertical Asymptotes of x = l, x = —2 . Vertical asymptote at x = -8 and x = 5 2. 1.) )𝑓( = _____ HOLE(S) VERTICAL ASYMPTOTE(S) HORIZONTAL. Join now. f(x) = 1 / (x + 6) Solution : Step 1: In the given rational function, clearly there is no common factor found at both numerator and denominator. A rational expression can have: any number of vertical asymptotes, only zero or one horizontal asymptote, only zero or one oblique (slanted) asymptote; Finding Horizontal or Oblique Asymptotes. Reduce the expression by canceling common factors in the numerator and the denominator The equation for rational function is f(x) = [p(x)]/[g(x)] The function has no vertical asymptote. Write an equation for a rational write a rational function with the given asymptotes function with: Vertical asymptotes at x = 4 and x = -2 x-intercepts at x = 1 and x = -4 y-intercept at 6 Preview y = Get more help from Chegg Get 1:1 help now from expert Precalculus tutors Solve it with our pre-calculus problem solver and calculator. It is fairly easy to find them but it depends on the degree of the top vs bottom polynomial.
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A rational function will be zero at a particular value of $$x$$ only if the numerator is zero at that $$x$$ and the denominator isn’t zero at that $$x$$ Formula:. Vertical Asymptote of x 1, Horizontal Asymptote of y 2 and x-intercept at x 3. a) a hole at x = 1 b) a vertical asymptote anywhere and a horizontal asymptote along the x-axis c) a hole at x = -2 and a vertical asymptote at x = 1 d) a vertical . Jul 06, 2020 · From the given information, it is observed that the vertical asymptotes are at x = -6 and x = -4 The x-intercepts at x = 2 and x = -2 and y intercept at 4 Note that, the vertical asymptotes are the value of x for which the denominator of the function is 0 The rational function f(x) = P(x) / Q(x) in lowest terms has horizontal asymptote y = a / b if the degree of the numerator, P ( x ), is equal to the degree of denominator, Q ( x ), where a is the leading coefficient of P ( x ) and b is leading coefficient of Q ( write a rational function with the given asymptotes x ) Draw a function that has the following characteristics: A zero at x = 3 A hole when x = 5 A vertical asymptote at x = -1 A horizontal asymptote at y = 3 A y-intercept at y = -2 (Draw the hole last after you've graphed the rest of the function!) Then write its equation below Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share …. Rational choice theory, also known as choice theory or rational action theory, is a framework for understanding and often formally modeling social and economic behavior. By …. EXPLANATION. Jul 06, 2020 · Rational Perspectives Acknowledgements and gratitude (1) This Christmas season I had intended to engage in a critical investigation of religion given the powerful theological si. 1.) )𝑓( = _____ HOLE(S) VERTICAL ASYMPTOTE(S) HORIZONTAL. Example 2 : Find the hole (if any) of the function given below This section covers: Revisiting Direct and Inverse Variation Polynomial Long Division Asymptotes of Rationals Drawing Rational Graphs — General Rules Finding Rational Functions from Graphs, Points, Tables, or Sign Charts Applications of Rational Functions More Practice Again, Rational Functions are just those with polynomials in the numerator and denominator, so they are the ratio of.We need to multiply the File Size: 358KB Page Count: 4 Asymptotes of a General Rational Function - Mathematics https://math.stackexchange.com/questions/2777035/ Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share …. Horizontal asymptote at y = 0 3.
Other function may have more than one horizontal asymptote. Explain why these steps are bypassed; that is, why gluconeogenesis is not simply a reversal of the reactions of glycolysis. Step 2: Click the blue arrow to submit and see the result! 6. Jul 06, 2020 · From the given information, it is observed that the vertical asymptotes are at x = -6 and x = -4 The x-intercepts at x = 2 and x = -2 and y intercept at 4 Note that, the vertical asymptotes are the value of x for which the denominator of the function is 0 A rational function is a function thatcan be written as the ratio of twopolynomials where the denominatorisn't zero. Method 2: For the rational function, f (x) In equation of Horizontal Asymptotes, 1. and x-intof Write a rational function with the following characteristics: 5. Finding All Asymptotes of a Rational Function Write Rational Author: DrPhilClark Views: 56K People also ask What is the asymptote of a function? Vertical Asymptote of x 1, Horizontal Asymptote of y 2 and x-intercept at x 3. Write an equation for write a rational function with the given asymptotes a rational function with: Vertical asymptotes at x = -5 and x = -4 x intercepts at x = 1 and x = 3 y intercept at 9. WRITING EQUATIONS OF RATIONAL FUNCTIONS To Identify Types of Discontinuity: Step 1: HOLES (Removable Discontinuities) SLANT ASYMPTOTES (Exists only if Horizontal Asymptote is not State each discontinuity, -intercept, and -intercept.
They stand for places where the x-value is not allowed. Vertical Asymptotes of 5 0, 2 xx and Horizontal Asymptote of y 4 8. write a rational function with the given asymptotes By …. 4. We write the function such that both the numerator and the denominator are prime. We can find a maximum of five fractions equivalent to given fractions Get the answers you need, now! 6. 7. The curves approach these asymptotes …. x-intercept at (-2, 0) 4. Jul 06, 2020 · From the given information, it is observed that the vertical asymptotes are at x = -6 and x = -4 The x-intercepts at x = 2 and x = -2 and y intercept at 4 Note that, the vertical asymptotes are the value of x for which the denominator of the function is 0 In the above graph, the horizontal asymptote is x = 1.
2 Apr 26, 2019 · Recognize asymptotes. Finding Asymptotes Vertical asymptotes are "holes" in the graph where the function cannot have a value. Writing rational functions given characteristics: 2/3 and x= 3. Solution to Problem 1: Since f has a vertical is at x = 2, then the denominator of the rational function contains the term (x - 2). Factor the numerator and denominator. Apr 26, 2019 · Recognize asymptotes. The first step to working with rational functions is to completely factor the polynomials. Join now. The roots, zeros, solutions, x-intercepts (whatever you want to write a rational function with the given asymptotes call them) of the rational functionwill be the places where p(x) = 0 Remember that an asymptote is a line that the graph of a function approaches but never touches. Examine the behavior of the graph at the x-intercepts to determine the zeroes Determine the factors of the denominator. The equation of the rational function is given by f(x) = (x - 2)/(2x + 2) Check answer graphically: The graph of the rational function obtained is shown below. Write Rational Function for Given Hole Equation of a Author: Mathispower4u Views: 105K [PDF] Write Rational Functions Given Information https://www.humbleisd.net/cms/lib2/TX01001414 Write a rational function that has a zero at 2, vertical asymptote at x=0, horizontal asymptote at y=0, and a hole at (1, - 1).
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Let me scroll over a little bit The equation of the rational function is given by f (x) = (x - 2)/ (2x + 2) Check answer graphically: The graph of the rational function obtained is shown below. The calculator can find horizontal, vertical, and slant asymptotes. Add comment Jan 31, 2018 · a vertical write a rational function with the given asymptotes asymptote at #x=-3# means #x+3# a factor in denominator only. Rational functions contain asymptotes, as seen in this example: In this example, there is a vertical asymptote at x = 3 and a horizontal asymptote at y = 1. For rational functions this may seem like a mess to deal with. The line x = a is called a Vertical Asymptote of the curve y = f (x) if at least one of the following Method 2:. The degree of the numerator and degree of the denominator determine whether or not there are any horizontal or oblique asymptotes Answer to Write an equation for a rational function with: Vertical asymptotes at c - 4 and* = 1 x intercepts at a = - 5 and x = -1 y intercept at 6 y=. Rational functions contain asymptotes, as seen in this example: In this example, there is a vertical asymptote at x = 3 and a horizontal asymptote at y = 1.
Problem 1: Write a rational function f that has a vertical asymptote at x = 2, a horizontal asymptote y = 3 and a zero at x = - 5. lo hi fx xxx 112 x x2 2 21 1 xx fx xx HA LOOK at the degrees, these are the same, the Horizontal asymptote is y=0 so the degree of the denominator must be higher than the numerator. Write an equation for rational function with given properties. An asymptote can be vertical, horizontal, or on write a rational function with the given asymptotes any angle. Note any restrictions in the domain of the function. An example of a rational function with no vertical asymptotes and no holes is . So, the denominator has no real roots. Factor the numerator and denominator. By looking into the graph of the function, it will be easy for us to find the vertical asymptotes.. However, there is a nice fact about rational functions that we can use here. Note any restrictions in the domain of the function. Use that information to sketch a graph.
A rational function with vertical asymptote x= 5 x = 5 and horizontal asymptote y= 1 2 y = 1 2.. #(2x^2-22x+56)/(5x^2-20x-105)# See its graph down below Free functions asymptotes calculator - find functions vertical and horizonatal asymptotes step-by-step This website uses cookies to ensure you get the best experience. Answered We can find a maximum of five fractions equivalent to given fractions 2. Answer to Write an equation for a rational function with: Vertical asymptotes at c - 4 and* = 1 x intercepts at a = - 5 and x = -1 y intercept at 6 y=. Descartes' rule of signs a vertical asymptote the leading-term test $\quad$ an oblique the intermediate $\quad$ asymptote value theorem direct variation the fundamental $\quad$ inverse variation theorem of algebra a horizontal line a polynomial function a vertical line a rational function $\quad$ parallel. Write a rational function with the following characteristics: 5. Rational Functions: Finding Horizontal and Slant Asymptotes 1 - Cool Math has free online cool math lessons, cool math games and fun math activities. Using the graph:. Write an equation for a rational function with: Vertical asymptotes at x = 4 and x = -2 x-intercepts at x = 1 and x = -4 y-intercept at 6 Preview y = Get write a rational function with the given asymptotes more help from Chegg Get 1:1 help now from expert Precalculus tutors Solve it with our pre-calculus problem solver and calculator.
Given parameter changes for rational functions, students will be able to predict the resulting changes on important attributes of the function, including domain and range and asymptotic behavior Jul 07, 2020 · Write an equation of a rational function that satisfies all of these conditions: 1. Matched Exercise 2: Find the equation of the rational function f of the form f(x) = (ax - 2 ) / (bx + c). The simplest polynomial we can write is x^2 + 1. So, the denominator has no real roots. Now, if you say this X approaches negative infinity, it would be the same thing. The calculator will find the vertical, horizontal and slant asymptotes of the function, with steps shown. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted write a rational function with the given asymptotes online community for developers to learn, share …. Jul 06, 2020 · From the given information, it is observed that the vertical asymptotes are at x = -6 and x = -4 The x-intercepts at x = 2 and x = -2 and y intercept at 4 Note that, the vertical asymptotes are the value of x for which the denominator of the function is 0 Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share …. Rational function has at most one horizontal asymptote. Specifically, the denominator of a rational function cannot be equal to zero The existence of the horizontal asymptote is related to the degrees of both polynomials in the numerator and the denominator of the given rational function. Jul 04, 2020 · A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. It is fairly easy to find them but it depends on the degree of the top vs bottom polynomial.
WRITING EQUATIONS OF RATIONAL FUNCTIONS To Identify Types of Discontinuity: Step 1: HOLES (Removable Discontinuities) SLANT ASYMPTOTES write a rational function with the given asymptotes (Exists only if Horizontal Asymptote is not State each discontinuity, -intercept, and -intercept. To find the vertical asymptote (s) of a rational function, simply set the denominator equal to 0 and solve for x Write out a function with the given characteristics. One feature of rational functions that is worth noting is the presence (or absence) of asymptotes: lines that the function gets arbitrarily close to but never touches or crosses. f(0) = …. Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share …. Then write an equation for the graph. Check the x intercept, the vertical and the horizontal asymptotes A function of the form where t(x) and n(x) are polynomials is called a rational function The graphs of rational functions can be recognised by the fact that they often break into two or more parts. Rational functions have various asymptotes. Horizontal asymptote at y = 0 3. Consider the simple rational function ; a plot of this function is shown below g.
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F(x) = p(x) / q(x) Domain. The domain of a rational function is all real values except where the denominator, q(x) = 0. This, this and this approach zero and once again you approach 1/2. Note any restrictions in the domain of the function. The following will aid in finding all asymptotes of a rational function. Hole. Method 1:. Let's think about the vertical asymptotes. Jul 01, 2020 · If the given write a rational function with the given asymptotes function has an infinite limit, then we can define the vertical asymptote based on that. If the degree of x in the numerator is less than the degree of x in the denominator then y = 0 is the Horizontal asymptote.
Asked by Squadon July write a rational function with the given asymptotes 11, 2016. y intercept at 9. The basic premise of rational choice theory is that aggregate social behavior results from the behavior of individual actors, each of whom is making their individual decisions Some of the given choices will not be used. Using the graph:. For the above rational function, the denominator is never zero, so there are no vertical asymptotes. Given parameter changes for rational functions, students will be able to predict the resulting changes on important attributes of the function, including domain and range and asymptotic behavior The leading coefficient of numerator is 1 and the leading coefficient of dominator is 1 of given rational function r (x), so, the horizontal asymptote is y = 1. The method is illustrated by an…. Vertical Asymptotes of x 0, x and Horizontal Asymptote of y xlLx-5 'L 6.
An asymptote is a straight line that generally serves as a kind of boundary for the graph of a function. Note any values that cause the denominator to be zero in this simplified version For each function, find the horizontal write a rational function with the given asymptotes intercepts, the vertical intercept, the vertical asymptotes, and the horizontal asymptote. Y is equal to 1/2. Given the rational function, f(x) Step 1: Write f(x) in reduced form. Jul 06, 2020 · From the given information, it is observed that the vertical asymptotes are at x = -6 and x = -4 The x-intercepts at x = 2 and x = -2 and y intercept at 4 Note that, the vertical asymptotes are the value of x for which the denominator of the function is 0 Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share …. Vertical Asymptotes of 5 0, 2 xx and Horizontal Asymptote of y 4 8. In the above graph, the horizontal asymptote is x = 1. Finding Vertical Asymptotes of Rational Functions An asymptote is a line that the graph of a function approaches but never touches. y= a / bif the degree of the numerator, P(x), is equal to the degree of denominator, Q(x), where ais the leading coefficientof P(x) and bis leading coefficient of Q(x) Write an equation for a rational function with: Vertical asymptotes at $x = -5$ and $x = 5$ $x$ intercepts at $x = -2$ and $x = -6$ Horizontal asymptote at $y = 6$. The x-intercepts of given rational function are − 2 _, 1 and y-intercept is 2 3 and vertical asymptotes are x = − 1, x = 3 and horizontal asymptote is y = 1 Jul 07, 2020 · Write an equation of a rational function that satisfies all of these conditions: 1.
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Given rational function, f (x) Write f (x) in reduced form f (x) - c is a factor in the denominator then x = c is the vertical asymptote.. Write the equation of the rational function with vertical asymptotes at x = 2 and x = 1, a zero at x = 5, and a horizontal asymptote at y = 0. Other function may have more than one horizontal asymptote…. The simplest polynomial we can write is x^2 + 1. The curves approach these asymptotes but never cross them. x intercepts at x = 1 and x = 3. Horizontal asymptotes occur when either, the degree of the numerator is less then or equal to the degree of the denominator write a rational function with the given asymptotes For rational functions, vertical asymptotes are vertical lines that correspond to the zeroes of the denominator. Roots.
Asked by Casey on January 10, 2012; Algebra. Briefly, an asymptote is a straight line that a graph comes closer and closer to but never touches The x-axis is a horizontal asymptote of that graph.The write a rational function with the given asymptotes graph and the x-axis come closer and closer but never touch More precisely: "The horizontal line y = b is a horizontal asymptote of the graph of y = f(x)" means: Upon naming any positive number, however small, it will be. When graphing rational functions where the degree of the numerator function is less than the degree of denominator function, we know that y = 0 is a horizontal asymptote Write a rational function with the following characteristics: 5. It can be asymptotic in the same direction depending on the given curve. Once in factored form, find all zeros 3. Be sure to describe the thermodynamics of the reactions, and the two reasons behind the thermodynamics.? Then write an equation for the graph. Note that the curve is asymptotic at opposite side of the line x = 1.
Vertical Asymptotes of xx 2. write a rational function with the given asymptotes
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2020-11-27 00:11:50
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https://mathoverflow.net/questions/296788/bloch-ogus-spectral-sequence
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# Bloch Ogus spectral sequence
Let $X$ be a smooth projective variety over $\mathbf{C}$, and $p : X_{\rm an}\to X_{\rm Zar}$ the obvious map of sites.
The Leray spectral sequence
$$H^r(X_{\rm Zar}, R^sp_*\mathbf{C})\Rightarrow H^{r+s}(X_{\rm an},\mathbf{C})$$ induces a filtration on $H^*(X_{\rm an},\mathbf{C})$ that agrees with the coniveau filtration, as shown by Bloch and Ogus in their paper on homology of schemes.
We have an exact sequence:
$$H^n(X_{\rm Zar}, R^np_*\mathbf{C})\to H^{2n}(X_{\rm an},\mathbf{C})\to H^1(X_{\rm Zar}, R^{2n-1}p_*\mathbf{C})$$ if I'm not wrong (can anyone confirm this, first of all?)
My question is: how can one describe $H^1(X_{\rm Zar}, R^{2n-1}p_*\mathbf{C})$? For example, $H^n(X_{\rm Zar}, R^np_*\mathbf{C})$ is $A^n(X)_{\rm alg}\otimes\mathbf{C}$, the Chow group of cycles up to algebraic equivalence.
Is there a Hodge decomposition for $H^1(X_{\rm Zar}, R^{2n-1}p_*\mathbf{C})$, induced by that of the cohomology of $\mathbf{C}$? Can one use the comparison with algebraic de Rham cohomology?
For instance one could say
$$Rp_*\mathbf{C} = Rp_*\Omega^{\bullet}_{X_{\rm an}}=Rp_*p^*\Omega^{\bullet}_X$$
where $\Omega^{\bullet}_X$ is the algebraic de Rham complex. Is the natural map $$\Omega_X^{\bullet}\to Rp_*p^*\Omega^{\bullet}_X$$ a quasi-isomorphism of Zariski sheaves on $X$?
• I almost read that as "bogus spectral..." 😊 – Suvrit Apr 2 '18 at 1:04
• You're not the first one to point that out to me :) – user92332 Apr 2 '18 at 1:06
• Can you explain where your sequence comes from? Usually the relationship between the terms of a spectral sequence and its abutment is a bit more complicated, so I don't see what you're using. – R. van Dobben de Bruyn Apr 20 '18 at 0:49
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2019-06-24 20:39:28
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https://ncertmcq.com/cbse-sample-papers-for-class-11-physics-term-2-set-4/
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Students can access the CBSE Sample Papers for Class 11 Physics with Solutions and marking scheme Term 2 Set 4 will help students in understanding the difficulty level of the exam.
## CBSE Sample Papers for Class 11 Physics Standard Term 2 Set 4 for Practice
Time Allowed: 2 Hours
Maximum Marks: 40
General Instructions:
• There are 12 questions in all. All questions are compulsory.
• This question paper has three sections: Section A, Section B and Section C.
• Section A contains three questions of two marks each, Section B contains eight questions of three marks each, Section C contains one case study-based question of five marks.
• There is no overall choice. However, an internal choice has been provided in one question of two marks and two questions of three marks. You have to attempt only one of the choices in such questions.
• You may use log tables if necessary but use of calculator is not allowed.
Section – A (2 Marks Each)
Question 1.
The excess pressure inside a soap bubble is thrice the excess pressure inside a ’second soap bubble. What is the ratio of volume of two bubbles ?
Question 2.
Why a thick glass tumbler cracks when boiling water is poured in it ?
OR
An alloy consist of n metals of masses m1 m2 m3 …, mn and specific heat capacities c1 c2, c3 …cn. If the specific heat capacity of alloy is c, then calculate c.
Question 3.
What is an ‘Indicator diagram’ ? What is its importance ?
Section – B (3 Marks Each)
Question 4.
Define the coefficient of thermal conductivity.
Question 5.
Consider a cycle tyre being filled with air by a pump. Let V be the volume of the tyre (fixed) and at each stroke of the pump ΔV(« V) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from P1 to P2 ?
Question 6.
Calculate the average kinetic energy for one molecule of a gas at constant volume.
Question 7.
The periodic time of a mass suspended by a spring (force constant k) is T If the spring is cut in three equal pieces, what will be the force constant of each part? If the same mass be suspended from one piece, what will be the periodic time?
Question 8.
By using Stokes law, derive an expression for terminal velocity. On what factors does it depend ?
OR
An air bubble of radius r rises steadily through a liquid of density p at the rate of v. Neglecting density of air, find the coefficient of viscosity of liquid.
Question 9.
A particle in linear simple harmonic motion has a velocity of 4 ms-1 at 3 m at 3 ms-1 at 4 m from mean position. What is the time taken to travel half the amplitude from its positive extreme position ?
Question 10.
The wave pattern on a stretched string is shown in Fig. Interpret what kind of wave this is and find
its wavelength.
Question 11.
A steel wire has a length of 12 m and a mass of 2.10 kg. What will be the speed of a transverse wave on this wire when a tension of 2.06 × 104 N is applied?
OR
List the factors affecting the speed of sound in a gaseous medium.
Section – C (5 Marks)
Question 12.
Case Study: Sagging of a bridge
A bridge is designed such that it can withstand the load of the flowing traffic, the force of winds and its own weight.
Let us consider the case of a beam loaded at the centre and supported near its ends as shown in Figure.
A beam of length l, breadth b, and depth d when loaded at the centre by a load W sags by an amount given by
δ = $$\frac{W l^{3}}{4 b d^{3} Y}$$
From the equation, we see that to reduce the bending for a given load, one should use a material with a large Young’s modulus Y. For a given material, increasing the depth d rather than the breadth b is more effective in reducing the bending, since 8 is proportional to d-3 and to b-1 (of course the length l of the span should be as small as possible).
Amongst bridge materials, steel has the highest and most favorable strength qualities, and it is therefore suitable for the most daring bridges with the longest spans. Normal building steel has compressive and tensile strengths of 370 N/sq. mm, about ten times the compressive strength of a medium concrete and a hundred times its tensile strength. A special merit of steel is its ductility due to which it deforms considerably before it breaks, because it begins to yield above a certain stress level.
(i) To reduce bending of a beam
(a) For a given length and material, depth should be greater than breadth.
(b) For a given length and material, breadth should be greater than depth.
(c) For a given length and material, depth should be equal to breadth.
(d) Breadth and depth has no effect. [1]
(ii) Compressive strength of normal building steel is about ………………….. times of the compressive strength of medium concrete.
(a) 2
(b) 10
(c) 100
(d) 1000 [1]
(iii) What is the special merit of steel over concrete is its
(a) Malleability
(b) Brittleness
(c) Conductivity
(d) Ductility [1]
(iv) A bar of length l, breadth b, and depth d, supported at two ends when loaded at the centre by a load W sags by an amount given by
(a) δ = $$\frac{W l^{3}}{4 b d^{3} \mathrm{Y}}$$
(b) δ = $$\frac{W l}{4 b d^{3} \mathrm{Y}}$$
(c) δ = $$\frac{W l^{3}}{4 b^{3} d Y}$$
(d) δ = $$\frac{W Y l^{3}}{4 b d^{3}}$$
(v) Why ductility is the special merit of steel?
(a) Ductility allows structures to bend and deform to some extent without rupturing.
(b) Ductility offers the structure a high rigidity
(c) Ductility prevents the structure to sag while overloaded
(d) Ductility offers less corrosion
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2022-11-27 08:40:21
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https://www.daniweb.com/community-center/threads/70627/how-high-can-we-count-game/3
|
278 + 278 -278 = 278
278 - (-278) = 556
Exp(556)=556e+0
Lets extend our number system...yes complex number!!!
Cube root of 1:
(1)^(1/3) = 1, [-1 (+/-) sqrt(3)*i]/2
Now you give me cube root of i
I wondered what happened to this game. Why doesn't anyone play it anymore? Lol.
2 + 2 = 4
4 * 4 = 16
16 - 2 = 14
14 - 7 = 7
7 * 7 = 49
49 * 49 = 2401
$$2^{\lfloor\log_2{2401}\rfloor + 1} = 4096$$
sideways 8:lol:
uh, josh, how did that fit the thread rules? :p
$$\infty = lim_{x \to 0}\frac{1}{x}$$
good luck to the next person :twisted:
$$\infty / 42 = \infty$$
$$\infty+\infty = 3$$
$$\frac{3}{-3} = -1$$
sinX/n = 6 :ooh:
6 * 11.5 = 69:d
$$69 = 13^2 - 100$$
From now on lets use lisp synatx!
(* (+ 69 43 23 (- 30 34) 34)
hah.. um, got me there
lisp lisp uses prefix operators instead of infix operators. so for example (+ 4 3 2) =4+3+2. OOps the above had an error! It should be :
(* (+ 69 43 23 (- 30 34) )34)
This would equal:
34(69+43+23+(30-34))
Get it?
1 + 0 - ( 1000000 * 0 ) = 0
(*(+11)1) = 2 :sweat:
0 + 0 = 1
2+2=22
$$22 * 3 + 600 = 666$$
666 / 3 = 222
222*1=222
222 / 2 = 111
This topic has been dead for over six months. Start a new discussion instead.
Have something to contribute to this discussion? Please be thoughtful, detailed and courteous, and be sure to adhere to our posting rules.
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2018-06-21 14:39:51
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|
https://www.dsprelated.com/freebooks/filters/Laplace_Analysis_Linear_Systems.html
|
## Laplace Analysis of Linear Systems
The differentiation theorem can be used to convert differential equations into algebraic equations, which are easier to solve. We will now show this by means of two examples.
### Moving Mass
Figure D.1 depicts a free mass driven by an external force along an ideal frictionless surface in one dimension. Figure D.2 shows the electrical equivalent circuit for this scenario in which the external force is represented by a voltage source emitting volts, and the mass is modeled by an inductor having the value Henrys.
From Newton's second law of motion '', we have
Taking the unilateral Laplace transform and applying the differentiation theorem twice yields
Thus, given
• Laplace transform of the driving force ,
• initial mass position, and
• initial mass velocity,
we can solve algebraically for , the Laplace transform of the mass position for all . This Laplace transform can then be inverted to obtain the mass position for all . This is the general outline of how Laplace-transform analysis goes for all linear, time-invariant (LTI) systems. For nonlinear and/or time-varying systems, Laplace-transform analysis cannot, strictly speaking, be used at all.
If the applied external force is zero, then, by linearity of the Laplace transform, so is , and we readily obtain
Since is the Laplace transform of the Heaviside unit-step function
we find that the position of the mass is given for all time by
Thus, for example, a nonzero initial position and zero initial velocity results in for all ; that is, the mass just sits there''.D.3 Similarly, any initial velocity is integrated with respect to time, meaning that the mass moves forever at the initial velocity.
To summarize, this simple example illustrated use the Laplace transform to solve for the motion of a simple physical system (an ideal mass) in response to initial conditions (no external driving forces). The system was described by a differential equation which was converted to an algebraic equation by the Laplace transform.
### Mass-Spring Oscillator Analysis
Consider now the mass-spring oscillator depicted physically in Fig.D.3, and in equivalent-circuit form in Fig.D.4.
By Newton's second law of motion, the force applied to a mass equals its mass times its acceleration:
By Hooke's law for ideal springs, the compression force applied to a spring is equal to the spring constant times the displacement :
By Newton's third law of motion (every action produces an equal and opposite reaction''), we have . That is, the compression force applied by the mass to the spring is equal and opposite to the accelerating force exerted in the negative- direction by the spring on the mass. In other words, the forces at the mass-spring contact-point sum to zero:
We have thus derived a second-order differential equation governing the motion of the mass and spring. (Note that in Fig.D.3 is both the position of the mass and compression of the spring at time .)
Taking the Laplace transform of both sides of this differential equation gives
To simplify notation, denote the initial position and velocity by and , respectively. Solving for gives
denoting the modulus and angle of the pole residue , respectively. From §D.1, the inverse Laplace transform of is , where is the Heaviside unit step function at time 0. Then by linearity, the solution for the motion of the mass is
If the initial velocity is zero (), the above formula reduces to and the mass simply oscillates sinusoidally at frequency , starting from its initial position . If instead the initial position is , we obtain
Next Section:
Example Analog Filter
Previous Section:
Laplace Transform Theorems
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2020-07-13 09:19:39
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https://www.toktol.com/notes/context/3257/maths/algebraic-expressions/choosing-the-letter
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Use adaptive quiz-based learning to study this topic faster and more effectively.
# Choosing the letter
In an algebraic expression, the choice of the letter is not important.
However some letters are used more frequently depending on their interpretation in the formula.
Letter Range Meaning Values Expression
$x$, $y$, $z$ $\R$ Position, generic variable $-3.14$ $\Tred{x}+\Torange{y}-3$
$t$, $s$ $\R$ Time $1.1$ $\Tred{t}^2$, $3\Torange{s}$
$m$, $n$, $p$, $q$ $\Z^+$, $\Z$ Index, generic integer $12$ $\Tred{n} = \Torange{p}^2 + \Tgreen{q}$
$\theta$ $\R$ Angle $45^\circ$ $\cos(\Tred{\theta})$
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2017-07-24 16:47:20
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|
https://docs.ocean.dwavesys.com/en/latest/examples/and.html
|
# Boolean AND Gate¶
This example solves a simple problem of a Boolean AND gate on a D-Wave system to demonstrate programming the underlying hardware more directly; in particular, minor-embedding a chain.
Other examples demonstrate more advanced steps that are typically needed for solving actual problems.
## Example Requirements¶
To run the code in this example, the following is required.
If you installed dwave-ocean-sdk and ran dwave config create, your installation should meet these requirements.
## Solution Steps¶
Section Solving Problems on a D-Wave System describes the process of solving problems on the quantum computer in two steps: (1) Formulate the problem as a binary quadratic model (BQM) and (2) Solve the BQM with a D-wave system or classical sampler. In this example, we mathematically formulate the BQM and use Ocean tools to solve it on a D-Wave system.
## Formulate the AND Gate as a BQM¶
Ocean tools can automate the representation of logic gates as a BQM, as demonstrated in the Multiple-Gate Circuit example. The Boolean NOT Gate example presents a mathematical formulation of a BQM for a Boolean gate in detail. Here we briefly repeat the steps of mathematically formulating a BQM while adding details on the underlying physical processes.
A D-Wave quantum processing unit (QPU) is a chip with interconnected qubits; for example, a D-Wave 2000Q has up to 2048 qubits connected in a Chimera topology. Programming it consists mostly of setting two inputs:
• Qubit bias weights: control the degree to which a qubit tends to a particular state.
• Qubit coupling strengths: control the degree to which two qubits tend to the same state.
The biases and couplings define an energy landscape, and the D-Wave quantum computer seeks the minimum energy of that landscape. Once you express your problem in a formulation[1] such that desired outcomes have low energy values and undesired outcomes high energy values, the D-Wave system solves your problem by finding the low-energy states.
[1] This formulation, called an objective function, corresponds to the Ising model traditionally used in statistical mechanics: given $$N$$ variables $$s_1,...,s_N$$, corresponding to physical Ising spins, where each variable $$s_i$$ can have values $$-1$$ or $$+1$$, the system energy for an assignment of values is, $E(\pmb{s}|\pmb{h},\pmb{J}) = \left\{ \sum_{i=1}^N h_i s_i + \sum_{i Here we use another binary quadratic model (BQM), the computer-science equivalent of the Ising model, the QUBO: given $$M$$ variables $$x_1,...,x_N$$, where each variable $$x_i$$ can have binary values $$0$$ or $$1$$, the system tries to find assignments of values that minimize \[E(q_i, q_{i,j}; x_i) = \sum_i^N q_ix_i + \sum_{i<j}^N q_{i,j}x_i x_j,$
where $$q_i$$ and $$q_{i,j}$$ are configurable (linear and quadratic) coefficients. To formulate a problem for the D-Wave system is to program $$q_i$$ and $$q_{i,j}$$ so that assignments of $$x_1,...,x_N$$ also represent solutions to the problem.
### AND as a Penalty Function¶
This example represents the AND operation, $$z \Leftrightarrow x_1 \wedge x_2$$, where $$x_1, x_2$$ are the gate’s inputs and $$z$$ its output, using a penalty function:
$x_1 x_2 - 2(x_1+x_2)z +3z.$
This penalty function represents the AND gate in that for assignments of variables that match valid states of the gate, the function evaluates at a lower value than assignments that would be invalid for the gate. Therefore, when the D-Wave system minimizes a BQM based on this penalty function, it finds those assignments of variables that match valid gate states.
You can verify that this penalty function represents the AND gate in the same way as was done in the Boolean NOT Gate example. See the D-Wave Problem-Solving Handbook for more information about penalty functions in general, and penalty functions for representing Boolean operations in particular.
### Formulating the Problem as a QUBO¶
For this example, the penalty function is quadratic, and easily reordered in the familiar QUBO formulation:
$E(q_i, q_{i,j}; x_i) = 3x_3 + x_1x_2 - 2x_1x_3 - 2x_2x_3$
where $$z=x_3$$ is the AND gate’s output, $$x_1, x_2$$ the inputs, linear coefficients are $$q_1=3$$, and quadratic coefficients are $$q_{1,2}=1, q_{1,3}=-2, q_{2,3}=-2$$. The coefficients matrix is,
$\begin{split}Q = \begin{bmatrix} 0 & 1 & -2\\ & 0 & -2\\ & & 3 \end{bmatrix}\end{split}$
See the Getting Started with the D-Wave System and D-Wave Problem-Solving Handbook books for more information about formulating problems as QUBOs.
The line of code below sets the QUBO coefficients for this AND gate.
>>> Q = {('x1', 'x2'): 1, ('x1', 'z'): -2, ('x2', 'z'): -2, ('z', 'z'): 3}
## Solve the Problem by Sampling: Automated Minor-Embedding¶
For reference, we first solve with the same steps used in the Boolean NOT Gate example before solving again while manually controlling additional parameters.
Again we use sampler DWaveSampler() from Ocean software’s dwave-system and its EmbeddingComposite() composite to minor-embed our unstructured problem (variables x1, x2, and z) on the sampler’s graph structure (the QPU’s numerically indexed qubits).
The next code sets up a D-Wave system as the sampler.
Note
In the code below, replace sampler parameters in the third line. If you configured a default solver, as described in Using a D-Wave System, you should be able to set the sampler without parameters as sampler = DWaveSampler(). You can see this information by running dwave config inspect in your terminal.
>>> from dwave.system.samplers import DWaveSampler
>>> from dwave.system.composites import EmbeddingComposite
>>> sampler = DWaveSampler(endpoint='https://URL_to_my_D-Wave_system/', token='ABC-123456789012345678901234567890', solver='My_D-Wave_Solver')
>>> sampler_embedded = EmbeddingComposite(sampler)
As before, we ask for 5000 samples.
>>> response = sampler_embedded.sample_qubo(Q, num_reads=5000)
>>> for datum in response.data(['sample', 'energy', 'num_occurrences']):
... print(datum.sample, "Energy: ", datum.energy, "Occurrences: ", datum.num_occurrences)
...
{'x1': 1, 'x2': 0, 'z': 0} Energy: 0.0 Occurrences: 1009
{'x1': 1, 'x2': 1, 'z': 1} Energy: 0.0 Occurrences: 1452
{'x1': 0, 'x2': 0, 'z': 0} Energy: 0.0 Occurrences: 1292
{'x1': 0, 'x2': 1, 'z': 0} Energy: 0.0 Occurrences: 1246
{'x1': 0, 'x2': 1, 'z': 0} Energy: 0.0 Occurrences: 1
All the returned samples from this execution represent valid value assignments for an AND gate, and minimize (are low-energy states of) the BQM.
Note that the last line of output from this execution shows a single sample that seems identical to the line above it. The next section addresses that.
## Solve the Problem by Sampling: Non-automated Minor-Embedding¶
This section looks more closely into minor-embedding. Above and in the Boolean NOT Gate example, dwave-system EmbeddingComposite() composite abstracted the minor-embedding.
### Minor-Embedding a NOT Gate¶
For simplicity, we first return to the NOT gate. The Boolean NOT Gate example found that a NOT gate can be represented by a BQM in QUBO form with the following coefficients:
>>> Q_not = {('x', 'x'): -1, ('x', 'z'): 2, ('z', 'x'): 0, ('z', 'z'): -1}
Minor embedding maps the two problem variables x and z to the indexed qubits of the D-Wave QPU. Here we do this mapping ourselves.
The next line of code looks at properties of the sampler. We select the first node, which on a QPU is a qubit, and print its adjacent nodes, i.e., coupled qubits.
>>> print(sampler.adjacency[sampler.nodelist[0]])
{128, 4, 5, 6, 7}
For the D-Wave system the above code ran on, we see that the first available qubit is adjacent to qubit 4 and four others.
We can map the NOT problem’s two linear coefficients and single quadratic coefficient, $$q_1=q_2=-1$$ and $$q_{1,2}=2$$, to biases on qubits 0 and 4 and coupling (0, 4). The figure below shows a minor embedding of the NOT gate into a D-Wave 2000Q QPU unit cell (four horizontal qubits connected to four vertical qubits via couplers).
A NOT gate minor embedded into the topmost left unit cell of a D-Wave 2000Q QPU. Variables $$x_1,x_2$$ are minor embedded as qubits 0 and 4 (blue circles). Biases $$q_1,q_2=-1,-1$$ and coupling strength $$q_{1,2}=2$$ are also shown.
The following code uses the FixedEmbeddingComposite composite to manually minor-embed the problem. Its last line prints a confirmation that indeed the two selected qubits are adjacent (coupled).
>>> from dwave.system.composites import FixedEmbeddingComposite
>>> sampler_embedded = FixedEmbeddingComposite(sampler, {'x': [0], 'z': [4]})
{'x': {'z'}, 'z': {'x'}}
As before, we ask for 5000 samples.
>>> response = sampler_embedded.sample_qubo(Q_not, num_reads=5000)
>>> for datum in response.data(['sample', 'energy', 'num_occurrences']):
... print(datum.sample, "Energy: ", datum.energy, "Occurrences: ", datum.num_occurrences)
...
{'x': 0, 'z': 1} Energy: -1.0 Occurrences: 2520
{'x': 1, 'z': 0} Energy: -1.0 Occurrences: 2474
{'x': 0, 'z': 0} Energy: 0.0 Occurrences: 4
{'x': 1, 'z': 1} Energy: 0.0 Occurrences: 2
### From NOT to AND: an Important Difference¶
• The BQM for a NOT gate, $$-x -z + 2xz$$, can be represented by a fully connected $$K_2$$ graph: its linear coefficients are weights of the two connected nodes with the single quadratic coefficient the weight of its connecting edge.
• The BQM for an AND gate, $$3z + x_1x_2 - 2x_1z - 2x_2z$$, needs a $$K_3$$ graph.
NOT gate $$K_2$$ complete graph (top) versus AND gate $$K_3$$ complete graph (bottom.)
We saw above how to minor-embed a $$K_2$$ graph on a D-Wave system. To minor-embed a fully connected $$K_3$$ graph requires chaining qubits.
### Minor-Embedding an AND Gate¶
To understand how a $$K_3$$ graph fits on the Chimera topology of the QPU, look at the Chimera unit cell structure shown below. You cannot connect 3 qubits in a closed loop. However, you can make a closed loop of 4 qubits using, say, qubits 0, 1, 4, and 5.
To fit the 3-qubit loop into a 4-sided structure, create a chain of 2 qubits to represent a single variable. For example, chain qubit 0 and qubit 4 to represent variable $$z$$.
The strength of the coupler between qubits 0 and 4, which represents variable $$z$$, must be set to correlate the qubits strongly, so that in most solutions they have a single value for $$z$$. (Remember the output in the Solve the Problem by Sampling: Automated Minor-Embedding section with its identical two last lines? This was likely due to the qubits in a chain taking different values.)
The code below uses Ocean’s dwave-system FixedEmbeddingComposite() composite for manual minor-embedding. Its last line prints a confirmation that indeed all three variables are connected. (coupled).
>>> from dwave.system.composites import FixedEmbeddingComposite
>>> embedding = {'x1': {1}, 'x2': {5}, 'z': {0, 4}}
>>> sampler_embedded = FixedEmbeddingComposite(sampler, embedding)
{'x1': {'x2', 'z'}, 'x2': {'x1', 'z'}, 'z': {'x1', 'x2'}}
>>> Q = {('x1', 'x2'): 1, ('x1', 'z'): -2, ('x2', 'z'): -2, ('z', 'z'): 3}
>>> for datum in response.data(['sample', 'energy', 'num_occurrences']):
... print(datum.sample, "Energy: ", datum.energy, "Occurrences: ", datum.num_occurrences)
...
{'z': 0, 'x1': 1, 'x2': 0} Energy: 0.0 Occurrences: 1088
{'z': 0, 'x1': 0, 'x2': 1} Energy: 0.0 Occurrences: 1806
{'z': 1, 'x1': 1, 'x2': 1} Energy: 0.0 Occurrences: 1126
{'z': 0, 'x1': 0, 'x2': 0} Energy: 0.0 Occurrences: 977
{'z': 1, 'x1': 0, 'x2': 1} Energy: 1.0 Occurrences: 2
{'z': 1, 'x1': 0, 'x2': 1} Energy: 1.0 Occurrences: 1
For comparison, the following code purposely weakens the chain strength (strength of the coupler between qubits 0 and 4, which represents variable $$z$$). The first line prints the range of values available for the D-Wave system this code is executed on. By default, FixedEmbeddingComposite() used the maximum chain strength, which is 2. By setting it to a low value of 0.25, the two qubits are not strongly correlated and the result is that many returned samples represent invalid states for an AND gate.
>>> print(sampler.properties['extended_j_range'])
[-2.0, 1.0]
>>> sampler_embedded = FixedEmbeddingComposite(sampler, embedding)
>>> response = sampler_embedded.sample_qubo(Q, num_reads=5000, chain_strength=0.25)
>>> for datum in response.data(['sample', 'energy', 'num_occurrences']):
... print(datum.sample, "Energy: ", datum.energy, "Occurrences: ", datum.num_occurrences)
...
{'z': 0, 'x1': 1, 'x2': 0} Energy: 0.0 Occurrences: 690
{'z': 0, 'x1': 0, 'x2': 1} Energy: 0.0 Occurrences: 936
{'z': 1, 'x1': 1, 'x2': 1} Energy: 0.0 Occurrences: 573
{'z': 0, 'x1': 0, 'x2': 0} Energy: 0.0 Occurrences: 984
{'z': 1, 'x1': 1, 'x2': 1} Energy: 0.0 Occurrences: 1
{'z': 1, 'x1': 1, 'x2': 0} Energy: 1.0 Occurrences: 525
{'z': 1, 'x1': 0, 'x2': 1} Energy: 1.0 Occurrences: 1289
{'z': 1, 'x1': 1, 'x2': 0} Energy: 1.0 Occurrences: 1
{'z': 0, 'x1': 1, 'x2': 1} Energy: 1.0 Occurrences: 1
|
2019-11-16 02:45:04
|
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|
https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Intermediate_Algebra_(OpenStax)/2%3A_Solving_Linear_Equations/2.E%3A_Foundation_(exercises)
|
# 2.E: Foundation (exercises)
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
## Chapter Review Exercises
### Use a General Strategy to Solve Linear Equations
Solve Equations Using the General Strategy for Solving Linear Equations
In the following exercises, determine whether each number is a solution to the equation.
$$10x−1=5x,x= \frac{1}{5}$$
$$−12n+5=8n,n=−\frac{5}{4}$$
no
In the following exercises, solve each linear equation.
$$6(x+6)=24$$
$$−(s+4)=18$$
$$s=−22$$
$$23−3(y−7)=8$$
$$\frac{1}{3}(6m+21)=m−7$$
$$m=−14$$
$$4(3.5y+0.25)=365$$
$$0.25(q−8)=0.1(q+7)$$
$$q=18$$
$$8(r−2)=6(r+10)$$
$$5+7(2−5x)=2(9x+1)−(13x−57)$$
$$x=−1$$
$$(9n+5)−(3n−7)=20−(4n−2)$$
$$2[−16+5(8k−6)]=8(3−4k)−32$$
$$k=\frac{3}{4}$$
Classify Equations
In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution.
$$17y−3(4−2y)=11(y−1)+12y−1$$
$$9u+32=15(u−4)−3(2u+21)$$
$$contradiction; no solution$$
$$−8(7m+4)=−6(8m+9)$$
Solve Equations with Fraction or Decimal Coefficients
In the following exercises, solve each equation.
$$\frac{2}{5}n−\frac{1}{10}=\frac{7}{10}$$
$$n=2$$
$$\frac{3}{4}a−\frac{1}{3}=\frac{1}{2}a+\frac{5}{6}$$
$$\frac{1}{2}(k+3)=\frac{1}{3}(k+16)$$
$$k=23$$
$$\frac{5y−1}{3}+4=\frac{-8y+4}{6}$$
$$0.8x−0.3=0.7x+0.2$$
$$x=5$$
$$0.10d+0.05(d−4)=2.05$$
### Use a Problem-Solving Strategy
Use a Problem Solving Strategy for Word Problems
In the following exercises, solve using the problem solving strategy for word problems.
Three-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert?
There are 116 people.
There are nine saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.
Solve Number Word Problems
In the following exercises, solve each number word problem.
The sum of a number and three is forty-one. Find the number.
38
One number is nine less than another. Their sum is negative twenty-seven. Find the numbers.
One number is two more than four times another. Their sum is negative thirteen. Find the numbers.
$$−3,−10$$
The sum of two consecutive integers is $$−135$$. Find the numbers.
Find three consecutive even integers whose sum is 234.
76, 78, 80
Find three consecutive odd integers whose sum is 51.
Koji has $5,502 in his savings account. This is$30 less than six times the amount in his checking account. How much money does Koji have in his checking account?
$922 Solve Percent Applications In the following exercises, translate and solve. What number is 67% of 250? 12.5% of what number is 20? Answer $$160$$ What percent of 125 is 150? In the following exercises, solve. The bill for Dino’s lunch was$19.45. He wanted to leave 20% of the total bill as a tip. How much should the tip be?
$$3.89$$
Dolores bought a crib on sale for $350. The sale price was 40% of the original price. What was the original price of the crib? Jaden earns$2,680 per month. He pays $938 a month for rent. What percent of his monthly pay goes to rent? Answer $$35%$$ Angel received a raise in his annual salary from$55,400 to $56,785. Find the percent change. Rowena’s monthly gasoline bill dropped from$83.75 last month to $56.95 this month. Find the percent change. Answer $$32%$$ Emmett bought a pair of shoes on sale at 40% off from an original price of$138. Find ⓐ the amount of discount and ⓑthe sale price.
Lacey bought a pair of boots on sale for $95. The original price of the boots was$200. Find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percent, if needed.)
ⓐ $$105$$ ⓑ $$52.5%$$
Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350% mark-up. Find ⓐthe amount of the mark-up and ⓑ the list price. Solve Simple Interest Applications In the following exercises, solve. Winston deposited$3,294 in a bank account with interest rate 2.6% How much interest was earned in five years?
$$428.22$$
Moira borrowed $4,500 from her grandfather to pay for her first year of college. Three years later, she repaid the$4,500 plus $243 interest. What was the rate of interest? Jaime’s refrigerator loan statement said he would pay$1,026 in interest for a four-year loan at 13.5%. How much did Jaime borrow to buy the refrigerator?
$$1,900$$
### Solve a formula for a Specific Variable
Solve a Formula for a Specific Variable
In the following exercises, solve the formula for the specified variable.
Solve the formula
$$V=LWH$$ for L.
Solve the formula
$$A=\frac{1}{2}d_1d_2$$ for $$d_2$$.
$$d_2=\frac{2A}{d_1}$$
Solve the formula
$$h=48t+\frac{1}{2}at^2$$ for t.
Solve the formula
4x−3y=12 for y.
$$y=\frac{4x}{3}−4$$
Use Formulas to Solve Geometry Applications
In the following exercises, solve using a geometry formula.
What is the height of a triangle with area 67.567.5 square meters and base 9 meters?
The measure of the smallest angle in a right triangle is 45°45° less than the measure of the next larger angle. Find the measures of all three angles.
$$22.5°,67.5°,90°$$
The perimeter of a triangle is 97 feet. One side of the triangle is eleven feet more than the smallest side. The third side is six feet more than twice the smallest side. Find the lengths of all sides.
Find the length of the hypotenuse.
$$26$$
Find the length of the missing side. Round to the nearest tenth, if necessary.
Sergio needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is eight feet tall and Sergio has 10 feet of wire. How far from the base of the antenna can he attach the wire? Approximate to the nearest tenth, if necessary.
6 feet
Seong is building shelving in his garage. The shelves are 36 inches wide and 15 inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?
The length of a rectangle is 12 cm more than the width. The perimeter is 74 cm. Find the length and the width.
$$24.5$$ cm, $$12.5$$ cm
The width of a rectangle is three more than twice the length. The perimeter is 96 inches. Find the length and the width.
The perimeter of a triangle is 35 feet. One side of the triangle is five feet longer than the second side. The third side is three feet longer than the second side. Find the length of each side.
9 ft, 14 ft, 12 ft
### Solve Mixture and Uniform Motion Applications
Solve Coin Word Problems
In the following exercises, solve.
Paulette has $140 in$5 and $10 bills. The number of$10 bills is one less than twice the number of $5 bills. How many of each does she have? Lenny has$3.69 in pennies, dimes, and quarters. The number of pennies is three more than the number of dimes. The number of quarters is twice the number of dimes. How many of each coin does he have?
nine pennies, six dimes, 12 quarters
Solve Ticket and Stamp Word Problems
In the following exercises, solve each ticket or stamp word problem.
Tickets for a basketball game cost $2 for students and$5 for adults. The number of students was three less than 10 times the number of adults. The total amount of money from ticket sales was $619. How many of each ticket were sold? 125 tickets were sold for the jazz band concert for a total of$1,022. Student tickets cost $6 each and general admission tickets cost$10 each. How many of each kind of ticket were sold?
Yumi spent $34.15 buying stamps. The number of$0.56 stamps she bought was 10 less than four times the number of $0.41 stamps. How many of each did she buy? Solve Mixture Word Problems In the following exercises, solve. Marquese is making 10 pounds of trail mix from raisins and nuts. Raisins cost$3.45 per pound and nuts cost $7.95 per pound. How many pounds of raisins and how many pounds of nuts should Marquese use for the trail mix to cost him$6.96 per pound?
$$2.2$$ lbs of raisins, $$7.8$$ lbs of nuts
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tile. She will use basic tiles that cost $8 per square foot and decorator tiles that cost$20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be $10 per square foot? Enrique borrowed$23,500 to buy a car. He pays his uncle 2% interest on the $4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total$23,500? (Round your answer to the nearest tenth of a percent.)
$$9.7%$$
Solve Uniform Motion Applications
In the following exercises, solve.
When Gabe drives from Sacramento to Redding it takes him 2.2 hours. It takes Elsa two hours to drive the same distance. Elsa’s speed is seven miles per hour faster than Gabe’s speed. Find Gabe’s speed and Elsa’s speed.
Louellen and Tracy met at a restaurant on the road between Chicago and Nashville. Louellen had left Chicago and drove 3.2 hours towards Nashville. Tracy had left Nashville and drove 4 hours towards Chicago, at a speed one mile per hour faster than Louellen’s speed. The distance between Chicago and Nashville is 472 miles. Find Louellen’s speed and Tracy’s speed.
Louellen 65 mph, Tracy 66 mph
Two busses leave Amarillo at the same time. The Albuquerque bus heads west on the I-40 at a speed of 72 miles per hour, and the Oklahoma City bus heads east on the I-40 at a speed of 78 miles per hour. How many hours will it take them to be 375 miles apart?
Kyle rowed his boat upstream for 50 minutes. It took him 30 minutes to row back downstream. His speed going upstream is two miles per hour slower than his speed going downstream. Find Kyle’s upstream and downstream speeds.
upstream 3 mph, downstream 5 mph
At 6:30, Devon left her house and rode her bike on the flat road until 7:30. Then she started riding uphill and rode until 8:00. She rode a total of 15 miles. Her speed on the flat road was three miles per hour faster than her speed going uphill. Find Devon’s speed on the flat road and riding uphill.
Anthony drove from New York City to Baltimore, which is a distance of 192 miles. He left at 3:45 and had heavy traffic until 5:30. Traffic was light for the rest of the drive, and he arrived at 7:30. His speed in light traffic was four miles per hour more than twice his speed in heavy traffic. Find Anthony’s driving speed in heavy traffic and light traffic.
heavy traffic 32 mph, light traffic 66 mph
### Solve Linear Inequalities
Graph Inequalities on the Number Line
In the following exercises, graph the inequality on the number line and write in interval notation.
$$x<−1$$
$$x\geq −2.5$$
$$x\leq \frac{5}{4}$$
$$x>2$$
$$−2<x<0$$
$$-5\leq x<−3$$
$$0\leq x\leq 3.5$$
Solve Linear Inequalities
In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
$$n−12\leq 23$$
$$a+\frac{2}{3}\geq \frac{7}{12}$$
$$9x>54$$
$$\frac{q}{−2}\geq −24$$
$$6p>15p−30$$
$$9h−7(h−1)\leq 4h−23$$
$$5n−15(4−n)<10(n−6)+10n$$
$$\frac{3}{8}a−\frac{1}{12}a>\frac{5}{12}a+\frac{3}{4}$$
Translate Words to an Inequality and Solve
In the following exercises, translate and solve. Then write the solution in interval notation and graph on the number line.
Five more than z is at most 19.
Three less than c is at least 360.
Nine times n exceeds 42.
Negative two times a is no more than eight.
Solve Applications with Linear Inequalities
In the following exercises, solve.
Julianne has a weekly food budget of $231 for her family. If she plans to budget the same amount for each of the seven days of the week, what is the maximum amount she can spend on food each day? Answer$33 per day
Rogelio paints watercolors. He got a $100 gift card to the art supply store and wants to use it to buy 12″ × 16″ canvases. Each canvas costs$10.99. What is the maximum number of canvases he can buy with his gift card?
Briana has been offered a sales job in another city. The offer was for $42,500 plus 8% of her total sales. In order to make it worth the move, Briana needs to have an annual salary of at least$66,500. What would her total sales need to be for her to move?
at least $300,000 Renee’s car costs her$195 per month plus $0.09 per mile. How many miles can Renee drive so that her monthly car expenses are no more than$250?
Costa is an accountant. During tax season, he charges $125 to do a simple tax return. His expenses for buying software, renting an office, and advertising are$6,000. How many tax returns must he do if he wants to make a profit of at least $8,000? Answer at least 112 jobs Jenna is planning a five-day resort vacation with three of her friends. It will cost her$279 for airfare, $300 for food and entertainment, and$65 per day for her share of the hotel. She has $550 saved towards her vacation and can earn$25 per hour as an assistant in her uncle’s photography studio. How many hours must she work in order to have enough money for her vacation?
### Solve Compound Inequalities
Solve Compound Inequalities with “and”
In each of the following exercises, solve each inequality, graph the solution, and write the solution in interval notation.
$$x\leq 5$$ and $$x>−3$$
$$4x−2\leq 4$$ and
$$7x−1>−8$$
$$5(3x−2)\leq 5$$ and
$$4(x+2)<3$$
$$34(x−8)\leq 3$$ and
$$15(x−5)\leq 3$$
$$34x−5\geq −2$$ and
$$−3(x+1)\geq 6$$
$$−5\leq 4x−1<7$$
Solve Compound Inequalities with “or”
In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
$$5−2x\leq −1$$ or
$$6+3x\leq 4$$
$$3(2x−3)<−5$$ or
$$4x−1>3$$
$$34x−2>4$$ or $$4(2−x)>0$$
$$2(x+3)\geq 0$$ or
$$3(x+4)\leq 6$$
$$12x−3\leq 4$$ or
$$13(x−6)\geq −2$$
Solve Applications with Compound Inequalities
In the following exercises, solve.
Liam is playing a number game with his sister Audry. Liam is thinking of a number and wants Audry to guess it. Five more than three times her number is between 2 and 32. Write a compound inequality that shows the range of numbers that Liam might be thinking of.
Elouise is creating a rectangular garden in her back yard. The length of the garden is 12 feet. The perimeter of the garden must be at least 36 feet and no more than 48 feet. Use a compound inequality to find the range of values for the width of the garden.
$$6\leq w\leq 12$$
### Solve Absolute Value Inequalities
Solve Absolute Value Equations
In the following exercises, solve.
$$|x|=8$$
$$|y|=−14$$
no solution
$$|z|=0$$
$$|3x−4|+5=7$$
$$x=2,x=\frac{2}{3}$$
$$4|x−1|+2=10$$
$$−2|x−3|+8=−4$$
$$x=9,x=−3$$
$$|12x+5|+4=1$$
$$|6x−5|=|2x+3|$$
$$x=2,x=14$$
Solve Absolute Value Inequalities with “less than”
In the following exercises, solve each inequality. Graph the solution and write the solution in interval notation.
$$|x|\leq 8$$
$$|2x−5|\leq 3$$
$$|6x−5|<7$$
$$|5x+1|\leq −2$$
Solve Absolute Value Inequalities with “greater than”
In the following exercises, solve. Graph the solution and write the solution in interval notation.
$$|x|>6$$
$$|x|\geq 2$$
$$|x−5|>−2$$
$$|x−7|\geq 1$$
$$3|x|+4\geq 1$$
Solve Applications with Absolute Value
In the following exercises, solve.
A craft beer brewer needs 215,000 bottle per day. But this total can vary by as much as 5,000 bottles. What is the maximum and minimum expected usage at the bottling company?
The minimum to maximum expected usage is 210,000 to 220,000 bottles
At Fancy Grocery, the ideal weight of a loaf of bread is 16 ounces. By law, the actual weight can vary from the ideal by 1.5 ounces. What range of weight will be acceptable to the inspector without causing the bakery being fined?
## Practice Test
In the following exercises, solve each equation.
$$−5(2x+1)=45$$
$$x=−5$$
$$\frac{1}{4}(12m+28)=6+2(3m+1)$$
$$8(3a+5)−7(4a−3)=20−3a$$
$$a=41$$
$$0.1d+0.25(d+8)=4.1$$
$$14n−3(4n+5)=−9+2(n−8)$$
$$3(3u+2)+4[6−8(u−1)]=3(u−2)$$
$$\frac{3}{4}x−\frac{2}{3}=\frac{1}{2}x+\frac{5}{6}$$
$$x=6$$
$$|3x−4|=8$$
$$|2x−1|=|4x+3|$$
$$x=−2,x=−13$$
Solve the formula
$$x+2y=5$$ for y.
In the following exercises, graph the inequality on the number line and write in interval notation.
$$x\geq −3.5$$
$$x<\frac{11}{4}$$
$$−2\leq x<5$$
In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation.
$$8k\geq 5k−120$$
$$3c−10(c−2)<5c+16$$
$$\frac{3}{4}x−5\geq −2$$ and
$$−3(x+1)\geq 6$$
$$3(2x−3)<−5$$ or
$$4x−1>3$$
$$\frac{1}{2}x−3\leq 4$$ or
$$\frac{1}{3}(x−6)\geq −2$$
$$|4x−3|\geq 5$$
In the following exercises, translate to an equation or inequality and solve.
Four less than twice x is 16.
Find the length of the missing side.
$$10.8$$
One number is four more than twice another. Their sum is $$−47$$. Find the numbers.
The sum of two consecutive odd integers is $$−112$$.. Find the numbers.
$$−57,−55$$
Marcus bought a television on sale for $626.50 The original price of the television was$895. Find ⓐ the amount of discount and ⓑ the discount rate.
Bonita has $2.95 in dimes and quarters in her pocket. If she has five more dimes than quarters, how many of each coin does she have? Answer 12 dimes, seven quarters Kim is making eight gallons of punch from fruit juice and soda. The fruit juice costs$6.04 per gallon and the soda costs $4.28 per gallon. How much fruit juice and how much soda should she use so that the punch costs$5.71 per gallon?
The measure of one angle of a triangle is twice the measure of the smallest angle. The measure of the third angle is three times the measure of the smallest angle. Find the measures of all three angles.
$$30°,60°,90°$$
The length of a rectangle is five feet more than four times the width. The perimeter is 60 feet. Find the dimensions of the rectangle.
Two planes leave Dallas at the same time. One heads east at a speed of 428 miles per hour. The other plane heads west at a speed of 382 miles per hour. How many hours will it take them to be 2,025 miles apart?
$$2.5$$ hours
Leon drove from his house in Cincinnati to his sister’s house in Cleveland, a distance of 252 miles. It took him $$4\frac{1}{2}$$ hours. For the first half hour, he had heavy traffic, and the rest of the time his speed was five miles per hour less than twice his speed in heavy traffic. What was his speed in heavy traffic?
Sara has a budget of $1,000 for costumes for the 18 members of her musical theater group. What is the maximum she can spend for each costume? Answer At most$55.56 per costume.
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2019-07-19 04:19:46
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https://www.gradesaver.com/textbooks/math/calculus/calculus-3rd-edition/chapter-11-infinite-series-11-6-power-series-exercises-page-577/20
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## Calculus (3rd Edition)
The radius of converges is $R=1$ and the series converges at $-1\leq x \leq 1$.
Apply the ratio test: \begin{aligned} \rho &=\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right|\\ &=\lim _{n \rightarrow \infty}\left|\frac{x^{n+1}}{(n+1)^{4}+2} \frac{n^{4}+2}{x^{n}} \right| \\ &= |x|\lim _{n \rightarrow \infty}\left|\frac{n^{4}+2}{(n+1)^{4}+2} \right| \\ &= |x| \end{aligned} Then the radius of converges is $R=1$ and the series converges for $-1\lt x\lt 1$. At $x=1$ $\sum _{n=0}^{\infty}\frac{1}{n^4+1}$ converges by the comparison test and at $x= -1$ $\sum _{n=0}^{\infty}\frac{(-1)^n}{n^4+1}$ also converges.
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2021-04-23 01:48:18
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https://math.stackexchange.com/tags/derivatives/new
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# Tag Info
1
$$f'(x)=\lim_{h \to 0} \frac{h \sin (\pi/h)-0}{h}= \lim_{h \to 0} \sin (\pi/h)=\text{does not exist}.$$ $L=\lim_{x \to 0} \sin(\pi/x)$ does not exist for two sequeces $x_n=\frac{1}{n}$ and $x'_n=\frac{1}{(n+1/2)}$, let $g(x)=\sin(\pi/x)$, then $g(x_n)=0, g(x'_n)=1$ these being different there are two accumulation points. So, the limit $L$ does not exist. ...
1
The ODE: $$(xln(y) + xy)dx + (yln(x) + xy)dy=0~~~~(1)$$ can be re written as $$\int \frac{xdx}{x+\ln x}+\int \frac{ydy}{y+\ln y}=c~~~~(2)$$ by dividing (1) by $(x+\ln x)(y+\ln y)$ (2) is separable yest the integrals are not doable. So $[(x+\ln x)(y+\ln y)]^{-1}$ can be taken as the integrating factor for (1).
3
Both coefficient terms are separable, so that you can separate terms in $x$ and $y$. $$\frac{x\,dx}{\ln x+x}+\frac{y\,dy}{\ln y+y}=0.$$
1
The curve is indeed not the graph of a function. At any point $(x,y)$ on the curve, if an open disk about that point is small enough, then that portion of the curve that is within that neighborhood is the graph of a function, and the slope of the tangent line to the graph of that function is $-x/y.$ Derivatives are local, that is the slope of a curve at a ...
1
You can still think of it in terms of the slope of a tangent line, and even in terms of a limit. However, as you've pointed out, $x^2 + y^2 = r^2$ isn't a function because it fails the vertical line test. However, by the Implicit Function Theorem we can consider $F(x,y) = x^2 + y^2 - r^2$, and for any $(x_{0},y_{0})$ where $\frac{\partial F}{\partial y}\ne ... 7 From the mean-value theorem you get $$\frac{f(x)-f(0)}{x-0} > 2$$ for all nonzero$x$. It follows that $$f(x) \ge f(0) + 2x \text{ for } x > 0$$ and $$f(x) \le f(0) + 2x \text{ for } x < 0$$ so that$f$necessarily takes both positive and negative values. Now conclude with the intermediate value theorem. 1 While each$x\in(-r,\,r)$is compatible with two choices of$y$, continuous motion along the circumference well-defines the choice of$y$at each point, giving a local$y$-as-a-function-of-$x$behaviour wherever$dy/dx$is finite and nonzero (i.e.$x,\,y$are both nonzero), which happens at all but four of the circumference's points. This local behaviour is ... 0$\pi_1(t|v_1)=b^*(t)^{n-1}(v_1-b^*(t))$As$\pi_1(t|v_1) = \color{red}{b^*(t)^{n-1}}\times \color{blue}{(v_1-b^*(t))}$so according the product rule$\frac {d\pi_1'(t|v_1)}{dt} = \frac {d\color{red}{b^*(t)^{n-1}}}{dt}[\color{blue}{(v_1-b^*(t))}] + [\color{red}{b^*(t)^{n-1}}]\frac {d\color{blue}{(v_1-b^*(t))}}{dt}\color{red}{b^*(t)^{n-1}} = \color{green}(\...
1
This is hint in the form of a suggestion, as one way to approach the problem. Since you don't have to derive the expression for $h(t)$, you could first check that it satisfies the integral equation, and second show that the integral equation has a unique solution. One way to show uniqueness would be to derive from the integral equation, an ordinary ...
2
This is only a broad outline and not a detailed answer. $f$ has right-hand and left-hand derivatives at every point. These are both monotone functions and hence they are continuous except at countable number of points. At any point where one the derivatives is continuous the function is actually differentiable. Hence $f$ is differentiable at all but ...
1
Well, if $i \neq j$ then $\frac{ \partial \sigma(x_i)}{\partial x_j} = 0$ so $\nabla f$ is sparse, only the n entries along the diagonal are non-zero, etc.
1
Check that $$\int_0^x (x-t)^2 \sin^2\frac{t}{2} d\,t= \sin x - (x - \frac{x^3}{6})$$ WA link
2
To show it is constant, show that the derivative is $=0$. \begin{align}\frac {\mathrm d}{\mathrm dx}\sum_{k=0}^n(-1)^{n-k}f^{(n-k)}g^{(k)}&=\sum_{k=0}^n(-1)^{n-k}(f^{(n-k+1)}g^{(k)}+f^{(n-k)}g^{(k+1)})\\ &=\sum_{k=0}^n(-1)^{n-k}f^{(n+1-k)}g^{(k)}-\sum_{k=1}^{n+1}(-1)^{n-k}f^{(n+1-k)}g^{(k)}\\ &=(-1)^nf^{(n+1)}g^ {(0)}-(-1)^{-1}f^{(0)}g^{(n+1)}\\... 2 You are right. Left & right derivatives and directional derivative are different notions – they coexist in fact, also in one-dimensional spaces such as \mathbf{R}. The directional derivative can be defined on a generic vector- or affine space or on a differential manifold, without the existence of a norm or scalar product. It's therefore useful not ... 1 The main feature of the Leibniz law f(x)g(x)' = f'(x)g(x) + f(x)g'(x) is that it turns a product into a sum. Another way to write it to show that more explicitly is \frac{d}{dx}\left(f(x)g(x)\right)=\left(\left.\frac{\partial}{\partial s}\right\rvert_{s,t=x}+\left.\frac{\partial}{\partial t}\right\rvert_{s,t=x}\right)\left(f(s)g(t)\right)=\frac{df}{dx}g(...
2
Anyway, no need for L'Hospital's rule here. Just use Maclaurin's expansions at the relevant orders and compose them where required: $\mathrm e^x=1+x+o(x)$; $\sin^2x=x^2+o(x^2)$, so $\mathrm e^{\sin^2x}=1+x^2+o(x^2)=1+o(x)$; $\sin 2x=2x+o(x)$. Therefore $$\frac{\mathrm e^{\sin^2x}-\mathrm e^x}{ {\sin2x}}=\frac{-x+o(x)}{2x+o(x)}=-\frac12+o(1).$$
5
Just to give an alternative to J.G.'s approach, we have \begin{align} {e^{\sin^2x}-e^x\over\sin2x} &={(e^{\sin^2x}-1)-(e^x-1)\over2\sin x\cos x}\\ &={1\over2\cos x}\left({e^{\sin^2x}-1\over\sin^2x}\sin x-{e^x-1\over x}\cdot{x\over\sin x} \right)\\ &\to{1\over2\cdot1}\left(1\cdot0-1\cdot1 \right)\\ &=-{1\over2} \end{align}
0
First of all, the standard notation for the second (and higher) derivatives is misleading, because it is non-algebraic (i.e., the ratios don't cancel). It's even more problematic when using partial differentials, because the symbols themselves are equivocal within the same expression. In any case, what happens when you take a derivative is that you first ...
9
You want$$\underbrace{\lim_{x\to0}e^x}_{1}\cdot\underbrace{\lim_{x\to0}\frac{e^{\sin^2x-x}-1}{\sin^2x-x}}_{1}\cdot\lim_{x\to0}\frac{\sin^2x-x}{\sin(2x)}$$(the second limit uses $\lim_{y\to0}\frac{e^y-1}{y}=1$). The last limit is$$\underbrace{\lim_{x\to0}\frac12\tan x}_0-\underbrace{\lim_{x\to0}\frac{x}{\sin(2x)}}_{1/2}=-\frac12.$$
1
You can simply use the equivalence of the functions sinus and exponential at $x=0$. Thus $\sin(x)$ is equivalent to $x$ at $x=0$, and $(\sin(x))^2$ is equivalent to $x^2$ at $x=0$. In addition, $\exp(x)$ is equivalent to $1+x$ at $x=0$. Bearing this in mind, you find that $\exp( (\sin(x))^2 ) - \exp(x)$ is equivalent to $(1+x^2) - (1+x) = x(x-1)$ at $x=0$. ...
2
Hint: You have $$\frac{1}{f(f-1)}\,f'=1,$$ which becomes $$\int\frac1{f(f-1)}\,df=\int1\,dx.$$
0
The directional derivative is not the same as the limit approaching from the left or the right. If you use the negative unit vector, you're asking what the slope is if you're traveling to the right vs. to the left. You get the negative of the slope if you use the negative unit vector. But that is correct. The divide by the magnitude of v ($|v|$) is ...
2
Hint: $$f^\prime = f (f-1)$$ Is a separable differential equation. It's also A Bernoulli's differential equation: $$f'+f= f^2$$ $$-\left (\dfrac 1 f \right)'+\dfrac 1 f=1$$ $$u'-u=-1$$ Then use integrating factor: $$(ue^{-x})'=-e^{-x}$$ Inetgrate and unsibstitute $u=\dfrac 1f$.
1
What was the original statement of the problem? If we interpret $u(t)$ as a vector, then it's not a single vector, but rather an infinite family of different vectors — one for each real value of $t$. And we can find the corresponding family of answers, but I doubt that's what this question means. It looks more likely that the given $u(t)$ represents a line, ...
2
You have $$\dfrac{\sin (60+\alpha)}{\sin \alpha}=\dfrac{5}{4}$$ $$\dfrac{\sin 60 \cos \alpha+\cos 60 \sin \alpha}{\sin \alpha}=\dfrac{5}{4}$$ $$\Rightarrow \cot \alpha = \dfrac{\sqrt{3}}{2}$$ $$\Rightarrow \sin \alpha = \dfrac{1}{\sqrt{1+\cot ^2 \alpha}}=\dfrac{2}{\sqrt 7}$$ $$\therefore \sin (60+\alpha) = \dfrac{5}{4} \cdot \dfrac{2}{\sqrt 7}$$
1
The given solution is not correct - although its final result is right - because we do not know whether $f'$ exists around $2$ and $1$, resp. So, we should only use the existence of the two given derivatives and this is possible: We know $$\lim_{t\to 0}\frac{f(2+t)-f(2)}{t}=f'(2)=6 \text{ and } \lim_{t\to 0}\frac{f(1+t)-f(1)}{t}=f'(1)=4$$ Hence, only using ...
0
This is some version of the "l'Hospital" rule. Or some truncated version of Taylor expansion. I don't like it. What you can do is this : using Taylor expansion for function $f$ at point $x$, you have : $$f(y)=f(x)+(y-x)f'(x) + o(y-x)$$ So, putting $x=2$ and $y=2+2h+h^2$ : $$f(2h+2+h^2) = f(2) + (2h+h^2)f'(2)+o(h) = f(2)+h((2+h)f'(2)+o(1))$$ and ...
3
For the first part, just rewrite $n(f(x_0 + \frac{1}{n}) - f(x_0))$ as $$\frac{f(x_0 + \frac{1}{n}) - f(x_0)}{x_0 + \frac{1}{n} - x_0}$$ and apply the definition of differentiability. For a counterexample to the converse part, note $g : \mathbb{R} \to \mathbb{R}$ $$g(x) = \begin{cases} 1,\ x \geq 0\\ 0,\ x < 0 \end{cases}$$ satisfies $$\lim_{n \to \... 2 f is concave and positive, and therefore an increasing function. It follows that L = \lim_{x \to \infty} f(x) exists as a finite value or + \infty. f' is decreasing, so that A = \sum_{n=1}^\infty f'(n) converges if and only if$$ \int_1^\infty f'(x) \, dx = \lim_{x \to \infty} f(x) - f(1) < \infty \, , $$i.e. if L is finite. Also$$ \left( \...
0
Another counter example: $$\int_0^2{(x-1)}{dx} = \int_0^2{(1-x)}dx = 0$$ But: $$\int_0^2{(x-1)(1-x)}dx = -\int_0^2{(x^2+2x+1)}dx = -8/3 -4 - 2$$
2
For the first question, consider the case of $f(x) = g(x) = \sin(x)$. Then the integral from $0$ to $2\pi$ would be $$\int_0^{2\pi}\sin^2(x)dx = \pi$$ So it doesn't have to equal $0$, meaning that the first statement is not necessarily true. For the second question, let $f(x) = g(x) = \sin(x)+1$. Let $\phi(x) = \cos(x)-\sin(x)$. The sum of the integrals ...
0
Write the function as $$\frac{\left(\sqrt{x^2-x+1}-a x-b\right) \left(\sqrt{x^2-x+1}+a x+b\right)}{\sqrt{x^2-x+1}+a x+b}$$ Expand, simplify and collect $x$ $$\frac{-\left(a^2-1\right) x^2-x(2ab+1)-b^2+1}{\sqrt{x^2-x+1}+a x+b}$$ to give $0$ as limit it must be $$\begin{cases} a^2-1=0&a=\pm 1\\ 2ab+1=0&b=-\frac{1}{2a}\\ \end{cases}$$ $a=1;\;b=-\... 0 There is another way to solve $$y'=y+x$$ Let$y=z-x$to make $$z'-1=z\implies z'-z=1$$ Now, the homogeneous solution is$z=c e^{x}$. Use now the variation of parameter to get $$c' \,e^{x}=1 \implies c'=e^{-x}\implies c=-e^{-x}+k\implies z=-1+ke^{x}$$ Back to$y$$$y=-x-1+ke^{x}$$ and using the condition$k=2$$$y=2e^{x}-x-1$$ 1 Yes, continuity at$c$is an essential requirement. Otherwise, you can make$f$discontinuous at$c$, which would imply$f$is not differentiable at$c$. $$f'(c)=\lim_{x\to c}\frac{f(x)-f(c)}{x-c}$$ Since$f$is continuous at$c$,$\lim_{x\to c}(f(x)-f(c))=\lim_{x\to c}(x-c)=0$, and you can apply L'Hospital's rule: $$\lim_{x\to c}\frac{f(x)-f(c)}{x-c}=\... 2 You went wrong right at the beginning (assuming that you wrote the problem correctly).$$H = g \circ g = g(g(x)) $$Composition not multiplication. I'm assuming that you can get g(3)= 4 easily. So$$H' = g \circ g = g'(g(x))g'(x)$$Using rule for derivate inverses.$$g'(3) = \frac{1}{f'(g(3))} = \frac{1}{f'(4)} = 2g'(4) = \frac{1}{f'(g(4))} = \frac{1}{... 0 They are. When your functions are "nice" enough (in this case, for example,$C^3$or more), third derivatives commute (with no change of any sign). And this easily follows from second derivatives' commutativity (Schwarz's theorem). For example: $$\partial_j\partial_k f=\partial_k\partial_j f \;\Rightarrow\; \partial_i(\partial_j\partial_k f)=\... 1 I solve y' = y + x, \; y(0) = 1 \tag 1 in another "real way", as follows: write the equation as y' - y = x; \tag 2 make the clever observation that (e^{-x}y)' = -e^{-x}y + e^{-x}y' = e^{-x}y' - e^{-x}y = e^{-x}(y' - y); \tag 3 in light of (2) this becomes (e^{-x}y)' = xe^{-x}; \tag 4 integrate 'twixt 0 and any value of x: e^{-x}y(x) ... 0 Note that \lim_{x\to \pi/2}{\arctan\left(\frac{x}{\tan(x)-x}\right)}=0. Then this is just the limit definition of the derivative:$$ \lim_{x\to \pi/2}\frac{\arctan\left(\frac{x}{\tan(x)-x}\right)-0}{x-\pi/2} = \lim_{x\to \pi/2}\frac{d}{dx}{\arctan\left(\frac{x}{\tan(x)-x}\right)} $$A tedious chain-rule calculation produces:$$ = \lim_{x\to \pi/2}\... 2 This is trivial... when you know the theory of differential equations. I will lead you to a solution by an ad-hoc trial and error process. You correctly observe that$(e^x)'=e^x$. If we plug this tentative solution in the equation, we have $$e^x\color{red}=x+e^x$$ which is not what we want because of the term$x$. So let us try$y=e^x-x, and we get $$e^x-1\... 4 Here is a proof directly from the definition of the derivative. We have:$$\begin{align}\frac{d}{dx}f(x)^{2} &= \lim_{h\to 0}\frac{f(x+h)^{2} - f(x)^{2}}{h} \\&= \lim_{h\to 0}\frac{\big(f(x + h) - f(x)\big)\big(f(x + h) + f(x)\big)}{h}\\&=\lim_{h\to 0}\frac{f(x + h) - f(x)}{h}\big(f(x+h) + f(x)\big)\\&=\lim_{h\to 0}\frac{f(x + h) - f(x)}{h}\... 1 As hint:$$\lim_{t \to 0}\frac{f^2(x+t)-f^2(x)}{t}=\\ \lim_{t \to 0}\frac{f^2(x+t)-f(x+t)f(x)+f(x+t)f(x)-f^2(x)}{t}=\\ \lim_{t \to 0}\frac{f(x+t)(f(x+t)-f(x))+f(x)(f(x+t)-f(x))}{t}=\\ \lim_{t \to 0}\frac{f(x+t)(f(x+t)-f(x))}{t}+\lim_{t \to 0}\frac{f(x)(f(x+t)-f(x))}{t}=\\$$can you take over now ? 1 You can use FTOC, and you will obtain\sin(t^2)$, then just evaluate at your test points. 1 If we simplify$A = \frac {\sqrt 3}{4}(a^2)(2) + (3a)\frac 4{(\sqrt 3)(a^2)},$we get$A = \frac {\sqrt 3}{2}a^2 + \frac {4\sqrt 3}{a}.$Now differentiate. Each term is pretty simple, just apply the power rule.$\frac {dA}{da} = \sqrt 3a - \frac {4\sqrt 3}{a^2}$The$\sqrt 3$is just a constant, and should be treated like any other constant. It just rides ... 1 No. Define$f$by$f(x)=0$for$ x\le0$and$f(x)=x^2\sin(1/x)$for$x>0$. One can show$f$is differentiable and that$f'$is not continuous at 0. Obviously, the left-hand limit of$f'$at 0 exists. 1 The first implication is false. $$(\forall x\in \Bbb R)\; \; f(x)-x\le 0$$ implies that the function$ g:x\mapsto f(x)-x $is negative but not necessarily decreasing$(g'(x)=f'(x)-1\le 0 $Take for example $$f(x)=x-x^2$$ then $$x>1 \implies f'(x)-1<-2$$ The second is semi true : In fact, For$ x\ge 0$, $$(\forall t\in[0,x])\; f'(t)\le 1\implies$$ $$\... 1 Try f(x)=\ln (x+1). It can be shown that f(x)\le x but f'(-0.5)=2>1 1 Of course, it is not always true. As you supposed, let \dot{x} = f(t,x) with x(0) = x_0. Then,$$ \dfrac{dT}{dx}(t,x)= \dfrac{\partial T}{\partial t} \dfrac{dt}{dx}+\dfrac{\partial T}{\partial x} $$which is not guaranteed to be identically zero. Think of a situation where a mass traverses the floor while losing its kinetic energy. Clearly in this case, ... 1 Use the product rule: \dfrac {d (u v)} {d a} = u \dfrac {dv} {da} + v \dfrac {du} {da} In this case, u = 18^2 and v = a. So you get 18^2 \times \dfrac {da} {da} + a \dfrac {d (18^2)} {da}. This of course works out to 18^2 \times 1 + a \times 0. 1 \frac{1}{x}=x^{-1}, hence$$\frac{d}{dx}\frac{1}{x}=(-1)x^{-2}=-\frac{1}{x^2}$$1 If$c$is a constant, then$(cf(x))'=c(f(x))'$; you get the square because$\frac{1}{x}=x^{-1}$and$(x^{-1})'=(-1)\cdot x^{-2}=-\frac{1}{x^2}\$. To obtain the correct result you have to use these two rules.
Top 50 recent answers are included
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2020-12-01 09:40:40
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https://www.ademcetinkaya.com/2023/02/jbi-janus-international-group-inc.html
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Outlook: Janus International Group Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating.
Time series to forecast n: 16 Feb 2023 for (n+4 weeks)
## Abstract
Janus International Group Inc. Common Stock prediction model is evaluated with Multi-Task Learning (ML) and Ridge Regression1,2,3,4 and it is concluded that the JBI stock is predictable in the short/long term. According to price forecasts for (n+4 weeks) period, the dominant strategy among neural network is: Buy
## Key Points
1. How can neural networks improve predictions?
2. Operational Risk
3. Can neural networks predict stock market?
## JBI Target Price Prediction Modeling Methodology
We consider Janus International Group Inc. Common Stock Decision Process with Multi-Task Learning (ML) where A is the set of discrete actions of JBI stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4
F(Ridge Regression)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Multi-Task Learning (ML)) X S(n):→ (n+4 weeks) $∑ i = 1 n r i$
n:Time series to forecast
p:Price signals of JBI stock
j:Nash equilibria (Neural Network)
k:Dominated move
a:Best response for target price
For further technical information as per how our model work we invite you to visit the article below:
How do AC Investment Research machine learning (predictive) algorithms actually work?
## JBI Stock Forecast (Buy or Sell) for (n+4 weeks)
Sample Set: Neural Network
Stock/Index: JBI Janus International Group Inc. Common Stock
Time series to forecast n: 16 Feb 2023 for (n+4 weeks)
According to price forecasts for (n+4 weeks) period, the dominant strategy among neural network is: Buy
X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)
Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)
Z axis (Grey to Black): *Technical Analysis%
## IFRS Reconciliation Adjustments for Janus International Group Inc. Common Stock
1. For floating-rate financial assets and floating-rate financial liabilities, periodic re-estimation of cash flows to reflect the movements in the market rates of interest alters the effective interest rate. If a floating-rate financial asset or a floating-rate financial liability is recognised initially at an amount equal to the principal receivable or payable on maturity, re-estimating the future interest payments normally has no significant effect on the carrying amount of the asset or the liability.
2. If the group of items does have offsetting risk positions (for example, a group of sales and expenses denominated in a foreign currency hedged together for foreign currency risk) then an entity shall present the hedging gains or losses in a separate line item in the statement of profit or loss and other comprehensive income. Consider, for example, a hedge of the foreign currency risk of a net position of foreign currency sales of FC100 and foreign currency expenses of FC80 using a forward exchange contract for FC20. The gain or loss on the forward exchange contract that is reclassified from the cash flow hedge reserve to profit or loss (when the net position affects profit or loss) shall be presented in a separate line item from the hedged sales and expenses. Moreover, if the sales occur in an earlier period than the expenses, the sales revenue is still measured at the spot exchange rate in accordance with IAS 21. The related hedging gain or loss is presented in a separate line item, so that profit or loss reflects the effect of hedging the net position, with a corresponding adjustment to the cash flow hedge reserve. When the hedged expenses affect profit or loss in a later period, the hedging gain or loss previously recognised in the cash flow hedge reserve on the sales is reclassified to profit or loss and presented as a separate line item from those that include the hedged expenses, which are measured at the spot exchange rate in accordance with IAS 21.
3. Hedging relationships that qualified for hedge accounting in accordance with IAS 39 that also qualify for hedge accounting in accordance with the criteria of this Standard (see paragraph 6.4.1), after taking into account any rebalancing of the hedging relationship on transition (see paragraph 7.2.25(b)), shall be regarded as continuing hedging relationships.
4. When a group of items that constitute a net position is designated as a hedged item, an entity shall designate the overall group of items that includes the items that can make up the net position. An entity is not permitted to designate a non-specific abstract amount of a net position. For example, an entity has a group of firm sale commitments in nine months' time for FC100 and a group of firm purchase commitments in 18 months' time for FC120. The entity cannot designate an abstract amount of a net position up to FC20. Instead, it must designate a gross amount of purchases and a gross amount of sales that together give rise to the hedged net position. An entity shall designate gross positions that give rise to the net position so that the entity is able to comply with the requirements for the accounting for qualifying hedging relationships.
*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.
## Conclusions
Janus International Group Inc. Common Stock is assigned short-term Ba1 & long-term Ba1 estimated rating. Janus International Group Inc. Common Stock prediction model is evaluated with Multi-Task Learning (ML) and Ridge Regression1,2,3,4 and it is concluded that the JBI stock is predictable in the short/long term. According to price forecasts for (n+4 weeks) period, the dominant strategy among neural network is: Buy
### JBI Janus International Group Inc. Common Stock Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementBaa2B1
Balance SheetBaa2Baa2
Leverage RatiosBaa2C
Cash FlowCC
Rates of Return and ProfitabilityCB3
*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?
### Prediction Confidence Score
Trust metric by Neural Network: 74 out of 100 with 616 signals.
## References
1. Breusch, T. S. (1978), "Testing for autocorrelation in dynamic linear models," Australian Economic Papers, 17, 334–355.
2. H. Khalil and J. Grizzle. Nonlinear systems, volume 3. Prentice hall Upper Saddle River, 2002.
3. Bessler, D. A. S. W. Fuller (1993), "Cointegration between U.S. wheat markets," Journal of Regional Science, 33, 481–501.
4. C. Wu and Y. Lin. Minimizing risk models in Markov decision processes with policies depending on target values. Journal of Mathematical Analysis and Applications, 231(1):47–67, 1999
5. Çetinkaya, A., Zhang, Y.Z., Hao, Y.M. and Ma, X.Y., What are buy sell or hold recommendations?(AIRC Stock Forecast). AC Investment Research Journal, 101(3).
6. Arora S, Li Y, Liang Y, Ma T. 2016. RAND-WALK: a latent variable model approach to word embeddings. Trans. Assoc. Comput. Linguist. 4:385–99
7. D. Bertsekas and J. Tsitsiklis. Neuro-dynamic programming. Athena Scientific, 1996.
Frequently Asked QuestionsQ: What is the prediction methodology for JBI stock?
A: JBI stock prediction methodology: We evaluate the prediction models Multi-Task Learning (ML) and Ridge Regression
Q: Is JBI stock a buy or sell?
A: The dominant strategy among neural network is to Buy JBI Stock.
Q: Is Janus International Group Inc. Common Stock stock a good investment?
A: The consensus rating for Janus International Group Inc. Common Stock is Buy and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of JBI stock?
A: The consensus rating for JBI is Buy.
Q: What is the prediction period for JBI stock?
A: The prediction period for JBI is (n+4 weeks)
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2023-03-21 07:58:44
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https://socratic.org/questions/there-were-five-people-in-group-a-with-a-mean-lq-of-100-and-five-in-group-b-with
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There were five people in group A, with a mean lQ of 100, and five in group B, with a mean IQ of 74. When Jack left group A for group B, both means increased, and the total of the two new means was 180. What Is Jack's IQ?
Aug 29, 2016
Jack's IQ is $80$.
Explanation:
Suppose that, Jack's IQ is $j$, and those of the rest of the $4$
persons in group A, be, ${x}_{1} , {x}_{2} , {x}_{3} , {x}_{4}$.
Accordingly, $\frac{{x}_{1} + {x}_{2} + {x}_{3} + {x}_{4} + j}{5} = 100. \ldots \ldots \ldots . \left(1\right)$.
After, leaving the group by Jack, the new mean for the group A is
$= \frac{{x}_{1} + {x}_{2} + {x}_{3} + {x}_{4}}{4.} \ldots \ldots \ldots \ldots \ldots \ldots . \left(1 '\right)$.
Let ${y}_{i} , 1 \le i \le 5 ,$ be the IQs of $5$ persons of group B. Since, the
average IQ of Group be is $74$, we have,
$\frac{{y}_{1} + {y}_{2} + {y}_{3} + {y}_{4} + {y}_{5}}{5} = 74. \ldots \ldots \ldots . . \left(2\right)$
Finally, after Jack's joining the group B, since it has now $6$ members, the new mean becomes,
$\frac{{y}_{1} + {y}_{2} + {y}_{3} + {y}_{4} + {y}_{5} + j}{6.} \ldots \ldots \ldots \ldots \ldots \ldots \left(2 '\right)$
Using $\left(1 '\right) \mathmr{and} \left(2 '\right)$ in what is given, we get,
$\frac{{x}_{1} + {x}_{2} + {x}_{3} + {x}_{4}}{4} + \frac{{y}_{1} + {y}_{2} + {y}_{3} + {y}_{4} + {y}_{5} + j}{6} = 180$, or,
3((x_1+x_2+x_3+x_4)+2(y_1+y_2+y_3+y_4+y_5+j)=2160...(3)
Here, $\left(1\right) \Rightarrow \left({x}_{1} + {x}_{2} + {x}_{3} + {x}_{4}\right) = 500 - j$, and,
$\left(2\right) \Rightarrow \left({y}_{1} + {y}_{2} + {y}_{3} + {y}_{4} + {y}_{5}\right) = 370$.
Utilising these in $\left(3\right)$,
$3 \left(500 - j\right) + 2 \left(370 + j\right) = 2160$
$\therefore 1500 - 3 j + 740 + 2 j = 2160$, i.e.,
$j = 80$.
Hence, Jack's IQ is $80$.
Enjoy maths.!
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2022-05-22 07:47:45
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