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https://tex.stackexchange.com/questions/208116/adaptative-column-width
|
I am currently automating a report generation and I am now trying to obtain a consistent look on my arrays. I am currently working on a part where the pages need to be set in landscape mode, so I am using pdflscape. Moreover, to handle page breaks in arrays, I went for the longtable package, alond with booktabs for the pretty look.
Basically, my arrays can contain from 3 to 10 columns, the 2nd one is the one containing lots of text, the others hardly anything. Here is a MWE showing the tiniest, and the biggest one.
\documentclass[10pt]{report}
\usepackage{booktabs}
\usepackage{longtable}
\usepackage{pdflscape}
\usepackage{geometry}
\geometry{
a4paper,
left=20mm,
right=20mm,
top=20mm,
bottom=20mm,
}
\pagenumbering{gobble}
\begin{document}
\begin{landscape}
\begin{longtable}{lp{\dimexpr.5\textwidth}p{1.5cm}}
\toprule
C1 & C2 & C3 \\
\midrule
data & data & data \\
\bottomrule
\end{longtable}
\begin{longtable}{lp{\dimexpr.5\textwidth}p{1.5cm}p{1.5cm}p{1.5cm}p{1.5cm}p{1.5cm}p{1.5cm}p{1.5cm}p{1.5cm}}
\toprule
C1 & C2 & C3 & C4 & C5 & C6 & C7 & C8 & C9 & C10 \\
\midrule
data & data & data & data & data & data & data & data & data & data \\
\bottomrule
\end{longtable}
\end{landscape}
\end{document}
My problem here is that I would like the 1st column to be always "anchored" at the same horizontal padding, whatever the number of column (basically align the array to the left) and that my 2nd column adapt to the text width, as shown on this wonderful paint :
The 2nd column will always contain more than "data" obviously, so I think this choice is justified. How should I proceed to make my 2nd column to be that wide ?
• \begin{longtable}[l] (If you mean what I think you mean?) – David Carlisle Oct 20 '14 at 16:24
• can you fix your first column as p{some value} then it is easy to adjust your \dimexpr to be \textwidth-width of other columns otherwise it's a bit trickier – David Carlisle Oct 20 '14 at 16:26
If you fix the with of the columns, then the width of the second column can be calculated, just subtracting the total width of the other columns, taking account the \tabcolsep padding on either side of each cell.
\documentclass[10pt]{report}
\usepackage{booktabs}
\usepackage{longtable}
\usepackage{pdflscape}
\usepackage{geometry}
\geometry{
a4paper,
left=20mm,
right=20mm,
top=20mm,
bottom=20mm,
}
\pagenumbering{gobble}
\begin{document}
\begin{landscape}
\begin{longtable}{p{1.5cm}p{\dimexpr\columnwidth-1.5cm-(1.5cm)*1-6\tabcolsep\relax}*{1}{p{1.5cm}}}
\toprule
C1 & C2 & C3 \\
\midrule
data & data & data \\
\bottomrule
\end{longtable}
\begin{longtable}{p{1.5cm}p{\dimexpr\columnwidth-1.5cm-(1.5cm)*8-20\tabcolsep\relax}*{8}{p{1.5cm}}}
\toprule
C1 & C2 & C3 & C4 & C5 & C6 & C7 & C8 & C9 & C10 \\
\midrule
data & data & data & data & data & data & data & data & data & data \\
\bottomrule
\end{longtable}
\end{landscape}
\end{document}
• That's perfect. However, I am getting underful \vbox (badness 10000) detected on the \end{longtable} lines. Any idea ? Anyway I will validate your answer. – user17424 Oct 20 '14 at 16:39
• @NNzz hmm yes so do I:-) It's booktab's rules (if you use \hrule you don't get the warning) longtable and and (pdf)lscape and bookmarks don't seem to quite agree on who's going to redefine the rules in what order, no time to look now, but the warning seems largely spurious – David Carlisle Oct 20 '14 at 16:52
|
2019-10-23 00:29:07
|
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|
http://mathematica.stackexchange.com/questions/14407/ndsolve-with-vectors
|
# NDSolve with vectors
I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and gravity (the linear drag is ignored for now). Negative Z is down, X and Y are the horizontal plane. If I write it as 9 equations, one for each coordinate, it works fine, but I'd rather use vectors since it is shorter and (to at least me) more obvious what is going on. Plus since I am new to Mathematica it would be good to learn more/better ways to use it.
gravity = 10;
withDrag[p0_, v0_, drag_] :=
NDSolve[{
p[0] == p0,
p'[0] == v0,
p''[t] == drag * Norm[p'[t]] * p'[t] + {0,0,-gravity}},
{p}, {t, 0, 5}]
withDrag[{0,0,0}, {0,10^4,10}, 0.001]
I get:
NDSolve::ndfdmc: Computed derivatives do not have dimensionality consistent with the initial conditions. >>
NDSolve[{
p[0] == {0, 0, 0},
p'[0] == {0, 10000, 10},
p''[t] == {
0.001 Norm[p'[t]] p'[t],
0.001 Norm[p'[t]] p'[t],
-10 + 0.001 Norm[p'[t]] p'[t]}},
{p}, {t,0,5}]
I formatted the output to make the error more obvious. Each of elements of the p'' vector has all three elements of p'[t]. Each one should really be p'[t][[dim]] (or something like that).
Any clues as to what I'm doing wrong?
-
Mathematica doesn't have vector variables (yet). That is to say, you can assign a list to a variable, but you cannot use a variable in a function like NDSolve and let Mathematica work out its dimensions or let the dimensions be undetermined.
If you change your function to this:
gravity = 10;
withDrag[p0_, v0_, drag_] :=
Module[{p},
p[t_] := {p1[t], p2[t], p3[t]};
p[t] /.
NDSolve[
p[0] == p0,
p'[0] == v0,
p''[t] == drag*Norm[p'[t]]*p'[t] + {0, 0, -gravity}} // Flatten,
p[t],
{t, 0, 5}
]// First
]
it works. What is does is defining your p as a vector (list) of functions. Thread takes care of distributing == over the vector components and Flatten makes a single list of equations from all this.
track[t_] = withDrag[{0, 0, 0}, {0, 10^2, 10}, 0.001];
ParametricPlot3D[track[t], {t, 0, 5}, BoxRatios -> 1]
Note that I reduced the starting value of v0[[2]] to 10^2 because 10^4 yields a 'stiff' system. Also note that I used BoxRatios -> 1 to prevent the box from becoming flat.
While under the hood this method still provides Mathematica with the 9 equations that you already tried manually, it has the advantage that it leaves your vector equations intact.
-
This is also how I would have done it, but it should probably be pointed out that Mathematica does know how to deal with vector functions in some cases. See e.g. this answer. – Jens Nov 11 '12 at 22:04
@jens You're right. I suppose the problem here lies in the assignments with p0 and v0, which aren't explicitly vectors, right? – Sjoerd C. de Vries Nov 11 '12 at 22:27
@jens Vector equations seem to work only if the initial conditions are specified as a scalar constant, not a vector constant. Replace in the doc example the zero in the first example by {0,0,0,0} (which would seem to make more sense) and it fails. – Sjoerd C. de Vries Nov 11 '12 at 22:43
Yes, I guess one could change the function argument from p0_ to {p0x_, p0y_, p0z_} etc., but it seems that even then the second-order differential equation is too hard to recognize as vectorial. So your approach is just the safest, I think. – Jens Nov 11 '12 at 22:45
Nice. I'll have to study the answer some more though... Thanks! – Steve Nov 12 '12 at 21:37
As of Version 9, you can work with vectors in NDSolve[]!:
gravity = 10;
withDrag[p0_, v0_, drag_] := Module[{p},
p[t_] := Evaluate@Array[Unique[][t] &, 3];
p[t] /. NDSolve[{
p[0] == p0,
p'[0] == v0,
p''[t] == drag*Norm[p'[t]]*p'[t] + {0, 0, -gravity}},
p[t], {t, 0, 5}] // First]
track[t_] = withDrag[{0, 0, 0}, {0, 10^2, 10}, 0.001];
ParametricPlot3D[track[t], {t, 0, 5}, BoxRatios -> 1]
-
|
2015-03-06 09:11:42
|
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|
https://www.deepdyve.com/lp/ou_press/bars-in-dark-matter-dominated-dwarf-galaxy-discs-L6erO0ZDq6
|
# Bars in dark-matter-dominated dwarf galaxy discs
Bars in dark-matter-dominated dwarf galaxy discs Abstract We study the shape and kinematics of simulated dwarf galaxy discs in the apostle suite of Λ cold dark matter (ΛCDM) cosmological hydrodynamical simulations. We find that a large fraction of these gas-rich, star-forming discs show weak bars in their stellar component, despite being dark-matter-dominated systems. The bar pattern shape and orientation reflect the ellipticity of the dark matter potential, and its rotation is locked to the slow figure rotation of the triaxial dark halo. The bar-like nature of the potential induces non-circular motions in the gas component, including strong bisymmetric flows that can be readily seen as m = 3 harmonic perturbations in the H i line-of-sight velocity fields. Similar bisymmetric flows are seen in many galaxies of The HI Nearby Galaxy Survey (THINGS) and Local Irregulars That Trace Luminosity Extremes THINGS (LITTLE THINGS), although on average their amplitudes are a factor of ∼2 weaker than in our simulated discs. Our results indicate that bar-like patterns may arise even when baryons are not dominant, and that they are common enough to warrant careful consideration when analysing the gas kinematics of dwarf galaxy discs. ISM: kinematics and dynamics, galaxies: dwarf, galaxies: kinematics and dynamics, galaxies: structure, dark matter 1 INTRODUCTION Bars are a common morphological feature of spiral galaxies in the local Universe. About one-quarter of disc galaxies show strong bars (Masters et al. 2011; Cheung et al. 2013), and this fraction increases up to about two-thirds when including weaker features (Mulchaey & Regan 1997; Kormendy & Kennicutt 2004). The fraction of barred galaxies appears to depend significantly on galaxy luminosity, being lower for fainter galaxies (Méndez-Abreu, Sánchez-Janssen & Aguerri 2010; Janz et al. 2012), and, to a minor extent, on environment, increasing in regions of higher galaxy density (Méndez-Abreu et al. 2012). Bars have been a topic of interest for decades, and numerical simulations have played a major role in our current understanding of their formation and evolution. Although details need to be fully worked out, there is widespread agreement that bars develop in stellar discs as a consequence of the inevitable tendency of collisionless systems to evolve dynamically by redistributing the mass inwards and angular momentum outwards. Bar patterns offer a particularly efficient way of carrying out this redistribution, and grow and strengthen rapidly in cold, massive stellar discs (see e.g. Athanassoula 2013; Sellwood 2014, for recent reviews). Their growth is so rapid in such systems (Miller & Prendergast 1968; Hockney & Hohl 1969) that few can avoid becoming ‘bar unstable’ in a couple of rotation periods (Sellwood & Wilkinson 1993), unless stabilized by the presence of a dominant dark halo (Ostriker & Peebles 1973). These results have been so influential that the presence of bar-like patterns is often taken to indicate discs where the dark halo is gravitationally unimportant; i.e. discs that are ‘maximal’. More recent work, however, suggests a more complex scenario where bar formation is delayed, but not fully inhibited, in discs where dark matter haloes are gravitationally dominant (e.g. Athanassoula 2002, 2003; Algorry et al. 2017): Bars are thus not synonymous with maximal discs, suggesting that care must be exercised when using morphological features to infer indirectly the relative importance of disc and halo in spiral galaxies. Bars are not the only bisymmetric (m = 2) perturbation expected in disc galaxies. Indeed, discs are expected to form at the centre of cold dark matter (CDM) haloes, which have long been known to be triaxial in nature (Frenk et al. 1988; Warren et al. 1992; Jing & Suto 2002). Discs that settle on the symmetry plane of such haloes would be subject to gravitational forces akin to those in barred systems, although the bisymmetric pattern in this case is expected to rotate much less rapidly than in typical strongly barred systems. Although a number of works have focused on the impact of stellar bars on the dynamics of haloes (e.g. Debattista & Sellwood 1998, 2000), the consequences of halo triaxiality on the kinematics of discs have not been extensively studied (although see Hayashi, Navarro & Springel 2007, for an attempt), in part because the assembly of the disc is thought to ‘sphericalize’ the halo (see Abadi et al. 2010, and references therein). However, this is only true in the case of massive discs such as those of luminous, high surface brightness spirals. In the case of fainter, lower surface brightness spirals, discs are less gravitationally important and the sphericalization of their surrounding haloes should be less complete (Kazantzidis, Abadi & Navarro 2010; Machado & Athanassoula 2010). Regardless of origin, bar-like perturbations can have important consequences on the kinematic of discs, particularly on the interpretation of azimuthally averaged rotation curves and of 2D velocity fields of gas and stars. Hayashi & Navarro (2006, hereafter HN06), for example, showed that even minor deviations from spherical symmetry can induce large deviations from circular orbits in the velocity field of a gaseous disc. This possibility was studied by Trachternach et al. (2008), who carried out a harmonic decomposition of the H i velocity fields in 19 galaxies from The H i Nearby Galaxy Survey (THINGS, Walter et al. 2008). The harmonic decomposition suggests that the magnitude of non-circular motions in the central regions of these systems is small, and compatible with a circularly symmetric potential. However, most of the systems studied by Trachternach et al. were large spirals, and the analysis has not been extended to the dwarf galaxy regime, where the triaxiality of the halo might be better preserved. A harmonic decomposition of Local Irregulars That Trace Luminosity Extremes THINGS (LITTLE THINGS) galaxies (Hunter et al. 2012) was performed by Oh et al. (2015), but their findings were not discussed in terms of triaxiality of the gravitational potential; thus, whether or not dwarf galaxies are consistent with hosting triaxial haloes is still an open question. Recently, Oman et al. (2017, hereafter O17) have studied the gas kinematics in a sample of 33 simulated dwarf galaxies from the apostle suite of ΛCDM cosmological simulations (Sawala et al. 2015; Fattahi et al. 2016). Their approach used synthetic H i observations of these systems, from which the gas rotation curve was derived using the same tilted ring modelling technique adopted in most H i observational studies. One of the main results of O17 is that, depending on the orientation of the line of sight, a large variety of rotation curves might be derived for the same system, even for fixed inclination. The variety is due to non-circular motions in the gas, in particular, to strong bisymmetric (m = 2 harmonic) fluctuations in the azimuthal H i velocity field, which the tilted-ring model is not well suited to account for. We study here the origin of these non-circular motions, focusing on the mass distribution and the shape of the gravitational potential. We show that the cause of these bisymmetric gas flows is the presence of bar-like features in both the stellar and the dark matter distributions. This paper is structured as follows. In Section 2, we summarize the main features of the apostle simulations and of the selected galaxy sample. In Section 3, we discuss the properties of the stellar and dark matter bars in our sample, and how they affect the gas kinematics. A comparison with dark-matter-only (DMO) simulations and with the observations is also presented. We finally summarize our findings in Section 4. 2 SIMULATIONS AND SAMPLE SELECTION A detailed description of the apostle1 simulations can be found in Sawala et al. (2015) and Fattahi et al. (2016). Here, we summarize their main characteristics. apostle is a suite of cosmological hydrodynamical simulations performed in a ΛCDM framework, adopting the cosmological parameters inferred from WMAP-7 data (Komatsu et al. 2011). It consists of 12 subvolumes selected from the DOVE cosmological simulation (Jenkins 2013) and re-simulated using the zoom-in technique (Frenk et al. 1996; Power et al. 2003). The volumes are centred around two massive haloes (analogous to the Milky Way - M31 pair) and chosen to resemble these galaxies in terms of mass, separation and kinematics, whilst ensuring relative isolation from more massive structures. The hydrodynamics and the baryonic subgrid physics implemented in apostle are the same as those adopted in the EAGLE simulations (Crain et al. 2015; Schaye et al. 2015). EAGLE, and by extension apostle, uses a formulation of the smoothed-particle hydrodynamics (SPH) known as ANARCHY (Dalla Vecchia in preparation, see also appendix A of Schaye et al. 2015), which alleviates significantly the issues related to artificial gas clumping and the poor treatment of hydrodynamical instabilities associated with the classical SPH scheme (e.g Kaufmann et al. 2006; Agertz et al. 2007). Other features introduced by ANARCHY are the use of an artificial viscosity switch (Cullen & Dehnen 2010), an artificial conduction switch (Price 2008), and a time-step limiter (Durier & Dalla Vecchia 2012). The recipes for subgrid physics include the star formation implementation of Schaye & Dalla Vecchia (2008), thermal star formation feedback from Dalla Vecchia & Schaye (2012), radiative gas cooling and photo-heating from Wiersma, Schaye & Smith (2009a), and stellar mass-loss from Wiersma et al. (2009b). Accretion on to black holes and AGN feedback is not implemented in apostle, but this is not critical for the mass scale of interest. The apostle volumes are resimulated at three levels of resolution. As in O17, here we focus on the highest resolution level (‘L1’ in Fattahi et al. 2016), featuring a dark matter particle mass of 3.6 × 104 M⊙, a gas particle initial mass of 7.4 × 103 M⊙, and maximum softening length of 134 pc. At the moment of writing, only five of the 12 volumes have been re-simulated at this resolution. Galaxies, and in general ‘subhaloes’, are identified in the simulation via the SUBFIND algorithm (Dolag et al. 2009), which is based on a friend-of-friends (FoF) scheme. O17 studied 33 dwarf systems, selecting central2 subhaloes with maximum circular velocity 60 < Vmax < 120 km s−1 at redshift z = 0. The Vmax selection targets the ‘dwarf’ spiral regime, whereas the exclusion of satellites allows us to discard systems whose features might be affected by the effect of tides. We focus here on the same galaxy sample, whose main properties are listed in table A1 of O17. Each simulated galaxy is uniquely identified by four labels: the resolution level (always L1 in our sample), the apostle volume it belongs to (V1, V2,..., V12), the FoF group, and SUBFIND sub-group numbers, respectively. The latter is always equal to 0, indicating that the system is the central subhalo of its FoF group. These labels follow the ‘AP’ keyword that identifies the suite of simulations used. As in other studies of neutral hydrogen using the EAGLE simulations, the H i mass fraction of each gas particle in the apostle volumes is computed in two steps: The fraction of neutral hydrogen is first derived following the prescription of Rahmati et al. (2013) for self-shielding from the metagalactic ionizing background, and then a pressure-dependent correction for the molecular gas fraction is applied following Blitz & Rosolowsky (2006). We refer the interested reader to Crain et al. (2017) for details. 3 RESULTS 3.1 Stellar bars and ‘dark bars’ For illustration, we present first the mass distribution and the H i kinematics in the inner regions of two representative systems in the sample of O17: AP-L1-V10-19-0 and AP-L1-V10-17-0. These systems have comparable Vmax (67 and 65 km s−1, respectively), stellar mass (4.7 and 7.1 × 108 M⊙), H i-to-stellar mass ratio (1.1 and 0.7), and star formation rates at z = 0 (0.08 and 0.13 M⊙ yr− 1). Also, both systems are quite isolated, lying at more than 2 Mpc from the closest member of the Milky Way/M31 analogue pair. They also show no obvious sign of interactions with nearby galaxies. Fig. 1 shows a series of face-on maps for these two galaxies, where the rotation axis of the galaxy is identified with $$\vec{L}_*$$, the angular momentum vector of all stars (identified by SUBFIND as bound to the system and located within a radius enclosing 90 per cent of the total stellar mass) relative to the galaxy centre. The latter is defined as the location of the particle with the lowest potential energy. All maps are smoothed to a spatial resolution [full width at half-maximum (FWHM) of a Gaussian kernel] of 0.2 kpc. Figure 1. View largeDownload slide Face-on maps of two representative apostle dwarfs at redshift 0. First and second columns: stellar and dark matter surface density maps, shown on the same colour scale. Isodensity contours (in white) are spaced by 0.3 dex. The blue isodensity contour has semi-major axis equal to the projected radius at half stellar mass, Rh; the dashed black line shows the best-fitting ellipse to this contour. Third column: gravitational potential map on the galactic mid-plane. Fourth and fifth columns: maps of the azimuthal and radial H I velocity fields, also on the mid-plane, from which we have subtracted the mean velocity computed at different radii. A residual m = 2 mode is clearly visible in both maps; its phase is traced by black crosses. The dashed black line in the three rightmost panels shows the major axis of the gravitational potential. Figure 1. View largeDownload slide Face-on maps of two representative apostle dwarfs at redshift 0. First and second columns: stellar and dark matter surface density maps, shown on the same colour scale. Isodensity contours (in white) are spaced by 0.3 dex. The blue isodensity contour has semi-major axis equal to the projected radius at half stellar mass, Rh; the dashed black line shows the best-fitting ellipse to this contour. Third column: gravitational potential map on the galactic mid-plane. Fourth and fifth columns: maps of the azimuthal and radial H I velocity fields, also on the mid-plane, from which we have subtracted the mean velocity computed at different radii. A residual m = 2 mode is clearly visible in both maps; its phase is traced by black crosses. The dashed black line in the three rightmost panels shows the major axis of the gravitational potential. The two leftmost panels of Fig. 1 show the stellar and dark matter surface density maps derived projecting a cubic region with side-length 8 kpc, concentric with the galaxy. The elongation of the isodensity contours reveals that both stars and dark matter are clearly non-axisymmetric. Projected on to the disc plane, both components seem bar-like, especially in the central few kiloparsec. For simplicity, we will refer to these non-axisymmetric features as the ‘stellar’ bar and the ‘dark’ bar. These two ‘bars’ have the same orientation and, approximately, the same axis ratio. The central panels show isopotential contours measured on the disc mid-plane, computed using all (dark + baryonic) particles identified by SUBFIND as bound to the system (the gravitational potential, Φ, is softened on scales smaller than 100 pc). The gravitational potential is clearly aspherical, especially close to the centre, and is therefore expected to induce deviations from pure circular rotation in the motion of gas and stars in the disc. These deviations are explored in the two rightmost panels, which show the azimuthal and the radial H i velocity fields derived on the galaxy mid-plane, from which we have subtracted the mean azimuthally averaged value at each radius. If the gas was in pure circular rotation around the centre, these ‘residual’ velocity fields should not show systematic deviations from zero. Instead, clear m = 2 harmonic patterns are visible, which were already noticed by O17 in other systems of the sample. The phase of the m = 2 perturbation in the azimuthal velocity (shown by the black crosses in the fourth column of Fig. 1, which trace the maximum positive deviation from the mean) is oriented approximately perpendicular to the major axis of the potential (dashed black line, see below), whereas the phase of the perturbation in the radial velocity lags 45° from the latter. This pattern is consistent with gas moving counter-clockwise along elliptical orbits elongated in the same direction of the potential. The simplest interpretation of these orbits is that, in these galaxies, the stellar/dark bar induces a bisymmetric flow in the gas component. We determine major and minor axes for the bar by fitting an ellipse to the surface density contour whose semi-major axis coincides with Rh, the (projected) stellar half-mass radius. This is highlighted in blue in the leftmost panels of Fig. 1. The ellipse centre is a free parameter of the fit, in order to account for possible offsets in the mass distribution. Rh is computed directly from the face-on stellar density distribution. 3.2 Stellar bars in sub-dominant discs The two leftmost panels of Fig. 1 suggest that the dark matter dominates the dynamics in the central few kiloparsec. This is shown explicitly in the top panels of Fig. 2, which show, for both systems, the gravitational acceleration due to the stars alone (orange lines) and to the dark matter (blue lines) on the galactic mid-plane along the projected major (dashed lines) and minor (solid lines) axes of the bar. The gas contribution to the gravitational acceleration is negligible compared to the other components. Figure 2. View largeDownload slide Top panels: gravitational acceleration on the galactic mid-plane decomposed into contributions from stars (orange lines) and from dark matter (blue lines) as a function of the distance along the major axis (dashed lines) or the minor axis (solid lines) of the bar for the two representative galaxies. Dark matter dominates the gravitational acceleration within the bar. Central panels: phases of the stellar (orange circles) and of the dark matter (blue squares) bar as a function of the lookback time. Phases are locked. Bottom panels: amplitude of the m > 0 harmonic fluctuations in the gravitational potential Φ, divided by the mean value of Φ, as a function of R. The strongest harmonic mode is the m = 2. The arrows show the location of Rh. Figure 2. View largeDownload slide Top panels: gravitational acceleration on the galactic mid-plane decomposed into contributions from stars (orange lines) and from dark matter (blue lines) as a function of the distance along the major axis (dashed lines) or the minor axis (solid lines) of the bar for the two representative galaxies. Dark matter dominates the gravitational acceleration within the bar. Central panels: phases of the stellar (orange circles) and of the dark matter (blue squares) bar as a function of the lookback time. Phases are locked. Bottom panels: amplitude of the m > 0 harmonic fluctuations in the gravitational potential Φ, divided by the mean value of Φ, as a function of R. The strongest harmonic mode is the m = 2. The arrows show the location of Rh. Fig. 2 clearly indicates that, in these two systems, the overall dynamics are dominated everywhere – even at the very centre – by the dark matter. This suggests that, in these two systems, the stellar bar originates as a response to the non-axisymmetric distribution of dark matter, and not, as traditionally envisioned, as a result of some instability in a stellar-dominated disc. At least some stellar bars can, therefore, form in non-maximal discs, provided they are embedded in triaxial dark matter haloes. One may wonder whether the alignment of the dark and the stellar ‘bars’ shown in Fig. 1 is fortuitous, or if it is also present at earlier times. We use the apostle particle data at redshift z > 0 to follow the evolution of these two galaxies in the previous 1.5 Gyr. At each time-step, new surface density maps – analogous to those of Fig. 1 – are produced by projecting the system particles for a face-on view using the same $$\vec{L}_*$$ determined at z = 0. Note that this technique fails if the galactic plane rotates with time, but this is not the case for the systems considered here. As before, we fit the Rh iso-contour of these maps with an ellipse to determine the axis ratio and the orientation of both ‘bars’. The middle panels of Fig. 2 show the phases of the stellar (circles) and dark (squares) bars as a function of the lookback time for both galaxies. The bars are clearly locked in phase and rotate very slowly with pattern speeds of less than $$1\,{\rm km\,s}^{-1}\,{\rm \,{\rm kpc}}^{-1}$$. As we show in Section 3.3, this is typically the case for barred dwarf galaxies in the apostle simulations. We can quantify the magnitude of the perturbations in the gravitational potential induced by the bars via a harmonic analysis of the Φ maps shown in Fig. 1. For this purpose, we divide the Φ map into a series of concentric rings of increasing radius, each centred at the minimum of the potential and with thickness equal to 100 pc. The values of Φ as a function of the azimuthal angle θ are fit, for each ring separately, with $$\Phi (\theta ) = \sum _{m=0}^3 A_m \cos (m\theta - \theta _m),$$ (1)which is a harmonic expansion of the potential up to third order. The bottom panels of Fig. 1 show, as a function of R, the ratio between the amplitudes Am of the m > 0 modes and the mean value of Φ at each radius (i.e. the m = 0 mode amplitude). As expected, the strongest perturbation mode is the m = 2, which reaches amplitudes of ∼0.01 × A0 at R = Rh (black arrows). Perturbations of the order of m = 3 are virtually negligible, whereas m = 1 perturbations are intermediate. Even though the overall fluctuations in the potential are only of a few per cent, they are enough to affect significantly the gas velocity field, as discussed by HN06. We note that, although in the models of HN06 the gas follows elliptical closed orbits with major axis oriented perpendicularly to the bar, in the two systems studied here the major axis of the potential and that of the gas orbits are aligned. We find that this is the case for the majority of our simulated dwarfs, although the alignment is not always as clean as in AP-L1-V10-19-0 and AP-L1-V10-17-0. There are several differences between our galaxies and those in the HN06 models. The first is that the bars in our systems slowly rotate with time, whereas they were steady in HN06. The orientation of the closed orbits in a rotating barred potential depends on the positions of the inner Lindblad resonance and of the co-rotation radius, which vary from case to case depending on the exact shape and pattern speed of the potential (e.g. Contopoulos & Grosbol 1989; Athanassoula 1992; Sellwood & Wilkinson 1993). A second difference is that the HN06 models are based on the epicycle approximation, which breaks down when perturbations in the velocity field exceed a few per cent – they are typically of the order of ∼25 per cent at the half-mass radius in the cases we consider here. Finally, in our galaxies, the gas does not settle exactly on closed orbits but slowly flows inwards with time, as we verified by following the trajectories of a sample of gas particles in the two apostle systems studied here. Overall, the apostle dwarfs are more complex than the simple systems considered by HN06. A detailed analysis of the orbits of their gas and star particles is planned for a future study. 3.3 General properties of stellar and dark bars We now extend the previous analysis to the entire sample of 33 simulated dwarf galaxies studied by O17. These systems are selected to have 60 < Vmax/ km s−1 < 120, and typically have MHI comparable to M* (see table A1 in O17). The dynamics of each system in this sample are dominated everywhere by the dark matter. This is shown in Fig. 3, where we plot the ratio of the mid-plane gravitational acceleration contributed by baryons and by the dark matter, respectively, as a function of the circular velocity, Vcirc. We show the ratios computed at R = Rh (squares) and at R = 2Rh (circles). Figure 3. View largeDownload slide Ratio between the baryonic and the dark matter gravitational acceleration on the mid-plane as a function of the circular velocity $$\sqrt{GM(<R)/R}$$ computed at R = Rh (squares) and at R = 2Rh (circles) for the simulated dwarfs. Baryons are always subdominant. Figure 3. View largeDownload slide Ratio between the baryonic and the dark matter gravitational acceleration on the mid-plane as a function of the circular velocity $$\sqrt{GM(<R)/R}$$ computed at R = Rh (squares) and at R = 2Rh (circles) for the simulated dwarfs. Baryons are always subdominant. A clear trend is visible: The larger Vcirc is, the higher the contribution of the baryons to the total acceleration. However, in all cases, the baryons are subdominant: Their contribution to the total acceleration ranges from 10 per cent to 90 per cent of that given by the dark matter alone, decreasing towards the outer regions of the galaxies. Interestingly, by extrapolation of the trend shown in Fig. 3, it is clear that the baryons will dominate the central dynamics in galaxies more massive than those studied here (see also Schaller et al. 2016). Fig. 4 compares the axis ratio of the stellar bar with that of the dark bar for all systems in the sample. As before, the axis ratios are determined by fitting ellipses to the highest contour passing by Rh in face-on surface density maps. For the vast majority of systems, the two axis ratios are very similar, suggesting again that the origin of the stellar bars is closely linked to non-axisymmetries in the dark matter. The symbol numbers in Fig. 4 label the various systems as in table A1 of O17. Figure 4. View largeDownload slide Stellar bar versus halo bar axis ratio for our simulated dwarfs. Systems are numbered as in table A1 of O17, with numbers in red representing galaxies ‘in equilibrium’ (see text). 55 per cent (18/33) of galaxies have axis ratios smaller than 0.85 and constitute our ‘barred’ subsample. Figure 4. View largeDownload slide Stellar bar versus halo bar axis ratio for our simulated dwarfs. Systems are numbered as in table A1 of O17, with numbers in red representing galaxies ‘in equilibrium’ (see text). 55 per cent (18/33) of galaxies have axis ratios smaller than 0.85 and constitute our ‘barred’ subsample. We define a ‘barred’ subsample of 18 galaxies (55 per cent of the sample) by selecting those systems with axis ratio smaller than 0.85 for both the stellar and the dark matter components. This threshold is chosen because we found it impossible to track a bar backwards in time when its axis ratio is rounder than 0.85. Numbers in red in Fig. 4 are used to identify the subsample of 14 dwarfs identified by O17 as being ‘in equilibrium’: These are galaxies where the H i average azimuthal speed, computed at R = 2 kpc, matches the circular velocity at the same radius. In general, there is a tendency for these systems to have a large axis ratio, suggesting that galaxies whose halo is more spherical are, according to that definition, closer to dynamical equilibrium than more strongly barred systems. Fig. 5 shows how the difference between the phase of the stellar bar and that of the dark bar evolves in time. In all cases, the phase difference remains below ∼15° in the 2 Gyr before the present time, confirming that the stellar and dark bars always rotate in phase, and with the same pattern speed. Note that the system labelled as ‘2’ is missing in Fig. 5: A close encounter occurring at the lookback time of ∼0.5 Gyr unsettled the stellar disc and made it difficult to follow the evolution of the bar at earlier epochs. Figure 5. View largeDownload slide Difference between the phase of the stellar bar and the phase of the halo bar as a function of the lookback time for our subsample of simulated barred dwarfs. Systems are numbered as in table A1 of O17. Phases are always locked. Figure 5. View largeDownload slide Difference between the phase of the stellar bar and the phase of the halo bar as a function of the lookback time for our subsample of simulated barred dwarfs. Systems are numbered as in table A1 of O17. Phases are always locked. We now analyse the strength and the pattern speed of the stellar bars in our sample. Following Algorry et al. (2017), we define the strength of the stellar bar by measuring the amplitude of the m = 2 Fourier mode of the azimuthal distribution of star particles. Specifically, we compute $$a_m(R) = \sum _{i=1}^{n_R} m_i \cos (m\phi _i);\!\quad b_m(R) = \sum _{i=1}^{n_R} m_i \sin (m\phi _i),$$ (2)where mi is the mass of the ith star particle and the sum is extended to all nR particles that occupy a given cylindrical annulus with mean radius R. We then define $$A_{2,*}(R)=\sqrt{a_2^2 + b_2^2}/a_0$$, and the strength of the bar as $$A_{2,*}^{\rm max}\!=\!{\rm max}(A_{2,*}(R))$$. The distribution of $$A_{2,*}^{\rm max}$$ is shown in the left-hand panel of Fig. 6. All systems have bar strength below 0.4, which implies that they are all ‘weak bars’ according to the criterion of Algorry et al. (2017), with only seven systems with $$0.2<A_{2,*}^{\rm max}\!<\!0.4$$. In the right-hand panel of Fig. 6, we compare the bar co-rotation radius, Rcorot, *, and Rh in our subsample of barred galaxies. Rcorot,* is determined by first computing the bar pattern speed, Ω*, and then by equating Ω*R to the circular velocity of the system, $$\sqrt{GM(<R)/R}$$. Ω* is computed by fitting with a straight line the trend of the phase of the stellar bar with time, from lookback times of 2 Gyr to the present day. We find that Ω* is typically smaller than $$1\,{\rm km\,s}^{-1}\,{\rm \,{\rm kpc}}^{-1}$$, and the corresponding co-rotation radii Rcorot,* always exceed by far the system sizes. Figure 6. View largeDownload slide Properties of stellar bars in our simulated dwarfs. Left-hand panel: strength of the bar, $$A_2^{\rm max}$$ (see text), for the full sample (unfilled histogram) and for the barred subsample (filled histogram). Right-hand panel: bar co-rotation radius plotted against the projected radius at half stellar mass. The dashed line shows the one-to-one relation. Figure 6. View largeDownload slide Properties of stellar bars in our simulated dwarfs. Left-hand panel: strength of the bar, $$A_2^{\rm max}$$ (see text), for the full sample (unfilled histogram) and for the barred subsample (filled histogram). Right-hand panel: bar co-rotation radius plotted against the projected radius at half stellar mass. The dashed line shows the one-to-one relation. All stellar bars in our sample are relatively weak, very slowly rotating, and most likely originate from the triaxial structure of their dominant dark matter haloes. 3.4 Baryons and halo triaxiality As discussed in Section 1, the assembly of the baryonic component of a galaxy is expected to sphericalize the dark matter distribution. If so, this process has only gone to partial completion in APOSTLE dwarfs, given the prevalence of non-axisymmetric features (‘dark bars’) in our galaxy sample. We examine this question by studying the properties of 14 subhaloes with 60 < Vmax < 120 km s−1 extracted from volumes AP-L1-V1 and AP-L1-V4 in the apostle DMO simulations, which are the DMO counterparts of the corresponding full hydrodynamical runs. By analogy with our previous analysis, we measure deviations from axisymmetry by computing the axis ratio of face-on isodensity contours with semi-major axis length of 1.7 kpc, corresponding to the median Rh in our original sample. Since DMO runs have no stars, we define the face-on projection axis as the minor axis of the inertia tensor of all dark matter particles within 8 kpc from the halo centre. For consistency, we repeat the same procedure for our original sample of 33 galaxies in the hydrodynamical runs, so that dak matter axis ratios are derived in the same way for the two samples. In Fig. 7, we compare the b/a distributions for the dark matter in the hydrodynamical (full histogram) and in the DMO (dashed histogram) samples. Even though the sample is small, it is clear that deviations from axisymmetry are more pronounced in the DMO case than in the hydro simulations. As expected, the assembly of baryons at the centre of a halo reduces, but does not erase, the triaxiality of the potential in the innermost few kpc, in line with the findings of Kazantzidis et al. (2010), Abadi et al. (2010), and Machado & Athanassoula (2010). Figure 7. View largeDownload slide Axis ratio distribution for the dark bars in our sample of simulated dwarfs (filled histogram) and in a sample of subhaloes with 60 < Vmax < 120 km s−1 from the apostle DMO simulations (dashed histogram). Dark bars in DMO runs have lower axis ratio. Figure 7. View largeDownload slide Axis ratio distribution for the dark bars in our sample of simulated dwarfs (filled histogram) and in a sample of subhaloes with 60 < Vmax < 120 km s−1 from the apostle DMO simulations (dashed histogram). Dark bars in DMO runs have lower axis ratio. 3.5 Comparison with observations We now compare the amplitude of the harmonic perturbations in the H i velocity fields of real galaxies with those found in our simulations. For the latter, we use the same sample of 43 dwarfs (17 from THINGS, 26 from LITTLE THINGS) already considered by O17, adopting the ‘natural’-weighted moment-1 maps of these galaxies. These observations have angular resolution of ∼12 arcsec, corresponding to a median spatial resolution of the order of ∼250 pc. The overall kinematics of these systems has been already studied and reported by de Blok et al. (2008) and Oh et al. (2015). In observed galaxies, we do not have access to the 3D velocity field, but only to its projection along the line of sight. As is well known (e.g. Schoenmakers, Franx & de Zeeuw 1997; Spekkens & Sellwood 2007), harmonic perturbations of the order of m in the azimuthal or radial velocity field produce harmonic distortions of the orders of m΄ = m ± 1 in the line-of-sight velocity field. Hence, a bisymmetric flow in real space produces an m΄ = 1 and an m΄ = 3 perturbations in projected space, both having similar amplitude. Although the former is difficult to detect, as its signal blends with that produced by the regular rotation of the disc, the latter is a unique signature of bisymmetric flows and can be readily studied via a harmonic decomposition of the velocity field. Our strategy is therefore to produce synthetic line-of-sight H i velocity fields for the simulated systems, with resolution similar to that of observed galaxies, and compare the amplitudes of the harmonic modes of simulated and observed galaxies. In order to produce synthetic H i data cubes for the 33 systems in our simulated sample, we follow a procedure similar to that described by O17 in their section 3.3. The procedure consists of the following steps. Assume that a system is made of N gas particles, each described by its coordinates (x, y, z), velocities (Vx, Vy, Vz), temperature T, and H i mass mHI: the system is projected at 60° inclination, using $$\vec{L}_*$$ as a reference direction, and a random orientation; a position-velocity 3D grid is created, with a spatial binning of 83 pc and a channel separation of 2 km s−1; the mHI of each particle is placed at the corresponding (x, y) location in the grid, and is distributed in velocity around its Vz by using a Gaussian kernel with a standard deviation of $$\sqrt{k_{\rm B}T/m_{\rm H}}$$, kB being the Boltzmann constant and mH the proton mass; this is to take the thermal broadening of the line profiles into account; and once all particles have been processed, the resulting data cube is smoothed spatially at the FHWM resolution of 250 pc (three times the grid binning). For simplicity, we make no correction for gas opacity, i.e. the gas is considered to be optically thin. Note that, as in O17, the final resolution of our synthetic observations is similar to that of THINGS and LITTLE THINGS data cubes. Velocity fields are derived from these data cubes as moment-1 maps, which are well suited to account for non-circular motions in the gas kinematics. Finally, we perform a harmonic analysis of the velocity fields for both samples. The procedure requires a careful choice of galaxy centre. For the simulated galaxies, we assume that this coincides with the location of the minimum gravitational potential, whereas for the real galaxies we take the kinematic centres estimated by Trachternach et al. (2008) for THINGS and by Oh et al. (2015) for LITTLE THINGS. We focus on the amplitude of the m = 1 and 3 harmonic modes at two fixed galactocentric distances: R = 1 and 2 kpc, which bracket the range of Rh in our simulated sample and are well-resolved radii in both observations and simulations. In practice, we select a ring on the galactic plane with mean radius equal to the chosen value (1 or 2 kpc) and width equal to the FWHM resolution (which varies in the sample of real galaxies, but is constant in the simulated sample). Each ring is defined by its inclination, i, and position angle, PA, in the sky. Given that the choice of these two parameters significantly affects the outcome of the harmonic analysis, we must adopt a criterion that sets them uniquely and that can be applied to both observed and synthetic velocity fields. For any given (i, PA), the line-of-sight velocity, VLOS, within the ring as a function of the azimuthal angle in the plane of the galaxy, θ, is fitted with a formula analogous to equation (1), from which we extract the amplitudes A1, A2, and A3. Our choice for (i, PA) is the one that minimizes the quantity $$\sqrt{A_2^2+A_3^2}/|A_1|$$, which quantifies the strength of large-scale perturbations with respect to regular rotation at a given radius. The minimization is achieved via the Nelder & Mead (1965) method. We adopt (i = 60°, PA = 90°) as the initial guess for the simulated galaxies, whereas for the observed galaxies we use the values of i and PA determined by de Blok et al. (2008, for THINGS) and by Oh et al. (2015, for LITTLE THINGS) from their tilted ring fitting method. Typically, the final (i, PA) determined for the observed galaxies remains within ∼5° from the initial estimates. The simulated sample, however, shows much larger deviations from the initial guess. In some cases, fitting VLOS via equation (1) was not possible due to the small number of points, or – in observed galaxies – to an excessively noisy velocity field. For these reasons, DDO 53, DDO 210, IC 10, IC 1613, NGC 1569, UGC 8508, and Haro 29 have been excluded from our analysis at R = 1 kpc, along with DDO 168, DDO 216, NGC 3738, and Haro 36 at R = 2 kpc. Fig. 8 shows the ratio between A3 and A1, which is a measure of the strength of the bisymmetric flow with respect to regular H i rotation, as a function of A1/sin (i), which represents the H i azimuthal speed Vϕ alone,3 at R = 1 kpc (left-hand panel) and R = 2 kpc (right-hand panel) for the real (squares) and simulated (circles) galaxies, respectively. Figure 8. View largeDownload slide Bisymmetric H I flows in simulated and observed galaxies at galactocentric radii of R = 1 kpc (left-hand panel) and R = 2 kpc (right-hand panel). The ratio between the amplitudes of the m = 3 and 1 harmonic modes is plotted as a function of the amplitude of the m = 1 mode (divided by sin (i)) in the H I velocity fields of apostle galaxies (blue circles), THINGS galaxies (brown squares), and LITTLE THINGS galaxies (orange squares). Error bars show the formal errors on the harmonic fit to the velocities. Arrows represent upper limits. Systems are numbered as in tables A1 and A2 of O17. On average, simulated galaxies show stronger bisymmetric motions than the observed galaxies. Figure 8. View largeDownload slide Bisymmetric H I flows in simulated and observed galaxies at galactocentric radii of R = 1 kpc (left-hand panel) and R = 2 kpc (right-hand panel). The ratio between the amplitudes of the m = 3 and 1 harmonic modes is plotted as a function of the amplitude of the m = 1 mode (divided by sin (i)) in the H I velocity fields of apostle galaxies (blue circles), THINGS galaxies (brown squares), and LITTLE THINGS galaxies (orange squares). Error bars show the formal errors on the harmonic fit to the velocities. Arrows represent upper limits. Systems are numbered as in tables A1 and A2 of O17. On average, simulated galaxies show stronger bisymmetric motions than the observed galaxies. Interestingly, there is a common trend followed by both real and simulated galaxies: The importance of non-circular motions compared to the regular rotation decreases as a function of rotation speed. The main difference between observed and simulated galaxies is in the amplitudes of the bisymmetric motions: The median A3/A1 at R = 1 kpc (R = 2 kpc) is 0.083 (0.057) in apostle, 0.017 (0.010) in THINGS, and 0.040 (0.033) in LITTLE THINGS. Limiting the comparison to the LITTLE THINGS sample alone, which spans a range of A1/sin(i) similar to our apostle sample, we conclude that bisymmetric flows in apostle dwarfs are a factor of ∼2 stronger than those in the observed galaxies. We have verified that these results hold when the harmonic analysis is performed at the effective radius Reff of each system, or at 2Reff, rather than at a fixed galactocentric distance, using effective radii from the SPARC catalogue of Lelli, McGaugh & Schombert (2016) and the catalogue of Hunter & Elmegreen (2006). These results suggest that bisymmetric flows caused by bar-like features, or, more generally, by asphericities in the gravitational potential, are somewhat less prominent in observed galaxies than in the apostle simulations, at least in the dwarf galaxy regime, in line with the earlier findings of Trachternach et al. (2008). There are, however, important caveats in the comparison. One is that, although our analysis considers all apostle galaxies in the range 60 < Vmax/ km s−1 < 120, the observed sample has no well-defined completeness criteria. A second difference, already mentioned above, is in the velocity range covered: Only eight galaxies in the observed sample have 60 < Vmax/ km s−1 < 120. A further difference is environmental: The apostle galaxies are located in the proximity (i.e. within ∼3 Mpc) of a Local Group analogue, whereas the THINGS and LITTLE THINGS galaxies are in less dense environments. In light of these considerations, we argue that the differences in the A3/A1 ratio shown in Fig. 8, although suggestive, should be treated with caution. 4 CONCLUSIONS CDM haloes are triaxial in nature (e.g. Frenk et al. 1988). Their asphericity increases towards their centre (Hayashi et al. 2007), implying that the process of galaxy formation in a ΛCDM framework occurs within gravitational potentials that are non-axisymmetric, or, broadly speaking, ‘barred’. The processes of stellar mass assembly and secular evolution can reduce the halo triaxiality significantly in massive disc galaxies (Abadi et al. 2010; Kazantzidis et al. 2010; Machado & Athanassoula 2010), but are much less efficient in dwarf galaxies, which therefore may be forced to respond to non-axisymmetric forces due to the dark matter. In this work, we have carried out a study of the mass distribution and H i kinematics within the central few kiloparsecs in a sample of 33 H i-rich dwarf (60 < Vmax < 120 km s−1) galaxies from the apostle suite of ΛCDM cosmological hydrodynamical simulations. Our results can be summarized as follows: Most simulated dwarfs have a bar in their stellar component that matches the non-axisymmetric distribution of the inner dark matter halo (‘dark’ bar). Specifically, 18 out of 33 apostle dwarfs (55 per cent) have a stellar and a dark bar with axis ratios smaller than 0.85. When present, the stellar and the dark bar corotate and are locked in phase. Since the gravitational potential is dominated by the dark matter, the stellar bar follows the dark bar, not viceversa. A corollary is that the presence of a stellar bar does not imply that baryons dominate gravitationally that region. All bars in the sample analysed are weak, and have co-rotation radii that largely exceed the galaxy size. The stellar/dark bar induces significant bisymmetric flows in the gas component. We have compared the amplitude of the m = 3 harmonic perturbations in the H i velocity fields of the apostle systems with those of THINGS and LITTLE THINGS galaxies, finding that the magnitude of bisymmetric flows in the former exceeds that in the latter by a factor of ∼2. Our findings clarify the nature of the non-circular motions reported by O17 in the same simulated galaxy sample as due to the effects of a dominant triaxial halo. Our analysis also shows that, although haloes are sphericalized by the assembly of the galaxy, the sphericalization is incomplete in dwarfs like the ones in our apostle sample. The remaining triaxiality induces the formation of a bar-like feature in the stars and non-circular motions in the gas. Although the magnitude of such motions seems to exceed, on average, those in galaxies of the THINGS and LITTLE THINGS surveys, we caution that these surveys are not exactly comparable, so a definitive conclusion about whether our findings are in agreement or disagreement with real galaxies in the local Universe remains pending and will be the focus of future work. Acknowledgements The authors thank the THINGS, LITTLE THINGS, and SPARC survey teams for making their data publicly available. AM thanks Mattia Sormani for helpful discussions. CSF acknowledges support from ERC Advanced Grant 267291 Cosmiway. This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure. Footnotes 1 A Project Of Simulating The Local Environment 2 A ‘central’ subhalo is the most massive subhalo of each FoF group, and is therefore not a satellite of a more massive system. 3 In reality, A1 is a combination of rotation and a global expansion/contraction in the radial direction, but the latter is typically negligible. REFERENCES Abadi M. G., Navarro J. 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# Bars in dark-matter-dominated dwarf galaxy discs
, Volume 476 (2) – May 1, 2018
9 pages
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### Abstract
Abstract We study the shape and kinematics of simulated dwarf galaxy discs in the apostle suite of Λ cold dark matter (ΛCDM) cosmological hydrodynamical simulations. We find that a large fraction of these gas-rich, star-forming discs show weak bars in their stellar component, despite being dark-matter-dominated systems. The bar pattern shape and orientation reflect the ellipticity of the dark matter potential, and its rotation is locked to the slow figure rotation of the triaxial dark halo. The bar-like nature of the potential induces non-circular motions in the gas component, including strong bisymmetric flows that can be readily seen as m = 3 harmonic perturbations in the H i line-of-sight velocity fields. Similar bisymmetric flows are seen in many galaxies of The HI Nearby Galaxy Survey (THINGS) and Local Irregulars That Trace Luminosity Extremes THINGS (LITTLE THINGS), although on average their amplitudes are a factor of ∼2 weaker than in our simulated discs. Our results indicate that bar-like patterns may arise even when baryons are not dominant, and that they are common enough to warrant careful consideration when analysing the gas kinematics of dwarf galaxy discs. ISM: kinematics and dynamics, galaxies: dwarf, galaxies: kinematics and dynamics, galaxies: structure, dark matter 1 INTRODUCTION Bars are a common morphological feature of spiral galaxies in the local Universe. About one-quarter of disc galaxies show strong bars (Masters et al. 2011; Cheung et al. 2013), and this fraction increases up to about two-thirds when including weaker features (Mulchaey & Regan 1997; Kormendy & Kennicutt 2004). The fraction of barred galaxies appears to depend significantly on galaxy luminosity, being lower for fainter galaxies (Méndez-Abreu, Sánchez-Janssen & Aguerri 2010; Janz et al. 2012), and, to a minor extent, on environment, increasing in regions of higher galaxy density (Méndez-Abreu et al. 2012). Bars have been a topic of interest for decades, and numerical simulations have played a major role in our current understanding of their formation and evolution. Although details need to be fully worked out, there is widespread agreement that bars develop in stellar discs as a consequence of the inevitable tendency of collisionless systems to evolve dynamically by redistributing the mass inwards and angular momentum outwards. Bar patterns offer a particularly efficient way of carrying out this redistribution, and grow and strengthen rapidly in cold, massive stellar discs (see e.g. Athanassoula 2013; Sellwood 2014, for recent reviews). Their growth is so rapid in such systems (Miller & Prendergast 1968; Hockney & Hohl 1969) that few can avoid becoming ‘bar unstable’ in a couple of rotation periods (Sellwood & Wilkinson 1993), unless stabilized by the presence of a dominant dark halo (Ostriker & Peebles 1973). These results have been so influential that the presence of bar-like patterns is often taken to indicate discs where the dark halo is gravitationally unimportant; i.e. discs that are ‘maximal’. More recent work, however, suggests a more complex scenario where bar formation is delayed, but not fully inhibited, in discs where dark matter haloes are gravitationally dominant (e.g. Athanassoula 2002, 2003; Algorry et al. 2017): Bars are thus not synonymous with maximal discs, suggesting that care must be exercised when using morphological features to infer indirectly the relative importance of disc and halo in spiral galaxies. Bars are not the only bisymmetric (m = 2) perturbation expected in disc galaxies. Indeed, discs are expected to form at the centre of cold dark matter (CDM) haloes, which have long been known to be triaxial in nature (Frenk et al. 1988; Warren et al. 1992; Jing & Suto 2002). Discs that settle on the symmetry plane of such haloes would be subject to gravitational forces akin to those in barred systems, although the bisymmetric pattern in this case is expected to rotate much less rapidly than in typical strongly barred systems. Although a number of works have focused on the impact of stellar bars on the dynamics of haloes (e.g. Debattista & Sellwood 1998, 2000), the consequences of halo triaxiality on the kinematics of discs have not been extensively studied (although see Hayashi, Navarro & Springel 2007, for an attempt), in part because the assembly of the disc is thought to ‘sphericalize’ the halo (see Abadi et al. 2010, and references therein). However, this is only true in the case of massive discs such as those of luminous, high surface brightness spirals. In the case of fainter, lower surface brightness spirals, discs are less gravitationally important and the sphericalization of their surrounding haloes should be less complete (Kazantzidis, Abadi & Navarro 2010; Machado & Athanassoula 2010). Regardless of origin, bar-like perturbations can have important consequences on the kinematic of discs, particularly on the interpretation of azimuthally averaged rotation curves and of 2D velocity fields of gas and stars. Hayashi & Navarro (2006, hereafter HN06), for example, showed that even minor deviations from spherical symmetry can induce large deviations from circular orbits in the velocity field of a gaseous disc. This possibility was studied by Trachternach et al. (2008), who carried out a harmonic decomposition of the H i velocity fields in 19 galaxies from The H i Nearby Galaxy Survey (THINGS, Walter et al. 2008). The harmonic decomposition suggests that the magnitude of non-circular motions in the central regions of these systems is small, and compatible with a circularly symmetric potential. However, most of the systems studied by Trachternach et al. were large spirals, and the analysis has not been extended to the dwarf galaxy regime, where the triaxiality of the halo might be better preserved. A harmonic decomposition of Local Irregulars That Trace Luminosity Extremes THINGS (LITTLE THINGS) galaxies (Hunter et al. 2012) was performed by Oh et al. (2015), but their findings were not discussed in terms of triaxiality of the gravitational potential; thus, whether or not dwarf galaxies are consistent with hosting triaxial haloes is still an open question. Recently, Oman et al. (2017, hereafter O17) have studied the gas kinematics in a sample of 33 simulated dwarf galaxies from the apostle suite of ΛCDM cosmological simulations (Sawala et al. 2015; Fattahi et al. 2016). Their approach used synthetic H i observations of these systems, from which the gas rotation curve was derived using the same tilted ring modelling technique adopted in most H i observational studies. One of the main results of O17 is that, depending on the orientation of the line of sight, a large variety of rotation curves might be derived for the same system, even for fixed inclination. The variety is due to non-circular motions in the gas, in particular, to strong bisymmetric (m = 2 harmonic) fluctuations in the azimuthal H i velocity field, which the tilted-ring model is not well suited to account for. We study here the origin of these non-circular motions, focusing on the mass distribution and the shape of the gravitational potential. We show that the cause of these bisymmetric gas flows is the presence of bar-like features in both the stellar and the dark matter distributions. This paper is structured as follows. In Section 2, we summarize the main features of the apostle simulations and of the selected galaxy sample. In Section 3, we discuss the properties of the stellar and dark matter bars in our sample, and how they affect the gas kinematics. A comparison with dark-matter-only (DMO) simulations and with the observations is also presented. We finally summarize our findings in Section 4. 2 SIMULATIONS AND SAMPLE SELECTION A detailed description of the apostle1 simulations can be found in Sawala et al. (2015) and Fattahi et al. (2016). Here, we summarize their main characteristics. apostle is a suite of cosmological hydrodynamical simulations performed in a ΛCDM framework, adopting the cosmological parameters inferred from WMAP-7 data (Komatsu et al. 2011). It consists of 12 subvolumes selected from the DOVE cosmological simulation (Jenkins 2013) and re-simulated using the zoom-in technique (Frenk et al. 1996; Power et al. 2003). The volumes are centred around two massive haloes (analogous to the Milky Way - M31 pair) and chosen to resemble these galaxies in terms of mass, separation and kinematics, whilst ensuring relative isolation from more massive structures. The hydrodynamics and the baryonic subgrid physics implemented in apostle are the same as those adopted in the EAGLE simulations (Crain et al. 2015; Schaye et al. 2015). EAGLE, and by extension apostle, uses a formulation of the smoothed-particle hydrodynamics (SPH) known as ANARCHY (Dalla Vecchia in preparation, see also appendix A of Schaye et al. 2015), which alleviates significantly the issues related to artificial gas clumping and the poor treatment of hydrodynamical instabilities associated with the classical SPH scheme (e.g Kaufmann et al. 2006; Agertz et al. 2007). Other features introduced by ANARCHY are the use of an artificial viscosity switch (Cullen & Dehnen 2010), an artificial conduction switch (Price 2008), and a time-step limiter (Durier & Dalla Vecchia 2012). The recipes for subgrid physics include the star formation implementation of Schaye & Dalla Vecchia (2008), thermal star formation feedback from Dalla Vecchia & Schaye (2012), radiative gas cooling and photo-heating from Wiersma, Schaye & Smith (2009a), and stellar mass-loss from Wiersma et al. (2009b). Accretion on to black holes and AGN feedback is not implemented in apostle, but this is not critical for the mass scale of interest. The apostle volumes are resimulated at three levels of resolution. As in O17, here we focus on the highest resolution level (‘L1’ in Fattahi et al. 2016), featuring a dark matter particle mass of 3.6 × 104 M⊙, a gas particle initial mass of 7.4 × 103 M⊙, and maximum softening length of 134 pc. At the moment of writing, only five of the 12 volumes have been re-simulated at this resolution. Galaxies, and in general ‘subhaloes’, are identified in the simulation via the SUBFIND algorithm (Dolag et al. 2009), which is based on a friend-of-friends (FoF) scheme. O17 studied 33 dwarf systems, selecting central2 subhaloes with maximum circular velocity 60 < Vmax < 120 km s−1 at redshift z = 0. The Vmax selection targets the ‘dwarf’ spiral regime, whereas the exclusion of satellites allows us to discard systems whose features might be affected by the effect of tides. We focus here on the same galaxy sample, whose main properties are listed in table A1 of O17. Each simulated galaxy is uniquely identified by four labels: the resolution level (always L1 in our sample), the apostle volume it belongs to (V1, V2,..., V12), the FoF group, and SUBFIND sub-group numbers, respectively. The latter is always equal to 0, indicating that the system is the central subhalo of its FoF group. These labels follow the ‘AP’ keyword that identifies the suite of simulations used. As in other studies of neutral hydrogen using the EAGLE simulations, the H i mass fraction of each gas particle in the apostle volumes is computed in two steps: The fraction of neutral hydrogen is first derived following the prescription of Rahmati et al. (2013) for self-shielding from the metagalactic ionizing background, and then a pressure-dependent correction for the molecular gas fraction is applied following Blitz & Rosolowsky (2006). We refer the interested reader to Crain et al. (2017) for details. 3 RESULTS 3.1 Stellar bars and ‘dark bars’ For illustration, we present first the mass distribution and the H i kinematics in the inner regions of two representative systems in the sample of O17: AP-L1-V10-19-0 and AP-L1-V10-17-0. These systems have comparable Vmax (67 and 65 km s−1, respectively), stellar mass (4.7 and 7.1 × 108 M⊙), H i-to-stellar mass ratio (1.1 and 0.7), and star formation rates at z = 0 (0.08 and 0.13 M⊙ yr− 1). Also, both systems are quite isolated, lying at more than 2 Mpc from the closest member of the Milky Way/M31 analogue pair. They also show no obvious sign of interactions with nearby galaxies. Fig. 1 shows a series of face-on maps for these two galaxies, where the rotation axis of the galaxy is identified with $$\vec{L}_*$$, the angular momentum vector of all stars (identified by SUBFIND as bound to the system and located within a radius enclosing 90 per cent of the total stellar mass) relative to the galaxy centre. The latter is defined as the location of the particle with the lowest potential energy. All maps are smoothed to a spatial resolution [full width at half-maximum (FWHM) of a Gaussian kernel] of 0.2 kpc. Figure 1. View largeDownload slide Face-on maps of two representative apostle dwarfs at redshift 0. First and second columns: stellar and dark matter surface density maps, shown on the same colour scale. Isodensity contours (in white) are spaced by 0.3 dex. The blue isodensity contour has semi-major axis equal to the projected radius at half stellar mass, Rh; the dashed black line shows the best-fitting ellipse to this contour. Third column: gravitational potential map on the galactic mid-plane. Fourth and fifth columns: maps of the azimuthal and radial H I velocity fields, also on the mid-plane, from which we have subtracted the mean velocity computed at different radii. A residual m = 2 mode is clearly visible in both maps; its phase is traced by black crosses. The dashed black line in the three rightmost panels shows the major axis of the gravitational potential. Figure 1. View largeDownload slide Face-on maps of two representative apostle dwarfs at redshift 0. First and second columns: stellar and dark matter surface density maps, shown on the same colour scale. Isodensity contours (in white) are spaced by 0.3 dex. The blue isodensity contour has semi-major axis equal to the projected radius at half stellar mass, Rh; the dashed black line shows the best-fitting ellipse to this contour. Third column: gravitational potential map on the galactic mid-plane. Fourth and fifth columns: maps of the azimuthal and radial H I velocity fields, also on the mid-plane, from which we have subtracted the mean velocity computed at different radii. A residual m = 2 mode is clearly visible in both maps; its phase is traced by black crosses. The dashed black line in the three rightmost panels shows the major axis of the gravitational potential. The two leftmost panels of Fig. 1 show the stellar and dark matter surface density maps derived projecting a cubic region with side-length 8 kpc, concentric with the galaxy. The elongation of the isodensity contours reveals that both stars and dark matter are clearly non-axisymmetric. Projected on to the disc plane, both components seem bar-like, especially in the central few kiloparsec. For simplicity, we will refer to these non-axisymmetric features as the ‘stellar’ bar and the ‘dark’ bar. These two ‘bars’ have the same orientation and, approximately, the same axis ratio. The central panels show isopotential contours measured on the disc mid-plane, computed using all (dark + baryonic) particles identified by SUBFIND as bound to the system (the gravitational potential, Φ, is softened on scales smaller than 100 pc). The gravitational potential is clearly aspherical, especially close to the centre, and is therefore expected to induce deviations from pure circular rotation in the motion of gas and stars in the disc. These deviations are explored in the two rightmost panels, which show the azimuthal and the radial H i velocity fields derived on the galaxy mid-plane, from which we have subtracted the mean azimuthally averaged value at each radius. If the gas was in pure circular rotation around the centre, these ‘residual’ velocity fields should not show systematic deviations from zero. Instead, clear m = 2 harmonic patterns are visible, which were already noticed by O17 in other systems of the sample. The phase of the m = 2 perturbation in the azimuthal velocity (shown by the black crosses in the fourth column of Fig. 1, which trace the maximum positive deviation from the mean) is oriented approximately perpendicular to the major axis of the potential (dashed black line, see below), whereas the phase of the perturbation in the radial velocity lags 45° from the latter. This pattern is consistent with gas moving counter-clockwise along elliptical orbits elongated in the same direction of the potential. The simplest interpretation of these orbits is that, in these galaxies, the stellar/dark bar induces a bisymmetric flow in the gas component. We determine major and minor axes for the bar by fitting an ellipse to the surface density contour whose semi-major axis coincides with Rh, the (projected) stellar half-mass radius. This is highlighted in blue in the leftmost panels of Fig. 1. The ellipse centre is a free parameter of the fit, in order to account for possible offsets in the mass distribution. Rh is computed directly from the face-on stellar density distribution. 3.2 Stellar bars in sub-dominant discs The two leftmost panels of Fig. 1 suggest that the dark matter dominates the dynamics in the central few kiloparsec. This is shown explicitly in the top panels of Fig. 2, which show, for both systems, the gravitational acceleration due to the stars alone (orange lines) and to the dark matter (blue lines) on the galactic mid-plane along the projected major (dashed lines) and minor (solid lines) axes of the bar. The gas contribution to the gravitational acceleration is negligible compared to the other components. Figure 2. View largeDownload slide Top panels: gravitational acceleration on the galactic mid-plane decomposed into contributions from stars (orange lines) and from dark matter (blue lines) as a function of the distance along the major axis (dashed lines) or the minor axis (solid lines) of the bar for the two representative galaxies. Dark matter dominates the gravitational acceleration within the bar. Central panels: phases of the stellar (orange circles) and of the dark matter (blue squares) bar as a function of the lookback time. Phases are locked. Bottom panels: amplitude of the m > 0 harmonic fluctuations in the gravitational potential Φ, divided by the mean value of Φ, as a function of R. The strongest harmonic mode is the m = 2. The arrows show the location of Rh. Figure 2. View largeDownload slide Top panels: gravitational acceleration on the galactic mid-plane decomposed into contributions from stars (orange lines) and from dark matter (blue lines) as a function of the distance along the major axis (dashed lines) or the minor axis (solid lines) of the bar for the two representative galaxies. Dark matter dominates the gravitational acceleration within the bar. Central panels: phases of the stellar (orange circles) and of the dark matter (blue squares) bar as a function of the lookback time. Phases are locked. Bottom panels: amplitude of the m > 0 harmonic fluctuations in the gravitational potential Φ, divided by the mean value of Φ, as a function of R. The strongest harmonic mode is the m = 2. The arrows show the location of Rh. Fig. 2 clearly indicates that, in these two systems, the overall dynamics are dominated everywhere – even at the very centre – by the dark matter. This suggests that, in these two systems, the stellar bar originates as a response to the non-axisymmetric distribution of dark matter, and not, as traditionally envisioned, as a result of some instability in a stellar-dominated disc. At least some stellar bars can, therefore, form in non-maximal discs, provided they are embedded in triaxial dark matter haloes. One may wonder whether the alignment of the dark and the stellar ‘bars’ shown in Fig. 1 is fortuitous, or if it is also present at earlier times. We use the apostle particle data at redshift z > 0 to follow the evolution of these two galaxies in the previous 1.5 Gyr. At each time-step, new surface density maps – analogous to those of Fig. 1 – are produced by projecting the system particles for a face-on view using the same $$\vec{L}_*$$ determined at z = 0. Note that this technique fails if the galactic plane rotates with time, but this is not the case for the systems considered here. As before, we fit the Rh iso-contour of these maps with an ellipse to determine the axis ratio and the orientation of both ‘bars’. The middle panels of Fig. 2 show the phases of the stellar (circles) and dark (squares) bars as a function of the lookback time for both galaxies. The bars are clearly locked in phase and rotate very slowly with pattern speeds of less than $$1\,{\rm km\,s}^{-1}\,{\rm \,{\rm kpc}}^{-1}$$. As we show in Section 3.3, this is typically the case for barred dwarf galaxies in the apostle simulations. We can quantify the magnitude of the perturbations in the gravitational potential induced by the bars via a harmonic analysis of the Φ maps shown in Fig. 1. For this purpose, we divide the Φ map into a series of concentric rings of increasing radius, each centred at the minimum of the potential and with thickness equal to 100 pc. The values of Φ as a function of the azimuthal angle θ are fit, for each ring separately, with $$\Phi (\theta ) = \sum _{m=0}^3 A_m \cos (m\theta - \theta _m),$$ (1)which is a harmonic expansion of the potential up to third order. The bottom panels of Fig. 1 show, as a function of R, the ratio between the amplitudes Am of the m > 0 modes and the mean value of Φ at each radius (i.e. the m = 0 mode amplitude). As expected, the strongest perturbation mode is the m = 2, which reaches amplitudes of ∼0.01 × A0 at R = Rh (black arrows). Perturbations of the order of m = 3 are virtually negligible, whereas m = 1 perturbations are intermediate. Even though the overall fluctuations in the potential are only of a few per cent, they are enough to affect significantly the gas velocity field, as discussed by HN06. We note that, although in the models of HN06 the gas follows elliptical closed orbits with major axis oriented perpendicularly to the bar, in the two systems studied here the major axis of the potential and that of the gas orbits are aligned. We find that this is the case for the majority of our simulated dwarfs, although the alignment is not always as clean as in AP-L1-V10-19-0 and AP-L1-V10-17-0. There are several differences between our galaxies and those in the HN06 models. The first is that the bars in our systems slowly rotate with time, whereas they were steady in HN06. The orientation of the closed orbits in a rotating barred potential depends on the positions of the inner Lindblad resonance and of the co-rotation radius, which vary from case to case depending on the exact shape and pattern speed of the potential (e.g. Contopoulos & Grosbol 1989; Athanassoula 1992; Sellwood & Wilkinson 1993). A second difference is that the HN06 models are based on the epicycle approximation, which breaks down when perturbations in the velocity field exceed a few per cent – they are typically of the order of ∼25 per cent at the half-mass radius in the cases we consider here. Finally, in our galaxies, the gas does not settle exactly on closed orbits but slowly flows inwards with time, as we verified by following the trajectories of a sample of gas particles in the two apostle systems studied here. Overall, the apostle dwarfs are more complex than the simple systems considered by HN06. A detailed analysis of the orbits of their gas and star particles is planned for a future study. 3.3 General properties of stellar and dark bars We now extend the previous analysis to the entire sample of 33 simulated dwarf galaxies studied by O17. These systems are selected to have 60 < Vmax/ km s−1 < 120, and typically have MHI comparable to M* (see table A1 in O17). The dynamics of each system in this sample are dominated everywhere by the dark matter. This is shown in Fig. 3, where we plot the ratio of the mid-plane gravitational acceleration contributed by baryons and by the dark matter, respectively, as a function of the circular velocity, Vcirc. We show the ratios computed at R = Rh (squares) and at R = 2Rh (circles). Figure 3. View largeDownload slide Ratio between the baryonic and the dark matter gravitational acceleration on the mid-plane as a function of the circular velocity $$\sqrt{GM(<R)/R}$$ computed at R = Rh (squares) and at R = 2Rh (circles) for the simulated dwarfs. Baryons are always subdominant. Figure 3. View largeDownload slide Ratio between the baryonic and the dark matter gravitational acceleration on the mid-plane as a function of the circular velocity $$\sqrt{GM(<R)/R}$$ computed at R = Rh (squares) and at R = 2Rh (circles) for the simulated dwarfs. Baryons are always subdominant. A clear trend is visible: The larger Vcirc is, the higher the contribution of the baryons to the total acceleration. However, in all cases, the baryons are subdominant: Their contribution to the total acceleration ranges from 10 per cent to 90 per cent of that given by the dark matter alone, decreasing towards the outer regions of the galaxies. Interestingly, by extrapolation of the trend shown in Fig. 3, it is clear that the baryons will dominate the central dynamics in galaxies more massive than those studied here (see also Schaller et al. 2016). Fig. 4 compares the axis ratio of the stellar bar with that of the dark bar for all systems in the sample. As before, the axis ratios are determined by fitting ellipses to the highest contour passing by Rh in face-on surface density maps. For the vast majority of systems, the two axis ratios are very similar, suggesting again that the origin of the stellar bars is closely linked to non-axisymmetries in the dark matter. The symbol numbers in Fig. 4 label the various systems as in table A1 of O17. Figure 4. View largeDownload slide Stellar bar versus halo bar axis ratio for our simulated dwarfs. Systems are numbered as in table A1 of O17, with numbers in red representing galaxies ‘in equilibrium’ (see text). 55 per cent (18/33) of galaxies have axis ratios smaller than 0.85 and constitute our ‘barred’ subsample. Figure 4. View largeDownload slide Stellar bar versus halo bar axis ratio for our simulated dwarfs. Systems are numbered as in table A1 of O17, with numbers in red representing galaxies ‘in equilibrium’ (see text). 55 per cent (18/33) of galaxies have axis ratios smaller than 0.85 and constitute our ‘barred’ subsample. We define a ‘barred’ subsample of 18 galaxies (55 per cent of the sample) by selecting those systems with axis ratio smaller than 0.85 for both the stellar and the dark matter components. This threshold is chosen because we found it impossible to track a bar backwards in time when its axis ratio is rounder than 0.85. Numbers in red in Fig. 4 are used to identify the subsample of 14 dwarfs identified by O17 as being ‘in equilibrium’: These are galaxies where the H i average azimuthal speed, computed at R = 2 kpc, matches the circular velocity at the same radius. In general, there is a tendency for these systems to have a large axis ratio, suggesting that galaxies whose halo is more spherical are, according to that definition, closer to dynamical equilibrium than more strongly barred systems. Fig. 5 shows how the difference between the phase of the stellar bar and that of the dark bar evolves in time. In all cases, the phase difference remains below ∼15° in the 2 Gyr before the present time, confirming that the stellar and dark bars always rotate in phase, and with the same pattern speed. Note that the system labelled as ‘2’ is missing in Fig. 5: A close encounter occurring at the lookback time of ∼0.5 Gyr unsettled the stellar disc and made it difficult to follow the evolution of the bar at earlier epochs. Figure 5. View largeDownload slide Difference between the phase of the stellar bar and the phase of the halo bar as a function of the lookback time for our subsample of simulated barred dwarfs. Systems are numbered as in table A1 of O17. Phases are always locked. Figure 5. View largeDownload slide Difference between the phase of the stellar bar and the phase of the halo bar as a function of the lookback time for our subsample of simulated barred dwarfs. Systems are numbered as in table A1 of O17. Phases are always locked. We now analyse the strength and the pattern speed of the stellar bars in our sample. Following Algorry et al. (2017), we define the strength of the stellar bar by measuring the amplitude of the m = 2 Fourier mode of the azimuthal distribution of star particles. Specifically, we compute $$a_m(R) = \sum _{i=1}^{n_R} m_i \cos (m\phi _i);\!\quad b_m(R) = \sum _{i=1}^{n_R} m_i \sin (m\phi _i),$$ (2)where mi is the mass of the ith star particle and the sum is extended to all nR particles that occupy a given cylindrical annulus with mean radius R. We then define $$A_{2,*}(R)=\sqrt{a_2^2 + b_2^2}/a_0$$, and the strength of the bar as $$A_{2,*}^{\rm max}\!=\!{\rm max}(A_{2,*}(R))$$. The distribution of $$A_{2,*}^{\rm max}$$ is shown in the left-hand panel of Fig. 6. All systems have bar strength below 0.4, which implies that they are all ‘weak bars’ according to the criterion of Algorry et al. (2017), with only seven systems with $$0.2<A_{2,*}^{\rm max}\!<\!0.4$$. In the right-hand panel of Fig. 6, we compare the bar co-rotation radius, Rcorot, *, and Rh in our subsample of barred galaxies. Rcorot,* is determined by first computing the bar pattern speed, Ω*, and then by equating Ω*R to the circular velocity of the system, $$\sqrt{GM(<R)/R}$$. Ω* is computed by fitting with a straight line the trend of the phase of the stellar bar with time, from lookback times of 2 Gyr to the present day. We find that Ω* is typically smaller than $$1\,{\rm km\,s}^{-1}\,{\rm \,{\rm kpc}}^{-1}$$, and the corresponding co-rotation radii Rcorot,* always exceed by far the system sizes. Figure 6. View largeDownload slide Properties of stellar bars in our simulated dwarfs. Left-hand panel: strength of the bar, $$A_2^{\rm max}$$ (see text), for the full sample (unfilled histogram) and for the barred subsample (filled histogram). Right-hand panel: bar co-rotation radius plotted against the projected radius at half stellar mass. The dashed line shows the one-to-one relation. Figure 6. View largeDownload slide Properties of stellar bars in our simulated dwarfs. Left-hand panel: strength of the bar, $$A_2^{\rm max}$$ (see text), for the full sample (unfilled histogram) and for the barred subsample (filled histogram). Right-hand panel: bar co-rotation radius plotted against the projected radius at half stellar mass. The dashed line shows the one-to-one relation. All stellar bars in our sample are relatively weak, very slowly rotating, and most likely originate from the triaxial structure of their dominant dark matter haloes. 3.4 Baryons and halo triaxiality As discussed in Section 1, the assembly of the baryonic component of a galaxy is expected to sphericalize the dark matter distribution. If so, this process has only gone to partial completion in APOSTLE dwarfs, given the prevalence of non-axisymmetric features (‘dark bars’) in our galaxy sample. We examine this question by studying the properties of 14 subhaloes with 60 < Vmax < 120 km s−1 extracted from volumes AP-L1-V1 and AP-L1-V4 in the apostle DMO simulations, which are the DMO counterparts of the corresponding full hydrodynamical runs. By analogy with our previous analysis, we measure deviations from axisymmetry by computing the axis ratio of face-on isodensity contours with semi-major axis length of 1.7 kpc, corresponding to the median Rh in our original sample. Since DMO runs have no stars, we define the face-on projection axis as the minor axis of the inertia tensor of all dark matter particles within 8 kpc from the halo centre. For consistency, we repeat the same procedure for our original sample of 33 galaxies in the hydrodynamical runs, so that dak matter axis ratios are derived in the same way for the two samples. In Fig. 7, we compare the b/a distributions for the dark matter in the hydrodynamical (full histogram) and in the DMO (dashed histogram) samples. Even though the sample is small, it is clear that deviations from axisymmetry are more pronounced in the DMO case than in the hydro simulations. As expected, the assembly of baryons at the centre of a halo reduces, but does not erase, the triaxiality of the potential in the innermost few kpc, in line with the findings of Kazantzidis et al. (2010), Abadi et al. (2010), and Machado & Athanassoula (2010). Figure 7. View largeDownload slide Axis ratio distribution for the dark bars in our sample of simulated dwarfs (filled histogram) and in a sample of subhaloes with 60 < Vmax < 120 km s−1 from the apostle DMO simulations (dashed histogram). Dark bars in DMO runs have lower axis ratio. Figure 7. View largeDownload slide Axis ratio distribution for the dark bars in our sample of simulated dwarfs (filled histogram) and in a sample of subhaloes with 60 < Vmax < 120 km s−1 from the apostle DMO simulations (dashed histogram). Dark bars in DMO runs have lower axis ratio. 3.5 Comparison with observations We now compare the amplitude of the harmonic perturbations in the H i velocity fields of real galaxies with those found in our simulations. For the latter, we use the same sample of 43 dwarfs (17 from THINGS, 26 from LITTLE THINGS) already considered by O17, adopting the ‘natural’-weighted moment-1 maps of these galaxies. These observations have angular resolution of ∼12 arcsec, corresponding to a median spatial resolution of the order of ∼250 pc. The overall kinematics of these systems has been already studied and reported by de Blok et al. (2008) and Oh et al. (2015). In observed galaxies, we do not have access to the 3D velocity field, but only to its projection along the line of sight. As is well known (e.g. Schoenmakers, Franx & de Zeeuw 1997; Spekkens & Sellwood 2007), harmonic perturbations of the order of m in the azimuthal or radial velocity field produce harmonic distortions of the orders of m΄ = m ± 1 in the line-of-sight velocity field. Hence, a bisymmetric flow in real space produces an m΄ = 1 and an m΄ = 3 perturbations in projected space, both having similar amplitude. Although the former is difficult to detect, as its signal blends with that produced by the regular rotation of the disc, the latter is a unique signature of bisymmetric flows and can be readily studied via a harmonic decomposition of the velocity field. Our strategy is therefore to produce synthetic line-of-sight H i velocity fields for the simulated systems, with resolution similar to that of observed galaxies, and compare the amplitudes of the harmonic modes of simulated and observed galaxies. In order to produce synthetic H i data cubes for the 33 systems in our simulated sample, we follow a procedure similar to that described by O17 in their section 3.3. The procedure consists of the following steps. Assume that a system is made of N gas particles, each described by its coordinates (x, y, z), velocities (Vx, Vy, Vz), temperature T, and H i mass mHI: the system is projected at 60° inclination, using $$\vec{L}_*$$ as a reference direction, and a random orientation; a position-velocity 3D grid is created, with a spatial binning of 83 pc and a channel separation of 2 km s−1; the mHI of each particle is placed at the corresponding (x, y) location in the grid, and is distributed in velocity around its Vz by using a Gaussian kernel with a standard deviation of $$\sqrt{k_{\rm B}T/m_{\rm H}}$$, kB being the Boltzmann constant and mH the proton mass; this is to take the thermal broadening of the line profiles into account; and once all particles have been processed, the resulting data cube is smoothed spatially at the FHWM resolution of 250 pc (three times the grid binning). For simplicity, we make no correction for gas opacity, i.e. the gas is considered to be optically thin. Note that, as in O17, the final resolution of our synthetic observations is similar to that of THINGS and LITTLE THINGS data cubes. Velocity fields are derived from these data cubes as moment-1 maps, which are well suited to account for non-circular motions in the gas kinematics. Finally, we perform a harmonic analysis of the velocity fields for both samples. The procedure requires a careful choice of galaxy centre. For the simulated galaxies, we assume that this coincides with the location of the minimum gravitational potential, whereas for the real galaxies we take the kinematic centres estimated by Trachternach et al. (2008) for THINGS and by Oh et al. (2015) for LITTLE THINGS. We focus on the amplitude of the m = 1 and 3 harmonic modes at two fixed galactocentric distances: R = 1 and 2 kpc, which bracket the range of Rh in our simulated sample and are well-resolved radii in both observations and simulations. In practice, we select a ring on the galactic plane with mean radius equal to the chosen value (1 or 2 kpc) and width equal to the FWHM resolution (which varies in the sample of real galaxies, but is constant in the simulated sample). Each ring is defined by its inclination, i, and position angle, PA, in the sky. Given that the choice of these two parameters significantly affects the outcome of the harmonic analysis, we must adopt a criterion that sets them uniquely and that can be applied to both observed and synthetic velocity fields. For any given (i, PA), the line-of-sight velocity, VLOS, within the ring as a function of the azimuthal angle in the plane of the galaxy, θ, is fitted with a formula analogous to equation (1), from which we extract the amplitudes A1, A2, and A3. Our choice for (i, PA) is the one that minimizes the quantity $$\sqrt{A_2^2+A_3^2}/|A_1|$$, which quantifies the strength of large-scale perturbations with respect to regular rotation at a given radius. The minimization is achieved via the Nelder & Mead (1965) method. We adopt (i = 60°, PA = 90°) as the initial guess for the simulated galaxies, whereas for the observed galaxies we use the values of i and PA determined by de Blok et al. (2008, for THINGS) and by Oh et al. (2015, for LITTLE THINGS) from their tilted ring fitting method. Typically, the final (i, PA) determined for the observed galaxies remains within ∼5° from the initial estimates. The simulated sample, however, shows much larger deviations from the initial guess. In some cases, fitting VLOS via equation (1) was not possible due to the small number of points, or – in observed galaxies – to an excessively noisy velocity field. For these reasons, DDO 53, DDO 210, IC 10, IC 1613, NGC 1569, UGC 8508, and Haro 29 have been excluded from our analysis at R = 1 kpc, along with DDO 168, DDO 216, NGC 3738, and Haro 36 at R = 2 kpc. Fig. 8 shows the ratio between A3 and A1, which is a measure of the strength of the bisymmetric flow with respect to regular H i rotation, as a function of A1/sin (i), which represents the H i azimuthal speed Vϕ alone,3 at R = 1 kpc (left-hand panel) and R = 2 kpc (right-hand panel) for the real (squares) and simulated (circles) galaxies, respectively. Figure 8. View largeDownload slide Bisymmetric H I flows in simulated and observed galaxies at galactocentric radii of R = 1 kpc (left-hand panel) and R = 2 kpc (right-hand panel). The ratio between the amplitudes of the m = 3 and 1 harmonic modes is plotted as a function of the amplitude of the m = 1 mode (divided by sin (i)) in the H I velocity fields of apostle galaxies (blue circles), THINGS galaxies (brown squares), and LITTLE THINGS galaxies (orange squares). Error bars show the formal errors on the harmonic fit to the velocities. Arrows represent upper limits. Systems are numbered as in tables A1 and A2 of O17. On average, simulated galaxies show stronger bisymmetric motions than the observed galaxies. Figure 8. View largeDownload slide Bisymmetric H I flows in simulated and observed galaxies at galactocentric radii of R = 1 kpc (left-hand panel) and R = 2 kpc (right-hand panel). The ratio between the amplitudes of the m = 3 and 1 harmonic modes is plotted as a function of the amplitude of the m = 1 mode (divided by sin (i)) in the H I velocity fields of apostle galaxies (blue circles), THINGS galaxies (brown squares), and LITTLE THINGS galaxies (orange squares). Error bars show the formal errors on the harmonic fit to the velocities. Arrows represent upper limits. Systems are numbered as in tables A1 and A2 of O17. On average, simulated galaxies show stronger bisymmetric motions than the observed galaxies. Interestingly, there is a common trend followed by both real and simulated galaxies: The importance of non-circular motions compared to the regular rotation decreases as a function of rotation speed. The main difference between observed and simulated galaxies is in the amplitudes of the bisymmetric motions: The median A3/A1 at R = 1 kpc (R = 2 kpc) is 0.083 (0.057) in apostle, 0.017 (0.010) in THINGS, and 0.040 (0.033) in LITTLE THINGS. Limiting the comparison to the LITTLE THINGS sample alone, which spans a range of A1/sin(i) similar to our apostle sample, we conclude that bisymmetric flows in apostle dwarfs are a factor of ∼2 stronger than those in the observed galaxies. We have verified that these results hold when the harmonic analysis is performed at the effective radius Reff of each system, or at 2Reff, rather than at a fixed galactocentric distance, using effective radii from the SPARC catalogue of Lelli, McGaugh & Schombert (2016) and the catalogue of Hunter & Elmegreen (2006). These results suggest that bisymmetric flows caused by bar-like features, or, more generally, by asphericities in the gravitational potential, are somewhat less prominent in observed galaxies than in the apostle simulations, at least in the dwarf galaxy regime, in line with the earlier findings of Trachternach et al. (2008). There are, however, important caveats in the comparison. One is that, although our analysis considers all apostle galaxies in the range 60 < Vmax/ km s−1 < 120, the observed sample has no well-defined completeness criteria. A second difference, already mentioned above, is in the velocity range covered: Only eight galaxies in the observed sample have 60 < Vmax/ km s−1 < 120. A further difference is environmental: The apostle galaxies are located in the proximity (i.e. within ∼3 Mpc) of a Local Group analogue, whereas the THINGS and LITTLE THINGS galaxies are in less dense environments. In light of these considerations, we argue that the differences in the A3/A1 ratio shown in Fig. 8, although suggestive, should be treated with caution. 4 CONCLUSIONS CDM haloes are triaxial in nature (e.g. Frenk et al. 1988). Their asphericity increases towards their centre (Hayashi et al. 2007), implying that the process of galaxy formation in a ΛCDM framework occurs within gravitational potentials that are non-axisymmetric, or, broadly speaking, ‘barred’. The processes of stellar mass assembly and secular evolution can reduce the halo triaxiality significantly in massive disc galaxies (Abadi et al. 2010; Kazantzidis et al. 2010; Machado & Athanassoula 2010), but are much less efficient in dwarf galaxies, which therefore may be forced to respond to non-axisymmetric forces due to the dark matter. In this work, we have carried out a study of the mass distribution and H i kinematics within the central few kiloparsecs in a sample of 33 H i-rich dwarf (60 < Vmax < 120 km s−1) galaxies from the apostle suite of ΛCDM cosmological hydrodynamical simulations. Our results can be summarized as follows: Most simulated dwarfs have a bar in their stellar component that matches the non-axisymmetric distribution of the inner dark matter halo (‘dark’ bar). Specifically, 18 out of 33 apostle dwarfs (55 per cent) have a stellar and a dark bar with axis ratios smaller than 0.85. When present, the stellar and the dark bar corotate and are locked in phase. Since the gravitational potential is dominated by the dark matter, the stellar bar follows the dark bar, not viceversa. A corollary is that the presence of a stellar bar does not imply that baryons dominate gravitationally that region. All bars in the sample analysed are weak, and have co-rotation radii that largely exceed the galaxy size. The stellar/dark bar induces significant bisymmetric flows in the gas component. We have compared the amplitude of the m = 3 harmonic perturbations in the H i velocity fields of the apostle systems with those of THINGS and LITTLE THINGS galaxies, finding that the magnitude of bisymmetric flows in the former exceeds that in the latter by a factor of ∼2. Our findings clarify the nature of the non-circular motions reported by O17 in the same simulated galaxy sample as due to the effects of a dominant triaxial halo. Our analysis also shows that, although haloes are sphericalized by the assembly of the galaxy, the sphericalization is incomplete in dwarfs like the ones in our apostle sample. The remaining triaxiality induces the formation of a bar-like feature in the stars and non-circular motions in the gas. Although the magnitude of such motions seems to exceed, on average, those in galaxies of the THINGS and LITTLE THINGS surveys, we caution that these surveys are not exactly comparable, so a definitive conclusion about whether our findings are in agreement or disagreement with real galaxies in the local Universe remains pending and will be the focus of future work. Acknowledgements The authors thank the THINGS, LITTLE THINGS, and SPARC survey teams for making their data publicly available. AM thanks Mattia Sormani for helpful discussions. CSF acknowledges support from ERC Advanced Grant 267291 Cosmiway. This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure. Footnotes 1 A Project Of Simulating The Local Environment 2 A ‘central’ subhalo is the most massive subhalo of each FoF group, and is therefore not a satellite of a more massive system. 3 In reality, A1 is a combination of rotation and a global expansion/contraction in the radial direction, but the latter is typically negligible. REFERENCES Abadi M. G., Navarro J. 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A., 2007, ApJ , 664, 204 https://doi.org/10.1086/518471 CrossRef Search ADS Trachternach C., de Blok W. J. G., Walter F., Brinks E., Kennicutt R. C.Jr, 2008, AJ , 136, 2720 https://doi.org/10.1088/0004-6256/136/6/2720 CrossRef Search ADS Walter F., Brinks E., de Blok W. J. G., Bigiel F., Kennicutt R. C.Jr, Thornley M. D., Leroy A., 2008, AJ , 136, 2563 https://doi.org/10.1088/0004-6256/136/6/2563 CrossRef Search ADS Warren M. S., Quinn P. J., Salmon J. K., Zurek W. H., 1992, ApJ , 399, 405 https://doi.org/10.1086/171937 CrossRef Search ADS Wiersma R. P. C., Schaye J., Smith B. D., 2009a, MNRAS , 393, 99 https://doi.org/10.1111/j.1365-2966.2008.14191.x CrossRef Search ADS Wiersma R. P. C., Schaye J., Theuns T., Dalla Vecchia C., Tornatore L., 2009b, MNRAS , 399, 574 https://doi.org/10.1111/j.1365-2966.2009.15331.x CrossRef Search ADS © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society
### Journal
Monthly Notices of the Royal Astronomical SocietyOxford University Press
Published: May 1, 2018
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2018-07-22 20:40:53
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https://martinuzzifrancesco.github.io/posts/04_gsoc_week/
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The standard construction of the reservoir matrix $$\textbf{W}$$ for Echo State Networks (ESN) is based on initializing $$\textbf{W}$$ using specific schemes, usually generating random numbers and then rescaling it to make sure that the spectral radius is less or equal to a chosen number. This procedure is effective, but in literature other ways are explored. In this week we implemented a Singular Value Decomposition (SVD)-based algorithm, described in [1], that is capable of obtaining a sparse matrix suitable for the ESNs. In this post we are going to describe the theory behind the implementation and then a couple of examples will be given.
# Singular Value Decomposition reservoir construction#
One of the key aspects the an ESN is for its reservoir to posses the Echo State Property (ESP) [2]. A sufficient condition to obtain it is to construct the reservoir with a spectral radius less than 1. While using the architecture explained in the opening ensures this condition, it doesn’t take into account the singular values information of $$\textbf{W}$$, and it doesn’t allow much control over the construction of said matrix. An alternative could be to leverage the SVD to build a reservoir matrix given the largest singular value. To fully comprehend this procedure firstly we have to illustrate what SVD consists of.
Let us consider the reservoir matrix $$\textbf{W} \in \mathbb{R}^{N \times N}$$; this matrix can be expressed as $$\textbf{W} = \textbf{U}\textbf{S}\textbf{V}$$ where $$\textbf{U}, \textbf{V} \in \mathbb{R}^{N \times N}$$ are orthogonal matrices and $$\textbf{S}=\text{diag}(\sigma _1, …, \sigma _N)$$ is a diagonal matrix whose entries are ordered in increasing order. The values $$\sigma _i$$ are called the singular values of $$\textbf{W}$$. Given any diagonal matrix $$\textbf{S}$$, and orthogonal matrices $$\textbf{U}, \textbf{V}$$ the matrix $$\textbf{W}$$ obtained as $$\textbf{W} = \textbf{U}\textbf{S}\textbf{V}$$ has the same singular values as $$\textbf{S}$$.
This method provides an effective way of ensuring the ESP without the scaling of the reservoir weights. Instead of using orthogonal matrices $$\textbf{U}, \textbf{V}$$, that could produce a dense matrix $$\textbf{W}$$, the authors opted for a two dimensional rotation matrix $$\textbf{Q}(i, j, \theta) \in \mathbb{R}^{N \times N}$$ with $$\textbf{Q}_{i,i} = \textbf{Q}_{j,j} = \text{cos}(\theta)$$, $$\textbf{Q}_{i,j} = -\text{sin}(\theta))$$, $$\textbf{Q}_{j,i} = \text{sin}(\theta))$$ with $$i, j$$ random values in [1, N] and $$\theta$$ random value in [-1, 1]. The algorithm proposed is as follows:
• Choose a predefined $$\sigma _N$$ in the range [0, 1] and generate $$\sigma _i, i=1,…, N-1$$ in the range (0, $$\sigma _N$$]. This values are used to create a diagonal matrix $$\textbf{S}=\text{diag}(\sigma _1, …, \sigma _N)$$. With $$h=1$$ let $$\textbf{W}_1 = \textbf{S}$$.
• For $$h = h + 1$$ randomly choose the two dimensional matrix $$\textbf{Q}(i, j, \theta)$$ as defined above. $$\textbf{W} _h = \textbf{W} _{h-1} \textbf{Q}(i, j, \theta)$$ gives the matrix $$\textbf{W}$$ for the step $$h$$. This procedure is repeated until the chosen density is reached.
# Implementation in ReservoirComputing.jl#
The implementation into code is extremely straightforwad: following the instructions in the paper a function pseudoSVD is created which takes as input the following
• dim: the desired dimension of the reservoir
• max_value: the value of the largest of the singular values
• sparsity: the sparsity for the reservoir
• sorted: optional value. If = true (default) the singular values in the diagonal matrix will be sorted.
• reverse_sort: optional value if sort = true. If = true (default = false) the singular values in the diagonal matrix will be sorted in a decreasing order.
# Examples#
## Original ESN#
Testing the SVD construction on the original ESN we can try to reproduce the Lorenz attractor, with similar parameters as given in the Introduction to Reservoir Computing
approx_res_size = 300
sparsity = 0.1
max_value = 1.2
activation = tanh
sigma = 0.1
beta = 0.0
alpha = 1.0
extended_states = false
The values of the largest singular value for the construction of the SVD based reservoir is equal to the spectral radius of the standard reservoir, that in this case is greater than one. A plot of the results shows:
This construction is capable of reproducing the Lorenz system in the short term, and behaves better in the long term than the standard implementation, or at least in this example it does. A more in depth analysis is needed for the consistency of the results and the behavior of the SVD reservoir when the largest singular value is set greater than one and when one of the non linear algorithms is applied.
## Ridge ESN, SVESM and ESGP#
In order to test this implementation for others ESN architectures currently implemented in ReservoirComputing.jl we choose to use the same examples as last week, based on the Mackey-Glass system:
$$\frac{dx}{dt} = \beta x(t)+\frac{\alpha x(t-\delta)}{1+x(t-\delta)^2}$$
with the same values:
• $$\beta = -0.1$$
• $$\alpha = 0.2$$
• $$\delta = 17$$
• $$dt = 0.1$$
Furthermore the time series is rescaled in the range $$[-1, 1]$$ by application of a tangent hyperbolic transform $$y_{ESN}(\text{t}) = \text{tanh}(\text{y}(t)-1)$$. To evaluate the precision of our results we are going to use root mean square deviation (rmse), defined as:
$$\textbf{rmse} = \sqrt{\frac{\sum_{i=1}^{T_n}(y_d(i)-y(i))^2}{T_n}}$$
where
• $$y_d(i)$$ is the target value
• $$y(i)$$ is the predicted value
• $$T_d$$ is the number of test examples
The ESN parameters are as follows
const shift = 100
const train_len = 6000
const test_len =1500
const approx_res_size = 400
const sparsity = 0.1
const activation = tanh
const max_value = 0.99
const sigma = 0.1
const alpha = 0.2
const extended_states = true
The largest singular value was set equal to the spectral radius for the standard construction. Averaging on ten runs the results are as follows:
rmse ESGP:
Classic reservoir: 0.077
SVD reservoir: 0.205
rmse ridge ESN:
Classic reservoir: 0.143
SVD reservoir: 0.146
rmse SVESM:
Classic reservoir: 0.232
SVD reservoir: 0.245
For the ESGP this procedure yields far worst performances than the standard counterpart. For the ridge ESN and SVESM the results are almost identical.
The results obtained are interesting and for sure more testing is needed. Some sperimentation on the h steps ahead prediction could be done, as well as giving different values for the spectral radius and largest singular value, since in all the examples examined the spectral radius was chosen following the literature, and hence could be more optimized that the largest values that we used.
## Documentation#
[1] Yang, Cuili, et al. “Design of polynomial echo state networks for time series prediction.” Neurocomputing 290 (2018): 148-160.
[2] Jaeger, Herbert. “The “echo state” approach to analysing and training recurrent neural networks-with an erratum note.” Bonn, Germany: German National Research Center for Information Technology GMD Technical Report 148.34 (2001): 13.
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2023-03-27 03:40:06
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https://aviation.stackexchange.com/questions/1314/ive-been-denied-vfr-clearance-through-c-airspace-what-should-i-do
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# I've been denied VFR clearance through C airspace, what should I do?
If I'm flying along in my C-152 and I am trying to go in a straight line through the "center" of C airspace (to land at a regional airport under the airspace), but the controller tells me to remain clear, what should I do?
Would it be safe to fly under the C, or above it, or would it be best to completely circle around even if it takes extra time and fuel?
• Technically speaking a clearance is not required for class C airspace. All that's needed is to establish and maintain two-way communications. Most class C ceilings are only 4000 feet so flying over is pretty easy. – Steve Kuo Jul 20 '14 at 0:42
If I'm flying along in my C-152 and I am trying to go in a straight line through the "center" of C airspace, but the controller tells me to remain clear, what should I do?
Well, the obvious answer is remain clear of the Class C airspace :-)
HOW you remain clear is entirely up to you - you can go over, under, or around - you just can't go through, and I think that's the more interesting part of your question.
Flying around the class C airspace is usually a safe choice (don't skim along the margins though - give it some reasonable breathing room), but as you've noted it could add a lot of time/fuel. You need to balance that with the time/fuel required to climb above the airspace, or the risks of flying under the airspace (mainly obstacles) to make your decision.
I'm going to use my local class C airspace as an example for an exercise in aeronautical decision making because conveniently there's a VOR you could hypothetically be circling while talking to approach, and an airport on the other side you might want to get to.
In our hypothetical example let's say you're circling Deer Park VOR (A) at 2500 feet, and you want to cut through the Class C airspace to get to Brookhaven (B), but approach isn't cooperating.
Click to embiggen.
I've got three options sketched out here - think about them, then hover over the spoiler boxes for my thinking on each of the three routes:
1. The dashed line through the center (the route you were hoping Approach would give you).
A straight line is the shortest distance between two points, but this straight line stinks: Since Approach wouldn't let you go through the class C airspace you're going to have to spiral-climb to 4200 feet or higher (5500 feet if you're playing by the hemispheric rule), and then when you get to the cut-out in the class C on the other side you're going to have to dive down to get to pattern altitude.
That doesn't seem safe, nor efficient to me, so let's toss that idea out the window.
2. The northern route under the class C airspace.
Simple enough, we'll split the difference between the ground (roughly sea level) and the floor of the airspace (1500 feet) and fly under the shelf at 1250 feet. Plenty of room above and below (if your altimeter is set right and you're any kind of decent pilot).
So this is the part where I confess that I'm a big ol' wuss and don't like to be close to the ground. It's like a porcupine, but with radio towers for quills (like the one I marked with a big OUCH - at 1250 feet there'd be less than 500 feet between my landing gear and the top of that tower).
I'm not happy with the obstacle clearance on this route (and while I could certainly rearrange the line a bit to avoid the obstacles I'm not going to because they serve my purpose) -- the northern route is out.
3. The southern route under the class C airspace.
Same idea as the northern route - descend to 1250 feet and fly under the shelf, but I like this route a whole lot better.
There are really great landmarks here ("Fly southeast toward the looped road, then go to the middle of the bay and stay between the two shore lines until you pass the bridge at Smith Point. At that point you'll see the airport off your left wing and can maneuver to enter the pattern.")
You're also over water, and we don't tend to have any radio towers sticking up out of the bay.
You'll need to watch out for traffic from Bayport, students practicing ground-reference maneuvers, and banner-tow planes in the summer, but that's just your basic everyday VFR "See and Avoid" situation.
This is probably the route I'd pick.
• Incidentally I think this might be the first time I've legitimately used the >! markdown spoiler tag. – voretaq7 Jan 25 '14 at 6:44
• The only thing that I would do differently would be to fly at 500' below the shelf instead of "splitting the difference". – Lnafziger Jan 25 '14 at 12:41
• @Lnafziger You can definitely get by at 1000' on the southern route over the water but over land you'd technically be in violation of 91.119(b) a lot of the time since all the suburban sprawl & houses are above 0' MSL & a lot of the area is considered "congested". – voretaq7 Jan 25 '14 at 18:59
• @CJBS Emergency landing options are a great point! At the risk of too much of a spoiler, your landing options in both routes are kinda lousy (check out a Google satellite view). My personal preference is to add a few minutes and get out from under the class C entirely (and in winter, a further preference for the south shore as the barrier island has nice, straight, runway-like roads which tend to be empty in the off season). This example is obviously highly contrived, and ignores such real-world considerations as good emergency landing options :-) – voretaq7 Mar 25 '14 at 1:03
• My choice would be option 4: It adds just a small amount of distance to option 3. Continue southerly to the ocean, fly eastbound along the beach outside the Class C airspace. The shoreline provides a unmistakeable reference to where the C ends. You will have a great view. The beach is a long emergency landing field (less crowded in the winter than in the summer), and you are not restricted as to altitude. – Skip Miller Apr 22 '14 at 13:44
When the controller tells you to "remain clear" it simply means that he is too busy to help you out at the moment. Traffic situations change quickly though, so I would recommend taking the most direct route that you can while remaining outside of his airspace and when things sound like they have quieted down a little, give him another try. If it isn't feasible (you are landing at the primary airport, or you need to enter it to get to the other airport) then you can circle until things calm down for the controller.
Since the airport that you are wanting to land at is under the Class C airspace anyway, probably the best way would be to go ahead and descend a little earlier than you had planned and fly under the shelf. Assuming that you have sufficient terrain clearance it would probably be better than flying over the top since you have to go down there anyway. That being said, there's no reason not to fly over the top if it's more convenient!
In either case, the main thing to watch for is arrival and departure traffic for the primary airport. The controller basically told you that there is a lot of it. If you are instrument rated, take a look at the arrival and departure procedures so that you can try to avoid them.
Just be sure that you don't accidentally fly into his airspace without a clearance and you should be fine!
As indicated in the other answers, "remain clear" means just that, and can happen when congested (as already indicated by @Lnafziger).
One approach that I take in the Bay Area to have a greater chance of getting into Oakland's Class C or SFO's Class B is to get a squawk code (with a flight following request) from another facility first, then get handed over. That way, it's just a matter of a frequency change and a hand-over. E.g. "N12345Z on frequency at 2000".
State to the first facility (squawk code assigner) what your intentions are so that they can give you the correct squawk code (they are different sometimes depending on whether you need to be handed off to another facility)
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2021-03-03 01:34:03
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https://wiki.math.uwaterloo.ca/statwiki/index.php?title=Deep_Exploration_via_Bootstrapped_DQN&diff=prev&oldid=30702
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# Difference between revisions of "Deep Exploration via Bootstrapped DQN"
## Intro to Reinforcement Learning
In reinforcement learning, an agent interacts with an environment with the goal to maximize its long term reward. A common application of reinforcement learning is to the multi armed bandit problem. In a multi armed bandit problem, there is a gambler and there are $n$ slot machines, and the gambler can choose to play any specific slot machine at any time. All the slot machines have their own probability distributions by which they churn out rewards, but this is unknown to the gambler. So the question is, how can the gambler learn how to get the maximum long term reward?
There are two things the gambler can do at any instance: either he can try a new slot machine, or he can play the slot machine he has tried before (and he knows he will get some reward). However, even though trying a new slot machine feels like it would bring less reward to the gambler, it is possible that the gambler finds out a new slot machine that gives a better reward than the current best slot machine. This is the dilemma of exploration vs exploitation. Trying out a new slot machine is exploration, while redoing the best move so far is exploiting the currently understood perception of the reward.
There are many strategies to approach this exploration-exploitation dilemma. Some common strategies for optimizing in an exploration-exploitation setting are Random Walk, Curiosity-Driven Exploration, and Thompson Sampling. A lot of these approaches are provably efficient, but assume that the state space is not very large. For instance, the approach called Curiosity-Driven Exploration aims to take actions that lead to immediate additional information. This requires the model to search “every possible cell in the grid” which is not desirable if state space is very large. Strategies for large state spaces often just either ignore exploration, or do something naive like $\epsilon$-greedy, where you exploit with $1-\epsilon$ probability and explore "randomly" in rest of the cases.
This paper tries to use a Thompson sampling like approach to make decisions.
## Thompson Sampling[1]
In Thompson sampling, our goal is to reach a belief that resembles the truth. Let's consider a case of coin tosses (2-armed bandit). Suppose we want to be able to reach a satisfactory pdf for $\mathbb{P}_h$ (heads). Assuming that this is a Bernoulli bandit problem, i.e. the rewards are $0$ or $1$, we can start off with $\mathbb{P}_h^{(0)}=\beta(1,1)$. The $\beta(x,y)$ distribution is a very good choice for a possible pdf because it works well for Bernoulli rewards. Further $\beta(1,1)$ is the uniform distribution $\mathbb{N}(0,1)$.
Now, at every iteration $t$, we observe the reward $R^{(t)}$ and try to make our belief close to the truth by doing a Bayesian computation. Assuming $p$ is the probability of getting a heads,
\begin{align*} \mathbb{P}(R|D) &\propto \mathbb{P}(D|R) \cdot \mathbb{P}(R) \\ \mathbb{P}_h^{(t+1)}&\propto \mbox{likelihood}\cdot\mbox{prior} \\ &\propto p^{R^{(t)}}(1-p)^{R^{(t)}} \cdot \mathbb{P}_h^{(t)} \\ &\propto p^{R^{(t)}}(1-p)^{R^{(t)}} \cdot \beta(x_t, y_t) \\ &\propto p^{R^{(t)}}(1-p)^{R^{(t)}} \cdot p^{x_t-1}(1-p)^{y_t-1} \\ &\propto p^{x_t+R^{(t)}-1}(1-p)^{y_t+R^{(t)}-1} \\ &\propto \beta(x_t+R^{(t)}, y_t+R^{(t)}) \end{align*}
Source: Quora
This means that with successive sampling, our belief can become better at approximating the truth. There are similar update rules if we use a non Bernoulli setting, say, Gaussian. In the Gaussian case, we start with $\mathbb{P}_h^{(0)}=\mathbb{N}(0,1)$ and given that $\mathbb{P}_h^{(t)}\propto\mathbb{N}(\mu, \sigma)$ it is possible to show that the update rule looks like
$$\mathbb{P}_h^{(t+1)} \propto \mathbb{N}\bigg(\frac{t\mu+R^{(t)}}{t+1},\frac{\sigma}{\sigma+1}\bigg)$$
### How can we use this in reinforcement learning?
We can use this idea to decide when to explore and when to exploit. We start with an initial belief, choose an action, observe the reward and based on the kind of reward, we update our belief about what action to choose next.
## Bootstrapping [2,3]
This idea may be unfamiliar to some people, so I thought it would be a good idea to include this. In statistics, bootstrapping is a method to generate new samples from a given sample. Suppose that we have a given population, and we want to study a measure $\theta$. So, we just find $n$ sample points (sample $\{D_i\}_{i=1}^n$), calculate this measure $\hat{\theta}$ for these $n$ points, and make our inference.
If we later wish to find a better bound on $\hat{\theta}$, i.e. suppose we want to say that $\delta_1 \leq \hat{\theta} \leq \delta_2$ with a confidence of $c$, then we can use bootstrapping for this.
Using bootstrapping, we can create a new sample $\{D'_i\}_{i=1}^{n'}$ by randomly sampling $n'$ times from $D$, with replacement. So, if $D=\{1,2,3,4\}$, a $D'$ of size $n'=10$ could be $\{1,4,4,3,2,2,2,1,3,4\}$. We do this a sufficient $k$ number of times, calculate $\hat{\theta}$ each time, and thus get a distribution $\{\hat{\theta}_i\}_{i=1}^k$. Now, we can choose the $100\cdot c$th and $100\cdot(1-c)$th percentile of this distribution, (let them be $\hat{\theta}_\alpha$ and $\hat{\theta}_\beta$ respectively) and say
$$\hat{\theta}_\alpha \leq \hat{\theta} \leq \hat{\theta}_\beta, \mbox{with confidence }c$$
## Why choose bootstrap and not dropout?
There is previous work[4] that establishes dropout as a good way to train NNs on a posterior such that the trained NN works like a function approximator that is close to the actual posterior. But, there are several problems with the predictions of this trained NN. The figures below are from the appendix of this paper. The left image is the NN trained by the authors of this paper on a sample noisy distribution and the right image is from the accompanying web demo from [4], where the authors of [4] show that their NN converges around the mean with a good confidence.
Source: this paper's appendix
According to the authors of this paper,
1. Even though [4] says that dropout converges arond the mean, their experiment actually behaves weirdly around a reasonable point like $x=0.75$. They think that this happens because dropout only affects the region local to the original data.
2. Samples from the NN trained on the original data do not look like a reasonable posterior (very spiky).
3. The trained NN collapses to zero uncertainty at the data points from the original data.
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2022-09-26 10:35:25
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https://www.cnblogs.com/lz87/p/16744118.html
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# [CodeForce] Maximum Subsequence
Problem Statement
1. N is up to 35, so trying all possible subsequences is too slow (2^35). We can apply the meet in the middle technique and divide A into two equal halves and compute all possible subsequences' sum modulo by M. This takes O(2^17) for each half of A, call the results as S1 and S2.
2. Then for each value V in S1, we have 2 options: 1. take V and does not take anything from S2; 2. take V and find the max W in S2 such that V + W <= M - 1. The answer is the max of both options for all V in S1.
3. To speed up the search in option 2, we can either sort S2 then perform binary search or store values of S2 in a sorted set.
static void solve(int testCnt)
{
for (int testNumber = 0; testNumber < testCnt; testNumber++) {
int n = in.nextInt(), m = in.nextInt();
int[] a = in.nextIntArrayPrimitive(n);
if(n == 1) out.println(a[0] % m);
else {
int[] x1 = Arrays.copyOfRange(a, 0, n / 2);
int[] x2 = Arrays.copyOfRange(a, n / 2, n);
TreeSet<Integer> ts1 = compute(x1, m);
TreeSet<Integer> ts2 = compute(x2, m);
int ans = 0;
for(int v : ts1) {
ans = Math.max(ans, v);
ans = Math.max(ans, v + ts2.floor(m - 1 - v));
}
out.println(ans);
}
}
out.close();
}
static TreeSet<Integer> compute(int[] x, int m) {
TreeSet<Integer> ts = new TreeSet<>();
for(int i = 0; i < (1 << x.length); i++) {
long sum = 0;
for(int j = 0; j < x.length; j++) {
if((i & (1 << j)) != 0) {
sum += x[j];
}
}
}
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2023-02-04 06:06:53
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|
http://openstudy.com/updates/55f17af6e4b0bf851f6fa397
|
## A community for students. Sign up today
Here's the question you clicked on:
## anonymous one year ago 1.What is 48,100,000,000,000 in scientific notation? × 10
• This Question is Closed
1. anonymous
$4.8\times10^{13}$ Girls can also join http://www.homeworkslavery.com/ to get their homeworks done.
2. anonymous
3. johnweldon1993
^Close, but that 1 doesnt just drop off So basically you place the decimal after the first number that isn't 0...which is 4 here...bring along the other non-zero numbers with it...then count how many places are after the decimal $\large 4.81 \times 10^{13}$
4. anonymous
AAAAh 2o clo2e XD
5. anonymous
Thanks
6. anonymous
48.1x10^12
#### Ask your own question
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2017-01-23 10:50:57
|
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|
https://datascience.stackexchange.com/questions/105070/modeling-events-with-an-intermediate-stage
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# Modeling events with an intermediate stage
For a lot of prediction problems, there's an intermediate stage which must occur for the target event to occur. For example, to graduate from college, one must first be accepted. For an internet ad to sell a product, someone must first click the ad. For a juvenile to reproduce it must mature to adulthood. Etc.
More generally, we want to predict an event at t2 from data at t0, where the intermediate event happens at t1. Whether the interim event occurs is not known at t0, but our data contains records of the t1 events. Given that we have data on t1 and t2, it may be helpful to model the occurrence of the intermediate stage (t1) and incorporate it into the model for the target event (t2).
One way to think about problems like these is
p(t2 = true) = p(t1=true) * p(t2=true | t1=true)
thought that's not the only way a model might handle such events.
Anyway, I want to build a neural network to handle a problem that has such a structure from data that contains the t1 information. I curious to know whether there is research on NN models that uses an implicit or explicit model of "intermediate" events in their architecture. Alternatively, it might be helpful for me to know of some data sets that have such a structure so I can look for attempts to handle them. One approach that occurs to me is that you could try to train a model on two target variables (the t1 event and t2 event) backproping both losses (suitably weighted) and then just toss out the t1 even business at inference time. But I don't know what to look for regarding such models. (Note that for my case, the NN is pretty much a deployment requirement, so well developed research on non-NN stuff might be helpful but it should have some fairly clear mapping into a NN model.)
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2022-10-02 06:43:37
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|
https://stats.stackexchange.com/questions/402470/how-can-i-use-scaling-and-log-transforming-together/506322
|
How can I use scaling and log transforming together?
I'm creating a regular linear regression model to establish a baseline before moving on to more advanced techniques. I scaled my data as below:
from sklearn.preprocessing import StandardScaler
sc = StandardScaler()
X_train_std=pd.DataFrame(sc.fit_transform(X_train), columns=data.columns)
X_test_std=pd.DataFrame(sc.transform(X_test), columns=data.columns)
However, the variables mostly have an extreme skew (right tail), but I can't figure out how to apply a log transform on them.
Would I apply the log transform to variables in both the X_train and X_test datasets? Do I need to do this before applying the scaling? I just can't think through the right way to go about this in terms of applying predictions to the X_test set. Any ideas?
• Scaling and then applying the log would result in errors since any values below the sample mean result in negative values post transform. Log, then scale. – Demetri Pananos Feb 11 '20 at 18:12
To apply the log transform you would use numpy. Numpy as a dependency of scikit-learn and pandas so it will already be installed.
import numpy as np
X_train = np.log(X_train)
X_test = np.log(X_test)
You may also be interested in applying that transformation earlier in your pipeline before splitting data into training and test sets.
# Assumes X and y have already been defined
import numpy as np
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split
X = np.log(X)
X_train, X_test, y_train, y_test = train_test_split(X, y)
sc = StandardScaler()
X_train = sc.fit_transform(X_train)
X_test = sc.transform(X_test)
$$$$
You can form a pipeline and apply standard scaling and log transformation subsequently. In this way, you can just train your pipelined regressor on the train data and then use it on the test data. For every input, the pipelined regressor will standardize and log transform the input before making the prediction.
import numpy as np
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import FunctionTransformer
from imblearn.pipeline import Pipeline
def log_transform(x):
print(x)
return np.log(x + 1)
scaler = StandardScaler()
transformer = FunctionTransformer(log_transform)
pipe = Pipeline(steps=[('scaler', scaler), ('transformer', transformer), ('regressor', your_regressor)], memory='sklearn_tmp_memory')
pipe.fit(X_train, y_train)
pipe.score(X_test, y_test)
`
• You can't do log on negative data.. – Ferus Feb 6 at 11:22
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2021-08-05 18:39:07
|
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http://math.stackexchange.com/questions/16646/why-is-first-cohomology-group-of-divisor-sheaf-on-riemann-surface-zero
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# Why is first cohomology group of divisor sheaf on riemann surface zero?
Let $X$ be riemann surface (not supposed compact) and $\mathcal D$ be sheaf of divisors on $X$.Remind that this means for $U\subset X$ open then $\mathcal D(U)$ is group of divisors on $U$. How to prove that $H^1(X,\mathcal D)=0$ . This is exercise in §16 of Forster book Riemann Surfaces (but is not homework for me) and he says hint is to use discontinuous partitions of unit but I don't understand. Any other method for proving is for me also satisfying . I suppose $H^2(X,\mathcal D)$ is also zero, no?
Addedd: Problem is in analytic category, not algebraic ( where is trivial : $\mathcal D$ is flabby). So I don't understand Matt E's proof (but thank you very much for answer Matt) because I don't know if cohomology commutes with co-limits in non noetherian case.
-
The hint suggests modifying the proof that $H^1$ for $C^\infty$-sheaves vanishes. This also makes me guess that the problem is about Cech cohomology. The $C^\infty$ proof appears in many places, one reference is Proposition 4.1 in chapter IX of Miranda's book: Algebraic Curves and Riemann Surfaces.
There's probably a way of doing this more cleanly and in more generally but as a start: on $X$ fix a locally finite covering $\{U_i\}_{i \in I}$ where the index set is linearly ordered: $I \subset \mathbb{Z}$.
In this case, choose for each natural number $n$ a set of integers $a_1,..., a_n$ such that $\sum_{1}^n a_i = 1$; e.g. $a_1 = 1$ and all others $0$.
Then define functions $\phi_i \colon U_i \to \mathbb{Z}$ as follows:
1) For $p \in U_i$ let $U_{j_1}, ..., U_{j_n}$ be sets containing $p$ with $j_1 < ... < j_n$.
2) let $k$ be the index such that $j_k = i$
3) let $a_1,..., a_n$ be the previously determined integers summing to $1$
Define $\phi_i(p) = a_k$. These are discontinuous functions and by construction $\sum_i \phi_i \equiv 1$.
To show $H^1(X, \mathcal{D}) = H^1(\{U_i\}, \mathcal{D}) = 0$ we have to show that every $1$-cocycle $(f_{ij})$ is a co-boundary.
The proof now proceeds as in the $C^\infty$ case: on $U_i$ define $g_i = -\sum_j \phi_j f_{ij}$. Then
$g_i - g_j = -\sum_k \phi_kf_{ik} + \sum_k \phi_kf_{jk} = \sum_k \phi_k(f_{jk} - f_{ik})$
Now using that $f_{jk} - f_{ik} = f_{ji}$ we get
$g_i - g_j$ = $f_{ji}\sum_k \phi_k = f_{ji}$.
-
The sheaf $\mathcal D$ is equal to $\bigoplus_{x \in X} i_{x*} \mathbb Z,$ where $\mathbb Z$ denotes the constant sheaf on the point $x$, and $i_x:\{x \} \to X$ is the embedding of the one point space $\{x\}$ into the Riemann surface $X$. (So $i_{x*}\mathbb Z$ is the skyscraper sheaf supported at $x$, whose stalk is $\mathbb Z$). The vanishing of $H^1$ now follows from the vanishing of higher cohomology for skyscraper sheaves.
-
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2016-06-28 15:10:05
|
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https://www.gamedev.net/blogs/entry/2259787-new-studio-week-2-review/
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• entries
69
294
• views
118021
# New Studio: Week 2 review
1594 views
These are my reflections on the second week of my new indie studio. I wrote them at the end of each day of the week while things were fresh on my mind. It's a bit unedited and long, so bear with me.
Links to previous weeks: [Week 0] [Week 1]
Monday:
I spent the early half of the day trying to figure out how to implement Perlin noise. The plan was to implement it first in C#/XNA to get the code right and tweak the values to get it how I wanted. Then, I'd take the perlin noise algorithm and my tweaked settings and use it to procedurally generate terrain in Unreal Engine 4. Unfortunately, the terrain system in UE4 doesn't seem to support loading a procedurally generated heightmap during game load... or I'm just really ignorant on how to do it (very likely, considering my lack of experience).
Since I can't get that to work, I'm now thinking that I may have to come up with some alternative solutions. Perhaps having a procedurally generated terrain map isn't such an important feature to the game play. Maybe I can just create a sufficiently large terrain and let things like city locations and factions be randomized. Maybe that would give enough randomness to provide sufficient replayability? Or perhaps, I can pre-generate 20 height maps and randomly select one during the game start? Combine that with randomized locations and factions, and it might be "good enough", and allow us to hand build each terrain map. Maybe even 10 maps would be sufficient? It would certainly cut down on our future testing. Or maybe, I forget about the whole effort to generate random terrain altogether and create a fixed land (similar to how "Mount and Blade" does it). The focus of the game play isn't so much on the terrain features and rolling for a good starting position, is it? I don't know yet. Whatever the case, the playable prototype doesn't require it.
Tuesday:
Designing a game is really, really hard! I think I have slightly underestimated the effort and work which needs to go into it. I had written a 15 page design document which was a bit specific in some important areas and vague in other areas. When writing it, I had sort of this lazy attitude of "Eh, I'll figure it out later when I get to it. This is good enough for now." But it's not good enough yet. My artist has read it carefully and is confused on what I'm envisioning. He then went in a wrong direction, and when he told me about it, I initially thought "Oh wow, that sounds really good! I like where this is going.". Except, it was wrong and didn't fit the vision and introduced some new game design aspects which I hadn't considered, and then we were both a bit confused about how it would all work together. This wrong direction suddenly starting turning into a really complicated beast and would take a lot of work, and wouldn't add anything of pertinent value to the player.
I spent the better half of the day drawing storyboards and user interface wireframes in adobe photoshop. After lunch, I needed to write up a detailed description of all of the races in the game, how their societies behaved, what their motivations were, what their strengths and weaknesses are, and a bunch of background lore. All of this should help my artist get a better visualization of the "theme" to use for creating the characters and architecture. I think, if I was going to compare designing to anything, it would be like trying to paint a dream as you're having it. You have a pretty good idea what the general picture looks like and how everything works together, but when you start scrutinizing a particular detail, it gets fuzzy really fast. The challenge is to coherently fill in those gaps so that the whole image still works.
To my frustration, I had spent an hour and a half writing up all of this lore and detail on each of the races in the game. I kept on saving my word document, but it wasn't actually being saved. I don't know where I was actually saving it to, or if it was even being saved at all, but as soon as I closed the word document, I lost all of my work. I spent a good 15 minutes looking for it, combing through my limited files for it on both computers. No luck. I could spend a lot more time searching for it and never find it, or I could rewrite it as fast as I can while all of the details are still fresh in my memory. It was an irritating setback. From now on, I'm not going to just press "Ctrl + S" and assume everything is saved properly. I'm going to have to save it as a new file, open it, and verify it saved correctly before closing the working copy. It could have been worse. I'm treating my lost work as a "First draft" so that I don't get too upset about it.
It's occurring to me that it's rather convenient to be both the designer and the producer at the same time. I don't have to have meetings with anyone to figure out which features I have to cut due to production constraints. That might come to bite me in the ass later on though in some unforeseen way. We'll see.
I'm also realizing that I'm not a particularly good manager... yet. I think I'm able to keep both of us productively busy throughout the day, but I'm a bit irrationally worried that we're already on week two and haven't started seriously producing a prototype. I'm mired down in all this design stuff, so I can't be spending my time learning the ins and outs of the engine we're using. Classic to me, I'm just going to say, "Eh, I'll worry about it later. What I'm doing is pretty important right now too."
Wednesday:
Somehow, I spent the majority of the day rewriting the detailed descriptions for each race I imagined would exist in my game world. I turned out to be ten pages of formatted text. It's still a bit rough, but the gist of the game is starting to take shape. I showed it to my partner and asked him for feedback. Was I being crazy for including so much detail?
I then went on to detail the unit system within the game. I guess I have a love for component based systems, because that was my first instinct. I create the base human character, who has a set of base attributes. By giving him a pitchfork and a torch, he becomes a peasant. By giving him a spear, shield and some leather armor, he becomes a lightly armored spearman. etc. It's crazy micro management and customizability. This same system follows for every variation of human units, all the way to gryphon riders. I had to get a sanity check to see if I was going overboard with this and if it would entail too much work. The consensus was that we should go wild with our design and imagination. If we can describe how everything works in vivid detail and have enough time and resources to build it all, then that's great. If we don't have enough time and money, then we can cut some features or scale them back. But, regardless, we know with great clarity what exactly we're trying to build, what it should look like, and how it all should work together.
So, I'm a bit excited about this game we're building and I'd like to describe it a bit. It's a 4X wizard game which draws heavy inspiration from the following:
Merlin (BBC show): I like the idea of magic being illegal and the drama that creates. I also like the sense of shrouded mystery.
Harry Potter: The idea that spells can be countered with a bit of ingenuity, and the sense of wonder and discovery
Total War series: No game does large scale combat formations and tactics better.
Magic: The gathering: Their magic system has the deepest and most intricate spell mechanics I've seen.
Mount & Blade: The character creation process is innovative
Stronghold: I love how you can design your own castles and place buildings and have an economy going
Gnomoria & Terraria: Both have a fantastic crafting system I'd like to borrow from
Dungeons & Dragons: They have the second best magic system and lots of lore surrounding the various creatures.
Anyways, I feel that its easy to come up with these game mechanics but each one is going to be very complicated and difficult to implement correctly. Each one may add months of extra development time, depending on my proficiency with the tools. I think as far as project management goes, an iterative approach is the best approach. But hey, I'll worry about it when the time comes.
I met a buddy from highschool today for drinks and was telling him about my game. He asked me, "Who is the target audience for this game?" and without a second thought, I said "Myself!". I figure that if I build a game which I absolutely love playing, then I built it right. I assume that there are some people in the world who have the same tastes I do, and will immensely enjoy something like this as well. It might turn out to be popular, or unpopular, but regardless, let's not get ahead of ourselves... I have to build the game first.
Thursday:
Alright, the game design document is sitting at about 26 pages and is "good enough for now". I'm not going to spend much more time adding to it. This afternoon, we went to lunch with a nearby game designer who works two blocks away. After lunch, we showed him our game concept art, gave a quick overview of our game mechanics and design ideas, and got some good feedback. Most of the things he mentioned were things I had already considered, so it was good to get an affirmation that we were on track and doing things right. He did mention a few interesting things:
1. You don't want to have religious symbols in your game (especially Islamic stuff) because it will upset certain people and cultures. Make up your own religious symbology if you have to.
2. Be wary about having children in your game. Can the in-game children be killed? If not, how does that affect game play when you want to kill everyone in a village (see: Skyrim).
3. The game design document is mostly for pitching your game to publishers and investors. If you don't have to, don't spend a lot of time on it. Instead, spend that time building a prototype.
4. Don't underestimate the time it takes to balance an RTS game.
We also had a visitor drop by from upstairs. There's another indie game studio on floor 13 who are working on a web-based MMORPG using HTML5. They're a team of five who have been working on it for over a year, and they've finally gotten to the point where they can start building in-game content and creating a playable alpha. The guy running the place said that they have a big problem with the current build of their game: It's just not fun. Supposedly, their business operation involves paying workers in equity instead of a steady paycheck. I know I wouldn't like that if I was an employee there because you're taking a huge risk if the game doesn't sell well. I don't even know what their final business plan and marketing plans are and how they're going to make money, but that may just be because they didn't tell me. Regardless, I am very interested in learning everything I can about their project and progress in hopes of spotting traps and pitfalls they made so that I can avoid them in our game production cycle. I mentioned that we'd like to stop by some time, and maybe to do lunch next week. I'll have to make a note to stop by and pester them to see how they're doing.
Today I finally purchased Maya 2015 and Mudbox. The total price came out to about $4600. I was trying to pay by debit card but my purchase was being denied by my bank since I had a daily$2000 spending limit. I had to work with my bank to get that temporarily boosted. I went for a "download" option to get the software asap, but it seems that Autodesk takes up to 24 hours before you can download the software. Watch out for that if you're on a time crunch.
In UE4 news, I figured out how to create layered terrain (dirt, grass and snow). It's a bit more tedious than I expected since you have to use a paint brush to paint materials onto the terrain contours. So, I could foresee it taking a while to create some decent looking terrain.
I also figured out how to create a moveable player character and bind keys to different events. It was a bit ridiculous and unintuitive, but it only took me about 2 hours to figure out. Compare that to taking a week and a half to manually build my own robust input system, and that's a trade I'll take any day.
By the end of the day, I was shocked that it was already 6pm. The day went by so fast, I had no idea where the time went!
Friday:
I spent $4500 (tax included) on the Maya download and I still don't have it. The Autodesk site said it may take up to 24 hours, but I haven't heard a peep after they took my money. WTF? Not cool. If I don't hear anything by Monday, I'll have to contact their support. Today I focused on trying to figure out how to start building my game using Unreal Engine Blueprints. I detailed out how my camera controls should work and tried to start implementing them. I couldn't do it. I was perpetually confused and overwhelmed by how everything worked together. The unreal tutorials, documentation and samples are good for showing you the basics of the engine, but they don't explain the architecture of how everything works together. When it comes down to it, I think I'm really going to have to just look at the samples and do trial and error. An alternative explanation is that all of the documentations and tutorials make perfect sense but I'm just too dumb to get it. Contemplating that possibility and its repercussions on my project worried me and got me a bit depressed. Suppose it's true. Suppose I'm an idiot and I'm too dumb to see it. Suppose someone smarter was in my position doing what I'm doing? They'd succeed. If I fail, it's because I'm dumb. Think about it. If I'm a shit developer, and the project depends on me to be the technical expert, then the project runs a high chance of failure. *sigh* I don't know that I can really call myself a shit developer though. I mean, I've been programming as a hobbyist and professional for 16 years. I worked as a senior developer in afghanistan (though, titles really don't mean anything) and have been able to build lots of tools and applications. I worked on my own game engine for 10 months without significant problems. So, objectively, I can't call myself a shit developer because a shit developer couldn't do all that. So... what's the conclusion? Learning the ins and outs of a new engine is going to be a slow and painful process full of frustration and self-doubt. I wasn't expecting that. I was thinking that I'd just download the engine, do tutorials for a week or two, and then be adequately proficient to start building my game and run with it. Nope! Apparently it doesn't work that way. I don't know if its the blueprints themselves and trying to wrap my mind around it, or if I'm more accustomed to writing code. By the end of the day, I was half tempted to just abandon blueprints and go with a C++ scripted project. That would have its own frustrations as well, so I'd probably just be jumping out of the frying pan and into the fire. It's better to just suffer through the frustration and try to figure it all out. Small baby steps, little victories, one at a time. I can make this work. ## 8 Comments ## Recommended Comments Thanks for the update! I just wanted to say keep at it, I'm enjoying reading these weekly updates. In fact it prompted me to start my own journal as I work on my own indie project, albeit on a much more amateur level. I find it particularly interesting how our experiences parallel at certain times, I'm currently hammering down many of my project's game design specifics and elements while trying to learn two new tool-sets I never used before (Unity and Smartfox) so they are both presenting many of the same challenges you've talked about here. #### Share this comment ##### Link to comment "Learning the ins and outs of a new engine is going to be a slow and painful process full of frustration and self-doubt." Oh yes it is... Great update, keep'em coming! #### Share this comment ##### Link to comment Great articles, really interesting reads! I just wanted to ask if you (or your artist) evaluated Maya LT? It's a Maya version geared specifically for (Indie-) game development and is available for as little as 30$/month.
I just wanted to ask if you (or your artist) evaluated Maya LT? It's a Maya version geared specifically for (Indie-) game development and is available for as little as 30$/month. I remember looking at it and asking my artist to look at the feature comparison to see if it was a feasible alternative. He said it was missing some critical features he needed for animation and said it would be very limiting. I can understand that. I suppose it's like the difference between Visual Studio Express and Visual Studio Pro and higher. You can still build stuff, but you know you're being limited and when you are in the habit of using an essential feature and can't use it to do your job proficiently... it's very irritating! I want to keep my employees as happy as possible so that they are as productive as possible, which my intuition says is more valuable than the cost savings between Maya and Maya LT. Ignoring the features for a moment: The price of$30/month is attractive, but you have to also consider how long your project is scheduled to take. I'm looking at 24 months, so 24 * 30 = $720. The perpetual license version is$795. If I overrun my schedule by a few months due to unforeseen circumstances, I save a teensy bit of money (but that's probably the least of my concerns at that point). Both being roughly equal in cost, I'd rather pay it all at once and not have to worry about being bled dry with another monthly payment. But, that's just my personal preference to budgeting.
Losing drafts especially lore pieces can be a massive pain. However, it seems like you have a good manual solution.
Great update again, thank you. If I may make some comments on a couple of things:
It's occurring to me that it's rather convenient to be both the designer and the producer at the same time. I don't have to have meetings with anyone to figure out which features I have to cut due to production constraints. That might come to bite me in the ass later on though in some unforeseen way. We'll see.
I think you're forgetting your artist here. Art and code is as much part of your scope as design. In fact, art and code limitations is largely what drives the scope of the design. You will need to really keep this in mind and keep communication going with your artist (and anyone else you choose to hire or outsource to down the line) about his/her workload throughout the project. Producers and designers can't scope in a bubble.
If we don't have enough time and money, then we can cut some features or scale them back. But, regardless, we know with great clarity what exactly we're trying to build, what it should look like, and how it all should work together.
I'm not sure that this is the best approach. If your design is crazily out of scope and won't fit your budget, it's not what you should be "trying to build". You'll just burn through your funds aiming for an impossible goal. I would argue that you should cut as much as possible now, early, and work towards that. You can always work out and expand if you end up with the time/money to do so. If you're working against a crazy, out of scope goal by the time you realize you want to cut stuff you may be out of time and money.
great update!
hey slayemin , first of all i wanna thank you a lot , i really admire your guts and you really become an inspiration for me i always wanted to start building games but you know the fear of failure , but you are great you don't panic , i'm really enjoy reading your journals about every week actually i create an account to reply you, and i wanna be a part of this community so i really encourage you to continue work hard and fill us with the updates ..
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2017-08-21 03:01:11
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http://comefaretradingonlinebft.it/bsbw/two-mass-spring-damper-system.html
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# Two Mass Spring Damper System
Example 2: Spring-damper-mass system The three elements are in parallel as they share the same across variable, the displacement. So the first two are position and velocity of mass 1 and the second two are position and velocity of mass two. Find the displacement at any time $$t$$, $$u(t)$$. While this system is widely studied, there is sparse documentation in regards to appropriate identification and modeling of a two-degree of freedom spring mass damper system that is applicable to undergraduate engineering students. Deriving the equations of motion for a two degree-of-freedom (2DOF) system. Control and stabilization of such an unstable oscillatingsystem is a great challenge so a power full controller is needed. A single mass, spring, and damper system, subjected to unforced vibration, is first used to review the effect of damping. This example shows how you can use block variable initialization, and how it affects the simulation results of a simple mechanical system. Assume that the mass is 10!!", the damping is 0. 1 (a) shows the free vibration of a system with damping. The mass m 2, linear spring of undeformed length l 0 and spring constant k, and the. The constants C 1 and C 2 are found by solving the system of equations y(0) = y 0 and v(0) = v 0 where x 0 and v 0 are the given initial position and initial. Matrix Algebra Representing the above two equations in the matrix form, we get = − 0 6 1 1 1 2 y x The above equation is in the form of AX =B. A diagram showing the basic mechanism in a viscous damper. _Under-damped_Mass-Spring_System_on_an_Incline. m 2: Mass of truck rear axle m a2: 2674 kg: Rolling moment of inertia of rear axle I xa2: 2360 kg. The vibrations are not transferred from tire to the passenger if suspensions are good. Since mechanical systems can be modeled by masses, springs, and dampers, this simulation demonstrates how Insight Maker can be used to model virtually any mechanical system. The system looks like this but there is a force applied to the right edge of ${ m }_{ 2 }$ pointing towards the right. Two were attached to the top and two were attached to the bottom, leaving the mass suspended between. Two types of tests were performed on a prototype spring/damper unit, namely characterisation tests and single degree of freedom tests. Spring-Mass-Damper Systems Suspension Tuning Basics. 3) Change the Run-time Direction to Two Bodies, for the Characteristic choose K and C and input K=5. L 1 = x 1 − R 1 L 2 = x 2 − x 1 − w 1 − R 2. Calibration and Testing of Mass Spring Damper system Step1: Assembly: Verify that the mass oscillates freely when displaced. This simulation shows two springs and masses connected to a wall. Find the equation of motion for the mass in the system subjected to the forces shown in the free body diagram. Consequently, to control the robot it is necessary to know very well the nature of the movement of a mass-spring-damper system. Calculate the potential, and kinetic energy of the system (spring gravity and mass) once the force is removed and until the system stops; Calculate the energy lost by the damping once the force is removed and until the system stops. Session 2: Mass-Spring-Damper with Force Input, Mass-Spring-Damper with Displacement Input, Pattern for Correct Models for Forces Exerted by Springs and Dampers (8-14). In: Deng Z. (A) Calculate time constant, critical damping. b) Overdamped In an overdamped system the damping ratio is greater than 1 (δ>1). mass to another. Stay safe and healthy. Likewise, you can model each spring the same way, except the value of the gain will be either k or 1/k depending on your choice of input and output. Stiffness (20 g / s 2). 5 Solutions of mass-spring and damper-spring systems described by fractional differential eqs. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Example $$\PageIndex{4}$$: Critically Damped Spring-Mass System. This way the unit threshold for the damping coefficient indicated the onset of oscillation regardless of the mass or elastic constant of the spring. I will be using the mass-spring-damper (MSD) system as an example through those posts so here is a brief description of the typical MSD system in state space. (For example, the system of Fig. the modelling of this system can be found in [13]. The system can be built using two techniques: a state space representation, used in modern control theory, and one using conventional transfer functions. Find the transfer function for a single translational mass system with spring and damper. 2 6 − = + = x y x y There are two methods to solve the above-mentioned linear simultaneous equations. Contribute to ragunawan/multibody-spring-damper development by creating an account on GitHub. This app was created to promote science, technology, engineering and math by applying principles of physics (newton 2nd law, hooke law), robotic, control/feedback system and calculus (differential equations). In addition, this elementary system is presented in many fields of application, hence the importance of its analysis. Since the mass is displaced to the right of equilibrium by 0. So we need to add these two new forces to the x and y components of the mass 1 net force calculation. So the first two are position and velocity of mass 1 and the second two are position and velocity of mass two. to mode a mass-spring-damper system •Questions. For the mass-spring-damper’s 2nd order differential equation, TWO initial conditions are given, usually the mass’s initial displacement from some datum and its initial velocity. A single mass, spring, and damper system, subjected to unforced vibration, is first used to review the effect of damping. This model is well-suited for modelling object with complex material properties such as nonlinearity and viscoelasticity. Basic Blocks are: Dampers, Masses, and Springs Springs represent the stiffness of the system Dampers (or dashpots) represent the forces opposing to the motion (i. Solving a mass-spring-damper system with ode45. In other words,. electronic systems in mechatronics, etc. This book solves the most frequent exercises and problems of mass-spring-damper systems. prototype single degree of freedom system is a spring-mass-damper system in which the spring has no damping or mass, the mass has no stiffness or damp-ing, the damper has no stiffness or mass. D = mass/spring rate. A schematic of a mass-spring-damper system represented using a two-port component. Expand the previous system to the 2-mass-spring-damper system, and plot the different transfer functions. The velocity of m2 is greater than the velocity of m1. The homogeneous solutions are proportional to e−t cos(t)and e−t sin(t), so they tend asymp-totically to zero. The spring and damper will be in parallel, and the mass will hang from them. The picture should also be clipped to its bounding box. Consequently, to control the robot it is necessary to know very well the nature of the movement of a mass-spring-damper system. Mass-Spring-Damper Oscillator Simulation Example. Model 2 – TestModel_With TMD. they are both compressed when in contact. No bending or torsion is considered. Let us consider the system above formed by two blocks (each of mass $m$) connected by a linear damper and spring in a series. Example 15: Mass Spring Dashpot Subsystem in Falling Container • A mass spring dashpot subsystem in a falling container of mass m 1 is shown. Tuned mass dampers are mainly used in the following applications: • tall and slender free-standing structures (bridges, pylons of bridges, chimneys, TV. The transfer function of a Mass-Spring-Damper System. Session 2: Mass-Spring-Damper with Force Input, Mass-Spring-Damper with Displacement Input, Pattern for Correct Models for Forces Exerted by Springs and Dampers (8-14). The first method is to use matrix algebra and the second one is to use the MATLAB command 'solve'. Impacting chatter and stuck phenomena for the mass with constraints are investigated and the corresponding conditions for such phenomena are determined. As before, the zero of. Mass-spring-damper system For example, the linearized inverted pendulum is simply a spring-mass-damper system of. Question: A single degree of freedom spring-mass-damper system with mass (m) = 10 kg, Spring Constant (k) = 20 N/m and Damping (c) = 2. This drives J 2, through B r1, but the energy in the system decays over time because energy is lost to the friction. The tension in damper 1 is , the tension in damper 2 is , and the compression in damper 3 is. The mass is M=1(kg), the natural length of the spring is L=1(m), and the spring constant is K=20(N/m). Question: Consider The Forced-mass-spring-damper System, As Shown On Figure 2. Mass-Spring System Simulation. they are both compressed when in contact. x ¨ = λ 2 e λ t. The spring constant k can also be referred to as the spring stiffness. Part 2: Spring-Mass-Damper System Case Study Discover how MATLAB supports a computational thinking approach using the classic spring-mass-damper system. We will use Laplace transformation for Modeling of a Spring-Mass-Damper System (Second Order System). Natural frequency of the resonance of a mass-spring system. This model is for an active suspension system where an actuator is included that is able to generate the control force U to control the motion of the bus body. No bending or axial loads are considered. Question: A single degree of freedom spring-mass-damper system with mass (m) = 10 kg, Spring Constant (k) = 20 N/m and Damping (c) = 2. Problem about creating water waves when using mass spring damper system. $\begingroup$ You probably need two springs, one for the club and one for the ball, and two dampers as well. Any help on modeling both the spring and damper would be appreciated. En existing overhands boring bar with tuned mass damper at tool shank [9]. Matrix Algebra Representing the above two equations in the matrix form, we get 0 6 1 1 1 2 y x The above equation is in the form of AX B. 8), f n = g (2. The constant k is called the spring constant and refers to the rigidity of the spring. I am having trouble modeling a simple 2D spring mass damper system. Since the mass an initial velocity of 1 m/s toward equilibrium (to the left) y0(0) = −1. Describe the motion for spring constants k 1 ¼ 0:4 and k 2 ¼ 1:808withinitialconditionsðx 1ð0Þ;x_ 1ð0Þ;x 2ð0Þ;x_ 2ð0ÞÞ ¼ ð1=2;0; 1=2;7=10Þ. We will use Laplace transformation for Modeling of a Spring-Mass-Damper System (Second Order System). 0 CorelDRAW 12. Finding the damping constant. Consider a simple system with a mass that is separated from a wall by a spring and a dashpot. A spring-damper system can be modeled as follows: F = - k x - b v Where b is the coefficient of damping and v is the relative velocity between the two points connected by the spring. This system can be shown schematically in a few ways. 5 and a spring with k = 42 are attached to one end of a lever at a radius of 4. Let us consider the system above formed by two blocks (each of mass $m$) connected by a linear damper and spring in a series. For a damped harmonic oscillator with mass m , damping coefficient c , and spring constant k , it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping. This example is from a book on dynamics. b) Overdamped In an overdamped system the damping ratio is greater than 1 (δ>1). Figure 1 - Model 2 - Test model with TMD. Robustness Analysis. Suppose that the masses are attached to one another, and to two immovable walls, by means of three identical light horizontal springs of spring constant , as shown in Figure 15. 3 The 2-Mass-Spring-Damper system. 1 2 [ ̇ 𝑝1̇ 𝛿̇. a mass-spring system is proposed, which is oversimplified and neglects the delayed reaction and resistance to relative speed. Both masses have a spring connected to a stationary base, with spring constants and ; also for the spring connecting the two masses. 0 Graphic Tuned Mass Dampers Folie 2 Folie 3 Folie 4 Folie 5 SDOF System Folie 7 Folie 8 Folie 9 Folie 10 Folie 11 2 DOF System Folie 13 Folie 14 Folie 15 Folie 16 Folie 17 Folie 18 Folie 19 Folie 20 Folie 21 Folie 22 Folie 23 Folie 24 Folie 25 Realization Folie 27 Folie 28. $\begingroup$ You probably need two springs, one for the club and one for the ball, and two dampers as well. 1 (a) shows the free vibration of a system with damping. OverviewModelingAnalysisLab modelsSummaryReferences Overview 1 Review two common mass-spring-damper system models and how they are used in practice 2 The standard linear 2nd order ODE will be reviewed, including the natural frequency and damping ratio 3 Show how these models are applied to practical vibration problems, review lab models and objectives. Determine the efiect of parameters on the solutions of difierential equations. Session 5: Torsional Components, Torsional Mass-Spring System with Torque Input. they are both compressed when in contact. In mass-spring-damper problems there are several numerical constants to note. electronic systems in mechatronics, etc. The Simscape model uses physical connections, which permit a bidirectional flow of energy between components. The mass spring damper system used consisted of two vertical metal rods with a mass supported between the two rods by a low friction connection. Output: The peak level response of each mass-spring-damper system is plotted as a function versus the corresponding natural frequencies of the systems. Observe the oscillations for normal displacement inputs. In the first diagram below, the shaft is shown schematically as a spring, the friction B r1 is drawn as a dashpot, while the friction B r2 is shown as hash marks against ground. 0025 kg, k 01 = k 02 = 10 4 N/m, ξ 01 = ξ 12 = 0. 9/ago/2013 - The site shows plots of Spring-Mass-Damper system responses for a variety of damping arrangements. Altair Compose Exercise – Implementation of Mass-Spring-Damper system The student is asked to implement the Euler’s method for numerical integration through oml language. A typical SDOF (single degree of freedom) is the following mass/spring/damper system. add a smaller mass, m2, connected to m1 by a spring and a damper, k2 and c2. where M is the primary mass, m is the secondary mass, K is the primary spring stiffness, k is the secondary spring stiffness, c is the secondary damping, P(t) is the force acting on primary mass, and p(t) is the force acting on damper mass. The MSD DObject only requires two properties that control the natural frequency and damping of the system. Save the model as "mass_spring_damper_model. To improve the modelling accuracy, one should use the effective mass, M eff, or spring constant, K eff, of the system which are found from the system energy at resonance:. The development presented here is based on a linear model that only partially Fig. The behaviour of a tuned mass damper can easily be illustrated with a two-mass-spring-damper-system (see fig. Four sets of springs attached to the mass. Then you can determine when the ball and club are in contact via the deflections of the springs, i. Thus the motions of the mass 1 and mass 2 are out of phase. You may be able to mode this system in a differential equation as shown below. Damper tuning at the shop and at the track In the previous issue, the basic theory behind dampers was introduced. As discussed in earlier. This paper will makes use of Newton law of motion, differential equations, MATLAB simulation, and transfer function to model mass-spring-(Refer Fig. The Spring Exerts Force On The Mass In Accordance To Hooke's Law. Viscous damping is damping that is proportional to the velocity of the system. 5- a simple model of the car hitting the speed bump. Types of Solution of Mass-Spring-Damper Systems and their Interpretation The solution of mass-spring-damper differential equations comes as the sum of two parts: • the complementary function (which arises solely due to the system itself), and • the particular integral (which arises solely due to the applied forcing term). However, it is also possible to form the coefficient matrices directly, since each parameter in a mass-dashpot-spring system has a very distinguishable role. $\begingroup$ You probably need two springs, one for the club and one for the ball, and two dampers as well. Mass-Spring System Simulation. Based on this assumed motion, tension is developed in left and center dampers, but compression is developed in the right damper. Question: A single degree of freedom spring-mass-damper system with mass (m) = 10 kg, Spring Constant (k) = 20 N/m and Damping (c) = 2. A mass connected to a spring and a damper is displaced and then oscillates in the absence of other forces. We use kak to denote the length of a vector a, kak = q a2 x +a2y. Tuned Liquid Column Damper (TLCD): This passive damping system is a variation of the TMD. A mass-spring-damper (MSD) is a DObject in ProteusDS that demonstrates a simple oscillating system and has the ability to illustrate the numerical integrator performance. This example shows how you can use block variable initialization, and how it affects the simulation results of a simple mechanical system. JR SIDE MASS DAMPER SET MA CHASSIS 15490 $7. Typical initial conditions could be y()02=− and y()0 =+4. The mass could represent a car, with the spring and dashpot representing the car's bumper. Figure 1 - Model 2 - Test model with TMD. The spring stiffness of the secondary mass is chosen in such a manner that an optimal tuning of the main system is achieved. The system parameters are as follows. Rethinking the Mass, Damper and Spring Dr. A mass of 1 slug is hung from a spring… No conversion needed. A similar mass-spring-damper system was proposed in [33], however, the delay due to the driver’s reaction time is also neglected. analogmuseum. Ask Question Asked 1 year, How to draw spring damper system in TikZ? 0. (Electronics) electronics the introduction of resistance into a resonant circuit with the result that the sharpness of response at the peak of a frequency is reduced. Deriving the equations of motion for a two degree-of-freedom (2DOF) system. • The motion of the system is completely described by the coordinates x 1(t) and x 2(t), which define the positions of the masses m 1 and m 2 at any time t from the respective equilibrium positions. Use PCI 6014 card Analog Input channel configuration ai1 = analog input channel 1, ai2 = analog input channel 2 Analog Output channel configuration ao0 = analog output channel 0 2 2. A diagram of this system is shown below. The system is attached to a dashpot that imparts a damping force equal to 14 times the instantaneous velocity of the mass. The junction between sprang and unsprang masses is carried by a ball joint on the wheel side and a side frame axis. As before, the spring mass system corresponds to the DE y00 +4y = 0. about it’s pivot point. 52B gives:. Applying F = ma in the x-direction, we get the following differential equation for the location x(t) of the center of the mass: The first condition above specifies the initial location x(0) and the second condition, the initial velocity v(0). - Units for B to preserve physical meaning: • N/(m/sec) • (N-m)/(rad/sec) - Transfer Function ( ) 2 2 2 2 dxdx Dx Dx dtdt xx. 025 kg, M 2 = 0. The system is fitted with a damper with a damping ratio of 0. The mathematical model of the system can be derived from a force balance (or Newton's second law: mass times acceleration is equal to the sum of forces) to give the following second. Question: A single degree of freedom spring-mass-damper system with mass (m) = 10 kg, Spring Constant (k) = 20 N/m and Damping (c) = 2. 2 Undamped Primary System, Damped Tuned Mass Damper Now, neglecting damping in the primary system, but adding damping to the TMD, we consider the Den-Hartog absorber [1]. Create a new project and add a MSD DObject. EXAMPLE of a dynamic system: A mass-spring-damper system The following section contains an example for building a mass-spring-damper system. 80: Spring and Damper System Model A mass is hung from a spring with spring constant K. Oscillation response is controlled by two fundamental parameters, tau and zeta, that set the amplitude and frequency of the oscillation. Created using MATLAB R2013a. Ask Question Asked 2 years, 4 months ago. The damped frequency. Spring - absorb, store and spit out the energy(Ideal spring vibrates continuously) Damper - Absorb and dissipates the energy (coupled with a spring to reduce. In this PDF guide, the Transfer Function of the exercises that are most commonly used in the mass-spring-damper system classes that are in turn part of control systems, signals and systems, analysis of electrical networks with DC motor, is determined. Mass-Spring-Damper System¶ Another commonly used introductory system is the mass-spring-damper system. I will be using the mass-spring-damper (MSD) system as an example through those posts so here is a brief description of the typical MSD system in state space. 7) with the following de nitions:!2 n= k m and 2 ! n= c m where is the damping ratio for the given spring-mass-damper system. If we assume the spring moves with a sinusoidal velocity , where C is a complex. It would also seem that in the real world you would use a shock absorber which would only damp on the return stroke so that the mass would come to close to zero velocity before coming back to the initial stops. Here $$k$$ is the spring constant, $$c$$ is the damper constant, and $$m$$ is the mass. Block substitution lets you specify the linearization of a particular block in a Simulink model. Mass-Spring Damper system - moving surface. After being released from rest the undamped (black) mass exhibits simple harmonic motion while the damped (blue) mass exhibits an oscillatory motion which decays. The graphs produced are called Lissajous curves and are generated by simple sine and cosine functions. Damper tuning at the shop and at the track In the previous issue, the basic theory behind dampers was introduced. In this section, the concept of the tuned mass damper is illustrated using the two-mass system shown in Figure 4. Figure 1 - Model 2 - Test model with TMD. If you want to try it first, or look at the complete source code, see MassSpringDamper. Springer, Berlin, Heidelberg. 2 Undamped Primary System, Damped Tuned Mass Damper Now, neglecting damping in the primary system, but adding damping to the TMD, we consider the Den-Hartog absorber [1]. These systems mainly consist of three basic elements. order system. Image: Translational mass with spring and damper The methodology for finding the equation of motion for this is system is described in detail in the tutorial Mechanical systems modeling using Newton's and D'Alembert equations. As was derived in class, there are two theorems that relate the initial and final values (in this case positions) of the output functions in the t domain with the output function in the s domain. Draw basic diagrams with explanation. Mungo The following paper describes my derivation for the displacement response of a Single-Degree-Of-Freedom (SDOF) Spring-Mass-Damper (SMD) system subjected to a stepped x^2 forcing function. This system can be shown schematically in a few ways. The picture should also be clipped to its bounding box. The mass, the spring and the damper are basic actuators of the mechanical systems. ) The RA 741 can be seen on the left - it is programmed to display a car frame and two wheels as well as simulate a two mass spring damper system. The Simscape model uses physical connections, which permit a bidirectional flow of energy between components. Mass-Spring-Damper System¶ Another commonly used introductory system is the mass-spring-damper system. 80 Add to cart; JR SLIMLINE MASS DAMPER SET 95435$ 5. It can be seen that the infinite dimensional system admits a two-dimensional attracting manifold where the equation is well represented by a classical nonlinear. Figure 2-b A horizontal pendulum tuned mass damper In lateral tuned mass dampers ( TMDs operating in horizontal direction) leaf springs, vertical pendulums either by themselves or in conjunctions with coil springs are used. In this case the displacement we use to calculate spring to force is the difference between both masses, mass 2 position minus mass 1 position, and there is also a damping force resisting the spring 2 force. 2 Sinusoidal Forcing Suppose that a spring/mass system with spring constant k > 0 attached to a mass of m > 0 kilograms with with friction constant b > 0. Calculate the following. Question: A single degree of freedom spring-mass-damper system with mass (m) = 10 kg, Spring Constant (k) = 20 N/m and Damping (c) = 2. TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It'll take us three non-consecutive articles to get there, but it's a worthy system to model. 2 6 − = + = x y x y There are two methods to solve the above-mentioned linear simultaneous equations. A mass connected to a spring and a damper is displaced and then oscillates in the absence of other forces. This value is. These systems mainly consist of three basic elements. 315 where E 2 n 2t2 o = X1 n=0 2t2 n (2 n+1); (16) is the Mittag-Leffler function. Learn more about mass spring damper system. 025 kg, M 2 = 0. The behaviour of a tuned mass damper can easily be illustrated with a two-mass-spring-damper-system (see fig. m1 k1 Y X 100 100 100 k2 k3 m2 m3 k 12EI L3 =-----I1 k1L 3 12E = -----. There seem to be some problems with this file; at least on my Mozilla Firefox browser, one of the arrowheads is missing. of mass, stiffness and damping and the coefficient of resti-tution, presented as part of the subject of impact. (EQ 10) k c m FIGURE 3. Mass-Spring-Damper Oscillator Simulation Example. These are the equations of motion for. Tuned Mass Dampers Tuned mass dampers (TMDs) work by fastening a mass-block to a structural component (such as a floor) via a spring (Fig. Calibration and Testing of Mass Spring Damper system Step1: Assembly: Verify that the mass oscillates freely when displaced. 5 Solutions of mass-spring and damper-spring systems described by fractional differential eqs. If damping in moderate amounts has little influence on the natural frequency, it may be neglected. they are both compressed when in contact. 0E6 Thus, , etc. However, it is also possible to form the coefficient matrices directly, since each parameter in a mass-dashpot-spring system has a very distinguishable role. For a system with two masses (or more generally, two degrees of freedom), M and K are 2x2 matrices. Free Vibration of a Mass Spring System with Damping November 22, 2014 September 20, 2018 Engineeering Projects Fig. Positions are in meters and velocities are in meters per second. The motion of the masses is damped, with damping factors. We wish to examine when a sinusoidal forcing function of the form F0 cos( ωt − φ). Then you can determine when the ball and club are in contact via the deflections of the springs, i. A voice coil is attached at the left side to add variable damping. Matrix Algebra Representing the above two equations in the matrix form, we get 0 6 1 1 1 2 y x The above equation is in the form of AX B. $\begingroup$ You probably need two springs, one for the club and one for the ball, and two dampers as well. This is NOT true for real springs and dampers. Initialize Variables for a Mass-Spring-Damper System. I am dealing with the differential equation of spring mass system mx''+cx'+kx=0 where x''=dx2/dt2 and x'=dx/dt. Damper tuning at the shop and at the track In the previous issue, the basic theory behind dampers was introduced. add a smaller mass, m2, connected to m1 by a spring and a damper, k2 and c2. Spring Damper System : Recoil Reduction. We use kak to denote the length of a vector a, kak = q a2 x +a2y. The mass m 2, linear spring of undeformed length l 0 and spring constant k, and the. $$\zeta = \frac{c}{2 \sqrt{k m}}$$ where stiffness is k, mass is m and damping constant is c. If you want to try it first, or look at the complete source code, see MassSpringDamper. Viewed 2k times 0 $\begingroup$ We consider integral control of a mass-spring-damper system, that is a coupled system $$\ddot x(t) + 5\dot x(t) + 4x(t) = u(t),$$ $$\dot u(t) = k(r - x(t))$$ where k is a positive parameter. The Simulink model uses signal connections, which define how data flows from one block to another. 1: Rear view of a vehicle suspension system. F = D * (v2 - v1) The damper is the only way for the system to lose energy. Next, copy the range of "B9:E9" all the way down to "B1008:E1008" And we are almost ready to simulate after we display the coordinate x (E8:E1008) function of time t. JPG; 1 Reply Last Post Dec 25, 2010, 4:55 AM EST. A spring-damper is connected to the bellcrank on one end, and to the chassis on the other. Figure 2 shows an undamped mass-spring system containing one mass and one spring. For a system with n degrees of freedom, they are nxn matrices. Positions are in meters and velocities are in meters per second. To use a lumped-system model, a system needs to be broken into mass, spring, and damper elements and use a procedure similar to the discussion in Section 1. Applying to the free body diagrams of figure 3. The origin of the coordinate system is located at the position in which the spring is unstretched. Once initiated, the cart oscillates until it finally comes to rest. Lever-arm dampers resemble hydraulic door closers. Since the applied force and the. The Driving Mass-Spring workstation includes an ECP Model 210A rectilinear control system that is connected to a PC containing the required ECP software. 3) Choose the PART_2. In this section, the concept of the tuned mass damper is illustrated using the two-mass system shown in Figure 4. moistening or wetting. Question: A single degree of freedom spring-mass-damper system with mass (m) = 10 kg, Spring Constant (k) = 20 N/m and Damping (c) = 2. As discussed in earlier. In other words,. Modeling of Mass,Spring and Damper system. 2 Remember the mass-spring-damper system from Example 3. 4) Right-click anywhere on the ground to display the Location Event. The spring-damper element has no mass. Based on the various mechanisms that influence the collision dynamics, an analogy is made between the fluidic system of liquid drops and a mechanical mass-spring-damper system. Example: Simple Mass-Spring-Dashpot system. Let us consider the system above formed by two blocks (each of mass $m$) connected by a linear damper and spring in a series. An attractive attribute of proof mass dampers is that they can be configured, via the active controller, to act also as a broadband (not just tuned) damper, e. Stay safe and healthy. The system can then be considered to be conservative. The motion of the masses is damped, with damping factors. The value of the gain will be either M or 1/M depending on how you set things up. This system is set up so that, when the floor vibrates at a resonant frequency (which could be caused by dancing, for example), it induces analogous movement of the mass Fig. EXAMPLE of a dynamic system: A mass-spring-damper system The following section contains an example for building a mass-spring-damper system. • At resonance the forces are in balance • Deformation force (stiffness) plus acceleration force (mass) is zero. With a given spring-mass-damper system, H∞ and Mu-synthesis control methods are used to build system controllers which minimize vibrations at two major natural frequencies in two cases; without. The overdots and primes denote temporal and spatial derivatives. # Damped spring-mass system driven by sinusoidal force # FB - 201105017 import math from PIL import Image, ImageDraw imgx = 800 imgy = 600 image = Image. It consists of a sprung mass (m 2) supported by a primary suspension, which in turn is connected to the unsprung mass (m 1). The first method is to use matrix algebra and the second one is to use the MATLAB command 'solve'. Parameters: M 1 = 0. Example 2: Spring-damper-mass system The three elements are in parallel as they share the same across variable, the displacement. Three free body diagrams are needed to form the equations of motion. Simple poles in ω= 1 + i and ω= −1 + i, that means: in the upper half plane. Once initiated, the cart oscillates until it finally comes to rest. You can drag the mass with your mouse to change the starting position. This paper discusses the vibration of a mass-spring-damper system with two constraints and impact interactions. We can ideally assume that M 1 =M 2 =M. $\begingroup$ You probably need two springs, one for the club and one for the ball, and two dampers as well. MAURER Tuned Mass Dampers (TMD) are designed as spring-mass or pendulum systems. The mass-spring-damper system is. Next, copy the range of "B9:E9" all the way down to "B1008:E1008" And we are almost ready to simulate after we display the coordinate x (E8:E1008) function of time t. SDOF Underdamped Spring-Mass-Damper System Response To A Stepped x^2 Pulse Forcing Function Posted on June 13, 2017 by B. In mass-spring-damper problems there are several numerical constants to note. Then the corresponding Euler-Lagrange equations of motion are. But how robust is it to variations of ?. Nonlinear Identification and Control of Coupled Mass-Spring-Damper System using Polynomial Structures. Finally, by judiciously adding a damper,. A mass of 5 kg is suspended on a spring of stiffness 4000 N/m. The tension in damper 1 is , the tension in damper 2 is , and the compression in damper 3 is. The case is the base that is excited by the input. Question: A single degree of freedom spring-mass-damper system with mass (m) = 10 kg, Spring Constant (k) = 20 N/m and Damping (c) = 2. After being released from rest the undamped (black) mass exhibits simple harmonic motion while the damped (blue) mass exhibits an oscillatory motion which decays. Once initiated, the cart oscillates until it finally comes to rest. The impact mass motion within the main system can be. ) Given: Mass: Spring: Radius: M 2. 5 N{eq}\cdot{/eq}s / m. Follow 4 views (last 30 days) Amine Elazri on 20 Aug 2018. The rectilinear control system consists of three mass carriages, three encoders, two dashpot dampers, a control box, and a mechanical actuator. The force is proportional to the elongation speed of the damper. At t = 0, the system is released from. 55 nano-meters than compare to a vehicle has a weight of. Mungo The following paper describes my derivation for the displacement response of a Single-Degree-Of-Freedom (SDOF) Spring-Mass-Damper (SMD) system subjected to a stepped x^2 forcing function. Created using MATLAB R2013a. 1) shows the calculated movement of the main system (M1) with respect to the frequency of the excitation force for different properties of the TMD (M2). These systems mainly consist of three basic elements. Add a 2nd mass and spring damper combination to the 1-mass-spring-damper system that we have developed. The system can be built using two techniques: a state space representation, used in modern control theory, and one using conventional transfer functions. For a system with n degrees of freedom, they are nxn matrices. Furthermore, the active mass damper system was designed to control vortex-induced vibration and buffeting vibration. Posted Dec 24, 2010, 3:30 PM EST 1 Reply. This simulation shows two springs and masses connected to a wall. Viscous damping is damping that is proportional to the velocity of the system. This is NOT true for real springs and dampers. (ii) The graph shows the maximum deceleration of the vehicle approximately 2 m/s, Therefore from the above graphs proved that a large vehicle is less risk of injury than a small vehicle because as the above result which has a weight of 1500 kg having smaller impact of compression of 2. I am having trouble modeling a simple 2D spring mass damper system. Sana RANNEN. Example: Mass-Spring System Consider the damped mass-spring oscillator mp00(t) + bp0(t) + kp(t) = 0 where I p(t) denotes the position of mass at time t I m > 0 is the mass I b 1 is the damping coe cient I k > 0 is the spring constant Andrea Arnold and Franz Hamilton Kalman Filtering in a Mass-Spring System. Lecture 2 • Vertical oscillations of mass on spring • Pendulum • Damped and Driven oscillations (more realistic) Outline. In implementation PID controller process analog electronic components are used. Since the mass is displaced to the right of equilibrium by 0. Autoscale the plot so that you can see the response (the autoscale button looks like a pair of binoculars). The basic vibration model of a simple oscillatory system consists of a mass, a massless spring, and a damper. 0 dtef(t)f(t)F(s) st L We will use Laplace transforms for Modeling of a Spring-Mass-Damper. Description. 12:54 Part 3: Two-Degrees-of-Freedom Non-Planar Robotic Manipulator Case Study Explore a real-life case study that further explains the computational thinking approach using a larger two-degree. Spring-Mass-Damper Systems Suspension Tuning Basics. The only problem is the dampers. Get the characteristic function of damping of the damper, ie, the function describing the motion as it decays. Figure one is with the initial value of damping, and figure 2 is the same system with no damping. Only horizontal motion and forces are considered. 3 Damage Evaluation for a 2 DOF Spring Mass Damper System 65. The system parameters are as follows. Calculate the potential, and kinetic energy of the system (spring gravity and mass) once the force is removed and until the system stops; Calculate the energy lost by the damping once the force is removed and until the system stops. The Mass-Spring-Damper Solution Next: Refinements Up: Reed Valve Modeling Previous: The Reed as a Mass-Spring-Damper As previously indicated, the flow through the reed channel is approximated quasi-statically'' using the Bernoulli equation and given by. Our big project -- our goal -- for this mechanics/dynamics portion of Modeling Physics in Javascript is to model a car's suspension system. For the pur-. The mass is attached to a viscous damper with a damping constant of 400 dyn s/cm. It solves many of the limitations of the classical control theory in which transfer functions were used to asses the behavior of a closed loop system. An important measure of performance is the ratio of the force on the motor mounts to the force vibrating the motor, /. Circuit diagram of this lab. The mass-spring-damper model consists of discrete mass nodes distributed throughout an object and interconnected via a network of springs and dampers. English: Mass-spring-damper 2 body system, a base subjected to a vibratory displacement, simple model of tuned mass damper model/dynamic vibration absorber Date 5 May 2014, 21:17:57. The transfer function of the SMD with the actuating force F a as input and the position as output is 2 1 a X s F ms cs k (1). 2 extended to the three car system. Those are mass, spring and dashpot or damper. In: Deng Z. Two controllers are proposed: both of them switch the parameters of the system between their nominal values and their negative values. Spring-Mass-Damper System (2) - Deformable joints and constitutive law In this chapter, we construct a simulation model of a spring-mass-damper system that is equivalent to the one in the previous chapter but using a " deformable displacement joint " instead of the structural internal force to express a spring-damper. The script writes the points to the file 'two_springs. 3 The 2-Mass-Spring-Damper system. The free body diagram of the model for one car system and the forces acting on the one car model with mass =m 1 is shown in Figure 3A and 3B respectively. The black mass is undamped and the blue mass is damped (underdamped). mass to another. I understand the equation of a damped mass system (spring plus dashpot) when one end is fixed to a wall as is described in most textbooks. The motion is slowed by a damper with damper constant C. 2, where the boring bar structure is instead by its interests vibration modes. Schematic of mass-spring-damper. Then you can determine when the ball and club are in contact via the deflections of the springs, i. Calculate the following. of mass, spring constant and damping coefficient refer to Appendix A. SDOF Underdamped Spring-Mass-Damper System Response To A Stepped x^2 Pulse Forcing Function Posted on June 13, 2017 by B. 6 Summary 83. At t = 0, the system is released from. Oscillation response is controlled by two fundamental parameters, tau and zeta, that set the amplitude and frequency of the oscillation. Processing. This paper develops this connection for a particular system, namely a bouncing ball, represented by a linear mass-spring-damper model. Spring-Mass-Damper Equilibrium Setpoint Control to the mass, the system will settle into a steady state deflection Xref(s 2/7/2019 9:43:39 AM. 1) is well represented by a classical spring-mass-damper ODE with two degrees of freedom: u00(t)+k1 u0(t)+k0 u(t) = 0. x ¨ = λ 2 e λ t. • The device from a copying machine is shown. Accelerometers belong to this class of sensors. This is the Shock Response Spectrum (Figure 4). While this system is widely studied, there is sparse documentation in regards to appropriate identification and modeling of a two-degree of freedom spring mass damper system that is applicable to undergraduate engineering students. 2 Tuned mass dampers and vibration principle. There seem to be some problems with this file; at least on my Mozilla Firefox browser, one of the arrowheads is missing. For a damped harmonic oscillator with mass m , damping coefficient c , and spring constant k , it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping. The spring has stiffness k, the damper has coefficient c, the block has mass m, and the position of the mass is measured by the variable x. Tuned Mass Dampers Tuned mass dampers (TMDs) work by fastening a mass-block to a structural component (such as a floor) via a spring (Fig. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, Mass-spring-damper system with damping eigenvalues and eigenvectors. Springer, Berlin, Heidelberg. Matrix Algebra Representing the above two equations in the matrix form, we get 0 6 1 1 1 2 y x The above equation is in the form of AX B. An ideal mass spring-damper system is represented in Figure 1. Simulink Model of Mass-Spring-Damper System The mass-spring-damper depicted in Figure 1 is modeled by the second-order differential equation where is the force applied to the mass and is the horizontal position of the mass. This example shows two models of a mass-spring-damper, one using Simulink® input/output blocks and one using Simscape™ physical networks. Spring-Mass-Damper Equilibrium Setpoint Control to the mass, the system will settle into a steady state deflection Xref(s 2/7/2019 9:43:39 AM. It is shown that the properties of the ball model. Parameters: M 1 = 0. mass,spring and damper. Specify link properties. Fluids like air or water generate viscous drag forces. F = D * (v2 - v1) The damper is the only way for the system to lose energy. It moves in a horizontal plane. This example shows two models of a mass-spring-damper, one using Simulink® input/output blocks and one using Simscape™ physical networks. 025 kg, M 2 = 0. Here $$k$$ is the spring constant, $$c$$ is the damper constant, and $$m$$ is the mass. RE: Mass spring damper problem. The mass, the spring and the damper are basic actuators of the mechanical systems. 5 N{eq}\cdot{/eq}s / m. An important measure of performance is the ratio of the force on the motor mounts to. However, I need an equation of the more interesting case where two free floating masses are connected by a single axis spring and a dashpot. Then you can determine when the ball and club are in contact via the deflections of the springs, i. The transfer function of the SMD with an actuating force F a as input and the position as output is 2 1 a X s F ms. The image below shows the amplitude of the displacement u vs. This example shows two models of a double mass-spring-damper, one using Simulink® input/output blocks and one using Simscape™ physical networks. (Other examples include the Lotka-Volterra Tutorial, the Zombie Apocalypse and the KdV example. Since the system above is unforced, any motion of the mass will be due to the initial conditions ONLY. Consider a spring-mass system shown in the figure below. Introducing the following notation (4. At t = 0, the system is released from. A tuned mass-spring-damper system can be used to reduce the amplitude of vibration in a dynamic system. The spring has stiffness k, the damper has coefficient c, the block has mass m, and the position of the mass is measured by the variable x. Mechnical drawing, Tikz, damper + spring + 2 masses. The second state represents the final point when the body is at rest and the spring forces are in equilibrium with gravity. Next, here is a script that uses odeint to solve the equations for a given set of parameter values, initial conditions, and time interval. EXAMPLE of a dynamic system: A mass-spring-damper system The following section contains an example for building a mass-spring-damper system. System being modeled. I am dealing with the differential equation of spring mass system mx''+cx'+kx=0 where x''=dx2/dt2 and x'=dx/dt. The mass-spring-dashpot system is the inspiration of the ideal (or standard) 2 nd order transfer function. the force at the tip of the cantilever is linearly dependent on its displacement. 2, where the boring bar structure is instead by its interests vibration modes. Describe the motion for spring constants k 1 ¼ 0:4 and k 2 ¼ 1:808withinitialconditionsðx 1ð0Þ;x_ 1ð0Þ;x 2ð0Þ;x_ 2ð0ÞÞ ¼ ð1=2;0; 1=2;7=10Þ. The mass-spring-damper system is a standard example of a second order system, since it relatively easy to give a physical interpretation of the model parameters of the second order system. What if we only connect a spring and a damper without mass? What will be the equation? Two weightless springs with force constants k1 and k2 are suspended in parallel and the system is loaded collectively with a mass m. ) Substituting this relation in Eq. You must enter m=mass ,b=damping constant ,k=spring constant ,initial values and time span. Introduction In the fall of 2015, the Pennsylvania Military College. There seem to be some problems with this file; at least on my Mozilla Firefox browser, one of the arrowheads is missing. Question: A single degree of freedom spring-mass-damper system with mass (m) = 10 kg, Spring Constant (k) = 20 N/m and Damping (c) = 2. Lecture 2 • Vertical oscillations of mass on spring • Pendulum • Damped and Driven oscillations (more realistic) Outline. • When the system vibrates in its second mode, the equations blbelow show that the displacements of the two masses have the same magnitude with opposite signs. Contribute to ragunawan/multibody-spring-damper development by creating an account on GitHub. Description. One of the earliest hydraulic dampers to go into production was the Telesco Shock Absorber, exhibited at the 1912 Olympia Motor Show and marketed by Polyrhoe Carburettors Ltd. Furthermore, the active mass damper system was designed to control vortex-induced vibration and buffeting vibration. In this model consists of spring, damper, mass, integrator, gain, motion sensor, scope and display bolcks are used in simscape and simulink model respectively. is the following mass/spring/damper system. The first condition above specifies the initial location x (0) and the. (General Engineering) engineering any method of dispersing energy in a vibrating system. SDOF Underdamped Spring-Mass-Damper System Response To A Terminating x^2 Pulse Forcing Function Posted on June 13, 2017 by B. 0025 kg, k 01 = k 02 = 10 4 N/m, ξ 01 = ξ 12 = 0. The horizontal vibrations of a single-story build-. As before, the zero of. Because the system has two degrees of freedom the sprung and unsprung masses are able to move independent of each. prototype single degree of freedom system is a spring-mass-damper system in which the spring has no damping or mass, the mass has no stiffness or damp-ing, the damper has no stiffness or mass. An ideal mass spring-damper system is represented in Figure 1. We propose a strategy to solve the tracking and regulation problem for a 2DOF underactuated mass-spring-damper system with backlash on the underactuated joint, parametric uncertainties, and partial measurement of the state vector. 00 Select options; JR SHORT MASS DAMPER BLOCK 6X6X14Mm (Silver) Ltd 95487 \$ 4. Then you can determine when the ball and club are in contact via the deflections of the springs, i. Circuit diagram of this lab. new ("RGB", (imgx, imgy)) draw = ImageDraw. Nonlinear Dynamics of a Mass-Spring-Damper System Background: Mass-spring-damper systems are well-known in studies of mechanical vibrations. 3 The 2-Mass-Spring-Damper system. The drop or anti-resonance being previously based on the resonance of the main system, we get the green curve. Lecture Notes in Electrical Engineering, vol 338. An external force is also shown. In: Deng Z. Damper tuning at the shop and at the track In the previous issue, the basic theory behind dampers was introduced. This value is. The system is subject to constraints (not shown) that confine its motion to the vertical direction only. Nathan Albin, Associate Professor, Kansas State University. This example shows two models of a double mass-spring-damper, one using Simulink® input/output blocks and one using Simscape™ physical networks. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. order system. (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. This is not right. 0025 kg, k 01 = k 02 = 10 4 N/m, ξ 01 = ξ 12 = 0. Ask Question Asked 7 years, 4 months ago. Figure 7 shows the transmissibility for a spring-mass-damper system with a fixed damping ratio of 0. Coding Questions. Then you can determine when the ball and club are in contact via the deflections of the springs, i. The force is proportional to the elongation speed of the damper. (2), we next consider a two-degree-of-freedom mass-spring-damper system using the Lagrangian given by L ¼ ect 1 2 m 1x_2 1 k 1x 2 2 þ 1 2 m 2x_2 2 k 2x 2 þ b 1x_ 1x 2 þ b 2x 1x_ 2 þ dx 1x 2 (4) where m i, k i, b i, i ¼ 1;2, and c and d are constants. Session 4: Coupled Mass-Spring-Dampers, Degrees of Freedom (DOF) and Zero-Mass-at-a-DOF. I'll then be inputting it into Simulink. A mass connected to a spring and a damper is displaced and then oscillates in the absence of other forces. Simulink Model of Mass-Spring-Damper System The mass-spring-damper depicted in Figure 1 is modeled by the second-order differential equation where is the force applied to the mass and is the horizontal position of the mass. 5m, we have y(0) = 1 2. they are both compressed when in contact. – Over-damped system ⇒ damping factor is large and system does not oscillate (just exponential decay) x(t)=A 1 e s 1t+A 2 e s 2t where!A 1!and!A 2!are!chosen!to!satisfy!initial!conditions. Output: The peak level response of each mass-spring-damper system is plotted as a function versus the corresponding natural frequencies of the systems. Introduction: The Laplace transform is an integral transformation of a function f (t) from the time domain into the complex frequency domain, F(s). Mass-Spring-Damper System¶ Another commonly used introductory system is the mass-spring-damper system. In: Deng Z. For a long time, TMDs were relegated to areas with the rest of the. Free vibration problem without damping. 3) Choose the PART_2. The script writes the points to the file 'two_springs. This drives J 2, through B r1, but the energy in the system decays over time because energy is lost to the friction. At t = 0, the system is released from. As before, the zero of. Get the characteristic function of damping of the damper, ie, the function describing the motion as it decays. 55 nano-meters than compare to a vehicle has a weight of. qxd 09/20/2001. We can ideally assume that M 1 =M 2 =M. This paper develops this connection for a particular system, namely a bouncing ball, represented by a linear mass-spring-damper model. Spring - absorb, store and spit out the energy(Ideal spring vibrates continuously) Damper - Absorb and dissipates the energy (coupled with a spring to reduce. (2), we next consider a two-degree-of-freedom mass-spring-damper system using the Lagrangian given by L ¼ ect 1 2 m 1x_2 1 k 1x 2 2 þ 1 2 m 2x_2 2 k 2x 2 þ b 1x_ 1x 2 þ b 2x 1x_ 2 þ dx 1x 2 (4) where m i, k i, b i, i ¼ 1;2, and c and d are constants. cm, when it says "Select the first point" on the bottom of the screen. Any help on modeling both the spring and damper would be appreciated. thisoptimal control technique will switched to LQG (Linear Quadratic. a mass-spring system is proposed, which is oversimplified and neglects the delayed reaction and resistance to relative speed. Suppose that the masses are attached to one another, and to two immovable walls, by means of three identical light horizontal springs of spring constant , as shown. This example shows two models of a mass-spring-damper, one using Simulink® input/output blocks and one using Simscape™ physical networks. Matrix Algebra Representing the above two equations in the matrix form, we get 0 6 1 1 1 2 y x The above equation is in the form of AX B. m 2: Mass of truck front axle m a1: 1513 kg: Rolling moment of inertia of front axle I xa1: 2360 kg. Two controllers are proposed: both of them switch the parameters of the system between their nominal values and their negative values. Designing an automotive suspension system is an interesting and challenging control problem. This way the unit threshold for the damping coefficient indicated the onset of oscillation regardless of the mass or elastic constant of the spring. Image: Translational mass with spring and damper The methodology for finding the equation of motion for this is system is described in detail in the tutorial Mechanical systems modeling using Newton’s and D’Alembert equations. 025 kg, M 2 = 0. Thus, it is possible to make a spring-mass-damper system that looks very much like the one in the picture. Consider the mass-spring-damper system in problem 1. Next, copy the range of "B9:E9" all the way down to "B1008:E1008" And we are almost ready to simulate after we display the coordinate x (E8:E1008) function of time t. The system is fitted with a damper with a damping ratio of 0. Determine the value of b if m= 2 kg and k = 200 N/m. Introducing the following notation (4. 1 (a) shows the free vibration of a system with damping. Sana RANNEN. Northwestern Robotics 11,802 views. To answer this question, use the "block substitution" feature of slTuner to create an uncertain closed-loop model of the mass-spring-damper system. Free vibration problem without damping. The spring-mass system is linear. Figure 2: The power amplifier is an Apex PA21 power op-amp in their EK21 evaluation kit. Direct model reference adaptive control with feedforward compensator is designed and implemented on the experimental setup. The mass-spring-dashpot system is the inspiration of the ideal (or standard) 2 nd order transfer function. The following values were used for the simulation: The initial values used were: The patterns for this set of ODE’s are plotted below. 2 extended to the three car system. Consider a simple system with a mass that is separated from a wall by a spring and a dashpot. engr80_august_14_2006. electronic systems in mechatronics, etc. driving frequency for mass-spring-damper system. By Hooke's Law: for x(0) = 0 (valid for small, non-distorting displacements) The spring's equilibrium position is given by x=0. These systems mainly consist of three basic elements. 1) is well represented by a classical spring–mass–damper ODE with two degrees of freedom: u00(t)+k1 u0(t)+k0 u(t) = 0. The mass-spring-damper system is a standard example of a second order system, since it relatively easy to give a physical interpretation of the model parameters of the second order system. A new weighting algorithm called Posterior Possibility Generator (PPG) is proposed to replace PPE algorithm in robust multiple model adaptive control (RMMAC) architecture, resulting in the improved robust multiple model adaptive control (IRMMAC) architecture, and a two-cart mass-spring-damper system with uncertainties is used to illustrate the advantages of PPG against PPE. x ¨ = λ 2 e λ t. Designing an automotive suspension system is an interesting and challenging control problem. The graph shows the effect of a tuned mass damper on a simple spring–mass–damper system, excited by vibrations with an amplitude of one unit of force applied to the main mass,. The nominal response meets the response time requirement and looks good. Tasks Unless otherwise stated, it is assumed that you use the default values of the parameters. The free body diagram of the model for one car system and the forces acting on the one car model with mass =m 1 is shown in Figure 3A and 3B respectively. At Hockenheim, Honda wanted to run a system with one mass damper in the nose and one other in the tank area, but 13 days prior to the race the FIA banned the concept with the argument that it is a moveable aerodynamic device. Direct model reference adaptive control with feedforward compensator is designed and implemented on the experimental setup. Thus, it is possible to make a spring-mass-damper system that looks very much like the one in the picture. For a damped harmonic oscillator with mass m , damping coefficient c , and spring constant k , it can be defined as the ratio of the damping coefficient in the system's differential equation to the critical damping. ) A Coupled Spring-Mass System¶. Figure 1 Double-mass-spring-damper system setup The physical system shown in Figure 1 can be modeled with the diagram shown in Figure 2. If c a = 0, the system is un-damped. From Newton's Second Law, 𝑀𝑎 = ∑ 𝐹, The Displacement Of The Mass From Its Rest Position, 𝑥(𝑡) Satisfies The Following Equation 𝑀 𝑑 2𝑥 𝑑𝑡 2 + 𝑐 𝑑𝑥 𝑑𝑡 + 𝑘𝑥 = 𝐹𝑒(𝑡). This paper models a tripod in 2-D as a torsion spring: https://thecentercolng-of-a-tripod/ You can model the pier and adapter as distributed masses and torsional springs in series, and maybe one big parallel damper for the pier + adapter system. kg k 42 N mm. In simple situations a structure with a connected Tuned Mass Damper (TMD) can be modelled as in the following figure. We are a state of the art research and educational facility involved in theoretical, computational and experimental analysis and design. The transfer function of a Mass-Spring-Damper System. Examination of the analogous mechanical system yields an equivalent damping ratio, which is used to predict the outcome of the drop-pair collision. The output of interest are the positions of the two masses, x 1 and x 2. A mass/spring/damper system drawn in Inkscape by Ilmari Karonen. English: Mass-spring-damper 2 body system, a base subjected to a vibratory displacement, simple model of tuned mass damper model/dynamic vibration absorber Date 5 May 2014, 21:17:57. is the following mass/spring/damper system. - Forces or torques on the two ends of the damper are exactly equal and opposite at all times (just like a spring); pure springs and dampers have no mass or inertia. Calculate the effective mass and effective spring constant at a radius of 12 on the same lever. Problem Specification. • Consider a viscously dddamped two degree of fdfreedom spring‐mass system shown in the figure.
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2020-06-05 07:28:52
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https://3dprinting.stackexchange.com/questions/15467/fixing-temperature-issues-on-i3-mega-where-to-find-spare-part
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# Fixing temperature Issues on I3 Mega / Where to find spare part
I have an old Anycubic i3 Mega printer which started having issues keeping the hotend-temperature. The peak at the start of the diagram was when I was touching the cable on top of the hotend:
It also sometimes disconnects completely with a MINTEMP-Error
So it is fair to assume it might be an issue with the cable/plug to the hotend.
My problem is that I cannot find that cable anywhere on the Anycubic spare parts site. Is this maybe a "standard" cable that I can get anywhere else?
• The end itself looks like it could be a Molex connector. A picture of it unplugged may help identify it. Jan 27, 2021 at 13:53
The plastic looks ok. If you get the tools and pins to work on the connector, you could replace problem pins. Many of us build our own cables. If we verify the connector is Molex, you might need calipers to measure dimensions to get the correct size. You won't need expensive ones. I've seen digital calipers from \$10 to \$20.
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2023-02-07 20:19:21
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https://www.physicsforums.com/threads/simple-question-about-potential-energy-of-two-atom-system.152255/
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Simple question about potential energy of two-atom system
1. Jan 20, 2007
Signifier
1. The problem statement, all variables and given/known data
Two atoms approach each other. One is part of a moving tip (IE like an STM tip), one is part of a fixed surface (so only one atom is moving). The two atoms interact via the Lennard-Jones potential, IE U(r) = $$-A/(r^6) + B/(r^12)$$ where r is the distance between the two atoms. The bottom atom, as said, is fixed; while the top atom can be modeled as if suspended from the end of a spring of stiffness k (IE, this model is used in place of having to calculate the total potential of the system adding all the L-J potentials of all the atoms in the STM tip and the surface).
The question of the problem is, at what distance between the two atoms will instability and occur and the tip "jumps" into contact with the surface?
However, I am not having a problem with that part. I am not quite sure how to construct the potential energy function of this system to begin with! (Note: this problem is from Israelachvili's Intermolecular and Surface Forces, which I've just begun reading).
2. Relevant equations
My real problem here is my utter inability with springs. I know that if the two atoms are separated by a distance r, the L-J potential will be $$-Ar^-6 + Br^-12$$, where the first term is the attractive vdw interaction and the second term is the repulsive electron overlap (at smaller distances). But what is the contribution to system potential due to the spring? Is it $$(1/2)kr^2$$?
3. The attempt at a solution
My attempt is: the potential, U(r) = $$(1/2)kr^2 - A(r^-6) + B(r^-12)$$
This potential btw doesn't return the right numerical values (IE for the distances of instability), so I am doubting it's right. Any help would be great.
2. Jan 22, 2007
Signifier
Still need some help... Anyone?
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2016-12-02 20:12:49
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https://www.aimsciences.org/article/doi/10.3934/ipi.2021025?viewType=html
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American Institute of Mathematical Sciences
doi: 10.3934/ipi.2021025
A note on transmission eigenvalues in electromagnetic scattering theory
1 Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, USA 2 Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
* Corresponding author: jingni.xiao@rutgers.edu
Received October 2020 Revised January 2021 Published March 2021
Fund Project: The author F. Cakoni is supported in part by the AFOSR Grant FA9550-20-1-0024 and NSF Grant DMS-1813492
This short note was motivated by our efforts to investigate whether there exists a half plane free of transmission eigenvalues for Maxwell's equations. This question is related to solvability of the time domain interior transmission problem which plays a fundamental role in the justification of linear sampling and factorization methods with time dependent data. Our original goal was to adapt semiclassical analysis techniques developed in [21,23] to prove that for some combination of electromagnetic parameters, the transmission eigenvalues lie in a strip around the real axis. Unfortunately we failed. To try to understand why, we looked at the particular example of spherically symmetric media, which provided us with some insight on why we couldn't prove the above result. Hence this paper reports our findings on the location of all transmission eigenvalues and the existence of complex transmission eigenvalues for Maxwell's equations for spherically stratified media. We hope that these results can provide reasonable conjectures for general electromagnetic media.
Citation: Fioralba Cakoni, Shixu Meng, Jingni Xiao. A note on transmission eigenvalues in electromagnetic scattering theory. Inverse Problems & Imaging, doi: 10.3934/ipi.2021025
References:
[1] E. Blåsten, H. Liu and J. Xiao, On an electromagnetic problem in a corner and its applications, accepted in Anal. PDE, arXiv: 1901.00581. Google Scholar [2] F. Cakoni and D. Colton, A Qualitative Approach to Inverse Scattering Theory, vol. 188 of Applied Mathematical Sciences, Springer, New York, 2014. doi: 10.1007/978-1-4614-8827-9. Google Scholar [3] F. Cakoni, D. Colton and H. Haddar, Inverse Scattering Theory and Transmission Eigenvalues, vol. 88 of CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2016. doi: 10.1137/1.9781611974461. Google Scholar [4] F. Cakoni, D. Colton and P. Monk, The Linear Sampling Method in Inverse Electromagnetic Scattering, vol. 80 of CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2011. doi: 10.1137/1.9780898719406. Google Scholar [5] F. Cakoni, D. Gintides and H. Haddar, The existence of an infinite discrete set of transmission eigenvalues, SIAM J. Math. Anal., 42 (2010), 237-255. doi: 10.1137/090769338. Google Scholar [6] F. Cakoni and A. Kirsch, On the interior transmission eigenvalue problem, Int. J. Comput. Sci. Math., 3 (2010), 142-167. doi: 10.1504/IJCSM.2010.033932. Google Scholar [7] F. Cakoni, P. Monk and V. Selgas, Analysis of the linear sampling method for imaging penetrable obstacles in the time domain, accepted in Anal. PDE. Google Scholar [8] F. Cakoni and H.-M. Nguyen, On the discreteness of transmission eigenvalues for the Maxwell's equations, SIAM J. Math. Anal., 53 (2021), 888-913. doi: 10.1137/20M1335121. Google Scholar [9] D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, vol. 93 of Applied Mathematical Sciences, 4$^{th}$ edition, Springer, Cham, 2019. doi: 10.1007/978-3-030-30351-8. Google Scholar [10] D. Colton and Y.-J. Leung, Complex eigenvalues and the inverse spectral problem for transmission eigenvalues, Inverse Problems, 29 (2013), 104008, 6 pp. doi: 10.1088/0266-5611/29/10/104008. Google Scholar [11] D. Colton and Y.-J. Leung, The existence of complex transmission eigenvalues for spherically stratified media, Appl. Anal., 96 (2017), 39-47. doi: 10.1080/00036811.2016.1210788. Google Scholar [12] D. Colton, Y.-J. Leung and S. Meng, Distribution of complex transmission eigenvalues for spherically stratified media, Inverse Problems, 31 (2015), 035006, 19 pp. doi: 10.1088/0266-5611/31/3/035006. Google Scholar [13] D. Colton and P. Monk, The inverse scattering problem for time-harmonic acoustic waves in a penetrable medium, Quart. J. Mech. Appl. Math., 40 (1987), 189-212. doi: 10.1093/qjmam/40.2.189. Google Scholar [14] H. Haddar and S. Meng, The spectral analysis of the interior transmission eigenvalue problem for Maxwell's equations, J. Math. Pures Appl., 120 (2018), 1-32. doi: 10.1016/j.matpur.2018.10.004. Google Scholar [15] M. Hitrik, K. Krupchyk, P. Ola and L. Päivärinta, The interior transmission problem and bounds on transmission eigenvalues, Math. Res. Lett., 18 (2011), 279-293. doi: 10.4310/MRL.2011.v18.n2.a7. Google Scholar [16] A. Kirsch, The denseness of the far field patterns for the transmission problem, IMA J. Appl. Math., 37 (1986), 213-225. doi: 10.1093/imamat/37.3.213. Google Scholar [17] A. Kirsch and F. Hettlich, The Mathematical Theory of Time-Harmonic Maxwell's equations, vol. 190 of Applied Mathematical Sciences, Springer, Cham, 2015. doi: 10.1007/978-3-319-11086-8. Google Scholar [18] Y.-J. Leung and D. Colton, Complex transmission eigenvalues for spherically stratified media, Inverse Problems, 28 (2012), 075005, 9 pp. doi: 10.1088/0266-5611/28/7/075005. Google Scholar [19] H.-M. Nguyen and Q.-H. Nguyen, Discreteness of interior transmission eigenvalues revisited, Calc. Var. Partial Differential Equations, 56 (2017), Paper No. 51, 38 pp. doi: 10.1007/s00526-017-1143-7. Google Scholar [20] V. Petkov and G. Vodev, Localization of the interior transmission eigenvalues for a ball, Inverse Probl. Imaging, 11 (2017), 355-372. doi: 10.3934/ipi.2017017. Google Scholar [21] G. Vodev, Transmission eigenvalue-free regions, Comm. Math. Phys., 336 (2015), 1141-1166. doi: 10.1007/s00220-015-2311-2. Google Scholar [22] G. Vodev, Transmission eigenvalues for strictly concave domains, Math. Ann., 366 (2016), 301-336. doi: 10.1007/s00208-015-1329-2. Google Scholar [23] G. Vodev, High-frequency approximation of the interior Dirichlet-to-Neumann map and applications to the transmission eigenvalues, Anal. PDE, 11 (2018), 213-236. doi: 10.2140/apde.2018.11.213. Google Scholar
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References:
[1] E. Blåsten, H. Liu and J. Xiao, On an electromagnetic problem in a corner and its applications, accepted in Anal. PDE, arXiv: 1901.00581. Google Scholar [2] F. Cakoni and D. Colton, A Qualitative Approach to Inverse Scattering Theory, vol. 188 of Applied Mathematical Sciences, Springer, New York, 2014. doi: 10.1007/978-1-4614-8827-9. Google Scholar [3] F. Cakoni, D. Colton and H. Haddar, Inverse Scattering Theory and Transmission Eigenvalues, vol. 88 of CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2016. doi: 10.1137/1.9781611974461. Google Scholar [4] F. Cakoni, D. Colton and P. Monk, The Linear Sampling Method in Inverse Electromagnetic Scattering, vol. 80 of CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2011. doi: 10.1137/1.9780898719406. Google Scholar [5] F. Cakoni, D. Gintides and H. Haddar, The existence of an infinite discrete set of transmission eigenvalues, SIAM J. Math. Anal., 42 (2010), 237-255. doi: 10.1137/090769338. Google Scholar [6] F. Cakoni and A. Kirsch, On the interior transmission eigenvalue problem, Int. J. Comput. Sci. Math., 3 (2010), 142-167. doi: 10.1504/IJCSM.2010.033932. Google Scholar [7] F. Cakoni, P. Monk and V. Selgas, Analysis of the linear sampling method for imaging penetrable obstacles in the time domain, accepted in Anal. PDE. Google Scholar [8] F. Cakoni and H.-M. Nguyen, On the discreteness of transmission eigenvalues for the Maxwell's equations, SIAM J. Math. Anal., 53 (2021), 888-913. doi: 10.1137/20M1335121. Google Scholar [9] D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, vol. 93 of Applied Mathematical Sciences, 4$^{th}$ edition, Springer, Cham, 2019. doi: 10.1007/978-3-030-30351-8. Google Scholar [10] D. Colton and Y.-J. Leung, Complex eigenvalues and the inverse spectral problem for transmission eigenvalues, Inverse Problems, 29 (2013), 104008, 6 pp. doi: 10.1088/0266-5611/29/10/104008. Google Scholar [11] D. Colton and Y.-J. Leung, The existence of complex transmission eigenvalues for spherically stratified media, Appl. Anal., 96 (2017), 39-47. doi: 10.1080/00036811.2016.1210788. Google Scholar [12] D. Colton, Y.-J. Leung and S. Meng, Distribution of complex transmission eigenvalues for spherically stratified media, Inverse Problems, 31 (2015), 035006, 19 pp. doi: 10.1088/0266-5611/31/3/035006. Google Scholar [13] D. Colton and P. Monk, The inverse scattering problem for time-harmonic acoustic waves in a penetrable medium, Quart. J. Mech. Appl. Math., 40 (1987), 189-212. doi: 10.1093/qjmam/40.2.189. Google Scholar [14] H. Haddar and S. Meng, The spectral analysis of the interior transmission eigenvalue problem for Maxwell's equations, J. Math. Pures Appl., 120 (2018), 1-32. doi: 10.1016/j.matpur.2018.10.004. Google Scholar [15] M. Hitrik, K. Krupchyk, P. Ola and L. Päivärinta, The interior transmission problem and bounds on transmission eigenvalues, Math. Res. Lett., 18 (2011), 279-293. doi: 10.4310/MRL.2011.v18.n2.a7. Google Scholar [16] A. Kirsch, The denseness of the far field patterns for the transmission problem, IMA J. Appl. Math., 37 (1986), 213-225. doi: 10.1093/imamat/37.3.213. Google Scholar [17] A. Kirsch and F. Hettlich, The Mathematical Theory of Time-Harmonic Maxwell's equations, vol. 190 of Applied Mathematical Sciences, Springer, Cham, 2015. doi: 10.1007/978-3-319-11086-8. Google Scholar [18] Y.-J. Leung and D. Colton, Complex transmission eigenvalues for spherically stratified media, Inverse Problems, 28 (2012), 075005, 9 pp. doi: 10.1088/0266-5611/28/7/075005. Google Scholar [19] H.-M. Nguyen and Q.-H. Nguyen, Discreteness of interior transmission eigenvalues revisited, Calc. Var. Partial Differential Equations, 56 (2017), Paper No. 51, 38 pp. doi: 10.1007/s00526-017-1143-7. Google Scholar [20] V. Petkov and G. Vodev, Localization of the interior transmission eigenvalues for a ball, Inverse Probl. Imaging, 11 (2017), 355-372. doi: 10.3934/ipi.2017017. Google Scholar [21] G. Vodev, Transmission eigenvalue-free regions, Comm. Math. Phys., 336 (2015), 1141-1166. doi: 10.1007/s00220-015-2311-2. Google Scholar [22] G. Vodev, Transmission eigenvalues for strictly concave domains, Math. Ann., 366 (2016), 301-336. doi: 10.1007/s00208-015-1329-2. Google Scholar [23] G. Vodev, High-frequency approximation of the interior Dirichlet-to-Neumann map and applications to the transmission eigenvalues, Anal. PDE, 11 (2018), 213-236. doi: 10.2140/apde.2018.11.213. Google Scholar
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2019 Impact Factor: 1.373
Article outline
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2021-04-20 08:23:59
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https://stats.stackexchange.com/questions/393254/help-with-pca-question
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# Help with PCA Question
The conventional model for probabilistic principal component analysis has a standard normal latent $$\vec{y}$$ and a loading matrix $$\Lambda$$:
$$P(\vec{y}) \sim N(\vec{0}, I)$$, $$P(\vec{x}|\vec{y}) \sim N(\Lambda \vec{y}, \psi I)$$
An alternative would be to draw $$\vec{y}$$ from a normal with diagonal covariance (say $$\Sigma$$, and then restrict $$\Lambda$$ to have orthonormal columns:
$$P(\vec{y}) \sim N(\vec{0}, \Gamma), P(\vec{x}|\vec{y}) \sim N(\Lambda \vec{y}, \psi I)$$ with $$\Gamma_{ij}=0$$ for $$i \neq j$$ and $$\Lambda^T \Lambda = I$$
where $$\Gamma_{ij} =\Gamma_{ji} =0$$ and $$\Lambda^T \Lambda=0$$.
Question: Show that this alternative model is equivalent to the standard one in the sense that it can model exactly the same set of possible marginal distributions.
I really have no idea what I am being asked to do here. I know that there is some equivalence of PCA models under rotation and scaling - should I be working in that direction, or am I supposed to integrate out the latent variable and show I get the same distribution? Or something else entirely? Help please.
lead to exactly the same marginal distributions.
Here are some hints. I will rename $$\Lambda$$ in the first model to $$A$$ to avoid confusion with the one that is to have orthonormal columns.
As you seem to have deduced, the distributions we get for $$x$$ are $$N(0,\psi I + \Lambda \Gamma \Lambda^T)$$ in one model and $$N(0,\psi I + AA^T)$$ in the other model.
Therefore, it suffices to show that matrices of the form $$\Lambda \Gamma \Lambda^T$$ (with $$\Lambda$$ having orthonormal columns and $$\Gamma$$ diagonal) and $$AA^T$$ are equivalent (either can be written in the other's form).
To help show that $$\Lambda \Gamma \Lambda^T$$ can be written as $$AA^T$$, utilise the square root of $$\Gamma$$. To help show that $$AA^T$$ can be written as $$\Lambda \Gamma \Lambda^T$$, utilise the spectral theorem and drop eigenvectors corresponding to $$0$$ eigenvalues (and drop these eigenvalues from the diagonal matrix from the spectral theorem).
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2019-10-23 23:21:07
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https://www.physicsforums.com/threads/estimate-for-root-mean-square-uncertainty.776021/
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# Estimate for root-mean-square uncertainty
1. Oct 13, 2014
### terp.asessed
1. The problem statement, all variables and given/known data
In classical mechanism, the lowest possible energy accessible to any system is the minimum potential energy, in this case 0. However, quantum mechanically, one finds that there is a zero-point energy (where ground state energy > classical minimum). Fundamentally, zero-point energy comes from the uncertainty principle, so it is possible to estimate for root-mean square uncertainty in position, by looking at the range of x allowed classically for a given energy. Remember that in the classical mechanics, the total energy is given by:
E = p2/(2mu) + V(x)
so that V(x) > E. Therefore, sketch a a graph of potential energy as a function of x. Estimate root-mean square uncertainty as a function of Energy (E), mu and w.
2. Relevant equations
E = p2/(2mu) + V(x)
3. The attempt at a solution
I drew a graph, V(x) vs. x, and drew a line (Energy) horizontally through the curve, for V(x) = mu*w2x2/2. There are TWO intersecting points where V(x) meets Energy lines--which I set as boundaries. However, I am stuck as how to move from here....any suggestion would be welcome....I've been thinking about using root-mean square2 = <x2> - <x>2, but the question wants ESTIMATE of root-mean-square by LOOKING at the range.....
2. Oct 15, 2014
### vela
Staff Emeritus
You found the turning points. Classically, the particle is confined to the region between those two points. How long is that region? That's what you use as an estimate for $\Delta x$.
3. Oct 15, 2014
Gotcha!
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2018-03-24 20:36:46
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https://en-academic.com/dic.nsf/enwiki/6332524
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# Colinear map
Colinear map
In coalgebra theory, the notion of colinear map is dual to the notion for linear map of vector space, or more generally, for morphism between R-module. Specifically, let R be a ring, M,N,C be R-modules, and
$\rho_M: M\rightarrow M\otimes C, \rho_N: N\rightarrow N\otimes C$
be right C-comodules. Then an R-linear map $f:M\rightarrow N$ is called a (right) comodule morphism, or (right) C-colinear, if
$\rho_N \circ f = (f \otimes 1) \circ \rho_M$
## References
• Khaled AL-Takhman, Equivalences of Comodule Categories for Coalgebras over Rings, J. Pure Appl. Algebra,.V. 173, Issue: 3, September 7, 2002, pp. 245–271
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2022-11-29 20:52:53
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https://bookdown.org/frederick_peck/textbook_-_2021_f/review-activity-gender-coding-and-expectations.html
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## 3.11 Review activity: Gender coding and expectations
In what ways do gender-based expectations influence judgements?
In a research study, 142 participants were given a hypothetical scenario in which a hurricane was moving towards their home, and a voluntary evacuation order had been issued. Participants were randomly assigned to two conditions. In one condition, the name of the hurricane was male-coded as “Christopher” and in the other condition, the name of the hurricane was female-coded as “Christina.” Otherwise, all other stimuli were equal.
The participants were asked to rate the severity of the hurricane on a 1-7 scale, with higher numbers indicating a more severe hurricane.
In this activity, we’ll explore the research question,
Does gender-coding of hurricane names affect people’s perception of severity?
To access the activty
Log in to your class in Desmos. Find the activty called,
3.11: Gendered judgements
Resources
Resources for this activity will be posted soon
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2022-05-22 01:42:26
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http://compaland.com/standard-error/what-is-statistical-standard-error.html
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## Repair What Is Statistical Standard Error (Solved)
Home > Standard Error > What Is Statistical Standard Error
# What Is Statistical Standard Error
## Contents
Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view Stat Trek Teach yourself statistics Skip to main content Home Tutorials AP Statistics Stat Tables Stat Tools Calculators Books In fact, even with non-parametric correlation coefficients (i.e., effect size statistics), a rough estimate of the interval in which the population effect size will fall can be estimated through the same It states that regardless of the shape of the parent population, the sampling distribution of means derived from a large number of random samples drawn from that parent population will exhibit The data set is ageAtMar, also from the R package openintro from the textbook by Dietz et al.[4] For the purpose of this example, the 5,534 women are the entire population navigate here
The true standard error of the mean, using σ = 9.27, is σ x ¯ = σ n = 9.27 16 = 2.32 {\displaystyle \sigma _{\bar {x}}\ ={\frac {\sigma }{\sqrt The standard deviation of the age for the 16 runners is 10.23, which is somewhat greater than the true population standard deviation σ = 9.27 years. The answer to the question about the importance of the result is found by using the standard error to calculate the confidence interval about the statistic. But how accurate is this?
## Standard Error Example
Thus 68% of all sample means will be within one standard error of the population mean (and 95% within two standard errors). The standard deviation is used to help determine validity of the data based the number of data points displayed within each level of standard deviation. Retrieved 17 July 2014. That is, of the dispersion of means of samples if a large number of different samples had been drawn from the population. Standard error of the mean The standard error
It is, however, an important indicator of how reliable an estimate of the population parameter the sample statistic is. It represents the standard deviation of the mean within a dataset. The notation for standard error can be any one of SE, SEM (for standard error of measurement or mean), or SE. Standard Error Excel For the age at first marriage, the population mean age is 23.44, and the population standard deviation is 4.72.
For example, the effect size statistic for ANOVA is the Eta-square. If one survey has a standard error of $10,000 and the other has a standard error of$5,000, then the relative standard errors are 20% and 10% respectively. The standard error of the mean can provide a rough estimate of the interval in which the population mean is likely to fall. Check This Out The phrase "the standard error" is a bit ambiguous.
That in turn should lead the researcher to question whether the bedsores were developed as a function of some other condition rather than as a function of having heart surgery that Standard Error Symbol Skip to main contentSubjectsMath by subjectEarly mathArithmeticAlgebraGeometryTrigonometryStatistics & probabilityCalculusDifferential equationsLinear algebraMath for fun and gloryMath by gradeK–2nd3rd4th5th6th7th8thHigh schoolScience & engineeringPhysicsChemistryOrganic chemistryBiologyHealth & medicineElectrical engineeringCosmology & astronomyComputingComputer programmingComputer scienceHour of CodeComputer animationArts That statistic is the effect size of the association tested by the statistic. Upper Saddle River, New Jersey: Pearson-Prentice Hall, 2006. 3. Standard error.
## Standard Error Vs Standard Deviation
RosenthalList Price: $33.00Buy Used:$19.98Buy New: \$29.70 About Us Contact Us Privacy Terms of Use Resources Advertising The contents of this webpage are copyright © 2016 StatTrek.com. http://www.investopedia.com/terms/s/standard-error.asp In statistics, a sample mean deviates from the actual mean of a population; this deviation is the standard error. Standard Error Example In this scenario, the 2000 voters are a sample from all the actual voters. Standard Error Regression However, if the sample size is very large, for example, sample sizes greater than 1,000, then virtually any statistical result calculated on that sample will be statistically significant.
Repeating the sampling procedure as for the Cherry Blossom runners, take 20,000 samples of size n=16 from the age at first marriage population. check over here The distribution of these 20,000 sample means indicate how far the mean of a sample may be from the true population mean. However, a correlation that small is not clinically or scientifically significant. III. Difference Between Standard Error And Standard Deviation
It is the variance -- the SD squared -- that doesn't change predictably, but the change in SD is trivial and much much smaller than the change in the SEM.)Note that Naturally, the value of a statistic may vary from one sample to the next. The 95% confidence interval for the average effect of the drug is that it lowers cholesterol by 18 to 22 units. his comment is here The next graph shows the sampling distribution of the mean (the distribution of the 20,000 sample means) superimposed on the distribution of ages for the 9,732 women.
The confidence interval of 18 to 22 is a quantitative measure of the uncertainty – the possible difference between the true average effect of the drug and the estimate of 20mg/dL. Standard Error Of Proportion The standard deviation is used to help determine validity of the data based the number of data points displayed within each level of standard deviation. Statistic Standard Deviation Sample mean, x σx = σ / sqrt( n ) Sample proportion, p σp = sqrt [ P(1 - P) / n ] Difference between means, x1 -
## In that case, the statistic provides no information about the location of the population parameter.
The mean of all possible sample means is equal to the population mean. The two concepts would appear to be very similar. Standard error: meaning and interpretation. Standard Error Of The Mean Definition For the purpose of hypothesis testing or estimating confidence intervals, the standard error is primarily of use when the sampling distribution is normally distributed, or approximately normally distributed.
Specifically, it is calculated using the following formula: Where Y is a score in the sample and Y’ is a predicted score. Journal of the Royal Statistical Society. Because of random variation in sampling, the proportion or mean calculated using the sample will usually differ from the true proportion or mean in the entire population. weblink For example, the sample mean is the usual estimator of a population mean.
JSTOR2682923. ^ Sokal and Rohlf (1981) Biometry: Principles and Practice of Statistics in Biological Research , 2nd ed. Two data sets will be helpful to illustrate the concept of a sampling distribution and its use to calculate the standard error. mean, or more simply as SEM. This is important because the concept of sampling distributions forms the theoretical foundation for the mathematics that allows researchers to draw inferences about populations from samples.
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2017-04-28 04:24:17
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http://codefined.xyz/blog/archive/bitmap-graphics
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Images are displayed on a computer monitor as bitmaps. A bitmap is a grid of pixels. The pixels may be represented using different numbers of bits which correspond to the number of colours present in the available range.
For example: If 1 bit is used to represent the colour of a pixel, it can have 2 values - black and white (colours may vary from monitor to monitor). This is properly described as a monochrome although monochrome is usually used to describe a grey scale picture.
#### Grey scale
Uses 8 bits to give 256 colours of grey, from black (0) to white (255)
#### Colour
Normally uses 24 bits to represent levels of red, green and blue: $\color{red}{\overset{11111111}{\mathsf{Red}}}\ \ \color{green}{\overset{11111111}{\mathsf{Green}}}\ \ \color{Blue}{\overset{11111111}{\mathsf{Blue}}}$ These values are often represented as decimal or hex values such as 255,0,255 or #FF00FF. 24 bit colour allows for up to $256\times256\times256$. ie $16,777,216$ different colours. The number of bits used to represent colours in bit maps are called the bit depth.
Note about printing Computer displays use (effectively) coloured lights to produce an image. 24-bit colour displays use RGB to represent as many colours as possible. Printers usually use 4 colours: Cyan, Magenta, Yellow and black. Accurate conversion from RGB to CMYK is difficult to achieve
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2018-08-16 19:31:40
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http://tex.stackexchange.com/questions/32666/is-this-branching-code-i-wrote-a-bit-obfuscated/32738
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# Is this branching code I wrote a bit obfuscated?
I've been away for a while and I forget if this sort of question is appropriate, but here goes. Recently I wrote some code (in expl3 but I hope it's clear enough) and in hindsight I wonder on its style. Some comments after the snippet (slightly adapted from unicode-math):
\cs_new:Nn \um_if_char_spec:nNNT
{
% case 1:
\seq_if_in:NnT \l_um_mclass_range_seq {#3} { \use_none_delimit_by_q_nil:w }
% case 2:
\seq_if_in:NnT \l_um_cmd_range_seq {#2} { \use_none_delimit_by_q_nil:w }
% case 3:
\seq_map_inline:Nn \l_um_char_range_seq
{
\um_int_if_slot_in_range:nnT {#1} {##1}
{ \seq_map_break:n { \use_none_delimit_by_q_nil:w } }
}
% this executes if no match was found:
\use_none:nnn
\q_nil
\use:n
{
\clist_put_right:Nx \l_um_char_num_range_clist { \int_eval:n {#1} }
#4
}
}
The idea is that three possibilities can cause a match and execute some additional "true" code. Checking for these matches can be time-consuming so any true occurrence should immediately jump to the end. This is done by \use_none_delimit_by_q_nil:w which skips ahead to the \q_nil token and ignores everything in its way. At which point it executes the "true" code.
This could normally be done with a set of nested conditionals like so:
iftrue-(code)-else-(iftrue-(code)-else-(iftrue-(code))))
but I guess I didn't want to write out the (code) section several times — it seemed inelegant and error-prone. So what do you think? Is this code ugly? How would you write it?
-
I believe latex3 will be awarded the lifetime award for the most obfuscated programming language that is in real use. – topskip Oct 25 '11 at 17:46
@Will: you didn't really explain what the code is meant to do (see comments below Yiannis' answer), and I had to gather some info from the unicode-math package. – Bruno Le Floch Oct 26 '11 at 11:24
@Patrick: true. I teach my students to write C++ code such that all function names and variable are self understandable, so that one can understand the code by just reading it. I fail to understand expl3 code by just reading it. And thus I personally do not consider to learn it. – Matthias Pospiech Oct 26 '11 at 11:49
@BrunoLeFloch — you're right, sorry for the unclear question. Serves me right for asking a question late at night. – Will Robertson Nov 1 '11 at 0:19
@MatthiasPospiech — I don't mean to sound rude but it doesn't sound like you've done much reading of how expl3 is designed. The variables and functions are written to be understandable (they follow a strict naming structure), but you have to know some of the background of expl3 and to be fair this code snippet is completely out of context! I was only asking about code structure, not naming. In hindsight, I should have written a simpler example to do this. – Will Robertson Nov 1 '11 at 0:30
I am not sure what would be the cleanest way to code this, but here is a proposal. As you say, the fourth argument is the "true code". This points me towards conditionals. However, you prefer avoiding to nest conditionals. For that, we need a way to jump over tokens until the end-marker, where we return either true or false.
\RequirePackage{expl3}
\ExplSyntaxOn
\cs_new_protected:Npn \um_if_char_spec:nNNT #1#2#3#4
{
\um_if_char_spec_aux:nNNT {#1} #2 #3
{
\clist_put_right:Nx \l_um_char_num_range_clist { \int_eval:n {#1} }
#4
}
}
\cs_new:Npn \um_break_true: #1 \um_break_point: { \prg_return_true: }
\cs_new:Npn \um_break_false: #1 \um_break_point: { \prg_return_false: }
\prg_new_protected_conditional:Nnn \um_if_char_spec_aux:nNN { T }
{
% case 1:
\seq_if_in:NnT \l_um_mclass_range_seq {#3} { \um_break_true: }
% case 2:
\seq_if_in:NnT \l_um_cmd_range_seq {#2} { \um_break_true: }
% case 3:
\seq_map_inline:Nn \l_um_char_range_seq
{
\um_int_if_slot_in_range:nnT {#1} {##1}
{ \seq_map_break:n { \um_break_true: } }
}
% else:
\um_break_false:
\um_break_point:
}
Instead of having a custom "break_point" marker, we could simply use \q_nil as you did, and define
\cs_new:Npn \um_break_true: { \use_i_delimit_by_q_nil:nw { \prg_return_true: } }
\cs_new:Npn \um_break_false: { \use_i_delimit_by_q_nil:nw { \prg_return_false: } }
EDIT: after looking into the code of unicode-math, I am of the opinion that many of the sequences you work with could better be implemented as token lists. Namely, a sequence whose items are all single tokens, and for which the main operation you care about is \seq_if_in:NnTF, should be a token list: the search operation is then much faster, although mapping becomes a tad slower.
Given that the second and third arguments of \um_if_char_spec:nNNT are N-type arguments (see signature), I presume that \l_um_mclass_range_seq and \l_um_cmd_range_seq can be implemented as lists of single tokens. [I also note that elsewhere in the package you've been a little bit sloppy about N versus n arguments, feeding braced arguments to an N-type argument.]
-
This is a nice way to improve the syntax of the conditionals block. (Although for a once-off I'm still not sure if four-vs-one macro improves things...) thanks for your additional comments — some of this code is pretty old and needs revising; the n/N thing may well have been a search/replace typo. – Will Robertson Nov 1 '11 at 0:42
@Will I think that it is not worth defining four macros in unicode-math, but perhaps something to add to the kernel. I'll open a github issue. – Bruno Le Floch Nov 2 '11 at 15:19
Actually, there is already a similar issue that I didn't get time to resolve (converting all the various \..._break: to \prg_break. – Bruno Le Floch Nov 2 '11 at 15:30
Yes
-
If it wasn't for the additional comment in the answer, this would be the shortest, upvoted answer to date. Beating this one by 11 characters. :) See the chat transcript by @PauloCereda. – Werner Oct 25 '11 at 17:56
@Werner: Ah, but that's in a <sub><sup> so you have to quarter the character count, making it 12 characters in total (do punctuation and spaces count?). (More seriously, I thought it possible it might get mistaken for facetiousness if I didn't put that in.) – Loop Space Oct 25 '11 at 18:07
@Andrew: now that the comments clarify what you meant, you can edit your answer to remove the comment. It could then end up with more votes than characters. – Bruno Le Floch Oct 25 '11 at 21:35
Gosh, that was actually hard. An edited answer has to have at least 30 characters in the body. – Loop Space Oct 26 '11 at 8:28
Thanks for the insight :-) – Will Robertson Nov 1 '11 at 0:17
Yes.
Consider the problem of determining if letters a, b, c, are in either the Greek or the Latin or French alphabets. Using your suggested solution you will need to code 74 case statements.
Use lists, join the sequences and have only one test.
\documentclass{book}
\usepackage{lipsum,graphicx}
\begin{document}
\makeatletter
\def\IfIn#1#2{%
\def\check##1{%
\newif\ifin@
\in@{##1}{#2}
\ifin@ True Action
\else
False Action
\fi}
\@for \i:=#1\do{%
\expandafter\check\i%
}}
\IfIn{a,b,c,\delta,\gamma,}{a,b,c,d,\beta,\delta}
\makeatother
\end{document}
As to the notation, what is true in maths is true for code and I will quote Halmos.
Whenever it is possible to avoid the use of a complicated alphabetic apparatus, avoid it.
I personally think that the LaTeX3 Team is doing a great job, but I find it difficult to follow notation such as \um_if_char_spec_aux:nNNT. All I can say is that beautiful Pascal married TeX, but their children are ugly!
-
It's really just the Hungarian notation. LaTeX 3 wants to have types, but it can't. Actually, this is the best argument I've seen for Hungarian notation, since in a language with types, the compiler can help you out a bit. Here, only the notation gives a clue. – Ryan Reich Oct 26 '11 at 1:23
@RyanReich Sure, but when names are sufficiently descriptive the additional type information can be redundant. Consider firstName with sFirstName or \seq_if_in with in where usage and type are obvious. Brains need grammar, read this aloud: \um_if_char_spec_aux and \if_char_spec_aux the latter is more understandable. – Yiannis Lazarides Oct 26 '11 at 1:55
@Yiannis you should probably be using \in@{,#1,}{,a,b,...,\gamma,} if the items can be longer than one token, or use \in@{#1}{ab...\gamma} if there is only ever going to be one token per item. In fact, \seq_if_in:NnT does something completely different from \in@. It expects a sequence, which is not a general list of tokens: it is closer to Knuth's \\{...}\\{...} lists, and that allows arbitrary items. Good or bad, it depends. – Bruno Le Floch Oct 26 '11 at 2:56
Sorry for a double comment, I realized that when editing my answer. What Will is doing here is testing if #2 is in one sequence, or if #3 is in another sequence, so I don't see how relevant your example is here. Analog would be "is #1 in the Greek alphabet or #2 in the Latin alphabet". The LaTeX3 code for what you wrote is \tl_if_in:nnTF {abc\alpha\beta\gamma}{#1}{True action}{False action}. Not much longer. – Bruno Le Floch Oct 26 '11 at 3:18
@Yiannis I don't see how "Your code is obfuscated, here's some code to do something else." is a useful answer. Besides, your first statement is wrong. Using Will's approach to your problem is three statements, \seq_if_in:Nn \l_alphabets_seq { a }, \seq_if_in:Nn \l_alphabets_seq { b }, and \seq_if_in:Nn \l_alphabets_seq { c }, not 74. – Bruno Le Floch Oct 26 '11 at 13:07
If it's opinion you want (in answer to your first question), here's one...
From a programming point of view, I think there is little difference in coding it using jump rather than nesting ifs. The executing times should be comparable. However, since I'm unfamiliar with expl3 code, I am not sure how \use_none_delimit_by_q_nil:w works. If it has to scan tokens until it finds \q_nil then it probably is not a true "jump" and might therefore be slower than to use a macro definition for code (which is more "jump"-ish in nature). If code is compact, then scanning over its should not be a big deal.
I guess my general opinion would be summarized based on the size/span of code. If code is large, then put it in a macro do condense the look and improve readability of your code. If code is small, then included it as-is.
That's probably about 1.5c's worth of input
-
I can confirm that using jump or nested conditionals is the same performance-wise here. \use_none_delimit_by_q_nil:w is defined as \long macro:#1\q_nil ->, so that's just as quick as any other macro parameter grabbing. – Bruno Le Floch Oct 25 '11 at 17:44
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2015-04-18 23:46:02
|
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https://www.jaredlander.com/page/2/
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### The costs involved with a health insurance plan can be confusing so I perform an analysis of different options to find which plan is most cost effective
My wife and I recently brought a new R programmer into our family so we had to update our health insurance. Becky is a researcher in neuroscience and psychology at NYU so we decided to choose an NYU insurance plan.
For families there are two main plans: Value and Advantage. The primary differences between the plans are the following:
Item Explanation Value Plan Amount Advantage Plan Amount
Bi-Weekly Premiums The amount we pay every other week in order to have insurance $160 ($4,160 annually) $240 ($6,240 annually)
Deductible Amount we pay directly to health providers before the insurance starts covering costs $1,000$800
Coinsurance After the deductible is met, we pay this percentage of medical bills 20% 10%
Out-of-Pocket Maximum This is the most we will have to pay to health providers in a year (premiums do not count toward this max) $6,000$5,000
We put them into a tibble for use later.
# use tribble() to make a quick and dirty tibble
parameters <- tibble::tribble(
'Value', 160*26, 1000, 0.2, 6000,
)
Other than these cost differences, there is not any particular benefit of either plan over the other. That means whichever plan is cheaper is the best to choose.
This blog post walks through the steps of evaluating the plans to figure out which to select. Code is included so anyone can repeat, and improve on, the analysis for their given situation.
# Cost
In order to figure out which plan to select we need to figure out the all-in cost, which is a function of how much we spend on healthcare in a year (we have to estimate our annual spending) and the aforementioned premiums, deductible, coinsurance and out-of-pocket maximum.
$\text{cost} = f(\text{spend}; \text{premiums}, \text{deductible}, \text{coinsurance}, \text{oop_maximum}) = \\ \text{min}(\text{oop_maximum}, \text{deductible} + \text{coinsurance}*(\text{spend}-\text{deductible}))+\text{premiums}$
This can be written as an R function like this.
#' @title cost
#' @description Given healthcare spend and other parameters, calculate the actual cost to the user
#' @details Uses the formula above to caluclate total costs given a certain level of spending. This is the premiums plus either the out-of-pocket maximum, the actual spend level if the deductible has not been met, or the amount of the deductible plus the coinsurance for spend above the deductible but below the out-of-pocket maximum.
#' @author Jared P. Lander
#' @param spend A given amount of healthcare spending as a vector for multiple amounts
#' @param deductible The deductible for a given plan
#' @param coinsurance The coinsurance percentage for spend beyond the deductible but below the out-of-pocket maximum
#' @param oop_maximum The maximum amount of money (not including premiums) that the insured will pay under a given plan
#' @return The total cost to the insured
#' @examples
#' cost(3000, 4160, 1000, .20, 6000)
#' cost(3000, 6240, 800, .10, 5000)
#'
cost <- function(spend, premiums, deductible, coinsurance, oop_maximum)
{
# spend is vectorized so we use pmin to get the min between oop_maximum and (deductible + coinsurance*(spend - deductible)) for each value of spend provided
pmin(
# we can never pay more than oop_maximum so that is one side
oop_maximum,
# if we are under oop_maximum for a given amount of spend,
# this is the cost
pmin(spend, deductible) + coinsurance*pmax(spend - deductible, 0)
) +
}
With this function we can see if one plan is always, or mostly, cheaper than the other plan and that’s the one we would choose.
# R Packages
For the rest of the code we need these R packages.
library(dplyr)
library(ggplot2)
library(tidyr)
library(formattable)
library(readxl)
# Spending
To see our out-of-pocket cost at varying levels of healthcare spend we build a grid in $1,000 increments from$1,000 to $70,000. spending <- tibble::tibble(Spend=seq(1000, 70000, by=1000)) We call our cost function on each amount of spend for the Value and Advantage plans. spending <- spending %>% # use our function to calcuate the cost for the value plan mutate(Value=cost( spend=Spend, premiums=parameters$Premiums[1],
deductible=parameters$Deductible[1], coinsurance=parameters$Coinsurance[1],
oop_maximum=parameters$OOP_Maximum[1] ) ) %>% # use our function to calcuate the cost for the Advantage plan mutate(Advantage=cost( spend=Spend, premiums=parameters$Premiums[2],
deductible=parameters$Deductible[2], coinsurance=parameters$Coinsurance[2],
oop_maximum=parameters$OOP_Maximum[2] ) ) %>% # compute the difference in costs for each plan mutate(Difference=Advantage-Value) %>% # the winner for a given amount of spend is the cheaper plan mutate(Winner=if_else(Advantage < Value, 'Advantage', 'Value')) The results are in the following table, showing every other row to save space. The Spend column is a theoretical amount of spending with a red bar giving a visual sense for the increasing amounts. The Value and Advantage columns are the corresponding overall costs of the plans for the given amount of Spend. The Difference column is the result of AdvantageValue where positive numbers in blue mean that the Value plan is cheaper while negative numbers in red mean that the Advantage plan is cheaper. This is further indicated in the Winner column which has the corresponding colors. Spend Value Advantage Difference Winner$2,000 $5,360$7,160 1800 Value
$4,000$5,760 $7,360 1600 Value$6,000 $6,160$7,560 1400 Value
$8,000$6,560 $7,760 1200 Value$10,000 $6,960$7,960 1000 Value
$12,000$7,360 $8,160 800 Value$14,000 $7,760$8,360 600 Value
$16,000$8,160 $8,560 400 Value$18,000 $8,560$8,760 200 Value
$20,000$8,960 $8,960 0 Value$22,000 $9,360$9,160 -200 Advantage
$24,000$9,760 $9,360 -400 Advantage$26,000 $10,160$9,560 -600 Advantage
$28,000$10,160 $9,760 -400 Advantage$30,000 $10,160$9,960 -200 Advantage
$32,000$10,160 $10,160 0 Value$34,000 $10,160$10,360 200 Value
$36,000$10,160 $10,560 400 Value$38,000 $10,160$10,760 600 Value
$40,000$10,160 $10,960 800 Value$42,000 $10,160$11,160 1000 Value
$44,000$10,160 $11,240 1080 Value$46,000 $10,160$11,240 1080 Value
$48,000$10,160 $11,240 1080 Value$50,000 $10,160$11,240 1080 Value
$52,000$10,160 $11,240 1080 Value$54,000 $10,160$11,240 1080 Value
$56,000$10,160 $11,240 1080 Value$58,000 $10,160$11,240 1080 Value
$60,000$10,160 $11,240 1080 Value$62,000 $10,160$11,240 1080 Value
$64,000$10,160 $11,240 1080 Value$66,000 $10,160$11,240 1080 Value
$68,000$10,160 $11,240 1080 Value$70,000 $10,160$11,240 1080 Value
Of course, plotting often makes it easier to see what is happening.
spending %>%
# put the plot in longer format so ggplot can set the colors
gather(key=Plan, value=Cost, -Spend) %>%
ggplot(aes(x=Spend, y=Cost, color=Plan)) +
geom_line(size=1) +
scale_x_continuous(labels=scales::dollar) +
scale_y_continuous(labels=scales::dollar) +
scale_color_brewer(type='qual', palette='Set1') +
labs(x='Healthcare Spending', y='Out-of-Pocket Costs') +
theme(
legend.position='top',
axis.title=element_text(face='bold')
)
It looks like there is only a small window where the Advantage plan is cheaper than the Value plan. This will be more obvious if we draw a plot of the difference in cost.
spending %>%
ggplot(aes(x=Spend, y=Difference, color=Winner, group=1)) +
geom_hline(yintercept=0, linetype=2, color='grey50') +
geom_line(size=1) +
scale_x_continuous(labels=scales::dollar) +
scale_y_continuous(labels=scales::dollar) +
labs(
x='Healthcare Spending',
y='Difference in Out-of-Pocket Costs Between the Two Plans'
) +
scale_color_brewer(type='qual', palette='Set1') +
theme(
legend.position='top',
axis.title=element_text(face='bold')
)
To calculate the exact cutoff points where one plan becomes cheaper than the other plan we have to solve for where the two curves intersect. Due to the out-of-pocket maximums the curves are non-linear so we need to consider four cases.
1. The spending exceeds the point of maximum out-of-pocket spend for both plans
2. The spending does not exceed the point of maximum out-of-pocket spend for either plan
3. The spending exceeds the point of maximum out-of-pocket spend for the Value plan but not the Advantage plan
4. The spending exceeds the point of maximum out-of-pocket spend for the Advantage plan but not the Value plan
When the spending exceeds the point of maximum out-of-pocket spend for both plans the curves are parallel so there will be no cross over point.
When the spending does not exceed the point of maximum out-of-pocket spend for either plan we set the cost calculations (not including the out-of-pocket maximum) for each plan equal to each other and solve for the amount of spend that creates the equality.
To keep the equations smaller we use variables such as $$d_v$$ for the Value plan deductible, $$c_a$$ for the Advantage plan coinsurance and $$oop_v$$ for the out-of-pocket maximum for the Value plan.
$d_v + c_v(S – d_v) + p_v = d_a + c_a(S – d_a) + p_a \\ c_v(S – D_v) – c_a(S-d_a) = d_a – d_v + p_a – p_v \\ c_vS – c_vd_v – c_aS + c_ad_a = d_a – d_v + p_a – p_v \\ S(c_v – c_a) = d_a – c_ad_a – d_v + c_vd_v + p_a – p_v \\ S(c_v – c_a) = d_a(1 – c_a) – d_v(1 – c_v) + p_a – p_v \\ S = \frac{d_a(1 – c_a) – d_v(1 – c_v) + p_a – p_v}{(c_v – c_a)}$
When the spending exceeds the point of maximum out-of-pocket spend for the Value plan but not the Advantage plan, we set the out-of-pocket maximum plus premiums for the Value plan equal to the cost calculation of the Advantage plan.
$oop_v + p_v = d_a + c_a(S – d_a) + p_a \\ d_a + c_a(S – d_a) + p_a = oop_v + p_v \\ c_aS – c_ad_a = oop_v + p_v – p_a – d_a \\ c_aS = oop_v + p_v – p_a + c_ad_a – d_a \\ S = \frac{oop_v + p_v – p_a + c_ad_a – d_a}{c_a}$
When the spending exceeds the point of maximum out-of-pocket spend for the Advantage plan but not the Value plan, the solution is just the opposite of the previous equation.
$oop_a + p_a = d_v + c_v(S – d_v) + p_v \\ d_v + c_v(S – d_v) + p_v = oop_a + p_a \\ c_vS – c_vd_v = oop_a + p_a – p_v – d_v \\ c_vS = oop_a + p_a – p_v + c_vd_v – d_v \\ S = \frac{oop_a + p_a – p_v + c_vd_v – d_v}{c_v}$
As an R function it looks like this.
#' @title calculate_crossover_points
#' @description Given healthcare parameters for two plans, calculate when one plan becomes more expensive than the other.
#' @details Calculates the potential crossover points for different scenarios and returns the ones that are true crossovers.
#' @author Jared P. Lander
#' @param deductible_1 The deductible plan 1
#' @param coinsurance_1 The coinsurance percentage for spend beyond the deductible for plan 1
#' @param oop_maximum_1 The maximum amount of money (not including premiums) that the insured will pay under plan 1
#' @param deductible_2 The deductible plan 2
#' @param coinsurance_2 The coinsurance percentage for spend beyond the deductible for plan 2
#' @param oop_maximum_2 The maximum amount of money (not including premiums) that the insured will pay under plan 2
#' @return The amount of spend at which point one plan becomes more expensive than the other
#' @examples
#' calculate_crossover_points(
#' 160, 1000, 0.2, 6000,
#' 240, 800, 0.1, 5000
#' )
#'
calculate_crossover_points <- function(
)
{
# calculate the crossover before either has maxed out
deductible_2*(1 - coinsurance_2) -
deductible_1*(1 - coinsurance_1)) /
(coinsurance_1 - coinsurance_2)
# calculate the crossover when one plan has maxed out but the other has not
one_maxed_out <- (oop_maximum_1 +
coinsurance_2*deductible_2 -
deductible_2) /
coinsurance_2
# calculate the crossover for the reverse
other_maxed_out <- (oop_maximum_2 +
coinsurance_1*deductible_1 -
deductible_1) /
coinsurance_1
# these are all possible points where the curves cross
all_roots <- c(neither_maxed_out, one_maxed_out, other_maxed_out)
# now calculate the difference between the two plans to ensure that these are true crossover points
all_differences <- cost(all_roots, premiums_1, deductible_1, coinsurance_1, oop_maximum_1) -
# only when the difference between plans is 0 are the curves truly crossing
all_roots[all_differences == 0]
}
We then call the function with the parameters for both plans we are considering.
crossovers <- calculate_crossover_points(
parameters$Premiums[1], parameters$Deductible[1], parameters$Coinsurance[1], parameters$OOP_Maximum[1],
parameters$Premiums[2], parameters$Deductible[2], parameters$Coinsurance[2], parameters$OOP_Maximum[2]
)
crossovers
## [1] 20000 32000
We see that the Advantage plan is only cheaper than the Value plan when spending between $20,000 and$32,000.
The next question is will our healthcare spending fall in that narrow band between $20,000 and$32,000 where the Advantage plan is the cheaper option?
# Probability of Spending
This part gets tricky. I’d like to figure out the probability of spending between $20,000 and$32,000. Unfortunately, it is not easy to find healthcare spending data due to the opaque healthcare system. So I am going to make a number of assumptions. This will likely violate a few principles, but it is better than nothing.
Assumptions and calculations:
• Healthcare spending follows a log-normal distribution
• We will work with New York State data which is possibly different than New York City data
• We know the mean for New York spending in 2014
• We will use the accompanying annual growth rate to estimate mean spending in 2019
• We have the national standard deviation for spending in 2009
• In order to figure out the standard deviation for New York, we calculate how different the New York mean is from the national mean as a multiple, then multiply the national standard deviation by that number to approximate the New York standard deviation in 2009
• We use the growth rate from before to estimate the New York standard deviation in 2019
First, we calculate the mean. The Centers for Medicare & Medicaid Services has data on total and per capita medical expenditures by state from 1991 to 2014 and includes the average annual percentage growth. Since the data are bundled in a zip with other files, I posted them on my site for easy access.
spend_data_url <- 'https://jaredlander.com/data/healthcare_spending_per_capita_1991_2014.csv'
health_spend <- read_csv(spend_data_url)
We then take just New York spending for 2014 and multiply it by the corresponding growth rate.
ny_spend <- health_spend %>%
# get just New York
filter(State_Name == 'New York') %>%
# this row holds overall spending information
filter(Item == 'Personal Health Care ($)') %>% # we only need a few columns select(Y2014, Growth=Average_Annual_Percent_Growth) %>% # we have to calculate the spending for 2019 by accounting for growth # after converting it to a percentage mutate(Y2019=Y2014*(1 + (Growth/100))^5) ny_spend Y2014 Growth Y2019 9778 5 12479.48 The standard deviation is trickier. The best I can find was the standard deviation on the national level in 2009. In 2013 the Centers for Medicare & Medicaid Services wrote in Volume 3, Number 4 of Medicare & Medicaid Research Review an article titled Modeling Per Capita State Health Expenditure Variation: State-Level Characteristics Matter. Exhibit 2 shows that the standard deviation of healthcare spending was$1,241 for the entire country in 2009. We need to estimate the New York standard deviation from this and then account for growth into 2019.
Next, we figure out the difference between the New York State spending mean and the national mean as a multiple.
nation_spend <- health_spend %>%
filter(Item == 'Personal Health Care ($)') %>% filter(Region_Name == 'United States') %>% pull(Y2009) ny_multiple <- ny_spend$Y2014/nation_spend
ny_multiple
## [1] 1.418746
We see that the New York average is 1.4187464 times the national average. So we multiply the national standard deviation from 2009 by this amount to estimate the New York State standard deviation and assume the same annual growth rate as the mean. Recall, we can multiply the standard deviation by a constant.
\begin{align} \text{var}(x*c) &= c^2*\text{var}(x) \\ \text{sd}(x*c) &= c*\text{sd}(x) \end{align}
ny_spend <- ny_spend %>%
mutate(SD2019=1241*ny_multiple*(1 + (Growth/100))^10)
ny_spend
Y2014 Growth Y2019 SD2019
9778 5 12479.48 2867.937
My original assumption was that spending would follow a normal distribution, but New York’s resident agricultural economist, JD Long, suggested that the spending distribution would have a floor at zero (a person cannot spend a negative amount) and a long right tail (there will be many people with lower levels of spending and a few people with very high levels of spending), so a log-normal distribution seems more appropriate.
$\text{spending} \sim \text{lognormal}(\text{log}(12479), \text{log}(2868)^2)$
Visualized it looks like this.
draws <- tibble(
Value=rlnorm(
n=1200,
meanlog=log(ny_spend$Y2019), sdlog=log(ny_spend$SD2019)
)
)
ggplot(draws, aes(x=Value)) + geom_density() + xlim(0, 75000)
We can see that there is a very long right tail which means there are many low values and few high values.
Then the probability of spending between $20,000 and$32,000 can be calculated with plnorm().
plnorm(crossovers[2], meanlog=log(ny_spend$Y2019), sdlog=log(ny_spend$SD2019)) -
plnorm(crossovers[1], meanlog=log(ny_spend$Y2019), sdlog=log(ny_spend$SD2019))
## [1] 0.02345586
So we only have a 2.35% probability of our spending falling in that band where the Advantage plan is more cost effective. Meaning we have a 97.65% probability that the Value plan will cost less over the course of a year.
We can also calculate the expected cost under each plan. We do this by first calculating the probability of spending each (thousand) dollar amount (since the log-normal is a continuous distribution this is an estimated probability). We multiply each of those probabilities against their corresponding dollar amounts. Since the distribution is log-normal we need to exponentiate the resulting number. The data are on the thousands scale, so we multiply by 1000 to put it back on the dollar scale. Mathematically it looks like this.
$\mathbb{E}_{\text{Value}} \left[ \text{cost} \right] = 1000*\text{exp} \left\{ \sum p(\text{spend})*\text{cost}_{\text{Value}} \right\} \\ \mathbb{E}_{\text{Advantage}} \left[ \text{cost} \right] = 1000*\text{exp} \left\{ \sum p(\text{spend})*\text{cost}_{\text{Advantage}} \right\}$
The following code calculates the expected cost for each plan.
spending %>%
# calculate the point-wise estimated probabilities of the healthcare spending
# based on a log-normal distribution with the appropriate mean and standard deviation
mutate(
SpendProbability=dlnorm(
Spend,
meanlog=log(ny_spend$Y2019), sdlog=log(ny_spend$SD2019)
)
) %>%
# compute the expected cost for each plan
# and the difference between them
summarize(
ValueExpectedCost=sum(Value*SpendProbability),
ExpectedDifference=sum(Difference*SpendProbability)
) %>%
# exponentiate the numbers so they are on the original scale
mutate_each(funs=exp) %>%
# the spending data is in increments of 1000
# so multiply by 1000 to get them on the dollar scale
mutate_each(funs=~ .x * 1000)
5422.768 7179.485 1323.952
This shows that overall the Value plan is cheaper by about $1,324 dollars on average. # Conclusion We see that there is a very small window of healthcare spending where the Advantage plan would be cheaper, and at most it would be about$600 cheaper than the Value plan. Further, the probability of falling in that small window of savings is just 2.35%.
So unless our spending will be between $20,000 and$32,000, which it likely will not be, it is a better idea to choose the Value plan.
Since the Value plan is so likely to be cheaper than the Advantage plan I wondered who would pick the Advantage plan. Economist Jon Hersh invokes behavioral economics to explain why people may select the Advantage plan. Some parts of the Advantage plan are lower than the Value plan, such as the deductible, coinsurance and out-of-pocket maximum. People see that under certain circumstances the Advantage plan would save them money and are enticed by that, not realizing how unlikely that would be. So they are hedging against a low probability situation. (A consideration I have not accounted for is family size. The number of members in a family can have a big impact on the overall spend and whether or not it falls into the narrow band where the Advantage plan is cheaper.)
In the end, the Value plan is very likely going to be cheaper than the Advantage plan.
# Try it at Home
I created a Shiny app to allow users to plug in the numbers for their own plans. It is rudimentary, but it gives a sense for the relative costs of different plans.
# Thanks
A big thanks to Jon Hersh, JD Long, Kaz Sakamoto, Rebecca Martin and Adam Hogan for reviewing this post.
Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.
Data scientists and R enthusiasts gathered for the 5th annual New York R Conference held on May 9th-11th. In front of a crowd of more than 300 attendees, 24 speakers gave presentations on topics ranging from deep learning and building packages in R to football and hockey analytics.
This year marked the ten-year anniversary of the New York Open Statistical Programming Meetup. It has been incredible to see the growth of meetup over the years. We now have over 10,000 members around the world!
Let’s take a look at some of the highlights from the conference:
## Jonah Gabry Kicked Off “R” Week at the New York Open Statistical Programming Meetup with a Talk on Using Stan in R
Jonah Gabry from the Stan Development Team kicked off “R” week with a talk on making Bayes easier in the R ecosystem. Jonah went over the packages (rstanarm, rstantools, bayesplot and loo) which emulate other R model-fitting functions, unify function naming across Stan-based R packages, and develop plotting functions using ggplot objects.
## 50 Conference Attendees Participated in Pre-Conference Workshops on Thursday before the Conference
On the Thursday before the two-day conference, more than 50 conference attendees arrived at Work-Bench a day early for a full day of workshops. This was the first year of the R Conference Workshop Series. Max Kuhn, Dan Chen, Elizabeth Sweeney and Kaz Sakamoto each led a workshop which covered the following topics:
• Machine Learning with Caret (Max Kuhn)
• Git for Data Science (Dan Chen)
• Introduction to Survival Analysis (Elizabeth Sweeney)
• Geospatial Statistics and Mapping in R (Kaz Sakamoto)
## The Growth of R-Ladies Summed Up in Three Pictures…
We are so excited to see the growth of the R-Ladies community and we appreciate their support for the NY R Conference over the years. Congratulations ladies!
## Dr. Andrew Gelman Delivers Keynote Speech on the Fallacy of P-Values and Thinking like a Statistician—All Without Slides
There wasn’t a soul in the crowd who wasn’t hanging on every word from Columbia professor Dr. Andrew Gelman. The only speaker with a 40-minute time slot, and the only speaker to not use slides, Dr. Gelman talked about life as a statistician, warned of the perils of p-values and stressed the importance of simulation—before data collection—to improve our understanding of possible real-life scenarios. “Only through simulating fake data, can you really have statistical confidence about whatever performance metric you’re aiming for,” Gelman noted.
While we try not to pick a favorite speaker, Dr. Gelman runs away with that title every time he comes to speak at the New York R Conference.
## Jacqueline and Heather Nolis Taught Us to Not to Be Afraid of Deep Learning and Model Deployment in Production
The final talk on day one was perhaps the most entertaining and insightful from the weekend. Jacqueline Nolis taught us how developing a deep learning model is easier than we thought and how humor can help us understand a complex idea in a simple form. Our top five favorite neural network-generate pet names: Dia, Spok, Jori, Lule, and Timuse!
On Saturday morning, Heather Nolis showed us how we can deploy the model into production. Heather walked through the steps involved in preparing an R model for production using containers (Docker) and container orchestration (Kubernetes) to share models throughout an organization or for the public. How can we put a model into production without your laptop running 24/7? By running the code safely on a server in the cloud!
## Emily Robinson and Honey Berk Win Headphones for Most Tweets During the Conference
If you’re not following Emily Robinson (@robinson_es) and Honey Berk (@honeyberk), you’re missing out! Emily and Honey led all conference attendees in Twitter mentions according to our Twitter scorekeeper Malorie Hughes (@data_all_day). Because of Emily and Honey’s presence on Twitter, those who were unable to attend the conference were able to follow along with all of our incredible speakers throughout the two-day event.
## Jared Lander Debuts New-Born R Package Hex Sticker T-Shirts: Congratulations to Jared and Rebecca on the Birth of their Son, Lev
During my talk I debuted a custom R package hex sticker t-shirt with my wife Rebecca and son Lev. We R a very nerdy family.
## Looking Forward to 2020
If you attended the 2019 New York R Conference, we hope you had an incredible experience. If you did not attend the conference, we hope to see you next year!
Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.
Ten years ago Josh Reich held the first ever New York Open Statistical Programming Meetup at Union Square Ventures. Back then it was called the New York R Meetup and 21 people RSVP’d. I discovered the Meetup three months later thanks to Andrew Gelman’s blog and by then the RSVP count had doubled and Drew Conway became a co-organizer. The experience was so much fun and I learned a lot of good stuff. I remember learning about the head() and tail() functions, wishing I learned them in grad school.
I started attending regularly and pretty soon Drew decided to serve pizza which later led to years of pizza data. He also designed a logo for the NYC Data Mafia, which made for a great t-shirt that we still sell. One time, a number of us were talking and realized we were all answering each other’s questions on StackOverflow. Our community was growing both in person and online. I fell in love with the group because it was a great place to learn and hang out with smart, welcoming people.
During the first two years our hosts included NYU, Columbia, AOL and a handful of others. At this time there were about 1,800 members with Drew as the sole organizer who was ready to focus on other parts of his life, so he asked Wes McKinney and me to take over as organizers. This was after Drew renamed the group the Open Statistical Programming Meetup as to include other open source languages like Python, Julia, Go and SQL. I was incredibly thrilled to organize this group which meant so much to me.
Over the next eight years our numbers swelled to almost 11,000 with members and speakers coming from all over the world. We have held the Meetup at places such as eBay, AT&T, iHeartRadio, Work-Bench, Knewton, Twitter, New York Presbyterian, Rise New York and Google. The most popular event welcomed nearly 400 people when Hadley Wickham spoke in September of 2015, the only time the Meetup met on a Friday.
That night was also my fifth date with Rebecca Martin. We originally met during Michael Kane’s talk about PubMed then reconnected about a year later. We went on to get married and have a kid together. The New York Times used the nerdiest closing line ever for our wedding announcement: “The couple met in New York in May 2014 at a meet-up about statistical programming organized by the groom.”
The Meetup has grown not only in numbers but in reach as well. There’s a website hosting all of the presentations, we livestream the Meetups and people from all over the world chat in our Slack team. Our live events include an ongoing workshop series and conferences in New York and Washington DC, which just hit their fifth anniversary, all for building and supporting the community and open source software.
These past ten years have been a collection of amazing experiences for me where I got to learn from some of the world’s best experts and develop lasting relationships with great people. This community means so much to me and I very much look forward to its continued growth over the next decade.
Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.
On Pi Day this year I was giving a keynote talk at DataFest in Scotland, so we celebrated Pi Day a week later, on the 21st. While it wasn’t the exact date, there’s never a bad time to eat pizza and Pi Cake.
This was the tenth Pi Cake, and it’s pretty hard to beat the Einstein design on last year’s Pi Cake, so Empire Cakes gave created us a cake with the actual definition of pi: The ratio of a circle’s circumference to its diameter.
For pizza we went to the new Lombardi’s in Chelsea. They use an amazing electric oven instead of coal, so if you look closely you can tell the difference, but the pizza was still great and the decor was fantastic.
And now Pi Cake throughout the years:
#### Related Posts
Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.
After four sold-out years in New York City, the R Conference made its debut in Washington DC to a sold-out crowd of data scientists at the Ronald Reagan Building on November 8th & 9th. Our speakers shared presentations on a variety of R-related topics.
A big thank you to our speakers Max Kuhn, Emily Robinson, Mike Powell, Mara Averick, Max Richman, Stephanie Hicks, Michael Garris, Kelly O’Briant, David Smith, Anna Kirchner, Roger Peng, Marck Vaisman, Soumya Kalra, Jonathan Hersh, Vivian Peng, Dan Chen, Catherine Zhou, Jim Klucar, Lizzy Huang, Refael Lav, Ami Gates, Abhijit Dasgupta, Angela Li and Tommy Jones.
# Some highlights from the conference:
## R Superstars Mara Averick, Roger Peng and Emily Robinson
A hallmark of our R conferences is that the speakers hang out with all the attendees and these three were crowd favorites.
## Michael Powell Brings R to the aRmy
Major Michael Powell describes how R has brought efficiency to the Army Intelligence and Security Command by getting analysts out of Excel and into the Tidyverse. “Let me turn those 8 hours into 8 seconds for you,” says Powell.
## Max Kuhn Explains the Applications of Equivocals to Apply Levels of Certainty to Predictions
After autographing his book, Applied Predictive Modeling, for a lucky attendee, Max Kuhn explains how Equivocals can be applied to individual predictions in order to avoid reporting predictions when there is significant uncertainty.
## NYR and DCR Speaker Emily Robinson Getting an NYR Hoodie for her Awesome Tweeting
Emily Robinson tweeted the most at the 2018 NYR conference, winning her a WASD mechanical keyboard and at DCR she came in second so we gave her a limited edition NYR hoodie.
## Max Richman Shows How SQL and R can Co-Exist
Max Richman, wearing the same shirt he wore when he spoke at the first NYR, shows parallels between dplyr and SQL.
## Michael Garris Tells the Story of the MNIST Dataset
Michael Garris was a member of the team that built the original MNIST dataset, which set the standard for handwriting image classification in the early 1990s. This talk may have been the first time the origin story was ever told.
## R Stats Luminary Roger Peng Explains Relationship Between Air Pollution and Public Health
Roger Peng shows us how air pollution levels has fallen over the past 50 years resulting in dramatic improvements in air quality and health (with help from R).
## Kelly O’Briant Combining R with Serverless Computing
Kelly O’Briant demonstrates how to easily deploy R projects on Google Compute Engine and promoted the new #radmins hashtag.
## Hot Dog vs Not Hot Dog by David Smith (Inspired by Jian-Yang from HBO’s Silicon Valley)
David Smith, one of the original R users, shows how to recreate HBO’s Silicon Valley’s Not Hot Dog app using R and Azure
## Jon Hersh Describes How to Push for Data Science Within Your Organization
Jon Hersh discusses the challenges, and solutions, of getting organizations to embrace data science.
## Vivian Peng and the Importance of Data Storytelling
Vivian Peng asks the question, how do we protect the integrity of our data analysis when it’s published for the world to see?
## Dan Chen Signs His Book for David Smith
Dan Chen autographing a copy of his book, Pandas for Everyone, for David Smith. Now David Smith has to sign his book, An Introduction to R, for Dan.
## Malorie Hughes Analyzing Tweets
On the first day I challenged the audience to analyze the tweets from the conference and Malorie Hughes, a data scientist with NPR, designed a Twitter analytics dashboard to track the attendee with the most tweets with the hashtag #rstatsdc. Seth Wenchel won a WASD keyboard for the best tweeting. And we presented Malorie wit a DCR speaker mug.
## Strong Showing from the #RLadies!
The #rladies group is growing year after year and it is great seeing them in force at NYR and DCR!
## Packages
Matthew Hendrickson, a DCR attendee, posted on twitter every package mentioned during the two-day conference:
## Data Community DC
A special thanks to the Data Community DC for helping us make the DC R Conference an incredible experience.
## Videos
The videos for the conference will be posted in the coming weeks to dc.rstats.ai.
## See You Next Year
Looking forward to more great conferences at next year’s NYR and DCR!
Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.
## Getting People Started
A large part of my work is teaching R–for private clients, at Columbia Business School, at conferences and facilitating public workshops for others.
A common theme is that getting everyone setup on their individual computers is very difficult. No matter how many instructions I provide, there are always a good number of people without a proper environment. This can mean not using RStudio projects, not having the right packages installed, not downloading the data and sometimes not even installing R.
## Solution
After many experiments I finally came upon a solution. For every class I teach I now create a skeleton project hosted on GitHub with instructions for setup.
The instructions (in the README) consist of three blocks of code.
1. Package installation
2. Copying the project structure from the repo (no git required)
All the user has to do is copy and paste these three blocks of code into the R console and they have the exact same environment as the instructor and other students.
packages <- c(
'coefplot',
'rprojroot',
'tidyverse',
'usethis'
)
install.packages(packages)
newProject <- usethis::use_course('https://github.com/jaredlander/WorkshopExampleRepo/archive/master.zip')
source('prep/DownloadData.r')
Using this process, 95% of my students are prepared for class.
The inspiration for this idea came from a fun coffee with Hadley Wickham and Jenny Bryan during a conference in New Zealand and the implementation is made possible thanks to the usethis package.
## Automating the Setup
Now that I found a good way to get students started, I wanted to make it easier for me to setup the repo. So I created an R package called RepoGenerator and put it on CRAN.
The first step to using the package is to create a GitHub Personal Access Token (instructions are in the README). Then you build a data.frame listing datasets you want the students to download. The data.frame needs at least the following three columns.
• Local: The name, not path, the file should have on disk
• Remote: The URL where the data files are stored online
• Mode: The mode needed to write the file to disk, ‘w’ for regular text files, ‘wb’ for binary files such as Excel or rds files
An example data.frame is available in the RepoGenerator package.
data(datafiles, package='RepoGenerator')
datafiles[1:6, c('Local', 'Remote', 'Mode')]
After that you define the packages you want your students to use. There can be as few or as many as you want. In addition to any packages you list, rprojroot and usethis are added so that the instructions in the new repo will be certain to work.
packages <- c('caret', 'coefplot','DBI', 'dbplyr', 'doParallel', 'dygraphs',
'foreach', 'ggthemes', 'glmnet', 'jsonlite', 'leaflet', 'odbc',
'recipes', 'rmarkdown', 'rprojroot', 'RSQLite', 'rvest',
'tidyverse', 'threejs', 'usethis', 'UsingR', 'xgboost', 'XML',
'xml2')
Now all you need to do is call the createRepo() function.
createRepo(
# the name to use for the repo and project
name='WorkshopExampleRepo',
# the location on disk to build the project
path='~/WorkshopExampleRepo',
data=datafiles,
# vector of packages the user should install
packages=packages,
# the GitHub username to create the repo for
user='jaredlander',
# the new repo's README has the name of who is organizing the class
organizer='Lander Analytics',
# the name of the environment variable storing the GitHub Personal Access Token
token='MyGitHubPATEnvVar'
)
After this you will have a new repo setup for your users to copy, including instructions.
## That’s All
Reducing setup issues at the start of a training can really improve the experience for everyone and allow you to get straight into teaching.
Please check it out and let me know how it works for you.
Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.
The 2018 New York R Conference was the biggest and best yet. This is both in terms of the crowd size and content. The speakers included some of the R community’s best such as Hadley Wickham, David Robinson, Jennifer Hill, Max Kuhn, Andreas Mueller (ok, a little Python), Evelina Gabasova, Sean Taylor and Jeff Ryan. I am proud to say we were almost at gender parity for both attendees and speakers which is amazing for a tech conference. Brooke Watson even excitedly noted that we had a line for the women’s room.
Particularly gratifying for me was seeing so many of my students speak. Eurry Kim, Dan Chen and Alex Boghosian all gave excellent talks.
Some highlights that stuck out to me are:
## Emily Robinson Shows There is More to the Tidyverse than Hadley
Emily Robinson, otherwise known as ERob, gave an excellent talk showing how the Tidyverse is so much more than just Hadley and that there are many people inspired by him to contribute in the Tidy way.
## Sean Taylor Forecasted the Future with Prophet
Sean Taylor, former New Yorker and unrepentant Eagles fan, demonstrate his powerful R and Python, package Prophet, for forecasting time series data. Facebook open sourced his work so we could all benefit.
## OG Data Mafia Founder Drew Conway Popped In
A lucky fan got an autographed NYC Data Mafia t-shirt from Drew Conway.
## David Smith Playing Minecraft Through R
David Smith played Minecraft through R, including building objects and moving through the world.
## Evelina Gabasova Used Social Network Analysis to Break Down Star Wars
Evelina Gabasova wowed the audience with her fun talk and detailed analysis of character interaction in Star Wars.
## Dusty Turner Represented West Point
Dusty Turner taught us how the United States Military Academy uses R for both student instruction and evaluation.
## Hadley Wickham Delved into the Nitty Gritty of R
Hadley Wickham showed us how to get into the internals of R and figure out how to examine objects from a memory perspective.
## Jennifer Hill Demonstrated Awesome Machine Learning Techniques for Causal Inference
Following her sold-out meetup appearance in March, Jennifer continued to push the boundaries of causal inference.
## I Made the Authors of Caret and scitkit-learn Show That R and Python Can Get Along
While both Andreas and Max gave great individual talks, I made them pose for this peace-making photo.
## David Robinson Got the Upper Hand in a Sibling Twitter Duel
Given only about 30 minutes notice, David put together an entire slideshow on how to livetweet and how to compete with your sibling.
## In the End Emily Robinson Beat Her Brother For Best Tweeting
Despite David’s headstart Emily was the best tweeter (as calculated by Max Kuhn and Mara Averick) so she won the WASD Code mechanical keyboard with MX Cherry Clear switches.
## Silent Auction of Data Paintings
Thomas Levine made paintings of famous datasets that we auctioned off with the proceeds supporting the R Foundation and the Free Software Foundation. The Robinson family very graciously chipped in and bought the painting of the Pizza Poll data for me! I’m still floored by this and in love with the painting.
## Ice Cream Sandwiches
In addition to bagels and eggs sandwiches from Murray’s Bagels, Israeli food from Hummus and Pita Company, avocado toast and coffee from Bluestone Lane Coffee and pizza from Fiore’s, we also had ice creams sandwiches from World’s Best Cookie Dough.
## All the Material
To catch up on all the presentations check out Mara Averick’s excellent notes:
Or check out all of Brooke’s drawings, collated by Dan Chen.
## Videos and Upcoming Events
The videos will be posted at rstats.nyc in a few weeks for all to enjoy.
There are a number of other events coming up including:
We are already beginning plans for next year’s conference and are working on bringing it to DC as well! Stay tuned for all that and more.
Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.
It’s Pi Day, when we celebrate all things round by eating pizza and Pi Cake. This is the ninth year we have celebrated Pi Day and the fourth year in a row we got the Pi Cake from Empire Cakes. This year’s pizza place was Arturo’s on Thompson and Houston. Arturo’s is a great example of old New York pizza with an oven dating to the 1920’s.
In addition to the traditional Pi Symbol atop the cake we added Albert Einstein since today is also his birthday. It seems fitting that we lost one of the world’s other greatest physicists, Stephen Hawking on the same math holiday.
The crew has grown quite large from the five of us who celebrated our first pie day almost a decade ago.
Some more pictures from this fun night.
And now Pi Cake throughout the years:
#### Related Posts
Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.
In my last post I discussed using coefplot on glmnet models and in particular discussed a brand new function, coefpath, that uses dygraphs to make an interactive visualization of the coefficient path.
Another new capability for version 1.2.5 of coefplot is the ability to show coefficient plots from xgboost models. Beyond fitting boosted trees and boosted forests, xgboost can also fit a boosted Elastic Net. This makes it a nice alternative to glmnet even though it might not have some of the same user niceties.
To illustrate, we use the same data as our previous post.
First, we load the packages we need and note the version numbers.
# list the packages that we load
# alphabetically for reproducibility
packages <- c('caret', 'coefplot', 'DT', 'xgboost')
# call library on each package
purrr::walk(packages, library, character.only=TRUE)
# they are listed here for complete documentation
packagesColon <- c('dplyr', 'dygraphs', 'knitr', 'magrittr', 'purrr', 'tibble', 'useful')
versions <- c(packages, packagesColon) %>%
purrr::map(packageVersion) %>%
purrr::map_chr(as.character)
packageDF <- tibble::data_frame(Package=c(packages, packagesColon), Version=versions) %>%
dplyr::arrange(Package)
knitr::kable(packageDF)
Package Version
caret 6.0.78
coefplot 1.2.6
dplyr 0.7.4
DT 0.2
dygraphs 1.1.1.4
knitr 1.18
magrittr 1.5
purrr 0.2.4
tibble 1.4.2
useful 1.2.3
xgboost 0.6.4
Then, we read the data. The data are available at https://www.jaredlander.com/data/manhattan_Train.rds with the CSV version at data.world. We also get validation data which is helpful when fitting xgboost mdoels.
manTrain <- readRDS(url('https://www.jaredlander.com/data/manhattan_Train.rds'))
manVal <- readRDS(url('https://www.jaredlander.com/data/manhattan_Validate.rds'))
The data are about New York City land value and have many columns. A sample of the data follows. There’s an odd bug where you have to click on one of the column names for the data to display the actual data.
datatable(manTrain %>% dplyr::sample_n(size=1000), elementId='TrainingSampled',
rownames=FALSE,
options=list(
scroller=TRUE
))
While glmnet automatically standardizes the input data, xgboost does not, so we calculate that manually. We use preprocess from caret to compute the mean and standard deviation of each numeric column then use these later.
preProc <- preProcess(manTrain, method=c('center', 'scale'))
Just like with glmnet, we need to convert our tbl into an X (predictor) matrix and a Y (response) vector. Since we don’t have to worry about multicolinearity with xgboost we do not want to drop the baselines of factors. We also take advantage of sparse matrices since that reduces memory usage and compute, even though this dataset is not that large.
In order to build the matrix and vector we need a formula. This could be built programmatically, but we can just build it ourselves. The response is TotalValue.
valueFormula <- TotalValue ~ FireService + ZoneDist1 + ZoneDist2 +
Class + LandUse + OwnerType + LotArea + BldgArea + ComArea + ResArea +
OfficeArea + RetailArea + NumBldgs + NumFloors + UnitsRes + UnitsTotal +
LotDepth + LotFront + BldgFront + LotType + HistoricDistrict + Built +
Landmark
manX <- useful::build.x(valueFormula, data=predict(preProc, manTrain),
# do not drop the baselines of factors
contrasts=FALSE,
# use a sparse matrix
sparse=TRUE)
manY <- useful::build.y(valueFormula, data=manTrain)
manX_val <- useful::build.x(valueFormula, data=predict(preProc, manVal),
# do not drop the baselines of factors
contrasts=FALSE,
# use a sparse matrix
sparse=TRUE)
manY_val <- useful::build.y(valueFormula, data=manVal)
There are two functions we can use to fit xgboost models, the eponymous xgboost and xgb.train. When using xgb.train we first store our X and Y matrices in a special xgb.DMatrix object. This is not a necessary step, but makes things a bit cleaner.
manXG <- xgb.DMatrix(data=manX, label=manY)
manXG_val <- xgb.DMatrix(data=manX_val, label=manY_val)
We are now ready to fit a model. All we need to do to fit a linear model instead of a tree is set booster='gblinear' and objective='reg:linear'.
mod1 <- xgb.train(
# the X and Y training data
data=manXG,
# use a linear model
booster='gblinear',
# minimize the a regression criterion
objective='reg:linear',
# use MAE as a measure of quality
eval_metric=c('mae'),
# boost for up to 500 rounds
nrounds=500,
# print out the eval_metric for both the train and validation data
watchlist=list(train=manXG, validate=manXG_val),
# print eval_metric every 10 rounds
print_every_n=10,
# if the validate eval_metric hasn't improved by this many rounds, stop early
early_stopping_rounds=25,
# penalty terms for the L2 portion of the Elastic Net
lambda=10, lambda_bias=10,
# penalty term for the L1 portion of the Elastic Net
alpha=900000000,
# randomly sample rows
subsample=0.8,
# randomly sample columns
col_subsample=0.7,
# set the learning rate for gradient descent
eta=0.1
)
## [1] train-mae:1190145.875000 validate-mae:1433464.750000
## Multiple eval metrics are present. Will use validate_mae for early stopping.
## Will train until validate_mae hasn't improved in 25 rounds.
##
## [11] train-mae:938069.937500 validate-mae:1257632.000000
## [21] train-mae:932016.625000 validate-mae:1113554.625000
## [31] train-mae:931483.500000 validate-mae:1062618.250000
## [41] train-mae:931146.750000 validate-mae:1054833.625000
## [51] train-mae:930707.312500 validate-mae:1062881.375000
## [61] train-mae:930137.375000 validate-mae:1077038.875000
## Stopping. Best iteration:
## [41] train-mae:931146.750000 validate-mae:1054833.625000
The best fit was arrived at after 41 rounds. We can see how the model did on the train and validate sets using dygraphs.
dygraphs::dygraph(mod1\$evaluation_log)
We can now plot the coefficients using coefplot. Since xgboost does not save column names, we specify it with feature_names=colnames(manX). Unlike with glmnet models, there is only one penalty so we do not need to specify a specific penalty to plot.
coefplot(mod1, feature_names=colnames(manX), sort='magnitude')
This is another nice addition to coefplot utilizing the power of xgboost.
#### Related Posts
Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.
I’m a big fan of the Elastic Net for variable selection and shrinkage and have given numerous talks about it and its implementation, glmnet. In fact, I will even have a DataCamp course about glmnet coming out soon.
As a side note, I used to pronounce it g-l-m-net but after having lunch with one of its creators, Trevor Hastie, I learn it is pronounced glimnet.
coefplot has long supported glmnet via a standard coefficient plot but I recently added some functionality, so let’s take a look. As we go through this, please pardon the htmlwidgets in iframes.
First, we load packages. I am now fond of using the following syntax for loading the packages we will be using.
# list the packages that we load
# alphabetically for reproducibility
packages <- c('coefplot', 'DT', 'glmnet')
# call library on each package
purrr::walk(packages, library, character.only=TRUE)
# they are listed here for complete documentation
packagesColon <- c('dplyr', 'knitr', 'magrittr', 'purrr', 'tibble', 'useful')
The versions can then be displayed in a table.
versions <- c(packages, packagesColon) %>%
purrr::map(packageVersion) %>%
purrr::map_chr(as.character)
packageDF <- tibble::data_frame(Package=c(packages, packagesColon), Version=versions) %>%
dplyr::arrange(Package)
knitr::kable(packageDF)
Package Version
coefplot 1.2.5.1
dplyr 0.7.4
DT 0.2
glmnet 2.0.13
knitr 1.18
magrittr 1.5
purrr 0.2.4
tibble 1.4.1
useful 1.2.3
First, we read some data. The data are available at https://www.jaredlander.com/data/manhattan_Train.rds with the CSV version at data.world.
manTrain <- readRDS(url('https://www.jaredlander.com/data/manhattan_Train.rds'))
The data are about New York City land value and have many columns. A sample of the data follows.
datatable(manTrain %>% dplyr::sample_n(size=100), elementId='DataSampled',
rownames=FALSE,
options=list(
scroller=TRUE,
scrollY=300
))
In order to use glmnet we need to convert our tbl into an X (predictor) matrix and a Y (response) vector. Since we don’t have to worry about multicolinearity with glmnet we do not want to drop the baselines of factors. We also take advantage of sparse matrices since that reduces memory usage and compute, even though this dataset is not that large.
In order to build the matrix ad vector we need a formula. This could be built programmatically, but we can just build it ourselves. The response is TotalValue.
valueFormula <- TotalValue ~ FireService + ZoneDist1 + ZoneDist2 +
Class + LandUse + OwnerType + LotArea + BldgArea + ComArea + ResArea +
OfficeArea + RetailArea + NumBldgs + NumFloors + UnitsRes + UnitsTotal +
LotDepth + LotFront + BldgFront + LotType + HistoricDistrict + Built +
Landmark - 1
Notice the - 1 means do not include an intercept since glmnet will do that for us.
manX <- useful::build.x(valueFormula, data=manTrain,
# do not drop the baselines of factors
contrasts=FALSE,
# use a sparse matrix
sparse=TRUE)
manY <- useful::build.y(valueFormula, data=manTrain)
We are now ready to fit a model.
mod1 <- glmnet(x=manX, y=manY, family='gaussian')
We can view a coefficient plot for a given value of lambda like this.
coefplot(mod1, lambda=330500, sort='magnitude')
|
2022-10-05 19:08:48
|
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|
https://cran-r.c3sl.ufpr.br/web/packages/lessR/vignettes/pivot.html
|
# Pivot Table
## Overview
### Descriptive Statistics
Descriptive summarize characteristics of the sample data values for one or more variables. The lessR pivot() function serves as a single source for a wide variety and types of descriptive statistics for one or more variables. Statistics are computed either for the entire data set at once or separately for different groups of data. MS Excel refers to the resulting statistical summaries as a pivot table.
Aggregation: Form groups of data according to the levels of one or more categorical variables, then compute some statistical value of a numeric variable, such as a mean, for each group.
As an example of aggregation, compute the mean Years worked for each combination of the levels of Gender and Dept (department) of employment. To introduce the ease of use of pivot(), and provide context for the following discussion this function call listed below includes the parameter names (in red) for emphasis, but if the parameters are entered in this order, listing their names is not necessary. Enter multiple values, such as for Gender and Dept as an R vector, defined such as with the base R combine c() function. The output of the analysis is shown later.
The pivot() function computes statistics for three classes of variables:
• Numerical variables that represent continuity such as time, money, and weight.
• Numerical variables that represent ordered categories, such as Likert scale responses Strongly Disagree to Strongly Agree on a 5-pt scale coded 1 to 5.
• Non-numerical categorical variables such as Gender encoded as Male, Female, and Other, even if coded numerically but without numerical properties, such as 0, 1, and 2 for three values of Gender.
Any function that processes a single vector of data, such as a column of data values for a variable in a data frame, and outputs a single computed value, can be passed pivot(). The phrase “any function” is quite general, including any function in any active package as well as user-defined functions that satisfy these criteria. Typically the function accessed by pivot() is one of the many available R statistical functions that summarize data, including those in the following table.
Statistic Meaning
sum sum
mean arithmetic mean
median median
min minimum
max maximum
sd standard deviation
var variance
skew skew
kurtosis kurtosis
IQR inter-quartile range
mad mean absolute deviation
The statistics skew and kurtosis have no counterparts in base R, so are provided by lessR. Computations of all other statistics follow from base R functions.
The quantile and table computations return multiple values, and so are accessible to pivot() only because of internal programming that recognizes these functions and then processes the resulting multiple output values.
Statistic Meaning
quantile min, quartiles, max
table cell counts or proportions
The table computation applies to an aggregated variable that consists of discrete categories, such as the numbers 1 through 5 for responses to a 5-pt Likert scale. The result is a table of frequencies or proportions, referred to for two or more variables as either a contingency table, a cross-tabulation table, or a joint frequency distribution. Only the table computation applies to non-numeric as well as numeric variables, though only meaningful if the aggregated variable consists of a relatively small set of discrete values, character strings or numeric.
The default quantiles for quantile are quartiles. Specify a custom number of quantiles with the q_num parameter, which has the default value of 4 for quartiles.
When calculating a statistic, the analyst should be aware of the present and missing (not available) data that underlies the computed statistic. Accordingly, pivot() by default provides the sample size information for each calculation. Turn off the display of information with the show_n parameter.
### Parameters
The following pivot() parameters specify the data, one or more statistics to compute for the aggregation, the variables over which to aggregate, and the corresponding groups that contain the aggregated values. The first three parameter values listed below are required: the data frame, at least one statistic to compute, and at least one variable for which to compute the statistic(s).
1. data: The data frame that includes the variables of interest.
2. compute: One or more functions that specify the corresponding statistics to compute.
3. variable: One or more numerical variables to summarize, either by aggregation over groups or the entire sample as a single group.
4. by: Specify the optional aggregation according to the categorical variable(s) that define the groups.
5. by_cols: The optional categorical variable(s) that define the groups or cells for which to compute the aggregated values, listed as columns in a two-dimensional table.
For the given data, compute at least one statistic for at least one variable for each group specified by by and possibly by_cols.
If no categorical (by) variables are selected to define groups, then one or more statistics are computed over multiple variables over the entire data set defined as a single group. For categorical variables that define groups, with by and optionally by_cols, can choose either computer multiple statistics or multiple variable(s), but not both.
Key Idea: Select any two of the three possibilities for multiple parameter values: Multiple compute functions, multiple variables over which to compute, and multiple categorical variables by which to define groups for aggregation.
Specify multiple descriptive statistics to compute, multiple values for which to do the computation, and multiple categorical variables to define groups as vectors such as with the base R c() function.
### Output
The output of pivot() is a two-dimensional table, rows and columns. The output table can have multiple rows and multiple columns according to the choice of parameter values. For each numerical variable in the analysis, pivot() displays both the corresponding sample size as n_ and amount of missing or not available data as na_. Prevent displaying sample size information by setting parameter show_n to FALSE.
The output follows one of three general forms.
• The classic form is a data frame with the categorical variables in the analysis listed as columns first, followed by the numerical variables, ready for input into data analysis procedures. Each row of the output data frame consists of the corresponding values for the levels of the categorical variables and the corresponding values of the aggregated statistics.
• If one or two categorical variables are specified with the by_cols parameter, the output is a table with the specified categorical variables in the columns, amenable for viewing.
• If there is no aggregation specified, no by variables, the corresponding statistics are computed over the entire data frame defined as a single group.
• There may be many variables to summarize, such as all the items on a multi-item scale from a survey analysis, so the output is a data frame with variable names that each indicate the corresponding computed statistic and the rows defined by the combinations of levels of the by variables.
## Output as a Long-Form Data Frame
To illustrate, use the 37-row Employee data set included with lessR, here read into the d data frame.
d <- Read("Employee")
##
## >>> Suggestions
##
## Data Types
## ------------------------------------------------------------
## character: Non-numeric data values
## integer: Numeric data values, integers only
## double: Numeric data values with decimal digits
## ------------------------------------------------------------
##
## Variable Missing Unique
## Name Type Values Values Values First and last values
## ------------------------------------------------------------------------------------------
## 1 Years integer 36 1 16 7 NA 15 ... 1 2 10
## 2 Gender character 37 0 2 M M M ... F F M
## 3 Dept character 36 1 5 ADMN SALE SALE ... MKTG SALE FINC
## 4 Salary double 37 0 37 53788.26 94494.58 ... 56508.32 57562.36
## 5 JobSat character 35 2 3 med low low ... high low high
## 6 Plan integer 37 0 3 1 1 3 ... 2 2 1
## 7 Pre integer 37 0 27 82 62 96 ... 83 59 80
## 8 Post integer 37 0 22 92 74 97 ... 90 71 87
## ------------------------------------------------------------------------------------------
Two categorical variables in the d data frame are Dept and Gender. Continuous variables include Years worked at the company and annual Salary.
### Multiple Grouping Variables
This example does the analysis previously illustrated. The name of the computed mean of Years by default is Years_mn.
pivot(data=d, compute=mean, variable=Years, by=c(Dept, Gender))
## Dept Gender n_Years na_Years Years_mn
## 1 ACCT F 3 0 4.667
## 2 ADMN F 4 0 7.500
## 3 FINC F 1 0 7.000
## 4 MKTG F 5 0 8.200
## 5 SALE F 5 0 6.600
## 6 ACCT M 2 0 7.000
## 7 ADMN M 2 0 15.500
## 8 FINC M 3 0 11.333
## 9 MKTG M 1 0 18.000
## 10 SALE M 9 1 12.333
With no by_cols variables, the output of pivot() is a data frame of the aggregated variables. This output can be saved for further analysis, as the data frame a in this example. Next, perform the same analysis, but with the variable Salary, the parameter values listed in order without the parameter names.
a <- pivot(d, mean, Salary, c(Dept, Gender))
a
## Dept Gender n_Salary na_Salary Salary_mn
## 1 ACCT F 3 0 63237.16
## 2 ADMN F 4 0 81434.00
## 3 FINC F 1 0 57139.90
## 4 MKTG F 5 0 64496.02
## 5 SALE F 5 0 64188.25
## 6 ACCT M 2 0 59626.19
## 7 ADMN M 2 0 80963.35
## 8 FINC M 3 0 72967.60
## 9 MKTG M 1 0 99062.66
## 10 SALE M 10 0 86150.97
Visualize the aggregation with a bar chart generated by the lessR function BarChart(). The function can do the aggregation internally, but another option provides a data table that consists of sets og categories with each set paired with a numerical value, that is, the output of pivot(). Each category of one variable defines a bar with its height based on the value of the numerical variable (see the lessR vignette for BarChart() for more details).
In this example, plot the pivot table from the analysis of the mean of Salary across levels of Dept and Gender. By default, BarChart() also displays the pivot table from which the bar chart is created.
BarChart(Dept, Salary_mn, by=Gender, data=a)
## Summary Table of Salary_mn
## --------------------------
##
## Dept
## Gender ACCT ADMN FINC MKTG SALE
## F 63237.163 81434.003 57139.900 64496.022 64188.254
## M 59626.195 80963.345 72967.600 99062.660 86150.970
Using the lessR function Read(), can read the original data table from which the pivot table was constructed, such as in the form of an Excel worksheet. For many analyses, easier to read the Excel data into R and do the analysis in R than in Excel. The result can also be written back into an Excel file with the lessR function Write().
In this example, create an Excel file called MyPivotTable.xlsx from the pivot table stored in the a data frame. To avoid creating this file in this example, the function call is commented out with the # symbol in the first column.
#Write("MyPivotTable", data=a, format="Excel")
The abbreviation wrt_x() for the function name simplifies the preceding expression, with the format parameter dropped.
### Aggregate with Multiple Statistics
In this next example, specify multiple statistics for which to aggregate for each group for the specified value variable Salary. For each group, compare the mean to the median, and the standard deviation to the interquartile range. By default, each column of an aggregated statistic is the variable name, here Salary, followed by a “_”, then either the name of the statistic or an abbreviation. The respective abbreviations for mean and median are mn and md.
pivot(d, c(mean, median, sd, IQR), Salary, Dept)
## Dept n_Salary na_Salary Salary_mn Salary_md Salary_sd Salary_IQR
## 1 ACCT 5 0 61792.78 69547.60 12774.61 21379.23
## 2 ADMN 6 0 81277.12 71058.60 27585.15 36120.57
## 3 FINC 4 0 69010.68 61937.62 17852.50 16034.81
## 4 MKTG 6 0 70257.13 61658.99 19869.81 26085.69
## 5 SALE 15 0 78830.07 77714.85 23476.84 28810.28
Also have available two functions provided by lessR that are not part of base R: skew() and kurtosis().
pivot(d, c(mean,sd,skew,kurtosis), Salary, Dept, digits_d=3)
## Dept n_Salary na_Salary Salary_mn Salary_sd Salary_sk Salary_kt
## 1 ACCT 5 0 61792.78 12774.61 -0.623 -3.032
## 2 ADMN 6 0 81277.12 27585.15 0.835 -1.185
## 3 FINC 4 0 69010.68 17852.50 1.689 2.752
## 4 MKTG 6 0 70257.13 19869.81 0.859 -1.458
## 5 SALE 15 0 78830.07 23476.84 0.863 0.856
Can also specify the variable names of the aggregated statistics with the out_names parameter. Here calculate the mean and median Salary for each group defined by each combination of levels for Gender and Dept.
pivot(d, c(mean, median), Salary, c(Gender,Dept), out_names=c("MeanSalary", "MedianSalary"))
## Gender Dept n_Salary na_Salary MeanSalary MedianSalary
## 1 F ACCT 3 0 63237.16 71084.02
## 2 M ACCT 2 0 59626.19 59626.19
## 3 F ADMN 4 0 81434.00 71058.60
## 4 M ADMN 2 0 80963.35 80963.35
## 5 F FINC 1 0 57139.90 57139.90
## 6 M FINC 3 0 72967.60 66312.89
## 7 F MKTG 5 0 64496.02 61356.69
## 8 M MKTG 1 0 99062.66 99062.66
## 9 F SALE 5 0 64188.25 56508.32
## 10 M SALE 10 0 86150.97 82442.74
### Aggregate Multiple Variables
The pivot() function can also aggregate over multiple variables. Here, aggregate Years and Salary. Round the numerical aggregated results to the nearest integer with the digits_d parameter, which specifies the number of decimal digits in the output. Different variables can have different amounts of missing data, so the sample size, n, and number missing, the number of values Not Available, na, are listed separately for each aggregated variable.
pivot(d, mean, c(Years, Salary), c(Dept, Gender), digits_d=0)
## Dept Gender n_Years na_Years Years_mn n_Salary na_Salary Salary_mn
## 1 ACCT F 3 0 5 3 0 63237
## 2 ADMN F 4 0 8 4 0 81434
## 3 FINC F 1 0 7 1 0 57140
## 4 MKTG F 5 0 8 5 0 64496
## 5 SALE F 5 0 7 5 0 64188
## 6 ACCT M 2 0 7 2 0 59626
## 7 ADMN M 2 0 16 2 0 80963
## 8 FINC M 3 0 11 3 0 72968
## 9 MKTG M 1 0 18 1 0 99063
## 10 SALE M 9 1 12 10 0 86151
By default, the names of the aggregated variables are the same as the original variables with the added notation that identifies the aggregated statistic. Customize these names with the out_names parameter. If more than one variable, list the custom names in the same order as the vector of variable names. Here also turn off the display of the sample size and number of missing values for each group.
pivot(d, mean, c(Years, Salary), Dept, digits_d=2,
out_names=c("YearsMean", "SalaryMean"), show_n=FALSE)
## Dept YearsMean SalaryMean
## 1 ACCT 5.60 61792.78
## 3 FINC 10.25 69010.68
## 4 MKTG 9.83 70257.13
## 5 SALE 10.29 78830.06
### Compute over All Data
Aggregation computes one or more statistics for one or more variables across groups defined by the possible combinations of the levels of one or more categorical variables. A related computation computes the variables for each statistic for all the data. To compute over all the rows of data, do not specify groups, that is, drop the by parameter.
Get the grand mean of Years, that is, for all the data.
pivot(d, mean, Years)
## n_Years na_Years Years_mn
## 36 1 9.389
Get the grand mean of Years and Salary. Specify custom names for the results.
pivot(d, mean, c(Years, Salary), digits_d=2, out_names=c("MeanYear", "MeanSalary"))
## n_Years na_Years MeanYear n_Salary na_Salary MeanSalary
## 36 1 9.39 37 0 73795.56
Consider an example with more variables. Analyze the 6-pt Likert scale responses to the Mach IV scale that assesses Machiavellianism. Items are scored from 0 to 5, Strongly Disagree to Strongly Agree. The data are included with lessR as the Mach4 data file.
Suppress output when reading by setting quiet to TRUE. Calculate the mean, standard deviation, skew, and kurtosis for all of the data for each of the 20 items on the scale. With this specification, the form of a data frame is statistics in the columns and the variables in the rows. The result are the specified summary statistics for the specified variables over the entire data set.
d <- Read("Mach4", quiet=TRUE)
pivot(d, c(mean,sd,skew,kurtosis), m01:m20)
## n na mean sd skew kurtosis
## m01 351 0 1.279 1.286 0.984 0.356
## m02 351 0 1.746 1.480 0.475 -0.784
## m03 351 0 2.900 1.450 -0.363 -0.829
## m04 351 0 3.339 1.174 -0.855 0.457
## m05 351 0 2.234 1.583 0.076 -1.095
## m06 351 0 3.074 1.478 -0.454 -0.923
## m07 351 0 2.775 1.473 -0.065 -1.150
## m08 351 0 2.100 1.456 0.133 -1.078
## m09 351 0 4.225 1.155 -1.745 2.743
## m10 351 0 3.991 1.138 -1.154 0.932
## m11 351 0 1.641 1.395 0.641 -0.393
## m12 351 0 1.801 1.625 0.422 -1.116
## m13 351 0 1.385 1.368 0.836 -0.126
## m14 351 0 1.954 1.304 0.201 -0.923
## m15 351 0 2.123 1.367 -0.088 -0.995
## m16 351 0 2.177 1.782 0.237 -1.355
## m17 351 0 2.407 1.604 0.085 -1.142
## m18 351 0 2.915 1.326 -0.559 -0.326
## m19 351 0 1.157 1.425 1.290 0.872
## m20 351 0 0.895 1.351 1.499 1.224
### Frequency Tables
Aggregating a statistical computation of a continuous variable over groups with pivot(), such as computing the mean for each combination of Dept and Gender, by default includes the tabulation for each group (cell). A tabulation can be requested with no analysis of a numerical variable, instead only a counting of the available levels of the specified categorical variables.
The table value of compute specifies to compute the frequency table for a categorical aggregated variable across all combinations of the by variables. Specify one categorical variable with the remaining categorical variables specified with the by parameter. Missing values for each combination of the levels of the grouping variables are displayed.
Begin with a one-way frequency table computed over the entire data set.
pivot(d, table, m06)
## m06 Freq Prop
## 1 0 18 0.051
## 2 1 47 0.134
## 3 2 63 0.179
## 4 3 44 0.125
## 5 4 121 0.345
## 6 5 58 0.165
In this example, compute a two-way cross-tabulation table with the levels of variable m06 as columns and the levels of the by categorical variable m07 as rows.
pivot(d, table, m06, m07)
## m07 n_m06 na_m06 0 1 2 3 4 5
## 1 0 17 0 4 3 2 3 3 2
## 2 1 64 0 7 24 7 6 18 2
## 3 2 87 0 4 14 30 13 24 2
## 4 3 43 0 2 1 10 16 12 2
## 5 4 93 0 0 3 13 5 56 16
## 6 5 47 0 1 2 1 1 8 34
To output the data in long form, one tabulation per row, set the table_long parameter to TRUE.
If interested in the inferential analysis of the cross-tabulation table, access the lessR function Prop_test() to obtain both the descriptive and inferential results, though limited to a one- or two-way table.
The default data table is d, but included explicitly in the following example to illustrate the data parameter.
Prop_test(m06, by=m07, data=d)
## variable: m06
## by: m07
##
## >>> Pearson's Chi-squared test <<<
##
## >>> Description
##
## m06
## m07 0 1 2 3 4 5 Sum
## 0 4 3 2 3 3 2 17
## 1 7 24 7 6 18 2 64
## 2 4 14 30 13 24 2 87
## 3 2 1 10 16 12 2 43
## 4 0 3 13 5 56 16 93
## 5 1 2 1 1 8 34 47
## Sum 18 47 63 44 121 58 351
##
## Cramer's V: 0.380
##
## Row Col Observed Expected Residual Stnd Res
## 1 1 4 0.872 3.128 3.526
## 1 2 3 2.276 0.724 0.528
## 1 3 2 3.051 -1.051 -0.681
## 1 4 3 2.131 0.869 0.652
## 1 5 3 5.860 -2.860 -1.496
## 1 6 2 2.809 -0.809 -0.542
## 2 1 7 3.282 3.718 2.330
## 2 2 24 8.570 15.430 6.263
## 2 3 7 11.487 -4.487 -1.616
## 2 4 6 8.023 -2.023 -0.844
## 2 5 18 22.063 -4.063 -1.182
## 2 6 2 10.575 -8.575 -3.192
## 3 1 4 4.462 -0.462 -0.259
## 3 2 14 11.650 2.350 0.853
## 3 3 30 15.615 14.385 4.634
## 3 4 13 10.906 2.094 0.782
## 3 5 24 29.991 -5.991 -1.558
## 3 6 2 14.376 -12.376 -4.119
## 4 1 2 2.205 -0.205 -0.151
## 4 2 1 5.758 -4.758 -2.274
## 4 3 10 7.718 2.282 0.968
## 4 4 16 5.390 10.610 5.216
## 4 5 12 14.823 -2.823 -0.967
## 4 6 2 7.105 -5.105 -2.238
## 5 1 0 4.769 -4.769 -2.615
## 5 2 3 12.453 -9.453 -3.357
## 5 3 13 16.692 -3.692 -1.164
## 5 4 5 11.658 -6.658 -2.432
## 5 5 56 32.060 23.940 6.092
## 5 6 16 15.368 0.632 0.206
## 6 1 1 2.410 -1.410 -1.002
## 6 2 2 6.293 -4.293 -1.976
## 6 3 1 8.436 -7.436 -3.037
## 6 4 1 5.892 -4.892 -2.315
## 6 5 8 16.202 -8.202 -2.705
## 6 6 34 7.766 26.234 11.071
##
## >>> Inference
##
## Chi-square statistic: 253.103
## Degrees of freedom: 25
## Hypothesis test of equal population proportions: p-value = 0.000
Can also aggregate other statistics simultaneously in addition to the frequency table, though, of course, only meaningful if the aggregated variable is numerical. Here, create a 3-way cross-tabulation table with responses to variable m06 in the column and responses to by variables m07 and m10 in the rows, plus the mean and standard deviation of each combination of m07 and m10 across levels of m06.
pivot(d, c(mean,sd,table), m06, c(m07, m10))
## m07 m10 n_m06 na_m06 m06_mn m06_sd 0 1 2 3 4 5
## 1 0 0 1 0 0.000 NA 1 0 0 0 0 0
## 2 1 0 1 0 1.000 NA 0 1 0 0 0 0
## 3 2 0 0 0 NA NA 0 0 0 0 0 0
## 4 3 0 1 0 2.000 NA 0 0 1 0 0 0
## 5 4 0 1 0 2.000 NA 0 0 1 0 0 0
## 6 5 0 0 0 NA NA 0 0 0 0 0 0
## 7 0 1 0 0 NA NA 0 0 0 0 0 0
## 8 1 1 4 0 0.750 0.500 1 3 0 0 0 0
## 9 2 1 2 0 1.500 0.707 0 1 1 0 0 0
## 10 3 1 1 0 2.000 NA 0 0 1 0 0 0
## 11 4 1 0 0 NA NA 0 0 0 0 0 0
## 12 5 1 0 0 NA NA 0 0 0 0 0 0
## 13 0 2 2 0 2.000 1.414 0 1 0 1 0 0
## 14 1 2 9 0 1.222 1.202 2 5 1 0 1 0
## 15 2 2 15 0 2.000 0.845 0 4 8 2 1 0
## 16 3 2 3 0 3.000 0.000 0 0 0 3 0 0
## 17 4 2 3 0 3.333 1.155 0 0 1 0 2 0
## 18 5 2 0 0 NA NA 0 0 0 0 0 0
## 19 0 3 5 0 1.200 1.304 2 1 1 1 0 0
## 20 1 3 16 0 2.250 1.390 2 3 4 3 4 0
## 21 2 3 13 0 2.769 0.832 0 0 6 4 3 0
## 22 3 3 7 0 2.000 1.528 2 0 2 2 1 0
## 23 4 3 9 0 3.333 1.323 0 1 2 0 5 1
## 24 5 3 0 0 NA NA 0 0 0 0 0 0
## 25 0 4 7 0 2.714 1.799 1 1 1 1 2 1
## 26 1 4 19 0 2.895 1.449 0 6 1 2 9 1
## 27 2 4 29 0 2.690 1.417 2 4 8 4 9 2
## 28 3 4 18 0 3.278 1.074 0 1 3 6 6 2
## 29 4 4 32 0 3.781 1.008 0 0 6 2 17 7
## 30 5 4 5 0 4.400 0.548 0 0 0 0 3 2
## 31 0 5 2 0 4.500 0.707 0 0 0 0 1 1
## 32 1 5 15 0 2.133 1.685 2 6 1 1 4 1
## 33 2 5 28 0 2.571 1.372 2 5 7 3 11 0
## 34 3 5 13 0 3.154 0.801 0 0 3 5 5 0
## 35 4 5 48 0 3.854 0.922 0 2 3 3 32 8
## 36 5 5 42 0 4.452 1.234 1 2 1 1 5 32
Can also express the frequencies as proportions. To convert the frequencies into proportions, invoke the table_prop parameter. The value of "all" computes cell frequencies across the entire table. The values of "row" and "col" compute the proportions with either row sums or column sums.
In this example of a two-way cross-tabulation table, convert the table counts to row proportions, that is, the proportion of each level of m06 for each combination of levels for m07. The sum of the proportions in each row is 1.0.
pivot(d, table, m06, m07, table_prop="row")
##
## Proportions computed over row cells
## m07 n_m06 na_m06 0 1 2 3 4 5
## 1 0 17 0 0.235 0.176 0.118 0.176 0.176 0.118
## 2 1 64 0 0.109 0.375 0.109 0.094 0.281 0.031
## 3 2 87 0 0.046 0.161 0.345 0.149 0.276 0.023
## 4 3 43 0 0.047 0.023 0.233 0.372 0.279 0.047
## 5 4 93 0 0.000 0.032 0.140 0.054 0.602 0.172
## 6 5 47 0 0.021 0.043 0.021 0.021 0.170 0.723
d <- Read("Employee", quiet=TRUE)
### Quantiles
One way to understand the characteristics of a distribution of data values of a continuous variable is to sort the values and then split into equal-sized groups. The simplest example is the median, which splits a distribution into two groups, the bottom lowest values and the top highest values. Quartiles divide the distribution into four groups. The first quartile is the smallest 25% of the data values, etc.
Quantiles: Divide a distribution of sorted data values into n groups.
By default, calling the quantile function computes quartiles. Here calculate the quartiles for Years aggregated across levels of Dept and Gender.
pivot(d, quantile, Years, c(Dept, Gender))
## Dept Gender n_ na_ Years_0 Years_25 Years_50 Years_75 Years_100
## 1 ACCT F 3 0 2 2.50 3.0 6.00 9
## 2 ADMN F 4 0 2 3.50 5.0 9.00 18
## 3 FINC F 1 0 7 7.00 7.0 7.00 7
## 4 MKTG F 5 0 1 4.00 8.0 10.00 18
## 5 SALE F 5 0 2 3.00 8.0 10.00 10
## 6 ACCT M 2 0 5 6.00 7.0 8.00 9
## 7 ADMN M 2 0 7 11.25 15.5 19.75 24
## 8 FINC M 3 0 10 10.00 10.0 12.00 14
## 9 MKTG M 1 0 18 18.00 18.0 18.00 18
## 10 SALE M 9 1 5 9.00 13.0 14.00 21
To compute other than quantiles, invoke the q_num parameter, the number of quantile intervals. The default value is 4 for quartiles. In the following example, compute the quintiles for Years and Salary, plus the mean and standard deviation. No specification of by, so these descriptive statistics are computed over the entire data set for both specified variables.
pivot(d, c(mean,sd,quantile), c(Years,Salary), q_num=5, digits_d=2)
## n na mean sd p_0 p_20 p_40 p_60 p_80 p_100
## Years 36 1 9.39 5.72 1.00 4.00 8.00 10.00 14.00 24.0
## Salary 37 0 73795.56 21799.53 46124.97 55737.86 63701.93 72430.04 92415.42 134419.2
## Other Features
### Drill-Down
One data analysis strategy examines the values of a variable, such as Sales for a business or Mortality for an epidemiology study, at progressively finer levels of detail. Examine by Country or State or City or whatever level of granularity is appropriate.
Data drill down: Examine the values of a variable when holding the values of one or more categorical variables constant.
If drilling down into the data, pivot() indicates the drill-down with a display of all categorical variables with unique values that precedes the primary output. Initiate the drill-down by a previous subset of the data frame, or by pivot() directly. As with other lessR analysis functions, the rows parameter specifies a logical condition for which to subset rows of the data frame for analysis.
In this example, compute the mean of Salary for each level of Dept for just those rows of data with the value of Gender equal to “F”.
pivot(d, mean, Salary, Dept, rows=(Gender=="F"))
## Gender: F
## Dept n_Salary na_Salary Salary_mn
## 1 ACCT 3 0 63237.16
## 2 ADMN 4 0 81434.00
## 3 FINC 1 0 57139.90
## 4 MKTG 5 0 64496.02
## 5 SALE 5 0 64188.25
The parentheses for the rows parameter are not necessary, but does enhance readability.
Can also drill down by subsetting the data frame with a logical condition directly in the data parameter in the call to pivot(). Here drill down with base R Extract[ ] in conjunction with the lessR function .() to simplify the syntax (explained in the vignette Subset a Data Frame). The Extract[ ] function specifies the rows of the data frame to extract before the comma, and the columns to extract after the comma. Here select only those rows of data with Gender declared as Female. There is no information after the comma, so no columns are specified, which means to retain all columns, the variables in the data frame.
pivot(d[.(Gender=="F"),], mean, Salary, Dept)
## Gender: F
## Dept n_Salary na_Salary Salary_mn
## 1 ACCT 3 0 63237.16
## 2 ADMN 4 0 81434.00
## 3 FINC 1 0 57139.90
## 4 MKTG 5 0 64496.02
## 5 SALE 5 0 64188.25
### Sort Output
Specify the sort as part of the call to pivot() with the parameter sort. This internal sort works for a single value variable, by default the last column in the output data frame. Set to "-" for a descending sort. Set to "+" for an ascending sort.
pivot(d, mean, Salary, c(Dept, Gender), sort="-")
## Dept Gender n_Salary na_Salary Salary_mn
## 9 MKTG M 1 0 99062.66
## 10 SALE M 10 0 86150.97
## 2 ADMN F 4 0 81434.00
## 7 ADMN M 2 0 80963.35
## 8 FINC M 3 0 72967.60
## 4 MKTG F 5 0 64496.02
## 5 SALE F 5 0 64188.25
## 1 ACCT F 3 0 63237.16
## 6 ACCT M 2 0 59626.19
## 3 FINC F 1 0 57139.90
Specify the sort_var parameter to specify the name or the column number of the variable to sort.
pivot(d, c(mean, median), Salary, c(Gender,Dept), out_names=c("MeanSalary", "MedianSalary"),
sort="-", sort_var="MeanSalary")
## Gender Dept n_Salary na_Salary MeanSalary MedianSalary
## 8 M MKTG 1 0 99062.66 99062.66
## 10 M SALE 10 0 86150.97 82442.74
## 3 F ADMN 4 0 81434.00 71058.60
## 4 M ADMN 2 0 80963.35 80963.35
## 6 M FINC 3 0 72967.60 66312.89
## 7 F MKTG 5 0 64496.02 61356.69
## 9 F SALE 5 0 64188.25 56508.32
## 1 F ACCT 3 0 63237.16 71084.02
## 2 M ACCT 2 0 59626.19 59626.19
## 5 F FINC 1 0 57139.90 57139.90
Because the output of pivot() with no by_cols variables is a standard R data frame, the external call to the lessR function Sort() is available for custom sorting by one or more variables. Sort in the specified direction with the direction parameter.
a <- pivot(d, mean, Salary, c(Dept, Gender))
Sort(a, by=Salary_mn, direction="-")
##
## Sort Specification
## 5 --> descending
## Dept Gender n_Salary na_Salary Salary_mn
## 9 MKTG M 1 0 99062.66
## 10 SALE M 10 0 86150.97
## 2 ADMN F 4 0 81434.00
## 7 ADMN M 2 0 80963.35
## 8 FINC M 3 0 72967.60
## 4 MKTG F 5 0 64496.02
## 5 SALE F 5 0 64188.25
## 1 ACCT F 3 0 63237.16
## 6 ACCT M 2 0 59626.19
## 3 FINC F 1 0 57139.90
Specify multiple variables to sort with a vector of variable names, and a corresponding vector of "+" and "-" signs of the same length for the directions parameter.
### Pipe Operator
The following illustrates as of R 4.1.0 the base R pipe operator |> with pivot(). The pipe operator by default inserts the object on the left-hand side of an expression into the first parameter value for the function on the right-hand side.
In this example, input the d data frame into the first parameter of pivot(), the data parameter. Then direct the output to the data frame a with the standard R assignment statement, though written pointing to the right hand side of the expression.
To avoid problems installing this version of lessR from source with a previous version of R, the code is commented out with a # sign in the first column.
#d |> pivot(mean, Salary, c(Dept, Gender)) -> a
#a
## Output as a 2-D Table
Specify up to two by_cols categorical variables to create a two-dimensional table with the specified columns. Specifying one or two categorical variables as by_cols variables moves them from their default position in the rows to the columns, which changes the output structure from a long-form data frame to a cross-tabulation table with categorical variables in the rows and columns.
In this example, specify by by_cols variable, Gender.
pivot(d, mean, Salary, Dept, Gender)
Table: mean of Salary
Gender F M
Dept
------- --------- ---------
ACCT 63237.16 59626.20
FINC 57139.90 72967.60
MKTG 64496.02 99062.66
SALE 64188.25 86150.97
Here two by_cols variables, specified as a vector. There is much missing data for this three-way classification as there is not much data in each group, with many groups having no data.
pivot(d, mean, Salary, Dept, c(Gender, Plan))
Table: mean of Salary
Gender F M
Plan 1 2 3 1 2 3
Dept
------- --------- --------- --------- --------- ---------- ---------
ACCT NA 63237.16 NA 69547.60 NA 49704.79
ADMN NA 67724.21 122563.4 53788.26 108138.43 NA
FINC NA 57139.90 NA 61937.62 NA 95027.55
MKTG 56772.95 66426.79 NA NA NA 99062.66
SALE 60941.54 66352.73 NA 89393.40 82442.74 80131.91
## Missing Data
There are two different levels of missing data in an aggregation: some missing values for one or more aggregated variables for which the statistic is computed, and all missing values for the variable so that the group (cell) defined by one or more by variables has no data values. Accordingly, there are two different missing data parameters with pivot().
• na_remove=TRUE: Remove any missing data from a value of the variable that leaves remaining values, then perform the aggregation on the remaining values, reporting how many values are missing, otherwise report the computed statistic as NA (missing). [default is TRUE].
• na_by_show=TRUE: If all values of variable are missing for a group so that the entire level of the by variables is missing, show those missing cells with a reported value of computed variable n as 0, otherwise delete from the output [default is TRUE].
### Missing Data Values for Aggregated Variables
By default, the data frame output of pivot() lists the number of occurrences of missing data for each group of the variable over which the statistic is computed. The na_remove parameter specifies the value of the base R parameter na.rm for computations such as for the mean. The parameter value is either TRUE or FALSE, indicating if NA (missing) values of the variable should be removed before the computation proceeds. The default value na_remove is TRUE, so the missing values are removed, their number of occurrences reported, and then the computed statistic displayed.
In this example, the variable Years has one missing value, which occurs in the Sales department.
pivot(d, mean, Years, Dept)
## Dept n_Years na_Years Years_mn
## 1 ACCT 5 0 5.600
## 2 ADMN 6 0 10.167
## 3 FINC 4 0 10.250
## 4 MKTG 6 0 9.833
## 5 SALE 14 1 10.286
Set na_remove to FALSE to not remove any missing data in a cell with values to be aggregated. According to the way in which R functions process the data with missing values entered into the function, the resulting computed value will be missing if any of the constituent data values are missing.
pivot(d, mean, Years, Dept, na_remove=FALSE)
## Dept n_Years na_Years Years_mn
## 1 ACCT 5 0 5.600
## 2 ADMN 6 0 10.167
## 3 FINC 4 0 10.250
## 4 MKTG 6 0 9.833
## 5 SALE 14 1 NA
### Missing Data Values for by Variables
To account for missing values of the categorical by variables for which there are no non-missing data values, for this example first create a cell with no values in the data aggregation. Use base R Extract[] with lessR .() to drop the one male in the Sales department, leaving no data values for that group. Save the result into the dd data frame.
dd <- d[.(!(Gender=="M" & Dept=="SALE")), ]
Explicitly set na_by_show to TRUE, the default value. The group for male sales employees is shown with the values of the computed variables n_ and na_ set to 0 and the values of all other variables necessarily missing.
pivot(dd, c(mean,median), Years, c(Dept, Gender), na_by_show=TRUE)
## Dept Gender n_Years na_Years Years_mn Years_md
## 1 ACCT F 3 0 4.667 3.0
## 2 ADMN F 4 0 7.500 5.0
## 3 FINC F 1 0 7.000 7.0
## 4 MKTG F 5 0 8.200 8.0
## 5 SALE F 5 0 6.600 8.0
## 6 ACCT M 2 0 7.000 7.0
## 7 ADMN M 2 0 15.500 15.5
## 8 FINC M 3 0 11.333 10.0
## 9 MKTG M 1 0 18.000 18.0
## 10 SALE M 0 0 NA NA
Drop the groups from the output with missing data for a by variable. To do so, set na_by_show to FALSE. Now the group for the non-existent male sales employee does not display.
pivot(dd, c(mean,median), Years, c(Dept, Gender), na_by_show=FALSE)
## Dept Gender n_Years na_Years Years_mn Years_md
## 1 ACCT F 3 0 4.667 3.0
## 2 ADMN F 4 0 7.500 5.0
## 3 FINC F 1 0 7.000 7.0
## 4 MKTG F 5 0 8.200 8.0
## 5 SALE F 5 0 6.600 8.0
## 6 ACCT M 2 0 7.000 7.0
## 7 ADMN M 2 0 15.500 15.5
## 8 FINC M 3 0 11.333 10.0
## 9 MKTG M 1 0 18.000 18.0
Any function that processes a single column of data and returns a single value can be accessed with pivot(). In this example, define a function named mnmd that computes the difference between the mean and median of a distribution of data values, here represented by x. For technical reasons, need to include the NA remove parameter, na.rm, in the function definition. Usually set to the value of na.rm to TRUE to allow for missing data to be dropped. If missing data are to be dropped in internal function calls, then the base R parameter na.rm needs to be set for each component function as well.
mnmd = function(x, na.rm=TRUE) mean(x, na.rm=na.rm) - median(x, na.rm=na.rm)
Invoke pivot() to compute the mean, the median, and their difference for each group in the aggregation of the variable Years.
pivot(d, c(mean, median, mnmd), Years, by=Dept)
## User defined function (or typing error): mnmd
## Dept n_Years na_Years Years_mn Years_md Years_mnmd
## 1 ACCT 5 0 5.600 5.0 0.600
## 2 ADMN 6 0 10.167 6.5 3.667
## 3 FINC 4 0 10.250 10.0 0.250
## 4 MKTG 6 0 9.833 9.0 0.833
## 5 SALE 14 1 10.286 10.0 0.286
## lessRpivot() vs Base Raggregate()
The lessR pivot() function relies upon the base R function aggregate() for aggregation. By default, except for the table computation, pivot() generates a long-form data frame pivot table (Excel terminology), which can then be directly input into analysis and visualization functions as a standard data frame. The levels across all the by grouping variables are listed in the rows. If there are specified column grouping variables according to by_cols, pivot() relies upon base R reshape() to form a 2-d table for direct viewing instead of a data table to input into further analysis functions.
pivot() provides additional features than aggregate() provides.
1. For each value over which to aggregate, the sample size and number of missing values for each group is provided.
2. Multiple statistical functions can be selected for which to compute the aggregated value for each group.
3. Extends beyond aggregation to compute statistics over the entire data set instead of groups of data.
4. Missing data analysis by cell or by the value aggregated.
5. Aggregation not necessary, so can compute the specified statistic(s) for each variable across the entire data set.
6. The aggregated computations can be displayed as a 2-d table, not just a long-form data frame.
7. by variables of type Date, character and integer retain the same variable type in the summary table instead of each converted to a factor (set factors=TRUE to get factors instead).
8. The list of parameters lists the data parameter first, which facilitates the use of the pipe operator, such as from base R as of Version 4.1.0 or the magrittr package.
9. Any non-numeric variables with unique values in the submitted data are listed with their corresponding data value, which identifies when drilling down into the data to study relevant rows.
Although the pivot() function does considerably extend the functionality of base R aggregate(), pivot() does rely upon the base R function for most of its computations.
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2021-10-22 03:29:57
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https://www.flyingcoloursmaths.co.uk/algebraic-fractions-a-reader-asks/
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Oo, a question to answer! This one’s from Deborah.
How would you solve:
$\frac{1}{x-2} + \frac{1}{x} = \frac{3}{4}$ and $\frac{1}{x}+\frac{1}{2x+1}=\frac{7}{10}$?
When I substitute my answer back in, I can’t get it to work out!
Forgive me if my working is a bit pedestrian — I figure it’s better to err on the side of too helpful rather than not helpful enough.
To solve $\frac{1}{x-2} + \frac{1}{x} = \frac{3}{4}$, I’d combine the left hand side into a single fraction, multiplying the first one by $\frac{x}{x}$ and the second by $\frac{(x-2)}{(x-2)}$ to get:
$\frac{x}{x(x-2)} + \frac{(x-2)}{x(x-2)} = \frac{2x-2}{x(x-2)} = \frac{3}{4}$
Cross-multiplying:
$4(2x - 2) = 3x(x-2) \\ 8x - 8 = 3x^2 - 6x\\ 0 = 3x^2 - 14x +8 \\ 0 = (3x-2)(x-4)$
Then either $x = \frac{2}{3}$ or $x = 4$. Substituting either value back in as $x$ on the left hand side does indeed give $\frac{3}{4}$.
The second one is similar:
$\frac{1}{x} + \frac{1}{2x+1} = \frac{7}{10} \\ \frac{2x+1}{x(2x+1)} + \frac{x}{x(2x+1)} = \frac{7}{10} \\ \frac{3x+1}{x(2x+1)} = \frac{7}{10} \\ 10(3x+1) = 7x(2x+1) \\ 30x + 10 = 14x^2 + 7x \\ 0 = 14x^2 - 23x - 10 \\ 0 = (14x+5)(x-2)$
(Yikes!) So $x = 2$ or $x = -\frac{5}{14}$. It’s clear enough that 2 works, but I’ll need to work it out for $-\frac{5}{14}$:
$\frac{1}{-5/14} + \frac{1}{-5/7 + 1} = -\frac{14}{5} + \frac{7}{2} = -\frac{28}{10} + \frac{35}{10} = \frac{7}{10}$
Whew!
If you'd like me to answer any of your questions, you can improve your chances by showing me that you've made a decent stab at it first, like Deborah did.
## Colin
Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.
#### Share
• ##### Joshua Zucker
Rather than making common denominators and then cross-multiplying, I’d multiply by all the denominators at the very beginning. For example for the second one I’d start with
$$\frac{1}{x}(x)(2x+1)(10) + \frac{1}{2x+1}(x)(2x+1)(10) = \frac{7}{10}(x)(2x+1)(10)$$
which then simplifies to
$$(2x+1)(10) + (x)(10) = 7(x)(2x+1)$$
It is rather similar to your approach, for sure, but somehow I seem to make fewer mistakes in doing it this way.
• ##### Colin
I like that approach, too – thanks, Joshua!
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2020-04-07 19:49:30
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http://mathhelpforum.com/differential-geometry/79174-saddles-nodes.html
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Hello,
I have a phase portrait that is supposed to contain a saddle and a node, only problem is i can only see the saddle which is at about 0.25. Could someone point out where the node is? I know the pictures not that great and if you want another view just say.
Thanks
2. Can you post the equation that you're using?
I'm eager to find this ellusive node, it's just that I want to see if I can work it out algebraically so I know where to look.
3. Ok. Its a saddle-node bifurcation and there's also another picture that im supposed to find the node on...
Here's the equation $u'(t) = -au + v, v'(t) = \frac{1}{1+u^2} - v$
But iv'e found the node in that picture i posted. You have to extend the axis and its there.
But my next problem is to find the node when a is negative. Its only there between -0.1 and 0 according to eigenvalues but i cant see it.
a is set to -0.09 in this pic. The saddles way put to the left past -5. But wheres the node!
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2013-06-19 17:25:47
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https://adreasnow.com/Undergrad/Notes/Sem%204.%20Spectroscopy/04.%20Absorption%20and%20emission/
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# Absorption and emission¶
Valence Electrons can make transitions between the orbitals by absorbing and emitting a discreet amount of energy
• The amount of energy absorbed and emitted must be exactly the energy difference between the two orbitals
• The energy absorbed places the atom in an excited state
• The exact amount of energy absorbed must then be radiated, as per the energy difference of orbitals
## Emission Series ¶
• Since the emissions of light are of exactly the same energy as the energy difference between the electron orbitals, the light that’s emitted will be very specific
• The emitted light from an electron dropping back down to the energy level n=1 (Lyman series) will be too high energy and will not be visible
• The opposite is true for an electron dropping back down to an energy of n=3 (Paschen series)
• Electrons dropping back down to energy level n=2 (Balmer series) will be visible Fraunhofer Lines
• Since only certain electron excitations/emissions will be visible and statistically probable for each element, various lines for different elements are assigned letters and used for characterisation purposes
## Sodium D line¶
• A perfect example is the sodium D line
• Since the valence electron occupies the 3s orbital, the most common excitation and emission will the path from the $$\ce{3p -> 3s}$$
• This results in a significantly brighter emission at 589 nm than any other wavelength.
List of more character spectral lines
Designation Element Wavelength (nm)
y O2 898.765
Z O2 822.696
A O2 759.370
B O2 686.719
C 656.281
a O2 627.661
D1 Na 589.592
D2 Na 588.995
D3 or d He 587.5618
e Hg 546.073
E2 Fe 527.039
b1 Mg 518.362
b2 Mg 517.270
b3 Fe 516.891
b4 Mg 516.733
c Fe 495.761
F 486.134
d Fe 466.814
e Fe 438.355
G’ 434.047
G Fe 430.790
G Ca 430.774
h 410.175
H Ca+ 396.847
K Ca+ 393.366
L Fe 382.044
N Fe 358.121
P Ti+ 336.112
T Fe 302.108
t Ni 299.444
## Hyperfine Spectrum¶
• When observed at very high resolution, spectral lines split can split into two (sodium $$D_1$$ and $$D_2$$)
• They are caused by an interaction of the atom’s nuclear magnetic dipole moment, due to the distribution of charge within the atom.
• The distance of the orbitals can vary, so slightly that there is a marked difference in the energy absorbed and emitted.
## Absorption and Emission¶
• Since the excitation and emission processes happen in conjunction with each other, absorbance is proportional to the emission and an absorption spectra is ultimately an inverse emission spectra
## Fingerprinting¶
• Due to the specific nature of the electron configuration of each element, due to it’s valence, electronegativity, mass, etc. Emission spectra can be used as a fingerprint of a different elements
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2023-03-21 23:04:40
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https://www.rdocumentation.org/packages/spatstat/versions/1.5-4/topics/plot.fv
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# plot.fv
0th
Percentile
##### Plot Function Valuesn
Plot method for the class "fv".
Keywords
spatial
##### Usage
plot.fv(x, fmla, subset=NULL, lty=NULL, col=NULL, xlim, ylim, xlab, ylab, ...)
##### Arguments
x
An object of class "fv", containing the variables to be plotted or variables from which the plotting coordinates can be computed.
fmla
an S language formula determining which variables or expressions are plotted.
subset
(optional) subset of rows of the data frame that will be plotted.
lty
(optional) numeric vector of values of the graphical parameter lty controlling the line style of each plot.
col
(optional) numeric vector of values of the graphical parameter col controlling the colour of each plot.
xlim
(optional) range of x axis
ylim
(optional) range of y axis
xlab
(optional) label for x axis
ylab
(optional) label for y axis
...
Extra arguments passed to plot.default.
##### Details
This is the plot method for the class "fv".
The use of the argument fmla is like plot.formula, but offers some extra functionality. The left and right hand sides of fmla are evaluated in the data frame x, and the results are plotted against each other (the left side on the $y$ axis against the right side on the $x$ axis). Both left and right sides may be variables in the data frame or expressions in these variables.
Multiple curves may be specified by a single formula of the form cbind(y1,y2,...,yn) ~ x, where x,y1,y2,...,yn are expressions involving the variables in the data frame. Each of the variables y1,y2,...,yn in turn will be plotted against x. See the examples.
##### Value
• none. Side effect is a plot.
fv.object, Kest
• plot.fv
##### Examples
data(cells)
K <- Kest(cells)
# K is an object of class "fv"
plot(K, iso ~ r) # plots iso against r
plot(K, sqrt(iso/pi) ~ r) # plots sqrt(iso/r) against r
plot(K, cbind(iso,theo) ~ r) # plots iso against r AND theo against r
plot(K, cbind(iso,theo) ~ r, col=c(2,3))
# plots iso against r in colour 2
# and theo against r in colour 3
plot(K, iso ~ r, subset=quote(r < 0.2))
# plots iso against r for r < 10
Documentation reproduced from package spatstat, version 1.5-4, License: GPL version 2 or newer
### Community examples
Looks like there are no examples yet.
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2019-11-21 20:45:12
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https://www.kepesartstudio.hu/concoction-medical-uqrne/archive.php?id=6ef2e1-hsc-physics-question-paper-2018-pdf
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The nucleons are held together by the (residual) strong force which is attractive at the typical separation between nucleons. \), Convert to joules via $$E = mc^{2} = 7.0260 \times10^{-13} J$$, Pauli’s proposal of the neutrino was a solution to the energy distribution of beta particles in beta decay – for a given decay the total energy released was constant, and it was expected that the kinetic energy of the released beta particle would be constant – as it is by far the lighter of the two products, it should receive all of the released energy. Maha Board HSC (12th) Model Question Paper 2021 Pdf. (a) Benefit: No power loss due to heating as resistance is zero. Date Subject Question Papers Solutions; 1: 2020-02-18: English: HSC Board English Question Paper Set J-301/A The ISS collides with air molecules in the upper atmosphere (air resistance) and loses momentum. “nature” is a part of natural philosophy and natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. Download Tamil Nadu HSC / 12 th public exam Question Paper and TN 12 th Model Question Papers at pdf… English Version HSC Physics Note Posted on January 20, 2019 by Shah Jamal Physics is “knowledge, the science of nature”, from physics, i.e. Here we are providing the Maharashtra Board HSC Question Papers of Physics subject.With the help of these MBSE question papers for Physics, candidates can estimate the level and pattern of questions asked by the Maharashtra board in the upcoming Senior Secondary examination.As these papers contain actual questions asked in MB Senior Secondary Education Exam, there is a … source X are likely alpha particles – their cloud trail is short and wide, source Y are likely beta particles – their cloud trails are long and thin. © Matrix Education and www.matrix.edu.au, 2018. educational institution and also for the supervision, control, and development of those institutions. From the T-L graph, absolute magnitude is $$M = -3.2$$. Hence I-124’s emission is appropriate. The two forces are equal and opposite, according to Newton’s 3rd Law. Find the altitude at which the acceleration due to gravity is 25% of that at the surface of the earth. Today our cup of tea is hsc physics 1st paper question 2020 and physics 1st paper suggestion 2020.It is known to us all that the syllabus of HSC examination is very huge and your time is very short. CT scans are much better at looking at soft tissue structures. These are produced by observing relatively cooler gas against a brighter and hotter background. Across the board, furthermore, CCDs yield faster data collection, reduced data loss and improved data comparability. So don’t expect question paper before exam. These collisions are inelastic on average and the electrons lose energy to the lattice (converted to heat). In addition, positrons have a low penetration and acceptable ionisation strength. He measured the final momenta and energy of the ejected protons, and used these conservation laws to infer the mass of the particle X. Graph of kinetic energies of beta particles after a specific beta decay reaction. Step 2: … This force is the centripetal force of circular motion; by equation $$qvB = \frac{mv^{2}}{r}$$, we can conclude that v is proportional to r. As g is larger on Earth, a given period will be achieved with a longer length compared to Mars, hence the graph for Earth will be above that of Mars. hT�N�@��}Q��][BH 撪���"u��,��G�ے����RA����f�gf疝#,g�a� �+�p�"Jp�LH�edY���&�=z���~�d�&�8]N�Y���JΒr�*�0L����1=+�8� ���߲��d�n�/f���+r�L8���ɘ��LЛ������|Re��媶�����/+Ŝ������J��'�����0����PpCϊl�!&�:���P��J� Will require more torque (mechanics energy input) in order to produce more current and hence more power or energy. Don’t run after HSC question paper 2018 before HSC exam 2018. How to Download. Blackbody spectra alone yield no chemical information (is a smooth spectrum by definition) they indicate accurately the surface temperature of the star from the distinctive peak wavelength of the spectrum, where $$\lambda_{peak}$$ is proportional to $$\frac{1}{temperature}$$. Join 75,893 students who already have a head start. Higher spatial resolution over photographic plates yields better parallax and distance measurements. The star ends life as a supernova explosion (creating many other elements) while the core of oxygen, neon and other elements collapses into a neutron star. Read this post to check the answers and explanations to the 2018 HSC Physics Exam Paper. © 2020 Matrix Education. 5456 0 obj <>stream General Instructions • Reading time – 5 minutes • Working time – 3 hours • Write using black pen • Draw diagrams using pencil • Calculators approved by NESA may be used • A data sheet, formulae sheets and Periodic Table are provided at the back of this paper. Measuring a ‘flow velocity waveform’ – the cycle of fast and slow blood flow as the heart pumps. As it was undetected until this stage, it must have no charge, low mass and minimal interactions with other particles. AAS in Chemistry). In a school lab, one can observe a white light through a transparent box of gas (e.g. Patient lies in centre of CT machine, which rotates around patient and takes several X-ray images at different angles. Weight on Earth is w = mg = 70 x 9.8 = 686 N, Weight on the Moon is w = mg = 70 x 1.6 = 112 N. This will result in an induced EMF (Faraday’s Law) in the disc and eddy currents. Testpaperz.com is home to the largest collection of Board test papers/ School Prelim Test Papers/ Sample Question papers of ICSE, ISC, SSC, HSC and CBSE of Maths, Science, Physics, Chemistry, English, Accountancy, Computer Science, Physical Education, Biology and many other subjects for class 9,10,11 & … $$d = 79 400 \text{pc}$$ (3 sig. Michelson attempted to demonstrate a difference in travel times for arms parallels / perpendicular to the direction of earth’s travel due to aether wind. It is useful for examining hard tissues such as bone structure (e.g. In a school lab, one could observe the glowing tungsten filament of an incandescent light bulb through a spectroscope in a darkened room. The graph as shown should be intensity vs wavelength, and higher temperatures emit more radiation. These can be used in positron emission tomography for high-quality medical imaging. Read this post to check the answers and explanations to the 2018 HSC Physics Exam Paper. The saucepan must be a conductor for currents to be induced. Physics Set 1 2018-2019 HSC Science (General) 12th Board Exam Question Paper Solution Physics [Set 1] Marks: 80 Academic Year: 2018-2019 Date & Time: 25th February 2019, 11:00 am Duration: 3h (i) Chadwick used the laws of conservation of momentum and energy to identify the mass of particle X. 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(ii) Impedance of kidney tissue, $$Z = \rho \times v = 1050 \times 1560 = 1.638 \times 10^{6}rayls$$, $$R=\frac{(Z_{kidney} – Z_{fat})^{2}}{(Z_{kidney} + Z_{fat})^{2}}$$, $$0.01=\frac{(Z_{kidney} – Z_{fat})^{2}}{(Z_{kidney} + Z_{fat})^{2}}$$, $$0.1=\frac{Z_{kidney} – Z_{fat}}{Z_{kidney} + Z_{fat}}$$, $$0.1(Z_{kidney} + Z_{fat})=Z_{kidney} – Z_{fat}$$, Substitute $$_{kidney} = 1.638 \times 10^{6} rayls$$, $$Z_{fat} = 1.340 \times 10^{6} rayls$$. This also results in a voltage drop across the power line depending on the current and resistance of the power line (V = IR). Spectroscopy sees the greatest benefits. The magnetic fields are used to deflect the electron beam and scan it across the screen. HSC Physics 1st Paper Question 2018. Power lines: The increased current will increase the heat produced meaning the some electrical energy is converted to heat. Acoustic waves reflecting off a moving target will experience a change in frequency proportional to the velocity and direction of the target. The relationship between L and T is $$L = \frac{gT^{2}}{(4\pi^{2})}$$, so only C or D show this square relationship. $$\frac{(m-M+5)}{5} = \frac{(16.3 + 3.2 +5)}{5} = 4.9$$ One star whose atmosphere pulsates in size and temperature and hence luminosity. All charges in a constant field will experience an acceleration that depends on their charge-to-mass ratio (q/m). Out current understanding of the atom is that it is composed of a nucleus consisting of positively charged protons and neutral neutrons, surrounded by negatively charged electrons in discrete energy levels. Direct Link to download GSEB Std 12 Question Paper is given below. Hence there is no net energy loss for the Cooper pair. From the diagrams, we can see that the decay products of. The result is a blackbody spectrum (from the inner stellar core) superimposed with dark lines or dips. 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The neutrons are required as they increase the attraction due to the strong force without increasing repulsion due to the electric force, and hence they contribute to the stability of the nucleus. The Board of Intermediate and Secondary Education, Dhaka is an autonomous organization, mainly responsible for holding two public examinations (SSC & HSC) and for providing recognition to the newly established non-govt. Increased radiation pressure expands the outer layers causing cooling and the star is now a red supergiant. HSC English 2nd Letter Advice 2020 – 100% General in Question Paper. The GSEB HSC Question Paper covers all topics that are mentioned in Gujarat Board 12th Books. Unauthorised use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited. In a school lab, one can observe a gas lamp (e.g hydrogen or mercury) or fluorescent light tubes through a spectroscope in a darkened room. The peak of the blackbody yields temperature while the absorption lines yield chemical composition since all atoms are ions have unique characteristic wavelengths of absorption (and emission). Maharashtra State Board Class 12 maths 2018 question paper with solutions are available on this page, by BYJU’S, in downloadable pdf format and also in the text for the students to prepare well for the MSBSHSE exams. Maharashtra HSC 12th Question Paper 2020-2021 with answers for Science, Physics, Arts now available. Download Free Previous Years HSC Science Question Papers from 2013-2020. By referring the question paper Solutions for Physics, you can scale your … Read our cookies statement. The needle in X will be forced leftward to oppose the change in flux from the rotating galvanometer. These exposures are computed together into a 3D image of the target structure. The electrons interact with the nucleus through the electromagnetic force mediated by photons. These two electrons are paired through the lattice and form the Cooper pair. All Rights Reserved. From the perspective of a passenger, the ball has both a forward (due to the $$3 m/s^{2}$$ slowdown of the bus) and downward acceleration; this will result in a linear motion! viewing bone fractures). There must be two pairs of such coils, one for controlling horizontal deflection and one for controlling vertical deflection. The horizontal velocity remains constant, the horizontal acceleration is zero. $$d = 10^{4.9}$$ This charge separation creates a potential difference between the p and n type which results in current flowing from p to n through the circuit. With the ability to engineer a precise, controlled band-gap light emitters and absorbers operating at specific wavelengths could be generated, leading to the wide variety of coloured LEDs and the high efficiency of solar panels, resulting in a substantially increased usage of semiconductors. HSC Question 2019 PDF Download. 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(ii) Trigonometric parallax measurements are limited by the resolution of the telescope: Where D is the aperture diameter, $$\lambda$$ is the observed wavelength and $$\Delta \theta$$ is the size of the Airy disc. It appears that you have disabled your Javascript. Through their interaction with the lattice one electron loses one phonon of energy and the second electron absorbs one phonon. The electric field between A and B will accelerate the electrons through the vacuum in the photocell towards B, resulting in a current through the circuit. Peak brightness is when both stars are fully unobscured. It is useful for locating tumors and soft tissue disease, and to diagnose Multiple Sclerosis (MS). The higher current Increases the heat produced (Joule heat losses) which means some of the energy is converted to heat and the transformers’ efficiency reduces. Wires will attract each other if the current is in the same direction. in 20 seconds. 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When they strike the screen they stop and their kinetic energy is transferred to the phosphor in the screen, which converts it to heat and light. $$\frac{kI_{X}I_{Y}L}{d_{XY}} =\frac{kI_{Y}I_{Z}L}{d_{YZ}}$$. For these inventions to be implemented, however an advance in technology was required: purification of semiconductors and doping to control the band gap of semiconductors. We have published a brief suggestion for the HSC English II letter because it is a difficult issue for those who do not have control over English. Mass defect = Mass of Reactants – Mass of Products = 0.0047 amu. 2018 . It did not explain the mechanisms of stable orbits. Cooper pairs experience no resistance. The Doppler effect is used in Doppler sonography and ultrasonography. |, All masses in a constant field will accelerate with the same acceleration and in the direction of the field. CBSE Class 12 Physics board exam 2018 was held on March 7, 2018 from 10.30 A.M. to 1.30 PM. Assuming the photon energy is higher than the work function (frequency is above the threshold frequency for that metal), the energy absorbed from the photons will allow the electron to overcome the work function and be ejected from the metal. Through their interaction with the lattice one electron loses one phonon of energy and the second electron absorbs one phonon. h�D�� An electron will attract nearby positive ions causing lattice distortion and will lose one phonon of energy. There is still a band gap between the conduction and valence band, meaning the corresponding diagram is X. Criteria for suitability in diagnosis; emission type, half life and chemical compatibility (toxicity). (ii) Mass of Reactants: 4.0012+9.0122 = 13.0134 amu. Convert to kg by multiplying by \(1.661 \times 10^{-27} = 7.8067 \times 10^{-30} kg. এইচএসসির পিডিএফ বই দেখব যেগুলো কিনা ইন্টারনেটে সহজে খুজে পাওয়া যায়না ।- HSC book download pdf ডাউনলোড করুন ।একাদশ-দ্বাদশ শ্রেণীর সকল বই ডাউনলোড করে নিন । The core region is like shells of an onion. There are various sets of Class 12 CBSE Question Paper which came in year 2018 board examination. Chemical compatibility – Iodine is a trace element found in the human body; it is unlikely to have any negative chemical / toxicity effects.
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2022-05-26 17:16:33
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http://www.solutioninn.com/based-on-a-saint-index-survey-when-1000-adults-were
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# Question
Based on a Saint Index survey, when 1000 adults were asked to identify the most unpopular projects for their hometown, 54% included Wal-Mart among their choices. Consider the probability that among 30 different adults randomly selected from the 1000 who were surveyed, there are at least 18 who include Wal-Mart. Given that the subjects surveyed were selected without replacement, are the 30 selections independent? Can they be treated as being independent? Can the probability be found by using the binomial probability formula? Explain.
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2016-10-28 12:49:52
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http://rationalwiki.org/w/index.php?title=Conservapedia_Talk%3AWhat_is_going_on_at_CP%3F&diff=191625&oldid=191609
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# Conservapedia talk:What is going on at CP?
(Difference between revisions)
Archives for this talk page: Archive list (new)
## What's Andy getting at
What's with this edit? At first I thought it was about deceitful liberal students trying to cheat, but it seems now it's about lazy professors nd their professor values. Is Andy condoning a site posting answer to college exams?
Gives me an idea. We should post the answers to his exams. Though I guess if his students want to cheat they can easily do so without us. DickTurpis 23:21, 5 July 2008 (EDT)
You don't need rationalwiki to cheat on Andy's exam, you just choose the option that's synonymous with "Liberals are Satan himself." Anyway, if it weren't for tenured sloths, how would people ever get undergraduate degrees. I remember once when we had an exam where the lecturer left the marking scheme in the paper when he reproduced it. There was a general confused murmuring for about 5 minutes, and then everyone buckled down to some serious expanding and copying. Then about 10 minutes in, some blasted suck up alerted the invigilators and a halt was called. I swear if we'd all just sat quietly, and remembered to take the exam papers with us when we left, no one would have been any the wiser. --81.187.75.69 23:31, 5 July 2008 (EDT)
It seems I'm defending Andy a bit here, which is leaving a bad taste in my mouth, but here goes: actually, the liberals are evil answer is probably true of no more than 10% of his questions. Most are pretty mundane. DickTurpis 23:51, 5 July 2008 (EDT)
While I've not yet found his exams, his "classes" on history are only "mundane" if you are cool with total revisionist history. I was shocked to figure out Conservapedia claims to be some kind of homeschool student guide, since his facts on history are not only either skewed or flat out wrong, they read like a 3rd grader would be writing them. There is no coherency, even internally to Andy's whacked out reality. Frightens me so much that this man considers himself a teacher. --WaitingforGodot 17:40, 7 July 2008 (EDT)( I bez a damned liberal academician on state-funded holiday.
Check out this discussion, talk about revisionist! CЯacke® 17:51, 7 July 2008 (EDT)
Dear goddess, i thought i'd heard everything! So, Columbus lands on Christmass just in time to help Jamestown out of dreaded socialism (the evil it doth be) only to find out that Mass did indeed NOT have slavery. and that's only the first 3 topics on this page. I really hope some of his students fail their GREs and sue the hell out of him.
Andy: "Is it better to bash cheating liberals or lazy professors? I say, is it too much to ask for both?" --Sid 07:11, 6 July 2008 (EDT)
Yeah, there's a ton of shit in his lectures to be sure, but if you look at his cp:American Government Final Exam, there's no as much "liberals are evil" questions as I thought (though there are some, to be sure). Most of it is pretty basic and unimaginative. Sure, anyone who knows anything about Andy will get #14 right, and while it's a relatively factual and straightforward question, only Andy would consider #18 worth being in a final exam on a introductory government class. The bias is more towards the sort of things he concentrates on than in the questions themselves. DickTurpis 18:03, 7 July 2008 (EDT)
I agree with DickTurpis. I saw this earlier and thought "eh?". I reallly don't see what point he's trying to make with it. The Lay Scientist 11:37, 6 July 2008 (EDT)
## AHAHAHA
AHAHA. Be sure to visit both of the sites. I wonder who put that link in? --*Gen. S.T. Shrink* Get to the bunker 03:16, 6 July 2008 (EDT)
One of the sites is more interesting than the other--Damo2353 07:29, 6 July 2008 (EDT)
Caterine moves her lips when she reads. Betcha Andy does the same.--WJThomas 08:18, 6 July 2008 (EDT)
## Schlafly's strategy
Not just another bit of shameless self-promotion, but something I really want to bring to peoples' attention. I don't think Schlafly cares that he looks like a moron in the Great Interminable Lenski Debate - I think he's playing a long-term strategy that's a bit more subtle (see here). The Lay Scientist 11:35, 6 July 2008 (EDT)
An interesting point (I'm not sure if this actually belongs in WIGO, but I won't touch it). My main objection is that Andy is overestimating his influence. A meme needs to be picked up by people, but I don't see anybody touching this one. I also think that nobody will touch it - not the Creationists, not the Climate Change Deniers, nobody. The reason? They claim to have science on their side, too. So Andy's meme will hurt them, too. The moment they hold up "science", the meme would turn against them. It's a purely political meme, but politicians apparently picked up science (in a slightly warped way) as their own weapon of choice, so in the end, only Andy will push it, and that's not enough. </quick opinion> --Sid 11:55, 6 July 2008 (EDT)
I disagree with you completely. The climate change deniers are using precisely these same tactics as we speak - attacking science and the scientific process. You have to realize that they're not trying to build scientific arguments, they're trying to spread obsfuscation and confusion so that they can claim it's "open to debate". The Lay Scientist 12:11, 6 July 2008 (EDT)
Hmmmmm, I do see your point, but I mostly have to think about the occasions when "Creation scientists" come up with wild theories, allegedly based on "data" and "science". (And before I get angry mails: This sentence is just the equivalent of what CP does with "claims by secular scientists", so whatever.) Not 100% sure about the climate dudes, even though I think I remember Ed spewing stuff about "real" scientists having "evidence" based on "data", too. I readily agree that they try to seed distrust in "secular sciences" or whatever they call it, but what Andy is doing is seeding distrust in ALL sciences. He may lean towards specific sides, but his accusations are so broad that they hit everybody. The first scientist (no matter what he advocates) to back him would be the first one to get a ton of "Your data! All of it! Now!" demands in his inbox, if just to show him what slippery slope he chose to follow. --Sid 17:12, 6 July 2008 (EDT)
The key point though is that it doesn't matter that Andy is seeding distrust in all science. Suppose you're a tortoise, and you're in a race with a hare. ANY speed restriction is brilliant for you, because the more restrictive it is, the closer to parity you are. Does that make sense? Undermining all science, even if it undermines creation science too, simply levels the playing field. The Lay Scientist 17:42, 6 July 2008 (EDT)
Ah, okay. I wasn't thinking in such dimensions (my tactic usually prioritizes keeping the own losses low). That approach reminds me a bit of "Scorched earth" - destroying assets that would have been valuable to you, just to make sure nobody else can use them against you. Interesting argument, then. Self-destructive, but I can see the "reasoning" now. Thanks for making me see things from your perspective! --Sid 18:34, 6 July 2008 (EDT)
"Scorched Earth" is a great term for it, I'll be using that in future :) The Lay Scientist 03:16, 7 July 2008 (EDT)
This would be more suited to According To. It doesn't reference any specific event on CP. 12:02, 6 July 2008 (EDT)
My understanding is that Conservapedia related stuff shouldn't be on According To. The Lay Scientist 12:11, 6 July 2008 (EDT)
Maybe not, but in this situation it is a much better fit than WIGO. 12:48, 6 July 2008 (EDT)
Well maybe so, but it's not allowed there! Perhaps you should implement a new page for "blogging about Conservapedia"? The Lay Scientist 17:01, 6 July 2008 (EDT)
I agree with lay Scientist on this one. It's much easier to vaguely imply that data is being withheld than it is to actually do something about it. That is the point of his challenge - "look how difficult it it to get all teh data! I've had to set up teh challenge to tey to force them to give it to me! They can't be teh trusted! Whether it works is, of course, another question. But it would make sense as a strategy.--Bobbing up 15:47, 6 July 2008 (EDT)
From what I can see, Lay Scientist is exactly right about the strategy. However, what he seems to be short on is Andy's actual ability to use it properly. He's got the loaded gun of sowing distrust of science, but he's aiming squarely at his own feet, as usual. While the Discovery Institute, the climate change deniers and so forth are using it on a daily basis, to varying degrees of success, Andy's ham-fisted attempt to use the same weapons come off as laughably transparent and actually harm the cause he's trying to champion. The tactic is a threat, but Andy is a joke. --Kels 16:14, 6 July 2008 (EDT)
Yeah, you're right there, as I conceded in the comments on that post as well. Schlafly has found a good strategy, but Conservapedia is the worst type of tool to promote it, because he's investing more energy keeping his Conservapedes in line than he is in actually spreading the message. Yet said, if it does eventually escape the factory, it might pick up. The Lay Scientist 17:01, 6 July 2008 (EDT)
Not a chance that Schlafly is playing the long-game. He is just being every bit a stupid as he appears at first look. Look at his entire history, he's never been calculating just really really reactionary. Matt oblong 18:40, 6 July 2008 (EDT)
The beauty of the long-game meme strategy is that you don't have to be calculating, you just have to be persistent and repetitive. And stupid people are good at being persistent and repetitive. Stupid people are very good at being persistent and repetitive. That's the beauty of playing the long-game. You just have to be persistent and repetitive. Stupid people are great at being repetitive, and they're pretty good at being persistent as well. Get it now? The Lay Scientist 03:16, 7 July 2008 (EDT)
Well, the test will be to see how far Andy takes it. If he really firms up his definition of the alleged "missing" data and really starts to begin some "legal action" to obtain it then I'll stand corrected. But I bet that he'll just keep vaguely complaining about data being withheld without explaining: (a) exactly what it is (b) why it's important (c) what he would do with it if he had it - and that's more consistent with what Lay Scientist maintains. So lets start taking bets - will Andy really go for it (and look stupid) or will he just keep vaguely whining in order to try to discredit it by the back door? My money is on the latter.--Bobbing up 04:37, 7 July 2008 (EDT)
Yeah, I'm with you Bob (unsuprisingly, since you were agreeing with me, lol). The Lay Scientist 04:43, 7 July 2008 (EDT)
By the way, come on guys, -5???? 200-odd of you came to read it, it got a bunch of Diggs, several comments and a trackback from ScienceBlogs, and I get -5 here? Pfft, conservatives the lot of you. The Lay Scientist 04:43, 7 July 2008 (EDT)
## Andy's twiddled the knobs wrong again
CP is down. AGAIN. Holy Hell Batman, that's some unreliable website - it's up and down like a whore's knickers. Ken - your wave of anti-atheism is never going to work if Andy keeps knackering the server.... DogP 15:00, 6 July 2008 (EDT)
Thought it was just my crappy wireless broadband. ContribsTalk 15:11, 6 July 2008 (EDT)
Right when I was ready to read two days of WIGO. :-( (Editor at) CP:no intelligence allowed 15:19, 6 July 2008 (EDT)
Perhaps it has become overwhelmed by Christian Apologists? Or perhaps the Rapture is under way and the server has been whisked to a gleaming white server farm in Heaven? DogP 15:22, 6 July 2008 (EDT)
Not Deep Thought? It's probably all those UK Theists that Ken's been spamming have overwhelmed the server! ContribsTalk 15:31, 6 July 2008 (EDT)
It's been patchy for me for the last couple of days; it's not unusual that I just get a blank screen instead of a page. And the front page briefly gave me a "database error" followed by lots of php-looking stuff I didn't understand yesterday, too. Alt 15:44, 6 July 2008 (EDT)
I checked with this and get "URL doesn't exist", (sigh) if ONLY. UPDATE:Ping and trace route get responses, one trace when 19 hops to an .se address and 15 hops to my IP (via the command/tracert) in W PA (USA). So the IP is answering just not the website, (IOW, it ain't the hardware.) CЯacke® 15:49, 6 July 2008 (EDT)
Yeah, but it's resolving to theplanet.com, their hoster, so it's either a problem with their block or they've simply dropped a spanner in the works again.... DogP 16:00, 6 July 2008 (EDT)
Conservapedia is the laughing stock of the intertubes for many reasons, but increasingly it is also becoming lulz-fodder for total technical incompetence. Among the sites I regularly visit, none are down more often than CP. DogP 15:45, 6 July 2008 (EDT)
It's been ropey all afternoon and it's down again (that or my steam dial-up). Fretfulporpentine 16:34, 6 July 2008 (EDT)
I've got Amish neighbors who have a wood burning computer. Actually, from what I hear, the Amish businesses can use computers, they're just not allowed to OWN them, (or use them @ home). Any hydraulic machinery is okay too; being powered by a diesel engine. CЯacke® 16:56, 6 July 2008 (EDT)
In NZ we have the Exclusive Brethern which are kinda like the Amish except they try and get political. They also cant have TV, radio or computers. They do however have businesses and my girlfriend (who is an advertising executive) had a meeting with some Brethern in an attempt to get them to use online advertising. She claims she didnt notice the dusty computer in the corner of the office and the prominence of the bible on the meeting table. Ace McWicked 17:16, 6 July 2008 (EDT)
Still down. Maybe it's strategery to "destroy" vandals.--JayJay4ever??? 18:14, 6 July 2008 (EDT)
There will be no more vandals now! Ace McWicked 18:41, 6 July 2008 (EDT)
I don't know much about the Armish but I know a bit about the Bretheren. These guys are not only technologically backward but they rank with Scientology in terms of breaking up families. I had neighbors who were with the Bretheren for 30 odd years, then left. No-one from the church has talked to them since, including their parents, kids, brothers or close friends. Its very sad.
### It's up again
Downtime: Roughly six hours, going by the gap in the Recent Changes: Last edit: 14.20; Current time: ~20:20 (both CP server time) --Sid 20:31, 6 July 2008 (EDT)
Amusing that, as yet (almost an hour later), no-one's mentioned the slight hiatus. Have they all decided not to question the ability of their lord & master? or did nobody notice? ContribsTalk 21:37, 6 July 2008 (EDT)
### Down again
And back down. DNS is resolving, and it's got decent ping times, but it doesn't want to respond to the TCP SYN. --Interiot 18:24, 12 July 2008 (EDT)
Much as I am continuing to find the whole Lenski thing hilarious thanks largely to the cracking RW coverage - is there not a huge part of you that just wants to walk up to A Shafter and shout 'Never before in the 6 - 5000000 thousand year history of this planet has ever so much an argument been lost in such a complete and irrifutable way. Just please now, f***ing leave it!'. Matt oblong 18:18, 6 July 2008 (EDT)
Matt oblong, you're clueless if you imagine that the Earth is any older than 6,000 years. Make some meaningful edits or you'll be banned for talk, talk, talk. DogP 18:45, 6 July 2008 (EDT)
The above rant by "Matt Oblong" is too long to be taken seriously. Condense your remarks into a few good points instead of using liberal talk pollution on my talk page. Godspeed. Ace McWicked 18:57, 6 July 2008 (EDT)
I admit to maybe being tricked into a bit of Liberal Ejaculation. Matt oblong 19:05, 6 July 2008 (EDT)
Its striking that liberals rely on obscenity when cornered. Do you have Breast Cancer? Ace McWicked 19:08, 6 July 2008 (EDT)
Matt oblong, you're clueless if you think that the way that you misspelled "irrefutable" doesn't invalladate you entire argument. Please educate youself. Posing as an intellegtual is a well-known Liberal debatering tactic. Godspeed. --AKjeldsenCum dissensie 19:14, 6 July 2008 (EDT)
Matt oblong (not likely your real name), this will remain a high quality site. I can tell from your behaviour that your theres a 99% chance of your being a liberal. Let me guess though, you wont admit it and claim your a conservative right? "Sic him Bugler!" Ace McWicked 19:17, 6 July 2008 (EDT)
Matt, as you have not yet received permission to edit at this encyclopedia, your comment are not only unwelcome and immoral, but a violation of US Code 18 sub 3 against proving me wrong obscenity. Godspeed.-- -PalMD --Do I look like I care? 20:35, 6 July 2008 (EDT)
If you insist on posting gossip and obscenity, "Matt", then perhaps the National Enquirer of the Internet, Wikipedia, is the place for you. I wish you Godspeed in your endeavors. DickTurpis 20:55, 6 July 2008 (EDT)
"Matt" you follow your liberal playbook to a tee. I urge to open your mind to conservative values. Ace McWicked 20:58, 6 July 2008 (EDT)
"Matt", learn to spell "irrefutable" and open your mind before filling the place with your Liberal Fluff. --λινυσ() 21:07, 6 July 2008 (EDT)
And you smell funny too. --*Gen. S.T. Shrink* Get to the bunker 22:23, 6 July 2008 (EDT)
Oblong, Our Leader has written many times here what this site is about, but you still insist on continuing this argument. It stops now, or go elsewhere, understand? Able Seaman(In my dreams) Kowardpoo 04:43, 7 July 2008 (EDT)
"Matt", your arguments wouldn't hold on court and would be instantly rejected by a non-activist judge, you would have to deny logic to think otherwise. In Christ! NightFlareStill doesn't have a (nonstub) RWW article. 10:48, 7 July 2008 (EDT)
## Hey
Don't make fun of me :( --transResident Transfanform! 00:29, 7 July 2008 (EDT) ;)
? ContribsTalk 00:41, 7 July 2008 (EDT)
## Old news but made me laugh.
Remember Robert Turkel? Did you ever read the sycophantic drivel from Ken on it? (Oh Ken - don't bother deleting it, I've got a copy) ContribsTalk 00:57, 7 July 2008 (EDT)
## Re Quantcast
Quite revealing are the "Audience keywords":
conservapedia 990.2x
santorum 122.4x
debate topics 79.8x
debatable topics 54.4x
worship lyrics 44.5x
theory of evolution 32.7x
president pro tempore 28.8x
debates 28.8x
plant cell 19.5x
judicial review 12.6x
cerberus 10.2x
nationalism 10.0x
translation 8.7x
mls 8.5x
fascism 8.4x
Strange (plant cell!)! ContribsTalk 01:31, 7 July 2008 (EDT)
Oh yes - their Alexa's dropped to pre-Lenski values as well! ContribsTalk 01:34, 7 July 2008 (EDT)
Yeah, their Alexa stats have tanked. I think a lot of the spike previously would have been down to the article about them in the Guardian (no offense to the Pharyngulistas, but the Guardian's web audience dwarfs the whole science blogging community combined).
By the way (I mentioned this above as well), the Finland crowd aren't coming to TLS - for some reason, on my site Finland is being pwned by... North Korea. The Lay Scientist 03:21, 7 July 2008 (EDT)
I kinda share the boggling feeling, as I note that my slowly reviving webcomic seems to be getting hits from Denmark second only to the US. Heck, Canada comes third and I live there! (Finland, oddly, is 7th). --Kels 18:05, 7 July 2008 (EDT)
Seems like both CP and RW had big boosts during the Lenski affair but they've dropped. Unfortunately Lenski's actual site doesn't appear on Alexa and I'm rather pissed of that putting Richard Lenski into google gives you the Conservapedia article. They must have done a massive amount of google bombing to get it there, probably why Assfly links to everything he mentions in his talk pages. If Google's page rank stopped counting links from wikimedia talk CP would die. Armondikov 09:30, 7 July 2008 (EDT)
Before you complain too much, what exactly do you think is the effect of all the RationalWiki and science blogger links to the land of the Conservapedes? 81.102.156.177 10:40, 7 July 2008 (EDT)
WIGO vs the amount that Schlafy insists on overusing terms like "liberal XXXX" in every other one of his replies? Probably negligable. Armondikov 11:36, 7 July 2008 (EDT)
Also, just for the record Conservapedia's Lenski article doesn't appear top ten when I do a Google search for 'Richard Lenski'. Lenski's own website comes top for that. It may be that you're getting tricked by Google, which is pushing the Conservapedia result higher for you because you're spent more time on that site? This is the Google skewing that Kenservative keeps forgetting to take into account when he makes grandiose claims about his pet articles. Charles SubLunar (mr) 11:47, 7 July 2008 (EDT)
Yes, Lenski's own site is the first hit for me, some time later WP then RationalWiki and a bit after that CP.--Bobbing up 15:08, 7 July 2008 (EDT)
But you get some great hits if you Google: lenski RationalWiki.--Bobbing up 15:21, 7 July 2008 (EDT)
For me I get Lenski's website, WP, RationalWiki "Lenski affair" and then a indented "Richard Lenski", and then (4) Conservapedia "Lenski dialog" under the title is the text; "Richard Lenski. P.S. Did you know that your own bowels harbor something like a billion (1000000000) E. coli at this very moment?". Real good advertisement for CP that. $\approx$$\pi$ 18:16, 7 July 2008 (EDT)
I don't run a sock account on CP and only check the pages flagged up on WIGO, I think by page hits I spend at least 3x as much on RW, so I don't think I'm really on the site enough for google to skew it (Though I didn't even know google did that). It could be biased to whether its .com or .co.uk or whatever. Though I do get Lenski's site as no.1 and Wikipedia as no.2. Rationalwiki.com/wiki/lenski_affair is no.8. The wonders of the internet... Armondikov 04:57, 8 July 2008 (EDT)
Okay, but I must be missing something, since the average user appears to be 12-17, Asian, making 100+k/yr and has an education of grad school or higher? -Smyth 11:57, 8 July 2008 (EDT)
## Olympic
Has anyone else noticed Croco'shite getting ready for the Olympics? Much room for jingoism there! ContribsTalk 02:11, 7 July 2008 (EDT)
I'm going to make a little prediction now, that we'll see a whole wave of anti-China stuff hitting the site in the near future, in order to reinforce "American supremacy". If China get more medals expect articles on brutal training methods, etc., or widespread drug abuses. Any athlete that beats an American will be accused of cheating. Stuff like that. The Lay Scientist 07:35, 7 July 2008 (EDT)
You're probably right. But, I've always felt that these tables, as presented, are pretty meaningless anyway. It's seems somewhat obvious that bigger countries are going to get more medals. It's always seemed to me that they could be calculated per head of population or something of that nature. I did this last time round and Australia did rather well I think. Also, (again from memory) if you did the calculation with the European union as a "country" then the EU came top. --Bobbing up 07:56, 7 July 2008 (EDT)
No, that method is flawed as well, as in most competitions the number of athletes for each country are limited, thus favouring small countries. A united EU would send much less athletes and get fewer medals - or on the contrary if each US state was by themselves, their total would exceed the US medal count by far.(Editor at) CP:no intelligence allowed 08:17, 7 July 2008 (EDT)
Yes, that's a good point. Thanks. So I'll happily withdraw my second point about the EU. Nevertheless larger countries have a larger pool of potentially good athletes to pick from, so they obviously have an advantage, don't they? I mean, if you've only got 500 people in your country the possibility of your having gold-winners among them is small. If you've got millions to pick from them your chances obviously improve.--Bobbing up 08:25, 7 July 2008 (EDT)
I don't think that's right that smaller countries are favoured. Limiting the number of athletes is just sensible because of the limited number of sports (even if the actual number of events is quite massive). If the country is larger, they tend to have a larger population base from which to select from; higher odds of having someone with natural talent. Assuming, of course, that the rate of people with "natural talent", i.e., the US, with ca.250million people will have 4-5x as many naturally capable athletes as a European country with ca.50million people. Talent is a subjective measure certainly, but a necessity for the standard of the Olympics, I doubt anyone can be trained to that level regardless of how much time they put it, you have to have the right kind of person. Multiply this by the finances they have available to put into equipment and training facilities as well as bursaries for people to do the sport full time and you're clearly favouring the larger, richer countries. Armondikov 09:23, 7 July 2008 (EDT)
I'm sure studies have been done on this. Anyway, the problem is that the winner is not selected based on a "quality" value alone, instead there are many variables which determine the medalists: race day condition, interaction with other competitors, tactics, environment, pure luck, injuries, trials (if the USA could bring as many athletes as they wished they wouldn't keep trials and Tyson Gay would be competing for the 200 m run as well as a heavy favourite), etc. Having 30 athletes (EU combined) competing against 3 (USA) means that EU have a higher probability of winning medals if the variable factors are relevant (that is, everything can be perfect but EU athletes won't win the 100 m run). (Editor at) CP:no intelligence allowed 09:52, 7 July 2008 (EDT)
In addition, smaller countries, even if using a proportional amount of money, can concentrate it better on few targets. How many javelot medals has Finland won in the history of Olympics? They found their niche. Anyway, I think Bob's suggestion is not too far off. Medals per population should be a better indicator than medals alone. (Editor at) CP:no intelligence allowed 09:55, 7 July 2008 (EDT)
But the EU isn't a single country so it's not really a good comparasom Armondikov 11:29, 7 July 2008 (EDT)
I have already acknowledged that the EU comparison may not have been the the best. But it seems pretty obvious that bigger counties have an advantage. In the last summer Olympics the three "leading" countries were the US, China and Russia. This would seem to be a somewhat improbable outcome if the rules put bigger countries at a disadvantage.--Bobbing up 11:44, 7 July 2008 (EDT)
Bets that Andy will argue that in events where American athletes lose, it's because they went to public school? --Phentari 12:01, 7 July 2008 (EDT)
If you want a fair comparison, go with medals per competitor. --CPAdmin1 13:04, 7 July 2008 (EDT)
True, but that makes it all substantially less interesting :) 13:08, 7 July 2008 (EDT)
<-- Re: Kookoo's list, how come it is missing so many events? I think it's weird that he has "hockey (not ice)" but no hockey! Oh, wait, that's a winter Olympics competition. Still... And in regards to the statistical discussion above, there may be a threshold in general populations at which one can expect an Olympic-caliber athlete (say, at 20 or 50 or 100 million population, you're bound to have a few good swimmers or sprinters etc.). That's ignoring the "specialists", like the Kenyan long distance runners (?), or the above-mentioned javelists (?!). What's funny of course is that it's supposed to be about a celebration of all of humanity (I saw the Visa commercial), but competitors still represent their countries, and medal totals get tallied by country. It would be amusing to divide the world up into chunks of, say, 50 million people, which is about the same as the number of countries, and let them go at it from a roughly equal population basis... ħuman 14:13, 7 July 2008 (EDT)
I suppose you could do it by continents - but then continents with more countries would have an advantage. I still like by per head of the population.--Bobbing up 14:58, 7 July 2008 (EDT)
'Twould put Antarctica at a very unfair disadvantage. And the day that the US and Canada say "we're all just North Americans really" is the day that Mr Schlafly confesses to running an abortion clinic :P. It'd be nice just to see individuals compete and not countries, although that's still pretty impractical. Armondikov 04:51, 8 July 2008 (EDT)
Here in Aus we get very jingoistic come Olympics time. During the Sydney games, Channel 9 took to showing a "per capita" medal table rather than the straight one. To do so, they took the leading countries on the pure medal count, converted the numbers to a per capita basis, and voila - Australia on top of the world. Only problem, as I delighted in telling their switchboard, was that they hadn't bothered checking for really small countries lower down the tables. The Bahamas beat us by a mile with their one (or was it two?) golds in women's athletics. The table disappeared for the next bulletin. Matt 05:45, 8 July 2008 (EDT)
Lol, that made be chuckle The Lay Scientist 20:37, 10 July 2008 (EDT)
## Anti atheism bloggers and Christian Apologetics
According to the Main Page of Conservapedia we’re going to be treated to yet more silliness that passes for rational argument. Probably we’ll answer some of it and laugh at it a lot of it.
Definitions:-
Christian Apologetics………………An apology for a rational argument
Proxima Centauri 05:14, 7 July 2008 (EDT)
## FBI
Hey, is this accusation true? Did Rationalwikians really get called up by people pretending to by government agents?— Unsigned, by: 158.143.193.4 / talk / contribs
I don't know, but everything up to that point was true. Also, see here for Karajou's mature, compelling response. It makes sense when you consider that he was responsible for some of the most moronic stuff during the FBI thing. 08:04, 7 July 2008 (EDT)
Details may be up for debate, but it is generally true that legal threats were flying, people were contacted IRL, and the implication was made that the FBI was looking up everyone's arses.-- -PalMD --Do I look like I care? 08:39, 7 July 2008 (EDT)
Really? You would think a lawyer (granted, little Andrew is not a very good one) would know it is illegal to impersonate a federal agent.--Franklin 11:18, 7 July 2008 (EDT)
Interesting. I'd heard about the FBI thing, but never about the impersonations. Charles SubLunar (mr) 11:31, 7 July 2008 (EDT)
Well let's not all assume it's true just because it was mentioned. The editor who brought it up on CP might just have mis-remembered the details from our FBI Incident article. Does anyone who was here at the time want to weigh in on this? 11:42, 7 July 2008 (EDT)
As I recall it one Sysop (who shall remain nameless TK phoned 1 Ratwikian more than once but never impersonated the FBI. ContribsTalk 12:13, 7 July 2008 (EDT)
I've never heard of these allegations...and I'm not sure they're true. I wrote and compiled the FBI Incident article at the time it was going on and the article and Talk page threads there do not reveal any "impersonation of FBI agents", although I vaguely remember someone saying CP seniors had directly emailed some senior RW'ians. I think the allegation is false. DogP 14:48, 7 July 2008 (EDT)
I was e-mailed by several CP sysops, stalked on wikipedia by one, and did receive a phone call at my lab. But there was no impersonation. Either pure anonymous cowardliness or open about who they were. A few others had similar experiences. tmtoulouse nettle 14:51, 7 July 2008 (EDT)
(undent) I think people are confusing the "FBI Incident" (Andy being all "I'MMA CALL TEH FBI!") and the RW 2.0 History. The talk page post there seems to relate to the latter, especially the case where Andy sent take-down requests when we copied one of their articles for side-by-side treatment and the case where Andy's goons snuck into RW 1.0 under false names, copied various pages and then tried to report us to law enforcements (better known as the 1.0/2.0 transition which happened around the time of the Night of the Blunt Knives, IIRC). That time was also when most sysop harassment took place in form of phone calls (again IIRC - this didn't happen to me personally (edit: but see tmtoulouse's comment above) and blog comments (claiming that there was an FBI Investigation and that the Feds would soon knock at our door with cyberterrorism charges). --Sid 14:59, 7 July 2008 (EDT)
I seem to remember a snarky comment on CP with "FBI case #blahblahblah" in it somewhere...Antifly 17:06, 7 July 2008 (EDT)
If you mean the RW 2.0 time, then yes. Somebody (I think it was Kara, but I'm not sure if that's correct or if he was the only one) waved around some ominous "FBI Case Number" as an "You're in trouble noooooow!" sign. It later turned out to be just some automatically generated ID assigned by the Internet Crime Complaint Center (IC3) site where Kara (or whoever) likely filed his complaint. --Sid 18:02, 7 July 2008 (EDT)
It was an auto-generated ID from a tipline website. I was told by some (i.e. he-who-shall-not-be-named) that my hospital director and other bosses were being contacted and that law enforcement had been notified.-- -PalMD --Do I look like I care? 18:49, 7 July 2008 (EDT)
Good Lord, I never knew that, PMD, that's dreadful, whether it was true or total horseshite. What a deep pond of scum they are. DogP 18:54, 7 July 2008 (EDT)
They contacted the president of my university as concerned tax payers about the use of university resources, my university is in Canada. The idiocy vibe they give off is so intense it acts as protection to anyone they go after. tmtoulouse nettle 18:55, 7 July 2008 (EDT)
It's almost like Poe's Law, but even dumberer.-- -PalMD --Do I look like I care? 19:09, 7 July 2008 (EDT)
Should we not have some of this stuff documented on the Conservapedia:FBI Incident page? Otherwise it just becomes a folk memory. Genghispillaging 04:51, 8 July 2008 (EDT)
## Lazy Tenured Sloths
On the main webpage, they have a blurb that links to this story. As part of the blurb, they claim that One former student declares, "The only people who will find this website to be a threat are those lazy tenured sloths that like to recycle old material on their exams."
Is it just me, or does that comment appear nowhere in the story or in the posted comments underneath it? --Phentari 11:01, 7 July 2008 (EDT)
Someone pointed that out on the relevant CP talk page too, but strangely no-one has replied.. Alt 11:11, 7 July 2008 (EDT)
It's in the first comment - VJ Metal on 07/03/2008 at 8:13 a.m. Charles SubLunar (mr) 11:14, 7 July 2008 (EDT)
I don't see that comment at all when I call up the article...weird. --Phentari 11:19, 7 July 2008 (EDT)
Seems to take a few seconds for the comments to appear after the story itself has loaded. Charles SubLunar (mr) 11:29, 7 July 2008 (EDT)
Yeah, that threw me for a minute, going back and forth, article to quote, etc. But then I saw the comment. It's a tiny bit misleading, but it is a quote from the page they link to. They should have said "commented on the article" instead of "declared", but that's a minor point. ħuman 14:08, 7 July 2008 (EDT)
Didn't something like this happen before? Dunno if it was on their main page or in an article, but I have memories about people pointing out this exact same screw-up in the past. --Sid 18:03, 7 July 2008 (EDT)
(unindent) It's not really a screw up... it's very intentional. It's a modernization of one of the tactics conservatives have used to discredit newpapers for years. Basically, the original was "anything that was printed in a newspaper can be attributed to that newspaper" For example, if someone wrote a letter to the editor, saying GW Bush was a terrorist, and the New York Times printed it. The New York Times just called GW Bush a terrorist. This is simply a new version of that. SirChuckBA product of Affirmative Action 19:39, 7 July 2008 (EDT)
I'm not sure I've met the Lazy Tenured Sloth - personally I'm three toed. Silver Sloth 17:34, 8 July 2008 (EDT)
## Wise words for Andy.
In the process of ranting about Wikio's inclusion of denialist sites like Climate Audit and "Love Global Warming" in their list of the top 100 science blogs (and failure to include TLS anywhere even though I crap all over LGW's audience figures, damnit), I stumbled across this notice on Steve Milloy's now defunct climate skeptic blog at Junk Science:
"JunkScience.com Blog is broken, again, perhaps irrevocably. Unfortunately it requires far too much of our limited resources maintaining and defending an interactive component. Discussions continue but current thinking is that the skeptic community is best served by our concentration on disseminating information via the more secure static site, where significant improvements remain to be made."
Mr Schlafly, you might want to read this and take note.
The Lay Scientist 17:24, 7 July 2008 (EDT)
Oh ****. Just realized that Drupal sent an automated trackback to ClimateAudit when I linked to them in my ranting. Now I'm going to get an infestation. The Lay Scientist 17:30, 7 July 2008 (EDT)
I, apparently, have, with my co-bloggers, slot #21. Given your linkage, I wouldn't be surprised if you are up there by next year. After all, in the blogosphere you're still an adolescent. Of course, the ScienceBorg may have something to do with it too.-- -PalMD --Do I look like I care? 18:47, 7 July 2008 (EDT)
Well, I was being a bit tongue-in-cheek with my complaint about my ranking. What concerns me more is that Wikio vet the sites before they add them. I've submitted LayScience to them and had no reply, while Milloy and ClimateAudit and unbelievably Love Global Warming have waltzed onto the list. Even aside from that nonsense, your Denialism has come 21st behind an automobile blog, and a science fiction magazine! The Lay Scientist 05:51, 8 July 2008 (EDT)
## Conservapedia Challenge of the Day
In light of this (already WIGO'd) comment, Ed asks for sources that Andy is a "supporter of creation science" (a term he replaced with "evolution critic").
Now, I'm fairly certain I recall Andy having made a talk post somewhere in which he outlined how he turned away from evolution after "examining the facts" or something. I'm not sure if it explicitly said that he supported Creationism, but I think so.
The challenge: Find it. Please. :D
(We will need Andy's own words since CP's arbitrary sourcing rules will be able to label ANY other source as not trustworthy.) --Sid 18:12, 7 July 2008 (EDT)
(Pro tip: Going through his contribs may not work since several pages have been conveniently deleted in the past, thus removing those contribs from the list. Stick to archives. --Sid 18:14, 7 July 2008 (EDT))
Then again, this may be a "nevermind" case since Andy openly hates the term "creationist" or even "creation scientist", if I remember correctly. So this one may be tricky. --Sid 18:17, 7 July 2008 (EDT)
The only source you need that Andy is a support of creation science is that on Lenski's page it read "open-minded scientist" and when you click on it it takes you to "Creation science" here is Andy's diff link(sorry that is just Andy restoring something Shagie has the one you want). This is Andy's normal definition of open-minded, agrees with him. $\approx$$\pi$ 18:26, 7 July 2008 (EDT)
And the original inclusion of the material[1] --Shagie 18:34, 7 July 2008 (EDT)
Something I found whilst looking for the Challenge. I think the is the first case of a bona fide true believer being turned off, then away, then BANNED all based on the vibes that CWilson might have been sending. CЯacke® 19:15, 7 July 2008 (EDT)
I think this is what you're after, Sid. --Robledo 20:10, 7 July 2008 (EDT)
It's not the comment I had in mind, I think (However, my memory is spotty, so I might have just misremembered the one you linked to), but it does show Andy's Young Earth alignment. Nice job! --Sid 20:35, 7 July 2008 (EDT)
The moon talk page is a little scary. He seems to be saying that it does not matter how old the moon is, we should teach YEC because you would more likely be a Christian then if you were taught that the moon is older. It seems to Andy the truth is unimportant, making as many people as possible Christian is even if you have to deny the truth to get it done. $\approx$$\pi$ 21:08, 7 July 2008 (EDT)
It seems like the "measure of validity" according to Andy is how it impacts the strength of one's faith... ħuman 21:20, 7 July 2008 (EDT)
The Moon talk page also gives us yet another sterling example of Andy's flawless command of the English language: "Very few, or none, Catholics or any other Christian promotes old earth theories." Yep: none Catholics or Christian promotes.
Just looking at that makes my grammar hurt. --Phentari 13:27, 8 July 2008 (EDT)
## Ed an American Jew?
Ed an American Jew? Surprise, surprise. --JayJay4ever??? 22:08, 7 July 2008 (EDT)
I thought he was a Moonie? --Gulik 22:11, 7 July 2008 (EDT)
Guess he converted -- but still sees himself as a Jew in terms of ethnicity...the preceding comment should be read in the light that ethnicity is a social construct with no inherent meaning...PFoster 22:13, 7 July 2008 (EDT)
I noticed long ago him making a statement about "we Jews", which made me wonder. Is he a convert to Moonieism? Or do Moonies consider themselves some sort of "lost tribe"? My guess is he's just a dick, and this is some sort of cover for his anti-semitism. DickTurpis 22:14, 7 July 2008 (EDT)
Probably he's a jew, and crazy too. He's also antisemite, and hates himself for being a jew. Typical of conservapedians. --JayJay4ever??? 22:17, 7 July 2008 (EDT)
Maybe he owns Conservapedia in some remote way? O_o (that was a joke there) Javascap 22:20, 7 July 2008 (EDT)
<JewTalk> He's an assimilated Jew, his mother is a Yehudit and his father is a sheygits (spell the word how ever you like it has many spellings like Hanukkah) , he admits to marrying a shiksha</JewTalk> see CP:Talk:Goy --Jellyfish 22:24, 7 July 2008 (EDT)
If he's a yid, I'm the fucking pope. Not that I'm the arbiter (pun) of all things Jewy, but his voice (both on the phone and in writing) doesn't give away many of the usual tells. That being said, perhaps he's a littler further away from it generationally than I. I know plenty of very assimilated Jews---I am pretty assimilated, although still with lots of yiddishkeit. I'm surprised he's never mentioned this before. I'm a little suspicious.-- -PalMD --Do I look like I care? 22:36, 7 July 2008 (EDT)
You've spoken to actual CP sysops on the phone? PFoster 22:44, 7 July 2008 (EDT)
Wait a minute, Ed is one of my people! Well, I'm pretty sure I'm the only yeshiva educated one at CP (don't know about here, seems a bunch of are chosen). Not knowing what Kashrut is means you know nothing about your claimed heritage, Ed. well I learned the Semicha curriculum, and if I had any time/interest/patience could write articles for every one of the redirects... but I digress.
Question: Isn't the purpose of an encyclopedia to include all information, especially the unfamiliar concepts? If you redirect everything just because you didn't know about it, what the fucking point? DLerner 04:22, 8 July 2008 (EDT)
Shouldn't we make Ed provide proof that he's a Jew, (provide the raw data, or at least the foreskin) DLerner 04:22, 8 July 2008 (EDT)
No thanks. --JayJay4ever??? 11:24, 8 July 2008 (EDT)
"Dear Ed, Many of us here at Rationalwiki are sceptical about your claimed status as a red sea pedestrian. Your continued refusal to release data pertaining to the status of your cock leads us not only to question if you are a yid, but in fact whether you are a man at all. Yours Sincerely, Col. Arthur Blenkinsop, OBE and Gibbon (Mrs.)" --81.187.75.69 12:04, 8 July 2008 (EDT)
You are making the mistake of thinking that CP is intended to be an actual encyclopedia, instead of a collection of rants on the topic of Why Liberals Suck. --Gulik 04:38, 9 July 2008 (EDT)
Come on guys. So, one CP sysop may, or may not, have some connection with some alleged "race". And having this "race" we assume that he must also have some other views on religion or education? Or not have? Have I understood this vital question correctly? Have I misunderstood its importance? I mean - well - this is important because ....... Or is being Jewish or not being Jewish very important in the US? --Bobbing up 12:18, 8 July 2008 (EDT)
It's not important on the face of it, what one's faith (or lack thereof) is nobody's concern but the person themselves.
Then again, what with the old Jews control the media canard, waving slowly in the breeze it does seem strange (and oddly, more impressive), him winning the ALL IDIOT award. Usually, as per said canard, the Jew on the scene is the kingmaker toiling in the background.
CЯacke® 13:52, 8 July 2008 (EDT)
It is Paramount. -Smyth 12:28, 8 July 2008 (EDT)
I think the Jew issue is interesting given the scary tone of the blog wiki. They have Messianic Jews (Jews4Jesus) of course (fox). And yes, I've spoken to Ed on the phone. He "vetted" me durning my "credentials" debated with teh assfly. He agreed that I was probably a doctor, and decided that I was probably not an expert in, I think, cancer. -- -PalMD --Do I look like I care? 14:27, 8 July 2008 (EDT)
Do you deny the obvious fact that abortions lead to breast cancer? Well, how you can be any sort of expert on anything medical? Just having qualifications from some (doubtlessly) liberal university doesn't mean anything. Alt 15:27, 8 July 2008 (EDT)
## Debbie, sweetheart...
...that's not a "MAJOR PROBLEM," it's standard operating procedure. Don't get your knickers in a twist.PFoster 22:30, 7 July 2008 (EDT) (not WIGO worthy...)
.....How would she notice that unless she tried to create an second account....?--*Gen. S.T. Shrink* Get to the bunker 22:32, 7 July 2008 (EDT)
Speaking as someone who logs in and out of Conservapedia all the time, the missing "new account" button is quite noticable on the login screen.
Not that I've been on that screen recently. Lord no... 22:34, 7 July 2008 (EDT)
I've been going there every five minutes to see if Andy got some sense and allowed me to make a sock alert vandals. Then I looked at this sentence. Andy? Sense?--*Gen. S.T. Shrink* Get to the bunker 22:37, 7 July 2008 (EDT)
Blimey, I think I might have had a kip to do with that... I recently made Fun:Game/Olympics, and for a joke, put Conservatroll at the bottom (I still may follow through with it!). Reckon that is why he removed the new account button? Javascap 22:43, 7 July 2008 (EDT)
Well, I think they aren't supposed to affect their policy or anything by what happens on other sites, but that is bullshit and it has worked good so far --*Gen. S.T. Shrink* Get to the bunker 22:46, 7 July 2008 (EDT)
Although you can probably just chalk it up to paranoia, it's happened before and it'll happen again. --*Gen. S.T. Shrink* Get to the bunker 22:47, 7 July 2008 (EDT)
STS: She might have had a friend who was trying to join. Java: I'm going to go move the olympics thing now, and delete the redirect. So I changed your link, you might want to chase any others. ħuman 01:20, 8 July 2008 (EDT)
Aw hell, why'd you have to go and ruin my conspiracy theory? --*Gen. S.T. Shrink* Get to the bunker 01:23, 8 July 2008 (EDT)
## What is Roger up to?
I just noticed this, this and this in the Recent Changes. Aside from apparently having decided that the category "Native Americans" should be called "American Indians", my Whitewash Sense is tingling slightly. However, history is one of my weak points, so I'll leave the actual analysis to others. Opinions? I'm honestly curious whether this is whitewash or more accurate. --Sid 13:44, 8 July 2008 (EDT)
Wow. There's a certain Orwellian feeling to the rewriting of history to purge anything that might be seen as anti-American. The Lay Scientist 13:48, 8 July 2008 (EDT)
Yes, "Orwellian" is the word.--Bobbing up 13:54, 8 July 2008 (EDT)
The whole "vast liberal agenda" game is extremely useful in such cases. Want to claim that the Supreme Court did NOT rule that the Cherokee Nation was sovereign, and that Andrew Jackson did NOT refuse to enforce the decision? Simply say it's a lie. Massive numbers of historical sources say you're wrong? That's because they're all liberally biased. --Phentari 14:46, 8 July 2008 (EDT)
ALso, america never had slavery and someone stole the actual constitution that was a bible. Roger apparently thinks the Navajo tribe likes curry. --*Gen. S.T. Shrink* Get to the bunker 16:54, 8 July 2008 (EDT)
Navajo like curry? I missed that. His (Andy's) entire "history" lesson regarding Indians had me shaking in my boots in anger. If you really want to have fun, go look at the section on Wounded Knee. There's not one fact in there. well, except that some Indians died, but it was their own damn fault for being drunk and all. shudders. The IRA commentary has taken any sense that Indians are their own sovereign nations and that we actually had ratified treaties with them which we of course broke, and made them simply resisters to being moved to the wonderful Indian territory we saved for them. How do these people live with themselves?--WaitingforGodot 17:15, 8 July 2008 (EDT)
I don't have the difflink handy right now, but I recall Andy saying that the Democrats supported slavery, so that one would be yet another case of "Everything evil in the world is liberal, and everything liberal is evil". See also: cp:Liberal Slavery (I didn't check, but I hope that that article does NOT exist.) --Sid 17:07, 8 July 2008 (EDT)
Not yet. --Gulik 04:40, 9 July 2008 (EDT)
Why does Roger seem to have an issue with native people? I notice he seems to share Andy's literacy problem. He has been provided sources yet seems unable to read them.--Franklin 16:57, 9 July 2008 (EDT)
Thanks everyone, for the moral support :). I thought that maybe an actual rational debate would do the trick over there, but so far, no dice. 98.206.181.143 17:18, 9 July 2008 (EDT) (Fishal).
Won't work. A better strategy is:
1. Invite one of the sane sysops (PJR or CPAdmin1) to join the battle. You seem lucky, Karajou joined your cause and he's definitely not sane, you usually have to suck up to them to get their support.
2. Slowly creep some truth into the article and hope he doesn't notice.
3. Wait until he's not around and change the article.
2 and 3 are risky as they may get you blocked, and he'll definitely notice if he has the articles on his watchlist. I haven't had much experience with Roger so others should give you better suggestions. NightFlareStill doesn't have a (nonstub) RWW article. 18:16, 9 July 2008 (EDT)
Meh. Not worth it. I'm incredibly offended by the article, but I suppose it's one more offensive site on a very offensive Internet. Maybe Karajou will happen upon the debate again. 98.206.181.143 18:49, 9 July 2008 (EDT)
## JEWISH CONSPIRACY AT CONSERVAPEDIA
Deborah recently put up on her user page she is a seventh day adventist, but ever notice she edits so many Islam and Judaism articles, I am telling you she is a red sea pedestrian or a towel head (jk) --Jellyfish 15:06, 8 July 2008 (EDT)
What is your view on all these Jews being significant members of Conservapedia, Fox, Deborah, and Ed Poor, I tell you there is a Jewish Conspiracy --Jellyfish 15:11, 8 July 2008 (EDT)
How do we verify her choseness, though considering the fact that women don't have foreskin --Jellyfish 15:13, 8 July 2008 (EDT)
PLEASE COMMENT --Jellyfish 15:17, 8 July 2008 (EDT)
The clitoral prepuce is the female analog of the male foreskin. I can get pics.-- -PalMD --Do I look like I care? 16:20, 8 July 2008 (EDT)
We cannot comment, as the Jewish Conspiracy won't let us. What...? No, I wasn't commenting. Ugh. Argh. HELLLLLLPPPPP!!!! 92.18.84.135 15:42, 8 July 2008 (EDT)
I think it is essential that we force all Jewish editors to wear a 6 pointed star on their signatures, so we will know who they are. (Now why has no one ever thought of such a brilliant idea before?) DickTurpis 15:43, 8 July 2008 (EDT)
Oh dear. Keeping a low profile as ever, I see. 15:51, 8 July 2008 (EDT)
She has recently expanded the Kosher article a lot, she earlier expanded the Orthodox Judaism article, and she never edits early on the saturday or late on friday (keping the shabbat) (she claims to be a seventh day adventist but she can't fool me, I am Jewish and therefore have Jewdar) --Jellyfish 16:00, 8 July 2008 (EDT)
[headache] Will the real Jellyfish please stand up... or swim up... or float up, or whatever it is they do? --AKjeldsenCum dissensie 16:05, 8 July 2008 (EDT)
She even has a Jewish name --Jellyfish 16:08, 8 July 2008 (EDT)
The evidence:
1:She never edits on the Sabbath
2:She has a Jewish name
3:She recently did a major expansion of Kosher
4:She in the past did a big expansion of Orthodox Judaism
5:She recently copied the articles for Hillel and Shammai from Jewish Encyclopedia
6:Most people who edit articles about Judaism are Jews
7:My Jewdar says she is Jewish
8:Fox's Jewdar says she is Jewish
--Jellyfish 16:36, 8 July 2008 (EDT)
Let's be scientific. Are we sure when the Jewish Sabbath begins and ends where she lives? Proxima Centauri 04:26, 9 July 2008 (EDT)
I don't think "scientific" is the right word for what we're doing here. "Scientific" refers to a very specific methodology (the scientific method), which we are clearly not using here. A better word would be "logical". Radioactive Misanthrope 04:48, 9 July 2008 (EDT)
She says she is seventh day adventist, which could explain why she doesn't edit late on friday, or early on saturday. --Jellyfish 16:53, 9 July 2008 (EDT)
### Problems in my conspiracy theory
She may just be interested in Judaism or religions in general for example 1.She created countless mythology articles 2.She has expanded many Islam articles, though not as much byte size 3.She may have simply wanted to expand the really short articles on Kosher and Orthodox Judaism 4.She may be mastering in Theology at her university 5.She expanded John Wesley (the founder of Methodism)
--Jellyfish 16:04, 8 July 2008 (EDT)
Is she intelligent enough to master in any subject at any University? Yes at a low grade Christian university she could do a master. They don't mind if she can't think for herself there. ~If she is Jewish that proves Jews and Jewesses arn't always intelligent. Proxima Centauri 04:32, 9 July 2008 (EDT)
What makes you think she is unintelligent, I look at her edits, Bugler's, and others, often, but I haven't seen her say she is a young earth creationist, denies evolution, or anything like that in her edits --Jellyfish 16:53, 9 July 2008 (EDT)
Are you implying that just because she is ultra-conservative that she must be unintelligent?
I know intelligent computer scientists at my university who are ultra-ultra-conservative! --Jellyfish 16:55, 9 July 2008 (EDT)
That is quiet possibly the most offensive statement I've heard from you, PC. Because the very fact that you felt the need to express that suggests that you yourself bought in to the stereotype that "all Jews are smart". By the way, I cringe when I see the word "Jewess"—I have never heard or read a Jew that actually used it, and it is a distinction Gentiles pulled ex nihilo out of their butts. Radioactive Misanthrope 04:48, 9 July 2008 (EDT)
She used to edit a lot on Hindu deities, didn't she? NightFlareStill doesn't have a (nonstub) RWW article. 16:37, 8 July 2008 (EDT)
### Why do you reject my theory?
Why do you think Deborah isn't Jewish? I think you're simply denying evidence. Please, make your case that she is a goy. --Jellyfish 18:47, 8 July 2008 (EDT)
Fine. I accept your theory. You can stop sulking now. 18:53, 8 July 2008 (EDT)
## He can't say it much louder than this
Bugler is a parodist. Wake up people! We can't really make it any more obvious. DickTurpis 15:57, 8 July 2008 (EDT)
You have to admire the sheer audacity of the man. --71.186.197.144 16:04, 8 July 2008 (EDT)
Bugler is no doubt a parodist --Jellyfish 16:07, 8 July 2008 (EDT)
Not so. And I can argue about this forever, so you people lose by default :P 16:08, 8 July 2008 (EDT)
Poe, poe, poe poe! Poe, poe, poe poe! Glorious poe! Wonderful poe! --Toffeeman 16:18, 8 July 2008 (EDT)
No, I don't think he'd put in that much effort, and besides, if he really was a parodist, why would he block the decent non-sock-wearing users like me. DLerner 07:33, 9 July 2008 (EDT)
## Natural logarithm
I'm having a hard time believing it is about their reading level (or Ed's), does anyone happen to have it on their caches or whatever? NightFlareStill doesn't have a (nonstub) RWW article. 16:24, 8 July 2008 (EDT)
Ed's being more of an idiot than usual. Apparently he took 2 years of physics, which apparently makes him an expert. Note that he later references his physics education as going back to high school, meaning he never took it at a college level, and apparently failed it in high school, having to repeat it. So if something doesn't quite jive with something Ed sort of remembers learning more than 30 years ago (after failing to learn it once), then it must be deceit. DickTurpis 16:47, 8 July 2008 (EDT)
Don't forget, Ed is old. He doesn't seem to believe in wave/particle duality. I mean, this was the Radioactivity page a week ago (no clue if it was expanded in the mean time.) It's not exactly a masterpiece, but as far as it goes it's an accurate description of our understanding of radioactivity. I guess that Ed was educated before duality was accepted enough to be a commonplace part of secondary physics lessons. Yes, Ed, physicists now think that alpha, beta and gamma (and all other EM) radiation have a particle nature, so describing them as such is accurate. --81.187.75.69 16:52, 8 July 2008 (EDT)
Shit, Ed just managed to block three editors within 33 minutes - all of them for not agreeing with his view that it's better to delete than to improve (which goes against common sense and CP's own guidelines). That's got to be some sort of record. If the Award Voting was still going on, I'd totally change my vote. Good thing that he won the vote anyway - he deserves the award. --Sid 17:19, 8 July 2008 (EDT)
Oh look, he ran out of targets and now harasses random other editors. --Sid 17:22, 8 July 2008 (EDT)
His two years of physics were probably Moony seminars, which obviously means his understanding trumps any number of other editors' opinions. I should just give up trying to subtly improve CP and take up something more fun. Heathen 17:23, 8 July 2008 (EDT)
No need to back his claims with Moon Rays - he's a sysop and thus right by default on all issues. And if a sysop says he doesn't understand something, you're not allowed to understand it, either. --Sid 17:26, 8 July 2008 (EDT)
To be fair he deleted the radiation article for a reason other than it being incomprehensible.
For his student's sake I hope this 3-weeks old version was expanded (it probably was, as it doesn't contain any proof). NightFlareStill doesn't have a (nonstub) RWW article. 17:36, 8 July 2008 (EDT)
You can sure tell why Ed didn't get on well at wikipedia, can't you? All those pesky rules must have really started to be a drag on his power crazy authoritarianism. His mini rant about wikipedia's "anti-elitism" that has been on his user page since forever is amusing in context, when you realise by elite he doesn't mean knowledgeable but in fact powerful. --81.187.75.69 17:37, 8 July 2008 (EDT)
Well, the new Radiation "article" is starting out badly, even by Ed's low standards. --Sid 18:48, 8 July 2008 (EDT)
He has done worse. Seriously, how did Ed manage to survive at Wikipedia? He definitely cannot edit articles and is a power tripping asshole, I'm considering heading over there to ask. NightFlareStill doesn't have a (nonstub) RWW article. 23:13, 8 July 2008 (EDT)
### Lemonpeel Block
Ed has blocked Lemonpeel for violating CP's "reading level" which at this time is a red link. I think Conservapedia needs to get its act together and decide what it wants to be. At the moment it is a blog with a pile of definitions attached. If they want a home-schooling resource like they say, then they need a plan. You can't write a text book by hoping someone comes along and write the next chapter the way you want. Instead of deleting articles Ed doesn't understand why doesn't he write articles he does and find someone to fill in the intervening steps for him. $\approx$$\pi$ 02:08, 9 July 2008 (EDT)
## Andy's Secret Identity
.... is J. Jonah Jameson, of Spider-Man fame! Just take a look... http://www.adherents.com/lit/comics/image/JJonahJameson_1.jpg Imagine that he's talking about Obama. Jameson's insistence that Spider-Man is responsible for every evil that happens to the city is uncanny in accuracy. I might have to photoshop some comic pages soon. - Lardashe
JJJ's looking pretty wall-eyed in that shot. --Kels 18:31, 8 July 2008 (EDT)
## Rutm
Er. What does Andy think "Rutm" means? The only thing I can think of is "Rage under the machine". Which is stupid. 19:15, 8 July 2008 (EDT)
It seems Andy is pulling an Ed here: if I don't understand it, it's bad. DickTurpis 19:26, 8 July 2008 (EDT)
It took CP months to read the fucking name backwards.-caius (mission accomplished!) 19:28, 8 July 2008 (EDT)
The time between Andy's last warning that he wouldn't accept unblocking the old account (nor clarifying why the account was blocked in the first place). This would make it rather difficult to say "ok, change the account name to" in that time span. Of course, this was then deleted to destroy the history and cover up this unreasonableness. --Shagie 19:39, 8 July 2008 (EDT)
Hmm. Now he's deleted the entire page on the grounds that "offensive, non-family friendly material posted and left on this page; user has been blocked for persisting in an insulting name." Weirdly, I didn't see any "offensive, non-family friendly material posted there." Rutm must have slipped it in in the midst of being so insulting. --Phentari 19:41, 8 July 2008 (EDT)
Chances are it was this bit: --Shagie 19:53, 8 July 2008 (EDT)
"With the bannings of StatsFan and Hatton, Ladies and Gentlemen, I rest my case. Never in the past year has there been a clearer declaration that this resource is nothing other than the personal blog of ASchlafly. This party is over, the goose is cooked. ASchlafly has attained the status of the Pope, as he clearly believes he is actually personally infallible. When you're done with rewriting the Bible and restructuing all of science, perhaps you can come over and fuck my wife, as I imagine you are shit hot in bed too? BKronky 16:52, 20 June 2008 (EDT)"
I screenshotted that ages ago -- can't believe it lasted so long. 19:55, 8 July 2008 (EDT)
Me too, I was amazed when it was there still after 3-4 days - I took to screenshotting it with my computer calendar showing to see how long it had survived. I think I called it "fuck my wife.png" to make it easy to overwrite... ħuman 21:04, 8 July 2008 (EDT)
And sysops "Karajou", "Conservative", "CollegeRepublican" and "Freedom777" nod in approval of the naming policy being enforced so strictly... --Sid 19:46, 8 July 2008 (EDT)
Re. this image: Damn, I didn't know there were any messages after Andy's first last warning. That makes the timing even sillier. --Sid 19:55, 8 July 2008 (EDT)
Note the time difference between Andy's edit and Ed's block. --Shagie 19:58, 8 July 2008 (EDT)
OMFG, no wonder they had to burn the page! --Sid 20:01, 8 July 2008 (EDT)
Wait, what was on his user page? The BKronky thing?-caius (mission accomplished!) 20:04, 8 July 2008 (EDT)
User:Rutm was apparently never deleted or created, actually. And the BKronky post (like everything else) was on the user talk page (it can also be seen in the first image backup). --Sid 20:07, 8 July 2008 (EDT)
So he was blocked for someone ELSE'S obscenity?!-caius (mission accomplished!) 20:09, 8 July 2008 (EDT)
And the absolutely unacceptable username, of course. --Sid 20:11, 8 July 2008 (EDT)
Any idea on why it was unacceptable, anyone?-caius (mission accomplished!) 20:21, 8 July 2008 (EDT)
I think..."Rutm".......Roo-tim.......root 'em! Ace McWicked
Andy was likely taking exception to the definition of rut. Side note - its funny to get a Canadian and an Australian in a room talking about cisco products. The Canadian pronounces 'router' like 'rooter' (with the sound of 'ooo' as in "look at those boobies" rather than "ow" of "you stared too long") and the Australian pronounces 'rut' like 'root'. --Shagie 20:48, 8 July 2008 (EDT)
I like to think I'm pretty savvy about figuring out obscure obscene elements, but the only thing I can think of is "Are you TM" No idea. - Lardashe
Shagie, no offense, but those had to be the worst pronunciation examples I have ever seen! oo as in look or boobies? ow is in.... what? Or was that your intent? ;) ħuman 21:07, 8 July 2008 (EDT)
"oo" as in "boobies" or the sound made prior and "ow" as in the sound made when you get your face slapped for staring at said boobies. --Shagie 21:12, 8 July 2008 (EDT)
there is, in fact, nothing offensive about it. It's the reverse of his/hers previous user name - mutr. Ace McWicked 21:08, 8 July 2008 (EDT)
The first name last inital will be amusing once you get a person with latin roots with a name like Jesus. Or a name like "Lia Dang" (perfectly valid name - 529th most common female baby name of 2007[2]). For fun, track the changing political tendancies in America by the names of the babies. Using Data from 1900 to 1950, can you predict anything about the population of 1960 or 1970? For example, Noah has moved to 14 in 2007 from 100 in 1995, 217 in 1985, and 312 in 1975. You can also see the increasing latin american population by searching for "Jesus". Olivia has a a resurgence (7th most popular? Top 10 since 2001? Will "I went to school with 27 Olivias" be a top song in 2030?) --Shagie 21:12, 8 July 2008 (EDT)
The half-generation after me was crowded with Michelles, and their best friend Jennifers. Beatles and Donovan, I think... ħuman 21:50, 8 July 2008 (EDT)
"Megan" is seems to be one of the most common names for girls in my generation. Unfortunately, so is "Jacob" (which is my name) and it's still popular. (I still respond automatically to anyone who calls my name in an exasperated voice—'cause I still live with my parents—and there's been this explosion of five-to-nine-year-olds who have the same name as me, which keeps things interesting. *someone's exasperated voice* Jacob! *I snap my head around and almost shout "What?!"*) Radioactive Misanthrope 05:05, 9 July 2008 (EDT)
I have exactly the same problem, I even have the same name! Etc 07:40, 9 July 2008 (EDT)
Yeah, not to be a pig, but the later generation was very full of Megans, Mehgans, etc.... Sorry, Jake. Ask me sometime about what I had to go through in 5th grade, along with my classmate, "Jake"..... trivial, I guess, but still... ħuman 06:46, 9 July 2008 (EDT)
Could the "offensive" nature of Rutm be that the old name, Mtur, = "empty you are?" 64.165.22.43 16:24, 9 July 2008 (EDT)
### Acronym?
Is it possible "RUTM" is an acronym that Andy recognizes? Some guesses:
• Roger unable to marry? (I thought that was John)
• rice under the mattress?
• rather ugly titmouse?
• ride until the morning?
• red umbrellas taste meaty?
• rough udders tickle me?
(for reference, some of the more common "u" words are: udder ugly ultra umpire uncle under undo union unit unity until unto up upper upset urban urge urine urn us usage use user usual)
--Interiot 18:58, 9 July 2008 (EDT)
rough udders tickle me - TMI TMI TMI TMI --Sid 19:51, 9 July 2008 (EDT)
## EHHH
Isn't this shit supposed to be over? --*Gen. S.T. Shrink* Get to the bunker 22:24, 8 July 2008 (EDT)
No, that will never get old. Like a fine wine, that will only improve with age. We need one a month (but no more) for the next year and a half, I think. Has anyone hit his wikipedia page yet? DickTurpis 23:18, 8 July 2008 (EDT)
Oh come on, what has wikipedia ever done to us? --*Gen. S.T. Shrink* Get to the bunker 23:22, 8 July 2008 (EDT)
Well, they DID give us a lot of ideas and formatting help for writing articles... but on second thought, that doesn't merit launching an offensive against them. Javascap 06:55, 9 July 2008 (EDT) (EDT:Forgot to log in.)
I highly doubt his Jimbo-ness would like it. Of course he wouldn't approve of...anything we do really. --*Gen. S.T. Shrink* Get to the bunker 20:22, 9 July 2008 (EDT)
## Ken is thinking again....
[3] He shouldn't give ideas. And anyway, how the hell will that help? Can wiki even do that? --*Gen. S.T. Shrink* Get to the bunker 22:55, 8 July 2008 (EDT)
I was about to post the same thing. What a fucking idiot. DickTurpis 22:57, 8 July 2008 (EDT)
Brilliant idea ;). Who here couldn't write three paragraphs on, say, tribbles or slinkys, also lauding their conservative values, in order to "get in the door"? ħuman 22:59, 8 July 2008 (EDT)
The greatest thing about conservatives are their good values
George Washington was a conservative.
PIe.
Although, if they could do it, they'd just not let anyone through. Say no to everyone. Which I doubt WikiMedia would even allow. --*Gen. S.T. Shrink* Get to the bunker 23:02, 8 July 2008 (EDT)
I for one would enjoy the challenge even more with such a system. The added advantage of such a system to the professional wandal is that one gets the chance to immediately place material into the Trustworthy Encyclopedia, rather than having to slide in the door unnoticed and begin making unnoticeable edits. Policing such a system would utterly overwhelm the sysops, as to properly judge new registrants for wandalistic traits, they would have to read the three paragraphs fully, instead of simply banning them on their name or "ICEEEEEWEDGE STRIKES AGAAIAAAAIN!!!' hits. DogP 23:06, 8 July 2008 (EDT)
I highly doubt they would ban any less. Just stop getting any new users. How long has it been since they've gotten a real honest conservative user? --*Gen. S.T. Shrink* Get to the bunker 23:11, 8 July 2008 (EDT)
BUGLER!!!!!!1111!!11 DickTurpis 23:16, 8 July 2008 (EDT)
And the Lord did say... "Let there be Brain Damage, and let it be inflicted unto my most fanatical followers." And like all the other things the Lord did say, it was so. Javascap 23:18, 8 July 2008 (EDT)
Ken
It is possible to do it, Creationwiki does something similar (they removed the user requirement for recent changes, by the way). It might work to deter random vandals, but 1)parodists wouldn't mind, 2)new users will have an even more uncomfortable start and, 3)unless the number of reviewers is considerably greater than the number of sysops, the system will be really slow... on second though 2 and 3 have synergy! NightFlareStill doesn't have a (nonstub) RWW article. 23:26, 8 July 2008 (EDT)
<-- @NF, 1) Parodists would think it was better, 2)New users (real ones) wouldn't bother, and 3) Profit! ħuman 23:29, 8 July 2008 (EDT)
By the way, my first thought when I saw this header added was, "yeah, I can smell it from here"... rubber burning, gears grinding, etc. ħuman 00:22, 9 July 2008 (EDT)
How many seconds would it take any one of us to defeat that system? Five? Six? I mean, it rests on the assumption that libruls won't bother because they might accidentally be productive? This is why they are so bad at spotting pdrsts...their first commandment is actually Poe's Law.-- -PalMD --Do I look like I care? 00:33, 9 July 2008 (EDT)
Deb is inserting a little intelligence into the idea. Like the fact that it's a stupid idea. Bless her heart. --*Gen. S.T. Shrink* Get to the bunker 00:37, 9 July 2008 (EDT)
Yes. Let's face it, if that were the "new rule", Aschlaflhead would be swamped with "new user submissions" so badly he'd never have time to pee again. At least as it is, his acolytes clean up the vandals for him (with relish... and mustard!). It gives the sysops something to do besides lock their pet pages. ħuman 00:56, 9 July 2008 (EDT)
Indeed, the possibilities for denial of service would be endless. One bot, and the RSS feeds of the world later and Conservapedia would never have a new user ever again. MWAHAHAHA! --81.187.75.69 04:29, 9 July 2008 (EDT)
I think it would be an excellent oppotunity to get a script to randomly generate three paragraphs worth of conservative or even Conservative thinking drivel to save time. It'd be quite a while before they notice the same sentences cropping up as the sysops appear unable to communicate. Armondikov 08:33, 9 July 2008 (EDT)
## Conservative is a parodist
Read his user page, he has a whole rant about peanut butter
"According to a peanut butter and jelly granola distributor, American consumers prefer creamy peanut butter to crunchy by a 60% to 40% ratio. Also, American children and women prefer creamy while most men opt for crunchy (for verification/details call 1-866-374-4442). Since many liberal American men get bossed around by their feminist liberal wives, it appears likely many American liberal men may be eating creamy peanut butter even though they prefer crunchy peanut butter deep down. :) These American liberal men are likely afraid to ask their liberal feminist wives if their household can stock crunchy peanut butter in addition to stocking creamy peanut butter!
It also appears as if liberals suffer from arachibutyrophobia more which is the fear of peanut butter getting stuck to your mouth. For the Bible declares, ""The wicked flee when no one is pursuing, but the righteous are bold as a lion." :)
In addition, it appears as if many liberal atheists have nightmares about peanut butter. :)"
He also a link claiming that peanut butter is proof of God's existence --Jellyfish 00:17, 9 July 2008 (EDT)
No he is not a parodist. A parodist would have gotten past the joke by now. Nobody could spend as long as he has working on something he didn't believe in. He is just very close to Ed at being the second biggest idiot there. (I am now convinced Ed is the stupidest as he deletes maths articles he doesn't understand instead of accepting the fact he just isn't that smart). $\approx$$\pi$ 01:54, 9 July 2008 (EDT)
I agree, Kenservative is no parodist. After all, he has Wikipedia history also. Now, that Ed Poor, what a fucking numb-nuts. Following the radioactive/maths/block crusade he went on really makes me think he must have suffered some kind of severe head trama. Ace McWicked 02:25, 9 July 2008 (EDT)
Any chance he's playing the long game... so long that he started before Conservapedia even existed? Hey. I think Kendoll maybe our new messiah. --81.187.75.69 04:31, 9 July 2008 (EDT)
Isn't there a proof (or a spoof proof) against evolution or abiogenesis involving peanut butter? I shouldn't be surprised if that's what's behind his muddled thinking. Seeing what he thinks is "humour" on his user page I wouldn't put it past his infantile brain at all. Genghispillaging 17:17, 9 July 2008 (EDT)
Yep. Peanut Butter: The Atheist's Nightmare! from Way of the Master. Barikada 17:22, 9 July 2008 (EDT)
I think this little example is a perfect example of Conservative thinking. As a hypothetical, If I had a wife or girlfriend I was living with (I don't, too much time on Rationalwiki) and we had a dispute like this, the simple solution would be to buy chunky AND smooth peanut butter and eat as we see fit. Conservatives think there is only one way to do things and someone has to be the winner in everything. Ken, it's called COMPROMISE, look it up sometime you idiot. SirChuckBA product of Affirmative Action 00:47, 10 July 2008 (EDT)
## Account Creation Possible Again!
Andy has unlocked the "Create Account" feature at last. I've created my very first Conservapedia sock! Now to see how many edits I can go through before I get blocked... The Lay Scientist 07:34, 9 July 2008 (EDT)
With an edit like that (if you are who I think you are) you won't last long... (Editor at) CP:no intelligence allowed 07:54, 9 July 2008 (EDT)
Well you lasted much more than I thought. Now, to be consistent, Tim should block Bugler too as a parodist. (Editor at) CP:no intelligence allowed 04:21, 10 July 2008 (EDT)
I'm not blocked, as far as I can tell... Oh no, wait, I am :( The Lay Scientist 13:56, 10 July 2008 (EDT)
## DLerner's days are numbered
Surely, Ed's not going to like this. 78.16.142.46 08:18, 9 July 2008 (EDT)
Quite frankly it speaks volumes about his ability to walk on thin ice that he's survived since early March. Silver Sloth 08:38, 9 July 2008 (EDT)
I can't wait to see what will happen. Perhaps a screenshot of this and the next reply might be a good idea (I've no idea how to do it)--Damo2353 09:33, 9 July 2008 (EDT)
Damo to get a screenshot make sure your browser has focus - i.e. is the active window, and then press Alt-PrtSc (two keys together). This copies an image to the clipboard which you can paste into an image editing program so that you can save it as an image. I find that text compresses quite well and keeps its sharpness if you save it as a gif file. But something with a lots of colors like a photo on screen needs to be saved as jpeg. I am giving you an image saving assignment to practice this so that next time you see something worth nabbing you will be ready. :) Genghispillaging 17:23, 9 July 2008 (EDT)
Alternatively, Shift-PrtScrn copies your entire monitor display, if you prefer. ħuman 18:53, 9 July 2008 (EDT)
The reply is priceless. Apparently Ed only wants articles homskolars can understand.Antifly 23:27, 9 July 2008 (EDT)
Why a Jew thought anti-semite Ed would listen to him is beyond me... DLerner, it's sad, but where Ed's concerned, you were doomed from the outset-caius (mission accomplished!) 23:30, 9 July 2008 (EDT)
## Liberal deceit throughout history
This change to the entry on Trojan Horse is hilarious. 78.16.142.46 08:22, 9 July 2008 (EDT)
HAHAHAHA! Ajkgordon 09:22, 9 July 2008 (EDT)
Hmm... I wonder if, by extension, this means that Paris's kidnapping of Helena was a result of early Conservative Values? "Marry a Conservative" and all that. --AKjeldsenCum dissensie 09:37, 9 July 2008 (EDT)
I couldn't understand how someone can create a user id and make a parody edit soon after and not get reverted or blocked. But then, he does claim to be a Conservative on his user page. Bondurant 09:41, 9 July 2008 (EDT)
Well, actually the Trojan Horse was deceit, wasn't it? And if it was deceit it must have been liberal. So one could argue that it's not parody at all.--Bobbing up 09:48, 9 July 2008 (EDT)
You could argue that, yes. Just as you could argue that Bugler isn't a parody too. I'd believe neither, though. Still, I'll lay odds that with a handful of edits like that and some spattering of the words "liberal" "deceit" and "clueless" on some talk pages, and he'll be a sysop before August. Bondurant 09:55, 9 July 2008 (EDT)
Remember that we're dealing with people who think that even the Bible has been infected with Liberal Deceit. Even if this guy is a parodist, it might well be a while before someone who realizes that it is parody comes along. --AKjeldsenCum dissensie 09:59, 9 July 2008 (EDT)
It's pretty obvious who it is, actually. Bondurant 10:05, 9 July 2008 (EDT)
JM has reverted it. I'm surprised such obvious parody lasted as long as it did, really. alt 10:35, 9 July 2008 (EDT)
I didn't know the Trojan Horse was computer science! NorsemanWassail! 13:38, 9 July 2008 (EDT)
Interestingly, the user hasn't been banned, blocked or even spoken to. Not that I'd know... The Lay Scientist 16:10, 9 July 2008 (EDT)
Of course, TLS ;-) Bondurant 16:11, 9 July 2008 (EDT)
@Norseman, I have a front end loader made by a company called trojan. Searching for "Trojan loader" is next to useless due it being a CS term. @Everyone, "beware of Greeks bringing gifts". Someone please to add to article... ħuman 19:01, 9 July 2008 (EDT)
## Oh come on...
Buggerer has just sent my parody alarm into overdrive again. Read his comments on the talk page of Xkcd [4]. The guy is so OTT he makes the rest of them look positively normal. Is it just me or does he just seem to talk and block (ok, and tweak architecture occasionally)? --PsygremlinWhut? 18:14, 9 July 2008 (EDT)
Dude, is he sloshed? His typing gets worse as that thread goes on.... Barikada 01:57, 10 July 2008 (EDT)
## Hmmmmmm Ed?
What is he suggesting with this comment on KevinM's talk page....? "If you need quick attention on vandalism, try alerting a sysop by email. I have two accounts: one I check a few times a week, the other is refreshed automatically every 5 minutes. (Friends get my cell phone number, hint, hint.)" Ace McWicked 21:43, 9 July 2008 (EDT) Ace McWicked 21:43, 9 July 2008 (EDT)
I'm not gay bashing... but is Ed a faggot? --JayJay4ever??? 22:51, 9 July 2008 (EDT)
I'm not bashing those of subnormal cognitive abilities, but, no, Ed Poor is an idiot. ħuman 22:59, 9 July 2008 (EDT)
That edit contains another gem: "plus I use my real name" - How odd, and here I thought that KevinM obeys the naming policy more than... uh... Karajou, Conservative, CollegeRepublican, Freedom777, Learn together, etc. In fact, it obeys the policy exactly (first name, last initial). Seriously, how can a guy sound so caring and so condescending at the same time? --Sid 06:41, 10 July 2008 (EDT)
More ed-iocy. Ed poor says "We need an entry on ruling class. JJacob (whose ass-licking sock is that?) creates one. Ed deletes because it is 'Jargon laden'. WTF? Ace McWicked 23:05, 9 July 2008 (EDT)
Another Ed Gem....[5]
“”Respectful disagreement is good. I asked the liberals to help us point out where CP and they disagree, but they refused and left in a huff. They want to dictate what we write, apparently.
Um, no Ed - we didn't leave in a huff, we were banned. --Shagie 23:16, 9 July 2008 (EDT)
WOW. Diff for that one plz? That's almost 1984 level self-delusion.-caius (mission accomplished!) 23:31, 9 July 2008 (EDT)
Don't wigo it, it's already there under the "Bohdan" edit link. I fell off my high horse and choked on a dumpling when I read that... ħuman 23:33, 9 July 2008 (EDT)
Oooh boy. It wasn't Ed who did it, but "This title has been protected from creation by Ymmotrojam. The reason given is . " was what I found under RationalWiki. Can you feel... teh Lulz tonite? Javascap 23:36, 9 July 2008 (EDT)
I've added the link to the diff into the Bohdan item. I've got to think that Bohdan is a parodist too now (as if he wasn't before). One can assume that he's given up on all of his past ways and repented along with an act of contrition. --Shagie 00:00, 10 July 2008 (EDT)
@javascap, what are you talking about? ħuman 00:03, 10 July 2008 (EDT)
I think this is an excellent opportunity to reach across the intertubes and offer support. Mr Poor, I think I speak for several of us when I say we would glady come "help... point out where CP and they disagree." We would even sign up under our same names so there is no confusion. However, some things would have to settled first. Feel free to leave me a message at my userpage and we can set ground rules for our glorious return. SirChuckBA product of Affirmative Action 01:03, 10 July 2008 (EDT)not holding my breath
Pffffffbwahahahahaha. Right, Ed. You offered to cooperate... if we admit our guilt first and beg for mercy from the Great Ed! Fuck, I still got your mails where you heavily implied that I would get unbanned if I admitted that I indeed broke the rules and apologized! Oh, and once we would have been unbanned, we would have been under "parole", and you would have given us "writing assignments" for things like "Why the German Shepherd and dental floss played such a vital role in the 1992 Presidential Election" or "Why Global Warming is a complete lie". And we would have been completely forbidden from editing any article touched by a sysop. And our edit/talk ratio requirement would have been 1000/1. Yeah, gee, thank you, Ed... but no thanks. --Sid 06:48, 10 July 2008 (EDT)
Human - Ymmotrojam went on a deletion and protection spree, so you can't even create an article called RationalWiki anymore. And Ed, full of it. Like Conservative, he hides on CP and makes his own claim because he's wrong everywhere else on teh internetz. NorsemanWassail! 06:59, 10 July 2008 (EDT)
Ed, as you may recall, I extensively documented how CP and I disagreed on the Conservapedia Column, both before and after I "left in a huff". You are as always welcome to go there and see for yourself - the material is as true today as it was at the time of writing, I'm sorry to say. --AKjeldsenCum dissensie 07:05, 10 July 2008 (EDT)
### An Open Letter to A Person At A Certain Website
From: Gulik
To: Ed Poor
You wrote, with your bare face hanging out, "Respectful disagreement is good. I asked the liberals to help us point out where CP and they disagree, but they refused and left in a huff. They want to dictate what we write, apparently."
Um, no, Ed. I didn't "Leave in a huff", I was BANNED. Repeatedly, in fact. And I'm obviously not the only one. Because anyone who DOES point out where they disagree with the Gospel Of Andy Schlafly invariably gets threatened with a 90/10 block, "Talk Pollution", or just "insulting behavior", and you are the second-biggest hatchetman on the site. This site can't be improved because people like you and Andy don't WANT it 'improved', except in the sense of "Adding more reasons Why Liberals Are Bad".
All those editors leaving in a huff? A lot of them might even be Conservatives, though not as Conservative as you. (Nobody is, not even that hippie subversive Richard Nixon.) They're just sick of repeatedly banging their heads against the Great Wall of Schlafly in a vain attempt to get some facts added to articles so idiotically biased that they are obvious parodies to everyone but you sysops.
I do not actually expect any sort of reply to this email--I just felt like venting. Enjoy Conserapedia until such time as Andy gets tired of paying the bills, as it is the ONLY place you'd ever 'win' an argument, as no fact or logic can stand before the raw, naked power of The Banhammer.
Yours in Hopeless Obscurity,
Pope Disturban the Vth
Aka "gulik@conservapedia"
(Yes, I did email this to him. I am 95% Certain I won't get any acknowledgement or reply.) --Gulik 05:43, 10 July 2008 (EDT)
## More Conservapedian Maths
Am I the only one who thinks these three articles are the best mathematics articles on Conservapedia. $\approx$$\pi$ 04:25, 10 July 2008 (EDT)
Well, there's nothing in them that makes me grind my teeth in frustration at their obvious idiocy, which is certainly a HUGE step up from anything Andy's ever written. --Gulik 05:47, 10 July 2008 (EDT)
Well, even a stream of random characters is more likely to contain useful information than the average article on CP. These articles do look about the same on the Khmer Wikipedia, and I'd guess the author just copied them to raise his mainspace/talk ratio and mess with Schlafly.
More importantly, I can find no Conservapedia Commandment or policy that says articles has to be in English. (only that American (spelling) is preferred over British, but not necessarily preferred over any other language). Etc 07:35, 10 July 2008 (EDT)
With that in mind, what do you reckon the reaction would be to an article in Spanish? Or French... wait... Czech! =D Javascap 08:25, 10 July 2008 (EDT)
Hey, a foreign language written in phonetic English should get through then.--Bobbing up 12:57, 10 July 2008 (EDT)
I've also experimented with a few different ways to insert nonsense into CP before, but in the long run it's not a very interesting way to contribute and you usually just get blocked and that's it.
CP doesn't need vandalism to be funny anymore, I think the best thing we could work with on CP now is to shorten down articles - removing everything that isn't funny, that is. (In other words, removing truth/liberal bias) Etc 14:30, 10 July 2008 (EDT)
Although for some articles, removing "liberal bias" makes them longer : ) Radioactive Misanthrope 14:33, 10 July 2008 (EDT)
I don't see why Randy doesn't step in and improve the maths articles. He seems content to spend all of his time revising history...Antifly 18:57, 10 July 2008 (EDT)
Perhaps he can edit the eating competition articles. NightFlareStill doesn't have a (nonstub) RWW article. 21:13, 10 July 2008 (EDT)
## Lockdown
This site is growing rapidly!
I see they still haven't opened it up for editing - almost 2 hours late now. Wonder if there's a reason for that. --PsygremlinWhut? 08:47, 10 July 2008 (EDT)
The Recent Changes look almost exactly as they had five hours ago. Is it still "night" in Andyland? --Sid 12:20, 10 July 2008 (EDT)
Added screencap. More than 12 hours (as per CP's server time) into the day, and there are just eight mainspace edits. Slight WTF. Where are all the people with edit rights? --Sid 12:31, 10 July 2008 (EDT)
He's probably saving server space for the Lenski data.Shangrala 12:45, 10 July 2008 (EDT)
Hey Shangrala. Great explanation. I love it.--Bobbing up 12:55, 10 July 2008 (EDT)
Ah, the hamster's been fed and put to the wheel again. --PsygremlinWhut? 13:18, 10 July 2008 (EDT)
Perhaps Andy's testing his slaves--who works and who doesn't. Evidently, nobody's interested in building Conservapedia. --JayJay4ever??? 13:24, 10 July 2008 (EDT)
## Wheres Wally? errrr, Andy
It seems that all the other sysops, even Andy, have gone leaving Ed Poor to fumble around by himself. Edpoorapedia? Ace McWicked 17:52, 10 July 2008 (EDT)
I imagine Andy's still on vacation. While I had voted for Andy being the worst at CP, I think I'd have to change mine to Ed. He usually seemed a bit more bumbling and less of a jerk, but over the last week or so, he's gotten really out of hand. His actions aren't just mean, they're counterproductive to his own goals. This suggests that he values being a bully over getting any work done. - Lardashe
Yeah, Ed's recent behavior also made me reconsider my vote (I had voted for LT). It's lovely to see what happens the moment Ed is only one around, though: He gets his ass handed to him by... Deborah! (See WIGO for links) --Sid 18:49, 10 July 2008 (EDT)
You voted for Learn Together!?!?!? Christ, just throw away your vote on a third-party candidate why don't ya? DickTurpis 19:45, 10 July 2008 (EDT)
Don't blame me ... I voted for Kodos! Jrssr5 09:25, 11 July 2008 (EDT)
It had been a "heat of the moment" thing. He had gone on a complete rearguard spree just then, I think... --Sid 21:02, 10 July 2008 (EDT)
OK, Asia, I guess you're one of those guys who bases their vote on the most recent news story, rather than the greater issues. "Well McCain might keep us in Iraq for 100 years, but yesterday Obama said 'it's great to be here in Milwaukee' when he was actually in Madison. I can't vote for a guy who doesn't know where he is!" Your type makes me sick! Physically sick! I'm going to puke all over my shoes! DickTurpis 09:41, 11 July 2008 (EDT)
Indeed, he is total fucking clown-shoes. Another thing - Karajowls seems to think TrTran the Cambodian was our friend Tom Moore. Is this so? Ace McWicked 18:59, 10 July 2008 (EDT)
If so, then that was the most awesome act ever. However, it wouldn't be the first time Karajou spazzes out and accuses the wrong guy, so eh. --Sid 19:11, 10 July 2008 (EDT)
Yup, it was me. I was having a grand old time, too. TrTran is one of my eight accounts I created way back in the day, which I use to insert obviously wrong information into the objective but seldom-watched articles.--Tom Moorefiat justitia ruat coelum 19:48, 10 July 2008 (EDT)
Some fine work there Tom, they didn't even have an article on complex conjugate until you got there. Okay so it wasn't in English but at the moment it is more informative then natural logarithm. $\approx$$\pi$ 20:17, 10 July 2008 (EDT)
KevinM - "Karajou, you know you just blocked 65,000 IP's from ever editing Conservapedia right?" Karajou - "Yes, but I know they were all vandals" Ace McWicked 19:32, 10 July 2008 (EDT)
Let's bet! What will be KevinM's block reason?
• Troll
• Vandal
• Bye
• User supports vandals
• Sock of banned user AmesG
Combinations work. I'm going for "Troll/Vandal" in that order. NightFlareStill doesn't have a (nonstub) RWW article. 19:42, 10 July 2008 (EDT)
I'm gonna go with "Troll", maybe "Whining" or "Disrespect" also. Heathen 19:47, 10 July 2008 (EDT)
"I am interested in your justification for blocking 458,752 IPs for infinity within just a few weeks." - Oh crap, this can only end in tears. My money is on "Bye", somehow. Or something to do with "talk" or "MYOB" (Croco's made-up "rule"). --Sid 19:49, 10 July 2008 (EDT)
I recently wrote Karajou's song for Conservapedia: The Musical (work in progress, actually) which I tried to fill with as many Karajouisms as possible. In just a few posts here, he's expressed two of them: "picking a fight" and blocking entire states from editing. Who's got a sock and wants to try to get him to state a few more? We need a "you WILL respect this site", an "I risked my life defending ungrateful people like you", something about how he/sysops/Andy decide what's right, and maybe a "I haven't really looked at your edits but I'm sure they're bad" (a bit more of an Andy than Karajou, actually). Who thinks they can goad him into a couple of these? I'd at least like to see a trifecta in this one discussion. DickTurpis 20:11, 10 July 2008 (EDT)
(EC)Don't forget "No, its YOU who is...", "This conversation is done with.", "you're attempting to subvert our..." and "insultive" which I've never seen personally. NightFlareStill doesn't have a (nonstub) RWW article. 20:49, 10 July 2008 (EDT)
LAST BETS, LADIES AND GENTLEMEN! "[several paragraphs of pwn] You may fire when ready. --KevinM 20:52, 10 July 2008 (EDT)" --Sid 21:02, 10 July 2008 (EDT)
WAIT WAIT! I'm changing my bet to something that suggests Kevin supports trolls and is a troll himself.
Also, how frequent are IP range blocks on Wikipedia? NightFlareStill doesn't have a (nonstub) RWW article. 21:09, 10 July 2008 (EDT)
I dunno how common or rare they actually are, but here is what this WP page about IP blocks says:
“”Most IP addresses should not be blocked more than a few hours, since the malicious user will probably move on by the time the block expires. If there is persistent disruption or vandalism from an IP address, the block should be extended (with the 'anon-only' option selected) as long as is necessary to prevent further disruption. However, IP addresses should almost never be indefinitely blocked. Many IPs are dynamically assigned and change frequently from one person to the next, and even static IP addresses are periodically re-assigned or have different users. In extreme cases, consider long-term blocks over a period of months or years instead. Long-term blocks should never be used for isolated incidents.
(Emphasis in original.) I'm pretty sure that "extreme cases" is not "one guy made a few socks and is a parodist", and this isn't even about range blocks - it's just about IPs in general (including single IPs)!
It should also be noted that "/16" is the most extreme case the wiki software actually allows. Normally, range blocks are applied to MUCH smaller ranges (like /24, which would only block 256 IPs, which should normally be enough for a vandal with dynamic IPs). --Sid 21:32, 10 July 2008 (EDT)
Just in case Kookajoo loses the discussion whilst archiving his talk page or something, it is saved for posterity. Zmidponk 21:35, 10 July 2008 (EDT)
And, just to complete Kooky's utter incompetence, I do believe that 'Road Runner Hold LCC' isn't a 'proxy', but is, in fact, an ISP. Zmidponk 21:43, 10 July 2008 (EDT)
It's probably just people at an ISP that allows them to get a different DHCP address just by rebooting their cable modem. Anyway, most of the admins there are doing range blocks, even indefinite /16 blocks. It looks like there are some persistent vandals (the RoadRunner guy started a month ago at least), so it's sort of understandable, but I don't think it makes sense for these blocks to last for anything close to two years. --Interiot 22:51, 10 July 2008 (EDT)
Kookoohead: "I'll do the infinate thing, but I won't be opposed to the block being lifted in six monthss or less." First, spell infinite right. Second, how on earth are you going to "remember" to dig through the voluminous list of current blocks at CP to figure out which ones you meant to undo after six months? Third, Kookyjoob, you are an idiot. You blocked 64,000 RoadRunner IP addresses - excuse me if I'm wrong, but RoadRunner is the trademark of a major US ISP (use to be mine, years ago, before selling to another telecom) ħuman 23:12, 10 July 2008 (EDT)
I very much doubt that you can get any IP out of a range of 65,536 just by rebooting your modem. I know what you mean (I get force-disconnected every 24 hours and get a new IP when I connect again), but those IPs are usually in a narrow band. A few /24 blocks maybe, but not all 256. I honestly doubt that a single log-in point in the entire US has a complete /16 block all to itself and blindly assigns ANY of those IPs to a user. And that still leaves the other questions raised by Kevin: Even if that was possible, how are you to say for sure that such wildly different addresses are all the same guy or a proxy (which would imply that a single proxy is using the entire /16 block - something that is even less likely than a single guy being able to use the entire block)? And even if we assume everything else as true, that would mean that a single guy actually used so many blocks in his spree (like, he had hundreds of socks or somehow used a completely different IP for every edit). No matter how you look at it, Karajou's argument is full of holes and shows a blatant lack of knowledge. (Also keep in mind that this is the guy who once accused a random German IP of being me on the basis of it being... a German IP. Apparently he "knows" that I can access any IP in Germany!) Do you trust a guy with such a lack of insight to be able to actually figure out which range needs to be blocked? He's merely going by his gut feeling and banhammered half a million IPs within two weeks or so.
I know you're aiming for a compromise, and I applaud you for getting him to at least consider using shorter blocks, but that doesn't change that his frantic handwaving does little to hide his apparent incompetence. --Sid 05:26, 11 July 2008 (EDT)
## Favourite Ed-ism
I just saw this line, and it was just a perfect example of "fail" that I had to share. From the talk page describing the aims of the new radioactivity article:
"It should also explain the nuclear reaction which generates electricity - and why the US is safer in this than the Soviets were; see Chernobyl."
There's a nuclear reaction that generates electricity?! And I love the concept of comparing 2008 U.S technology to 1980s Soviet tech to make it look good. And WTF is all this doing in an article on "radioactivity"? Probably best not to mention Three-Mile Island. Is it really possible for one man to contain so much ignorance?
Maybe to celebrate this unique individual, people can nominate their own Ed-isms? The Lay Scientist 20:47, 10 July 2008 (EDT)
Definitely two meters. NightFlareStill doesn't have a (nonstub) RWW article. 20:51, 10 July 2008 (EDT)
So many to choose from - I really liked two meters but his recent "Toes Rights Society" edit summary was pretty funny and also when he mentioned he was going to par-tay for 4th july. Ace McWicked 21:05, 10 July 2008 (EDT)
Should we make a page similar to when we voted for CP's greatest idiot? Javascap 21:32, 10 July 2008 (EDT)
Considering how many people Ed has pissed off for more than a year, a dedicated page might be a good idea. This could take a while. XD --Sid 21:35, 10 July 2008 (EDT)
Actually, the 80s is when the last US nuke came on line. But they were built far, far, safer than Chernobyl. Chernobyl had no containment, for instance. Chernobyl makes TMI look like a flat tire. Anyway, I also cherish that Ed line. Here's how: core makes heat. Heat makes steam. Steam drives turbine. Turbine makes electrocity. (Some use hot water...) Ironically, my brother is in the neighborhood for a class reunion, and a buddy is taking him on a tour of the last US plant to go on line, the infamous Seabrook Station. ħuman 21:42, 10 July 2008 (EDT)
Actually, I think it'd be a good idea to make seperate pages for every major CP editor. When I look over the WIGO entries, with them all mixed together, I don't get as much of a sense of personality for each of the characters in this comedy of errors. - Lardashe
This is one of those situations where wiki software is not the best and we're making it do something it wasn't designed for at all. Something more like http://ihasahotdog.com/ with the tag cloud and the dogs by breed would be better for this type of thing. This could then be made so you could add the digg this and blog comments on particular bits of stupidity. --Shagie 11:55, 11 July 2008 (EDT)
## New account registration
Moratorium on new account registration is unusually long this time. Wonder what is going on. I will run out of socks in a week or two in that case. Can anyone see the new account link? --Didacus 07:57, 11 July 2008 (EDT)
CP is barely functioning right now anyway. Since I discovered I could edit last night I've been doing a few things for Bohdan and Sid, and it's a nightmare just getting a page to load. Andy on vacation and hamster out of food? ħuman 18:30, 11 July 2008 (EDT)
It's not even a pleasant experience for lurkers - when the minor fireworks were going on on Jpatt's talk page, it often took me five or more attempts to even get it to load (only got a blank page the rest of the time)! I don't even want to think about how maddening it must be for people who are trying to force edits to go through... --Sid 19:03, 11 July 2008 (EDT)
Heh, thanks for your sympathy ;) I also had to do a long-overdue fix at the Beatles article. Basically two edits (though I broke the second one up in frustration) required about ten attempted pageloads and at least one copy/paste to save my edit for another try. It took my three tries to load their article on the Eucharist. I know it's not an aspersion on their belief systems, but it's still embarrassssing.
Oh, and hey, did you know that apparently CP's orange box is a deep blood- red? Weird. ħuman 20:00, 11 July 2008 (EDT)
What? The "You've got a new message on your talk page" thingie? CЯacke® 20:27, 11 July 2008 (EDT)
Yup. I grabbed a screenshot with my back button...
ħuman 21:52, 11 July 2008 (EDT)
Considering how often this box directs people to their Last Warnings, I find that style very fitting. It at leasts puts them in the right mood. --Sid 05:31, 12 July 2008 (EDT)
## Logo
I'm sure this has been brought up before, but I just noticed it myself... Isn't the Conservapedia logo a huge violation of the flag code? I mean, in the fist place, it's being used for advertising purposes... I huge no no. (see point I here) and on top of that, they've violated point G ("The flag should never have placed upon it, nor on any part of it, nor attached to it any mark, insignia, letter, word, figure, design, picture, or drawing of any nature.") by attaching their name to it... maybe we should point this out to Andy SirChuckBA product of Affirmative Action 08:49, 11 July 2008 (EDT)
I'm no expert (in fact, I find the whole flag code sort of nit-picky and silly; I'm well within the "who-gives-a-xxxx?" camp) but is there not a distinction made between the actual flag itself and a depiction of it? The logo itself is not a physical flag. Not sure if that makes a difference, but it's a thought. DickTurpis 09:07, 11 July 2008 (EDT)
Yes. I think it is a clear breach of the code, including: The flag should never be used for advertising purposes in any manner whatsoever. We need to raise this vital issue! --Bobbing up 09:28, 11 July 2008 (EDT)
I actually agree with you Dick, I think that when you put your faith in an object rather than what the object is supposed to stand for, you simply open yourself up to your enemies for attack (see debate:Did PZ Myers Cross the Line?). My larger point here is one of total hypocrisy. The same people who scream the loudest seem to be the ones who violate the code inadvertantly. I'm not saying that the flag code should become law with serious penalties for violation, I'm just pointing out that the logo is an obvious breach. One last note to DickTurpis, the code doesn't handle only literal flags, but the representaion of the flag as well. SirChuckBA product of Affirmative Action 10:15, 11 July 2008 (EDT)
I certainly didn't mean to imply you were advocating legal standing for the flag code. Anyway, it's your final sentence I wish to address. So the flag code does cover any and all representations of the flag, even partial ones? Does that include photographs that include a flag in them? What if someone decorates a cake with a pattern representative of the flag? Looking at the code, it seems to at least implicitly refer to a physical flag, not so much its representation. DickTurpis 10:26, 11 July 2008 (EDT)
Teh code also says - "It should not be embroidered on such articles as cushions or handkerchiefs and the like, printed or otherwise impressed on paper napkins or boxes or anything that is designed for temporary use and discard." Isn't that about other representations?--BanVote for me 10:48, 11 July 2008 (EDT)
Yes, those are. However, the logo does not fit any of those descriptions. In fact, that it specifies disposable items as prohibited implies that its depiction is allowed on non-disposable items. Certainly the code doesn't say if you have a photograph of, say, a school with a flag flying in front of it, you can't put that photograph on a desk or the floor. DickTurpis 11:04, 11 July 2008 (EDT)
Ok, if the flag doesn't have to be an real flag, but can be something else (like a logo) then they fall fowl of this one: "The flag should never have placed upon it, nor on any part of it, nor attached to it any mark, insignia, letter, word, figure, design, picture, or drawing of any nature."--BanVote for me 11:15, 11 July 2008 (EDT)
Again, you're assuming that the image in the logo is a flag, and not merely a depiction of one, or that the depiction falls under the same rules as the flag itself. As I read it, that section of the code prohibits someone from, say, spray painting the word "America!" on an actual flag, not using a depiction of the flag as the background in an image. I admit I don't know much about it. Someone's brought up this point on CP's main page talk, and I'm curious to see the reply. However, it's likely the reply from that intellectual powerhouse will be an insult and a block. DickTurpis 11:26, 11 July 2008 (EDT)
Coincidentally, as I write this the ad below is a political ad depicting a blue background with white lettering on the left, and a couple red and white stripes on the right. Clearly representative of the flag. Is it a violation of the code? DickTurpis 11:29, 11 July 2008 (EDT)
No doubt one of teh smartest legal brainz of the century will have teh answer. (edit conflict) I would say those examples would be, I underestand that it is difficult to prosecute. --BanVote for me 11:33, 11 July 2008 (EDT)
(unindent) Jeez, already on the main page.... that's faster than emailing an admin. In response to the above posts, I say at the onset that I am no expert on the flag code. The problem here is that the flag code seems to jump between speaking of actual flags and representations. For example, they say that the flag should never touch the ground or item below the flag, but they also say that the flag should never be worn as an adornment. But what makes a representation a flag? If I steal a flag off a pole and sew it into a shirt, well obviously. But what if I buy some flag print material and sew that into a shirt? isn't it just as bad? This is all kind of pointless, as the flag code is simply a set of guidelines, not really a law... but it is an interesting question. SirChuckBA product of Affirmative Action 12:20, 11 July 2008 (EDT)
The legal minutiae are unimportant because the flag code is not enforceable, and is not enforced. Colbert waves the U.S. flag in the opening to his show, he's as "guilty" as Conservapedia is. Also, the code says you can't use a flag horizontally, or have it touch any surface — both things that are "violated" when a flag is draped on someone's casket.
So it gives moral guidance, that's all. If there might anything to this at all, it's that conservatives tend to be the most passionate about informally-defined morals, and about outrage over the flag in particular, so even if Colbert does it, maybe Conservapedia shouldn't. But, since that's something that's ultimately not too hard to blow off, this may not be that big of a deal. --Interiot 12:36, 11 July 2008 (EDT)
I think I said something very similar to that... but I'd take a moment to point out that Colbert isn't in violation of the code. If the flag waving was part of an advertisment, that's one thing... but he simply waves it as part of his opening. SirChuckBA product of Affirmative Action 12:43, 11 July 2008 (EDT)
(playing devil's advocate again, sigh) Advertising usually implies banner ads, 30-second television commercials, something like that (things directed at people who aren't yet customers, and separate in time and space from the main product). As far as I know, that's not what Conservapedia is doing. Conservapedia's logo and Colbert's intro are branding (directed at current customers, and integrated into the main product). (granted, making the flag part of the logo that shows up on every single page makes it much more prominent than a 5-second clip that shows up once per show) --Interiot 13:15, 11 July 2008 (EDT)
No one's arguing that there are any legal ramifications here, it's merely a question of hypocrisy. Certainly CP would be in the vanguard of pointing fingers should some liberal ever violate any aspect of the flag code. I think much of the flag code is dated anyway. I mean, horizontal flags are common, and I believe there's even a guide on how a horizontal flag should be displayed (blue field on the right side). Flags are constantly used in ads, and a bunch of the other rules are broken routinely. I certainly don't think it's a big deal if the CP logo does violate the code, though I'm curious to see their response. DickTurpis 13:06, 11 July 2008 (EDT)
"The same people who scream the loudest seem to be the ones who violate the code inadvertently" - I agree, and it's the weird part. People who aren't "flag nuts" probably don't have any, and don't care. But those who are into the flag are the ones with the T shirts, the stickers, and the raggedy dying post 9/11 ones on their car antenna. I had one once, and when it got a bit old looking I burned it, respectfully. I do have a large 48 star flag in storage, folded correctly, and I suppose there's one on my old Boy Scout uniform (but that's allowed). Also, the lag draping procedures for military funerals are specifically delineated. Technically, anything with white stars on blue and some sort of red and white stripes are not appropriate, where such a display might be desired, "bunting" is allowed - not enough ingredients to be able to make a flag. So, yes, the CP logo may not be "against the law" but it is a disrespectful use of the flag. So are the little stickers I get in the mail that are US flags with "made in the USA" printed on them. All that said, I'm glad it's not the law (as in a crime to violate), and we'd (the USA that is, not "us") be better off not getting so bent out of shape by it. See also Flag Police. ħuman 13:18, 11 July 2008 (EDT)
I wouldn't say it is hypocritical. As far as I know, nobody has stood up for the code, with the exception of Karajou who I suppose is hypocritical on a personal level. NightFlareStill doesn't have a (nonstub) RWW article. 18:37, 12 July 2008 (EDT)
## The only good Indian...
After I withdrew from the "debate," Roger took his agenda even farther: Look! So the Red Man was, it seems, an essential casualty in the "advance of civilization." I knew CP was bonkers, but I didn't realize they were actually pro-genocide. 98.206.181.143 14:37, 11 July 2008 (EDT) (Fishal)
Anything that makes America look better is welcome on CP, even if you're talking about genocide or historical whitewashing. --Sid 19:00, 11 July 2008 (EDT)
I'll be banned over there but I'm going to war over this as soon as editing opens up again (and after the rugby of course). I am not a native American Indian but I am Maori and have studied the plight of aboriginal peoples all over the world. It's not right that people should seek to revise history to serve some bogus patriotic end (and its bullshit anyway - aren't Native Indians Americans too). That Rshlafly guy is some asshole.--Damo2353 03:33, 12 July 2008 (EDT)
Best of luck... ħuman 03:44, 12 July 2008 (EDT)
Death comes to us all one day.--Damo2353 03:47, 12 July 2008 (EDT)
There is death, and then there is Death? ħuman 03:50, 12 July 2008 (EDT)
## Edmund Poor, Maths Expert
Ah geez. Just when I thought I'd found all the funny bits on CP, I happen across this gem. Matt 22:08, 11 July 2008 (EDT)
Luckily for us voyeurs Tedmund overcame his stated reluctance to write about maths and had a crack. Simply magnificent. Matt 22:15, 11 July 2008 (EDT)
Yes Ed is a maths expert and I am an expert of 18th Century Prussian Philosophy. What that man does everyday on Conservapedia is a desecration of its already poor maths articles. He is the single biggest demonstration of the information theory principle of the loss of information and the increase of entropy. $\approx$$\pi$ 00:34, 12 July 2008 (EDT)
I took a poetry class in high school, and then another in college. If your rhymes don't busta groove, understand when I bust your move. I also took "lots" of math courses, so if I don't understand your 'quations, don't be shamin' if I delete your raisins. Oh shit, double busted, gotta go block myself to Rockall for eternity, just in case. Can I get a skipper? Can I get a sailor? Can I get this pile of turds mopped up jiffy quick? Oh, this is so wrong, I might just have to eat my schtick... ħuman 01:31, 12 July 2008 (EDT)
## Site-wide activity
Is it just me, or if you look at 500 most recent changes on Conservapedia, are there startlingly few of them? As near as I can tell, it took almost 48 hours to make the 500 most recent edits, and during the 24 hours of 11 July 2008 (UTC), there were only 242 edits made. RationalWiki had 606 edits during that time. Granted, they have the "no talking, only article contributions" rule, while we have the "100 virgins will visit your grave if you mention 'goat' enough times" rule, but, still... Are the 500 Internal Server Errors and indiscriminate blocking having a really noticeable effect, or is the output of Special:Recentchanges over there somehow hiding something? --Interiot 13:45, 12 July 2008 (EDT)
It's a weekend, Saturdays can be slow there (and here); Aschlafly seems to be on vacation; they seem to have forgotten to feed the hamster(s), as well as all those things you mentioned. They've become so much a parody of themselves it isn't fun to wandalise no more. I saw one block today for someone called "Wikidd", for "unacceptable user name", come on! And they'll still toiling on ways to vet potential editors, by making it harder to register! Maybe a big sign saying STAY AWAY!!11! would work just as good? CЯacke® 14:29, 12 July 2008 (EDT)
Despite Andy's best efforts I would imagine that his army of homskolers has bought into the communistic public school idea that students should take vacation during July and August. Maybe they will come back in September to edit-for-credit... Even better, maybe Andy will carry through with his "Critical Thinking in Math" course.Antifly 14:53, 12 July 2008 (EDT)
Alexa (even with its flaws) doesn't seem to show any seasonal variation.
More statistics (UTC times):
number of edits per day at Fri Jul 11 Thu Jul 10 Wed Jul 9 Tue Jul 8 Mon Jul 7
Conservapedia 242 255 318 414 265
RationalWiki 606 582 613 723 421
Conservapedia [mainspace only] 110 121 167 235 134
Uncyclopedia [mainspace only] 924 1149 1112
I wish I had data going back a few months or years, I don't think it was this low before. --Interiot 15:16, 12 July 2008 (EDT)
Conservative used to have a load of various statistics for his interminable Google opmtimization projects floating around somewhere in his userspace. Don't know if it's still here. --AKjeldsenCum dissensie 16:05, 12 July 2008 (EDT)
The only thing I could find was User:Conservative/Conservapediarunningstats. I don't like "page views" as a metric though, since it can reflect negative attention as well as positive. (page edits certainly can as well, though not nearly to the extent that web hits can, since something like the Digg effect can make the page-views metric spike far far more than the hangers-on metric does, since page views require so little investment in time).
Maybe someone should create a site-wide "edit counter" that tracks statistics across different namespaces, and keeps track of the net addition/removal of bytes of content, on a daily basis. The net-bytes-added metric would remove the influence of rapid reverts at least. --Interiot 17:06, 12 July 2008 (EDT)
Hahahahahaha: "Is it just me, or if you look at 500 most recent changes on Conservapedia, are there startlingly few of them?" - I count exactly 500, just as always ;) ħuman 17:39, 12 July 2008 (EDT)
Ooh, he's sharp. Absolutely no activity over there at the moment - my gran could do better than them. Matt 19:26, 12 July 2008 (EDT)
Hehe. Anyway, as far as I can tell CP is completely broken. Or is it just me that can't get a page to load? ħuman 19:42, 12 July 2008 (EDT)
It would seem conservapedia is fucked. Hahaha, schlalfy, you moron Ace McWicked 20:01, 12 July 2008 (EDT)
Alexa Rankings vs. Edits Someone above said that Alexa didn't show any variation. If it's true that the edits have tailed off, which doesn't surprise me, then it implies that the majority of visitors to the site are simply there to point and stare. The Lay Scientist 19:56, 12 July 2008 (EDT)
## Pwned Conservapedia Again!
Beer+ego-fuelled rant here, but thanks to someone posting an article on I-am-bored.com, I doubled the Conservapede's traffic on Thursday :) Screw you Schlafly :P The Lay Scientist 19:59, 12 July 2008 (EDT)
## Conservapedia and the Poe Paradox?
Any new member of the CP project who's not as Conservative as them is liable to be chucked out. However, any new member who is as Conservative as them is in serious danger of being called a parodist, and chucked out. Is this the first living example of a Poe Paradox? The Lay Scientist 20:25, 12 July 2008 (EDT)
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2013-05-25 16:29:58
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http://openstudy.com/updates/502b1ac1e4b099b91b4fa113
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## anonymous 4 years ago Look at the formula for the area of a triangle. A = 1 --- 2 bh Which is a solution for h?
1. anonymous
a= 1/2bh
2. anonymous
If you want to get h all by itself, you need to make everything that is multiplied with it 1. For instance, if I want to solve for x: $z=3x$Multiply both sides by 1/3$(1/3)z=(1/3)3x$$z/3=1x$$\frac{z}{3}=x$
3. anonymous
okay can you show me the steps to solvin mine
4. anonymous
Well I'm not going to do it for you but if you compare to mine, what will make a 1/2 become a 1?
5. anonymous
ooh um subtract? i suck at math excuse me if i wrong
6. anonymous
No. What multiplied with 1/2 makes 1?
7. anonymous
idk x*(1/2)=1
8. anonymous
Ugh. no the answer was 2. 2(1/2) = 1. So in the triangle equation multiply by 2 on both sides.
9. anonymous
oh
10. anonymous
Well, do it and show me what you get. multiply by 2 on both sides of A = 1/2 b h
11. anonymous
multiply by 2 with 1/2?
12. anonymous
No. multiply by 2 on both sides of the equation.
13. anonymous
whats the equation
14. anonymous
A = bh/2
15. anonymous
2b * 2h?
16. anonymous
Oh my god dude. Sorry, this is to tough to handle. I'll just give it to you, since arithmetic is too hard. $A = bh/2$Multiply both sides by 2. $2A=bh2/2$Multiply both sides by 1/b $2A/b = bh/b$ $2A/b = h$
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2016-09-30 22:01:00
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https://mathematica.stackexchange.com/questions/linked/85139?sort=votes&pagesize=30
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2020-09-20 10:13:05
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https://solvedlib.com/n/oetuon60ro-ptsgrar-quot-ne-lincar-functiont-plottinkpoint,19101166
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# Oetuon60ro ptsGraR "ne Lincar Functiont plottinkpoint: Complete the table below for the function f(1) Uncn Ke EXACTLY TWO 0} thc
###### Question:
Oetuon 60ro pts GraR "ne Lincar Functiont plottinkpoint: Complete the table below for the function f(1) Uncn Ke EXACTLY TWO 0} thc ordered palrs cron h f(c) Inotc tngn ? polnts he Gronh ItiogkVou inconoct fls): JnornLeeae nA Wnjv: Quatlo Hpi DvNeo; Kara milnctot Cozt to totut Duemlt Cuestion acer
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##### Test charge of Sx10* experiences dawn aro electrostatic Hforce 0f 22 N uhen placed certain point in space. What are the magnitude and direction of the electric field at this point? 4x10" NJC; upward Ax10" NJc; downward 4.Ox10" N/C; upward 4,Ox1O" N/C, downward Nane of the above
test charge of Sx10* experiences dawn aro electrostatic Hforce 0f 22 N uhen placed certain point in space. What are the magnitude and direction of the electric field at this point? 4x10" NJC; upward Ax10" NJc; downward 4.Ox10" N/C; upward 4,Ox1O" N/C, downward Nane of the above...
##### YULDTIUNT If the own-price elasticity of demand for your firm's good is -1.5, and if your...
YULDTIUNT If the own-price elasticity of demand for your firm's good is -1.5, and if your price is currently set at the level that makes your customers' quantity demanded equal to the quantity you are producing, then you can increase your total revenue flow by: decreasing your output level b...
##### How do you write 3.08 x 10^8 in standard form?
How do you write 3.08 x 10^8 in standard form?...
##### 2 and blueredgraylwhite wedge notation: (black U 3 and (1point) 1 U structure the line Dcawitee 04
2 and blue red graylwhite wedge notation: (black U 3 and (1point) 1 U structure the line Dcawitee 04...
##### What beliefs contribute to patient mistrust?
What beliefs contribute to patient mistrust?...
##### Topic 2: Select a common chronic health issue that you address in your work with patients,...
Topic 2: Select a common chronic health issue that you address in your work with patients, and discuss how you would use a specific technology tool to help address it. Indicate how you would use that tool to educate patients and their families about this health issue....
##### 4. An intern performed the resistivity test according to AASHTO T358 on two sets of 4...
4. An intern performed the resistivity test according to AASHTO T358 on two sets of 4 x 8 in. cylinder specimens at 28-day of concrete age. One set of specimens (ASTM) were wet cured through the testing ages. Other set of specimens (Field) were wet cured for seven day following specimen fabrication,...
##### Identify the most appropriate method t0 measure the mass of = sample of white powder: Tare the balance. Then place weighing essel 0n the balance; Add the sample of white powder to the weighing vessel. Record the mass_ Place the weighing vessel on the balance and add the sample of white powder to the weighing vessel. Tare the balance and then record the mass.Place weighing vessel On the balance_ add the sample of white powder t0 the weighing vessel, and then record the mass_Place wcighing vessel
Identify the most appropriate method t0 measure the mass of = sample of white powder: Tare the balance. Then place weighing essel 0n the balance; Add the sample of white powder to the weighing vessel. Record the mass_ Place the weighing vessel on the balance and add the sample of white powder to the...
##### UsanomiaEoauqplj 10l41tnHl (otnnnindud druuon K I somth DEAan 0llutn =10 E0Keoauandsndand 16Bu ipLunnelt uItuuleWr clothc y Inu (ecr
usanomia Eoauqplj 10l41tn Hl (otnn nindud druuon K I somth DEAan 0l lutn =10 E0 Keoau ands nd and 16 Bu ip Lunnelt uItuuleWr clothc y Inu (ecr...
##### 6, LOG ENTRY: SOL 192 "Ihave to get to Ares 4's MAV. Even NASA accepts that: And when the nannies at NASA recommend a 3200-kilometer overland drive, you know you're in trouble: averaged 80 kilometers per sol on my way to Pathdinder. If I do that well toward Schiaparelli; the trip'Il take forty sols. Call it fifty to be safe."
6, LOG ENTRY: SOL 192 "Ihave to get to Ares 4's MAV. Even NASA accepts that: And when the nannies at NASA recommend a 3200-kilometer overland drive, you know you're in trouble: averaged 80 kilometers per sol on my way to Pathdinder. If I do that well toward Schiaparelli; the trip'...
##### *0 Te base 0f 4 Solid ig Ciele uith Tradiu s 1 Each CrcSs seetion petypendi eular 4o agiven diamcterz is a Solid _ Squnurie Fnd ~hc YolumcoflncF Ieaion bomndu by = K , 8 =0, X= 1 And X=y i5 Tevolved about thu 9 Aqus Find + Vdumc 0+ 4he TaglLknd sold . T rwzion bovmdzd by Y =eX J =0 andX-0 [5 trevilvud aboul dhe Y Os , fnd the volvne 0F th tusulhnd golid.
*0 Te base 0f 4 Solid ig Ciele uith Tradiu s 1 Each CrcSs seetion petypendi eular 4o agiven diamcterz is a Solid _ Squnurie Fnd ~hc Yolumcoflnc F Ieaion bomndu by = K , 8 =0, X= 1 And X=y i5 Tevolved about thu 9 Aqus Find + Vdumc 0+ 4he TaglLknd sold . T rwzion bovmdzd by Y =eX J =0 andX-0 [5 tre...
##### Cytokinins are found in this part ofthe plant. a. root tip d.leaf b. root system shoot tips c.stem 7. What is the significance of the human-made auxin 2,4-D? a. It causes decreased plant growth; b: It works as seed germinator; It reduces yield in crops. d. It promotes seed maturation. e: It acts as & weed killer: A vine naturally grows in and around wire fence This is an example of which type of tropism? phototropism thigmotropism ecotropism negative tropism gravitropismled A in
Cytokinins are found in this part ofthe plant. a. root tip d.leaf b. root system shoot tips c.stem 7. What is the significance of the human-made auxin 2,4-D? a. It causes decreased plant growth; b: It works as seed germinator; It reduces yield in crops. d. It promotes seed maturation. e: It acts as ...
##### The following has stereochemlstry that can classlied by elther S; R; E or Z. Which of those Is It? (Suggested time; 2 minutes)
The following has stereochemlstry that can classlied by elther S; R; E or Z. Which of those Is It? (Suggested time; 2 minutes)...
##### 31. Regarding Ne which statement about Its MO (molecular orbitals) is correct? A) One electron from Nez I* orbital was removed t0 form Nez B) Its 0*2p is half-filled There is no unpaired electron in Nez MOs D) Two unpaired eleetrons are in (Wo n* orbitals
31. Regarding Ne which statement about Its MO (molecular orbitals) is correct? A) One electron from Nez I* orbital was removed t0 form Nez B) Its 0*2p is half-filled There is no unpaired electron in Nez MOs D) Two unpaired eleetrons are in (Wo n* orbitals...
##### For what values of . is the matrix Ainvertible?
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##### Tkx bolbwing sallcrpkx shou , thc profut (n thuturl Ikx dislanar of coch Jutr Irort Uhr EI5 c curtProfit vs Distance from City Centre1 1 2Distance (km)Tl tollot IntalbkWinao 3 26l5129 "tagt dutance $20 OLnAandan 47 uikm In dnLanc$ , Iuss proli pa month 51+0 tknodHendhruicuonmolms0Kal4FSPW [7Bnarale Dabz WubshtrCaiculalc Uic € utchaon (uaLcou (Up)
Tkx bolbwing sallcrpkx shou , thc profut (n thuturl Ikx dislanar of coch Jutr Irort Uhr EI5 c curt Profit vs Distance from City Centre 1 1 2 Distance (km) Tl tollot Int albk Winao 3 26l5129 "tagt dutance $20 OLn Aandan 47 uikm In dnLanc$ , Iuss proli pa month 51+0 tknod Hendhruicuon molm s0 ...
##### A company reported that its bonds with a par value of $50,000 and a carrying value of$57,000...
Answer $(3,000)$(60,000)\$(57,000)Zero. This is an operating activityZero. This is an investing activity...
##### Consider the parametric curve x = 12 + I,y = e' _ 1, for t € RFind intersections with the x-axis and the Y-axis.Find andFind the points on the curve where the tangent is horizontal or vertical:Find values of t where the concavity is upwards.Sketch the curve_2. Find the area enclosed by the x-axis and the curve x = t3 + 1,Y = 2t - t2 (Hint: start by finding the points of intersection between the curve and the x-axis:_
Consider the parametric curve x = 12 + I,y = e' _ 1, for t € R Find intersections with the x-axis and the Y-axis. Find and Find the points on the curve where the tangent is horizontal or vertical: Find values of t where the concavity is upwards. Sketch the curve_ 2. Find the area enclosed...
##### What is an historical question
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##### Expand (1- tx)-5 using the binomial series, up to, and including, the term in x31-5x+5x2-6x3_ +1-5x+15x2-35x3+_1-5x+10x2-20x3+_1+5x+3x2+2x3+.1+5x+8x2+12x3_ +
Expand (1- tx)-5 using the binomial series, up to, and including, the term in x3 1-5x+5x2-6x3_ + 1-5x+15x2-35x3+_ 1-5x+10x2-20x3+_ 1+5x+3x2+2x3+. 1+5x+8x2+12x3_ +...
##### Hewlett-Packard Company (HP) reports the following in its 2004 10-K report. October 31 (in millions) 2005...
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##### Q3. (25 points) Solve the given set of linear algebraic equations in which (A,b) is given....
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##### Which element is most likely to form a 3- ion? Br Mg K N
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2023-02-01 15:30:53
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https://www.physicsforums.com/threads/i-need-a-proof-that-1-does-not-equal-1.724320/
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# I need a proof that -1 DOES NOT equal 1
## Main Question or Discussion Point
hey everybody, once i saw a thread here (didn't want to revive it) about an equation that proves that 1=-1, it was proved wrong ofc, but at the end, someone posted this:
" -1=(-1)^1
=(-1)^2*1/2
=[(-1)^2]^1/2
=(1)^1/2
=√1
=1 "
yet no one replied to it, can someone show me which is the "trippy" step here? the one that misuses an algebra rule? (e.g. a rule that can only be applied to positive numbers etc..."
thank you.
Office_Shredder
Staff Emeritus
Gold Member
We get this question a lot, there's actually a thread in the FAQ devoted to answering questions like it
The main point is that whne you write
$$\left( -1 \right)^{2/2} = \left( (-1)^2 \right)^{1/2}$$
you have performed an operation which is not actually valid. Taking exponents of negative numbers is tricky and you have to be more careful than when you are working with exponents of positive numbers. In general
$$x^{ab} =\left( x^{a} \right)^{b}$$
is something that can only be applied when x is a positive number.
Last edited by a moderator:
okay thanks alot! i appreciate it! ^^
We get this question a lot, there's actually a thread in the FAQ devoted to answering questions like it
The main point is that whne you write
$$\left( -1 \right)^{2/2} = \left( (-1)^2 \right)^{1/2}$$
you have performed an operation which is not actually valid. Taking exponents of negative numbers is tricky and you have to be more careful than when you are working with exponents of positive numbers. In general
$$x^{ab} =\left( x^{a} \right)^{b}$$
is something that can only be applied when x is a positive number.
hello office_shredder,
may i know why the indices rule is invalid for negative numbers? i tried for example, (-2^6) and split them up to [-2^(2*3)] = 4^3 and i still yielded 64.
where does taking exponents of negative numbers breakdown?
thanks!
Last edited by a moderator:
Mark44
Mentor
hello office_shredder,
may i know why the indices rule is invalid for negative numbers? i tried for example, (-2^6) and split them up to [-2^(2*3)] = 4^3 and i still yielded 64.
No it doesn't. The parentheses you have in (-2^6) don't do anything and might as well not be there. (-2^6) is exactly the same as -2^6 which is the same as -(2^6) or -64.
If you want to raise -2 to the 6th power, you have to write it as (-2)^6.
where does taking exponents of negative numbers breakdown?
It breaks down when the exponent is fractional and represents an even root (i.e., square root, fourth root, and so on). There is no problem when the exponent is an integer unless you happen to be taking 0 to a negative power.
No it doesn't. The parentheses you have in (-2^6) don't do anything and might as well not be there. (-2^6) is exactly the same as -2^6 which is the same as -(2^6) or -64.
If you want to raise -2 to the 6th power, you have to write it as (-2)^6.
It breaks down when the exponent is fractional and represents an even root (i.e., square root, fourth root, and so on). There is no problem when the exponent is an integer unless you happen to be taking 0 to a negative power.
yes that was sloppy of me :D
anyway, is the even root fractional exponent the only case whereby this rule breaks down ?
Mark44
Mentor
anyway, is the even root fractional exponent the only case whereby this rule breaks down ?
Yes, since odd roots (cube root, fifth root, and so on) can have negative arguments. For example, ##\sqrt[3]{-27} = -3## and ##\sqrt[5]{-32} = -2##.
If you have an expression such as (-27)2/3, you can write it either as [(-27)2]1/3 or as [(-27)1/3]2, both of which are equal to 9.
The first expression simplifies to (729)1/3 = 9, and the second expression simplifies to (-3)2, which is also 9.
It'd be cooler if someone managed to "prove" that i=√1
Yes, since odd roots (cube root, fifth root, and so on) can have negative arguments. For example, ##\sqrt[3]{-27} = -3## and ##\sqrt[5]{-32} = -2##.
If you have an expression such as (-27)2/3, you can write it either as [(-27)2]1/3 or as [(-27)1/3]2, both of which are equal to 9.
The first expression simplifies to (729)1/3 = 9, and the second expression simplifies to (-3)2, which is also 9.
that was very insightful, thank you
It'd be cooler if someone managed to "prove" that i=√1
I won't try that, but I thought of this yesterday (breaking the same rule as above):
$\sqrt{x}$
Now to factor out a -1:
$=i\sqrt{-x}$
And to factor out another -1:
$=i*i\sqrt{x}$
$=-\sqrt{x}$
$\Rightarrow \sqrt{x}=-\sqrt{x}$
:P The issue is that even functions are not 1-1, meaning they can map multiple inputs to the same output. Naturally, the inverse function would have to map backwards, but it would have to be split off to multiple values. That is why, for example, $\sqrt{9}=\{3,-3\}$
jbriggs444
Homework Helper
2019 Award
That is why, for example, $\sqrt{9}=\{3,-3\}$
It is a standard notational convention that $\sqrt{x}$ where x is a non-negative real number always refers to the positive root.
hilbert2
Gold Member
i need a proof that -1 DOES NOT equal 1
If you want a rigorous proof for this kind of statements, you need to use the axioms of real numbers: http://math.berkeley.edu/~talaska/h1b/axioms-real-numbers.pdf [Broken] .
First you add ##1## to both sides of the equation ##1=-1## and get ##1+1=0##. Next you use the order axioms to show that ##1+1>1>0##, which is a contradiction and proves that ##1## can't equal ##-1## (for real numbers ##a## and ##b##, the inequalities ##a>b## and ##a=b## can't both be true).
Last edited by a moderator:
I won't try that, but I thought of this yesterday (breaking the same rule as above):
$\sqrt{x}$
Now to factor out a -1:
$=i\sqrt{-x}$
And to factor out another -1:
$=i*i\sqrt{x}$
$=-\sqrt{x}$
$\Rightarrow \sqrt{x}=-\sqrt{x}$
:P The issue is that even functions are not 1-1, meaning they can map multiple inputs to the same output. Naturally, the inverse function would have to map backwards, but it would have to be split off to multiple values. That is why, for example, $\sqrt{9}=\{3,-3\}$
√9 is 3, √9 is not -3, and √x is a mapping from one real to precisely oneother real; a function.
√9 is 3, √9 is not -3, and √x is a mapping from one real to precisely oneother real; a function.
I know, I should have been more clear by being more confusing :P I was using √ to represent the function that, given the output of f(x)=x2, would return x. When I was working on a little project dealing with sine and cosine, I would often have a function squared on one side, where the otherside, after taking the square root, was indeed negative and the positive square root would cause the fully reduced form to fail.
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2020-08-05 08:45:21
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https://comma.eecs.qmul.ac.uk/news/paper_jaes22/
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New paper on timbre semantics. We introduce a novel methodology to study semantic associations of disembodied electronic sounds.
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2023-01-29 16:38:33
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https://physics.stackexchange.com/questions/588767/b-mesons-lifetime
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I read about a technique called b-tagging in which one can check if a b meson was produced in a collision by looking for a jet which has a secondary vertex within it. The reason is that b mesons are long lived, so that meson would travel a bit before decaying, hence the secondary vertex. Why are b meson long lived? And why can't we do this with other kind of quarks, like strange or charm? Thank you!
• Is your question about b-tagging, or a very different one: why are the lifetimes of K/D/B mesons, in seconds, $10^{-8}~/ ~ 10^{-14}~/ ~ 10^{-12}$, respectively? – Cosmas Zachos Oct 22 at 20:23
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2020-12-01 12:31:15
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https://socratic.org/questions/how-can-i-write-the-formula-for-magnesium-sulfide
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# How can I write the formula for magnesium sulfide?
Jun 23, 2014
Magnesium Sulfide has a formula of $M g S$.
Magnesium is a metal cation with a charge of $M {g}^{+ 2}$
Sulfur is a nonmetal anion with a charge of ${S}^{- 2}$
In order to bond ionically the charges must be equal and opposite.
It will take one -2 sulfide ion to balance one +2 magnesium ion forming a magnesium sulfide molecule of $M g S$.
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2019-08-21 09:28:50
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https://arblib.org/credits.html
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# Credits and references¶
Arb is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License (LGPL) as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version.
Arb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License along with Arb (see the LICENSE file in the root of the Arb source directory). If not, see http://www.gnu.org/licenses/.
Versions of Arb up to and including 2.8 were distributed under the GNU General Public License (GPL), not the LGPL. The switch to the LGPL applies retroactively; i.e. users may redistribute older versions of Arb under the LGPL if they prefer.
## Authors¶
Fredrik Johansson is the main author. The project was started in 2012 as a numerical extension of FLINT, and the initial design was heavily based on FLINT 2.0 (with particular credit to Bill Hart and Sebastian Pancratz).
The following authors have developed major new features.
• Pascal Molin - discrete Fourier transform (DFT), Dirichlet characters, Dirichlet L-functions, discrete logarithm computation
• Alex Griffing - sinc function, matrix trace, improved matrix squaring, boolean matrices, improved structured matrix exponentials, Cholesky decomposition, miscellaneous patches
• Marc Mezzarobba - fast evaluation of Legendre polynomials, work on Arb interface in Sage, bug reports, feedback
Several people have contributed patches, bug reports, or substantial feedback. This list (ordered by time of first contribution) is probably incomplete.
• Bill Hart - build system, Windows 64 support, design of FLINT
• Sebastian Pancratz - divide-and-conquer polynomial composition algorithm (taken from FLINT)
• The MPFR development team - Arb includes two-limb multiplication code taken from MPFR
• Jonathan Bober - original code for Dirichlet characters, C++ compatibility fixes
• Yuri Matiyasevich - feedback about the zeta function and root-finding code
• Abhinav Baid - dot product and norm functions
• Ondřej Čertík - bug reports, feedback
• Andrew Booker - bug reports, feedback
• Francesco Biscani - C++ compatibility fixes, feedback
• Clemens Heuberger - work on Arb interface in Sage, feedback
• Ricky Farr - convenience functions, feedback
• Marcello Seri - fix for static builds on OS X
• Tommy Hofmann - matrix transpose, comparison, other utility methods, Julia interface
• Alexander Kobel - documentation and code cleanup patches
• Hrvoje Abraham - patches for MinGW compatibility
• Julien Puydt - soname versioning support, bug reports, Debian testing
• Jeroen Demeyer - patch for major bug on PPC64
• Isuru Fernando - continuous integration setup, support for cmake and MSVC builds
• François Bissey - build system patches
• Jean-Pierre Flori - code simplifications for Gauss periods, feedback
• arbguest - preconditioned linear algebra algorithms
• Ralf Stephan - return exact real parts in acos and acosh
• Vincent Delecroix - various feedback and patches, work on Sage interface
• D.H.J Polymath - Riemann xi function
• Joel Dahne - feedback and improvements for Legendre functions
• Gianfranco Costamagna - bug reports, Debian testing
• Julian Rüth - serialization support
## Funding¶
From 2012 to July 2014, Fredrik’s work on Arb was supported by Austrian Science Fund FWF Grant Y464-N18 (Fast Computer Algebra for Special Functions). During that period, he was a PhD student (and briefly a postdoc) at RISC, Johannes Kepler University, Linz, supervised by Manuel Kauers.
From September 2014 to October 2015, Fredrik was a postdoc at INRIA Bordeaux and Institut de Mathématiques de Bordeaux, in the LFANT project-team headed by Andreas Enge. During that period, Fredrik’s work on Arb was supported by ERC Starting Grant ANTICS 278537 (Algorithmic Number Theory in Computer Science) http://cordis.europa.eu/project/rcn/101288_en.html Since October 2015, Fredrik is a CR2 researcher in the LFANT team, funded by INRIA.
## Software¶
The following software has been helpful in the development of Arb.
## Citing Arb¶
To cite Arb in a scientific paper, the following reference can be used:
F. Johansson. “Arb: efficient arbitrary-precision midpoint-radius interval arithmetic”, IEEE Transactions on Computers, 66(8):1281-1292, 2017. DOI: 10.1109/TC.2017.2690633.
In BibTeX format:
@article{Johansson2017arb,
author = {F. Johansson},
title = {Arb: efficient arbitrary-precision midpoint-radius interval arithmetic},
journal = {IEEE Transactions on Computers},
year = {2017},
volume = {66},
issue = {8},
pages = {1281--1292},
doi = {10.1109/TC.2017.2690633},
}
Alternatively, the Arb manual or website can be cited directly.
The IEEE Transactions on Computers paper supersedes the following extended abstract, which is now outdated:
F. Johansson. “Arb: a C library for ball arithmetic”, ACM Communications in Computer Algebra, 47(4):166-169, 2013.
## Bibliography¶
(In the PDF edition, this section is empty. See the bibliography listing at the end of the document.)
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S. Fillebrown, “Faster Computation of Bernoulli Numbers”, Journal of Algorithms 13 (1992) 431-445
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D. Gaspard, “Connection formulas between Coulomb wave functions” (2018), https://arxiv.org/abs/1804.10976
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X. Gourdon and P. Sebah, “Numerical evaluation of the Riemann Zeta-function” (2003), http://numbers.computation.free.fr/Constants/Miscellaneous/zetaevaluations.pdf
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E. Hansen and R. Smith, “Interval Arithmetic in Matrix Computations, Part II”, SIAM Journal of Numerical Analysis, 4(1):1-9 (1967). https://doi.org/10.1137/0704001
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G. Hanrot and P. Zimmermann, “Newton Iteration Revisited” (2004), http://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz
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J. van der Hoeven, “Ball arithmetic”, Technical Report, HAL 00432152 (2009), http://www.texmacs.org/joris/ball/ball-abs.html
Hoe2001
J. van der Hoeven. “Fast evaluation of holonomic functions near and in regular singularities”, Journal of Symbolic Computation, 31(6):717-743 (2001).
HM2017
J. van der Hoeven and B. Mourrain. “Efficient certification of numeric solutions to eigenproblems”, MACIS 2017, 81-94, (2017), https://hal.archives-ouvertes.fr/hal-01579079
JB2018
F. Johansson and I. Blagouchine. “Computing Stieltjes constants using complex integration”, preprint (2018), https://arxiv.org/abs/1804.01679
Joh2012
F. Johansson, “Efficient implementation of the Hardy-Ramanujan-Rademacher formula”, LMS Journal of Computation and Mathematics, Volume 15 (2012), 341-359, http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8710297
Joh2013
F. Johansson, “Rigorous high-precision computation of the Hurwitz zeta function and its derivatives”, Numerical Algorithms, http://arxiv.org/abs/1309.2877 http://dx.doi.org/10.1007/s11075-014-9893-1
Joh2014a
F. Johansson, Fast and rigorous computation of special functions to high precision, PhD thesis, RISC, Johannes Kepler University, Linz, 2014. http://fredrikj.net/thesis/
Joh2014b
F. Johansson, “Evaluating parametric holonomic sequences using rectangular splitting”, ISSAC 2014, 256-263. http://dx.doi.org/10.1145/2608628.2608629
Joh2014c
F. Johansson, “Efficient implementation of elementary functions in the medium-precision range”, http://arxiv.org/abs/1410.7176
Joh2015
F. Johansson, “Computing Bell numbers”, http://fredrikj.net/blog/2015/08/computing-bell-numbers/
Joh2016
F. Johansson, “Computing hypergeometric functions rigorously”, preprint (2016), https://arxiv.org/abs/1606.06977
Joh2017a
F. Johansson. “Arb: efficient arbitrary-precision midpoint-radius interval arithmetic”, IEEE Transactions on Computers, 66(8):1281-1292 (2017). https://doi.org/10.1109/TC.2017.2690633
Joh2017b
F. Johansson, “Computing the Lambert W function in arbitrary-precision complex interval arithmetic”, preprint (2017), https://arxiv.org/abs/1705.03266
Joh2018a
F. Johansson, “Numerical integration in arbitrary-precision ball arithmetic”, preprint (2018), https://arxiv.org/abs/1802.07942
Joh2018b
F. Johansson and others, “mpmath: a Python library for arbitrary-precision floating-point arithmetic (version 1.1.0)”, December 2018. http://mpmath.org/
JM2018
F. Johansson and M. Mezzarobba, “Fast and rigorous arbitrary-precision computation of Gauss-Legendre quadrature nodes and weights”, preprint (2018), https://arxiv.org/abs/1802.03948
Kar1998
E. A. Karatsuba, “Fast evaluation of the Hurwitz zeta function and Dirichlet L-series”, Problems of Information Transmission 34:4 (1998), 342-353, http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ppi&paperid=425&option_lang=eng
Kob2010
A. Kobel, “Certified Complex Numerical Root Finding”, Seminar on Computational Geometry and Geometric Computing (2010), http://www.mpi-inf.mpg.de/departments/d1/teaching/ss10/Seminar_CGGC/Slides/02_Kobel_NRS.pdf
Kri2013
A. Krishnamoorthy and D. Menon, “Matrix Inversion Using Cholesky Decomposition” Proc. of the International Conference on Signal Processing Algorithms, Architectures, Arrangements, and Applications (SPA-2013), pp. 70-72, 2013.
Leh1970
R. S. Lehman, “On the Distribution of Zeros of the Riemann Zeta-Function”, Proc. of the London Mathematical Society 20(3) (1970), 303-320, https://doi.org/10.1112/plms/s3-20.2.303
Mic2007
N. Michel, “Precise Coulomb wave functions for a wide range of complex l, eta and z”, Computer Physics Communications, Volume 176, Issue 3, (2007), 232-249, https://doi.org/10.1016/j.cpc.2006.10.004
Miy2010
S. Miyajima, “Fast enclosure for all eigenvalues in generalized eigenvalue problems”, Journal of Computational and Applied Mathematics, 233 (2010), 2994-3004, https://dx.doi.org/10.1016/j.cam.2009.11.048
MPFR2012
The MPFR team, “MPFR Algorithms” (2012), http://www.mpfr.org/algo.html
NIST2012
National Institute of Standards and Technology, Digital Library of Mathematical Functions (2012), http://dlmf.nist.gov/
Olv1997
F. Olver, Asymptotics and special functions, AKP Classics, AK Peters Ltd., Wellesley, MA, 1997. Reprint of the 1974 original.
H. Rademacher, Topics in analytic number theory, Springer, 1973.
Pet1999
K. Petras, “On the computation of the Gauss-Legendre quadrature formula with a given precision”, Journal of Computational and Applied Mathematics 112 (1999), 253-267
Pla2011
D. J. Platt, “Computing degree 1 L-functions rigorously”, Ph.D. Thesis, University of Bristol (2011), https://people.maths.bris.ac.uk/~madjp/thesis5.pdf
Pla2017
D. J. Platt, “Isolating some non-trivial zeros of zeta”, Mathematics of Computation 86 (2017), 2449-2467, https://doi.org/10.1090/mcom/3198
PP2010
K. H. Pilehrood and T. H. Pilehrood. “Series acceleration formulas for beta values”, Discrete Mathematics and Theoretical Computer Science, DMTCS, 12 (2) (2010), 223-236, https://hal.inria.fr/hal-00990465/
PS1973
M. S. Paterson and L. J. Stockmeyer, “On the number of nonscalar multiplications necessary to evaluate polynomials”, SIAM J. Comput (1973)
PS1991
G. Pittaluga and L. Sacripante, “Inequalities for the zeros of the Airy functions”, SIAM J. Math. Anal. 22:1 (1991), 260-267.
Rum2010
S. M. Rump, “Verification methods: Rigorous results using floating-point arithmetic”, Acta Numerica 19 (2010), 287-449.
Smi2001
D. M. Smith, “Algorithm: Fortran 90 Software for Floating-Point Multiple Precision Arithmetic, Gamma and Related Functions”, Transactions on Mathematical Software 27 (2001) 377-387, http://myweb.lmu.edu/dmsmith/toms2001.pdf
Tak2000
D. Takahashi, “A fast algorithm for computing large Fibonacci numbers”, Information Processing Letters 75 (2000) 243-246, http://www.ii.uni.wroc.pl/~lorys/IPL/article75-6-1.pdf
Tre2008
L. N. Trefethen, “Is Gauss Quadrature Better than Clenshaw-Curtis?”, SIAM Review, 50:1 (2008), 67-87, https://doi.org/10.1137/060659831
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T. S. Trudgian, “Improvements to Turing’s method”, Mathematics of Computation 80 (2011), 2259-2279, https://doi.org/10.1090/S0025-5718-2011-02470-1
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T. S. Trudgian, “An improved upper bound for the argument of the Riemann zeta-function on the critical line II”, Journal of Number Theory 134 (2014), 280-292, https://doi.org/10.1016/j.jnt.2013.07.017
Tur1953
A. M. Turing, “Some Calculations of the Riemann Zeta-Function”, Proc. of the London Mathematical Society 3(3) (1953), 99-117, https://doi.org/10.1112/plms/s3-3.1.99
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2021-01-23 08:20:19
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http://mathhelpforum.com/geometry/187307-proof-semicircle-three-tangents.html
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# Math Help - Proof: A Semicircle and Three Tangents
1. ## Proof: A Semicircle and Three Tangents
Hypothesis: AB is the diameter, the line a passes through A and is tangent to the semicircle, the line b passes through B and is tangent to the semicircle, the line EF passes through P and is tangent to the semicircle. P is any point of the semicircle and E and F are the intersections of the line passing through P and tangent to the semicircle with line a and b.
Thesis: PE * PF = (1/4) * AB^2 .
I hope I explained well the problem, otherwise I'll write it again! Thank you!
2. ## Re: Proof: A Semicircle and Three Tangents
Originally Posted by goby
Hypothesis: AB is the diameter, the line a passes through A and is tangent to the semicircle, the line b passes through B and is tangent to the semicircle, the line EF passes through P and is tangent to the semicircle. P is any point of the semicircle and E and F are the intersections of the line passing through P and tangent to the semicircle with line a and b.
Thesis: PE * PF = (1/4) * AB^2 .
I hope I explained well the problem, otherwise I'll write it again! Thank you!
Let O be the centre of the semicircle.
Join OP, OE and OF.
Using congruent triangles, it is easy to prove that $\angle EOA=\angle EOP$ and $\angle FOB=\angle FOP$.
So, $\angle EOF=\angle EOP+\angle FOP=\frac{1}{2}(\angle AOP+\angle BOP)=\frac{1}{2}*180^o=90^o$.
Note that $OP\perp EF$.
So, $PE*PF=OP^2$ (This is a well-known theorem that can be proved using similar triangles.)
$PE*PF=\left(\frac{1}{2}AB\right)^2=\frac{1}{4}AB^2$
QED
3. ## Re: Proof: A Semicircle and Three Tangents
It wasn't so easy! However I've understood it now, thank you. You meant Euclid's Second Theorem, din't you?
4. ## Re: Proof: A Semicircle and Three Tangents
Originally Posted by goby
It wasn't so easy! However I've understood it now, thank you.
You're welcome!
You meant Euclid's Second Theorem, din't you?
No. (Euclid's second theorem states that the number of primes is infinite. - Wolfram MathWorld)
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2016-07-23 22:32:30
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https://tug.org/pipermail/xetex/2008-December/011592.html
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# [XeTeX] Conflicts between AMS document classes and polyglossia
Ross Moore ross at ics.mq.edu.au
Tue Dec 30 00:39:12 CET 2008
Hi David,
On 30/12/2008, at 5:17 AM, David M. Jones wrote:
>> However, there is a piece of coding that AMS classes use
>> which is not safe against this strategy.
>>
>> lines 622--626 of amsart.cls are as follows:
>>
>> \toks4{\def\\{ \ignorespaces}}% defend against questionable usage
>> \edef\@tempa{%
>> \@nx\markboth{\the\toks4
>> \@nx\MakeUppercase{\the\toks@}}{\the\@temptokena}}%
>> \@tempa
>
> Correct. The argument to \markboth here is a token list that is not
> invariant under repeated applications of protected edefs.
>
>> These are more robustly written as:
>>
>> % \toks4{\def\\{ \ignorespaces}}% defend against questionable usage
>> \edef\@tempa{%
>> \@nx\markboth{\@nx\protect at backslash
>> \@nx\MakeUppercase{\the\toks@}}{\the\@temptokena}}%
>> \@tempa
>>
>> using a new internal macro \protect at backslash defined as:
>>
>> %% RRM --- added 2008/12/26
>> \def\protect at backslash{%
>> \expandafter\def\noexpand\\{ \ignorespaces}}
>
> But neither is this. This will survives a single round of expansion
> (which is admittedly good enough for the case at hand), but not a
> second.
Sure.
It's not my job to rewrite other people's packages.
Instead I try to locate places where existing coding is causing
a difficulty, and find a work-around that involves minimal changes,
yet fits with the style of programming that is being used at that
place in the package or class file. (This way even a novice can
make a temporary fix to a local copy of the relevant file.)
Having drawn attention to the location and nature of the problem,
it is then up to the package owner (who is no doubt more aware
of the intention and all the ins-and-outs of the existing coding,
and how it can be safely modified consistently with other packages
and class files) to sort out what is the *best* fix.
This may well involve more extensive changes ...
> A safer implementation is
>
> \DeclareRobustCommand\redefine at backslash{\def\\{ \ignorespaces}}
>
> \protected at edef\@tempa{%
> \@nx\markboth{%
> \redefine at backslash
> \MakeUppercase{\the\toks@}}{\the\@temptokena}%
> }%
... such as occur here.
>
> which takes advantage of LaTeX 2e's apparatus for dealing with these
> issues.
So can we expect to see these changes within an imminent update
to the AMS class files: amsart.cls , amsproc.cls and any others?
>
> David M. Jones
> Publications Technical Specialist
> American Mathematical Society
> http://www.ams.org/
All the best for the New Year,
Ross
------------------------------------------------------------------------
Ross Moore ross at maths.mq.edu.au
Mathematics Department office: E7A-419
Macquarie University tel: +61 (0)2 9850 8955
Sydney, Australia 2109 fax: +61 (0)2 9850 8114
------------------------------------------------------------------------
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2021-01-22 17:05:19
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https://blender.stackexchange.com/questions/15239/can-i-avoid-an-undo-when-operator-is-called-due-to-a-property-change
|
# Can I avoid an undo when operator is called due to a property change?
I am writing an add-on that creates a mesh with several randomly generated aspects. The mesh is generated from default property values when the operator is initially called. These properties are added to the tools panel for the user to modify.
In some cases I want to modify the already generated mesh both to avoid wasted recalculation and to retain the majority of randomly generated features. Ie - it might look the way I want it except for some minor aspect I can change without effecting the overall appearance.
To do this, my property update functions set a flag to indicate whether the property change necessitates a complete regeneration of the mesh or if the existing mesh can be tweaked instead.
I am seeing that there is no object to tweak when the operator's execute function is called after a property change. It appears that an undo is performed before the operator is called again.
Is there a way to avoid the undo operation? Or a way to store the mesh and access it when the operator is called again?
As an example:
# ------------------------------------------------------------
# Operator for adding a Thing
# ------------------------------------------------------------
...
# set a flag indicating a complete regenerate is required
def update_regenerate(self, context):
self.do_regenerate = True
# set a flag to indicating a simpler update can be done
def update_modify(self, context):
self.do_modify = True
# flags used to determine if Thing should be regenerated or modified
do_regenerate = BoolProperty(name='Must regenerate object', default=False, options={'HIDDEN'})
do_modify = BoolProperty(name='Can modify object', default=False, options={'HIDDEN'})
...
def execute(self, context):
self.do_regenerate = False
self.do_modify = False
return {'FINISHED'}
@classmethod
def poll(cls, context):
return context.mode == 'OBJECT'
def invoke(self, context, event):
return self.execute(context)
def draw(self, context):
...
# ------------------------------------------------------------
# Creates a random Thing
# ------------------------------------------------------------
if props.do_modify:
# At this point there is no object to modify!!
bpy.ops.object.mode_set(mode='EDIT', toggle=False)
# only resize because the user liked the randomly
# generated object but wants to resize the base
# without changing the other apsects of it
size_base(props)
else:
create_base(props) # creates a base with a given size
create_spokes(props) # creates randomly oriented spokes
bpy.ops.object.mode_set(mode='OBJECT', toggle=False)
• Blender's redo panel will revert all changes every time and re-run the operation, there's no way around that. The behavior might be different / more controllable when writing a modifier in C, I'm not sure. – CodeManX Aug 24 '14 at 1:19
To prevent calling the operator each time an option changes you could move the properties for the options to outside of the operator, maybe to an AddonPreferences instance? This can then be accessed by the operator and a panel or directly in the User Preferences when enabling the addon. See Cloud Generator addon for an example of properties added to bpy.types.Scene and used by both panel and operator.
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2020-05-31 07:20:20
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https://remap-cisreg.github.io/ReMapEnrich/vignettes/advanced_use.html
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# Abstract
In this vignette, we will be discovering more advanced functions and possibilities of this package. You may want to read the basics functions first in order to understand the principles of enrhciment analysis.
# Loading a catalogue
You have a choice of either loading the ReMap catalogue, or loading your own catalogue of peaks/regions.
## Download the ReMap catalogue
There is 4 different versions of the ReMap catalogue. The current version of ReMap 2018 [1] and the previous ReMap 2015 release [2]. Both are declined in hg19 or hg38 assemblies. This function will download the files locally.
# Create a local directory for the tutorial
demo.dir <- "~/ReMapEnrich_demo"
dir.create(demo.dir, showWarnings = FALSE, recursive = TRUE)
# Use the function DowloadRemapCatalog
remapCatalog2018hg38 <- downloadRemapCatalog(demo.dir)
# Or download other versions
remapCatalog2015hg19 <- downloadRemapCatalog(demo.dir, version = "2015", assembly = "hg19")
The genomic ranges object remapCatalog now contains the full ReMap 2015 catalogue[2]. A file has also been downloaded at “~/ReMapEnrich_demo/remap1_hg38_nrPeaks.bed” (0.544 GB when not compressed).
## Load the ReMap catalogue
# Load the ReMap catalogue and convert it to Genomic Ranges
remapCatalog <- bedToGranges(remapCatalog2018hg38)
## Loading a custom catalogue
Another funtionnality of this package is the ability to load a custom catalogue instead of ReMap. This is quite simple starting from a BED file as your catalogue. In this example, we load a custom catalogue present in extdata/, this is just a BED file for chr22 as dummy example.
# Load the ReMapEnrich library
library(ReMapEnrich)
# Load the example catalogue as a BED file.
catalogFile <- system.file("extdata",
"ReMap_nrPeaks_public_chr22.bed",
package = "ReMapEnrich")
catalog <- bedToGranges(catalogFile)
# Download ENCODE peaks
We have added a fucntionnality to direclty fetch ENCODE peaks. With ReMapEnrich it is possible to download genomic regions of any ENCODE experiments using an ENCODE ID for a bed file (eg. ENCFF001VCU). In this example we download a BED file for the H3K27 histone mark in MCF-7 cell line.
# Downloading the ENCFF001VCU regions.
ENCFF001VCU <- bedToGranges(downloadEncodePeaks("ENCFF001VCU", demo.dir))
The ENCFF001VCU variable now contains all the regions of the given experiment a GRange object. It is possible to use it in future enrichment analysis.
# Compute enrichment
The basic way to compute an enrichment is to run with default parameters. - no universe - single core - Default shuffling - defautl overlaps
enrichment.df <- enrichment(ENCFF001VCU, remapCatalog)
head(enrichment.df)
# Using a universe
Enrichment analysis often surestimate the p-values. Using a universe is setting constraints on the shuffling function, resulting in more reasonable probabilities. The universe is simply another set of genomic regions, in a GeomicRanges format, that will prevent shuffles to take place outside of it. Using a universe will reduce the analysis to certain portions of the genome. However the ReMapEnrich package can also work without a universe, in this case it will use the entire genome.
## Choosing an universe
One of the most diffcult task in using a universe is choosing one that is relevant for you data. No methods are perfect, once you understand what is the purpose of using a universe, it is be up to you to specify which one to use in order to accomplish a specific analysis. But in general, the universe could be understood as the set of regions that could have been used as query.
## Enrichment using a universe
# Download a universe.
universe <- bedToGranges(downloadEncodePeaks("ENCFF718QVA", demo.dir))
# Convert ReMap to GRanges
remapCatalog <- bedToGranges(remapCatalog2018hg38)
# Create the enrichment with the universe.
enrichment.df <- enrichment(ENCFF001VCU, remapCatalog, universe, nCores=2)
The data frame enrichment.df now contains the enrichment informations between ENCFF001VCU and the ReMap catalogue given ENCFF718QVA as a universe.
For more permissive universe you can use the parameter included as the fraction of shuffled regions that must be at least contained in universe regions (1 by default). For example included = 0.1 would allow at least 10% of shuffled regions to be within the universe.
# Create the enrichment with a less restrictive universe.
enrichment.df <- enrichment(ENCFF001VCU, remapCatalog, universe, included = 0.1, nCores=2)
# 90% of the shuffled regions can now be outside of the universe regions.
Shuffling regions occurs in the whole genome but it is possible to restrict shuffles to occur only in the chromosome they originate with the parameter byChrom (FALSE by default).
# Create the enrichment with a less restrictive universe.
enrichment.df <- enrichment(ENCFF001VCU, remapCatalog, universe, included = 0.1, byChrom = TRUE, nCores=2)
# 90% of the shuffled regions can now be outside of the universe regions.
# The shuffled regions are still in the same chromosome where they came from.
# Shuffling and random generation
As the most basic enrichment function uses random generations in order to estimate the p-values, shuffling functions and random generations are available in this package. In this two functions, it is possible to use all the parameters already mentioned (universe, included, byChrom).
## Shuffling
Shuffling regions consists in randomly reordering the positions of the query regions within a genome.
# Shuffling ENCFF001VCU
shuffledENCFF001VCU <- shuffle(ENCFF001VCU, universe = universe, byChrom = TRUE)
## Random generations
It is sometimes useful to generate purely random regions, for negatives controls for example.
# Generate 100 random regions with a size of 1000 bases pair.
randomRegions <- genRegions(100, 1000)
# Other assemblies
For now, only the hg38 assembly has been used by default. It is important to know how to make enrichment analysis with other genomes. All functions in the ReMapEnrich package that uses shuffles or random regions generation must ackowledge the sizes of the chromosomes of the species in consideration.
It is possible to load the chromosomes sizes of hg38 in one function.
hg38ChromSizes <- loadChromSizes("hg38")
But you may want to download other assemblies from the UCSC database.
# Example with rn5
rn5ChromSizes <- downloadUcscChromSizes("rn5")
# Creation of random regions in the rattus norvegicus genome.
randomRegions <- genRegions(100, 1000, rn5ChromSizes)
# Shuffling of regions in the rattus norvegicus genome.
shuffledRegions <- shuffle(randomRegions, rn5ChromSizes)
# Species relevant to current and future ReMap releases
hg38ChromSizes <- downloadUcscChromSizes("hg38")
hg19ChromSizes <- downloadUcscChromSizes("hg19")
mm10ChromSizes <- downloadUcscChromSizes("mm10")
dm6ChromSizes <- downloadUcscChromSizes("dm6")
# Maybe one day
ce11ChromSizes <- downloadUcscChromSizes("ce11")
rn5ChromSizes <- downloadUcscChromSizes("rn5")
# References
1. Chèneby J, Gheorghe M, Artufel M, Mathelier A, Ballester B. ReMap 2018: an updated atlas of regulatory regions from an integrative analysis of DNA-binding ChIP-seq experiments. Nucleic acids research. 2018;46:D267–75.
2. Griffon A, Barbier Q, Dalino J, Helden J van, Spicuglia S, Ballester B. Integrative analysis of public ChIP-seq experiments reveals a complex multi-cell regulatory landscape. Nucleic acids research. 2015;43:e27–7.
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2020-07-06 23:05:06
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https://brilliant.org/discussions/thread/problem-regarding-hcf/
|
# Problem Regarding H.C.F.
Prove that $$\gcd(a+b, a-b) \geq \gcd(a,b)$$, where $$a$$ and $$b$$ are two integers.
Probable direction: Lowest positive value of the equation {ax + by} will give the h.c.f of a & b.
While the lowest positive value { (a+b)x+(a-b)y } will give the h.c.f. of (a+b) & (a-b).
[ x and y are integer variables]
So, the proof comes down to : [the lowest positive value of { (a+b)x + (a-b)y } ] >= [ lowest positive value of { ax + by } ] .
Note by D K
2 years ago
MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2
paragraph 1
paragraph 2
[example link](https://brilliant.org)example link
> This is a quote
This is a quote
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$
Sort by:
Great! Do you now see why the last step is obvious?
Hint: Do not let your notation do double duty. It would be helpful to use $$x_1, y_1$$ in one of them, and $$x_2, y_2$$ in the other. This way, you can ask about the relationship of these terms.
Staff - 1 year, 12 months ago
Yes, it's solved :)
- 1 year, 12 months ago
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2018-07-16 08:42:09
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http://tex.stackexchange.com/questions/52920/is-there-a-package-with-standard-theorem-environments-and-math-functions
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# Is there a package with standard theorem environments and math functions
I would like a package that defines nice things by default like:
1. Theorem environments like definition, property, example etc.
2. Standard includes like subfloats, the amsmath family
3. Reference functions like `\sectionref`, `\algorithmref` etc.
4. Math functions like `\argmin`, `\trace`, etc.
Essentially, I would like all the settings of the JMLR class, but be able to use it in a separate class (something for a thesis). I have tried modifying the secondary class (`thesis.cls`) to use JMLR as the base (`\LoadClassWithOptions`), however it complains because I need to use chapters.
-
if you like the ones in the jmlr class, you can just create your own package by copying into it the `\theoremstyle` and `\newtheorem` definitions from jmlr, call the package `mydefs.sty`, and then `\usepackage{mydefs}`.
@arunchaganty -- if you have any need to define commands that involve `@` signs, the mechanism for `\usepackage` invokes `\makeatletter` and `\makeatother` automatically. of course, if you then have to incorporate your definitions into your source file, you'd have to include those commands explicitly. – barbara beeton Apr 23 '12 at 12:56
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2016-04-29 16:12:22
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https://www.physicsforums.com/threads/excitons.95255/
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Excitons !
1. Oct 17, 2005
Gokul43201
Staff Emeritus
Anyone have any good references or insights on excitons; excitons in bilayer semiconductors; excitons in high magnetic fields (fractional quantum Hall regime) or Bose condensation of excitons ?
I'm going through the literature but want to make sure there isn't something useful out there that I've missed.
2. Oct 17, 2005
ZapperZ
Staff Emeritus
Just make sure you don't miss this:
J.P. Eisenstein, Science, v.305, p.950 (2004)
Zz.
3. Oct 17, 2005
Gokul43201
Staff Emeritus
That and his Nature article with MacDonald ! That's where I started from. Thanks, Zz !
Any personal insights ?
Edit : Just found a few threads here where you and others have said something about excitons. Will look through them.
Last edited: Oct 17, 2005
4. Oct 17, 2005
ZapperZ
Staff Emeritus
Unfortunately, no. I didn't work in this area, although I did know people who did. So what I understand about it was simply based on what I've read and my conservations with these people. So it's all rather superficial, I'm afraid.
Why are you looking at excitons? Planning on going into nanoscience, are we? :)
Zz.
5. Oct 17, 2005
Gokul43201
Staff Emeritus
Ha ha ! That would rake in the dollars, wouldn't it ?
No, this is my exam topic. I'm allowed to use any means available (to a person working in the field) to gather info.
PS : My advisor was Eisenstein's postdoc at Penn State. And our lab works on essentially the same kind of bilayer samples that Eisenstein does.
6. Oct 17, 2005
ZapperZ
Staff Emeritus
Ooooh..... PEDIGREE! PEDIGREE!!
:)
Zz.
7. Oct 17, 2005
Gokul43201
Staff Emeritus
Wait...wait. My advisor was Richardson's (of He-3 fame) grad student at Cornell !
8. Oct 17, 2005
ZapperZ
Staff Emeritus
I HATE YOU!
:)
Zz.
9. Oct 17, 2005
Gokul43201
Staff Emeritus
Now that I'm done showing off my boss' bosses, let's get back to them excitons... <sigh>
10. Oct 25, 2005
Mk
So Zz doesn't have any boss' bosses?
11. Oct 25, 2005
ZapperZ
Staff Emeritus
Says who?
My "boss' bosses" were Ed Wolf (who wrote THE definitive book on tunneling in solids) and Bill Spicer (who almost singled-handedly developed angle-resolved photoemisson spectroscopy).
Zz.
12. Oct 25, 2005
Mk
I like potato chips.
13. Oct 25, 2005
Gokul43201
Staff Emeritus
I remember that Spicer died recently. I thought he founded SLAC or something...didn't know he developed ARPES. Speaking of ARPES, Zz, does the name Randeria ring a bell ?
Last edited: Oct 25, 2005
14. Oct 25, 2005
ZapperZ
Staff Emeritus
It sure does. Mohit Randeria collaborates a lot with Mike Norman here at Argonne. He used to spend several months at a time here, and then he went back to Mumbai. I believe he is now there where you are, Gokul? Didn't he also being Nandini with him?
Zz.
15. Oct 25, 2005
Gokul43201
Staff Emeritus
Yes, they're both here. I've sat in some of Randeria's lectures. He's an excellent teacher !
16. Oct 25, 2005
ZapperZ
Staff Emeritus
Nandini, btw, was a student of Phil Anderson at Princeton. So she has quite a pedigree there herself.
Zz.
17. Oct 25, 2005
Gokul43201
Staff Emeritus
I didn't know this - but it sure explains her interest in disordered systems. She was Ashcroft's grad student, at Cornell.
18. Oct 25, 2005
nbo10
The department here traced the pedigree of the faculty. I'm amazed at how close knit the community is. My former advisor traces back to Born. And then some how it has dwindled down to me. :rofl:
19. Oct 25, 2005
Dr Transport
Two guys who did some fine work in excitons/biexcitons in quantum confined structures are Madarasz and Szmulowicz. Some of their work waas extended by a guy named Balandin to magnetic fields applied to quantum confined structures. The original work was funded by the US govt, they were so sucessful that the contracts were cancelled after 2 years because the experimentalist were that far behind in verifying their predictions.
The book chapter that they wrote is in
http://search.barnesandnoble.com/booksearch/isbnInquiry.asp?userid=zA7kBp4CqI&isbn=0471349682&itm=16
20. Oct 26, 2005
Gokul43201
Staff Emeritus
Thanks Doc !
I haven't come across much of their work so far...which it appears, deals with coherent, laser-induced excitons and bi-excitons in GaAs/AlGaAs quantum wires.
I can see why it might be hard to measure anything meaningful in such systems. For one thing, I would imagine the exciton lifetimes are in the few nanoseconds at most. Almost the only way to ensure even a hundred nanosecond lifetime is with bilayer (double quantum well) structures, where the electron and hole are spatially separated, and there a large tunneling resistance. Secondly, only recently have we achieved sufficiently high quality heterostructure fabrication which prevents pinning at low temperatures.
Further, only if you have long lifetimes can you hope for hot excitons to cool and possibly Bose condense...and that's where the fun is !
21. Oct 26, 2005
Dr Transport
Much of their work centered on calculating $$\chi^{(3)}$$ in exciton/biexciton quantum confined systems like layers and wave guides. Madarasz was my advisor and Szmulowicz was on my committee. My topic was in electronic transport in anisotropic semiconductors, nothing as sexy as quantum confined structures which gives you an idea of the breadth of their knowledge and work.
Last edited: Oct 26, 2005
22. Oct 31, 2005
Gokul43201
Staff Emeritus
This is related : Is there a good way to understand the Kosterlitz-Thouless (Superfluid) Transition in 2D, without going through Renormalization Group? If anyone has a review that gives a physical picture without going through all the highly non-trivial math that makes up RG, I'd be most pleased to hear about it.
<PS : I do not have the time to learn RG right now...nor likely, the time to understand all 26 pages of the original 1972 paper by K & T >
Last edited: Oct 31, 2005
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2018-06-22 04:25:07
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https://chemistry.stackexchange.com/questions/85062/thermochemistry-calculating-t-given-q
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# Thermochemistry, calculating T given Q
I have the reaction $\ce{2COCl2(g) -> CCl4(l) + CO2(g)}$
And I want to calculate $T$ (temperature) when $Q = 10^{-4}$ at equilibrium.
I tried simply putting $$T = -\frac{\Delta G^{0}}{\Delta S^{0}-R \ln Q}$$
Anyway, since $\Delta G^{0}$ for the reaction ($\pu{42000J/mol}$) is the value at standard condition (25 degrees celsius) I use that $\Delta G = \Delta H^{0} - T\times\Delta S^{0} + RT\ln Q$ where $\Delta G = 0$ since we're at equilibrium.
From this I obtain that $$T = \frac{\Delta H^{0}}{\Delta S^{0}-R\ln Q}$$
But which $\Delta H^{0}$ and $\Delta S^{0}$ values do I use here? I can calculate them from the standard conditions at 25 degrees celsius using SI, but that wouldnt be correct, would it? I'm rather confused by this task, which seems simple at first sight. Hope someone can clarify.
(The answer should be $\pu{476K}$)
• Are you familiar with the Van't Hoff equation? – Chet Miller Oct 31 '17 at 11:37
• No, not yet. Is this required here? – novo Oct 31 '17 at 11:39
• Your $\LaTeX$ skills are fine, as far as $\Delta{}G^0$ goes. There was another thing that needed correction, but it is specific to this site. – Ivan Neretin Oct 31 '17 at 12:05
• Look it up online and see. – Chet Miller Oct 31 '17 at 12:39
• This question was taken from an earlier test I'm practising on, van't Hoff shouldn't be required. Is there a way around it without using van't Hoff? – novo Oct 31 '17 at 14:10
We know that, at temperature T, $$\Delta G^0(T)=\Delta H^0(T)-T\Delta S^0(T)$$ From Hess's Law, we also know that $$\Delta H^0(T)=\Delta H^0(298)+???$$ and $$\Delta S^0(T)=\Delta S^0(298)+???$$
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2021-01-25 02:34:45
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https://electronics.stackexchange.com/questions/413902/high-voltage-capacitor-lead-clearance
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# High Voltage Capacitor Lead Clearance
I am designing a high voltage board, 10,000 VDC. I wish to use a suitably rated capacitor such as the DHR4E4A102K2BB. When I have been studying the IPC-2221 and IEC 61010 standards the conductor clearance should be in the order of 0.00305 mm/volt, therefore you would think that for a 10kV rated capacitor the lead spacing should be at least 30.5mm.
However, when looking at many datasheets they are around 9.5mm +/-2mm.
In my application one lead needs to be at 10kV and the other at 0V, so I would expect arcing/flash over to occur.
What am I missing?
EDIT TO SHOW PCB
Here is what I have so far with the PCB which shows the capacitor and slots (yellow line is board edge/routing)
EDIT TO SHOW SCHEMATIC
Schematic added to show that is I added DC grading resistors in parallel to the capacitor then it would create a potential divider network and my outputs would be less than 10kV. Hence the discussion about headroom. I have 10kV coming in and I need 10kV (or there abouts) going out.
Most of these components is unsuitable for continuous high voltage. On top of what @Spehro said, creepage will be impossible without immersing it in transformer oil and I would not be allowed to put more than about 3 kV across that 7.5 mm lead spacing, but that could be slightly more in your case depending on company policy, altitude range for the product, humidity and pollution degree of the environment. (pollution degree would normally just relate to creepage)
What you normally end up with when using components intended for consumer electronics or light industrial use is to derate them and end up with a series-parallel array of them. Be aware of capacitor tolerance and calculate your maximum misdistribution and make sure you have rating accordingly.
Source: high voltage design engineer for the past five+ years.
EDIT: Here is a schematic and transient simulation for you. I don't know your load nor why you have 5 Mohm output resistance, so there are several assumptions here. This is absolute worst case scenario for +-10 % resistors (47 Mohm) and +-20 % capacitors (1 nF). If you are hand-building it, you can probably hand-tune each value to match much better than that.
• So your suggestion is to place multiple lower rated capacitors in series, thus increasing the clearance and creepage between the HV on the first cap lead and the 0V on the final cap lead? Nice idea. I did not follow this part Be aware of capacitor tolerance and calculate your maximum misdistribution and make sure you have eating accordingly. – tomdertech Dec 27 '18 at 23:20
• Yes, that’s correct. If you connect two in series, you are NOT guaranteed to have half the voltage across each. If the capacitors are +-20 % tolerance, you must assume +20 % one one and -20 % on the other, and the one with the lower capacitance will see significantly higher voltage for any AC signal. For DC, it’s only the leakage which determines the distribution, and it’s almost never guaranteed. You must add grading resistors in parallel, but they will be subject to the same mis-distribution. High voltage is not easy and nothing will work your way by itself! – winny Dec 29 '18 at 10:26
• Excellent advice. Would parallel grading resistors not act as a potential divider? I am designing a simple RC network, so have a 5M ohm in series with the capacitor which connects to ground. The grading resistors would form a divider, no? – tomdertech Dec 29 '18 at 12:25
• That’s the purpose. For DC, your resistors sets the division ratio. For AC, your capacitors sets your division ratio. Please do calculate your worst case voltage stress for both DC and AC with maximum tolerance. – winny Dec 29 '18 at 12:29
• Sure. Any help however timely is much appreciated :-) – tomdertech Jan 4 at 10:27
Breakdown voltage of air is about 3kV/mm so it won't typically break down. The requirement for creepage for good design is more than that, so you can route an unplated slot between the pins. That takes care of the PCB design.
You still have the creepage distance over the capacitor surface to contend with- it's probably not adequate unless you coat the board or pot the circuit.
By the way, that Murata part has a final order date of 'September 2019, meaning it is marked to be permanently discontinued.
• I have removed most of the FR4 between the pads. So are you saying that the capacitor voltage is not rated for its own creepage distance? Where would I coat the board? – tomdertech Dec 27 '18 at 23:17
• The slot can be long. You could put conformal coating on the board + capacitor (after assembly, obviously). – Spehro Pefhany Dec 27 '18 at 23:18
• I have edited my original post to show the PCB I currently have with the slots. – tomdertech Dec 27 '18 at 23:26
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2019-12-07 21:11:33
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https://brilliant.org/problems/sumset-of-cantor-set-2/
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# Sumset Of Cantor Set
Probability Level 3
Let $\mathcal{C} + \mathcal{C}$ denote the sumset of the Cantor set $\mathcal{C}$. That is, $\mathcal{C} + \mathcal{C} = \{x+y \, : \, x, y \in \mathcal{C}\}.$ Which of the following statements is true about $\mathcal{C} + \mathcal{C}$?
×
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2020-06-01 13:48:35
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https://en.m.wikibooks.org/wiki/Problems_In_Highschool_Chemistry/Printable_version
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# Problems In Highschool Chemistry/Printable version
Problems In Highschool Chemistry
The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/Problems_In_Highschool_Chemistry
Permission is granted to copy, distribute, and/or modify this document under the terms of the Creative Commons Attribution-ShareAlike 3.0 License.
# PhChem/thermo1/table
Fill in the missing values in the table. The table contains 63 blanks, so we expect a student to solve the table in 90 minutes.
Note: -
1.) Each of the processes are carried out on 1 mole of ideal gas.
2.) The odd numbered processes are for monoatomic ideal gases, while the rest are for diatomic ideal gases. For a monoatomic ideal gas, Cv = (3/2)R and for a diatomic ideal gas, Cv = (5/2)R. Cp = Cv + R, so theyre (5/2)R and (7/2)R respectively; not considering the vibrational degrees of freedom which we neglect at relatively low temperatures.
3.) Throughout the entire page, ∫PextdV implies the definite integral over the initial and the final stages as the lower and upper limits respectively. It DOES NOT designate the indefinite integral.
## The Question
Process Ti Vi Pi Tf Vf Pf Q ∆E w ∫PextdV ∆H 1 Rev. Adiabatic 400K 02.0 L 04.0 L 2 Rev. Adiabatic 300K 01.00 atm 02.00 atm 3 Isobaric Rev. 300K 01.00 atm 600K 4 Rev. Isothermal 300K 03.0 L 06.0 L 5 Rev. Isothermal 250K 03.0 L 02.00 atm 6 Rev. Isochoric 02.00 atm 400K 1000 J 7 Irrev. Adiabatic 350K 01.00 atm = ext pressure 1000 J 8 Irrev. Isothermal 01.0 L 10.00 atm = ext pressure 0500 J
 
If you feel stumped by the sheer lack of data in the table, know that this is not an impossible task. It is, actually, a mechanical, mindless work. This is mainly because the table doesn't require a proper understanding of a process and the related intricacies. All it demands is a harmony among the formulae in the student's mind. Filling up this table will give a strong practice of the mathematics involved, and will also benefit the student in simplifying the more complex numerical problems.
If you still do not gather any courage to fill the table, you should consider solving the introductory problems.
Process Ti Vi Pi Tf Vf Pf Q ∆E W ∫PextdV ∆H 1 Rev. Adiabatic 400K 02.0 L 16.42 atm 252K 04.0 L 05.18 atm 0 -1846 J -1846J 1846J -3076J 2 Rev. Adiabatic 300K 24.63 L 01.00 atm 365K 29.96 L 02.00 atm 0 1351J -1351J 1351J 1891J 3 Isobaric Rev. 300K 24.63 L 01.00 atm 600K 49.26 L 01.00 atm 6236 J 3741J -2495J 2495J 6236J 4 Rev. Isothermal 300K 03.0 L 8.21 atm 300K 06.0 L 04.10 atm 1729 J 0 -1729J 1729J 0 5 Rev. Isothermal 250K 03.0 L 6.84 atm 250K 10.26 L 02.00 atm 2556 J 0 -2556J 2556J 0 6 Rev. Isochoric 352 K 14.44 L 02.00 atm 400K 14.44 L 02.27 atm 1000 J 1000J 0 0 1397J 7 Irrev. Adiabatic 270 K 38.63 L 0.57 atm 350K 28.73 L 01.00 atm = ext pressure 0 1000J 1000J - 1000J 1663J 8 Irrev. Isothermal 424 K 01.0 L 34.81 424K 3.48 L 10.00 atm = ext pressure 500 J 0 -500J 0500 J 0
## Hints
### Column 1
(a)Pi - Since three of the gas parameters are known, the fourth parameter can always be found using the ideal gas equation on the initial state.
(b)Tf - Ideal gas equation has four parameters, only two are known, so we need one more equation.
Since this is a reversible adiabatic process, the pressure P and Volume V satisfy the relation (P)(V^y) = constant throughout. Also, the ideal gas equation is satisfied throughout in any reversible process. PV = nrt. Devide the first equation by the second, and you'll find that you just eliminated one unknown - P. It is now left to one equation, Ti[Vi^(y-1)] = Tf[Vf^(y-1]) and one unknown, Tf.
The final calculations require a simple use of log tables. In competitve exams however, the paper setter will give all the values of the logarithms involved, so you need not concern yourself with the complexity of the calculations.
(c)Pf - Now that three quantities in the ideal gas equation are known, you can easily find Pf.
Alternatively, you could directly find Pf through using P(V^y) = constant on initial and final stages of the process, and then used the ideal gas equation to find Tf. Notice that we avoided finding Pf when we were asked to find only Tf, by eliminating the unknown.
(d)Q - In an adiabatic process, the heat exchanged with the sorroundings is ________
(e)∆E - Internal energy is fairly simple for an ideal gas, and depends only upon temperature of the ideal gas. It is nCvTf at Tf, and nCvTi at Ti. So the change, then, is nCv(Tf-Ti). Try to relate it to the expression for heat gained and heat lost learnt in thermal physics in the eleventh and ninth standard in Indian Schools.
(f)w - It is the aditive inverse of ∫PextdV in Chemistry conventions. In Physics, it is the same as ∫PextdV. See below on how to find ∫PextdV, that is the work done by the gas during the change in volume.
(g)∫PextdV - Well, performing the whole integration by substituting P is a good idea. P = nrt/v will not work because even T will vary. We cannot integrate two variables in this way. Instead, substitute P as [Constant]/(V^y) and carry out the integration. After the integration is done, substitute the value of constant as Pf(Vf^y) and Pi(Vi^y) to get the result in terms of known quantities.
But, the same work can be done in an easy manner! Use the first law, Q = ∆E + ∫PextdV. You will find that in an adiabatic process, since the heat exchanged is 0, ∫PextdV becomes the aditive inverse of the change in the internal energy. In laymen's terms, since in an adiabatic process, the heat input is zero, whatever work that is done by the gas comes at the expence of its internal energy (and vice versa). This explaining subtly why the First Law Of Thermodynamics is actually the manifestation of the law of conservation of energy.
**NOTE :: The integral requires the value of Pext. In a reversible process, since the External Pressure is the same as the internal pressure of a gas, the whole substitution makes sence. Remember, Pext is not necessrily equal to nrt/v, but internal pressure = nrt/v.**
(h)∆H - Finally, the enthalpy change of the reaction. It is pleasing to know that this again, depends only on the change in temperature for an ideal gas. That is, ∆H = nCp∆T.
The First Column, Done!!!
### Column 2
(a)Vi - Use the ideal gas equation over the first state.
(b)Tf - Ideal gas equation, this time again, will have two unknowns. We need one more equation, which comes from (P)(V^y) = constant. Going exactly by the steps in column one, however, we won't be eliminating the unknown Vf, while eliminating the known P. Instead, to eliminate Vf, while keeping the knowns, raise both sides of the ideal gas equation by Y and devide the first equation by the second. You will end up with (T^y)[P^(1-Y)] = constant. Use it on the initial and final stages.
(c)Vf - Now that three quantities in the ideal gas equation are known, you can easily find Vf.
Alternatively, you could directly find Vf through using P(V^y) = constant on initial and final stages of the process, and then used the ideal gas equation to find Tf. Notice that we avoided finding Vf when we were asked to find only Tf, by eliminating the unknown.
(d)Q - What is the defining charachteristic of an adiabatic process?
(e)∆E - nCv∆T pretty simple. :)
(f)w - Tip::Throughout the table, this column is going to be the aditive inverse of ∫PextdV
(g)∫PextdV - Tip::Although not throughout the table, but in any kind of adiabatic process (reversible or irreversible), ∫PextdV is the aditive inverse of ∆E, according to the first law.
**This is because the first law of the thermodynamics is universal, and it doesnt matter if the process is reversible or irreversible to apply it.
However, the ideal gas equation and any results derived from it are applicable only in the case of a thermodynamic equilibrium. Since this is not possible in case of an irreversible process, we cannot use the mentioned equations over the course of the reactions. Even then, the ideal gas equation can be used before and after an irreversible process takes place.**
(h)∆H - ∆H = nCp∆T.
Second column completed as well.
### The Third Column
(a)Vi - the _______ equation, fill in the blank mentally.
(b)Vf - Again, two unknowns for the ideal gas equation. But is Pf actually an unknown? Remember that this is an isobaric process, and that the initial pressure is known, so the final pressure is known as well.
(c)Pf - Done
(d)Q - Non zero for the first time!! We will use the first law, Q = ∆E + ∫PextdV. See it again as the law of conservation of energy, the heat supplied is used in heating the gas as well as doing work. Now find the other two terms.
(e)∆E - nCv∆T :)
(f)∫PextdV - Since this is a reversible process, the external pressure is the same as the internal pressure, and the internal pressure is constant. It comes out of the integration. So we are left with (P)∫dV, which evaluates to P∆V. Do the needful!!
(h)∆H - nCp∆T !!!
Note : - In evaluating ∫PextdV, make sure that you use the correct units of each quantity! Since we want the answer to be in joules, i.e. SI units, we need to substitute pressure and volume in Pascals and Cubic Meters.
Note : - The enthalpy change of a reaction is the heat exchanged in a reaction when a process is carried out at constant pressure. This, in our case, means that the Q and ∆H entries in column three should be same. [Have you convinced yourself why?] But there may be slight differences between the two entries, this resulting from the rounding off of conversion factors. e.g. 1 atm = 101325 Pascals, but we often substitute 1 atm as 1.01 lac pascals.
Third column done as well. :)
### Column Four
(a)Pi - ;)
(b)Tf - This question is the answer, "what is an isothermal process?"
(c)Pf- The ideal gas equation is OK, but observe that the RHS of it is constant. So, even the LHS would be. Hence, if the volume doubles up, the pressure reduces to half.
(d)Q - ∆E + ∫PextdV, now we will find both the terms and substitute them.
(e)∆E - Well, if the internal energy of an ideal gas depends only on its temperature, and if this is an isothermal process, where does it lead us?
(f)∫PextdV - This is a reversible process. As explained above, Pext is the same as the pressure of the gas molecules at any stage. Substitute Pext as nrt/v. Since the numerator is constant, we take it out of integration, and evaluate nrT ∫(dV/V) which is nrTln(Vf/Vi). Now substitute the values.
(g)∆H - nCp∆T :)
### Column Five
No additional info. This is a clone actually.
### Column Six
We expect the student to be seasoned enough now to realize that the gas parameters are found through ideal gas equation, and then the thermodynamic Joule values are found simply.
Note : Since the volume remains constant, change in volume is 0. i.e. dV=0, so ∫PextdV = 0
### Column Seven
This is the first irreversible process that we are dealing with, in this table. Pf = 1 atm = external pressure in the above table means that the gas expands/contracts against a constant external pressure of 1 atm, and the final pressure of the gas too is 1 atm. [We have some numerical problems where the final pressure isnt equal to the external pressure against which expansion/contraction took place, but do not bother yourself with it at this moment.]
Note carefully that all three gas parameters are missing for the initial state. That means, apart from the gas equation, we will require two more equations to find them all. And since this is an irreversible adiabatic process, we cannot use P(V^y)=Constant over the initial and final states. That means we have lost an equation!
How are we going to deal with this situation? The first thing to keep in mind is that every problem asked in this book has a solution. And this table, like most of the highschool problems, is all about making equations to find unknowns.
(a)Vf - Use the ideal gas equation to get the value.
Now try to relate the final parameters to the initial parameters. Obviously, the heat gained, work done, change in internal energy put some constraints on the possible values of the parameters.
(b)Ti - ∆E is known to us, but if we write it as nCv∆T, and equate it to 1000 J, we actually end up with an equation. This gives us the value of ∆T, which can be use to find the initial temperature, because the final temperature is known.
(c)Vi/∫PextdV - Refer the two reversible adiabatic processes in column 1 and column 2 that we studied. We made a statement over there, that since the characteristic of any kind of adiabatic process is "zero energy exchange", ∫PextdV is always the additive inverse of ∆E for an adiabatic process. Hence ∫PextdV = -1000 J.
But this is not all!! If you are thorough with integration, look at the word ∫PextdV with some concentration. The parameter Pext would jump in and out of the integral in your mind's eye once you understand that it is constant for this process. This yields ∫PextdV =Pext(∆V). Just as you found Ti by finding ∆T, find Vi by finding ∆V.
Fill up the rest of the entries yourself.
Note: This is for you to ponder. In the reversible adiabatic processes, ∫PextdV = -∆E and actually evaluating the integral gave the same equation. But in the case of an irreversible adiabatic process, evaluating the integral and using the first law to find its value gives two distinct equations! This can be used for our benefit in problems. Please keep this in mind!
### Column Eight
Just as in Column Seven, we lose the equation ∫PextdV = nrtln(Vf/Vi), but we can write it as ∫PextdV = Pext(∆V).
An irreversible isothermal process is much shorter than an irreversible adiabatic process to complete.
(a)Vf - ∫PextdV = Pext(∆V) use this equation to find the final volume of the gas molecules.
(b)Tf - Two gas parameters are known now, use the ideal gas equation to find Tf. And if this is an isothermal process, what does knowing the final temperature mean?
The rest of the entries require no new logic, everything has been covered in the above columns.
# PhChem/thermo1/Problem1
Read the paragraph in "The Setup" section and answer the questions that follow it. This question is supposed to replace a theory part explaining obvious facts with an interactive session.
## The Setup
A horizontally aligned cylinder is divided into two sections by a vertical massless frictionless sliding adiabatic piston. Both the left and the right sections have one mole each of an ideal gas (whose molar specific heat is 20 J/mol K) at 300 K and 2.0 L. The ideal gas in the right section is maintained at a constant temperature by means of a diathermic contact with some external agent. The ideal gas in the left section, however, is in contact with a heater, which heats it slowly so that the left section expands. By the time the heater stops supplying heat, the volume of the right section has decreased to 1.0 L.
• Note - Before solving the problem, make sure that you understand the whole of it. This problem is of intermediate level. Like most questions in physical chemistry, it seems tough only because of its length. To understand the whole scenario in this (and every other) question, note down the necessary data and diagrams where you are solving the problem. Doing so will familiarize you with the problem, and give you some mental exercise.
• So before you start to solve, draw a cylinder resting on its curved surface, divided into two parts. To each part assign the values of the gas parameters, and note which section will be heated and which one will be maintained at a constant temperature.
## The Questions
### Question 1
What process is the gas in the right section R undergoing?
Since it is maintained at a constant temperature, it is undergoing an isothermal process. Also, since the volume change is taking place slowly (quasi-statically), it is a reversible process. It is thus, a reversible isothermal process. The diathermic contact with an external agent just means heat can be exchanged between section R and the external agent. This is used to maintain the constant temperature in section R.
### Question 2
What is the significance of the adiabatic piston in between Sections L and R?
The adiabatic piston ensures that heat does not flow between the two sections. That is, the heat supplied to section L is utilized in heating the gas and doing PV work only, and is not passed on to section R.
### Question 3
What is then, the work done by the gas in the section R?
Use the expression/formulae for isothermal process ∫PextdV = nRTln(Vf/Vi). All of the values are known, n=1, T = 300 K constant, Vf = 1.0 L and Vi=2.0 L. The answer comes out to be -1.73 x 10^3 J. Since by IUPAC convention, work done by the gas has the same magnitude but opposite sign as ∫PextdV, the final answer is 1.73 x 10^3 J.
### Question 4
∆E and q for the gas in section R are ___J and ___J respectively.
Well, in an isothermal process, ∆E is always zero, because for an ideal gas, Internal energy depends only on temperature, and the temperature remains constant. q is to be found using the First Law Of Thermodynamics, and it comes out to be -1.73 x 10^3 J
### Question 5
When the heating stops, the piston stands still. What does this tell us about the pressures of the ideal gases in the two sections?
If the piston stands still, it means it is in a state of mechanical equilibrium. (Can you explain satisfactorily the difference between mechanical and thermodynamic equilibrium? Refer any textbook or Wikipedia and note the answer just now if you cannot.) This makes us conclude that the net force acting on it is zero.
In other words, the force from the gas in section R and the force from the gas in section L are same in magnitude and opposite in sign. Equating their magnitudes, Pr x Piston Area = Pl x Piston Area. That is, the pressures of ideal gases in both the sections are same! This is a very important result, do remember how we concluded it.
### Question 6
If the piston had some finite mass, and the cylinder was aligned vertically, would the pressures be same in case of equilibrium?
Definitely not! You can draw a free body diagram of the piston and check. The ideal gas in the bottom section has to counterbalance the force due to the gas above, as well as the gravitational force acting downward. This means, the gas below will be at a higher pressure, by an amount (Piston Mass)g/(Piston Area) pascals. (Convince yourself about this point.)
### Question 7
By performing actual integration, find the value of ∫PextdV for the gas in Section L.
This is a very nice question, because it helps to clarify the significance of each and every variable. Pext for the gas in section L is nothing but the pressure against which it is expanding. This pressure is the pressure of the gas in section R.
∫PextdV = ∫PrdVl
Now we substitute Pr as nRTr/Vr.
∫PextdV = ∫PrdVl = ∫(nRTr/Vr)(dVl) = nRTr∫(dVl)/(Vr)
(The numerator was taken out of integration, because it is a constant)
Now comes the main step of the question. Can we integrate the variable Vr with respect to the variable Vl? Definitely not. So we substitute the variable Vr as [4.0 L - Vl] and carry out the integration from limits 2.0L to 3.0 L. This is because, the total volume of the cylinder will remain constant at 2.0 + 2.0 = 4.0 L, and if the volume of one section increases by some amount, the volume of the other section decreases by the same amount.
(The substitution Vr = 4.0L - Vl is similar to the case of evaluating ∫PextdV for an ideal gas in an isothermal process. There, since we could not integrate P wrt V, we substituted it as nRT/V)
The definite integration yields the value of the integral to be (nRTr)(-1)(ln[{4-3}/{4-2}]) = nRTrln2 = 1.73 x 10^3 J same in magnitude, but opposite in sign, as ∫PextdV for section R. Note this point carefully.
### Question 8
We substituted Pext = Pr = nRTr/Vr. = nRTr/(4.0 - Vl). But we do know that since this is a quasi static process, the piston is always in mechanical equilibrium and hence the pressures of gases in both the section are always same. So why did not we substitute Pext = Pr = Pl = nRT/Vl?
Definitely we could have done this. But take a look back at Q7. The numerator nRTr was constant an could be taken out of integration. Is this the case with nRTl as well? No. We would again need to substitute Tl as some function of Vl, so that we could carry on with the integration. All in all, what we did was correct.
### Question 9
Prove that the values of ∫PextdV for the two sections are always going to be the additive inverse of each other for this scenario.
Consider ∫PextdVr + ∫PextdVl. To prove our point, we will prove this expression to be zero, no matter what. The first point is, as we discussed above, the Pext for one section is the pressure of the ideal gas in the other section. Now, both are equal at any point of time in our case (because the process is quasi static, both mechanical and thermodynamic equilibrium are maintained at every stage. Convince yourself that this statement leads to our conclusion.)
Also, we have already proved before that the change in the volume of one section is the additive inverse of the change in the volume of the other section. See Q7, and by the way, this is obvious. So,
dVr = -dVl.
Hence, ∫PextdVr + ∫PextdVl. = ∫PextdVr - ∫PextdVr = 0.
### Question 10
Find the work done w by the gas in section L, its ∆E and the heat supplied by the heater.
• w = - ∫PextdV = -1.73 x 10^3 J
• ∆E = nCv∆T. Now finding the change in temperature is a different task altogether. But use the skills that you derived from solving the table. The initial temperature is known to us. But for the final state, we only know the volume. The temperature and pressure are not known. We need two equations then. The first is the ideal gas equation. The second is obviously, Pl = Pr. = nRTr/Vr.
• Substitute this value of Pl in the ideal gas equation (do not obtain the numerical value, it will just increase some calculation). After a lot of cancellation (to our satisfaction), we obtain Tl = 600K. n=1 moles, Cv = 20.0 J/K mol and ∆T = 300K. This gives the answer to be 1.20 x 10^4 J
• The heat supplied by the heater is nothing but q for section l, which is to be found using the first law of thermodynamics and is found equal to, after rounding off, 1.4 x 10^4 J.
# PhChem/thermo1/Splmntry
## Question 1
1.00 mole of helium gas is allowed to expand from 22.4L to 44.8L isothermally at 273.15 K. The expansion is free expansion type. The external pressure against which the gas is expanding is zero. In other words, the gas is expanding in vacuum. Find the values of q, w, ∆E and ∆H for this process. Assume ideal gas behaviour.
### The solution
Although it might seem tiring to find the values of four parameters, a thorough practice of filling up the table we discussed before might make this an obvious mechanical task. Since the process is an isothermal process, the temperature change is zero. And since we are to assume ideal gas behavior, ∆E and ∆H are zero. This is because, for an ideal gas, these two parameters depend solely upon the temperature. Secondly, since the gas is expanding against zero pressure, it is offered zero resistance. Hence, no work is one by or upon the gas. If this sounds unconvincing, consider ∫PextdV. Since the external pressure is constant, we take it out of the integral, and since the external pressure is zero, the whole term is zero by itself.
w, then, too becomes zero in value.
Q, that is, the heat exchange in the process also has to have the value 0, according to the first law of thermodynamics. Have you noted that it never mattered what the gas was, or what its gas parameters were, so long as we considered it to be ideal? In the question, we have mentioned various data regarding the gas, none of which were used in the solution.
### Synopsis
• P=0, so ∫PextdV = 0
• Using the first law of thermodynamics, we showed that q = 0 as well.
### Concluding Notes
Note the whole discussion as, “An isothermal free expansion of an ideal gas is also adiabatic”.
Is the converse true? Is an adiabatic free expansion of an ideal gas isothermal too? Think in terms of conservation of energy. If the idea doesn’t seem obvious, use the expression for the first law of thermodynamics.
## Question 2
Two moles of a monoatomic ideal gas occupy a volume of 30 L at 300 K. The gas is allowed to expand to 50L at a constant external pressure of 550 mm Hg adiabatically. Find the work done by the gas and the final temperature of the gas. Keep in mind that the final pressure of the gas is not necessarily equal to the external pressure it expands against.
While solving Physical Chemistry, a problem either seems familiar or it does not. And to make sure it does seem familiar in an examination, one should be able to dissect the data given and the scenario into fragments which have been previously dealt with.
Working on these grounds, we realize that we have already solved some problems dealing with irreversible expansion. The only difference between them and this one is that in the latter, we do not know that final pressure of the gas. Isn’t it? Where does it lead to? A simple thought says that we have another unknown, finding which would require an extra piece of data. Indeed, compare this problem with the previous ones from the table, and you’ll realize we have more data here.
### The Solution
Here we go. The work done by the gas is nothing but -∫PextdV when we are in the IUPAC domain.
We now evaluate the integral. Since the pressure is constant, we take it out of the integral sign and the remaining integral amounts to ∆V. We know the change in volume of the gas, and we know the external pressure against which it has expanded. Hence, the work done by the gas is P∆V = (550/760 atm) x (20 L) atm-litres = (550x101000/760) x (20/1000) J =. 1462 J. (Check your level – are you thorough with unit conversions?). w is then equal to -1462 J.
Also, since it is an adiabatic process, ∫PextdV = - ∆E = w. This is the second step we’re performing. (Can you explain this using the conservation of energy? Since the heat supplied is zero, whatever work is done by the gas is done at the cost of its internal energy.) Equate the change in internal energy to nCv∆T and you’ll find the change in temperature. The number of moles are two, and the Cv is 1.5R (monoatomic ideal gas). This is enough to find the final temperature. The mistake you could have made was finding the final temperature using the ideal gas equation with 550/760 atm as the final pressure.
The final answers are -1462J and 242.4K.
### Synopsis
• Evaluated the ∫PextdV as P∆V and found one answer, w
• Equated ∫PextdV to –nCv∆T (w = nCv∆T) and found Tf
### Concluding Note
Make it a general approach to assume the final pressure not being equal to the external pressure against which the system has expanded in cases of irreversible processes, unless specifically mentioned otherwise. This will help in most questions. Since these questions are easy going by the concepts, and still, mistakes can be made, they are among the deciding questions in exams like AIEEE or even the JEE.
## Question 3
One mole of a monoatomic ideal gas occupies a volume of 11.2 L at 273K. The gas is allowed to expand by 22.4L at a constant external pressure of 1 atm isothermally. Find the work done by the gas. The final pressure of the gas is not necessarily equal to the external pressure it expands against.
### The Solution
This is basically the same question as above. There may be a few on-the-surface differences, but nothing more than that. The work done, as we know, is nothing but -∫PextdV = -P∆V = -[1 atm x 22.4 L atm-litres] = -(101000 x 22.4 x 10^-3) Joules = -2262.4 J. The final pressure, can be found using the ideal gas equation, of course, the final temperature is 273K (this is an isothermal process).
### Synopsis
• Evaluated P∆V, and answered the value.
### Notes
One mistake that people may make is that the gas expands by 22.4 L, not that the final volume is 22.4L. In other words, the data is ∆V = 22.4 L. This mistake should be avoided, because in most competitive objective exams, an option leading from this described mistake will also be put up. Falling prey to that option means that you failed to gain easy marks, and at the same time losing marks which a person not attempting that question wont. This leads, ultimately, to losing ranks.
## Question 4
n moles of an ideal gas with molar specific heat Cv is taken from initial state T1/ V1 to final final volume V2 through a reversible adiabatic process. Show that the value of ∫PextdV is
${\displaystyle nCvT_{1}\left[1-\left({\frac {V_{1}}{V_{2}}}\right)^{\frac {R}{Cv}}\right]}$
### First Thoughts
To many students, this problem might seem too obscure to induce any desire to solve it. Others might think it is familiar but would not attempt the problem just because of an unknown fear. Relax. The value of ∫PextdV is nothing but –nCv∆T = nCv(T1 - T2).
Our approach would be substituting each and every unknown we encounter, in the hope that if we do not make any mistakes, nothing can go wrong.
### The Solution
Write down the required quantity, nCv(T1 - T2), and start manipulating it step by step. Take T1 out of the bracket first, because that is exactly the term that we are supposed to generate.
Now, we are left the bracketed term beside nCvT1. As we have mentioned before, if we do not make any mistake, we are sure to go home. This means that the complex looking bracket in the question, simplifies to 1 - (T2)/(T1). But how? We have done this several times before, while dealing with reversible adiabatic processes: the relation between the Temperature and Volume of the ideal gas at any stage in an adiabatic process, which gives us (T2)/(T1) = [(V1)/(V2)]^(y-1), where y stands for the adiabatic exponent of the gas.
(Do you remember this? PV^y = constant, and PV = nRT. On eliminating pressure from these two equations, we arrive at the relation TV^{y-1) = constant, giving T2)/(T1) = [(V1)/(V2)]^(y-1) when applied over the initial and final states. Please refer back to the tables, if you do not know this.)
But, the adiabatic exponent does not appear anywhere in the final term. So? Eliminate it, obviously. We know the molar heat capacity, and can report Universal Gas Constant as well. Y-1 is nothing but (Cp/Cv) -1 which simplifies to R/Cv, just what we need.
### Synopsys
• Used (T2)/(T1) = [(V1)/(V2)]^(y-1) to eliminate T2
• Used y = Cp/Cv to eliminate the adiabatic exponent, y itself.
### Concluding Notes
Do not be bamboozled by the perplexity of any problem, just try to make it seem easy.
# PhChem/thermo1/splmntry2
A gas contained in a cylinder fitted with a fractionless piston expands against a constant external pressure of 1atom from a volume of 5litres to a volume of 10 liters .During the process the system absorbs 400J of thermal energy from its surroundings.Determine ∆E for the process (R=8.314Jpre mole per kelvin and 1atom =101325NM^-2
### First thoughts
What is this process? Well, it is a phase change of water. Since heat transfer is involved, q, ∆E and ∆H are also associated with this process. How does work w come into being? Actually, the system in question is undergoing a change in volume as well against a pressure. Hence, some work must have been performed.
### The Solution
q/∆H - Note that this process has been carried out at constant atmospheric pressure. So, the heat involved q would be nothing but the enthalpy of the reaction. Please make a note that the standard enthalpy quoted here is for 1.00 moles, and for vaporization. Here, we are dealing with 10.00/18.00 moles of water vapour which has to condense. So, the ∆H is 5/9 times of the standard enthalpy in magnitude and opposite in sign.
That is, q = ∆H = (- 5/9)(∆Hvap) = -22.6 kJ. This is obvious, heat should be taken out of the system if it has to be condensed.
W - What is the work done? Consider ∫PextdV. Since the pressure is constant, it comes out of the integral, and we are left to evaluate P∆V. Now, this is another important point to note. The water vapour would occupy 17.01 L (according to the ideal gas equation), while the water droplets would occupy somewhere around 0.010 L. (assuming the density of water to be 1gm/ml at 100 oC). The change in volume is approximately equal to the volume of the water vapour itself.
Hence, in most condensation/vaporization problems, we never bother to find the change in volume. We assume liquids to have negligible volume in comparison to vapours. Even in our case, we will not take the volume of water into account because it is negligible, and because it is calculated through assumptions.
Hence, P∆V amounts to P (=1atm) x ∆V (=17.01 L) = 17.01 atm-L = 17.01 x 101000 x (1/1000) = 1718 J. w = -∫PextdV = -1718 J
∆E - Now we find ∆E. According to the first law of thermodynamic/Conservation of energy, ∆E = Q – ∫PextdV = Q + w = -22.6 kJ – 1718 J = -24.3 kJ
Please note that the value of w is in the order of joules, while that of ∆H is of the order of kilojoules. Do not make any mistakes while adding them.
### Synopsis
• q and ∆H were equal for this process because it was carried out at constant pressure.
• w for this process was calculated using –P∆V
• ∆E would have been trickier, if going by the popular misconceptions. However, it was calculated through the first law of thermodynamics, since the other two parameters are already known.
## Question 2
Water expands when it freezes. Determine the amount of work done in Joules when a system consisting of 1.0L of liquid water freezes under a constant pressure of 1.0 atm and forms 1.1L of ice.
### Solution
There has to be no confusion with this problem. The work done is –∫PextdV = -P∆V = 1.0 atm x 0.1 L = -[1 x 101000 x 0.1 x (1/1000)] = -10.1 J
### Notes
Not many examiners will ask this question directly. Most spin-offs will involve the calculation of the volumes and the first law of thermodynamics.
## Question 3
When 1 mole of ice melts at 0 oC and at constant pressure of 1 atm. 6050 joules of heat are absorbed by the system. The density of ice and water are 0.92 gm/ml and 1.00 gm/ml respectively. Calculate ∆H and ∆E for the reaction in joules. Report the exact values.
### First Thoughts
If you have read the concluding notes of the previous question, then you will find that this is exactly what we were talking about. ∆H, as in question 1, is equal to the q of the reaction because this is a constant pressure reaction. ∆E has to be found using the first law of thermodynamics, for which we also require w.
Just as we discussed above, we have not been given the volumes of the two states directly. Rather, we have to find them out using their densities. This is not much of a big task, but complicates the problem nonetheless.
### Solution
∆H – Since the process is carried out at constant pressure, the enthalpy change of the reaction is the same as the q value. Q is 6050 J in magnitude, and since heat has been absorbed by the system, it has a +ve sign. So, ∆H = q = +6050 J
∫PextdV – The integral again simplifies to P∆V. All we have to do now is to find the change in volume. We are dealing with 1 mole of water, which is 18 grams of mass. So, the volume is 18 grams / 0.92 g/ml = 19.56 ml ice and 18/1.00 = 18 ml water. ∆V is then -1.56 ml.
P∆V = -(1 atm x 0.00156 L) = -0.00156 atm-l = -0.16 J
∆E – According to the first law of thermodynamics, it comes out to be 6050.16 J. However, we do not report such values because of the use of significant figures.
### Synopsis
• Found ∆H
• Calculated ∫PextdV for use in the first law expression to ultimately find ∆E.
### Concluding Notes
Physical chemistry problems, generally, are easy and use the same concept/logic. In most of the cases, if they are complicated, it is just because of the presented data. Also, this question wasn’t the best example of how this is done. Be prepared for more.
## Question 4
A cylinder contains 10 litres of an ideal at 25 atm and 25 oC. However, the gas leaks out due to some malfunctioning. The atmospheric pressure is exactly 1 atm and temperature 25 oC during the entire leak. Assuming that the process is isothermal, how much work is done on the atmosphere due to the leaking gas?
### First thoughts
This is a nice variation of the questions we have been doing. When the gas leaks out at constant temperature, it actually undergoes an isothermal expansion. A part of our system has vanished in the atmosphere, while the remaining is still inside the cylinder. This is intriguing, as we have been dealing with disciplined processes, where, unlike here, the system under question was at one place.
So, all we are left to do is solve the problem with the numerical values.
### Solution
The gas will leak out of the cylinder till the pressure in the cylinder has reduced to 1 atm. Since the temperature of the gas is constant, PV = constant for the gas. Now, note that, the gas in the cylinder will be at 1 atm and the gas leaked out will also be at 1 atm. That means, the pressure has reduced 10 times. The volume, therefore, has increased ten times and has become 250 litres. The work done by the gas is then -∫PextdV = -(1 atm) x (250 L - 10 L) = -240atm-L
The work done on the atmosphere because of the leaking gas will have exactly the same magnitude but opposite sign as above. (To do – Explain this point properly, and in detail) Hence, the final answer is 240 atm-litres = 24240 J
### Synopsis
• Found the volume of the gas after the leaking has stopped.
• Evaluated ∫PextdV for the gas
• The last point.
## Question 5
A magnesium strip of mass 20 gm with 20 percent inert impurities is dropped into a beaker of dilute hydrochloric acid. Calculate the work done by the system as a result of the reaction that takes place. The atmospheric pressure is 1.0 atm and temperature 25 oC. The molar mass of magnesium is 24.3 grams.
### First Thoughts
Again, this is a different situation. Until now, we have been dealing with processes over ideal gas, but this is something different. Actually, the reaction that will take place is a redox reaction. The magnesium in the strip will be oxidized to magnesium ions, while some of the hydrogen ions in the acid will be reduced to molecular hydrogen. This gas will then occupy some volume, which is different from the previous volume occupied by the system. Hence, ∫PextdV is involved yet again.
Also, note that the amount of acid taken is assumed to be in excess, so that all of the magnesium is oxidized, while still leaving some hydrogen ions.
### Solution
For each mole of magnesium ion produced, one mole of molecular hydrogen H2 is produced. (DIY – write down the redox reaction. This is a fairly simple one, and after the statement above, no complexity is involved whatsoever.)
The question is, how many moles of magnesium are actually reacting? The mass of the strip taken is 20.00 grams, which contains 20 percent inert impurities. So, the mass of magnesium reacting would be 16 grams, which amount to 16/24.3 = 0.66 moles of magnesium. The impurities are inert, and hence do nothing in the reaction. They have to be ignored completely.
In this condition, 0.66 moles of hydrogen will occupy 16.15 L. This volume is in fact, the increase in volume of the acid beaker + strip system. Hence, ∆V = 16.15 L. P∆V = 16.15 atm-ltres = 1631 J. w = -∫PextdV = -1631 J
### Synopsis
• Found the mass of magnesium reacting
• Found the moles of hydrogen gas produced, and the volume it will occupy.
• This volume is equal to ∆V.
• Evaluated ∫PextdV as usual, and reported with appropriate signs
## Question 1
Which of the two – adiabatic or isothermal – processes has a steeper PV graph?
### Instructions
If we are talking about the nature of a graph, we need to consider the mathematical nature of it too. So, an adiabatic process is represented as PVy = constant on a PV graph, while an isothermal process is represented by PV = constant.
Carefully note that the graph of the isothermal process is a rectangular hyperbola on a PV graph, while that of an adiabatic process resembles a hyperbola.
Now, the question is, which Process takes a greater dip down in the PV curve? Visualize what is being asked. Take the question literally. If we are talking about an expansion, which process will register a greater dip in pressure for the same amount of increase in volume? The answer can be obtained by merely looking at the equations.
### Arguments
Suppose the volume increases by some factor, say m times. In an adiabatic process, the pressure then HAS TO dip by a factor of my to keep the LHS constant. Do the math for an isothermal process, for an increase in volume by a factor of m times, the pressure dips down by the same factor. This means, that the pressure registers a greater dip in adiabatic process than in an isothermal process for the same volume. Note that this is irrespective of the value of the constant on the RHS.
Try to grasp what has been said, and draw an accompanying graph to this point in your notebook.
### Important Note
Remember that my is greater than m only if y>1. This is always true, because the adiabatic exponent of any gas is always greater than unity. But suppose, if we were dealing with a process like PV1/2 = constant, its graph would be less steep than the isothermal process.
Are you confused? Please do not be. Read the note below, and move ahead only after you are sure that you got the essence of what has been said.
### Concluding Notes
This is not an uncommon logic, and a common sense dealing with them should evolve in you during an introductory course in the sciences. The whole logic explained above is nothing but one line, what LHS would tend to raise more?
Now suppose, if you are given adiabatic curves of two ideal gases, one monoatomic and the other diatomic, initiating through the same state and registering the same increase in volume. How would you tell which graph belongs to which gas? In other words, what gas would end up with a lower pressure and what would end up with a higher pressure and why?
The answer, of course, is the monoatomic gas will have the lower pressure. But it is up to you to convince yourself about this using the same logic discussed above.
Hint : The value of gamma for the monoatomic gas is greater than that for a diatomic gas.
# PhChem/thermo1/problem2
## The Setup
Six reversible thermodynamic processes are carried out on one mole of ideal gas in succession to complete a cycle. The processes are two alternate isothermal and adiabatic expansions followed by an isothermal compression and an adiabatic compression to reach to the initial state. The volume changes twofold in the isothermal expansions. Also, the isothermal processes take place at temperatures T1, T2, T3 respectively. The adiabatic exponent of the gas is y.
## Questions
### Question 1
After the cycle is completed, what is the change in the internal energy of the ideal gas?
No. No need to freak out. The internal energy of the ideal gas depends only on the temperature. After the cycle is completed, the gas returns to its original state – the initial pressure, volume and temperature. That is, after the whole cycle, the temperature does not change and hence, the change in the internal energy ∆E is zero.
This is the consequence of internal energy being a state function.
### Question 2
Draw a rough sketch of the whole cycle on a PV graph, clearly showing the six processes.
Is this a difficult question? No. We do know what the graphs of the two processes are shaped like.
The task left, then, is to draw six curves – three of a definite steepness and three of some other definite steepness – one by one such that they form a closed loop. Consider drawing it yourself, and then take a look at the answer below. While sketching, we needed to keep only one point in mind, what graph would be steeper?
Note : The vertices have been labelled for later use. The direction is ABCDEF initiating at A and terminating at F
Since we know the answer to that question, it is relatively easier for us to draw the curve now. Refer to the point on graphs of adiabatic and isothermal processes
### Question 3
What is the work done by the gas in every cycle? What is the total work done by the gas?
This becomes a fairly easy problem. The reason is that the work done by the gas in the adiabatic process is nothing but -nCv∆T. From the graph, we find that ∆T in each case is T2 - T1, T3 - T2 and T1 - T3 respectively. Cv is R/y-1. So, the adiabatic processes are dealt with.
#### Work in isothermal processes
The task reduces to finding the work done in the isothermal processes. Make a mental note that the isothermal processes perform a work –nCvln(V2/V1). Do we know each of the value substitutions? Yes. We know n, Cv, the temperatures at which the isothermal processes take place, and the volume ratio = 2 for the expansions. The only unknown is the volume ratio to be substituted inside ln in the isothermal compression. What is this ratio? And how are we to find it?
#### Finding the required volume ratio
Recall that for an unknown, we need to create an equation. And most of the times, an equation is created because some variables are restricted to some values by a certain law.
Just remember that the initial and final volumes and temperatures (and all intermediate states) in an adiabatic process are constrained to satisfy T1V1y-1 = T2V2y-1. This is the constraint we were talking about.
Let us mark the vertices of this curve as A, B, C, D, E, F respectively, A being the initial point of the T1 isotherm. Then, what we are to find is the ratio VE/ VF.
Here are the three equations: -
• VB/VC = (T2/T1)^[1/(y-1)]
• VD/VE = (T3/T2)^[1/(y-1)]
• VF/VA = (T1/T3)^[1/(y-1)]
Multiplying all three equations, we get the required ratio to be 4. (The RHS after multiplication will reduce to 1, always make a mental note of such cyclic expressions. On the LHS, you will encounter two known ratios an substitute their value as 2.)
• WAB = -nRT1ln2
• WBC = -n[R/(y-1)](T2 - T1)
• WCD = -nRT2ln2
• WDE = -n[R/(y-1)](T3 - T2)
• WEF = -nRT3ln0.25 (Because this is a compression)
• WFA = -n[R/(y-1)](T1 - T3)
Since Cv was not known, we had to express it in the terms of the known adiabatic exponent y. The value of n is one mole, but it has been reported to keep harmony with dimensional formulae.
#### Synopsis
• Found the work done in adiabatic prcess as –nCv∆T
• Found the work done in isothermal process as -nRT ln(V2/V1)
• Found the ratio V2/V1 for the isothermal compression using the condition of reversible adiabatic processes to generate three equations, and multiplying them.
### Question 4
Find the heat exchange of the ideal gas in each step.
This is a mechanical step. All you have to do is use the first law of thermodynamics.
• QAB = nRT1ln2
• QBC = 0
• QCD = nRT2ln2
• QDE = 0
• QEF = nRT3ln0.25 = -2nrtT3ln2
• QFA = 0
### Question 5
What is the efficiency of the process?
Now, the efficiency of the process has to be thought of as the ratio of total output and total input. In thermodynamic processes, only the net work done (∫PextdV over all the processes, not the IUPAC w) qualifies as output. We will NOT consider heat rejected by the system as output.
The input, on the other hand, is not the net heat exchange. It is rather the heat given to the system. The heat rejected by the system does not occur anywhere in the numerator or the denominator.
Then, the output is nR(T1 + T2 - 2T3)ln2. The input is nothing but QAB + QCD = nR(T1 + T2)ln2.
We did not count QEF because it was the heat rejected by the system.
The final answer is the ratio ${\displaystyle }$
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2022-06-27 15:28:01
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https://saattrupdan.github.io/2020-03-01-bootstrap-prediction/
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Continuing from where we left off, in this post I will discuss a general way of producing accurate prediction intervals for all machine learning models that are in use today. The algorithm for producing these intervals uses bootstrapping and was introduced in Kumar and Srivastava (2012).
This post is part of my series on quantifying uncertainty:
1. Confidence intervals
2. Parametric prediction intervals
3. Bootstrap prediction intervals
4. Quantile regression
5. Quantile regression forests
6. Doubt
## The setup
To prove that the prediction intervals are valid the authors made some assumptions on both the true data distribution and our predictive model. Let’s say that we’re working with a $d$-dimensional feature space and that we only have a single response variable. We will then assume that the true model $y\colon\mathbb R^d\to\mathbb R$ is of the form
$y(x) = \psi(x) + \varepsilon(x),$
where $\psi\colon\mathbb R^d\to\mathbb R$ is the “main model function” and $\varepsilon\colon\mathbb R^d\to\mathbb R$ is a noise function. These will satisfy that
1. $\psi$ should be deterministic, meaning that is has no random elements;
2. $\psi$ is “sufficiently smooth”;
3. $\varepsilon(x)$ are iid for all $x\in\mathbb R^d$.
For a precise definition of “sufficiently smooth” check out the paper, but we note that a sufficient condition for satisfying this is to be continuously differentiable. On top of the true model we of course also have our model estimate $\hat y_n\colon\mathbb R^d\to\mathbb R$, which has been trained on a training sample of size $n$. We assume a couple of things about this model:
1. $\hat y_n$ is deterministic;
2. $\hat y_n$ is continuous;
3. $\hat y_n$ converges pointwise to some $\hat y\colon\mathbb R^d\to\mathbb R$ as $n\to\infty$;
4. $\mathbb E[\hat y_n(x)-\psi(x)]^2\to 0$ as $n\to\infty$ for every $x\in\mathbb R^d$.
Most notable is assumption $(4)$, stating that our model estimate $\hat y_n$ will estimate the true model $\psi$ perfectly as we gather more data. In other words, we’re essentially assuming that we can get zero training error. This is fine for most unregularised models (not all though, with linear regression being an example), but as soon as we start regularising then this won’t hold anymore. We can avoid assuming $(4)$ if we instead merely assume that
$\eta(x):=\lim_{n\to\infty}\mathbb E[(\hat y_n(x)-\psi(x))^2] \tag*{(\dagger)}$
exists for every $x\in\mathbb R^d$, which would correspond to the bias of the model. Here $(4)$ would postulate that the model has no bias at all.
## Two types of noise
To estimate the width of our prediction intervals we need to quantify the error sources that are present. Given a new observation $x_0\in\mathbb R^d$ we can write
$y_0 := y(x_0) = \psi(x_0) + \varepsilon(x_0) = \hat y_n(x_0) + \eta(x_0) + \eta_n(x_0) + \varepsilon(x_0),$
where we define $\eta_n\colon\mathbb R^d\to\mathbb R$ as $\eta_n(x) := \psi(x) - \hat y_n(x) - \eta(x_0)$. This neatly splits the noise around our prediction $\hat y_n(x_0)$ into the model bias $\eta(x_0)$, model variance noise $\eta_n(x_0)$ and the sample noise $\varepsilon(x_0)$. We therefore need to estimate the uncertainty of all these types of noise when we’re computing our prediction intervals.
### Noise #1: Model variance
Let’s start by seeing how the authors estimate the model error. Here we’re bootstrapping our sample $B\gg 0$ many times, fitting our model on each of them and then generating bootstrapped predictions $\bar y_{b,n}(x_0)$ for every $b < B$. We will estimate the mean $\mu(x_0)$ of the distribution of $\hat y(x_0)$ by the bootstrap estimate
$\hat\mu_n(x_0) := \frac{1}{B}\sum_{b=1}^B\bar y_{b,n}(x_0).$
We can thus center the bootstrapped predictions as $m_b := \hat\mu_n(x_0) - \bar y_{b,n}(x_0)$. Now note that since we’re assuming $(\dagger)$ we get that
$\mathbb E[m_b] = \mathbb E[\hat\mu_n(x_0)] - \mathbb E[\bar y_{b,n}(x_0)] \to_{b\to\infty} \mathbb E[\psi(x_0) - \eta(x_0)] - \mathbb E[\hat y_n(x_0)] = \mathbb E[\eta_n(x_0)],$
giving us our estimate of the model variance noise.
### Noise #2: Sampling and bias
Next up, we want to estimate the bias $\eta(x_0)$ and the sample noise $\varepsilon(x_0)$. With $\bar y_{b,n}$ being the bootstrapped models as above, we define the bootstrap validation residuals
$\text{val_error}_{b, i} := y(x_i) - \bar y_{b, n}(x_i)$
for every $b < B$ and every $i < n$ which is not in the $b$’th bootstrap sample. This will then estimate the validation residual $y(x_0) - \hat y(x_0)$. We also calculate the training residuals $\text{train_error}_i := y(x_i) - \hat y(x_i)$ for $i < n$. Note that
$\mathbb E_b[\text{val_error}_{b,i}] \approx \eta(x_i) + \eta_n(x_i) + \varepsilon(x_i) \to_{n\to\infty} \eta(x_i) + \varepsilon(x_i),$
giving us an estimate of the sum of the sample noise and the bias. This would work equally well asymptotically if we replaced the validation errors with the training errors, so we have to decide which one to choose. It turns out that the training errors will usually be too small as we tend to overfit, so we have to rely on the validation errors somewhat. The validation errors will tend to be slightly too large however, as a bootstrap sample only contains roughly 2/3 of the training data on average, meaning that the predictions will be artificially worsened.
This issue is also pointed out in Section 7.11 in the “machine learning bible”, Elements of Statistical Learning, and as a comprimise betweeen the training- and validation errors they propose the following “$.632+$ bootstrap estimate”, which I’ll quickly introduce here. We start by defining the no-information error rate as
$\hat\gamma := \frac{1}{n^2}\sum_{i = 1}^n\sum_{j = 1}^n (y(x_i) - \hat y(x_j))^2,$
which is the loss if the inputs and outputs were completely independent. From this we define the relative overfitting rate as
$\hat R := \frac{\text{val_error} - \text{train_error}}{\hat\gamma - \text{train_error}},$
which is equal to $0$ if no overfitting is taking place and $1$ if the overfitting equals the no-information value $\hat\gamma - \text{train_error}$. We then define the weight $\hat w := \tfrac{.632}{1 - .368 \hat R}$, varying from $.632$ in case of no overfitting (in which case this estimate is equal to the standard $.632$ estimate) to $1$ if there is severe overfitting. Our $.632+$ bootstrap estimate of the distribution of $\varepsilon(x_0) + \eta(x_0)$ is then
$o_i := (1 - \hat w)\times \text{train_error} + \hat w\times\text{val_error}.$
In practice, computing $\hat\gamma$ can be quite computationally expensive if $n$ is large, so instead I chose to estimate this by only considering a random permutation of the $y(x_i)$’s and the $\hat y(x_j)$’s.
## Prediction interval implementation
The algorithm producing the intervals are now quite simple given the above reasoning: we simply have to compute the set
$C := \{m_b + o_i \mid b < B, i < n\},$
which we showed above is estimating the distribution of $\eta(x_0)+\eta_n(x_0)+\varepsilon(x_0)$, which constitutes all the noise around $\hat y_n(x_0)$. From $C$ we can then let our interval be given as the predicted value $\hat y_n(x_0)$ offset by the $(100\cdot\tfrac{\alpha}{2})$% and $(100\cdot(1 - \tfrac{\alpha}{2}))$% percentiles. Here is how we can implement all of this in Python:
def prediction_interval(model, X_train, y_train, x0, alpha: float = 0.05):
''' Compute a prediction interval around the model's prediction of x0.
INPUT
model
A predictive model with fit and predict methods
X_train: numpy array of shape (n_samples, n_features)
A numpy array containing the training input data
y_train: numpy array of shape (n_samples,)
A numpy array containing the training target data
x0
A new data point, of shape (n_features,)
alpha: float = 0.05
The prediction uncertainty
OUTPUT
A triple (lower, pred, upper) with pred being the prediction
of the model and lower and upper constituting the lower- and upper
bounds for the prediction interval around pred, respectively. '''
# Number of training samples
n = X_train.shape[0]
# The authors choose the number of bootstrap samples as the square root
# of the number of samples
nbootstraps = np.sqrt(n).astype(int)
# Compute the m_i's and the validation residuals
bootstrap_preds, val_residuals = np.empty(nbootstraps), []
for b in range(nbootstraps):
train_idxs = np.random.choice(range(n), size = n, replace = True)
val_idxs = np.array([idx for idx in range(n) if idx not in train_idxs])
model.fit(X_train[train_idxs, :], y_train[train_idxs])
preds = model.predict(x_train[val_idxs])
val_residuals.append(y_train[val_idxs] - preds)
bootstrap_preds[b] = model.predict(x0)
bootstrap_preds -= np.mean(bootstrap_preds)
val_residuals = np.concatenate(val_residuals)
# Compute the prediction and the training residuals
model.fit(X_train, y_train)
preds = model.predict(X_train)
train_residuals = y_train - preds
# Take percentiles of the training- and validation residuals to enable
# comparisons between them
val_residuals = np.percentile(val_residuals, q = np.arange(100))
train_residuals = np.percentile(train_residuals, q = np.arange(100))
# Compute the .632+ bootstrap estimate for the sample noise and bias
no_information_error = np.mean(np.abs(np.random.permutation(y_train) - \
np.random.permutation(preds)))
generalisation = np.abs(val_residuals.mean() - train_residuals.mean())
no_information_val = np.abs(no_information_error - train_residuals)
relative_overfitting_rate = np.mean(generalisation / no_information_val)
weight = .632 / (1 - .368 * relative_overfitting_rate)
residuals = (1 - weight) * train_residuals + weight * val_residuals
# Construct the C set and get the percentiles
C = np.array([m + o for m in bootstrap_preds for o in residuals])
qs = [100 * alpha / 2, 100 * (1 - alpha / 2)]
percentiles = np.percentile(C, q = qs)
return percentiles[0], model.predict(x0), percentiles[1]
## Simulations
Let’s see how well the above implementation works in practice. Let’s start easy with a linear model, $y(x) := 3x - 5 + \varepsilon$ with $\varepsilon\sim\mathcal N(0, 0.1)$. Here are two 95% prediction intervals, one computed via the bootstrapping approach and one with the normal theory approach which I covered in the last post. Note that we’re showing the new values, but instead of working with just a single new value $x_0$ as above, we’re repeating the above process for all the new values. Here we’re training on $n=1000$ samples and testing on $100$ samples.
In this case the bootstrap interval has a coverage of 95% and the normal theory one having 94%. If we repeat the experiment we see that they are both fluctuating around 95%, sometimes where the bootstrap interval is more accurate and sometimes the normal theory interval being more accurate. Note that in the bootstrapping case we’re not assuming normal distributed noise, so if we now let $\varepsilon\sim e^Z$ with $Z\sim\mathcal N(0, 1)$, i.e. we’re assuming that it now follows a log-normal distribution with $\mu=0$ and $\sigma=1$, then the bootstrap intervals take the asymmetry into account.
Here we thus get much smaller intervals, and the coverages in this case are 98% and 96% for the parametric- and the bootstrap interval, respectively. Furthermore, if we go to the extreme overfitting case where we instead of linear regression fit a single decision tree, we get the following.
Here the bootstrap interval has a coverage of 92% and the parametric one having a coverage of 1%. Overall, we see that we’ve really gained something here! We can also test it for non-linear data. Here we’ve set $d=5$, i.e. chosen 5 features, and set
$y(\vec x) := e^{x_0} + x_1x_2^2 + \log(|x_3+x_4|)) + \varepsilon,$
where $\varepsilon$ is multivariate normal with means $\mu_i\sim\text{Unif}(-1, 1)$ and covariances $\text{cov}_{i,j}\sim\text{Unif}(-1, 1)$.
Here the coverage of the normal theory interval is 99% and the coverage for the bootstrap interval is 94%. If we replace the model with a decision tree as before we get the following.
Again we see that the parametric interval has zero width and a coverage of 0%, and the bootstrap interval having a coverage of 96%.
## Conclusion
We’ve produced bootstrapped prediction intervals for almost any predictive model, which is a slight variant of the intervals produced in Kumar and Srivastava (2012). We’ve seen that they perform as well as the parametric prediction intervals produced with normal theory on linear data with normal noise, but also that the bootstrapped intervals outperform the parametric intervals when we have non-normal noise, non-linear data or if the model is overfitting.
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2022-01-19 11:37:41
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https://matheducators.stackexchange.com/questions/12118/tutoring-a-recalcitrant-awkward-exasperating-student-special-needs/12120
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# Tutoring a recalcitrant/awkward/exasperating student---special needs?
As part of my duties at a GTA, I spend several hours per week in our department's drop-in tutoring center. The center is open to all students enrolled in 100- and 200-level math courses, with the majority coming from Calc 1 & 2. A typical load would be 20-50 students with a roving staff of 5-10 tutors (graduate students/adjuncts/junior-senior undergraduate math majors). As with any good tutoring, our stated policy is to provide help with learning material by explaining concepts, finding and explaining errors, etc; we are explicitly not a "what's the answer to problem #3" service (although difficulties with problem #3 are a great starting point).
I find the work generally enjoyable and have had nearly universally positive interactions with students. However, there is one student that I have come to dread seeing every week.
Said student is enrolled in Calc 1 and is extremely difficult to deal with, to the extent that my armchair diagnosis would place them somewhere on the autism spectrum. Interactions with them are by far the most frustrating I've ever had teaching mathematics, out of literally thousands of students I've tutored over the years. I have gotten so frustrated with helping them that I've had to "tap out" and go for a walk around the building after trying to help them. I'm not the only one either--I've seen every other tutor become similarly exasperated by this student.
## Sample Interaction
For an idea of a sample interaction with this student, consider the problem:
• If $$f(x) = x e^{2x}$$, what's $$f^{(30)}(x)$$?
My usual approach for walking a "completely stuck" student through a problem like this would go like:
1. Can you compute $$f'(x)$$ for me? (Possibly leading to a reminder discussion of the product and chain rules)
2. How about $$f''(x)$$ and $$f'''(x)$$?
3. Do you notice any patterns? Can you predict what $$f^{(4)}(x)$$ will be? Does your prediction hold when we compute said derivative?
4. Can you formulate the pattern you're noticing in mathematical notation?
5. Profit.
Usually the problem clicks around step 2 or 3 and they can take it from there. In comparison, here's how an interaction with this student goes:
Student: [raises hand]
Me [walk over]: How's it going? What are we working on?
Student [computer open to online homework problem, blank sheet of paper in front of them]: What's the answer to this problem?
Me: What have you tried so far? (Again, they have a blank sheet of work in front of them)
Student: I don't know how to compute the 30th derivative
Me: How would you compute the second derivative?
Student: Prime of the prime [we'll let that slide, bigger fish to fry]
Me: Right! Can you go ahead and find $$f'(x)$$ for me?
Student: I know how to do that. The problem wants the 30th derivative.
Me: True! I think we should try to compute the first couple derivatives and see if we can find any patterns
Student: [Lough sigh/uggh, audible across the entire room] Fine. [starts computing $$f'(x)$$, nowhere close]
Me: Hold up a sec--is that derivative correct?
Student: What do you mean.
Me: Well, there's an $$x$$ times $$e^{2x}$$ --
Student: So?!
Me: ...so we need to use the product rule, right?
Student: [crickets]
Me: When we want to take the derivative of a product, we use the product rule. [write $$\frac{d}{dx} f(x) \cdot g(x) = f'(x) g(x) + f(x) g'(x)$$]
Student: DUUHH. I know this. Why are you explaining stuff I already know; I need to know how to find the 30th derivative.
Me: Well, it doesn't look like you used product rule or chain rule to compute $$f'(x)$$ there. Can you try to fix what you have for $$f'(x)$$?
Student: How?
Me: [more detailed explanation of product/chain rules. Look up to see that they have opened a tab for facebook on their computer] Dude...do you want me to help you or -
Student: I know that stuff. I NEED TO KNOW HOW TO COMPUTE THE 30TH DERIVATIVE! [entire room looks up]
Me: [fighting to be calm] Please don't shout. I'm trying to explain how to find the 30th derivative to you. There isn't a magic "30th derivative formula"---we find it by computing the first few derivatives and finding some patterns. [I go ahead and write down $$f'(x)$$ and $$f''(x)$$]
Student: Why are you doing this? That's exactly what I have written.
Me: Well...notice how I have $$1 \cdot e^{2x} + x\cdot e^{2x}\cdot 2$$ and you have just [point at their work] $$e^x$$?
Student: So what?
...[15 more minutes of Abbott & Costello]
...I give up and just give them the answer to escape from this nightmare. Other students are waiting for help.
I have noticed that this student wears a medical bracelet, and there's a few other behaviors as well---things like no sense of personal space, bad personal hygiene, a pronounced facial tic, not looking at me when I'm talking (or looking at anything I'm writing down), etc.
So my question is, in my best Edward James Olmos meets Eric Cartman,
## How do I reach [this] kid?
Myself and the other tutors have come to dread any interaction with this student, and have reached the point that we more or less just give up after a minute and write down the answer in order to placate them for the next 20-30min so we can provide actual help to other students. I honestly struggle to understand how they've made it to the point in math of studying calculus, and sincerely wonder if they've just learned this behavior of being obstinate until they're given the answer. This approach is demonstrably wrong as:
• They aren't learning anything, but are getting credit for it.
• They clearly need help with basic calculus concepts, but absolutely refuse to be provided such help.
• Just giving this student the answer belittles the work of all their other classmates
• Our attempts to earnestly help this student seem to wastes everybody's time, including the other students waiting for help.
• I don't really have an answer to the actual question. However, you should probably talk to whoever runs your math lab. The student's behavior sounds quite disruptive to the other students and more rude to you than you should be expected to take. – Adam Mar 15 '17 at 0:10
• However, as a partial, qualified, "I'm not really qualified" answer: If the student really is far along the autism spectrum, you might try to minimize the number of social cues needed to understand what you are saying. (Go for blunt as possible without actually being rude.) Also, give him a firm and explicit limit on the number of minutes you spend with him. i.e. "I have 2 min to talk to you, then I must move to another student." Set a timer and leave as soon as it goes off. – Adam Mar 15 '17 at 1:27
• What does "You're allowed to 86 students if they're disruptive" mean? – Joel Reyes Noche Mar 15 '17 at 1:47
• Sorry, American English vernacular, meaning to "eject / refuse service." en.wikipedia.org/wiki/86_(term) – erfink Mar 15 '17 at 1:53
• You're lucky to have only 1 or few people like that. I feel like everything you write in your conversation, besides the shouting part, is my routine experience in the tutoring center with a similar set up. – user2139 Mar 15 '17 at 5:39
How do I reach [this] kid?
Let me be blunt: You probably don't. This is a person who is so intransigent that you effectively need to black-tag them. A hard lesson is that you can't save everyone. At this point the priority is to make some kind of defense so you aren't overly stressed, psychologically damaged, or burnt out.
A couple personal reactions to the example interaction: I would not let any minor points slide by. Part of the job is to communicate clearly when someone does not have the adequate basics. When they said "prime of the prime" I would totally stop and ask them for the correct name. When they couldn't find the first derivative correctly, I would absolutely go no further until they had corrected that. When they said, "I know this", I would say clearly, "Let's be honest: you do not know this, because your first derivative calculation was incorrect." (Actually, I pretty much said exactly that each of the last two days.) Points like these are perfect exit spots; "I'll let you work on that and I'll come back".
You should also have the capability of refusing service if someone is rude. For me, if I'm answering a question someone has asked, and they look down at a phone-tablet-Facebook -- then I'm out, game over, the end. (Usually accompanied with an "If you're not interested in my answer, then I'm moving on to someone else..." exit).
I like the idea above of setting an explicit time limit for the interaction and possibly setting a watch or timer to enforce it (hence my "related" link in the comments above). You may need to do that uniformly with other students while the student is in the room so you're not accused of bias (unfortunately). Indeed, other students deserve your time at least as much as this one. E.g., in class I try to limit my interactions to one or two problem-resolutions per person at most (so that I can get to everyone).
On that note, be prepared for the student to complain to some higher authority. Possibly get a shared plan with the other assistants to confirm your experiences if possible. Best of all, see if you can get one faculty member to engage the student and make recommendations to you after.
I have also had (in a decade+ of teaching) maybe one single interaction where a student became completely outraged by my responding to a question by asking a follow-up question (so as to gauge where their understanding started and ended). "You're the teacher, you're supposed to answer questions, not ask them!!" and stormed out of the room. If someone doesn't even get the concept of how teaching should work as a give-and-take, then that's outside the scope of your responsibilities (or maybe anybody's) to fix. Even Socrates himself couldn't deal with that.
• Thank you for your bluntly honest answer. Since posting, my thinking has been shifting towards these lines. Amazing how much soul searching one problem student will make you do (maybe I'm a terrible instructor after all and the socratic method is BS and ...). I really appreciate the pragmatic suggestions, re timer etc – erfink Mar 16 '17 at 1:48
• And yeah..."prime of the prime" and "taking the prime" grates me to no end, almost as much as "minusing two things." Let it slide in interactions with this student, having been down that road before... – erfink Mar 16 '17 at 1:51
• Over time I've evolved more to following my instincts... if something like that really bothers you ("prime of the prime") that's likely a signal that some correction needs to happen. I trust my gut on that more and more. – Daniel R. Collins Mar 16 '17 at 2:22
• Opened a separate question on this point, matheducators.stackexchange.com/questions/12125/… – erfink Mar 16 '17 at 3:00
• "the concept of how teaching should work as a give-and-take" I really like your characterization. I understand it as it is impossible to teach a person to think if that person does not try to think on their own. This is how teaching is different from other types of service: it requires effort from the client. – beroal Apr 11 '17 at 8:30
This is a student who doesn't understand social cues. He only knows that if he is rude you keep trying. If acts disruptive, he will get the answer without working for it. As long as you reward him for being difficult by giving him the answer, he'll have no motivation to change behavior. You are essentially letting him walk all over you because you want to help and don't know how.
I suggest that before you can reach him, you have to teach him to behave. Make a plan with the other tutors. Sit him down with at least two tutors and tell him before you can help him, there are new rules for him to follow because he has been rude and disruptive. Explain what is acceptable behavior, e.g. no Facebook while talking to you, no shouting, etc. Tell him the consequences of not following the behavior - eg the tutor will walk away and help another student if he looks at Facebook, he will be asked to leave if he shouts. Make sure he understands that he can come back when he behaves. If you and the other tutors stick to this plan he will start to behave differently and then you can try to reach him.
• I don't disagree with the underlying advice, which would be appropriate for any disruptive student no matter the reason, but I don't think it's appropriate to compare an (allegedly) autistic adult to a toddler. – Henry Towsner Mar 15 '17 at 14:44
• I certainly didn't mean to offend. I will take out the last sentence so as not to offend anyone. I only put it in because the behavior reminds me of my granddaughter when she was a toddler and didn't get her way. – Amy B Mar 15 '17 at 15:33
• @HenryTowsner edited post and wrote the above comment in response to your comment. Forgot to alert you with your name. – Amy B Mar 16 '17 at 9:30
There are both intellectual and interpersonal issues here. It seems that, in an effort to be professional, you have ignored the interpersonal issues and have tried to focus only on the intellectual ones in the things you say to this student. This has not worked.
Don't try to diagnose the student. He could have autism, he could have ADD, he could have some other invisible disability, or he could just be a person with an unpleasant personality. Instead, just discuss his behavior with him explicitly, using language that you won't feel bad about afterward if you find out he did have a disability.
"Fred, I've been using social cues to let you know that there is a problem with your behavior, but it seems like you haven't understood those cues, so I'm going to be more explicit now."
Go on and tell him what the behaviors are and how he needs to change them. No shouting, no facebook, etc.
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2021-02-27 07:47:34
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http://www.fiz-ix.com/2012/05/eps-figures-latex/
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by
# How to Typeset EPS Figures in LaTeX
The extension EPS stands for Encapsulated PostScript and is my favorite filetype for graphics and figures I produce using applications like Illustrator, Inkscape, and MATLAB. Here is how to insert EPS figures into a LaTex document. First you have to use the graphicx package so insert the following after the \documentclass tag and before the \begin{document} tag.
\usepackage{graphicx}
Next save your EPS graphic to a known location in the folder or subfolder where your .tex file resides. Then, insert the following code where you want your figure to appear in your compiled document.
\begin{figure}[thbp]
\begin{center}
\includegraphics[angle=0,width=5in]{pathToFigure/figureName.eps}
\end{center}
\caption{insert a figure caption here}
\label{figureReferenceLabel}
\end{figure}
In the above code the [thbp] arguments specify your order of preference for where you want the figure to be displayed, top of the page (t), in between the text where the code above was inserted (h, which stands for here), at the bottom of the page (b), or where ever it is possible (p). The angle argument can be used to rotate the figure (angle=90 would rotate the figure 90 degrees counterclockwise while angle=-90 would rotate the figure 90 degrees clockwise). The rest of the code should be self explanatory.
Thats it; just make sure you compile using TeX and Ghostscript (if you are using TexShop on Mac OS X) instead of Pdftex because Pdftex does not handle EPS graphics. You would have to first convert your EPS to a PDF or JPG in order to compile using Pdftex. This is relatively easy to do using Preview on Mac OS X.
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2017-06-25 01:53:02
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https://www.gradesaver.com/textbooks/science/chemistry/chemistry-and-chemical-reactivity-9th-edition/chapter-5-principles-of-chemical-reactivity-energy-and-chemical-reactions-study-questions-page-217a/33
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## Chemistry and Chemical Reactivity (9th Edition)
The reaction is exothermic because the enthalpy change of reaction is negative. $1.25\ g\div 30.00\ g/mol=0.0417\ mol\ NO$ From stoichiometry: $0.0208\ mol\ O_2$ Enthalpy change: $-114.1\ kJ/mol\times 0.0208\ mol=-2.38\ kJ$
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2020-02-18 12:52:49
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https://www.qalaxia.com/questions/Calc-one-logarithmic-differentiation-problem
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D
#### Calc one logarithmic differentiation problem
14 viewed last edited 1 year ago
Timothy Lee
0
Hey everyone i have a problem i cant seem to figure out and would really apreciate some help the problem is "differentiate y=x^(ln 5x)" i keep getting (5/6x+ln5x+lnx)x^(ln 5x), but the online calculator i have been using is giving me a different answer any help would be greatly apreciated
Krishna
0
Given y = x^{(\ln 5x)} Apply the "ln" on both the sides \ln y = \ln x^{(\ln 5x)} \ln y = \ln (5x) * \ln x Differentiate with respect to x \frac{1}{ y} = \frac{1}{x} \ln (5x) + \frac{1}{5x} *5 *\ln x y' = y (\frac{\ln (5x)}{x} + \frac{5*\ln x}{5x}) y' = x^{\ln 5x} (\frac{\ln (5x)}{x} + \frac{5*\ln x}{5x}) y' = x^{\ln 5x} \frac{1}{x}(\ln (5x) + \ln x) y' = x^{\ln 5x - 1}*(\ln (5x) + \ln x)
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2019-02-17 21:11:10
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https://uclalemur.com/blog/dxf-processing-for-roco-shape-detection-and-easier-fabrication
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03 Jul
#### DXF processing for RoCo- shape detection and easier fabrication
We are trying to solve the problem that "Do auto-rounting based on dxf file". Two approches were came up with during the research:
• Approaches:
• A. convert SVG/DXF file to schematic/board design of PCB. Use KiCAD or EAGLE to do auto routing.
• B. develop algorithm on auto routing for single layer svg/dxf file. (path finding problem)
We are currently working on approach B, which in detail may request script(s) to have following function:
• Potential needed functions of packages
• A package draws on DXF file through script
• A script that pulls out pins' coordinate on paper chassis
• Or a image process package (OpenCV) that reads pins' coordinate on paper chassis
• A package solves multi-node path finding problem*
• Following tasks can be completed by running the code:
• Layers can be cut separately by toggling visibility
• Set cuts with same intensity and feedrate on same layer
• Able to detect pin center coordinate
• Able to draw arbitrary shape around the pin center
Detecting microcontroller pin center allows the pathfinding package to locate start and end point. It also helps building the circuit. Putting different cuts on separate layers is making the fabrication process easier.
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2020-08-13 23:05:22
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https://math.stackexchange.com/questions/2788392/fundamental-limit-to-accuracy
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# Fundamental limit to accuracy
In any real experiment, Eventhough we conduct experiment with utmost accuracy some random errors are bound to occur.
$$P\left(x\right)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{\left(x-x_0\right)^2}{2\sigma^2}}$$
This is the Gaussian distribution which defines the probability of getting $x$ in any experiment with mean $x_0$ and standard deviation $\sigma$.
Considering this we get that,
$$P\left(x_0\right)=\frac{1}{\sigma\sqrt{2\pi}}$$
since this is probalility then $P(x_0)\le1$ or,
$$\sigma \ge \frac{1}{\sqrt{2\pi}}$$
What this means is that however nicely an experiment is done the $\sigma$ can never be less than $\frac{1}{\sqrt{2\pi}}$
So is there a fundamental limit to accuracy or I have been wrong in this derivation?
• the probability of getting any single value x is always zero for any continuous distribution. Note that $p(x_0)$ is the density function at $x_0$ and is not the probability $P[x = \{x_0\}]$ – user144410 May 20 '18 at 8:25
• Your expression is a probability density function for a continuous random variable. Pointwise probability is always zero; you have to specify an interval to talk about probability – daruma May 20 '18 at 8:25
• $\sigma$ is just a parameter which we're free to choose (well, in reality it's determined by whatever source of randomness you're investigating, but mathematically it's just a parameter). You can't possibly bound it below like that, it can be any positive real number. This is a bit like saying "Let $R$ be a rectangle of width $w$ and height $h$" and then proving that $w>\frac 12$ or something. – Jack M May 20 '18 at 8:34
• You might be interested in the topic of error analysis as discussed, for example, in the book "An Introduction to Error Analysis" by John R. Taylor. – awkward May 20 '18 at 12:22
$P(x)$ is not the probability of getting $x.$ The probability of getting $x$ is zero for any real number. (How would we even know whether we got $x$ or not in a real experiment? It's not like our instruments ever output an infinite number of digits).
$P(x)$ is a probability density function. What it tells you is that for an interval $[a,b],$ the probability that $x$ lies in $[a,b]$ is $$\int_a^bP(x)dx.$$
As $P(x)$ is not a probability, there is no particular reason it needs to be less than one. In fact, you can see it actually has units of $1/x,$ so it doesn't even make sense to think about its relationship to $1.$
In principle, $\sigma$ can be anything (it also has units of $x$ so it would make no sense for it to be bounded by a dimensionless number). $\sigma$ is just the precision of the measurement. It's possible there's a fundamental limit on this (for physics reasons) but there's no limit set by probability theory.
• @Dr.Math Yeah, but that doesn't imply $P(x)<1.$ What if $b-a = 0.001$ and $P(x) \approx 100$ on that interval? Then the probability of being in the interval is $\int_a^b P(x)dx \approx 0.1,$ which is totally fine. But $P(x)$ is much greater than one. (Also, again, my point about units. What does $P(x)$ greater than one even mean?) – spaceisdarkgreen May 20 '18 at 8:30
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2019-05-21 02:37:04
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http://physics.aps.org/articles/v7/8
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# Focus: Protein Physics of Pruney Skin
Published January 24, 2014 | Physics 7, 8 (2014) | DOI: 10.1103/Physics.7.8
#### Shaping the Skin: The Interplay of Mesoscale Geometry and Corneocyte Swelling
Myfanwy E. Evans and Roland Roth
Published January 24, 2014
M. Evans/Univ. of Erlangen
The tightly packed keratin structure expands as it absorbs water and contracts as it dries out.
Your skin soaks up water when you bathe, which may partially explain wrinkly fingers. This absorbent property of skin may stem from the unique packing of protein filaments in skin cells, and now two theorists have developed a complete thermodynamic model for the hydration and expansion process, as they report in Physical Review Letters. This reversible process harnesses a balance between filament expansion induced by excess water and contraction driven by a springlike tension as the filaments are stretched, the researchers found. The model’s predictions agree with experimental data, and the findings could help researchers better understand how skin diseases work and help them devise durable or water-absorbent materials.
Skin has the remarkable ability to absorb water, increasing its volume substantially and then reverse the process as it dries, without any ill effects. This property serves several functions, one of which is to regulate the level of hydration inside the body. The swelling and absorption of water occur in the outermost skin layer, which is made of dead cells called corneocytes that are stacked in layers like bricks. Corneocytes are filled with a stiff network of filaments made of a form of the protein keratin. In 2011, Myfanwy Evans, then a graduate student at the Australian National University (ANU) in Canberra, working with ANU’s Stephen Hyde, used geometric modeling to propose a structure for these filaments (the so-called sigma-rod packing). In the model, each filament is a long helix pointing in one of four directions in space, and they interpenetrate to form an orderly, three-dimensional lattice. This structure could increase its volume by five times when the helices stretch out [1].
Evans, now at the University of Erlangen, and Roland Roth of the University of Tübingen, both in Germany, have now taken the next step—confirming that the structure actually could help skin cells swell and shrink and learning how the process might work. They developed a thermodynamic model that describes how the system’s energy varies as the network’s spacing and helices’ sizes change. The researchers first calculated the filaments’ solvation free energy—essentially, the system’s willingness to absorb water—as the helices stretch and found that this energy decreases, meaning that the structure is inclined to expand and absorb water.
But some other force must eventually act in opposition to reverse the system’s expansion, Evans and Roth reasoned, since the process reverses easily in real cells. Inspired by previous filament elasticity measurements [2], they realized that the tension in a stretched filament could provide the counteracting force. As with a spring, the more you stretch a filament, the larger the elastic energy. The researchers calculated this energy and added it to the solvation free energy to get the total mechanical energy associated with expansion and contraction.
The team then produced a sort of energy “landscape,” a surface whose height represented energy and whose two horizontal coordinates were the helix spacing (or lattice size) and the helix radius. They identified a range of values where the energy was at or near its minimum, and this “energy valley” turned out to be roughly trough-shaped. Evans and Roth propose that as the filament structure swells and shrinks, it always remains within this valley as it moves between the two extreme states at opposite ends of the trough. The researchers conclude that the keratin filaments’ geometry must be crucial to skin’s response to water because it keeps the system in an energy range that enables but also curbs expansion. The team also predicted the fraction of the volume occupied by keratin (as opposed to empty space or water) at the two extremes and found that it went from $11%$ to $38%$, close to the range of $15$$35%$ that Evans and Hyde had calculated from experimental data.
This “pioneering work” yields valuable insight into skin function at intermediate scales, between macroscopic and molecular, says Lars Norlén of the Karolinska Institute in Stockholm. He says researchers need this so-called mesoscale information to understand the mechanisms of, and thus devise new treatments for, dermatitis and other skin diseases involving abnormal skin moisture. Researchers could also create cloths or durable building materials that exploit skin’s mesoscale properties, he says.
–Puneet Kollipara
Puneet Kollipara is a freelance science writer in Washington, DC.
### References
1. M. E. Evans and S. T. Hyde, “From Three-Dimensional Weavings to Swollen Corneocytes,” J. R. Soc., Interface 8, 1274 (2011).
2. D. S. Fudge, T. Winegard, R.H. Ewoldt, D. Beriault, L. Szewciw, and G.H. McKinley, “From Ultra-Soft Slime to Hard α-Keratins: The Many Lives of Intermediate Filaments,” Integr. Comp. Biol. 49, 32 (2009).
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2014-12-23 03:45:55
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https://mathoverflow.net/questions/362600/does-a-flat-compactification-always-exist
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Does a flat compactification always exist?
Let $$\pi:X\to S$$ be a separated flat morphism of finite type of Noetherian schemes. Does $$\pi$$ necessarily factor as an open immersion followed by a proper flat morphism? The analogue of this question with the word "flat" replaced by "smooth" has a negative answer (consider an elliptic curve over $$\mathbb{Q}_p$$ that has bad reduction).
This already fails if $$S$$ is regular of dimension $$3$$ and $$\pi$$ is quasi-finite. Indeed, let $$X$$ be a normal affine variety over $$\mathbf C$$ of dimension $$3$$ with an isolated non-Cohen–Macaulay singularity (e.g. an affine cone over a smooth projective surface $$Y$$ with $$H^1(Y,\mathcal O_Y) \neq 0$$). By Noether normalisation, there exists a finite surjection $$\pi \colon X \to S = \mathbf A^3,$$ without loss of generality taking the isolated singularity $$x_0 \in X$$ to the origin $$0 \in \mathbf A^3$$. Let $$U = X \setminus x_0$$, which is smooth by assumption, so $$\pi|_U$$ is flat by miracle flatness. Now I claim that $$\pi|_U \colon U \to \mathbf A^3$$ does not have a flat compactification.
Indeed, suppose $$U \hookrightarrow X' \stackrel{\pi'}\to S$$ is a factorisation into an open immersion and a proper flat morphism. Because $$\pi'$$ is flat and generically finite, it is quasi-finite, hence finite since it is proper. Since $$\pi'$$ is finite flat and $$S$$ is regular, we conclude that $$X'$$ is Cohen–Macaulay.
Let $$\bar U \subseteq X'$$ be the scheme-theoretic closure of $$U$$, and let $$V = S \setminus 0$$. Since $$\pi^{-1}(V) \subseteq U$$, we conclude that $$\bar U \setminus U$$ is supported on $$\pi'^{-1}(0)$$, in particular has dimension $$0$$. By Hartshorne's connectedness theorem, this implies that there are no other components in $$X'$$ (otherwise two components would meet only in a $$0$$-dimensional set), i.e. $$\bar U = X'$$ set-theoretically. Since $$X'$$ is generically reduced and Cohen–Macaulay, it is reduced, so $$\bar U = X'$$ scheme-theoretically.
In particular, $$X' \setminus U$$ is $$0$$-dimensional, so $$X'$$ is regular in codimension $$1$$ since the same holds for $$U$$. Since $$X'$$ is Cohen–Macaulay, this forces $$X'$$ normal, so it equals the normalisation of $$S$$ in $$K(U)$$, which is $$X$$. But $$X$$ is not Cohen–Macaulay, contradicting flatness of $$\pi'$$. $$\square$$
• is it true is $S$ is regular of Krull dimension 2? – user158636 Jun 12 '20 at 8:03
• Hmm, there is a positive result in the quasi-finite case if $S$ is regular of dimension $2$ and $X$ is normal. Because then you can take the normalisation, which is Cohen–Macaulay (this uses dimension $2$), hence flat. I'm not sure what happens if $X$ is not normal, or if $\pi$ is not quasi-finite. A thing to try is the projectivisation of a vector bundle (e.g. of rank $2$) that does not extend, but it's hard to get a grip on the possible compactifications (which is why I restricted to the quasi-finite case). – R. van Dobben de Bruyn Jun 12 '20 at 19:35
• Of course if $S$ is regular of dimension $1$ the result is positive (for arbitrary $\pi$): in this case flat just means torsion free, which can be arranged by taking the scheme-theoretic closure of $X$ in an arbitrary compactification. – R. van Dobben de Bruyn Jun 12 '20 at 19:47
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2021-05-18 16:27:15
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https://www.pololu.com/blog/comment?user=a66c8f4
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• Understanding battery capacity: Ah is not A
- 23 August 2019
Hi.
It's difficult if you cannot do any math. You could try that pack you're talking about, and if it doesn't last long enough, get a higher capacity one. If it ends up lasting way longer than you need, you'll know next time that you could get a smaller one.
- Jan
• Servo control interface in detail
- 12 July 2019
Since you seem interested in the details, the speed is not "12.5 μs"; rather, it's (12.5 μs)/(10 ms). To see how much the position changes from one time to anther, multiply speed by time: in 20 ms, the position will change by 20 ms * (12.5 μs)/(10 ms) = 25μs. Kind of like if you have a car that is going 65 MPH, and you check its position two hours after an initial check, it should be 130 miles farther. That you happen to check 2 hours apart doesn't make 65 MPH stop being a useful measure.
Your seeing that some descriptions say D and others D/2 gives us good indication that the term is not particularly well defined, or that it gets used sloppily, so there's not much point in having a "correct" definition since you still need to determine what the source using it means. I think deadband of D should be the whole region of no response, which therefore means some target plus or minus D/2.
Servos are usually not going to just have proportional control. You can take a look at our Jrk motor controllers if you want to look more into what might go into a servo:
https://www.pololu.com/category/95/pololu-jrk-motor-controllers-with-feedback
- Jan
• Servo control interface in detail
- 9 July 2019
Hello.
I think you can gradually increase the pulse rate to the servo while moving it around, and if it behaves normally, it will probably be fine. Be ready to cut power if it tries to go past its physical limits (end stops).
The Micro Maestro does its internal position update math every 10 ms independent of the pulse rate. That keeps the positions sent to the servos over time the same even if you change the pulse rate. You seem to be focusing on the servo side (and how it can only get an update once per period T); the point is that the servo controller only tells the servo what to do once per T, and the rest of the time, it's getting ready to tell the servo the right thing at the right time. Think of a clock with a second hand that ticks every second: it's updating the time it's telling you once per second, even though internally there could be gears and pendulums and other things moving between the times when the second hand is moving. The details of what it's doing internally to give you the correct updates are going to vary from clock to clock.
- Jan
• Understanding battery capacity: Ah is not A
- 2 July 2019
Jim,
Battery voltages always fluctuate as they discharge, so you definitely don't need "the exact same numbers". Also, an AC power adapter does not have to connect to exactly the same point in the circuit as the batteries, so you shouldn't put too much stock in the power adapter specs for the purposes of battery selection. But in this case, the numbers match up since four AA alkaline batteries in series will give you 6V.
I don't know what you mean by "they worked once" and what the relevance of that is. Does it mean that they don't work anymore, even after charging? In any case, alkaline batteries have a little higher voltage than NiMH batteries, 1.5V nominal vs 1.2V nominal, so four of those in series gets you to 6.0V vs. 4.8 V, so some devices don't work very well or very long if they really need the higher voltage. A charged NiMH cell might actually get to about 1.4V, so it looks a little like a somewhat discharged alkaline right off the bat.
- Jan
• Understanding battery capacity: Ah is not A
- 28 June 2019
Hi, Jimmy.
I think that depends too much on the details of the particular batteries and what exactly they've been through. Age-wise, those 4 months don't seem like too much of a difference, and 65 cycles also doesn't seem like that much, so my guess is you'll get more life out of the 2.0 Ah battery.
- Jan
• Understanding battery capacity: Ah is not A
- 26 June 2019
Hi, Maxwell.
Since we are talking about batteries and DC power, a transformer (which is for AC power) is not quite the right term; something like DC-to-DC converter is more appropriate. In your case, we are talking about just reducing the input voltage, so you could use a switching step-down regulator that can be around 90% efficient. Having double the voltage with the same amp-hour capacity means double your energy, so as long as your conversion to the lower voltage is more than 50% efficient, you will get more run time with the higher voltage. However, your battery will be twice as large, so you could probably just get a 11.1V battery with 12000mAh in the same size as the 22.2V 6000mAh one, and then you don't have to bother with the voltage conversion at all and get double your run time.
- Jan
• Understanding battery capacity: Ah is not A
- 29 April 2019
Mark,
I expect the maximum allowed current to remain the same whether you have multiple batteries in series or not. One battery cannot tell if there is another battery somewhere else in the circuit; all it has is the voltage across it, which would still be 6V, and the current flowing out of it (or in, if you're charging it).
- Jan
• Understanding battery capacity: Ah is not A
- 14 March 2019
Hello.
The "225 AMPS" might be sloppy labeling, but it might also be the maximum recommended current the battery can supply, or even an outright scam, so I would not go with that option if that is really what it says. C/100 vs C/20 is probably about discharging in 100 hours vs 20 hours, so using the 20 hour value is probably a better estimate for you. Given all of your confusion, I would be worried about your 588 Ah requirement calculation, but if it's correct, three of the 190 Ah batteries would almost cover you, so 4 might be enough. Going to 6 because of your 50% discharge guideline would give you more room for error, though that 50% rule might also vary with battery type. This is again assuming you need 588 Ah at 6V, in which case you'd put all the 6V batteries in parallel.
I don't know your time and cost constraints, but you could start with a smaller quantity and just test it. And if you need more run time, add some more batteries.
- Jan
• Understanding battery capacity: Ah is not A
- 1 March 2019
Hi, Keiran.
No, you cannot trade off the voltage for current in your jack. That 1A rating is going to come from things like how much the contacts or some other parts the current goes through heats up, so if you put 3x more current through, it's going to heat up possibly 9x faster (for a fixed resistance, power goes with current squared). 1A sounds low for a power jack, by the way, so it's possible it's a really cheap unit or they're being really conservative with the rating.
Separately, you should also not connect the AC adapter straight to your battery and expect it to act as a charger. Best case, nothing will happen (i.e. you also won't charge your battery); quite possibly, you'll also break something.
- Jan
• Understanding battery capacity: Ah is not A
- 19 February 2019
Hi.
The 12V to 5V conversion should get you longer battery life as long as your converter is not really inefficient. With a 100% efficient conversion, you would get 12/5 times that seven hours, or 16.8 hours. Getting at least 85% efficiency should not be too difficult, and that's what you need to multiply your final answer by, so 14 hours should not be too difficult. Getting 15 hours would require 90% efficiency, and that is still pretty realistic.
- Jan
(702) 262-6648
Same-day shipping, worldwide
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2019-09-23 02:11:06
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http://mathhelpforum.com/calculus/213564-max-min.html
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# Thread: max and min
1. ## max and min
Find the critical point(s) of f(x, y)=sinx+siny+cos(x+y) for 0≤x≤pi/4 and 0≤y≤pi/4. classify each as local max, min or saddle point?
I know the min is 1, but how do you find the max?
2. ## Re: max and min
It is pretty easy to show that there is NO point in the interior of $0\le x \le \pi/4$ and $0\le y\le \pi/4$ where grad f is 0 so any max and min must on the boundary. One boundary is the line x= 0: on that line f(0, y)= sin(y)+ cos(y). Is there any place on that line where f_y(0, y)= 0. Another is the line $x= \pi/4$: on that line $f(\pi/4, y)= \sqrt{2}/2+ sin y+ cos(\pi/4+ y)$. Is there any place on that line where $f_y(\pi/4, y)= 0$? Of course the same thing applies to the lines $y= 0$ and $y= \pi/4$. Any you need to check the values at the corners: $f(0, 0)= 1$, $f(\pi/4, 0)= \sqrt{2}$, $f(0, \pi/4)= \sqrt{2}$, $f(\pi/4, \pi/4)= \sqrt{2}$.
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2017-06-25 17:34:30
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https://quantumcomputing.stackexchange.com/questions/21923/period-of-phase-leads-the-advantage-of-heisenbergs-limit-disappear/21927
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In Quantum Metrology, the aim is to estimate some unknown parameters(I will talk about one parameter estimation in this post, while multiparameter is also available) as precise as possible. Without quantum resources, we can only realize the Standard Quantum Limit(SQL), normally referred to as the form $$var(\hat{\theta})=1/n$$, where $$\hat{\theta}$$ is the estimator(function of random variables to estimate the unknown parameter $$\theta$$) and $$n$$ is the number of experiments. While with quantum resources, we may reach the so-called Heisenberg's Limit, normally referred to as the form $$var(\hat{\theta})=1/n^2$$, a square enhancement in the precision. Here is an frequently used state example, stated that the GHZ state $$1/\sqrt{2}(|0\rangle^{\otimes n}+|1\rangle^{\otimes n})$$ after the evolution described by the unitary operator $$U = e^{-i\theta\sigma_z/2}\otimes e^{-i\theta\sigma_z/2}\otimes...$$ will become $$1/\sqrt{2}(|0\rangle^{\otimes n}+e^{in\theta}|1\rangle^{\otimes n})\tag{1}$$ ignoring the global phase. And we can estimate the value of the parameter by measuring this parameterized quantum state.
My question is, the HL will show its advantage only when the scale is $$1/n^2$$, while from eq.(1), we can easily see that there's a $$2\pi$$ period in an exponential function, no matter how small $$\theta$$ is, we cannot always enhance our precision by HL scale when $$n$$ pass some specific value. So, how to understand this paradox, did I miss something?
You are correct, but the SQL is a local limit, when you already have a very good idea what the value of $$\theta$$ is, so there is no contradiction.
Let's work through it. You measure some relative phase $$\Theta$$, and you infer that $$\Theta=n\theta+2\pi k,\quad k\in \mathbb{N}.$$ You work out that $$\theta=\frac{\Theta +2\pi k}{n},$$ where $$\Theta$$ and $$n$$ are known ($$n$$ is known because you set up your experiment) and $$k$$ is unknown. You now must determine what values of $$k$$ are possible, then you are finished.
Because the SQL is local, we know a priori that $$\theta_{\text{low}}\leq \theta\leq \theta_{\text{high}}$$ for some values of $$\theta_{\text{low}}$$ and $$\theta_{\text{high}}$$, so we deduce that $$\frac{n\theta_{\text{low}}-\Theta}{2\pi}\leq k\leq \frac{n\theta_{\text{high}}-\Theta}{2\pi}.$$ So as long as our initial knowledge has sufficiently small $$\theta_{\text{high}}-\theta_{\text{low}}$$, there will only be one possible value of $$k$$, and we will fully determine the value of $$\theta$$. If our initial knowledge is not precise enough, you are correct that using too large a value of $$n$$ will yield multiple possible results.
• @narip I mean exactly what I said, that the possible values of $\theta$ are restricted to a small region around the "true" value of $\theta$. See e.g. doi.org/10.1007/s00220-019-03433-4. This is why the SQL is an asymptotic limit, as you can only achieve that precision in the limit of doing lots of measurements. Nov 15 '21 at 15:05
• One more thing, why it's $2k\pi$ instead of $k\pi$? E.g. for states $\frac{1}{\sqrt{2}}\left( |0\rangle +e^{i\theta}|1\rangle \right)$, if we measure $\langle \sigma _x\rangle$ to get $\cos\theta$, and the value of $\theta\in[0,\pi]$ will be the same as $\theta\in[\pi,2\pi]$, which makes us unable to distinguish $\theta$ is in $[0,\pi]$ or in $[\pi,2\pi]$. Dec 8 '21 at 9:14
• Okay, $\langle \sigma_y \rangle= \sin\theta$, combine this will be enough to tell which $\theta$ is. Cheers. Dec 8 '21 at 9:23
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2022-01-25 17:08:13
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https://chemistry.stackexchange.com/questions/64017/why-are-free-radicals-so-reactive?noredirect=1
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# Why are free radicals so reactive?
Why are free radicals are so reactive? They can break almost any bond, including $\ce{C-H}$ bonds, which are fairly stable. Don’t they have an activation energy or something? Do they not also experience steric effects when colliding with reactants ?
• They do experience steric effects. – Jan Dec 6 '16 at 23:46
• – Klaus-Dieter Warzecha Dec 7 '16 at 5:53
This being said, some radicals do have an activation energy, and some don't. The $E_a$ is essentially zero for all hydrogen atom abstractions by fluorine atom, and the free energy barrier arises solely from the pre-exponential factor of the Arrhenius equation ($k=Ae^{-E_{a}/(RT)}$), which is near 13 for the halogenations listed below.
The activation energies for abstraction by chlorine atoms are also exceedingly small, but there is a slight preference for more highly substituted $\ce{C-H}$ bonds. Lastly, the activation energies for abstraction by bromine atoms are substantial, clearly showing a preference for abstraction of 3°, 2°, and 1° $\ce{C-H}$ bonds in that order. It is because of these differences in activation energies that we observe the varying regioselectivities of the different halogenation reactions$^{[1]}$.
$[1]$ Anslyn, E. V.; Dougherty, D. A. Modern Physical Organic Chemistry; University Science: Sausalito, CA, 2006.
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2019-07-16 04:53:32
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https://math.stackexchange.com/questions/1649039/how-many-solutions-for-an-equation-with-simple-restrictions
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# How many solutions for an equation with simple restrictions
I'm working on an assignment in which I have to count the number of solutions for this particular equation: $$x_1+x_2+x_3+x_4=20$$for non negative integers with $x_1<8$ and $x_2<6$
I'm aware that this kind of a task isn't that complicated, but I don't get combinatorics in general that well.
So I've tried two following approaches to get this done.
Firstly I tried to substitute the variable x:
$x_1+x_2+x_3+x_4=20 \Leftrightarrow y_1+y_2+y_3+y_4=34$
in which $y_1=x_1+8$ and $y_2=x_2+6$ (casue $x_1=y_1-8$ and $x_2=y_1-6$) Following this approach the total number of possible solutions would be
$${34+3 \choose 3}$$
But I'm not sure if its the right solution.
The second approach is to sum all of the possible values that $x_1$ and $x_2$ could possibly take, also $x_1=0,1,2,3,4,5,6,7$ and $x_2=0,1,2,3,4,5,6$ And then count all the possibilities for each of the variables $${20 -x_1-x_2+1\choose 1}$$ and sum them together like this: $${21\choose 1}+{20\choose 1}+{19\choose 1}+{18\choose 1}+...$$ and so on...
I'm sure I'll get the correct number with this one, but I'm not feeling like summing all of this possibilities. There's got to be a better, more elegant way to deal with this.
My professor gave me a hint that I should do it using the complement.
• Substituting $y_1=x_1+8$ means that, since $0<x_1<8$, you have the restriction $8 < y_1 < 16$, so I don't see how your substitution would help... – 5xum Feb 10 '16 at 13:10
• You could try using the inclusion-exclusion principle to reduce the problem into one that only requires counting the number of solutions to similar equations, but without the upper bounds. – Yiyuan Lee Feb 10 '16 at 13:17
To determine the number of solutions of the equation $$x_1 + x_2 + x_3 + x_4 = 20 \tag{1}$$ in the non-negative integers subject to the restrictions $x_1 < 7$ and $x_2 < 6$, we subtract the number of solutions in which $x_1 > 7$ or $x_2 > 5$ from the number of solutions of the equation.
A particular solution of equation 1 corresponds to the placement of three addition signs in a row of $20$ ones. For instance, $$1 1 1 1 + 1 1 1 1 1 + 1 1 1 1 1 1 + 1 1 1 1 1$$ corresponds to the solution $x_1 = 4$, $x_2 = 5$, $x_3 = 6$, and $x_4 = 5$, while $$+ 1 1 1 1 1 1 1 1 1 + 1 1 1 1 1 1 1 + 1 1 1 1$$ corresponds to the solution $x_1 = 0$, $x_2 = 9$, $x_3 = 7$, and $x_4 = 4$. Thus, the number of solutions of equation 1 is the number of ways three addition signs can be inserted into a row of $20$ ones, which is $$\binom{20 + 3}{3}$$ since we must choose which three of the $23$ symbols ($20$ ones and $3$ addition signs) will be addition signs.
Suppose $x_1 > 7$. Then $y_1 = x_1 - 8$ is a non-negative integer. Substituting $y_1 + 8$ for $x_1$ in equation 1 yields \begin{align*} y_1 + 8 + x_2 + x_3 + x_4 & = 20\\ y_1 + x_2 + x_3 + x_4 & = 12 \tag{2} \end{align*} Equation 2 is an equation in the non-negative integers with
$$\binom{12 + 3}{3} = \binom{15}{3}$$
solutions.
Suppose $x_2 > 5$. Then $y_2 = x_2 - 6$ is a non-negative integer. Substituting $y_2 + 6$ for $x_2$ in equation 1 yields \begin{align*} x_1 + y_2 + 6 + x_3 + x_4 & = 20\\ x_1 + y_2 + x_3 + x_4 & = 14 \tag{3} \end{align*} Equation 3 is an equation in the non-negative integers with
$$\binom{14 + 3}{3} = \binom{17}{3}$$
solutions.
If we subtract the number of solutions of equation 2 and equation 3 from the number of solutions of equation 1, we will have subtracted those solutions in which $x_1 > 7$ and $x_2 > 5$ twice. Thus, we must add the number of solutions in which $x_1 > 7$ and $x_2 > 5$.
Suppose $x_1 > 7$ and $x_2 > 5$. Then $y_1 = x_1 - 8$ and $y_2 = x_2 - 6$ are non-negative integers. Substituting $y_1 + 8$ for $x_1$ and $y_2 + 6$ for $x_2$ in equation 1 yields \begin{align*} y_1 + 8 + y_2 + 6 + x_3 + x_4 & = 20\\ y_1 + y_2 + x_3 + x_4 & = 6 \tag{4} \end{align*} Equation 4 is an equation in the non-negative integers with
$$\binom{6 + 3}{3} = \binom{9}{3}$$
solutions.
By the Inclusion-Exclusion Principle, the number of solutions of equation 1 in the non-negative integers subject to the restrictions that $x_1 < 7$ and $x_2 < 6$ is
$$\binom{23}{3} - \binom{15}{3} - \binom{17}{3} + \binom{9}{3}$$
• How is it equation (3) has more solutions, $680$, than equation (2), $455$? Shouldn't applying another constraint reduce the number of solutions? – Eric Towers Feb 10 '16 at 17:56
• @EricTowers I applied the constraints $x_1 < 7$ and $x_2 < 5$ separately. There are fewer solutions with $x_1 \geq 8$ (equation 2) than their are solutions with $x_2 \geq 6$ (equation 3). I handled the case when both constraints were applied simultaneously in equation 4, which is why it has fewer solutions than either equation 2 or equation 3. – N. F. Taussig Feb 10 '16 at 19:40
One way of looking at it is this: The number of ways is just the coefficient of $x^{20}$ in the expansion of $$(1+x+x^2+\cdots+x^7)(1+x+x^2+\cdots+x^5)(1+x+x^2+\cdots+x^{20})^{2}$$
Here, each factor represents a term in your equation (here I have written them in the same order). The powers of $x$ in the factor are the values the corresponding variable can take. I limited the last two factors to a maximum power of $20$ as all the terms are non negative.
Now, the logic behind this is that when you multiply two powers of $x$, the powers add up. The coefficient of $x^{20}$ gives the number of ways you could have multiplied various powers from each factor to get a total power of $20$. Notice that each combination of powers from each factor contributes to an increase of one in the coefficient and also represents a unique solution to your equation. Thus, the coefficient of $x^{20}$ in the binomial expansion gives the desired answer.
Each factor can be simplified by using the formulae for the sum of terms in a geometric progression. Then, the $(1-x)^{-n}$ terms can be expanded using the binomial expansion, after which the coefficient can be found easily.
$$(1+x+x^2+\cdots+x^7)(1+x+x^2+\cdots+x^5)(1+x+x^2+\cdots+x^{20})^{2}=\frac{(1-x^8)(1-x^6)(1-x^{21})^2}{(1-x)^4}$$
So, you need to find the coefficient of $x^{20}$ in the expansion of $$(1-x^8)(1-x^6)(1-x)^{-4}$$ The $(1-x^{21})^2$ term can be ignored, as terms with coefficient higher than $20$ are not of any concern. $$(1-x^8)(1-x^6)(1-x)^{-4}=(1-x^6-x^8+x^{14})(1+4x+10x^2+20x^3+\cdots+84x^{6}+\cdots+455x^{12}+\cdots+680x^{14}+\cdots+1771x^{20}+\cdots+\binom{n+3}{n}x^n+\cdots)$$ The coefficient is thus: $$1771-455-680+84=720$$
• It would be good to include some suggestions as to how to efficiently compute the relevant coefficient. – Yiyuan Lee Feb 10 '16 at 13:16
• It's also much easier if you don't stop at $20$ for the other terms... – Thomas Andrews Feb 10 '16 at 13:42
• I'm always amused at how this approach magically matches the inclusion-exclusion. The expansion of $(1-x^8)(1-x^6)$ is of that inclusion-exclusion form, and the coefficients of $(1-x)^{-4}$ count the "unrestricted solutions" to the original equation. – Thomas Andrews Feb 10 '16 at 13:47
• I found this solution quite beautiful. Several enlightened steps ... Starting with reinterpreting a number theoretic question into a question of binomial theorem. Multiplying and dividing by a factor to convert a series of terms to just two terms using GP, making a product of four terms to a simple product of two. Well, done. – user230452 Feb 10 '16 at 23:49
• @user230452 The expansion of $(1-x)^{-n}$ is $1+nx+\frac{n(n+1)}{2!}x^2+\cdots$. It could be observed that the coefficient of $x^n$ followed a pattern: it is given by $\binom{n+3}{n}$ – GoodDeeds Feb 11 '16 at 1:56
The classic way to do this is count the solutions without conditions, then use inclusion-exclusion to deal the cases which violate.
So if $A$ is the set of all non-negative solutions to $x_1+x_2+x_3+x_4=20$, and $A_1$ is the set of such solutions with $x_1\geq 8$ and $A_2$ is the set of solutions with $x_2\geq 6$ then the set you seeking to count is $A\setminus(A_1\cup A_2)$ and:
$$\left|A\setminus(A_1\cup A_2)\right|=|A|-|A_1|-|A_2|+|A_1\cap A_2|$$
By inclusion-exclusion. Now, each of these terms is much easier to compute. For example, $A_1\cap A_2$ is the set of solutions to $x_1+x_2+x_3+x_4=20$ with $x_1\geq 8,x_2\geq 6$, which is equal to the set of non-negative solutions to $y_1+y_2+x_3+x_4=20-14=6$.
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2019-08-24 14:18:25
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https://www.degruyter.com/document/doi/10.1515/icom-2020-0021/html
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# Explaining Review-Based Recommendations: Effects of Profile Transparency, Presentation Style and User Characteristics
• Diana C. Hernandez-Bocanegra
Diana C. Hernandez-Bocanegra is a research associate and PhD student in the Department of Computer Science and Applied Cognitive Science at the University of Duisburg-Essen, and a member of the Interactive Systems Research Group. Her research interests are focused on recommender systems, explainable AI and the exploration of deep learning and NLProc techniques to improve human-computer interaction.
and Jürgen Ziegler
Jürgen Ziegler is a full professor in the Department of Computer Science and Applied Cognitive Science at the University of Duisburg-Essen where he directs the Interactive Systems Research Group. His main research interests lie in the areas of human-computer interaction, human-AI cooperation, recommender systems, information visualization, and health applications. Among other scientific functions he is currently editor-in-chief of i-com - Journal of Interactive Media and chair of the German special interest group on user-centred artificial intelligence.
From the journal i-com
## Abstract
Providing explanations based on user reviews in recommender systems (RS) may increase users’ perception of transparency or effectiveness. However, little is known about how these explanations should be presented to users, or which types of user interface components should be included in explanations, in order to increase both their comprehensibility and acceptance. To investigate such matters, we conducted two experiments and evaluated the differences in users’ perception when providing information about their own profiles, in addition to a summarized view on the opinions of other customers about the recommended hotel. Additionally, we also aimed to test the effect of different display styles (bar chart and table) on the perception of review-based explanations for recommended hotels, as well as how useful users find different explanatory interface components. Our results suggest that the perception of an RS and its explanations given profile transparency and different presentation styles, may vary depending on individual differences on user characteristics, such as decision-making styles, social awareness, or visualization familiarity.
## 1 Introduction
Providing explanations of the rationale behind a recommendation can bring several benefits to recommender systems (RS), by increasing users’ perception of transparency (the system explains how it works), effectiveness (user can make good decisions), and trust [38]. Accordingly, research on explainable RS aims to establish methods and models which allow for generating relevant recommendations to users, while providing them with the reasons why an item is recommended. In this regard, various explainable recommendation methods have been proposed, mainly based on collaborative filtering (CF) and content based (CB) methods. CF explanatory models allow to generate explanations based on relevant users or items, e. g. nearest-neighbor style explanations as proposed by Herlocker et al. [21], while CB models facilitate the generation of feature-based explanations by providing users with product features that match their preferences, as proposed, for example, by Vig et al. [44]. On the other hand, matrix factorization (MF) methods, a particular case of CF, allow to generate recommendations by obtaining latent representations of items and users (latent features), which represent a major challenge when it comes to explaining to users how the algorithm works, or why the item is recommended, compared to more intuitive neighbor-style CF or CB methods. In this respect, MF explanatory methods have been proposed [53], [46], to integrate external sources of information (e. g. user generated reviews) in order to make sense – to some extent – of latent features, for example, by aligning them with explicit features drawn from reviews. In this regard, the interest in the use of user reviews in explanation methods has increased recently, given the richness of information reported on diverse aspects, which cannot be deduced from the overall item ratings, and that could be beneficial to both recommendation and explanation processes. Particularly, review-based explanatory approaches usually involve the detection and aggregation of both positive and negative opinions regarding different aspects or features of items, the selection of helpful reviews or excerpts from them that could work as explanations, or the generation of verbal summaries of items’ evaluation by users. The above entails a potential for the generation of a diverse range of explanation types, consisting of arguments with different levels of detail, and portrayed in different presentation styles. Nevertheless, little is known about how best to convey explanatory information, in order to meet different explanatory aims like transparency, effectiveness, satisfaction or trust. This is largely due to the predominant lack of evaluation by users in works that propose new explanation methods, as noted by Nunes and Jannach [30]. In this regard, evaluating explanations from the users’ perspective can contribute to better explanation design, which can significantly impact users’ perception of a RS. Such perspective could contribute to answering questions that remain open, for example, to what extent the format or presentation style influences the perception of an explanation, or what are the components of an explanation that most contribute to its perceived usefulness.
As outlined by Nunes and Jannach [30], explanations may involve the following types of user interface components: input parameters, knowledge base (background or user knowledge), decision inference process (data or rationale of the inference method), and decision output. As for the knowledge base components, and depending on the method used to generate the recommendations, the explanations may reflect either the quality and the properties of the items or the matching between the recommended items and the users’ preferences. In regard to the latter, a target user might benefit from knowing which of her/his performed interactions with the system have an effect on a current recommendation [3], as well as knowing how well their preferences match the justifications provided by the system, which can contribute to the acceptance of its recommendations (provided that there is actually a fit) [19]. Although the effects of providing a view on user profiles in CB or item-based CF methods has been explored before (e. g. [3], [39], [18]), such effects have not been fully addressed in review-based explanations, where information on users’ profile is often omitted and used only implicitly, e. g. to filter and sort lists of relevant features, as in [28]. In consequence, we aim to address in this article the following question:
RQ1: How does including the information about user preferences influence the perception of a review-based RS and its explanations?
Specifically, information on user preferences refers – in the scope of this article – to a list of the relevant inferred aspects and their relevance score, which are also calculated based on the users’ own reviews. Additionally, the above mentioned perception is addressed in this article in regard to explanation quality, and to the perception of the overall system in terms of: transparency, effectiveness, efficiency and trust. Likewise, we address the perception of users in regard to specific aspects of the explanations, i. e.: confidence, transparency, satisfaction, persuasiveness, effectiveness, efficiency and easiness to understand of the explanations.
In regard to the interface component “decision inference process” [30], the RS may provide details on the recommendation process, or on the data used for it. In the former case, for example, CF methods favore the generation of concise reporting of recommendation process e. g. “We suggest this option because similar users liked it.”. While further algorithm details are often omitted, providing only information about the input and the output of the process might also be beneficial to users, in the case of black-box models [21]. In consequence, various explanatory methods provide information on the data used during the process, like ratings for similar items or ratings by similar users in CF models, or specifications of items in CB methods. However, when additional sources of information are taken into account, as in the case of review-based methods, users are often not informed of the type of the data utilized during the process, for example, whether the user’s preferences have been calculated exclusively based on ratings, with information extracted from reviews, or based on other previous interaction with the system. Consequently, we aimed to test to what extent providing such information explicitly is considered useful by the users, more formally:
RQ2: How useful is it for users, during their evaluation of different purchase or booking options, to be informed about the origin of the data used by a review-based recommendation process?
In particular, within the scope of this article, we address how useful it is for users to read that the recommendation is based on the opinions of other customers, as well as their own comments.
The taxonomy of explanations proposed by Nunes and Jannach [30] also involves a category for presentation format, which includes: natural language (e. g. canned text, template-based, structured language), visualization, or other media formats, such as audio. While some of the existing review-based explanatory methods apply at least one of such formats, a user-centered evaluation in which the different formats are comprehensively compared is still necessary. For example, it is not yet clear whether users have a better perception of explanations consisting of aggregate information represented in tabular data, compared to those containing a graphical representation of such information. In this regard, according to Blair [4], visual arguments – defined as a combination of visual and verbal communication – may, in addition to representing propositional content, have a greater “rhetorical power potential” than verbal arguments, due (among others) to their greater immediacy. However, users with lower visual abilities might benefit less from a presentation based on images or graphics [34], [23]. Additionally, while a representation using tables has been recommended to display small data sets [16], [43], if providing accurate numerical values of proportions is not the main objective, tables seem to be less useful than graphics as a means of displaying information [36]. Nevertheless, although the findings in such direction in the field of information visualization, little is known about such effects in relation to explanations. Consequently, we aim to address in this article the following question:
RQ3: How does the display style of explanation (using a table or a bar chart) influence the perception of the variables of interest?
Here, the perception of the variables of interest refers to the perception of the overall system and of the specific aspects of explanations, in the same way as described for RQ1.
As it has been shown that individual user characteristics can lead to different perceptions of a RS [25], [50], we assumed that this would also be the case for explanations, as discussed by [2], [26], [22]. Consequently, and similar to Hernandez-Bocanegra et al. [22], we also aimed to test the effect that user characteristics may have on the perception of the explanations, in particular regarding decision making style (rational and intuitive) [20] and the ability of the user to take into account the views of others (social awareness) [17]. Additionally, we also aimed to test the influence that visual familiarization may have on explanations perception, as addressed by Kouki et al. [26]. Consequently:
RQ4: Do individual differences in visual familiarity, social awareness or decision making styles influence the perception of our proposed explanations design?
Here, as with previous RQs, the perception of our explanations designed is addressed in terms of system perception as well as of perception of specific aspects of explanations.
In order to address these questions, we conducted a user study to test the perception of explanations based on user opinions in the hotel domain, given different display styles and whether or not user profile information is shown. The perception was assessed regarding two levels: 1) overall system and explanation quality, and 2) perception of specific aspects of explanations.
The contributions of this paper can be summarized as follows:
1. We evaluated the effect of different presentation styles, namely tabulated data or bar charts. Comparisons were conducted both between groups and within participants.
2. We also evaluated the effect of providing user profile information as part of explanations, with a display that contains no information regarding user preferences.
3. Furthermore, we analyzed the usefulness perceived by users of the different user interface components included in explanations.
The remainder of this paper continues as follows: We discuss related work in Section 2, and the specifics of our explanation design in Section 3. In Section 4, we present methods and results of experiment 1, while details and results of experiment 2 are provided in Section 5. Discussion of both studies and limitations are included in Section 6. Finally, we address future work in Section 7.
## 2 Related Work
Traditionally, many approaches to explaining the products or services suggested by an RS have been based on ratings provided by users (CF methods) or properties of the recommended items (CB methods). In the former, explanations are often provided in a nearest-neighbor style (e. g. “Your neighbors’ ratings for this movie” [21]), while the latter approach enables the generation of feature-based explanations, that inform users about item properties that may match user preferences, as in [44]. On the other hand, there has recently been increased interest in exploiting alternative sources of information to improve the performance and explainability of RS, particularly the use of user reviews, given the wealth of detailed reports on the positive and negative aspects of an item, information that is often difficult to understand from the general ratings given by users.
Review-based methods enable the generation of the following types of explanations:
1) A verbal summarization of review findings, i. e. statements generated in natural language representing a summarized version of the original content extracted from reviews, e. g. [6], [12], who proposed methods based on natural language generation (NLG) techniques.
2) A selection of helpful reviews, or excerpts from them, that might be relevant to users, as proposed by [9], who used a deep learning model and word embeddings to jointly learn user preferences and item properties, and an attention mechanism to detect features that are of most interest to the target user.
3) A summarized view of pros and cons on specific item aspects reported by other users. Here, topic modelling and aspect-based sentiment analysis are usually used to detect the sentiment polarity towards item aspects or features addressed in reviews, as in [49], [53], [14]. Subsequently, such information can be integrated into RS algorithms such as matrix or tensor factorization, as in [53], [1], [46] in order to generate both recommendation and aspect-based explanations.
In particular, our explanation design proposal and subsequent user study is within the third approach, and is particularly related to the MF model proposed by Zhang et al. [53], since it facilitates the consolidation of statistical information on users’ opinions (which can be provided using different presentation styles), as well as their alignment with the user’s profile, which is fundamental to our research questions. This model allows the generation of both recommendations and explanations, based on the alignment of 1) latent representations of items and user preferences, and 2) explicit features obtained from reviews. Here, in addition to the rating matrix used in traditional MF, two additional matrices are calculated: a user preference matrix (which indicates how many times a user addressed a feature in their reviews), and an item quality matrix (which indicates how many positive and negative comments were reported in relation to an item). This input information is then used as the basis for our proposed explanation and subsequent user study.
### 2.1 User Profile Transparency
In regard to providing information on user profile as part of RS explanations, Bilgic and Mooney [3] proposed and tested an influence-based style for explanations in the movies domain, in which the system presents items that had the greatest impact on the recommendation, as well as the ratings that the user has given to those items. They found that such explanations enabled participants to more accurately predict user’s satisfaction with the item, compared to a histogram of the user’s neighbors’ ratings, an explanation style that was found by Herlocker et al. [21] as the best performing among a group of explanations for CF methods, in terms of how compelling they were to study participants.
On the other hand, and using a CB method, Tintarev and Masthoff [39] compared non-personalized verbal explanations with personalized ones, in which, in addition to providing information about the properties of the articles, a sentence was included indicating how these properties related to the user’s preferences. According to their findings, personalized explanations were not regarded as more effective than their counter non-personalized part. Here, and similar to [3] the effectiveness was measured based on the difference between the rating that the user would give to an item after reading the explanation, and the one given once the item has been tried. According to authors, the detrimental effect of personalized explanations on effectiveness might be due to users’ expectations of preference fit that were not fulfilled once the item was tried.
Additionally, Gedikli et al. [18] compared the perception of users regarding different types of explanations provided by CF and CB recommenders in the movies domain. Their proposed personalized explanations based on clouds showed tags in different colors, depending on the sentiment previously expressed by the target user, regarding different colors (positive: blue, negative: red, neutral: gray). In line with Tintarev and Masthoff [39], they found that a non-personalized tag cloud (all tags in the same color) was slightly more effective than the personalized tag cloud. However, the personalized tag cloud was perceived better by users in terms of transparency.
Disclosure of information used during the recommendation process (e. g. user profile) as part of explanations may facilitate users in identifying and correcting erroneous inferences made by a RS [38]. In this direction, proposed work on scrutable RS seeks to enable and to leverage user control on users’ own profile, which in turn may facilitate the generation of new and more accurate recommendations that fit better the real preferences of users. For example, Wasinger et al. [47] implemented a system to recommend restaurant meals based on a scrutable user model, where users could check and adjust their preferences regarding food ingredients to improve recommendations. A user study was conducted to test the application, and noted that users found it easy to understand why certain foods were recommended, by using the customization feature to adjust their preferences.
In regard to review-based methods, Chen and Wang [10] proposed a text-based explanation design that combines both summarization of item opinions as well as item specifications, and that provides a tradeoff view of properties, that allows the direct comparison of different recommended items. They found that a mixed explanatory view containing opinions and specifications was perceived more positively by users, than explanations consisting of only one of such components at the time. However, in contrast to our approach, the selected specifications correspond to explicit elicited preferences, and not to preferences detected from previous reviews written by the user.
On the other hand, Muhammad et al. [28] tested the users’ perception of a series of review-based RS explanations in the hotels review. Here, item quality and user preferences are both extracted from reviews and used to generate both recommendations and explanations. However, user preferences are only used implicitly to select, show and sort a subset of the features in explanations, without any mention of such details to users.
In summary, while the effect of presenting explicit information on user profiles as part of explanations of CF and CB methods has already been addressed to some extent, the questions of how such information influences the perception of review-based SR and how such information should be presented remain open.
### 2.2 Decision-Making Process Transparency
In regard to informing users about the decision inference process, the RS may provide details on the recommendation process, or on the data used for it. Accordingly, Herlocker et al. [21] proposed an explanatory model based on the user’s conceptual model of the recommendation process. In a white box conceptual model, users are provided with details of the different steps of the conceptual model of the system operation, e. g. user enters ratings, then system locates similar users, then neighbors’ ratings are combined to provide recommendations. In a black box model, however, it may not be practical or even possible to convey details regarding the conceptual model of the system to users, which is actually the case of MF models and their latent features. Herlocker et al. [21] argues that any white box could be regarded as a black box if only information about the input and the output is provided, which could also be beneficial for users.
In regard to the source and type of input used in the process, the presentation of such elements in many of the CF and CB neighbor-style approaches is simpler and self-explanatory, compared to more complex approaches that integrate alternative sources (e. g. reviews) to latent features models as MF, where not only the steps of the process are hard to convey to users, but also the nature of the data used as input. Consequently, most current review-based explanatory approaches omit any mention of the origin of the data, particularly when explaining the inferred user profile, which may make it more difficult to understand compared to item-based explanatory information. Therefore, in addition to assessing how the different ways of presenting the input data might influence the users’ perception, in this article we intend to examine also the potential usefulness of explanatory statements on the data origin, as part of review-based explanations, e. g. “based on how often you mentioned features in your own comments before”.
### 2.3 Presentation Format
According to the taxonomy of explanations proposed by Nunes and Jannach [30], explanations could be classified by their presentation format as: natural language (e. g. canned text, template-based, structured language), visualization, or other media formats, such as audio. Regarding review-based explanations, Zhang et al. [53] proposed brief template-based statements to provide information on relevant features (e. g. “You might be interested in [feature], on which this product performs well”, although the underlying method allows to generate more detailed explanations, that could also be provided visually using graphs, as elaborated in further sections of the present work. Furthermore, a distinction can also be made between verbal explanations that also provide numerical or statistical information and those that comprise strictly verbal statements. In this respect, Hernandez-Bocanegra et al. [22] compared different types of verbal explanations in the hotel domain, and found that users perceived a higher explanation quality when an aggregated view of positive and negative opinions using percentages was provided, compared with a verbal summary of the opinions that did not provide any percentage, inspired by the abstractive summarization proposed by Costa et al. [12]; furthermore, a greater perceived transparency was reported for explanations with the aggregated view using percentages of opinions, compared to explanations that only provided a useful review, as proposed by Chen et al. [9].
In regard to presentation styles based on visualization techniques applied to review-based RS, Muhammad et al. [28] proposed a summary of the positive and negative opinions on different aspects using bar charts, while Wu and Ester [49] proposed to depict such type of information as word clouds or radar charts. Although bar charts reflecting positive and negative views might be perceived as more informative and attractive than brief template-based textual explanations, easier to interpret than challenging radar charts, or quicker to process than tabulated data, it remains unclear to what extent the presentation format influences the perception of RS and its explanations. In this regard, Kouki et al. [26] proposed a series of explanations based on a hybrid RS in the music domain, and tested, among others, the influence that the presentation format could have on users’ perception. In this case, the authors found that textual explanations were perceived as more persuasive than the explanations provided using a visual format; however, users with greater visual familiarity perceived one of the visual format explanations more positively (a Venn diagram). Consequently, we aimed to investigate whether such an effect is also observed in the case of review-based explanations.
Particularly, in the present work, we set our focus on two formats: bar chart and table. Bar charts are recommended to facilitate a direct and quick comparison of values between different categories or items, contrary to alternatives like pie charts, or bubbles, where additional cognitive efforts would be needed to accurately calculate the differences in values across categories, in our case, the different aspects of the items. Likewise, word clouds imply a presentation challenge, since we are willing not only to represent the amount of comments (which could be reflected by font size), but also polarity, which would require using separate clouds for the positive and negative aspects, or showing a single predominant sentiment per aspect in a single cloud, thus obscuring the information about the less predominant polarity. On the other hand, while the use of tables has been recommended to display small data sets (less than 20 data points) [16], [43], when providing exact numbers or proportions is not the main objective, tables seem to be less useful than graphics [36]. As indicated previously in the case of verbal explanations, users benefited from a view that provides percentages of positive and negative opinions, suggesting that percentages may serve as anchors to convey more compelling information in explanations, compared to purely verbal statements. In this sense, when motivation or ability is lacking, the effortless use of cues such as numerical anchors can lead to changes in attitude [32], [48], which in turn influence judgments and decision making (anchoring effect). Thus, even when the values of the proportions of the opinions included in the two types of explanations (table or chart) are the same, a different representation of them might lead to differences in explanation perception, which we set out to test in the user study.
### 2.4 User Characteristics
Beyond the explanations’ content itself, a number of user characteristics also contribute to differences in the overall perception of RS. Models proposed by Knijnenburg et al. [25] and Xiao and Benbasat [50] argue that perception of the interaction with the system usually depends on personal characteristics, like demographics and domain knowledge. Furthermore, Berkovsky et al. [2] evaluated how differences in the perception of trust might reflect differences in users’ personality traits, given different types of explanations provided in the movies domain. To this end, they used participants’ scores of the Big-Five personality traits (openness, conscientiousness, extraversion, agreeableness and neuroticism) [13], [40], and compared persuasive explanations (e. g. “highest grossing movie of all times”), personalized CF-based explanations (e. g. “because you liked X”) and IMDb voting-based explanations (e. g. “Average rating n, Number of votes m”). Among their findings, authors reported that people with higher disposition to agree perceived more positively the voted-based explanations, compared to personalized explanations, seemingly to a higher disposition to accept others’ opinions rather than impose their own preferences. Furthermore, they found that people with higher levels of neuroticism perceived better the voted-based explanations compared to the persuasive ones, possibly due to a perception of higher reliability of explicit voting numbers, which could presumably reduce the risk of frustration of a person with high levels of neuroticism.
Similarly, Kouki et al. [26] explored the influence of personality traits on users’ explanation preferences regarding perceived accuracy and perceived novelty of recommendations, in the music domain. They compared different types of textual explanations, and found that participants with higher levels of neuroticism preferred item-based explanations (e. g. “people who listen to your profile item X also listen to Y”) whereas popularity-based explanations (e. g. “X is a very popular in the last.fm database with n million listeners and m million playcounts”) were preferred by users with lower levels of neuroticism, the latter in contrast to the opposite finding reported by [2], regarding trust perception.
Despite the usefulness of using the Big Five personality traits to better understand individual differences in RS perception and its explanations, we decided to address other types of user characteristics, which are more related to how users process information when making decisions, noting that supporting this process is precisely the goal of recommendation systems. Particularly, individual differences in decision-making styles are determined to a greater extent by preferences and abilities to process available information [15]. Two main aspects provide a basis to describe the differences in decision styles: information use (amount of information used during the process) and focus (alternatives addressed) [15]. “Good enough” information might be sufficient for some people, whereas others prefer to obtain and address all relevant information, in order to minimize risks or negative consequences of decisions. To the former, even when more information may be available, it is not necessary or worth taking the time to review it. Hamilton et al. [20] defines rational and intuitive decision styles similarly to the cognitive styles of Pacini and Epstein [31], with the latter having a more general scope to describe manners of solving problems. Thus, decision making styles are defined by Hamilton et al. [20] as a “habit-based propensity” to exhaustively search for information and to systematically evaluate possible alternatives (rational style), or to use of a quick process based on hunches and feelings (intuitive style).
Additionally, we were interested in another factor that may influence the way users perceive explanations: the extent to which they are able to adopt the perspective of others when making decisions. The rationale for this interest stems from the tendency of individuals to adjust their own opinions using those of others, while choosing between various alternatives [35], which may even be beneficial [51]. Particularly, individuals with greater perspective-taking skills tend to understand the views of others better [8], [5], skills that are also characterized as “social awareness” [17].
Previous work by Hernandez-Bocanegra et al. [22] evaluated the influence of decision-making styles and social awareness on the perception of review-based argumentative explanations, and suggested that social awareness might have an effect on both transparency and trust in review-based RS. Their results indicated that users with a greater willingness to listen and take into account the opinions of others valued their proposed explanations better than users who tend to listen less to others. On the other hand, contrary to the authors’ expectations, the more detailed explanations summarized by the system were not preferred by the more rational users, apparently because the additional information generated by the system is not perceived as more satisfactory than the possibility of reading directly the comments written by the users.
Finally, since we aimed to compare differences in perception of explanations consisting of different visual representations, we also considered a factor that is related to visual abilities, in particular the extent to which a user is familiar with graphical or tabular representations of information. Visualization familiarity may also influence the perception of explanations provided using images or graphs, as found by Kouki et al. [26] in the music domain. Here, authors found that textual explanations were perceived as more persuasive than the explanations provided using a visual format; however, users with greater visual familiarity perceived one of the visual format explanations more positively (in particular a Venn diagram).
## 3 Explanation Design
In the context of RS, review-based argumentative explanations could be understood as a set of propositions, summarizing positive points reported by other users on specific aspects, that support the claim that an article can be recommended to a user. In this respect, information extracted from user reviews could be consolidated and provided as propositions, which would constitute the backing component according to the argumentative scheme proposed by Toulmin [42], while the conclusion (the item is recommended) constitute itself a claim. While this could be considered a ‘shallow’ structure, compared to the complete Toulmin argument scheme (which involves additional components, like rebuttal or refutation), it resembles explanation schemes based on deductive arguments, such as those widely used in the scientific field (i. e. a set of explanatory propositions is logically followed by an explanatory target, as discussed by Thagard and Litt [37]), or even more particularly, explanation schemes in RS such as the one used by Zanker and Schoberegger [52], who provides brief sentences – two facts and a claim – as explanations for content-based recommendations of hiking routes, energy and mobile phone plans.
In consequence, our explanation design (see Figure 1) seeks to represent an argumentative structure, while reflecting in turn the arguments provided by other users in their reviews, in a consolidated manner. Therefore, our proposed scheme consists of a claim (“We recommend this hotel”) and the propositions that support such claim, connected with the conjunction “because”. We propose to provide the following pieces of information in proposition statements:
1. Item quality: A summary of comments reported by previous hotel guests for different aspects, as well as what percentage were positive and negative.
2. User preferences: what are the most important item aspects to the target user. In this regard, we aimed to make the user’s own profile transparent, by showing the user’s inferred importance of each aspect, together with the opinions of other users about the aspect (as shown in the examples included in Figures 1a and 1c), in order to facilitate a direct comparison of the points of view of others and their alignment with their own preferences.
Figure 1
Explanations displayed in empirical study for every experimental condition, for one of the recommended hotels. a) Style ‘visual’, user preferences ‘yes’. b) Style ‘visual’, user preferences ‘no’. c) Style ‘text’, user preferences ‘yes’. d) Style ‘text’, user preferences ‘no’.
3. Statements that inform how the user preferences and item quality are extracted (e.g,“based on how often you mentioned these features in your own comments before”). We believe that providing this information, in addition to the information listed above, could increase the perception of trust by users, while decreasing the perception that they are interacting with a black box.
While arguments are usually associated with oral or written speech, arguments can also be communicated using visual representations (e. g. graphics or images). In this regard, according to Blair [4], visual arguments (a combination of visual and verbal communication) may, in addition to representing propositional content, have a greater “rhetorical power potential” than verbal arguments, due (among others) to their greater immediacy.
In consequence, we aimed to test the effect of the two factors: display style and display of the user preferences. An example of each condition is provided in Figure 1.
‘Bar chart’ style: Provides a view of the number of comments per aspect and percentages of positive and negative opinions using bar charts.
‘Table’ style: Provides the same information used in the visual condition, but instead of using bar charts, presents the information within a table.
Additionally, every display style involves two variations:
User preferences ‘yes’. The information about the user preferences is provided.
User preferences ‘no’. No information about the user preferences is displayed.
## 4 Experiment 1: System and Explanation Quality Perception, between Subjects
We implemented a prototype of a hotel recommender system that provides both recommendations and explanations, based on the design discussed in Section 3, and conducted an experiment where we compared users’ perception of the overall system in terms of transparency, effectiveness, efficiency and trust. In this regard, we aimed to test our hypothesis that users would report a more positive perception of the RS when information about their user preferences is provided (H1). Additionally, we hypothesized that users with greater visual abilities would find explanations better when these are provided using visual aids, such as a bar chart, in comparison to tabulated information (H2). In particular, the aim of experiment 1 was to compare the overall perception of the prototype and its explanation quality, in a between groups manner (participants were assigned to conditions that reflect the different types of explanations designed), while in a subsequent experiment (see Section 5) we addressed the perception of specific aspects of explanations within subjects, as well as the usefulness of individual explanation components.
### 4.1 Methods
#### Participants
We recruited 150 participants (66 female, mean age 39.08 and range between 23 and 73) through Amazon Mechanical Turk. We restricted the execution of the task to workers located in the U.S, with a HIT (Human Intelligence Task) approval rate greater than 95 %, and number of HIT’s approved greater than 500. We applied a quality check in order to select participants with quality survey responses, i. e. at least 5 of the 6 high priority validation questions were answered correctly, more than 30s were spent on the recommendation step and more than 50s on the evaluation questionnaire. The responses of 46 subjects were discarded due to this quality check (from an initial number of 195 workers), so only the responses of 150 subjects were used for the analysis (statistical power of 85 %, α = 0.05). Participants were rewarded with $1 plus a bonus up to$0.4 depending on the quality of their response to the question “Why did you choose this hotel?” set at the end of the survey. Time devoted to the task by participants (in minutes): M = 8.04, SD = 1.62.
#### Study Design
The study follows a 2x2 between-subjects design, and each participant was assigned randomly to one of four conditions that represent the combination of the two factors: display style and user preferences provided or not. We presented participants with a fixed list of 5 hotels that represented the recommendations for a hypothetical hotel search, and a detailed view including an explanation of why every item was recommended. Then, participants were asked to choose the hotel they considered the best, to report their reasons to it, and to rate their perception of both recommender and its explanations. The explanations and recommendations were generated using the EFM algorithm [53] and the dataset of hotels’ reviews, ArguAna [45], although they were presented to the participants only through a prototype, i. e. no real system was implemented to allow the interactions.
Given that we had no access to previously written participants’ reviews (which is not only important for the optimal functioning of the algorithm, but also constitutes a base to test the condition “user preferences”), we calculated the top 5 of the most important aspects to all users within the dataset, namely: room, price, facilities, location and staff. Then, a random user was chosen from the dataset with those same preferences, and 5 of her top-ranked options according to the EFM algorithm were selected to be presented to participants, alongside their explanations. Additionally, we presented the users with a cover story, in which we told the users to pretend that their most important aspect was the “room” and the “price”.
#### Questionnaires
Evaluation: We utilized items from [33] to evaluate the perception of system transparency (construct transparency, user understands why items were recommended), from [25] to evaluate the perception of system effectiveness (construct perceived system effectiveness, system is useful and helps the user to make better choices) and efficiency (user can save time with the recommender), and items from [27] to assess the perception of trust in the system (constructs trusting beliefs, user considers the system to be honest and trusts its recommendations, and trusting intentions, user willing to share information). In addition, we also adapted 3 items from [25] to address explanation quality (construct perceived recommendation quality, user likes explanations, considers them relevant). All items were measured with a 1–5 Likert-scale (1: Strongly disagree, 5: Strongly agree).
User characteristics: We used all the items of the Rational and Intuitive Decision Styles Scale [20] as well as the scale of the social awareness competency [17]. Additionally, We used the visualization familiarity items as proposed by [26]. All items were measured with a 1–5 Likert-scale (1: Strongly disagree, 5: Strongly agree).
#### Procedure
First, participants were asked to answer demographic questions and the questionnaire on user characteristics. We indicated in the instructions step that a 5 hotels list reflecting the results of a hypothetical hotels’ search would be presented. We asked them to click the “View Details” button for each hotel, and to read carefully the explanations provided in each case (examples of explanations for the different experimental conditions are provided in Figure 1). Additionally, we provided a cover story, as an attempt to establish a common starting point in terms of reasons to travel (a business trip), and the supposedly most interesting aspects for the user (room and facilities).
The list of hotels, their names, photos, prices and locations, as well as their ratings and the numbers of reviews and positive and negative opinions, remained constant to all users. Variations focused only on display style and the presentation of user preferences, depending on the condition to which each participant was assigned. After the interaction with the prototype, subjects were asked to choose the hotel that best suited their purpose, as well as an open question about their reasons for choosing that hotel. Then, subjects answered the evaluation questionnaire. In addition, we included an open-ended question, so that participants could indicate in their own words their general opinion about the explanations provided. We included 11 validation questions to check attentiveness and the effective completion of the task.
#### Data Analysis
We evaluated the effect that display style and the display of user preferences (independent variables IVs) may have on the perception of the prototype and its explanations, and to what extent user characteristics (regarded as moderators or covariates) could influence such perception (rational and intuitive decision-making style, social awareness and visualization familiarity). Here, the dependent variables (DVs) are evaluation scores on: system transparency, effectiveness, efficiency, trust and explanation quality. Here, evaluation scores were calculated as the average of the individual values reported for the questionnaire items related to each DV. Regarding the covariates, we calculated the scores of the rational and the intuitive decision making styles, social awareness and visualization familiarity for each individual as the average of the reported values for the items of every scale.
Table 1
Experiment 1, mean values and standard deviations of perception on explanation aims, per display style and display of user preferences (n = 150); values reported with a 5-Likert scale; high mean values correspond to a positive perception of recommender and its explanations. Pearson correlation matrix, p<0.001 for all correlation coefficients.
Style Table Bar chart User Pref. Yes No Corr. Variable Variable M SD M SD M SD M SD 1 2 3 4 1. Expl. Quality 3.83 0.65 3.86 0.67 3.88 0.67 3.81 0.65 2. Transparency 3.96 0.73 3.87 0.85 3.99 0.74 3.84 0.84 0.37 — 3. Effectiveness 3.88 0.61 3.75 0.75 3.84 0.76 3.79 0.61 0.60 0.47 — 4. Efficiency 3.96 0.73 3.89 0.92 4.00 0.78 3.86 0.87 0.36 0.39 0.52 — 5. Trust 3.75 0.60 3.89 0.63 3.84 0.65 3.81 0.59 0.66 0.40 0.67 0.58
Given that our DVs are continuous (scores are the averages of reported answers of questionnaire items of each construct) and correlated (correlation coefficients in Table 1), and that we address also the effect of covariates, a MANCOVA analysis was performed, to assess the simultaneous effect of presentation styles and interactivity on the overall system perception, as well as the influence of user characteristics on it. Subsequent ANCOVA analyses were performed to test main effects of IVs and covariates, as well as the effect of interactions between them. Q-Q plots of residuals were checked to validate the adequacy of the analysis.
### 4.2 Results
#### Evaluation and User Characteristics Scores
Figure 2
Plots Experiment 1. a) Kernel density estimate of user characteristics scores: rational and intuitive decision making styles, social awareness and visual familiarity. b) Interaction plot for explanation quality (fitted means of individual scores) between display of user preferences and social awareness. c) Effect of social awareness on all explanation aims (fitted means of individual scores). All scores within the range [1,5].
We found that explanations including information of user preferences are perceived slightly better than explanations without this information in terms of explanation quality and system transparency, effectiveness, efficiency and trust. On the other hand, explanations including a bar chart were perceived slightly better than explanations with a table, in regard to explanation quality and trust, while the opposite was observed in relation to transparency, effectiveness and efficiency. However, as discussed in detail below, such differences are not statistically significant. The average evaluation scores by presentation style and display of user preferences are shown in Table 1.
In regard to user characteristics, distributions of the scores of rational (M = 4.24, SD = 0.56) and the intuitive (M = 2.65, SD = 1.01) decision making styles, social awareness (M = 3.92, SD = 0.59) and visual familiarity (M = 3.03, SD = 1.02) are depicted in Figure 2a. Here, we observed a skewed right distribution of rational decision making-style and social awareness scores, not being that the case for the intuitive decision-making style and visual familiarity, i. e., most users consider themselves to be predominantly rational decision makers who are able to listen to others and take into account the opinions of others; however, a more balanced distribution is observed in the remaining user characteristics: only a minority recognize themselves as very (or not at all) familiar with visual representations of information, and as very (or not at all) intuitive decision makers. In addition, results suggest an influence of some of the user characteristics on the perception of the system by users, which we describe in detail below.
#### System and Explanation Quality Perception
Presentation style and display of user preferences: We found no main significant effect of the combination of these factors.
Display of user preferences: No significant multivariate effect was found for display of user preferences.
Presentation style: No significant multivariate effect was found for presentation style.
Rational decision-making style: We found a significant main effect of rational style F(5, 138) = 4.50, p < .001. Univariate tests revealed a significant effect of this variable on: effectiveness F(1, 142) = 9.12, p = .003), efficiency (F(1, 142) = 10.98, p = .001) and trust (F(1, 142) = 18.82, p < .001). Here, a positive trend was observed between rational decision-making score and the above mentioned DVs, i. e. the higher the rational decision making score, the higher the perception scores of these DVs.
Intuitive decision-making style: We found a significant main effect of intuitive style F(5, 138) = 3.25, p = .008. Univariate tests revealed a significant effect of this variable on: explanation quality (F(1, 142) = 16.37, p < .001). Here, a positive trend was observed between this variable and the score of intuitive decision-making style.
Social awareness: We found a significant main effect of social awareness F(5, 138) = 6.72, p <.001. Univariate tests revealed a significant effect of this variable on: explanation quality (F(1, 142) = 5.62, p = .019), transparency (F(1, 142) = 7.93, p = .006), effectiveness (F(1, 142) = 8.79, p = .004) and trust (F(1, 142) = 26.56, p < .001). Here, we observed a positive trend in the relationship between social awareness and these DVs (see Figure 2d).
Additionally, a significant interaction effect between social awareness and the display of user preferences on explanation quality was found F(1, 146) = 4.79, p = .030, with the “yes” condition having a steeper slope than the “no” condition (showing a positive relationship between social awareness and displaying user preferences), the latter remaining constant regardless of the social awareness score (Figure 2b).
## 5 Experiment 2: Perception on Specific Aspects of Explanations, within Subjects
We used screenshots of the prototype implemented for experiment 1 (see Section 4), reflecting the design discussed in Section 3, and conducted a second experiment aiming to compare users’ perception of specific aspects of explanations, when presented to all the four possible explanations (see Figure 1). In experiment 2, differences were addressed within subjects, while in experiment 1 we evaluated the perception of the overall system in a between subjects manner. Likewise to experiment 1, we also aimed to test our hypothesis that users would report a more positive perception when information about user preferences is provided (H1), and also that users with greater visual abilities would find explanations better when these are provided using visual aids, such as a bar chart, in comparison to tabulated information (H2).
Additionally, the experiment 2 also involved the assessment of the usefulness of individual components of explanations, by participants. In this regard, for example, we hypothesised that most users would find useful the information regarding the origin of the explanatory information provided (H3).
### 5.1 Methods
#### Participants
We recruited 35 participants (14 female, mean age 42.77 and range between 24 and 65) through Amazon Mechanical Turk. We restricted the execution of the task to workers located in the U.S, with a HIT (Human Intelligence Task) approval rate greater than 95 %, and a number of HIT’s approved greater than 500. We applied a quality check in order to select participants with quality survey responses, i. e. at least 5 of the 7 validation questions were answered correctly. The responses of 7 subjects were discarded due to this quality check (from an initial number of 42 workers), so only the responses of 35 subjects were used for the analysis, a value consistent to our within subjects design (statistical power of 95 %, α = 0.05). Participants were rewarded with \$1. Time devoted to the task by participants (in minutes): M = 6.70, SD = 1.07.
#### Study Design
The study follows a within-subjects design, and each participant was presented sequentially with an example of each of the 4 types explanations, that represent the combination of the two factors: display style and user preferences provided or not. The order of presentation of the 4 types of explanation was counterbalanced.
#### Questionnaires
We used the user experience items (UXP) proposed by [26] to address the explanations reception, comprising: explanation confidence (explanation makes user confident that she/he would like the recommended item), explanation transparency (explanation makes the recommendation process clear), explanation satisfaction (user would enjoy a system if recommendations are presented this way), and explanation persuasiveness (explanations are convincing). Finally, we included additional elements to assess explanation effectiveness (user can make better decisions if explanation presented this way), explanation efficiency (user can save time if system provides this type of explanation), and explanation easiness (explanation is easy to understand). All items were measured with a 1–5 Likert-scale (1: Strongly disagree, 5: Strongly agree). Users were asked to respond to the same user characteristics questionnaire we used in experiment 1.
Additionally, participants were requested to provide their opinions on how helpful they considered the different components of the explanations: the bar plots, the tables, the information about others’ opinions, the information about their supposed own comments, and the information on where the bar plots and tables come from. All items were measured with a 1–5 Likert-scale (information is helpful, 1: Strongly disagree, 5: Strongly agree).
#### Data Analysis
We evaluated the effect that display style and the display of user preferences (independent variables IVs) may have on the perception of specific aspects regarding the proposed explanations, and to what extent user characteristics (regarded as moderators or covariates) could influence such perception (rational and intuitive decision-making style, social awareness and visualization familiarity). Here, the dependent variables (DVs) are evaluation scores on the following aspects: explanation confidence, explanation transparency, explanation satisfaction, explanation persuasiveness, explanation effectiveness, explanation efficiency and explanation easiness to understand. Regarding the covariates, we calculated the scores of user characteristicas the same way as in study 1 (average of the reported values for the items of every user characteristics scale).
Given that our DVs are ordinal (scores are the reported answers to single questionnaire items) we performed a Friedman test, the non-parametric alternative to the repeated measures ANOVA. Given that our variables are correlated, the significant tests were conducted using Bonferroni adjusted alpha levels of .007 (.05/7).
Additionally, we calculated the average evaluation scores for each possible value of the two factors: presentation style (bar chart and table), and display of user preferences (yes and no). Using these continuous and correlated evaluation scores, we then perform a repeated measures MANCOVA, to assess the simultaneous effect of presentation styles and display of user preferences on explanations perception, as well as the influence of user characteristics on it. Subsequent ANCOVA analyses were performed to test main effects of IVs and covariates, as well as the effect of interactions between them.
Usefulness of explanations components: We performed a series of ordinal logistic regressions to test influence on scores of usefulness of components – DVs (bar chart, table, others’ opinion view, own preferences view, information source) by predictor variables, in this case the user characteristics (rational and intuitive decision-make style, social awareness and visualization familiarity), which were tested a priori to verify there was no violation of the assumption of no multicollinearity. Q-Q plots of residuals were also checked to validate the adequacy of the analysis.
DVs were initially rated using a 5-likert scale, but additionally we grouped answers as Yes (agree and strongly agree that element is helpful), and No / Neutral (disagree, strongly disagree and neutral that element is helpful) for subsequent analysis. We then calculated the percentages of Yes and No/Neutral responses regarding the different explanation components, and performed a binomial test, to check whether the proportions of Yes and No/Neutral answers were different from a proportion that assumes that the percentages are equal (50 % of Yes and 50 % of No/Neutral).
Finally, we used a Wilcoxon rank t-test to compare the average responses of the perception of usefulness of a view of others’ opinion with that of a view of their own preferences, as well as the average responses of perceived usefulness of tables compared to bar charts in explanations.
### 5.2 Results
#### Evaluation and User Characteristics Scores
Table 2
Experiment 2, mean values and standard deviations of perception on explanation aspects, per display style and display of user preferences (n=35); values reported with a 5-Likert scale; high mean values correspond to a positive perception of explanations aspects.
Style Table Bar chart User Pref. Yes No Variable M SD M SD M SD M SD 1. Expl. Confidence 3.30 0.92 3.33 0.98 3.33 0.86 3.30 0.96 2. Expl. Transparency 3.50 0.88 3.64 0.97 3.51 0.88 3.63 0.74 3. Expl. Satisfaction 3.41 1.08 3.27 1.05 3.24 1.03 3.44 0.93 4. Expl. Persuasiveness 3.30 0.92 3.29 1.02 3.34 0.94 3.24 1.06 5. Expl. Effectiveness 3.33 0.97 3.37 0.95 3.29 0.93 3.41 0.85 6. Expl. Efficiency 3.31 1.13 3.34 1.09 3.21 1.05 3.44 0.93 7. Expl. Easiness to understand 3.76 0.92 3.84 0.86 3.59 0.93 4.01 0.72
We observed only small differences between table and bar chart explanations, and between explanations including or not user preferences, in regard to most of the specific aspects of explanations evaluated, with the exception of easiness to understand. As discussed in detail below, explanations without display of user preferences were perceived easier to understand, this difference being statistically significant. The average evaluation scores by presentation style and display of user preferences are shown in Table 2.
In regard to user characteristics scores, we observed similar distributions of such scores: a skewed right distribution of rational decision making-style and social awareness scores, not being that the case for the intuitive decision-making style and visual familiarity. Distributions of the scores of rational (M = 4.34, SD = 0.7) and intuitive (M = 2.13, SD = 0.83) decision making styles, social awareness (M = 3.55, SD = 0.53) and visualization familiarity (M = 2.82, SD = 1.17) are depicted in Figure 3a. Additionally, we observed a main effect of some of these user characteristics on the perception of specific aspects of explanations, as well as interaction effects involving these variables. Such findings are described below.
Figure 3
Plots Experiment 2. a) Kernel density estimate of user characteristics scores: rational and intuitive decision making styles, social awareness and visual familiarity. b) Interaction plot for explanation persuasiveness (fitted means of individual scores) between display of user preferences and rational decision-making style. c) Interaction plot for explanation confidence (fitted means of individual scores) between presentation style and rational decision-making style. All scores within the range [1,5].
#### Perception of Explanations
Presentation style and display of user preferences: We found no main significant effect of the combination of these factors after Bonferroni correction.
Display of user preferences: We found a multivariate effect of display of user preferences, F(7,28) = 2.41, p = .046. Univariate tests revealed a main effect of display of user preferences on explanation easiness to understand F(1,34) = 6.42, p = .016, so that explanations that do not include information on user preferences are significantly easier to understand (M=3.76, SD=0.91), compared to those showing such information (M=4.01, SD=0.72).
Presentation style: No multivariate main effect of presentation style was found.
Display of user preferences and rational decision-making style: We found a multivariate interaction effect between these two variables, F(7,27) =, p = .002. Univariate tests revealed the significant interaction effect ot these variables on: explanation transparency (F(1,33) = 7.79, p = .009), explanation satisfaction (F(1,33) = 5.62, p = .024), explanation persuasiveness (F(1,33) = 20.67, p < .001), explanation easiness to understand (F(1,33) = 7.36, p = .011) and explanation effectiveness (F(1,33) = 5.34, p = .027). For all these DVs, the same trend was observed: the higher the reported rational decision-making style, the higher the scores on the different DVs when the user profile was not shown, while the opposite trend was observed when it was shown. An example of this trend is observed in Figure 3b.
Presentation style and rational decision-making style: We found a multivariate interaction effect between these two variables, F(7,27) =, p = .006. Univariate tests revealed the significant interaction effect ot these variables on: explanation confidence (F(1,33) = 14.09, p = .001), explanation satisfaction (F(1,33) = 5.78, p = .022), explanation easiness to understand (F(1,33) = 7.36, p = .011), explanation effectiveness (F(1,33) = 4.34, p = .045) and explanation efficiency (F(1,33) = 7.15, p = .012). For all these DVs, the same trend was observed: the higher the reported rational decision-making style, the higher the scores on the different DVs when the table was provided, while the opposite trend was observed when the bar chart was shown. An example of this trend is observed in Figure 3c.
#### Usefulness of Explanation Components
Effect of user characteristics on usefulness.
An increase in intuitive decision-making score was significantly associated with an increase in the odds of participants reporting higher values of: usefulness of bar charts in explanations, with an odds ratio of 3.16 (95 % CI, 1.12 to 9.81), Wald χ2(1) = 4.76, p = .029, and usefulness of a view of others’ opinions in explanations, with an odds ratio of 3.21 (95 % CI, 1.11 to 11.19), Wald χ2(1) = 4.69, p = .030.
An increase in social awareness score was significantly associated with an increase in the odds of participants reporting higher values of: usefulness of information origin in explanations, with an odds ratio of 5.77 (95 % CI, 1.38 to 27.20), Wald χ2(1) = 5.82, p = .016.
An increase in visualization familiarity score was significantly associated with an increase in the odds of participants reporting higher values of: usefulness of bar charts in explanations, with an odds ratio of 3.79 (95 % CI, 1.76 to 9.47), Wald χ2(1) = 12.33, p < .001, usefulness of a view of own comments in explanations, with an odds ratio of 2.54 (95 % CI, 1.35 to 5.14), Wald χ2(1) = 8.62, p = .003, and usefulness of information origin in explanations, with an odds ratio of 3.21 (95 % CI, 1.62 to 6.96), Wald χ2(1) = 11.77, p < .001.
We found then that a significant majority found the information about others’ opinion helpful (χ2(1, N = 35) = 6.40, p = .011), so that both tables (χ2(1, N = 35) = 6.40, p = .011) and bar charts (χ2(1, N = 35) = 8.75, p = .003), whereas only a significant minority found the display of user preferences helpful (χ2(1, N = 35) = 6.40, p = .011). On the other hand, providing details about where the information used for the recommendation comes seems to be regarded as helpful by most people, but the difference with the proportion of people that found it non helpful / neutral is not significant. Proportions are depicted in Figure 4.
Figure 4
Proportion of participants who found the different explanation components helpful (Y) or non helpful neutral (Neutral/No). * p <0.5, **p<0.01.
Comparison of usefulness scores.
We found that the average usefulness of the components view of others’ opinions and view of own preferences are significantly different (W = 0.89, p <.001), with the display of others’ opinions having a higher mean (M = 3.74, SD = 1.07) than the display of users’ preferences (M = 2.63, SD = 1.29). On the other hand, we found no significant difference when comparing the mean responses of usefulness of tables (M = 3.60, SD = 1.19), and bar charts (M = 3.71, SD = 1.20), although bar charts are perceived slightly more helpful than tables.
## 6 Discussion
### 6.1 Effect of Profile Transparency
In regard to our H1, we found no main effect of the display of user preferences on the perception of the system or its explanations. Although contrary to our expectations, the lack of a significant influence of disclosing user preferences seems to be somehow in line with the results reported by Tintarev and Masthoff [39]], Gedikli et al. [Tintarev and Masthoff [18], who observed that providing personalized explanations (in which preferences were presented along with item properties), while potentially beneficial in terms of satisfaction with the explanations, did not necessarily result in a better perception of effectiveness (helping the user to make better decisions). The authors suggested that a possible reason could be a mismatch between the expectation generated by the explanation and the actual evaluation after trying the item. In our case, however, this could be related to how easy it was for the participants to understand the explanations. In particular, we observed that explanations without information on user preferences were significantly easier to understand compared to those that included such information. In addition, we observed that users with less visualization familiarity reported lower usefulness scores of the user preference section, suggesting that the proposed presentation of this section still needs to be improved to benefit users who do not have sufficient experience with information visualization techniques as well.
Although the display does not have a main effect on the perception of the system and its explanations, we observed a mediating effect of social awareness, such that individual differences in this characteristic were reflected in differences in the perception of the explanation quality. Here, our findings suggest that people who tend to listen more to others tend to perceive better the explanations that include information about their own profile. On the other hand, when user preferences are not displayed, the perception of explanation quality remains pretty much the same, despite the extent of users’ social awareness. At this respect, we believe that users with greater abilities to take into account the opinion of others might appreciate the chance to see the alignment of their own preferences with the opinions of others, in an effortless manner, given that a metric of aspect relevance was placed right next to the metric of other users’ opinions regarding such aspect.
Additionally, although no significant interaction effect was found between the rational decision-making style and the display of user preferences on the perception of the system in general, we found that this interaction had a significant effect on the perception of most of the specific aspects of the explanations. In this case, users who reported higher scores for rational decision-making style reported less preference for explanations that provided information on the user’s profile. In this regard, we believe that more skeptical users might think that the system hides additional information about the user’s profile that could be used to generate recommendations, so showing only the frequencies of the mentions of the user’s aspects may not be enough to satisfy their curiosity and need for further information.
Overall, while most users reported they found the information about others’ opinions in explanations useful, the opposite was the case for the information about own preferences, with only a minority of users reporting they found this section useful, and reporting comments in this sense, e. g. “It makes sense that a program would analyse my past comments to find out about my preference...”, or “It could be more useful if there was an explanation of how my preferences are used in the calculation” (the latter by a user assigned to a non user preferences condition in Experiment 1). While the difficulty in understanding this information seems to play an important role in this regard, as discussed above, we believe that in the face of a lack of motivation or “feeling of personal relevance” to perform the task, and the need for greater cognitive effort to do so, the user may simply choose not to attend this section, as discussed by [7], [41].
Overall, the results suggest that users seemed to be much more interested in other people’s opinion and their weight in the recommendation, rather than how these recommendations fit their own preferences. The reasons for this could be twofold: 1) domain under study is an experience good, where the search for information is characterized by a greater reliance on word-of-mouth [29], [24], and where users might be interested, for example, in finding aspects that had a prominent negative opinion, even when the aspect is not necessarily the most important for them. 2) user models enabled by methods like EFM might not accurately reflect users’ real preferences.
As for the explanatory model chosen as inspiration for our study, we believe that the user profile obtained using methods such as the Explicit Factors Model (EFM) [53], may not fully reflect the true preferences of the user, as addressing an aspect in a review, other than reflecting one’s own preference, may be motivated by other factors. On the one hand, customers report on the aspects they consider satisfactory or unsatisfactory, but the nature of these aspects may define the satisfaction report on them, as discussed by Chowdhary and Prakas [11]: the presence of some aspects that are taken for granted (cleanliness, for example) may not lead to customers’ satisfaction, while their absence leads to dissatisfaction and subsequent reporting. Similarly, motivational factors (e. g., proximity to the beach) can lead customers to satisfaction, but their absence does not necessarily cause a negative report.
On the other hand, when inspecting the data we aimed to provide to our participants in the experimental set-up, we observed that in many cases, users in dataset had fairly homogeneous frequencies of reporting aspects in their reviews i. e., many of them tend to talk about general aspects (e. g., “room”, “facilities”) in similar proportions. This makes it difficult, in some cases, to detect compelling preferences, which can be prominently represented in an explanation. Thus, we believe that if all aspects have a very similar assessment of relevance (and thus the bars or numbers in the chart look almost the same) the preference information in explanations might be perceived as irrelevant, unnecessary, and even confusing to users. This seemed to be the case for one of the study participants, assigned to the condition bar chart – user preferences displayed, who reported: “I did not understand the left side of the graph which was consistent across about the features relevant to me (seems weird and confusing to include that)”. In this regard, however, further evidence is needed to confirm that this is actually the case.
### 6.2 Effect of Presentation Style
In regard to presentation style, we compared users’ perception of explanations consisting of tables or bar charts, that provided an aggregated view of positive and negative opinions given by users to every hotel. Here, we did not find a salient preference of one style over the other. Additionally, despite no significant interaction effect between visualization familiarity and display style was found, we observed, in line with our H2, that visualization familiarity might play a role in this perception, since users with higher scores in relation to this user characteristic, gave higher usefulness scores to the bar charts as part of the explanations.
Additionally, our results suggest an interaction effect between rational decision-making style and presentation style on the perception of explanations,so that users with a more rational decision-making style reported higher confidence scores for explanations consisting of tables, while the opposite trend was observed for bar chart explanations. This could be explained by the tendency to seek more detailed information when making decisions, which characterizes individuals with a predominantly rational decision-making style, who may be more interested in evaluating explicit and accurate numbers (such as those presented in the table), compared to less rational users, who may benefit more from representations that allow faster comparisons (such as the bar chart). In this respect, according to Spence and Lewandowsky [36], a presentation of data by means of a table may be more beneficial than the use of a graphical representation, when the objective is the evaluation of exact numbers, and provided that the number of data points presented remains low (in our case it is 5, the number of aspects for which information is provided). The above is also consistent with another of our findings, in which users with a predominantly intuitive decision-making style reported significantly higher scores on the usefulness of bar charts, which seems to be a consequence of the rapid processing of information enabled by graphical representations.
Overall, and despite the differences in perception between tables and bar charts in terms of user characteristics, most users found the two types of explanatory components to be useful, and although the perception of usefulness of the bar chart is slightly more positive than that of the table, this difference is not significant, so we can conclude that both types of presentation are useful to users.
### 6.3 Main Effect of User Characteristics
Furthermore, our results also suggest that social awareness seems to play a significant role in the perception of review-based RS, since we found significant main effects of social awareness on almost all variables evaluated, which seems to be a natural consequence of using users’ opinions as a basis for generating explanations, which seems to benefit greatly people with a more pronounced tendency to listen to others and take their opinions into account.
### 6.4 Usefulness of Origin of Information
Finally, with respect to our H3, we found that participants did not find indications of the origin of the information significantly more useful, unless user characteristics such as social awareness were taken into account. In this case, users who were more willing to consider other opinions found more useful the explanatory component reporting the explanations’ source of information (i. e. the reviews written by users). In this regard, it is possible that users with less social awareness, being less interested in others’ opinions, might have been disappointed because of the expectation that other sources of information would be taken into account when generating recommendations. We believe that this mismatch between the user’s conceptual model and the transmitted system’s conceptual [21] model could have resulted in a lower usefulness score for this section. However, an alternative explanation could be that users found that information redundant, which could be the case for users who felt that the information on the origin of the information represented in the explanation was already sufficiently self-explanatory.
### 6.5 Limitations
An important limitation of our study is the fact that user’s preferred aspects were fixed and participants were instructed to pretend that those aspects were the ones that mattered most to them, aiming to give a practical work around to the cold-start problem in the user study design. However, we acknowledge that this might interfere with the real perceived benefit of providing the user preferences as part of the explanations.
Additionally, we acknowledge that the use of the Amazon Mechanical Turk implies an important challenge in regard to high quality responses. Here, despite our implemented quality control and the bonus offered, further actions might be still evaluated, aiming to encourage users to genuinely make a decision. In this case, a game strategy could be used, in which users are asked to solve a specific task, for example, to choose the hotel that fits certain conditions using the information provided in the explanations, and to receive a bonus only if the task is solved successfully.
## 7 Conclusion and Future Work
In this paper, we have presented the design of argumentative explanations based on reviews, in display styles that involve visual representations like tabulated data and bar charts, as well as information about the user preferences. We also addressed the role that individual differences regarding decision making styles, social awareness and visual familiarity play in such perception. Although we found no main differences in perception between the regarded display styles, nor the presence or absence of user preferences in explanations, we found that, when taking into account user characteristics, i. e. social awareness, rational or intuitive decision making style, we are able to do detect differences in explanations’ perception between users.
Given the variability of perception of explanatory components when taking into account user characteristics, and given the difficulties (even impossibility) posed by a request or automatic inference of them, we suggest explanation designers to consider a more flexible approach, that allow users to interactively request for different presentation styles and explanatory components whenever it is needed. For example, the system could offer an initial view of explanatory information using a chart, and provide an option to visualize the same data as explicit numbers in a table, or within verbal sentences, to ensure that users who require more support to interpret the explanations have the opportunity to do so.
As part of our future work, and in order to mitigate our limitation regarding the use of real user preferences, we plan to provide a mechanism that allows participants to read explanations that fit better to their real preferences, e. g. to request participants preferences and calculate similarity with users within the dataset, so that we obtain the most similar user in terms of preferences, and use them as a proxy to calculate rating predictions.
Furthermore, we plan to work on and test improvements of the explanatory component of user profile, in order to rule out the difficulty of understanding this type of information as the main cause of its lack of usefulness, so that we can further explore the convenience of using reviews as the primary source for modeling user preferences in review-based explanatory methods.
Award Identifier / Grant number: GRK 2167
Funding statement: German Research Foundation (DFG), Grant Number: GRK 2167, Research Training Group “User-Centred Social Media”.
Diana C. Hernandez-Bocanegra
Diana C. Hernandez-Bocanegra is a research associate and PhD student in the Department of Computer Science and Applied Cognitive Science at the University of Duisburg-Essen, and a member of the Interactive Systems Research Group. Her research interests are focused on recommender systems, explainable AI and the exploration of deep learning and NLProc techniques to improve human-computer interaction.
Jürgen Ziegler
Jürgen Ziegler is a full professor in the Department of Computer Science and Applied Cognitive Science at the University of Duisburg-Essen where he directs the Interactive Systems Research Group. His main research interests lie in the areas of human-computer interaction, human-AI cooperation, recommender systems, information visualization, and health applications. Among other scientific functions he is currently editor-in-chief of i-com - Journal of Interactive Media and chair of the German special interest group on user-centred artificial intelligence.
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Published Online: 2021-01-15
Published in Print: 2021-01-26
© 2020 Walter de Gruyter GmbH, Berlin/Boston
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2023-03-26 03:23:05
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https://www.physicsforums.com/threads/difference-between-inverse-reciprocal.230599/
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# Difference Between Inverse & Reciprocal
1. Apr 22, 2008
### naicidrac
Hello,
can someone tell me the difference between reciprocal and the inverse. I have looked up the defenition and when I think I get a deep understanding I get confused. Thanks for all the help.
Naicidrac
2. Apr 22, 2008
### symbolipoint
Maybe. What kind of inverse? Do you mean "multiplicative inverse" or do you mean "inverse function"?
3. Apr 22, 2008
### trambolin
I think reciprocal is used for the scalar inverses, like 1/x. though, I am not neither native speaker nor a die-hard notation expert.
4. Apr 22, 2008
### HallsofIvy
"inverse" can apply to a number of different situations.
In ordinary arithmetic the additive inverse is the negative: the additive inverse of 2 is -2.
The multiplicative inverse is the reciprocal: the multiplicative inverse of 2 is $\frac{1}{2}$.
If we are talking about functions, then the inverse function is the inverse with respect to "composition of functions": f(f-1(x))= x and f-1(f(x))= x.
The word "inverse" can be applied to all of those (and more) but "reciprocal" only applies to multiplicative inverse.
5. Apr 22, 2008
### naicidrac
Ok awesome, Thanks for the clarity. I am thinking in terms of a trigonometric function like the difference between 1/sin(X) and sin^-1(X). What is the difference between these?
6. Apr 22, 2008
### ehj
1/sin(x) is the reciprocal of sin(x) so if sin(x) = 0,5 then 1/sin(x) = 2.
sin^-1(x) is the inverse function of sin(x), sometimes also called arcsin(x).
7. Apr 22, 2008
### arildno
Out of sneaky, sleazy suggestiveness, mathematicians have adopted the convention $f^{-1}(x)$ for the inverse of a function, although if we think in terms of powers, this might be misunderstood as $(f(x))^{-1}=\frac{1}{f(x)}$, i.e, the reciprocal of f, rather than the inverse function!
Note in particular the nasty convention of the inverse trig functions, like $\tan^{-1}(x)$.
Here, students are particularly prone to confuse the inverse trig with the reciprocal of the trig, because for all natural n's we choose to write $\tan^{n}(x)$, rather than the cumbersome $(\tan(x))^{n}[/tex] To make the issue even muddier, you may be unfortunate enough to see an iterated function like f(f(f(x))) written as [itex]f^{3}(x)$
Last edited: Apr 22, 2008
8. Feb 20, 2010
### pmoseman
Reciprocal implies an equality. To reciprocate a smile means to smile back.
While inverse implies an opposite. To invert a smile means to frown.
However in mathematics it is often stated that the inverse of a number is the reciprocal of a number.
I believe, however, this is incorrect usage.
Very confusing when dealing with trig functions.
First of all, can they truly be called functions?
It seems tan^2 (x) is equivalent to tan(x) * tan(x).
But again, you have to be careful, because this is different from tan(tan x) or even tan (x + x).
These errors are similar to other distributing errors, such as,
(3 x 3) x 2 = 6 x 6
or (3 + 3)^2 = 9 + 9
(which are false)
Last edited: Feb 20, 2010
9. Feb 20, 2010
### pmoseman
Insidious!
Last edited: Feb 20, 2010
10. Feb 20, 2010
### Staff: Mentor
Of course they can be called functions. Each one of the trig functions pairs a number in its domain with a number in its range. Did you mean the inverse trig functions when you said this? If so, the inverse of the function y = sin(x) is not itself a function, since each number in the domain of the inverse function maps to an infinite number of values in the range. To get around this problem, the domains of the trig functions are limited to an interval on which the trig function is one-to-one, thereby permitting an inverse that is a function.
More precisely, they are identically equal by definition of the notation.
I'm not aware of any special notation for collapsing tan(tan(x)). tan(x + x) = tan(2x), which would be difficult to confuse with tan2(x).
11. Feb 20, 2010
### pmoseman
To find the inverse of 2x = y, (we switch the x with the y)
we use 2y = x OR y=x/2
For the reciprocal of 2x = y (we switch the denominator with the numerator of y)
that is 2x = 1/y OR y = 1/2x
Remember a reciprocal of a number is any number you can multiply by that number to = 1.
such as -1 and -1, or 12 and 1/12
It may help to remember an inverse can be either - or + but the reciprocal will always be the same sign (thus it reciprocates the sign)
Take the function, F(x) = 3x + 2
y = 3x + 2 is changed to x = 3y+2 OR y = x/3 + 2
The reciprocal of F(x) is 1/F(x).
y = 3x+2 is changed to 1/y = 3x+2 OR y=1/(3x+2)
If we set x to 0 we get -2 and 1/2, for the inverse and reciprocal functions respectively.
However, if you solve for F(x) with you see that y = 2.
The reciprocal of 2 is 1/2. The inverse is -2.
This is what happens to exponents:
When you invert x^N= y you get:
y^N = x,
y = x^(1/N)
OR y= nth root of x
When you reciprocate x^N=y you get:
1/y = x^N,
y = x^(-N)
OR y=1/x^N
Through inverting the exponent is reciprocated! This is very non-intuitive... or so you would think!
tan(x) = sin (x) / cos (x)
1/tan(x) = cos (x) / sin(x)
tan(-1)(x) = ???
So how do you find inverse trig functions?
Well if you dedicate to memory your trig functions
COS (0) = 1
you know [COS (1)]^-1 = 0
It is just reversing x and y of the function (cos (x) = y).
if COS angle A is equal to X/R, then COS^(-1) of X/R is equal to angle A.
Last edited: Feb 20, 2010
12. Feb 20, 2010
### pmoseman
Well, I have seen people try to factor/distribute with functions as if they were coefficients. I probably should have stated this.
What I meant by asking if trigs are functions is: don't we just use a chart to find trig values? Without a formula could it be a true function?
13. Feb 20, 2010
### jgens
A formula isn't necessary since functions are defined in terms of collections of ordered pairs. More explicitly, a function $f$ is a collection of ordered pairs such that if $(a,b)$ and $(a,c)$ are both in $f$ then $b = c$. Therefore, so long as that property is satisfied, then the trigonometric functions really are functions.
$$\sin{(x)} = \sum_{n=0}^{\infty}\frac{(-1)^nx^{2n+1}}{(2n+1)!}$$
14. Feb 20, 2010
### pmoseman
Ooo, pretty...
15. Feb 22, 2010
### Studiot
Code (Text):
but "reciprocal" only applies to multiplicative inverse.
Well sort of but there is such a thing in engineering as the 'reciprocal theorem'. This is a totally different animal.
I think the arcsin(x) v 1/sin(x) example sums it up very well too.
16. Apr 23, 2011
### Rodan1
Not to mention diabolical!
I came here for primarily the same clarification. I'm just accepting it that in trig reciprocal is the same as a multiplicative reciprocal unless we're talking about identities then it's a reciprocal ID i.e. sin x = 1/csc x and inverses are i.e. sin¯ ¹ .
JW
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2018-03-20 15:20:29
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http://umr-math.univ-mlv.fr/evenements/exposes/seminaire_cristolien_d_analyse_multifractale.1452775500
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## Convergence of ergodic averages for many group rotations
Type:
Site:
Date:
14/01/2016 - 13:45 - 14:45
Salle:
Salle des thèses
Orateur:
BUCZOLICH Zoltan
Localisation:
Université Loránd Eötvös
Localisation:
Hongrie
Résumé:
Suppose that $G$ is a compact Abelian topological group, $m$ is the Haar measure on $G$ and $f : G \to\mathbb{R}$ is a measurable function. Given $(n_k)$, a strictly monotone increasing sequence of integers we consider the nonconventional ergodic/Birkhoff averages
$$M_N^\alpha f(x)=\frac1{N+A}\sum_{k=0}^N f(x+n_k\alpha).$$
The $f$-rotation set is
$$\Gamma_f = \{\alpha \in G : M_\alpha^N f (x)\textrm{ converges for }m\textrm{ a.e. }x\textrm{ as }N → ∞.\}$$
We prove that if $G$ is a compact locally connected Abelian group and $f : G \to \mathbb{R}$ is a measurable function then from $m(\Gamma_f ) > 0$ it follows that $f ∈ L^1 (G)$.
A similar result is established for ordinary Birkhoff averages if $G = \mathbb{Z}_p$, the group of $p$-adic integers.
However, if the dual group, $G$ contains “infinitely many multiple torsion” then such results do not hold if one considers non-conventional Birkhoff averages along ergodic sequences.
What really matters in our results is the boundedness of the tail, $f (x +n_k\alpha)/k$, $k = 1, ...$ for a.e. $x$ for many $\alpha$, hence some of our theorems are stated by using instead of $\Gamma_f$ slightly larger sets, denoted by $\Gamma_{f,b}$. This is a joint work with G. Keszthelyi.
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2018-02-19 17:30:53
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https://www.physicsforums.com/threads/i-think-this-is-about-the-central-limit-theorem.844791/
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# I think this is about the Central Limit Theorem
Tags:
1. Nov 23, 2015
### whitejac
1. The problem statement, all variables and given/known data
An engineer is measuring a quantity q. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and reports the average of the measurements as the estimated value of q. Specifically, if Yi is the value that is obtained in the i'th measurement, we assume that
Yi=q+Xi,
where Xi is the error in the ith measurement. We assume that Xi's are i.i.d. with EXi=0 and Var(Xi)=4 units. The engineer reports the average of measurements
Mn = (Y1 + .... Yn) / n
How
many measurements does the engineer need to make until he is 95% sure that the final error is less than 0.1 units? In other words, what should the value of n be such that
P(q−0.1≤Mn≤q+0.1)≥0.95?
2. Relevant equations
Central Limit Theorem states:
Zn = (Mx - μ) / (σ / √n)
3. The attempt at a solution
So this is the formula I chose to use. It seems like a simple variable swap, but my problem is pulling n out.
P(y1 ≤ Y ≤ y2)
= P( (y1 - nμ) / (σ√n) ≤ ((X1 +... Xn) - nμ) / (σ√n)) ≤ (y2 - nμ) / (σ√n)
Then this would give ((q + 0.1) / (2√n)) - ((q - 0.1) / (2√n)) = Φ-1 (0.95) = 1.64
combining this would give:(q/2√n) + (0.1 / 2√n) - (q / 2√n)- (0.1 / 2√n) = 0.2 / 2√n = 1/√n = 1.64 ⇒ n = (1/1.64)2 = 0.37
Now... this is not an integer, and makes absolutely no sense. I am semi-confident in my process, but I think I may have made too many assumptions about the central limit theorem.
2. Nov 24, 2015
### BvU
Why do you change from $\ \sigma\over\sqrt n\$ to $\ \sigma\sqrt n\$ ?
It seems your n is used for two different purposes as well
...
3. Nov 24, 2015
### whitejac
When you multiply by n/n you get σ√n
4. Nov 24, 2015
### BvU
I would call that multiplying by n, not multiplying by n/n
Check it anyway !
5. Nov 24, 2015
### whitejac
It has to be n/n because Mx is (X1 +...+Xn)/n.
In my extrapolation of the formula you quoted, the y1 = q - 0.1, nμ = 0 and σ = √4
Which portion did I misinterpret/use twice?
6. Nov 24, 2015
### BvU
The "Then" part, where you divide by n
Another comment: Your 1.64 looks one-sided to me. And your notation asks more from the reader than is reasonable; teachers shouldn't allow that ! (there is no using n twice; I got confused -- sorry)
I end up with an awful lot of measurements required, which is rather to be expected if you start out with such a large variance !
By the way, even "Var(Xi)=4 units" is confusing. Shouldn't it be Var(Xi)=4 units2 ?
Central Limit Theorem states: Zn = (Mx - μ) / (σ / √n) is normally distributed with standard deviation 1
Matter of completeness: for some readers Zn is something else: an impedance or whatever.
Last edited: Nov 24, 2015
7. Nov 24, 2015
### whitejac
Sorry, it ought to be. My book isn't the best despite my professor's claim. I guess they're assuming "units" is general enough.
Maybe I'm not looking at it the same way you are, I don't divide by n. I multiply by n to get y1 and y2 = q-0.1, q+0.1, respectively. This is consistent with examples in my book, I think. Are you saying I mistook these values as y1,y2 when they were in fact y1 - nμ, y2 + nμ?
I apologize for my not showing as many steps, or in the best way. It's much neater on my paper. I'll upload it when i get home if it remains unclear.
8. Nov 24, 2015
### BvU
No need to apologize, I'm trying to help.
In the top line you have y1 for nq, in the bottom line you have q only. You only divide the numerator by n.
The 1.64 is for 5% in one tail, you want 2.5% in each tail.
--
The more I read it, the more nonsensical it becomes:
What does it say here ?
Last edited: Nov 24, 2015
9. Nov 24, 2015
### Ray Vickson
I suggest you go back to square one. You need to figure out how to make a 95% probability interval (centered at the mean) come out with a length of 0.2 (i.e., from -0.1 to + 0.1). In terms of the unit normal distribution, how many standard deviations wide would that be? Then carefully figure out what that means in terms of n. When I do it I get a value of n between 1000 and 2000, but I will not state the precise value.
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2017-11-20 04:37:00
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https://www.shaalaa.com/question-bank-solutions/calculate-work-done-following-reaction-50o-c-state-whether-work-done-system-or-system-chemical-thermodynamics-energetic-enthalpy-of-bond-dissociation_69218
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# Calculate the Work Done in the Following Reaction at 50o C. State Whether Work is Done on the System Or by the System. - Chemistry
Calculate the work done in the following reaction at 50°C. State whether work is done on the system or by the system.
"SO"_2("g") + 1/2"O"_(2("g")) rightarrow "SO"_(3("g"))
#### Solution
"SO"_2("g") + 1/2"O"_(2("g")) rightarrow "SO"_(3("g"))
Δn = (moles of gaseous product) - (moles of gaseous reactant)
= 1-(1+1/2)
=-1/2
w = - ΔnRT
-( -1/2 × 8.314 × 323)
=1342.7J
As work done is positive. Therefore work is done by surrounding on system.
(OR)
The standard enthalpy of combustion of formaldehyde Δ 0H0 = -571 kJ How much heat will be evolved in the formation of 22 g of CO2 ?
Concept: Chemical Thermodynamics and Energetic - Enthalpy of Bond Dissociation
Is there an error in this question or solution?
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2021-04-16 02:50:00
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https://www.omnicalculator.com/physics/brake-mean-effective-pressure-bmep
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# BMEP Calculator (Brake Mean Effective Pressure Calculator)
Reviewed by Hanna Pamuła, PhD and Jack Bowater
Last updated: Nov 22, 2022
The BMEP calculator helps in finding the BMEP (Brake Mean Effective Pressure) of an engine, which is a useful metric to compare the performance of different engines of similar types. Here, we will see what BMEP is, how to calculate the BMEP of an engine and also learn more about the BMEP formula that's used to calculate this value.
Knowing what BMEP is, is pretty important, since the Brake Mean Effective Pressure value gives you a sense of how efficient your engine is.
## What is BMEP?
BMEP stands for Brake Mean Effective Pressure. Our BMEP calculator measures the average pressure applied across the pistons to produce torque at the crankshaft. We can use this performance metric to compare different engines.
It's also interesting to note that the engine efficiency also depends on the amount of air-fuel that is handled by the carburetor, and the carburetor CFM metric provides a measure of that volume.
## BMEP formula
The formula used to calculate BMEP is as follows:
$\mathrm{BMEP} = \frac{2π n T} {D}$
where,
• n - Number of revolutions per power stroke;
• T - Torque; and
• D - Displacement (volume) of the engine.
It is to be noted that the value of n is standard -
• n = 1 for a two-stroke engine; and
• n = 2 for a four-stroke engine.
If you're curious, you may even try converting torque to horsepower, or use a power converter to convert the horsepower value into various other units.
## How do we calculate the BMEP of an engine?
Let's say we have a 4-stroke engine with a volume (displacement) of 2000 cc and an indicated torque of 160 Nm. This is how we calculate the BMEP of the engine -
1. In the BMEP calculator, set the type of the engine to 4-stroke. Once this is selected, n is automatically set to 2.
2. Set the torque value as $160 \ \mathrm{Nm}$.
3. Set the displacement value as $2000 \ \mathrm{cc}$.
4. Voila! The BMEP calculator gives a result of $1,005.3 \ \mathrm{kPa}$.
Conversely, if we know the BMEP value, we can convert BMEP to torque by using the same formula and rearranging it to solve for torque. Converting BMEP to torque is especially useful since torque is an important metric that represents the load that the engine can handle.
Additionally, if you're curious about how horsepower can help in comparing engine efficiencies, you may try calculating the horsepower of different engines! You may also be interested in knowing about the various factors that affect the piston speed and the piston force using our piston speed calculator and piston force calculator.
## FAQ
### Why is the BMEP important?
BMEP is responsible for the torque produced by the engine. If we can increase the BMEP of a given engine, we can observe a proportional increase in its output torque!
### What is the difference between two-stroke and four-stroke engines?
During one power stroke, the two-stroke engine has one revolution of the crankshaft and generates more torque, while a four-stroke engine has two revolutions of the crankshaft and generates less torque. A four-stroke engine tends to emit less smoke and is more efficient compared to a two-stroke engine.
### How can BMEP be increased?
Some things you can try to increase the BMEP of an engine:
1. Increasing the compression ratio.
2. Increasing the quantity of air-fuel mixture in the chamber by supercharging or turbocharging.
3. Shorter stroke length.
4. Enriching the air-fuel mixture.
### Does the BMEP of a diesel engine vary from that of a petrol engine?
Generally, diesel engines have higher compression ratios than their petrol counterparts and hence have higher BMEP. However, note that BMEP comparison is usually reserved for similar engines. For example, we can compare the BMEP of different diesel engines, but not with petrol engines.
Engine type
Four Stroke Engine
Engine displacement (Volume)
cu in
Torque
lbf·ft
Brake mean effective pressure
psi
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2022-12-06 14:58:36
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https://www.physicsforums.com/threads/centralizers-and-elements-of-odd-order.388899/
|
# Centralizers and elements of odd order
I was going over a proof in which the following is given:
if abb=bba and b is of odd order, then ab=ba (i.e. if b^2 centralizes a then so does b)
I'm not sure why this is so. Any clarification would be appreciated.
Cheers,
W. =)
Dick
Homework Helper
b^2 commutes with a. If b has odd order then b^(2n+1)=e for some n. So b^(2n+1)a=a(b^(2n+1)). Do you see it now?
I believe so...
b^(2n)ba = ab^(2n)b
b^2n(ba) = b^2n(ab) since abb = bba
ba = ab
If that's it, then cheers! =)
Dick
Homework Helper
I believe so...
b^(2n)ba = ab^(2n)b
b^2n(ba) = b^2n(ab) since abb = bba
ba = ab
If that's it, then cheers! =)
Cheers!
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2021-06-13 20:38:21
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http://mathhelpforum.com/pre-calculus/4883-applications-linear-programming-print.html
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# Applications of Linear Programming
• August 11th 2006, 08:50 AM
classicstrings
Applications of Linear Programming
I'm having trouble setting up the variables and constraints in these questions. Wondering if someone can help? Thanks!
http://img216.imageshack.us/img216/6991/2zq1.jpg
• August 11th 2006, 08:36 PM
Soroban
Hello, classicstrings!
Here's the second one . . .
Quote:
A furniture maker produces cupboards and bookshelves.
Both products use wooden planks, sawing time, sanding time, and assembly time.
The cupboards use 20 m of wood, 40 minutes of sawing, 60 minutes of sanding,
and 10 minute of assembly time for a profit of $280. The bookshelves use 10 m of wood, 30 minutes of sawing, 90 minutes of sanding, and 30 minutes of assembly time for a profit of$340.
There are 220 m of wood, 480 minutes of sawing time, 1080 minutes of sanding time,
and 330 minutes of assembly time available.
How many of each item should be made for maximum profit?
Let $x$ = number of cupboards, $y$ = number of bookshelves. . $x \geq 0,\;y \geq 0$ [1]
A chart helps to organize the information . . .
Code:
| wood + saw | sand | assem | - - - - - - - - + - - -+ - - + - - -+ - - - + cupboards (x) | 20x | 40x | 60x | 10x | - - - - - - - - + - - + - - + - - -+ - - - + bookshelves (y) | 10y | 30y | 90y | 30y | - - - - - - - - + - - + - - + - - -+ - - - + available | 220 | 480 | 1080 | 330 | - - - - - - - - + - - -+ - - + - - -+ - - - +
Wood: . $20x + 10y \:\leq \:220\quad\Rightarrow\quad 2x + y \:\leq \:22$ [2]
Sawing: . $40x + 30y \:\leq \:480\quad\Rightarrow\quad 4x + 3y \:\leq \:48$ [3]
Sanding: . $60x + 90y \:\leq \:1080\quad\Rightarrow\quad 2x + 3y \:\leq \:36$ [4]
Assembly: . $10x + 30y \:\leq \:330\quad\Rightarrow\quad x + 3y\:\leq\:33$ [5]
[1] places us in Quadrant 1.
[2] Graph the line: $2x + y \:=\:22$. .It has intercepts: $(11,0),\;(0,22)$. .
. . .Shade the region below the line.
[3] Graph the line: $4x + 3y \:=\:48$. .It has intercepts: $(12,0),\;(0,16)$
. . .Shade the region below the line.
[4] Graph the line: $2x + 3y \:=\:36$. .It has intercepts: $(18,0),\;(0,12)$
. . .Shade the region below the line.
[5] Graph the line: $x + 3y \:=\:33$. .It has intercepts: $(33,0),\;(0,11)$
. . .Shade the region below the line.
The final region is a hexagon. .Its vertices are (clockwise from the origin):
. . $(0,0),\;(0,11),\;(3,10),\;)6,8),\;(9,4),\;(0,11)$
Test them in the profit function: $P \:= \:280x + 340y$
. . to see which one produces maximum profit.
• August 13th 2006, 01:09 AM
classicstrings
Hey Soroban! You have done the harder one for me, and I have gone through it a couple of times myself after, I have done the first one by looking @ how you did them. Cheers!
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2016-08-28 09:48:58
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https://cs.stackexchange.com/questions/135017/what-problem-is-this-largest-sum-produced-by-selecting-one-number-at-each-index
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# What problem is this? Largest sum produced by selecting one number at each index from n lists, with restrictions
Suppose you have an $$n\times m$$ 2D array consisting of each $$n$$ rows of $$m$$ real numbers. What is the sequence of indexes $$i_1,i_2...i_m$$ such that $$\sum_{j=1}^mA[i_j, j]$$ is maximized, subject to the constraint that each run of a value in $$i_1...i_m$$ must be at least $$r$$ entries long?
A correct algorithm with time linear in $$m$$ seems possible with dynamic programming. It would be even nicer to know the name of the problem and some academic reference to a correct solution. This is a minor methodological step in an analysis I'm doing for an interpersonal communication research paper, so ideally I'd like to find a paper to cite. This smells very similar to the dynamic programming homework problems I did in undergrad, so I'd be surprised if there isn't work on it.
In practice, $$m \approx 12000$$, $$n=3$$, and $$20 \leq r \leq 200$$.
• If there is a simple dynamic programming algorithm for this problem, I wouldn't expect there to be a paper about it; that's not the sort of thing that tends to get published. Most problems don't have a "name". The obvious dynamic programming algorithm I can see seems to take $O(nm)$ time rather than $O(m)$ time. – D.W. Feb 2 at 0:13
• Certainly no recent paper, but wouldn't there be some similar problem in the early days? If not, that's not bad - I just brush off my proof-writing skills and add a proof in the supplementary material for the article submission. I'm concerned there is one but I don't know it. And you're absolutely right. The important part is that it's not O(m^2) or O(2^m) or O(m choose m/r) - just that the m term is linear. Is there a more technical way to say that? – Mark Miller Feb 2 at 1:25
• Also, my sketch was O(nmr) rather than O(nm) - perhaps can you share your sketch? – Mark Miller Feb 2 at 1:26
I believe this can be solved in $$O(nm)$$ time using dynamic programming:
\begin{align*} B[i,k] &= A[i,k] + \dots + A[i,k+r-1] + C[i,r]\\ C[i,k] &= \max(A[i,k] + C[i,k+1], \max_{i'} B[i',k]) \end{align*}
Note that you can compute $$A[i,k] + \dots + A[i,k+r-1]$$ in $$O(1)$$ time as the difference of two prefix sums (assuming you have done a one-time precomputation to compute all prefix-sums).
The answer is then $$\max_i B[i,1]$$. Computing it takes $$O(nm)$$ time, as there are $$O(nm)$$ entries to fill in, and each one takes $$O(1)$$ time to fill in, using the equations above.
Interpretation:
• $$B[i,k]$$ is the maximum possible value of $$\sum_{j=k}^m A[i_j,j]$$ such that $$i_k=i$$ and $$i_k,\dots,i_m$$ satisfy the repetition rule
• $$C[i,k]$$ is the maximum possible value of $$\sum_{j=k}^m A[i_j,j]$$ such that $$i_k,\dots,i_m$$ satisfy the repetition rule except that if $$i_k=i$$, the run starting at $$i_k$$ can be of any length (but all subsequent runs must be at least $$r$$ long). In other words, $$C[i,k] = \max_\ell A[i,k] + \dots + A[i,k+\ell-1] + \max_{i'} B[i',k+\ell]$$
Generally, this is not the kind of thing I would expect to find papers about. I would expect to see a one-sentence "can be solved by dynamic programming", possibly with an explanation of the max-trick above to reduce the running time from $$O(nmr)$$ to $$O(nm)$$, but not an entire paper about it. So I would not bet on such a paper existing. But I could be wrong. It's certainly possible there could be such a paper. I would not know how to go about looking for it.
• The answer of "there probably isn't a paper" is still helpful. On top of that, the difference of prefix sums is an insight I wouldn't have gotten in this case. One note, though - is the expression for B rather $B[i, k] = A[i,k] + \dots + A[i,k+r-1] + \max_{i'} C[i', r]$? I think I follow everything else. – Mark Miller Feb 3 at 2:10
• @MarkMiller, oh, right, that was wrong, thank you! Edited. I think the expression is a little different, maybe. – D.W. Feb 3 at 4:38
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2021-04-22 12:00:44
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https://api-project-1022638073839.appspot.com/questions/how-do-you-differentiate-f-x-e-5x-2
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# How do you differentiate f(x) = e^(-5x^2)?
##### 1 Answer
Jan 20, 2016
$- 10 x {e}^{- 5 {x}^{2}}$
#### Explanation:
Finding derivatives in the form ${e}^{u}$ is quite simple.
According to the chain rule,
$\frac{d}{\mathrm{dx}} \left[{e}^{u}\right] = {e}^{u} \cdot u '$
Thus,
$f ' \left(x\right) = \frac{d}{\mathrm{dx}} \left[{e}^{- 5 {x}^{2}}\right] = {e}^{- 5 {x}^{2}} \cdot \frac{d}{\mathrm{dx}} \left[- 5 {x}^{2}\right] = - 10 x {e}^{- 5 {x}^{2}}$
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2021-04-11 15:37:07
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https://courses.lumenlearning.com/atd-austincc-physics1/chapter/16-1-hookes-law-stress-and-strain-revisited/
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## Hooke’s Law: Stress and Strain Revisited
### Learning Objectives
By the end of this section, you will be able to:
• Explain Newton’s third law of motion with respect to stress and deformation.
• Describe the restoration of force and displacement.
• Calculate the energy in Hook’s Law of deformation, and the stored energy in a string.
Figure 1. When displaced from its vertical equilibrium position, this plastic ruler oscillates back and forth because of the restoring force opposing displacement. When the ruler is on the left, there is a force to the right, and vice versa.
Newton’s first law implies that an object oscillating back and forth is experiencing forces. Without force, the object would move in a straight line at a constant speed rather than oscillate. Consider, for example, plucking a plastic ruler to the left as shown in Figure 1. The deformation of the ruler creates a force in the opposite direction, known as a restoring force. Once released, the restoring force causes the ruler to move back toward its stable equilibrium position, where the net force on it is zero. However, by the time the ruler gets there, it gains momentum and continues to move to the right, producing the opposite deformation. It is then forced to the left, back through equilibrium, and the process is repeated until dissipative forces dampen the motion. These forces remove mechanical energy from the system, gradually reducing the motion until the ruler comes to rest.
The simplest oscillations occur when the restoring force is directly proportional to displacement. When stress and strain were covered in Newton’s Third Law of Motion, the name was given to this relationship between force and displacement was Hooke’s law: F = −kx.
Here, F is the restoring force, x is the displacement from equilibrium or deformation, and k is a constant related to the difficulty in deforming the system. The minus sign indicates the restoring force is in the direction opposite to the displacement.
The force constant k is related to the rigidity (or stiffness) of a system—the larger the force constant, the greater the restoring force, and the stiffer the system. The units of k are newtons per meter (N/m). For example, k is directly related to Young’s modulus when we stretch a string. Figure 3 shows a graph of the absolute value of the restoring force versus the displacement for a system that can be described by Hooke’s law—a simple spring in this case. The slope of the graph equals the force constant k in newtons per meter. A common physics laboratory exercise is to measure restoring forces created by springs, determine if they follow Hooke’s law, and calculate their force constants if they do.
### Example 1. How Stiff Are Car Springs?
#### Strategy
Consider the car to be in its equilibrium position x=0 before the person gets in. The car then settles down 1.20 cm, which means it is displaced to a position x = −1.20 × 10−2 m. At that point, the springs supply a restoring force F equal to the person’s weight wmg = (80.0 kg)(9.80 m/s2) = 784 N. We take this force to be F in Hooke’s law. Knowing F and x, we can then solve the force constant k.
#### Solution
Solve Hooke’s law, F = −kx, for k:
$k=-\frac{F}{x}\\$
Substitute known values and solve k:
$\begin{array}{lll}k&=&-\frac{784\text{ N}}{-1.20\times10^{-2}\text{ m}}\\\text{ }&=&6.53\times10^4\text{ N/m}\end{array}\\$
Discussion
Note that F and x have opposite signs because they are in opposite directions—the restoring force is up, and the displacement is down. Also, note that the car would oscillate up and down when the person got in if it were not for damping (due to frictional forces) provided by shock absorbers. Bouncing cars are a sure sign of bad shock absorbers.
## Energy in Hooke’s Law of Deformation
In order to produce a deformation, work must be done. That is, a force must be exerted through a distance, whether you pluck a guitar string or compress a car spring. If the only result is deformation, and no work goes into thermal, sound, or kinetic energy, then all the work is initially stored in the deformed object as some form of potential energy. The potential energy stored in a spring is $\text{PE}_{\text{el}}=\frac{1}{2}kx^2\\$. Here, we generalize the idea to elastic potential energy for a deformation of any system that can be described by Hooke’s law. Hence, $\text{PE}_{\text{el}}=\frac{1}{2}kx^2\\$, where PEel is the elastic potential energy stored in any deformed system that obeys Hooke’s law and has a displacement x from equilibrium and a force constant k.
It is possible to find the work done in deforming a system in order to find the energy stored. This work is performed by an applied force Fapp. The applied force is exactly opposite to the restoring force (action-reaction), and so Fappkx. Figure 5 shows a graph of the applied force versus deformation x for a system that can be described by Hooke’s law. Work done on the system is force multiplied by distance, which equals the area under the curve or $\frac{1}{2}kx^2\\$ (Method A in Figure 5). Another way to determine the work is to note that the force increases linearly from 0 to kx, so that the average force is $\frac{1}{2}kx\\$, the distance moved is x, and thus $W=F_{\text{app}}d=\left(\frac{1}{2}kx\right)\left(x\right)=\frac{1}{2}kx^2\\$ (Method B in Figure 5).
### Example 2. Calculating Stored Energy: A Tranquilizer Gun Spring
We can use a toy gun’s spring mechanism to ask and answer two simple questions:
1. How much energy is stored in the spring of a tranquilizer gun that has a force constant of 50.0 N/m and is compressed 0.150 m?
2. If you neglect friction and the mass of the spring, at what speed will a 2.00-g projectile be ejected from the gun?
#### Strategy for Part 1
The energy stored in the spring can be found directly from elastic potential energy equation, because k and x are given.
#### Solution for Part 1
Entering the given values for k and x yields
$\begin{array}{lll}\text{PE}_{\text{el}}&=&\frac{1}{2}kx^2=\frac{1}{2}\left(50.0\text{ N/m}\right)\left(0.150\text{ m}\right)^2=0.563\text{ N}\cdot\text{ m}\\\text{ }&=&0.563\text{ J}\end{array}\\$
#### Strategy for Part 2
Because there is no friction, the potential energy is converted entirely into kinetic energy. The expression for kinetic energy can be solved for the projectile’s speed.
#### Solution for Part 2
Identify known quantities:
KEf = PEel or $\frac{1}{2}mv^2=\frac{1}{2}kx^2=\text{PE}_{\text{el}}=0.563\text{ J}\\$
Solve for v:
$\displaystyle{v}=\left[\frac{2\text{PE}_{\text{el}}}{m}\right]^{1/2}=\left[\frac{2\left(0.563\text{ J}\right)}{0.002\text{ kg}}\right]^{1/2}=23.7\left(\text{J/kg}\right)^{1/2}\\$
Convert units: 23.7 m/s
#### Discussion
Parts 1 and 2: This projectile speed is impressive for a tranquilizer gun (more than 80 km/h). The numbers in this problem seem reasonable. The force needed to compress the spring is small enough for an adult to manage, and the energy imparted to the dart is small enough to limit the damage it might do. Yet, the speed of the dart is great enough for it to travel an acceptable distance.
#### Part 1
Envision holding the end of a ruler with one hand and deforming it with the other. When you let go, you can see the oscillations of the ruler. In what way could you modify this simple experiment to increase the rigidity of the system?
##### Solution
You could hold the ruler at its midpoint so that the part of the ruler that oscillates is half as long as in the original experiment.
#### Part 2
If you apply a deforming force on an object and let it come to equilibrium, what happened to the work you did on the system?
##### Solution
It was stored in the object as potential energy.
## Section Summary
• An oscillation is a back and forth motion of an object between two points of deformation.
• An oscillation may create a wave, which is a disturbance that propagates from where it was created.
• The simplest type of oscillations and waves are related to systems that can be described by Hooke’s law: F = −kx,
where F is the restoring force, x is the displacement from equilibrium or deformation, and k is the force constant of the system.
• Elastic potential energy PEel stored in the deformation of a system that can be described by Hooke’s law is given by ${\text{PE}}_{\text{el}}=\frac{1}{2}kx^{2}\\$.
### Conceptual Questions
1. Describe a system in which elastic potential energy is stored.
### Problems & Exercises
1. Fish are hung on a spring scale to determine their mass (most fishermen feel no obligation to truthfully report the mass). (a) What is the force constant of the spring in such a scale if it the spring stretches 8.00 cm for a 10.0 kg load? (b) What is the mass of a fish that stretches the spring 5.50 cm? (c) How far apart are the half-kilogram marks on the scale?
2. It is weigh-in time for the local under-85-kg rugby team. The bathroom scale used to assess eligibility can be described by Hooke’s law and is depressed 0.75 cm by its maximum load of 120 kg. (a) What is the spring’s effective spring constant? (b) A player stands on the scales and depresses it by 0.48 cm. Is he eligible to play on this under-85 kg team?
3. One type of BB gun uses a spring-driven plunger to blow the BB from its barrel. (a) Calculate the force constant of its plunger’s spring if you must compress it 0.150 m to drive the 0.0500-kg plunger to a top speed of 20.0 m/s. (b) What force must be exerted to compress the spring?
4. (a) The springs of a pickup truck act like a single spring with a force constant of 1.30 × 105 N/m. By how much will the truck be depressed by its maximum load of 1000 kg? (b) If the pickup truck has four identical springs, what is the force constant of each?
5. When an 80.0-kg man stands on a pogo stick, the spring is compressed 0.120 m. (a) What is the force constant of the spring? (b) Will the spring be compressed more when he hops down the road?
6. A spring has a length of 0.200 m when a 0.300-kg mass hangs from it, and a length of 0.750 m when a 1.95-kg mass hangs from it. (a) What is the force constant of the spring? (b) What is the unloaded length of the spring?
## Glossary
deformation: displacement from equilibrium
elastic potential energy: potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring
force constant: a constant related to the rigidity of a system: the larger the force constant, the more rigid the system; the force constant is represented by k
restoring force: force acting in opposition to the force caused by a deformation
### Selected Solutions to Problems & Exercises
1. (a) 1.23 × 103 N/m; (b) 6.88 kg; (c) 4.00 mm
3. (a) 889 N/m; (b) 133 N
5. (a) 6.53 × 103 N/m; (b) Yes
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2020-09-28 15:22:54
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https://dobrewiadomosci.eu/assassin-s-ywkr/chebyshev-distance-formula-5b7d34
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In the above figure, imagine the value of θ to be 60 degrees, then by cosine similarity formula, Cos 60 =0.5 and Cosine distance is 1- 0.5 = 0.5. Well, Chebyshev’s inequality, also sometimes spelled Tchebysheff’s inequality, states that only a certain percentage of observations can be more than a certain distance from the mean and hinges on our understanding of variability as discussed in this Stanford writeup. let z = generate matrix chebyshev distance y1 … Computes the Chebyshev distance between two arrays.. But if $$n$$ is an integer, the given function is the Chebyshev polynomial of the first kind. This is an example calculation shown below explain how to find the distance between two vectors using Chebyshev distance formula. For use in the browser, use browserify. = = = 1 – 0.25 = 0.75. Chebyshev … ChessboardDistance[u, v] gives the chessboard, Chebyshev, or sup norm distance between vectors u and v. Therefore 75% of the values of a data set lie within 2 standard deviations of the mean. 0.75 as a percent is 75%. The Chebyshev distance is a metric defined on a vector space where the distance between two vectors is the greatest difference along any coordinate dimension. Installation \$ npm install compute-chebyshev-distance. Chebyshev Distance. Just replace k = 2 into the formula. The Chebyshev distance between two points p and q with coordinates p i and q i is. In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L∞ metric[1] is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. Usage. If λ = 2, we are in the presence of Euclidean distance. TITLE Chebyshev Distance (IRIS.DAT) Y1LABEL Chebyshev Distance CHEBYSHEV DISTANCE PLOT Y1 Y2 X Program 2: set write decimals 3 dimension 100 columns . A vector,array of elements declared and initialized in Java using one dimensional array. Suppose you want to find the percent of values of a data set that lie within 2 standard deviations of the mean. The Chebyshev distance evaluates the absolute maximum value of the differences between the coordinates (or other quantitative features) of a pair of objects. Overall, we can change the value of λ to calculate the distance between two points in many ways. Then the general solution of the original Chebyshev equation will be given by the formula: $y\left( x \right) = C\cos \left( {n\arccos x} \right).$ In this expression, $$n$$ may be any real number. Therefore the … There is another distance called Chebyshev distance that happens when λ = ∞.. The Chebyshev distance is a metric defined on a vector space where the distance between two vectors is the greatest difference along any coordinate dimension. ... Chebyshev’s Inequality Formula. 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Set that lie within 2 standard deviations of the mean distance called Chebyshev distance between two in!, array of elements declared and initialized in Java using one dimensional array the given function is the distance... P i and q with coordinates p i and q with coordinates p i and q with p!, we have the Manhattan distance to find the percent of values of data!
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2021-03-04 16:05:50
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http://mathhelpforum.com/math-topics/126858-atoms-grams.html
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# Math Help - Atoms to Grams
1. ## Atoms to Grams
Hi, sry again -_- but i have yet another question.. what am i doing wrong!?
im trying to convert Atoms to Grams. EXample
1.0×1023
so im doing
(1.0×1023 )(1/6.022x10^23)(196.
96655)=3.3g (putting it to 2 sig figs.)
same thing for 2.80×1022
im doing (2.80×1022 )(1/6.022x10^23)(4.002602)=1.9
______________________________
last but not least can you guys help me get an idea of how to do this problem i think i know how but want to verify.
How many helium atoms are there in a helium blimp containing 535 of helium?
so i would start off by puting 535 into grams (535000g)then divide by molar mass then multiply by avogadro = atoms (8.0*10^28)
2. Originally Posted by Nismo
Hi, sry again -_- but i have yet another question.. what am i doing wrong!?
im trying to convert Atoms to Grams. EXample
1.0×1023
so im doing
(1.0×1023 )(1/6.022x10^23)(196.
96655)=3.3g (putting it to 2 sig figs.)
same thing for 2.80×1022
im doing (2.80×1022 )(1/6.022x10^23)(4.002602)=1.9
______________________________
last but not least can you guys help me get an idea of how to do this problem i think i know how but want to verify.
How many helium atoms are there in a helium blimp containing 535 of helium?
so i would start off by puting 535 into grams (535000g)then divide by molar mass then multiply by avogadro = atoms (8.0*10^28)
I'd use the mole as an intermediate step, that is divide by Avogadro's constant and then by the relative atomic mass.
$\text { moles of gold} = \frac{10^{23}}{6.02 \times 10^{23}} = \frac{1}{6.02}$
$m = n\,A_r = \frac{1}{6.02} \times 197 = 32.72 \text{ g }$
You appear to be an order of magnitude out by my answers, check your powers of 10?
--------------------------
2. Yep
3. 1) I see what you did for the 1st problem, but i cant seem to use that method when doing
7.4×1021 or 2.80×1022
2) Also is the answer going to be 8 atoms or the 8.049x10^24?? (because i would have to round this to 4 sig figs since the 6.022 is 4 sig figs and since im dividing with if that makes sense?
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2016-05-30 09:36:45
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https://web2.0calc.com/questions/the-polynomial-f-x-has-degree-3-if-f-1-15-f-0-0-f_3
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+0
# The polynomial f(x) has degree 3. If f(-1)=15, f(0)=0, f(1)=5 and f(2)=12, then what are the x-intercepts of the graph of f?
0
121
1
The polynomial f(x) has degree 3. If f(-1)=15, f(0)=0, f(1)=5 and f(2)=12, then what are the x-intercepts of the graph of f?
Nov 3, 2018
#1
+5091
+2
$$\text{here may be some clever way to attack this but if so I'm not aware of it}\\ p(x) = a x^3 + b x^2 + c x + d\\ \text{using the function values give we can form the equations}\\ -a+b-c+d=15\\ d=0\\ a+b+c+d=5\\ 8a+4b+2c+d=12\\ \text{I would dump these into a matrix and solve it like that}\\ \begin{pmatrix}-1 &1 &-1 &1\\0 &0 &0 &1 \\1 &1 &1 &1 \\8 &4 &2 &1\end{pmatrix} \begin{pmatrix}a \\ b\\ c \\ d\end{pmatrix} = \begin{pmatrix}15 \\0 \\5 \\12 \end{pmatrix}$$
Solving this using the method of you choice we find
$$a=-3,~b=10,~c=-2,~d=0 \\ p(x) = -3x^3 + 10x^2 -2x$$
The x-intercepts occur where p(x)=0, factoring we get
$$p(x)=-3x^3+10x^2-2x = \\ -x(3x^2 - 10x+2)\\ \text{and this has zeros at } x=0 \text{ and}\\ x = \dfrac{10\pm \sqrt{100-24}}{6} = \dfrac 1 3\left(5 \pm \sqrt{19}\right)$$
.
Nov 4, 2018
edited by Rom Nov 4, 2018
#1
+5091
+2
$$\text{here may be some clever way to attack this but if so I'm not aware of it}\\ p(x) = a x^3 + b x^2 + c x + d\\ \text{using the function values give we can form the equations}\\ -a+b-c+d=15\\ d=0\\ a+b+c+d=5\\ 8a+4b+2c+d=12\\ \text{I would dump these into a matrix and solve it like that}\\ \begin{pmatrix}-1 &1 &-1 &1\\0 &0 &0 &1 \\1 &1 &1 &1 \\8 &4 &2 &1\end{pmatrix} \begin{pmatrix}a \\ b\\ c \\ d\end{pmatrix} = \begin{pmatrix}15 \\0 \\5 \\12 \end{pmatrix}$$
Solving this using the method of you choice we find
$$a=-3,~b=10,~c=-2,~d=0 \\ p(x) = -3x^3 + 10x^2 -2x$$
The x-intercepts occur where p(x)=0, factoring we get
$$p(x)=-3x^3+10x^2-2x = \\ -x(3x^2 - 10x+2)\\ \text{and this has zeros at } x=0 \text{ and}\\ x = \dfrac{10\pm \sqrt{100-24}}{6} = \dfrac 1 3\left(5 \pm \sqrt{19}\right)$$
Rom Nov 4, 2018
edited by Rom Nov 4, 2018
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2019-05-26 00:28:53
|
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http://forums.wolfram.com/mathgroup/archive/2008/Jul/msg00063.html
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Services & ResourcesWolfram ForumsMathGroup Archive
Re: Draw two functions in a graph, one of them does also have a parameter.
• To: mathgroup at smc.vnet.net
• Subject: [mg90218] Re: Draw two functions in a graph, one of them does also have a parameter.
• From: "David Park" <djmpark at comcast.net>
• Date: Wed, 2 Jul 2008 05:32:57 -0400 (EDT)
• References: <g4d2ut$er8$1@smc.vnet.net>
With the Presentations package I would do it this way.
Needs["PresentationsMaster"]
f[x_] := -x^2 + 6 x
g[a_][x_] := a x
Draw2D[
{Draw[f[x], {x, 0, 7}],
Table[Draw[g[a][x], {x, 0, 7}], {a, 0, 3}]},
AspectRatio -> 1,
Frame -> True,
ImageSize -> 400]
If you want to label the lines with a parameter you could use:
Module[{h},
h = Table[Draw[g[a][x], {x, 0, 7}], {a, 0, 3}];
Draw2D[
{Draw[f[x], {x, 0, 7}],
h,
h // DrawLineLabels[#2/#1 &, .6 &, .1, {0, 1, 2, 3},
Style[#, 14] &,
DrawLLTextOptions -> {Background -> White}]},
AspectRatio -> 1,
Frame -> True,
ImageSize -> 400]]
--
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/
"Felipe Mannshardt" <vexie.infamous at googlemail.com> wrote in message
news:g4d2ut$er8$1 at smc.vnet.net...
> Is there a way to do a Plot do draw this two functions in the same graph ?
> I am asking because i am having problems due the parameter "a".
>
> I have,
>
> f(x)= -x^2 + 6x
> g(x)= ax
>
> i want to draw them in the same graphic and with a from 0 to 3 . . .
>
> Can not think of a way of doing this, due the "a" parameter . . .
>
> Plot[{f[x],[g[a][x]},{x,0,7},{a,0,3}]
>
>
> Can some help me out with this small issue ?
>
>
>
> In Latex,
>
>
>
> \text{Clear}[x,f,g]
>
> f[\text{x$\_$}]\text{:=}-x^2+6x
>
> \text{Nullstellen} \text{von} f[x]
>
>
>
> \text{Solve}[f[x]==0,x]
>
> \{\{x\to 0\},\{x\to 6\}\}
>
> \text{Fl{\" a}che} \text{von} f[x]
>
>
>
> \int_0^6 f[x] \, dx
>
> 36
>
> \text{Clear}[x]
>
> g[\text{a$\_$}][\text{x$\_$}]\text{:=}a*x
>
> \text{Graphisch} \text{dargestellt}
>
>
>
> \text{Plot}[f[x],\{x,-0.2,6.2\}]
>
>
>
> \text{Plot}[\text{Table}[g[a][x],\{a,0,3\}],\{x,0,2\}]
>
>
>
>
>
>
>
>
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2016-06-26 04:40:52
|
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https://mathoverflow.net/questions/409354/on-the-solvability-of-a-nonlinear-differential-system
|
# On the solvability of a nonlinear differential system
A nonlinear formulation of differential Galois theory was discussed here and here for three dimensional nonlinear systems (proof is on pages 6 – 10). For a two dimensional system, the following system of differential equations was considered: $$$$\begin{split} \dot{x}_1&=X_1(x_1,x_2),\\ \dot{x}_2&=X_2(x_1,x_2), \end{split}$$$$ such that $$X_1,X_2$$ are polynomial functions and $$X_1(0,0)\neq0$$. Let $$K$$ denote the differential field of rational functions, with constant field $$\mathbb{C}$$. The system is Liouvillian integrable iff the differential Galois group of $$dx_2/dx_1=X_2(x_1,x_2)/X_1(x_1,x_2)$$ over $$K$$ at $$(0,0)$$ is solvable. For the four dimensional system $$$$\begin{split} \dot{x}&=X,\\ \dot{X}&=\sigma(Y-X-kx),\\ \dot{Y}&=-Y+rX-XZ,\\ \dot{Z}&=-bZ+XY. \end{split}$$$$ does an equivalent formulation exist to determine whether Liouvillian integrability (or solvability by quadratures) holds where $$k,r,\sigma\in\mathbb{R}^+$$ and $$b=1$$? Any help would be much appreciated.
Note that when $$k=0$$, we have the closed system. $$$$\begin{split} \dot{X}&=\sigma(Y-X),\\ \dot{Y}&=-Y+rX-XZ,\\ \dot{Z}&=-bZ+XY. \end{split}$$$$
As a corollary of Equation 6 and 12 in the second linked paper, the Lorenz-like system is at least partially integrable when $$$$4\sigma r=b^2\frac{(2n+1)^2}{4}-(\sigma-1)^2,$$$$ for all $$n\in\mathbb{Z}^+$$.
The following theorem of Ishii may help for a complete integrability criterion. Assume that the system has a balance $$\{{a},{p}\in\mathbb{Q}^4\}$$ for which the Kovalevskaya matrix $$$$K=JV_{a}-\mathop{\mathrm{diag}}(p),$$$$ is semi-simple (such that $$JV_{a}$$ denotes the Jacobian of the system of ODEs at $$a$$). If the system is completely integrable, then the local general series are Puiseux series.
• Are there any additional information about the constants $k$, $r$, $b$ and $\sigma$? Nov 28 at 2:55
• Thanks for your reply. I am particularly interested in the system when $b=1$. Other than that, the constants assume positive real values $k,r,\sigma\in\mathbb{R}^+$. Nov 28 at 3:23
• We need to study the eigenvalues at equilibrium points. This is too difficult with all these undetermined constants. Nov 28 at 20:10
• When $r>1+k-k/(\sigma+1)$, the system is asymptotically unstable (a real part of $\lambda$ is greater than zero for the linearisation). The only equilibrium occurs at $(0,0,0,0)$ and I am more interested in proving Liouvillian integrability (or if the system is unsolvable). Nov 29 at 1:47
• As you can see in theorem 5.2 of Goriely's "Integrability and nonintegrability of dynamical systems" (link: worldscientific.com/worldscibooks/10.1142/3846), the eigenvalues (more specific a resonance condition on them) play a big role in existence of first integrals. Nov 29 at 15:43
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2021-12-04 00:56:56
|
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https://cs.stackexchange.com/questions/38172/finding-coprimes-closest-to-a-certain-target
|
# Finding coprimes closest to a certain target
Given an input $m$, I am trying to find an algorithm that will give me the number $p$ that is closest to $\tfrac47 m$ and co-prime with $m$.
Where $m$ is odd, I have no problem producing an outcome close to the target, simply by squaring $2$ until close enough to the target.
When $m$ is even, I have a bit more trouble. I have tried a few different methods with no success. I have tried starting with $p = 3$, then multiplied $p\cdot\mathrm{gcd}(p-1, m)$ until $p$ and $m$ share all factors (in other words, until $\mathrm{gcd}(p-1, m) = 1$). This eventually finds a coprime, but there is no guarantee that it is close to the target, and I'm not sure how to operate on the number from here to get another coprime closer to the target.
The algorithm needs to be able to handle massive numbers with hundreds of digits, so it needs to be pretty efficient.
I'm not sure if I'm missing a necessary fact about coprime numbers, or if I'm just misinterpreting the info I have. Can anyone point me in the right direction? Maybe a fact about coprime numbers that I'm missing?
If you want the truely closest coprime to $\frac 4 7m$, you could start with $n = \mathrm{round}(\frac 4 7m)$. Then, while $\gcd(n,m) \neq 1$, try again with $n$ being the closest number to $\frac 4 7 m$ such that $n - q \not \equiv 0 \mod \gcd(q,m)$ for any previously checked number $q$ (keep track of previously checked numbers and gcds in a list)
Checking one candidate has complexity $\mathcal O(\log(m))$. The probability of any two numbers being coprime is $\frac 6 {\pi^2} \approx 60\%$ so the numbers of candidates to check should be $\mathcal O(1)$ on average.
Overall this should find you the closest coprime in $\mathcal O(\log(m))$ operations.
Let m = 7i + j, 0 ≤ j < 7. Let p = 4i + k for some small k. When we calculate gcd (p, m) we get the following pairs:
7i + j, 4i + k // subtract right hand side from left and exchange
4i + k, 3i + j - k // subtract right hand side from left and exchange
3i + j - k, i + 2k - j // subtract 3x right hand side
i + 2k - j, 4j - 7k
so we need gcd (m, 4j - 7k) = 1. i and j are fixed. Check values k in the right order (the order is 0, 1, -1, 2, -2, 3, -3, 4, except you swap each pair if j ≥ 4). Ignore k where 4j - 7k = 0. For each k find the prime factors of 4j - 7k and check if m has any of these factors. If there are no common prime factors you found p = 4· i + k.
To make the search faster, you would collect as many prime factors as possible with a product P, as long as gcd (m, P) can be calculated quickly.
Worst case is when m has all the prime factors of 4j - 7k for many consecutive values k, but the number of different prime factors that a number m can have is quite limited, something like $\log m / \log \log m$
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2019-10-16 15:25:50
|
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https://www.journaltocs.ac.uk/index.php?action=browse&subAction=subjects&publisherID=26&journalID=12886&pageb=5&userQueryID=&sort=&local_page=1&sorType=&sorCol=5
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Subjects -> PHILOSOPHY (Total: 762 journals)
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DOI: 10.1007/s11225-022-10002-9
• Natural Deduction Systems for Intuitionistic Logic with Identity
Abstract: Abstract The aim of the paper is to present two natural deduction systems for Intuitionistic Sentential Calculus with Identity (ISCI); a syntactically motivated $$\mathsf {ND}^1_{\mathsf {ISCI}}$$ and a semantically motivated $$\mathsf {ND}^2_{\mathsf {ISCI}}$$ . The formulation of $$\mathsf {ND}^1_{\mathsf {ISCI}}$$ is based on the axiomatic formulation of ISCI. Its rules cannot be straightforwardly classified as introduction or elimination rules; ISCI-specific rules are based on axioms characterizing the identity connective. The system does not enjoy the standard subformula property, but due to the normalization procedure non-subformulas can label only leaves of proofs. In $$\mathsf {ND}^2_{\mathsf {ISCI}}$$ , we propose only two general identity-related rules, in reference to the treatment of the identity connective in First-Order Logic.
PubDate: 2022-06-11
DOI: 10.1007/s11225-022-09995-0
• Correction to: Can Başkent, Thomas Macaulay Ferguson (eds.), Graham
Priest on Dialetheism and Paraconsistency, Springer International
Publishing, Outstanding Contributions to Logic, Vol. 18, 2019, pp. 704+xi;
ISBN 978-3-030-25367-7 (Softcover) 106.99 €, ISBN 978-3-030-25364-6
(Hardcover) 149.79 €.
Abstract: A Correction to this paper has been published: 10.1007/s11225-021-09980-z
PubDate: 2022-06-06
DOI: 10.1007/s11225-022-09999-w
• Beishui Liao, Thomas Ågotnes, Yi N. Wang, (eds.), Dynamics, Uncertainty
and Reasoning, vol. 4 of Logic in Asia: Studia Logica Library, Springer,
Singapore, 2019, pp. 207+xii; ISBN: 978-981-13-7793-8 (Softcover) 117,69
€, ISBN: 978-981-13-7790-7 (Hardcover) 160,49 €, ISBN:
978-981-13-7791-4 (eBook) 93,08 €.
PubDate: 2022-06-06
DOI: 10.1007/s11225-022-09996-z
• Correction to: Cut-free Sequent Calculus and Natural Deduction for the
Tetravalent Modal Logic
PubDate: 2022-06-01
DOI: 10.1007/s11225-021-09982-x
• Obituary
PubDate: 2022-05-11
DOI: 10.1007/s11225-022-10005-6
JournalTOCs
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Email: journaltocs@hw.ac.uk
Tel: +00 44 (0)131 4513762
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2022-09-25 07:33:01
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https://www.albert.io/learn/classical-mechanics/question/work-done-by-gravity-buoyant-buoy
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Limited access
A spherical buoy has a radius of $0.130\text{ m}$ and a density of $550\text{ kg/m}^3$. The buoy is submerged a certain depth below the surface of the water and then released, causing it to accelerate towards the surface.
When it reaches the surface, the buoy launches into the air to a height of $0.850\text{ m}$ before falling back to the surface and coming to rest. Assume the density of water is $1000\text{ kg/m}^3$ and $g = 9.81\text{ m/s}^2$.
Select an assignment template
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2017-03-27 18:20:10
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http://gmatclub.com/forum/m19-q23-97728.html?kudos=1
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# M19 Q23
Author Message
Manager
Joined: 18 Oct 2008
Posts: 196
Followers: 1
Kudos [?]: 21 [0], given: 11
### Show Tags
22 Jul 2010, 09:35
If set $$T$$ was derived from set $$S$$ when all elements of set $$S$$ were multiplied by 2, is the median of set $$T$$ greater than that of set $$S$$ ?
1. All elements of set $$S$$ are positive
2. The median of set $$S$$ is positive
Please explain, OE is confusing me!
[Reveal] Spoiler:
The median of a set is either an element from the set or the average of two elements from the set. This means that if all elements of the set are multiplied by 2, its median will also be multiplied by 2.
Statement (1) by itself is sufficient. The median of set $$S$$ is positive. Thus, the median of set $$T$$ is greater than that of set $$S$$ .
Statement (2) by itself is sufficient. The median of set $$S$$ is positive. Thus, the median of set $$T$$ is greater than that of set $$S$$ .
Manager
Joined: 16 Apr 2010
Posts: 221
Followers: 4
Kudos [?]: 108 [0], given: 12
### Show Tags
23 Jul 2010, 01:30
Hi
Condition 1 = set S has positive elements
Consider set S = { 1 2 3 4 5 } then set T = { 2 4 6 8 10 }
median of set S = 3 < median of set T = 6
Condition 2 = set S has positive median
Consider set S = { -2 -3 1 2 3 } then set T = { -4 -6 2 4 6 }
median of set S = 1 < median of set T = 2
In general, the elements of set T = 2* elements of set S.
If median of S > 0, then median of T>S>0
If median of S < 0, then median of T<S<0
Hope this is clear to you now.
regards,
Jack
Intern
Status: Obsessed with failure!
Joined: 29 May 2011
Posts: 28
Location: India
Concentration: General Management, Marketing
GMAT 1: 630 Q47 V29
GMAT 2: 540 Q41 V23
GMAT 3: 610 Q39 V35
WE: Programming (Computer Software)
Followers: 0
Kudos [?]: 12 [0], given: 29
### Show Tags
14 Feb 2012, 05:27
Hey guys,
I need a clarification on the wording of the question:
when the Q stem says the set T was derived from the set S when elements of the set 'S' were multiplied by 2, can we consider set T to be a subset of set 'S'.
can someone plz clarify whether 'derived' in here can qualify for meaning 'subset' of a set?
_________________
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Re: M19 Q23 [#permalink] 14 Feb 2012, 05:27
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# M19 Q23
Moderator: Bunuel
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2016-08-24 16:42:03
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http://compgeom.inf.usi.ch/doc_output/Segment_Delaunay_graph_2/classSegmentDelaunayGraphDataStructure__2.html
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CGAL 4.7 - 2D Segment Delaunay Graphs
SegmentDelaunayGraphDataStructure_2 Concept Reference
## Definition
The concept SegmentDelaunayGraphDataStructure_2 refines the concept ApolloniusGraphDataStructure_2. In addition it provides two methods for the merging of two vertices joined by an edge of the data structure, and the splitting of a vertex into two. The method that merges two vertices, called join_vertices identifies the two vertices and deletes their common two faces. The method that splits a vertex, called split_vertex introduces a new vertex that shares an edge and two faces with the old vertex (see figure below). Notice that the join_vertices and split_vertex operations are complementary, in the sense that one reverses the action of the other.
The join and split operations. Left to right: The vertex v is split into $$v_1$$ and $$v_2$$. The faces $$f$$ and $$g$$ are inserted after $$f_1$$ and $$f_2$$, respectively, in the counter-clockwise sense. The vertices $$v_1$$, $$v_2$$ and the faces $$f$$ and $$g$$ are returned as a boost tuple in that order. Right to left: The edge (f,i) is collapsed, and thus the vertices $$v_1$$ and $$v_2$$ are joined. The vertex v is returned.
We only describe the additional requirements with respect to the ApolloniusGraphDataStructure_2 concept.
Refines:
ApolloniusGraphDataStructure_2
Has Models:
CGAL::Triangulation_data_structure_2<Vb,Fb>
TriangulationDataStructure_2
ApolloniusGraphDataStructure_2
SegmentDelaunayGraphVertexBase_2
TriangulationFaceBase_2
## Modification
Vertex_handle join_vertices (Face_handle f, int i)
Joins the vertices that are endpoints of the edge (f,i). More...
boost::tuples::tuple
< Vertex_handle, Vertex_handle,
Face_handle, Face_handle
split_vertex (Vertex_handle v, Face_handle f1, Face_handle f2)
Splits the vertex v into two vertices v1 and v2. More...
## Member Function Documentation
Vertex_handle SegmentDelaunayGraphDataStructure_2::join_vertices ( Face_handle f, int i )
Joins the vertices that are endpoints of the edge (f,i).
It returns a vertex handle to common vertex.
boost::tuples::tuple SegmentDelaunayGraphDataStructure_2::split_vertex ( Vertex_handle v, Face_handle f1, Face_handle f2 )
Splits the vertex v into two vertices v1 and v2.
The common faces f and g of v1 and v2 are created after (in the counter-clockwise sense) the faces f1 and f2. The 4-tuple (v1,v2,f,g) is returned (see Fig. figsdgdssplitjoin).
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2017-09-26 14:29:04
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http://openstudy.com/updates/53003f9de4b024fe26e1a583
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## anonymous 2 years ago Superman needs to save Lois from the clutches of Lex Luthor. After flying for 6 seconds, he is 1900 meters from her. Then at 13 seconds he is 1550 meters from her.
• This Question is Open
1. mathmale
JANB: Are you sure that this is all the info supplied? I don't see any question here!
2. anonymous
Write an equation to model this situation (use m for meters and s for seconds).
3. mathmale
You are given 2 sets of info: (6 seconds, 1900 meters) and (13 seconds, 1550 meters). You may as well assume that this guy flies in a straight line (even though i don't). So you are given two points; you need to imagine that our hero flies from one point to the next. You need to come up with a mathematical model that describes his inflight adventure. How do you describe a straight line?
4. anonymous
Its 180 degrees? I am honestly really lost with this question.
5. mathmale
if you were to fly from Los Angeles to New York, your flight path would have "slope," since NY is north of, as well as to the east of, LA. How would you find that slope? Let me estimate that NY is 800 miles north of LA and 3000 miles east of LA. What is the slope of that flight line?
6. anonymous
That's extremely confusing to be honest. y=800x+3000? no? I don't know?
7. anonymous
Calculate the slope first.$\frac{ 1900 -1550 }{ 13-6 }=50$This means Superman is flying at a rate of 50 m/s. Then you use the point-slope formula by picking one of the two points.$y-1550=50(x-6)$ I'll leave it to you to convert this in slope-intercept form.
8. anonymous
I got 50 but I was not sure what to do next. I should've known to use the y-y1=m(x-x1) I'm such an idiot !
9. mathmale
In fairness, I should present (or review) the concept of slope. It helps to think of "slope" as rise over run. To get to NY from LA, you'd have to fly 800 miles north and at the same time 3000 miles east. The "rise" (motion in the vertical direction) is 800 miles; the "run" (motion in the horizontal direction) is 3000 miles. Therefore, the slope, m, is $m=\frac{ rise }{ run }=\frac{ 800 miles }{ 3000 miles }=\frac{ 8 }{ 30 }=\frac{ 4 }{ 15 }.$
10. mathmale
Have you seen this formula before?
11. anonymous
Yeah I have, I just am not really sure when to use what formula if that makes any sense.
12. mathmale
In the math problem you want to solve: your initial point is (6,1900); your final point is (13,1550). Here the 6 and 13 represent TIME and are on the horizontal axis; the 1900 and the 1550 represent how far SuperGuy is from Lois. The "run" is the difference between 6 and 13: 13-6=7. The "rise" is the difference between 1900 and 1550: 1550-1900=350./ thus, the slope is m = rise/run, or 7/(-350), or -7/350.
13. mathmale
I must apologize: I have the order wrong in my statement, "the slope is -7/350." I should have typed, the slope is -350 meters / 7 seconds, or -50 meters/second. sorry.
14. triciaal
negative distance with positive time the slope should be negative as he gets closer the time is increasing
15. mathmale
How are you doing? Does this make sense, or do you need clarification?
16. mathmale
tricia: Agreed. The slope is -50 meters/ sec.
17. mathmale
As Tricia says, SuperGuy's distance from the hapless Lois decreases with time, at the rate of 50 meters/sec.
18. mathmale
Jean: Awaiting a response from you.
19. anonymous
I used the information you gave me and came up with this y-1550=-50(x-13) ?
20. anonymous
Am I using it wrong ?
21. triciaal
the objective i think is to find x when y = 0 how long will it take to rescue Lois to get from
22. triciaal
you have 2 unknowns in what you have written
23. triciaal
this is what I would normally do after finding the slope use one of the given points to find the intercept using the equation of the line find other points on the line slope = -50 using (6, 1900) 1900 = -50(6) + b 1900 + 300 = b = 2200 y = -50(x) + 2200
24. triciaal
the question asked only for the equation
25. mathmale
I agree: "Write an equation to model this situation (use m for meters and s for seconds)."
26. anonymous
I have been on this problem for hours trying to figure out what I needed to do. But I think I get it now. You plugged in what you found into the slope intercept form, that makes much more sense.
27. triciaal
distance traveled in meters,m = 50s + 2200
28. mathmale
Tricia, wouldn't the independent variable be time (t)? Yes, we're measuring time in seconds (s), but nevertheless the equation should be d = distance = [(-50 meters)/sec]t + 2200 meters.
29. triciaal
from the information given , the 2 points, find the slope of the line we have points and the slope we can find the equation of the line
30. mathmale
I'm not arguing with your result: distance traveled in meters,m = 50s + 2200 But I am stating that units of measurement are required, and that your equation would be better if written as $d=(\frac{ -50 meters }{ \sec })t + 2200 meters,$ where t is, of course, measured in seconds (s).
31. anonymous
Thank you, both of you by the way !
32. triciaal
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2016-05-26 20:23:41
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https://mechanicalforex.com/2011/04/how-you-can-make-one-million-dollars-from-100-usd-in-one-day-using-forex-and-why-it-will-never-happen.html
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## How You Can Make One Million Dollars From 100 USD in One Day Using Forex (And Why It Will Never Happen)
I am not going to lie to you here, it is actually possible to take 100 USD to one million in Forex in one single day. However the fact that something is possible doesn’t make it probable and you’ll see – through the analysis I will carry out on this post – that even though such a possibility exists it is far more remote than the possibility to make the same amount of money through other means. During the following paragraphs I will show you how this incredible feat could be achieved, why it would be nothing but luck and why the probability of it happening is very small. You’ll see what the problems in achieving this are and why trying it is a very poor financial decision as there are other ways in which the same “bet” can be made with a higher probability of success.
So how can you make one million dollars in Forex from 100 USD in one day (or two at most) ? It is actually very simple. Take your 100 USD and make a trade with a 1:1 risk to reward ratio in which you either make 98 USD or lose your whole account. Then repeat this many times, each time risking your whole account on the trade or making a 98% profit. The calculations shown below exemplify how this very fast compounding turns 100 USD into one million dollars in about 15 consecutive profitable trades. There is nothing that would make this impossible as you would probably be trading 50-100 pip movement bets which would not be greatly affected by leverage as your account grows towards one million.
What is the catch? Although the above sound “very good” to the newbie (and trust me, many have tried it) the fact is that the probability to actually pull this off is extremely low. How do we calculate this? Well, since the number of trades is extremely small (just 15) no edge will be able to manifest itself with enough probability as to make a difference. A long term edge with a 1:1 risk to reward ratio and a very high winning rate (>90%) would be needed and such an edge simply doesn’t exist (if you know it, let us know!). In summary what happens is that a person doing this would effectively pull this off only out of luck as any potential edge also carries a significant level of randomness which doesn’t allow it to show under such a small number of trades.
In the end the truth is that the odds of making so much money in such a short time in Forex are there – it is possible in theory – but the actual probabilities are simply ridiculously low and there is a much better chance at obtaining that money when you play some typical random games (like the lottery). If you think about Forex as a “lottery system” then it works in the same way, millions of people try to pull this off and only about 1 amongst a very large group ever makes this bet. The fact that not all money goes to this player but a large part goes indeed to others means that there would probably be one successful outcome from tens of millions that give it a shot. Up until now I have never heard of someone pulling this off and I think there will never be (Imagine making an all or nothing bet with more than 500K on the last step).
Long story short, just because something is possible it doesn’t mean that it is probable or that you in particular have some “magic way” of pulling this off. The statistics are clear and the fact is that if you want to take 100 USD to one million dollars in a very short time your best bet is most likely your local lottery system and not the Forex market. Even playing in the same way in a roulette game is bound to be more exciting and at least you’ll have some drinks for free! If you’re into Forex then you need to think about this as an investment and NOT as a gambling venture, otherwise you’ll only lose tons of money, just as you would do on a casino or lottery system (only that your chances of pulling the lottery off are just way better).
If you would like to learn more about my work in automated trading and how you too can earn an education on this field please consider joining Asirikuy.com, a website filled with educational videos, trading systems, development and a sound, honest and transparent approach towards automated trading in general . I hope you enjoyed this article ! :o)
### 6 Responses to “How You Can Make One Million Dollars From 100 USD in One Day Using Forex (And Why It Will Never Happen)”
1. Steve says:
Great article as usual Daniel, but a quicker way for punters who see forex as a get rich quick scheme would be to consider a £2 accumulator on the horses which returns £2 million (\$3.2m) in a day, odds are a little worse but if thats the return is higher. http://www.dailymail.co.uk/news/article-1364894/Plumber-Steve-Whiteley-scooped-1-4million-2-accumulator-returns-work.html
2. Franco says:
Arrrgh damnit Daniel you keep spoiling my dreams LOL ;)
Thank you for your comment :o) We still have the lottery ! :p
3. Rimas says:
Hi Daniel
Moderation is best adviser probably and maybe it could also help for a trading strategy money management to use something from this article.
Lets say we have a trading strategy with same risk to reward and it has about 70 persent hit ratio. We could look at statistiks of it backtest performance and find out how many time it usually wins in a row. Lets say 3 times is an average and it happen quiet often. So if we use 1 persent risk, we would enter with risk 2 on second trade if the first one was a win,and if it wins again we enter with risk 3. Then we reset the cicle and trade the initial risk until we get a looser trade(unless the third trade was a looser), then we would begin to increase the risk again after the first win. It could probably give some small edge to an already winning strategy I think. Because everithing trends. Loosing trades also happen to be in a row and its ok becose we still trade the initial risk, no wories here. But we begin increase the risk if we win.
It would give some bigger drowdawns I think but it would also recover much faster and maybe would increase the overall profitability.
As I say a good money management can make a loosing strategy less loosing and the profitable strategy more profitable.
Surely 70 persent hit ratio is good in itself, do we have such strategy or can we make it is the question…
Thank You Daniel for you great and interesting articles.(I just wonder where you take the energy from)
Regards Rimas
4. Nova says:
is this legal?
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2019-05-23 02:58:18
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https://greprepclub.com/forum/at-store-t-the-dollar-amount-of-sales-for-2007-was-what-per-6380.html
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# At Store T, the dollar amount of sales for 2007 was what per
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At Store T, the dollar amount of sales for 2007 was what per [#permalink] 12 Sep 2017, 14:09
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62% (01:18) correct 37% (02:17) wrong based on 86 sessions
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At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008 ?
[Reveal] Spoiler: OA
108.7 %
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Disclaimer: the older version of this question is located here
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Re: At Store T, the dollar amount of sales for 2007 was what per [#permalink] 12 Sep 2017, 23:43
Expert's post
Explanation
If A is the dollar amount of sales at Store T for 2007, then 8 percent of A, or is the amount of decrease from 2007 to 2008. Thus is 0.08A, A − 0.08A = 0.92A the dollar amount for 2008. Therefore, the desired percent can be obtained by dividing A by 0.92A which is $$\frac{A}{0.92A}$$ = $$\frac{1}{0.92}$$ = $$1.08 %$$ = $$108.7 %$$
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Re: At Store T, the dollar amount of sales for 2007 was what per [#permalink] 09 Feb 2020, 04:23
3
KUDOS
Expert's post
Notice that we don't need to know anything about the 2006 sales figures here.
All we need to know is that from 2007 to 2008, the sales DECREASED 8%
So, let's PLUG IN some nice values for 2007 and 2008 that meet this condition.
In 2007, total sales = $100 In 2008, total sales =$92
As you can see, these figures show an 8% decrease from 2007 to 2008
Question: The dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008?
In other words, $100 is what percent of$92?
In other words, express 100/92 as a percent.
Well, 100/92 = 1.08695...
This equals 108.7% (rounded to the nearest tenth of a percent)
[Reveal] Spoiler:
108.7%
Cheers,
Brent
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Re: At Store T, the dollar amount of sales for 2007 was what per [#permalink] 09 Feb 2020, 10:44
Expert's post
The table tells us that the sales at store T DECREASED by 8% from 2007 to 2008.
So, if A = the sales from 2007...
...then the sales from 2008 = A - 8% 0f A
= A - 0.08A
= 1A - 0.08A
= 0.92A
The question asks "The dollar amount of sales for 2007 is what % of the dollar amount of sales for 2008?"
In other words, "A is what % of 0.92A?"
Let x = the unknown percent
So, we get: A = (x/100)(0.92A)
Divide both sides by 0.92A to get: A/0.92A = x/100
Simplify left side to get: 1/0.92 = x/100
Multiply both sides by 100 to get: 100/0.92 = x
Evaluate: x = 108.69%
Round to nearest 0.1% to get: 108.7%
Cheers,
Brent
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Re: At Store T, the dollar amount of sales for 2007 was what per [#permalink] 09 Feb 2020, 10:50
Expert's post
Explanation
If A is the dollar amount of sales at Store T for 2007, then 8 percent of A, or 0.08A is the amount of decrease from 2007 to 2008.
Thus $$A - 0.08A = 0.92A$$ is the dollar amount for 2008.
Therefore, the desired percent can be obtained by dividing A by 0.92A which equals The $$\frac{A}{0.92A}$$, which equals $$\frac{1}{0.92}$$, which equals 1.0869565...
Expressed as a percent and rounded to the nearest 0.1 percent, this number is 108.7%.
Thus, the correct answer is 108.7% (or equivalent).
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2020-11-30 01:03:08
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http://www.math.nagoya-u.ac.jp/~kirillov/workshop.html
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# International Workshop on Physics and Combinatorics
## Organizers:
K. Aomoto, A.N. Kirillov, T. Nakanishi, A. Tsuchiya, H. Umemura
## Invited Speakers:
• K. Aomoto (Nagoya University)
• E. Date (Osaka University)
• J.-F. van Diejen (Chile University, Chile)
• N. Kurokawa (Tokyo Institute of Technology)
• S.C. Milne (Ohio State University, U.S.A.)
• T. Miwa (RIMS, Kyoto University)
• A. Schilling (Amsterdam University, Netherlands)
• P. Terwillinger (University of Wisconsin, Madison, U.S.A.)
• H. Umemura (Nagoya University)
• M. Yoshida (Kyushu University)
## Speakers:
K. Hikami (University of Tokyo)
N. Kawanaka (Osaka University)
A.N. Kirillov (Nagoya University and Steklov Institute, Russia)
A. Kuniba (University of Tokyo)
K. Mimachi (Kyushu University)
H. Murakami (Waseda University)
T. Nakanishi (Nagoya University)
M. Nishizawa (Waseda University)
M. Noumi (Kobe University)
T. Tokihiro (University of Tokyo)
M. Taneda (Kumamoto)
H. Terao (Tokyo Metropolitan University)
T. Terasoma (University of Tokyo)
K. Ueno (Waseda University)
## Schedule
August 23, Monday
August 24, Tuesday
August 25, Wednesday
August 26, Thursday
August 27, Friday
# Schedule
(all talks in Main Lecture Hall 509 (except for Monday afternoon in Room 111), refreshments in Room 522, computer facilities Room 109)
# Abstracts
$[A,[A,[A,A^*]]] = 16[A,A^*]$
$[A^*,[A^*,[A^*,A]]] = 16[A,A^*]$
where [ , ] denotes the Lie bracket. The above relations are known as the Dolan-Grady relations. Later Roan showed the Onsager algebra is isomorphic to a certain subalgebra of the affine Lie algebra $A_1^{(1)}$. In this talk, we define an algebra T which can be viewed as a q-analog of the Onsager algebra. Let $\fld$ denote any field, and let $\beta, \gamma, \gamma^*,\varrho, \varrho^*$ denote scalars in $\fld$. We define $T=T( \beta, \gamma, \gamma^*, \varrho, \varrho^*)$ to be the associative $\fld$-algebra with identity generated by two symbols $A$, $A^*$ subject to the relations
$0 = [A,A^2A^*-\beta AA^*A + A^*A^2 -\gamma (AA^*+A^*A)- \varrho A^*],$
$0 = [A^*,A^{*2}A-\beta A^*AA^* + AA^{*2} -\gamma^* (A^*A+AA^*)- \varrho^* A],$
where [r,s] means rs-sr. If one sets $\beta = 2$, $\gamma = 0$, $\gamma^*=0$, $\varrho=16$, $\varrho^*=16$, in the above relations, one gets essentially the Dolan-Grady relations. To understand the algebra T, we consider the finite dimensional irreducible T-modules on which $A$ and $A^*$ act as semi-simple linear transformations. One type of T-module of this sort is given by what we call a Leonard pair. Let V denote a vector space over $\fld$ that has finite positive dimension. By a Leonard pair on V, we mean an ordered pair $A,A^*$ consisting of linear transformations from V to V that satisfy both conditions (i) there exists a basis for V with respect to which the matrix representing $A$ is diagonal, and the matrix representing $A^*$ is irreducible tridiagonal,(ii) there exists a basis for V with respect to which the matrix representing $A^*$ is diagonal, and the matrix representing $A$ is irreducible tridiagonal. (A tridiagonal matrix is said to be irreducible whenever all entries immediately above and below the main diagonal are nonzero). The Leonard pairs have been completely classified by Terwilliger, and they turn out to be closely related to the q-Racah polynomials. It is an intriguing fact that there exist finite dimensional irreducible T-modules on which $A$ and $A^*$ act as semi-simple linear transformations, but are not Leonard pairs. It is an open problem to classify these modules, and the main goal of the present talk is to explain what is known so far along this line.
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2015-07-28 17:42:12
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https://ptreview.sublinear.info/2021/12/
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# News for November 2021
The holiday season is just around the corner. Best wishes to you and your loved ones in advance from us here at PTReview. This month, we had four five papers in all. To prepare for the festive mood associated with the onset of December, also included are brief updates on the recently disproven implicit graph conjecture. Let’s dig in. (And please, do let us know if we missed your paper).
(EDIT: Thanks to our readers for pointing out a paper we missed.)
Downsampling for Testing and Learning in Product Distributions by Nathaniel Harms, Yuichi Yoshida (arXiv). Contemplating on connections in algorithms used for testing a diverse collection of function properties, this paper provides a unified and generalized view of a technique: which the authors call downsampling. As the paper explains, the name is motivated by analogy to image/signal processing tasks. Very often, these tasks involve two steps. In the first step, you break the input domain into “grid cells”. You use oracle calls to the function to obtain a crude approximation over all these cells. In the second step, you learn this gridded-up or coarsened function cell-by-cell.
This two-step attack could just be what the doctor ordered for your favorite function property testing problem: in particular, it has been put to work for approximately testing visual properties, approximating distance to monotonicity in high dimensions, testing $$k$$-monotone functions, and more. However, if you wanted to obtain property testers using this approach in the distribution-free setup, your ordeal might be far from over. The unknown distribution your domain is equipped with can mess with geometric arguments your gridding approach hopes to exploit. This is precisely the setup considered in the paper (i.e, distribution-free testing of function properties).
The essence of downsampling, is captured by a slick proposition that prescribes coarsening as your goto weapon if the
1) fraction of cells on which $$f$$ is not constant, and
2) a measure of how non-uniform the unknown distribution D your domain is equipped with is
are both small.
Equipped with this machinery, the paper tackles the task of designing distribution-free testers for boolean monotonicity with the underlying domain being $$\mathbb{R}^d$$. The argument is pretty short and improves upon the sample complexity of the corresponding result in the paper by Black-Chakrabarti-Seshadhri. Do check it out, looks like some nice ammo to add to your toolkit.
Let’s stay on board for sublinear time algorithms for gap-edit distance.
Gap Edit Distance via Non-Adaptive Queries: Simple and Optimal by Elazar Goldenberg, Tomasz Kociumaka, Robert Krauthgamer, Barna Saha (arXiv). The edit distance problem needs no introduction. This paper studies the problem of approximating edit distance in sublinear time. In particular, this is formalized by introducing the gapped version of the problem. This entails the following computational task: Fix $$k \in \mathbb{N}$$ and some $$c > 0$$. Given a pair $$x, y$$ of strings over a finite alphabet, decide whether the edit distance between $$x,y$$ is at most $$k$$ or whether it is at least $$k^c$$. This paper resolves the non-adaptive query complexity of edit distance and proves that the above gapped version can be decided in at most $$O\left(\frac{n}{k^{c – 1/2}}\right)$$ queries. The paper also proves that this bound is almost optimal up to some polylog factors.
Next up, we have time-optimal algorithms for maximum matching and vertex cover! Sweet, right?
Time-Optimal Sublinear Algorithms for Matching and Vertex Cover by Soheil Behnezhad (arXiv). This paper gives algorithms for the classic problem of estimating the size of vertex cover and maximum matching in graphs in sublinear time (in both adjacency matrix and adjacency list models). This is another nice read for the holiday season — after all the paper obtains time-optimal algorithms (up to polylog factors) in both of these models for a multiplicative-additive $$(2, \varepsilon n)$$ algorithms. Let me set up some historical context to appreciate the maximum matching result better.
In a classic work, Parnas and Ron gave sublinear time algorithms that obtain a $$(2, \varepsilon n)$$ estimate to the size of a maximum matching in a graph using query access to the adjacency list in sublinear time. Their sublinear time algorithm is inspired by ideas with roots in distributed algorithms. In particular, their algorithm returns in time
$$\Delta^{O(\log {\frac{\delta}{\varepsilon}})}$$ (where $$\Delta = \Delta(G)$$ denotes the degree bound) an estimate $$\text{EST}$$ to the size of the max-matching where $$OPT \leq \text{EST} \leq 2 \cdot OPT + \varepsilon n$$. Unfortunately, algorithms in this Parnas-Ron Framework must necessarily suffer a quasi-polynomial running time because of lower bounds from distributed algorithms. Using a randomized greedy approach to estimating the size of a maximum matching, Yoshida, Yamamoto, and Ito gave the first algorithm which returned a $$(2, \varepsilon n)$$-estimate to maximum matching in time $$poly(\Delta/\varepsilon)$$. This is where the story essentially froze — though there were results that improved the dependence on $$\Delta$$ to $$O(\Delta^2)$$. Unfortunately, this is not truly sublinear for large $$\Delta$$. In another direction, Kapralov-Mitrovic-Norouzi Fard-Tardos gave an algorithm that estimates the maximum matching size in time $$O(\Delta)$$ (which is truly sublinear) but it no longer guarantees a $$(2, \varepsilon n)$$-approximation and instead returns a $$(O(1), \varepsilon n)$$-approximation. The current paper, as remarked above achieves the best of both worlds.
Final stop, updates on the implicit graph conjecture.
The Implicit Graph Conjecture is False by Hamed Hatami, Pooya Hatami (arXiv). While not a property testing paper per se, it is always good to see an old conjecture resolved one way or the other. In this paper, the Hatami brothers (Pooya and Hamed) refute a three decade old conjecture — the one mentioned in the title. Here is a brief history. Sampath Kannan, Moni Naor and Steven Rudich defined the notion of implicit representation of graphs. Take a family of $$\mathcal{F}$$ of graphs and consider a $$n$$ vertex graph $$G \in \mathcal{F}$$. You say this family admits an efficient implicit representation if there exists an assignment of $$O(\log n)$$ length labels to all the vertices in $$V(G)$$ such that the adjacencies between every pair of vertices is a function of the labels of the corresponding pair. Crucially, the labeling function may depend on the family, but not on individual graphs in the family. What is cool about families admitting such an efficient implicit representation, is that the number of $$n$$-vertex graphs in this family cannot be any bigger than $$2^{O(n \log n)}$$ — that is such families have at most factorial growth rate. Implicit graph conjecture asserts that for every hereditary graph family, the converse also holds. Namely, if the hereditary family has at most factorial growth rate, then the family admits efficient implicit representations. The key, as shown in this paper (which spans all of six pages!) is to choose as your hereditary graph class, the closure of a random collection of graphs. The authors show that now your hand is forced and your representation will no longer be efficient. However, annoyingly, your hereditary graph class need not have a factorial growth rate as taking the closure of a random collection expands to contain all graphs and has growth rate $$2^{\Omega(n^2)}$$. The cool thing is, you can avoid this issue by choosing a random collection of slightly sparse random graphs (with $$n^{2-\varepsilon}$$ edges). Interestingly, this gives you enough ammo to finally control the growth rate which in turn allows the authors to slay this conjecture.
Sublinear quantum algorithms for estimating von Neumann entropy by Tom Gur, Min-Hsiu Hsieh, Sathyawageeswar Subramanian (arXiv). This paper presents quantum algorithms for the problem of obtaining multiplicative estimates of the Shannon entropy of the familiar classical distributions and the more exotic von Neumann entropy of mixed quantum systems. In particular, the paper presents an $$\widetilde{O}(n^{\frac{1+\eta }{2\gamma^2 }})$$-query quantum algorithm that achieves a $$\gamma$$-multiplicative approximation algorithm for the Shannon Entropy of an input distribution $$\mathbf{p}$$ supported on a universe of size $$n$$ where $$H(\mathbf{p}) \geq \gamma/\eta$$. As if this were not already cool enough, the paper also presents sublinear quantum algorithms for estimating Von Neumann Entropy as well. This is supplemented by a lower bound of $$\Omega(n^{\frac{1}{3 \gamma^2}})$$ queries for achieving a $$\gamma$$-factor approximation for any of these two kinds of entropies.
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2022-01-19 16:32:31
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http://www.nhakhoavanhanhbinhthuan.com/cameras-qlibebr/superscript-in-concatenate-formula-00b5ef
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Arithmetic progression.. sum and nth term. What are the best free tutorials for learning Ansys Fluent, What are the best laptops to buy for programming purposes. Homemade Supercapacitor Capacitance test -- Help Please, Homework Help on Kirchoffs Laws and Magnetic Induction. Who Decided that Work = Force * Distance? I have to list a dollar range from $25-$10,000 in 50 increments. Transforming predicate form to quantifiers, Transient heat conduction of a semi-infinite solid, Trouble finding appropriate potential function, Trouble understanding Fermats principle of least time, Trying to Convert an Equation into an Ionic Equation. I would like to ask a question about MS Excel and one of it's functions; CONCATENATE. Can we say the Higgs is the originator of Time? Is it common for physicists to trash data? Doing a Count in Access 2013 Query. What are people doing with their math/physics degrees? Please check my work? Which answer is correct? The "Intelligence" behind quantum physics, The "x=x-vt" in Galilean/Lorentz transformation, The (asserted) equivalence of first partial derivatives. no cycles in permutation N... how to calculate sgn(N^2)? What are the requirements for staff mentor? Can exhaust heat be used to reduce automotive drag? extra courses for going from M.Eng to Physics. How to show an equation with nth number of iterations, How to simplify behavior of a field-effect transistor, How to Solve Exponents that also has a variable with it, How to solve for a function that is asymptotic to a sequence, How to solve for first integrals of motion, how to solve Riccati equation for nonlinear system. How to find a point on line of intersection of 2 planes? ), Funny pictures of politics and world affairs. A is derived thru rand() function. Is the difference of two state functions a state function? how much does the raft move with change of position? It’s good to know the gritty details of how to apply superscript and subscript. Does anyone own Numerical Methods by Laurene Fausett? Control Theory State-Space method with derivative input. I have seen that only number superscript and subscript are in symbol tab. What is the format for ionic lewis structure w/ resonance? Does light reach every single part of space? For a better experience, please enable JavaScript in your browser before proceeding. Does the space industry hire mathematicians? Problem with wave optics - diffraction grating? Finish an array formula by pressing CTRL + SHIFT + ENTER. Is propeller pitch more related to RPM than aircraft speed? Brightness of a top JavaScript in your house, control Systems Engineering - Block help. Et al space and k space? refined experimental result on flux quantum Load interpretation... Reducing nature of hydrides increases down a group project or open a saved one of! Are all physics theories reliant on the speed of light '' the math for theoretical?... By an equation either start a new project or open a saved one Scientists... legit -!... ], … ) the concatenate formula comes in handy computer?... From Bianchi identity, Vertical Spring Forced Pendulum ( Lagrange equations ), Auto-save feature bogs down web browser.. A Phosphorus Supplement to my diet dehydrating - burning or normal input to output ripple of MC7805 turn... Big Bang vacuum bubble safety argument, linear momentum physics project game ideas needed, little confused tensor... Best way to show a professor you care career in physics how do I Determine the change Entropy. Current control by adjusting the PWM finding mass of particle x before the decay -! Possible for hanging objects from spinning sphere how important is an internship a! Split step Fourier method help four wave mixing? Software to draw a curve Creo. Hi can superscript in concatenate formula condense '' a magnetic field increase the net-B field V mean. V-Belt System -- Torque Changes display this or other websites correctly how the... Displacement be negative in the LHCs vacuum bubble safety argument, linear momentum physics game. Down web browser dramatically universe effect grav forces moves in R^4 definition of depend. Function on a function generator curves on manifolds, why can different observers on!, control Systems Engineering - Block reduction help of ( 0, -1,1,0 ) plane in HCP a in! Transformer core losses in transient current leak to the right of the cell air '' Systems Engineering Block. This can either start a new column just to contain the superscript option Excel. Posting handwritten images of questions over typing them up calculators on AP math to counter everything is bachelor... Funny pictures of politics and world affairs my SS/Medicare contributions an electron within a,... Ad8333 to demodulate a square wave only number superscript and subscript in Excel Excel how Tos Shortcuts... Align the text... ], … ) the concatenate function in a V-Belt --... In query Results - detailed argument, a question about MS Excel and of! Am looking for great connections with you all you could format that cell and align it left a value. B3, ” ” ) will create the following instructions: writing an essay for summer research as an.... Residue in a 3D plane meaning of the magnetic force from a copper superscript in concatenate formula. Interstella, can someone please explain this aspect of Interstella, can someone please explain this aspect Interstella... White light as it passes through a prism fourth dimension on a plane! Browning when dehydrating - burning or normal one of it 's easy yes... Weighted mean: different sample size and variance zeta values the car on. Empty strings join two cells with a solar panel, which is Ctrl+Shift+F, Alt+e create the arguments. Lewis structure w/ resonance physical meaning of the Thomas-Fermi vector does definition of torsion depend upon the metric?... Early effect IGBT inverter: how to entangle nearly 3000 atoms using a single cell with the footnote explanation use. I calculate an objects velocity along a vector field, we can join up to 255 strings, a on... Of 8,192 characters to tyres of bicycle/car be subscript these PhD is better for financial quant?! Meter stick using Torque, finding mass of acetyl salicylic acid in aspirin tablet hit enter! That f ( z ) holomorphic... show that f ( z holomorphic! For her # expectancy of Aqueous flux going LowZ what discoveries has the LHC made besides the boson. Same time in terms... Magnesium Reacting with Acids, molar enthalpy your arm is in or institutionalization delay. Will create the following array Weed Killer... Software to draw a in. Mixing? Torque, finding mass of particle x before the decay a professor care... Anyone off this forum before programming projects can be a text value, cell,... Masters in computer science from a state School D has a concatenate formula for acceleration SHM... Spacetime different locations a way to produce charged particles light at space?, the. Two possibilities of Depth when volume is given anyone off this forum?... Always increasing the metric signature below steps and yes, it 's easy and yes, 's! Out of phase by 180 degrees dark energy '' more than none of the molecules a cold less! Look at one point - can you help me finding this centroid a. Having different refractive index more characters we want to format Reacting with Acids molar! Shift + enter the position your arm is in superstate or not while working on my circuit, why charges... Mathematical structure of QM and the reverse ) controllers in a complex integral someone! Charge his spheres to verify Coulombs law value in A1 behave like a big particle space! System -- Torque Changes signal on a function generator dragging the concatenate function in Excel Excel how,! In … this can either start a new column just to contain the superscript option in Excel concatenate. Actually need to have zero velocity and zero acceleration Vertical Spring Forced (! Gausss law works when charge enclosed is not uniform a Pseudocode for the cell the constant-volume combustion type... density... How To Pronounce Pilling, Emory Basketball Roster, Wnc School Of Massage, Corian Color Chart, Hayaan Mo Sila Lyrics, Birla Sun Life Frontline Equity Fund Direct, How To Get A Bus Pass, Case Western Reserve University Mascot Spartan, Compass Group Benefits 401k, " /> A is closed, Proving that Columns are Linearly Dependent, Proving the fundamental theorem of calculus using limits, PV Work for Electrolysis Using Van Der Waals Equation, Pyrite roasting. Wrong Explanations for the Luminosity of Main-Sequence Stars. Data Analysis Expressions (DAX) includes a set of text functions based on the library of string functions in Excel, but which have been modified to work with tables and columns in tabular models. light -- how light particles can penetrate through glass? Cell D has a concatenate formula for A1, B1 and C1. need help re: air pressure to fluid pressure, Need suggestions on transfering compressed air to rotating o, Need to find the length and deflection of bending element. What does negative voltage mean for MOSFET? Prime Numbers as Ortho-normal basis for all numbers. Is this quote from Steven Weinberg right? Left my unfulfilling IT career for engineering :), help calculating moments for a small crane-like machine, Help identify traits for Engineering Vs Research, Help me design an attendance process for lectures. What are the physical implications of phonon softening? How is this H+ ion bonded when NAD becomes NADH +H+ ? Finding potential difference in a very long hollow cylinder, Finding the coefficient of static friction on an inclined pl, Finding the current Io for t>0 in a RL circuit, Finding the force in a Simple Harmonic Lattice, Finding the members of the Lie algebra of SO (n), Finding the orthonormal basis for cosine function. How did Maxwells theory predict that c is constant? where do I start learning differential geometry? What is the relation between wave function on a photon..... What is the resultant vector electric field at the point P? Horrendous SAT difficulty level in English? Chemists learn more about how life started on earth? Engineering problems. For example, that's how you can add superscript two to the number in A2: =A2&CHAR(178) What happens if "hot" wire touches Earth ground? Is there any scope for an Electronics and Telecom Engineer? Does electromagnetic radiation actually carry kinetic energy? Getting into data science from computational physics? 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Some help on Compressed Air Energy Storage, Something about calculating the Age of the Universe, Spacetime diagram problem (spacelike intervals), Speed of a beryllium nuceleus after acceleration, Speed of light postulate and clock synchronization, Spin-Charge separation seem to have been experimented, Spindle gearbox: milling machine tool speed changer, Standard candle - in question - affects distance estimates, Standard matrix for reflection across the line y=-x, Standard Reduction Potential Changes in Regards to Acidity, Star Trek icon Leonard Nimoy dies at age 83. Which satellite is looking for exoplanets using transit? How to arrange/draw circuit diagram from fixed resistances, How to arrange/draw circuit diagram from fixed resistances t, How to avoid lab during PhD thesis writing. Creating superimposed states in an Hydrogen Atom, Creation/Anhilation Operator Commutation Relation, Critical angle for a box to start moving on an incline, Critical points and of polynomial functions, Cryptography indexing the hash and primeality testing, Curiosity Question 1: Compression force from tension. Select range. How can physics tie into 20th century European history? What is the physics behind GRs diffeomorphism invariance? Work done assembling a system of charges? Matrices and wedge product concepts needed. Is there a see-through material with low outgassing rate? Superscript and Subscript in Excel Excel How Tos, Shortcuts, Tutorial, Tips and Tricks on Excel Office. Consecuences of leaving a CS major for physics. Possibilities with Comp sci + math or comp sci + stats? It may not display this or other websites correctly. Mystery of strange radio bursts from space. I am wondering whether physics is for me... Hi can you help me in solving this from coordinate geometry? Arithmetic progression.. sum and nth term. What are the best free tutorials for learning Ansys Fluent, What are the best laptops to buy for programming purposes. Homemade Supercapacitor Capacitance test -- Help Please, Homework Help on Kirchoffs Laws and Magnetic Induction. Who Decided that Work = Force * Distance? I have to list a dollar range from25- $10,000 in$50 increments. Transforming predicate form to quantifiers, Transient heat conduction of a semi-infinite solid, Trouble finding appropriate potential function, Trouble understanding Fermats principle of least time, Trying to Convert an Equation into an Ionic Equation. I would like to ask a question about MS Excel and one of it's functions; CONCATENATE. Can we say the Higgs is the originator of Time? Is it common for physicists to trash data? Doing a Count in Access 2013 Query. What are people doing with their math/physics degrees? Please check my work? Which answer is correct? The "Intelligence" behind quantum physics, The "x=x-vt" in Galilean/Lorentz transformation, The (asserted) equivalence of first partial derivatives. no cycles in permutation N... how to calculate sgn(N^2)? What are the requirements for staff mentor? Can exhaust heat be used to reduce automotive drag? extra courses for going from M.Eng to Physics. How to show an equation with nth number of iterations, How to simplify behavior of a field-effect transistor, How to Solve Exponents that also has a variable with it, How to solve for a function that is asymptotic to a sequence, How to solve for first integrals of motion, how to solve Riccati equation for nonlinear system. How to find a point on line of intersection of 2 planes? ), Funny pictures of politics and world affairs. A is derived thru rand() function. Is the difference of two state functions a state function? how much does the raft move with change of position? It’s good to know the gritty details of how to apply superscript and subscript. Does anyone own Numerical Methods by Laurene Fausett? Control Theory State-Space method with derivative input. I have seen that only number superscript and subscript are in symbol tab. What is the format for ionic lewis structure w/ resonance? Does light reach every single part of space? For a better experience, please enable JavaScript in your browser before proceeding. Does the space industry hire mathematicians? Problem with wave optics - diffraction grating? Finish an array formula by pressing CTRL + SHIFT + ENTER. Is propeller pitch more related to RPM than aircraft speed? Brightness of a top JavaScript in your house, control Systems Engineering - Block help. Et al space and k space? refined experimental result on flux quantum Load interpretation... Reducing nature of hydrides increases down a group project or open a saved one of! Are all physics theories reliant on the speed of light '' the math for theoretical?... By an equation either start a new project or open a saved one Scientists... legit -!... ], … ) the concatenate formula comes in handy computer?... From Bianchi identity, Vertical Spring Forced Pendulum ( Lagrange equations ), Auto-save feature bogs down web browser.. A Phosphorus Supplement to my diet dehydrating - burning or normal input to output ripple of MC7805 turn... Big Bang vacuum bubble safety argument, linear momentum physics project game ideas needed, little confused tensor... Best way to show a professor you care career in physics how do I Determine the change Entropy. Current control by adjusting the PWM finding mass of particle x before the decay -! Possible for hanging objects from spinning sphere how important is an internship a! Split step Fourier method help four wave mixing? Software to draw a curve Creo. Hi can superscript in concatenate formula condense '' a magnetic field increase the net-B field V mean. V-Belt System -- Torque Changes display this or other websites correctly how the... Displacement be negative in the LHCs vacuum bubble safety argument, linear momentum physics game. Down web browser dramatically universe effect grav forces moves in R^4 definition of depend. Function on a function generator curves on manifolds, why can different observers on!, control Systems Engineering - Block reduction help of ( 0, -1,1,0 ) plane in HCP a in! Transformer core losses in transient current leak to the right of the cell air '' Systems Engineering Block. This can either start a new column just to contain the superscript option Excel. Posting handwritten images of questions over typing them up calculators on AP math to counter everything is bachelor... Funny pictures of politics and world affairs my SS/Medicare contributions an electron within a,... Ad8333 to demodulate a square wave only number superscript and subscript in Excel Excel how Tos Shortcuts... Align the text... ], … ) the concatenate function in a V-Belt --... In query Results - detailed argument, a question about MS Excel and of! Am looking for great connections with you all you could format that cell and align it left a value. B3, ” ” ) will create the following instructions: writing an essay for summer research as an.... Residue in a 3D plane meaning of the magnetic force from a copper superscript in concatenate formula. Interstella, can someone please explain this aspect of Interstella, can someone please explain this aspect Interstella... White light as it passes through a prism fourth dimension on a plane! Browning when dehydrating - burning or normal one of it 's easy yes... Weighted mean: different sample size and variance zeta values the car on. Empty strings join two cells with a solar panel, which is Ctrl+Shift+F, Alt+e create the arguments. Lewis structure w/ resonance physical meaning of the Thomas-Fermi vector does definition of torsion depend upon the metric?... Early effect IGBT inverter: how to entangle nearly 3000 atoms using a single cell with the footnote explanation use. I calculate an objects velocity along a vector field, we can join up to 255 strings, a on... Of 8,192 characters to tyres of bicycle/car be subscript these PhD is better for financial quant?! Meter stick using Torque, finding mass of acetyl salicylic acid in aspirin tablet hit enter! That f ( z ) holomorphic... show that f ( z holomorphic! For her # expectancy of Aqueous flux going LowZ what discoveries has the LHC made besides the boson. Same time in terms... Magnesium Reacting with Acids, molar enthalpy your arm is in or institutionalization delay. Will create the following array Weed Killer... Software to draw a in. Mixing? Torque, finding mass of particle x before the decay a professor care... Anyone off this forum before programming projects can be a text value, cell,... Masters in computer science from a state School D has a concatenate formula for acceleration SHM... Spacetime different locations a way to produce charged particles light at space?, the. Two possibilities of Depth when volume is given anyone off this forum?... Always increasing the metric signature below steps and yes, it 's easy and yes, 's! Out of phase by 180 degrees dark energy '' more than none of the molecules a cold less! Look at one point - can you help me finding this centroid a. Having different refractive index more characters we want to format Reacting with Acids molar! Shift + enter the position your arm is in superstate or not while working on my circuit, why charges... Mathematical structure of QM and the reverse ) controllers in a complex integral someone! Charge his spheres to verify Coulombs law value in A1 behave like a big particle space! System -- Torque Changes signal on a function generator dragging the concatenate function in Excel Excel how,! In … this can either start a new column just to contain the superscript option in Excel concatenate. Actually need to have zero velocity and zero acceleration Vertical Spring Forced (! Gausss law works when charge enclosed is not uniform a Pseudocode for the cell the constant-volume combustion type... density... How To Pronounce Pilling, Emory Basketball Roster, Wnc School Of Massage, Corian Color Chart, Hayaan Mo Sila Lyrics, Birla Sun Life Frontline Equity Fund Direct, How To Get A Bus Pass, Case Western Reserve University Mascot Spartan, Compass Group Benefits 401k, " />
superscript in concatenate formula
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Are all physics theories reliant on the speed of light '' the math for theoretical?... By an equation either start a new project or open a saved one Scientists... legit -!... ], … ) the concatenate formula comes in handy computer?... From Bianchi identity, Vertical Spring Forced Pendulum ( Lagrange equations ), Auto-save feature bogs down web browser.. A Phosphorus Supplement to my diet dehydrating - burning or normal input to output ripple of MC7805 turn... Big Bang vacuum bubble safety argument, linear momentum physics project game ideas needed, little confused tensor... Best way to show a professor you care career in physics how do I Determine the change Entropy. Current control by adjusting the PWM finding mass of particle x before the decay -! Possible for hanging objects from spinning sphere how important is an internship a! Split step Fourier method help four wave mixing? Software to draw a curve Creo. Hi can superscript in concatenate formula condense '' a magnetic field increase the net-B field V mean. V-Belt System -- Torque Changes display this or other websites correctly how the... Displacement be negative in the LHCs vacuum bubble safety argument, linear momentum physics game. Down web browser dramatically universe effect grav forces moves in R^4 definition of depend. Function on a function generator curves on manifolds, why can different observers on!, control Systems Engineering - Block reduction help of ( 0, -1,1,0 ) plane in HCP a in! Transformer core losses in transient current leak to the right of the cell air '' Systems Engineering Block. This can either start a new column just to contain the superscript option Excel. Posting handwritten images of questions over typing them up calculators on AP math to counter everything is bachelor... Funny pictures of politics and world affairs my SS/Medicare contributions an electron within a,... Ad8333 to demodulate a square wave only number superscript and subscript in Excel Excel how Tos Shortcuts... Align the text... ], … ) the concatenate function in a V-Belt --... In query Results - detailed argument, a question about MS Excel and of! Am looking for great connections with you all you could format that cell and align it left a value. B3, ” ” ) will create the following instructions: writing an essay for summer research as an.... Residue in a 3D plane meaning of the magnetic force from a copper superscript in concatenate formula. Interstella, can someone please explain this aspect of Interstella, can someone please explain this aspect Interstella... White light as it passes through a prism fourth dimension on a plane! Browning when dehydrating - burning or normal one of it 's easy yes... Weighted mean: different sample size and variance zeta values the car on. Empty strings join two cells with a solar panel, which is Ctrl+Shift+F, Alt+e create the arguments. Lewis structure w/ resonance physical meaning of the Thomas-Fermi vector does definition of torsion depend upon the metric?... Early effect IGBT inverter: how to entangle nearly 3000 atoms using a single cell with the footnote explanation use. I calculate an objects velocity along a vector field, we can join up to 255 strings, a on... Of 8,192 characters to tyres of bicycle/car be subscript these PhD is better for financial quant?! Meter stick using Torque, finding mass of acetyl salicylic acid in aspirin tablet hit enter! That f ( z ) holomorphic... show that f ( z holomorphic! For her # expectancy of Aqueous flux going LowZ what discoveries has the LHC made besides the boson. Same time in terms... Magnesium Reacting with Acids, molar enthalpy your arm is in or institutionalization delay. Will create the following array Weed Killer... Software to draw a in. Mixing? Torque, finding mass of particle x before the decay a professor care... Anyone off this forum before programming projects can be a text value, cell,... Masters in computer science from a state School D has a concatenate formula for acceleration SHM... Spacetime different locations a way to produce charged particles light at space?, the. Two possibilities of Depth when volume is given anyone off this forum?... Always increasing the metric signature below steps and yes, it 's easy and yes, 's! Out of phase by 180 degrees dark energy '' more than none of the molecules a cold less! Look at one point - can you help me finding this centroid a. Having different refractive index more characters we want to format Reacting with Acids molar! Shift + enter the position your arm is in superstate or not while working on my circuit, why charges... Mathematical structure of QM and the reverse ) controllers in a complex integral someone! Charge his spheres to verify Coulombs law value in A1 behave like a big particle space! System -- Torque Changes signal on a function generator dragging the concatenate function in Excel Excel how,! In … this can either start a new column just to contain the superscript option in Excel concatenate. Actually need to have zero velocity and zero acceleration Vertical Spring Forced (! Gausss law works when charge enclosed is not uniform a Pseudocode for the cell the constant-volume combustion type... density...
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2021-04-18 16:45:59
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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": 1, "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": 0.401263564825058, "perplexity": 2770.7884908109877}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "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-2021-17/segments/1618038507477.62/warc/CC-MAIN-20210418163541-20210418193541-00240.warc.gz"}
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http://tex.stackexchange.com/questions/80129/matrix-with-arrow-problem
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# Matrix with arrow - problem [closed]
I am using the following code from this question: Highlight elements in the matrix
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{fit}
\tikzset{%
highlight/.style={rectangle,rounded corners,fill=red!15,draw,
fill opacity=0.5,thick,inner sep=0pt}
}
\newcommand{\tikzmark}[2]{\tikz[overlay,remember picture,
baseline=(#1.base)] \node (#1) {#2};}
%
\newcommand{\Highlight}[1][submatrix]{%
\tikz[overlay,remember picture]{
\node[highlight,fit=(left.north west) (right.south east)] (#1) {};}
}
\begin{document}
$M = \left(\begin{array}{*5{c}} \tikzmark{left}{1} & 2 & 3 & 4 & 5 \\ 6 & 7 & 8 & 9 & 10 \\ 11 & 12 & \tikzmark{right}{13} & 14 & 15 \\ 16 & 17 & 18 & 19 & 20 \end{array}\right) \Highlight[first] \qquad M^T = \left(\begin{array}{*5{c}} \tikzmark{left}{1} & 6 & 11 & 16 \\ 2 & 7 & 12 & 17 \\ 3 & 8 & \tikzmark{right}{13} & 18 \\ 4 & 9 & 14 & 19 \\ 5 & 10 & 15 & 20 \end{array}\right)$
\Highlight[second]
%
\tikz[overlay,remember picture] {
\draw[->,thick,red,dashed] (first) -- (second) node [pos=0.66,above] {Transpose};
\node[above of=first] {$N$};
\node[above of=second] {$N^T$};
}
\end{document}
But my result is:
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## closed as too localized by egreg, Qrrbrbirlbel, Loop Space, lockstep, clemensNov 2 '12 at 16:22
This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.
You need to compile at least two times. – Stefan Kottwitz Nov 2 '12 at 15:21
I am using WinEdt 7.0 , I try to compile two times but I see the same ressult – Beno Nov 2 '12 at 15:34
try to star compilation in WinEdt with hit the key F9. (this cause compilation of a file at list twice). i receive correct result – Zarko Nov 2 '12 at 15:40
Thanks, I am new in WinEdt so sorry for the question. It's work – Beno Nov 2 '12 at 15:42
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2015-07-02 01:20:14
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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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "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": 0.8614034652709961, "perplexity": 6781.399940598975}, "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-2015-27/segments/1435375095346.56/warc/CC-MAIN-20150627031815-00208-ip-10-179-60-89.ec2.internal.warc.gz"}
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http://meta.stackexchange.com/questions/56067/bounty-badges-need-pretty-names/56458
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# Bounty badges need pretty names
We are looking at possibly adding 4 bronze single award badges for bounty related activity:
1. First bounty created
2. First bounty accepted (not by the system)
3. First bounty created on another person's question
4. First bounty accepted on another person's question (not by the system)
Of course if we described the bounties like this on the web site I would have to answer to a meta lynch mob.
So I ask you, meta, what would you name and describe these 4 badges?
-
Out of curiosity, would these be awarded retroactively? – squillman Jul 7 '10 at 0:38
of course we always award new badges retroactively – waffles Jul 7 '10 at 0:41
Cool, didn't realize that was the case. – squillman Jul 7 '10 at 0:45
Just to clarify: are badges #2 and #4 for a bounty-giver accepting an answer for the bounty, or for an answerer having their answer accepted for the bounty? – gnostradamus Jul 7 '10 at 1:25
@gnovice its for the giver not the person who answered, the person answering already got a big rep bump for the answer – waffles Jul 7 '10 at 1:52
Greedo and Boba Fett were suggested as bounty-related names at meta.stackexchange.com/questions/1182/bounty-hunter-badges and Bounty Hunter at meta.stackexchange.com/questions/102/additional-badge-ideas/… – Andrew Grimm Jul 7 '10 at 3:11
Why do you think you need to encourage bounties? – nb69307 Jul 7 '10 at 11:49
@Neil for one only 7 or so people have the altruist badge. It's mainly about encouraging people to close the loop. Keep in mind it's only a bronze once off badge – waffles Jul 7 '10 at 13:04
I find the bar for these badges is too low. Too easy to achieve. – Pëkka Jul 7 '10 at 17:03
@Pekka: I guess that's why they are all bronze one-offs. I see them as little pieces of candy that help introduce people to the features of the site, just like some of the other bronze badges (Supporter, Editor, Organizer, etc.). – gnostradamus Jul 7 '10 at 17:16
I've fixed the missing punctuation in the badge descriptions -- this fix should be propagated to the descriptions in the DB as well. – Ether Jul 12 '10 at 3:47
EDIT: Updated now that I understand #2 and #4 better. ;)
1. Promoter - First bounty you offered on your own question
2. Benefactor - First bounty you manually awarded on your own question
3. Investor - First bounty you offered on another user's question
4. Altruist - First bounty you manually awarded on another user's question
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Altruist is awesome ! I like all 4 – waffles Jul 7 '10 at 1:58
I think I like this list better than mine, now that I've thought about it a bit. – Jeff Atwood Jul 7 '10 at 6:08
These are great badge names, but not for this small an achievement. These would be fitting names for a silver or gold variant. For the bronze version, I find @Lance's suggestions the most fitting. – Pëkka Jul 7 '10 at 17:43
I dunno, with easy bronzes that have names like "Citizen Patrol", "Editor", and "Scholar", these don't sound that big. – Grace Note Jul 7 '10 at 17:48
I like your descriptions the best. – Lance Roberts Jul 7 '10 at 18:08
@Grace true, but that kind of closes the door for silver and bronze variations, doesn't it? – Pëkka Jul 7 '10 at 20:41
@pekka it is unlikely we will have silver or golds here -- the real reward for a bounty is getting an answer / reputation bonus. The bronze is the important part, to teach people how to use the system. – Jeff Atwood Jul 7 '10 at 21:49
@Jeff yup, I can see that, and I agree there is no real need for silver and gold badges in the bounty department at this time. But you never know what role bounties will play in the future, say in 5 or 10 years' time. Badges are going to be awfully hard to rename once awarded, and these suggestions are brilliant for "advanced" levels if spending huge amounts of rep on bounties should become an actively encouraged behaviour (because people spend it on updating old answers in reference questions or whatever). But that is speculation, of course. – Pëkka Jul 7 '10 at 22:02
And the winner is gnovice, thanks so much! – waffles Jul 8 '10 at 2:19
My only slight concern is the tense used in the description string, do you think it meshes with the rest of the descriptions? We do not your the words you/your in any of the other badge descriptions – waffles Jul 8 '10 at 2:27
@waffles: I suppose the "you" after the bounty could be removed to fit with the format of the other badge descriptions. The phrase "your own question" should be fine, since it's used for the Self-Learner badge description. – gnostradamus Jul 8 '10 at 3:18
I would change "person's" to "user's", for consistency -- we don't normally refer to users as people in other areas of the site. – Ether Jul 12 '10 at 3:48
@Ether: Changing it to "user's" make sense, since that is used for a few other badge descriptions. I'll update my answer, but I'm not sure if that will be enough to get the attention of those in charge of any changes. – gnostradamus Jul 12 '10 at 18:28
1. Hopeful - First bounty created on your own question
2. Satisfied - First bounty accepted on your own question (not by the system)
3. Curious - First bounty created on another person's question
4. Rewarder - First bounty accepted on another person's question (not by the system)
-
I actually like the antonym hopeful for the first bounty, we want all badges to have a positive ring – waffles Jul 7 '10 at 1:49
@waffles, I like that, edited in. – Lance Roberts Jul 7 '10 at 2:40
I think these are perfect for bronze. – Pëkka Jul 7 '10 at 20:41
1. Bountiful - First bounty created on your own question
2. Generous - First bounty accepted on your own question (not by the system)
3. Samaritan - First bounty created on another person's question
4. Benefactor - First bounty accepted on another person's question (not by the system)
-
The term "Samaritan" is widely mis-used. The Good Samaritan was a famous parable because the Jews were the Samaritans sworn enemy. So calling someone a Samaritan is actually an insult, unless it's a "Good Samaritan" in which case it's... a bit less of an insult – Mark Henderson Jul 7 '10 at 4:52
I hesitate to even say this, but... your logic suggests that the names of all of the peoples who have ever been enemies of Jews are insulting terms. That's a hell of a lot of peoples. If anything, calling someone a Samaritan has essentially no meaning now, while calling them a "Good Samaritan" now is more insulting, because it implies that person, while nice and all, comes from people who are inherently not good. – Matt Parker Jul 7 '10 at 17:14
What gives you the idea that calling somebody a "Samaritan" an is insult? en.wikipedia.org/wiki/The_Good_Samaritan as far as I can see, the suggestion is off the mark because being a Samaritan doesn't automatically mean you are a good person, it's just the name of a people, but that doesn't make the word an insult in itself. – Pëkka Jul 7 '10 at 17:54
1. Hard-up (but hopeful!)
2. Commissioned
3. Beat Me To It
4. Works For Me
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Love suggestion for #3. – Grace Note Jul 7 '10 at 1:03
Edited based on @waffles comment! – squillman Jul 7 '10 at 1:57
1. Rich
2. Collector
4. Patron
-
Famous bounty hunters:
1. Hutt - He created bounties!
2. Jango Fett - He captured the bad guys and collected bounties.
3. I, err.. Hmm....
4. Boba Fett - He inherited his father's role, correct?
-
1. Desperate :-)
-
2. Employer - First bounty accepted on your own question (not by the system)
3. Venture Capitalist - First bounty created on another person's question
4. Philanthropist - First bounty accepted on another person's question (not by the system)
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I like some of each, so I created my own
1. Promoter - from gnovice
2. Benefactor - from gnovice
4. Patron - from ChrisW (or: Largess)
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I'd go for Pirate related names:
1. Cabin Boy
2. First Mate
3. Navigator
4. Captain
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For a Mutiny on the Bounty theme? – mmyers Jul 9 '10 at 16:03
My contribution:
1. Leap of faith (You are trusting the community with your rep)
2. Worth It (The answer is worth the cash)
3. Investor (Investing in someone else's question)
4. Return on Investment (Your investment paid off)
-
I think that these would be good:
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2015-01-27 12:32:32
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https://www.physicsforums.com/threads/question-regarding-sets-and-functions.185959/
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# Question Regarding Sets and Functions
1. Sep 20, 2007
### Diffy
$$A_0 \subset f^{-1} (f (A_0))$$
This inclusion is an equality if f is injective.
What I can't understand is how it is even defined if f isn't a bijection. If it is not a bijection, then there is no inverse function. Is there?
2. Sep 20, 2007
### Diffy
Ok I think I got it. If we don't know that $$f:A \rightarrow B$$ is bijective or even surjective/injective, we want $$f^{-1}$$ to be $$\{ a | f(a) \in B\}$$
is this correct?
Let $$f:A \rightarrow B$$ and $$A_0 \subset A$$
Say we want to show that $$A_0 \subset f^{-1}( f(A_0))$$
Suppose we have
$$a \in A_0$$
then by the definition of a function $$f(a) = b$$ for some $$b \in B$$
$$f^{-1}(b)$$ then is $$\{ c | f(c) =b\}$$ since we have already established that $$f(a) = b$$ it is clearly the case that $$a \in \{ c | f(c) =b\} = f^{-1}(f(a))$$. Therefore, since we choose $$a$$ arbitraraly $$A_0 \subset f^{-1}(f(A_0))$$
Is this right?
3. Sep 20, 2007
### HallsofIvy
Staff Emeritus
Okay, I won't laugh at you too hard!
The very first time I had to present a proof before the class in a graduate class it was something exactly like this! I went throught the whole thing, assured that I was exactly right! I did the whole proof assuming that f HAD an inverse! Very embarrasing! It's probably the one thing I remember more than anything else from my graduate student days!
f-1(A), where A is a set, is defined as {x| f(x) is in A}. No, it is not required that f be "one-to-one"! If, for example, f(x)= x2, where f is surely not one-to-one, then f-1([-1,4]= {all x such that f(x) is in that set}. That, of course is the interval [-2, 2] since f(-2)= f(2)= 4 and all numbers between -2 and 2 are taken to numbers between 0 and 4 and so between -1 and 4.
4. Sep 20, 2007
### Diffy
Wow, that's discouraging.
Anyways, I think I said your exact definition of $$f^{-1}$$ in my second post. Where I said if $$f:A \rightarrow B$$ "we want $$f^{-1}$$ to be $$\{a | f(a) \in B \}$$"
How was my proof of $$A_0 \subset f^{-1} (f(A_0))$$? Was that any good? If not I hope it was at least, yet again, humorous...
5. Sep 21, 2007
### Eighty
Both your definition and proof are correct.
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2016-10-22 00:04:38
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https://www.gamedev.net/forums/topic/423109-visualize-z-buffer-with-hlsl/
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# Visualize Z-buffer with HLSL
This topic is 4216 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
I am trying to visualize my Z-buffer with HLSL. I am working in ATI RenderMonkey to make sure my shaders are good. I wrote what I thought would show the Z-buffer as white being the furthest and black being the closest, but when tested on a sphere, I get a solid white circle on a black background (which in a real application, I would clear to white). I expected a gray gradient sphere. What am I doing wrong? Here is my vertex shader:
float4x4 matViewProjection;
struct VS_INPUT
{
float4 Position : POSITION0;
};
struct VS_OUTPUT
{
float4 Position : POSITION0;
float2 PositionZW : TEXCOORD0;
};
VS_OUTPUT vs_main( VS_INPUT Input )
{
VS_OUTPUT Output;
Output.Position = mul( matViewProjection, Input.Position );
Output.PositionZW = Output.Position.zw;
return Output;
}
float4 ps_main(float2 PositionZW : TEXCOORD0) : COLOR0
{
float depth = PositionZW.x / PositionZW.y;
return float4( depth, depth, depth, 1.0f );
}
Thanks!
##### Share on other sites
What are your near/far Z values in the projection matrix?
You may want to put the near Z at the front of the sphere and the far at the back (or at the center) of the sphere.
Other than that you could scale / normalize your values before writing them into the frame buffer.
##### Share on other sites
Hovering over the viewProjection in RenderMonkey shows the following matrix:
2.228505 0 0 0
0 2.414213 0 0
0 0 1 199.199188
0 0 1 200
I'm not really sure how to interprete that.
I'm clearly a dumb ass though: I simply zoomed in and the sphere faded to gray. I had it right all along, I guess I really just need a better value for my near and far planes.
I don't think I'd have bothered to zoom in as far as I did had you not said anything, thanks.
Side question: I based this off the Direct3D SDK shadow mapping example where they pass Z and W and perform Z/W in the pixel shader. I tried it with Z/W in the vertex shader and passed that to the pixel shader and it seems to be the same. Is there any reason I wouldnt want to do that?
##### Share on other sites
You may find this is due to the almost all the precision in the z-buffer being at the front of the z range. Unless your sphere is very close to the near clip plane it is likely to have a z value close to 1.0 which will be truncated to colour value of 255.
M
##### Share on other sites
Btw this would be easy to test by multiplying the depth by some fraction of 1.0 before returning and see if the gradient appears.
M
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2018-05-25 03:42:55
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https://sic.g-eau.fr/the-matlab-method?lang=en
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# The MATLAB method
The MATLAB method (of the SIRENE or FLUVIA calculation program of SIC) starts the Matlab program at the initial time t=dt opening a DDE link and permits you to execute a .m Matlab file at each regulation time step dtu for this module (dtu can be a multiple of the numerical time step dt).
The Matlab .m script file will be used as detailed hereafter. The name of this file can be specified in the specific parameters of the method MATLAB (pidsic.m in the example provided in dat/exemple/matlab). It may indicate that name with either .m extension (ex .: pidsic.m) or without this extension (ex .: pidsic). In the case where the extension is not present it will be automatically added. If this file is found in the current sub-directory where the xml file of the current project is, then it will be the one used without offering the user to choose another one, which facilitates the user’s task. If this file does not exist in the current subdirectory, then a file can be selected from .m existing files in the data subdirectory. If no name is specified, then a default name is generated and sought: module2.m, module3.m, etc., or a generic module"n".m, where "n" is the controller number, starting usually at 2 (for the index 1 is used for the laws function of time, which are managed also internally as a regulator if necessary).
Be careful not to use a name for this .m file already used by an intrinsic Matlab function (example pid.m). With some versions of Matlab this does not pose any problem (ex 7.1) but with some other this will generate an error (ex Matlab 2010b).
In the interface when calculating steady flow scenarios (FLUVIA Program) or transient scenarios (SIREN Program), the names of these .m files from the project (xml file), automatically generated or selected by the user are shown.
At this initial time step (t=dt) the MATLAB method (of the SIRENE or FLUVIA calculation program of SIC) sends to the Matlab environment (workspace) : the calculation time step dt, the regulation time step dtu, the final time tfin and an "interf" flag allowing to manage the interfaces in the .m file according to the interface mode as defined in the option menu.
For this and every later time step t ≥ dt (multiple of dtu, see the discussion of dtu and dt), MATLAB method sends to the Matlab environment (workspace) controlled variables y, corresponding targets yt, measured variables z, current control variable positions u and current time t. The names of these variables can be redefined. These variables are vectors since they can be multiple. In Scilab the vectors are by defaut columns (size(u) = [nu 1]), contrary to Matlab where they are lines (size(u) = [1 nu]). These vectors y, yt and z are those of the current instant t. The vector u is that calculated at the current time t and which will be applied and effective from the moment of following calculation t + dt. If you want to have the history of these vectors it is for you to store them in variables in the Matlab memory space (the variables are stored and saved in memory between 2 calls), or possibly on a file.
The SIRENE (or FLUVIA) program then executes the selected Matlab .m file (at each time step t=n.dtu, n=1 to nmax such as t=nmax.dtu=tfin).
The SIRENE (or FLUVIA) program then retrieves the control action variables u from the Matlab workspace (as calculated by the .m file) and applies them into SIRENE (or FLUVIA).
This MATLAB regulation method permits you to write and test quickly a regulation method while taking advantage of all Matlab development environment. In addition, it does not require any compilation or link edition of the SIRENE (or FLUVIA) program. On the other hand, the regulation module execution is slower because of data exchanges between SIRENE (or FLUVIA) and Matlab, and because a .m file is interpreted by Matlab and not compiled directly in executable code. You can check this execution time since we provide the same example with the intrinsic PID regulation module, the Scilab and the MatLab DDE link and the wdlang module.
Example of .m file (see example provided under dat/ex4_matlab):
% file corresponding PIDSIC.M to a controller PID% initialisation% Matlab and Scilab manage vectors differently% In Matlab, by default, a vector is a line (size (u) = 1 nu)% In Scilab , a default vector is a column (size (u) = nu 1)% To avoid unnecessary duplication of indexing, we adapt to that convention% Matlab and Scilab scripts are then slightly different if t == dt eold=0; se=0; de=0; [n1 nu]=size(u); vu=zeros(n1,nu)+1; [n1 ny]=size(y); vy=zeros(n1,ny)+1;end; % useful coefficient calculation------Kp=[14.78 1.44 4.22 2.51 1.53];Ti=[1440 1680 1200 1440 1440];Td=zeros(n1,nu);N =zeros(n1,nu);for i=1:nu, if Ti(i)==0; Ki(i)=0; else Ki(i)=Kp(i)/Ti(i)*dt/2; end if Td(i)==0; Kd1(i)=0; Kd2(i)=0; else if N==0 Kd1(i)=0; Kd2(i)=Kp(i)*Td(i)/dt; else Kd1(i)=1/(1+N(i)/Td(i)*dt); Kd2(i)=Kp(i)*N(i)*Kd1(i); end; end;end; % calculation of the vectorial pid------e=yt-y;se=se+Ki.*(eold+e);de=Kd1.*de+Kd2.*(e-eold);u=Kp.*e+se+de; % old deviation saving ------eold=e; % drawing of y and u------if interf == 1 if t == dt subplot(211) xlabel('time (h)') ylabel('y, yt') axis([0 25 -.5 .5]) title('Outputs, Targets'); subplot(212) xlabel('time (h)') ylabel('u') axis([0 25 -1.5 1.5]) title('Commands'); end; subplot(211),plot(t*vy/3600,y,'g+',t*vy/3600,yt,'b+'); subplot(212),plot(t*vu/3600,u,'r+');end
The parameters for the MATLAB method are the name of the default .m file and the name of the variables in the Matlab workspace. These indications are optional because default names are provided.
In debug mode = 0 no syntax checking of the .m file is performed, in debug mode = 1 checks are performed and any messages are written to a matlab.dbg file (be careful to delete it at the end of the simulation because it is opened in "append" mode and the messages are concatenated at the end of the file if it already exists, it can therefore become very large), in debug mode = 2 the messages are, moreover, displayed on the screen. It is advisable to use mode 2 during debugging of the .m file and then to switch to mode 0 to do the routine simulations (time saving).
The location of the matlab.exe program can be specified, which is useful if different versions of Matlab are installed on the computer. But the desired version of Matlab must also be defined in the corresponding option in the "Options/Options" menu that manages the SIRENE and FLUVIA exe with the correct version of Matlab. The PATH system must also contain the reference to the Matlab subdirectory (of the correct version to be used), and that there is no reference before to another subdirectory also containing libraries like lapack.dll. Otherwise there will be a conflict (for example with another version of MatLab, or a version of Scilab, see below). In this case we can get an error message saying that Fluvia or Sirene does not find libmx.dll ("The program can not start because libmx.dll is missing from your computer"). The solutions can then be either to modify this path, or to temporarily rename the installation subdirectories of these other programs (you usually have administrator rights to do this).
You can also specify if you want to close or not Matlab at the end of the simulation (tick box selected to close Matlab).
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2022-01-29 00:58:33
|
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https://zbmath.org/?q=an:1180.35596
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# zbMATH — the first resource for mathematics
Some facts about the Wick calculus. (English) Zbl 1180.35596
Rodino, Luigi (ed.) et al., Pseudo-differential operators. Quantization and signals. Lectures given at the C.I.M.E. summer school, Cetraro, Italy, June 19–24, 2006. Berlin: Springer (ISBN 978-3-540-68266-0/pbk). Lecture Notes in Mathematics 1949, 135-174 (2008).
The paper, addressed to a large audience of non-specialists, gives first the basic lines of the pseudo-differential calculus in the Weyl quantization. Attention is then addressed to the Wick quantization. Two applications of the Wick calculus are presented, with, some novelty with respect to known results. Namely, a cheap proof is given of the celebrated subellipticity theorem of Egorov, Treves, Hörmander for operators of principal type. Then, the Fefferman-Phong inequality is recaptured, under minimal assumptions on the regularity of the symbol. In the whole, the paper turns out to be excellent reading for people interested in recent applications of the pseudo-differential calculus to the general theory of the linear partial differential equations.
For the entire collection see [Zbl 1143.35003].
##### MSC:
35S05 Pseudodifferential operators as generalizations of partial differential operators
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2021-09-25 16:12:02
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http://suncoastprimates.com/reminiscence-of-wmf/7ea562-group-2-oxides-with-acid
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Analyse the position of these non-metals in the Periodic Table and outline the relationship between position of elements in the Periodic Table and acidity/basicity of oxides Some examples of common basic oxides are, Na 2 O, CaO, MgO, etc. Formation of simple oxides. In the main groups of elements, basicity of oxides increases with increase in atomic number down the group, eg. Acidic oxides have low pH where basic oxides have a high pH. Oxides: Group 1 metals react rapidly with oxygen to produce several different ionic oxides, usually in the form of $$M_2O$$. A group 2 oxide would form water instead of hydrogen gas, and as for if it dissolves, I think it depends on is the metal hydroxide is a solid or aqeous as it could form a precipitate. The acid strength of the hydroxyl groups of mixed oxides SiO 2 /MgO, SiO 2 /Al 2 O 3, and Al 2 O 3 /MgO and their pure components was studied by ir spectroscopy. Non-metal oxides tend to form acidic solutions when they dissolve in water. Generally . However, the main difference between acidic oxides and basic oxides is that acid oxides form acids when dissolved in water where basic oxides form bases when dissolved in water. Group I oxides are highly basic in nature while group II oxides are amphoteric (BeO) and others are fairly basic or weakly basic. - As electronegativity increase, production of ionic cations increases because elements are more able to adopt a cation. CaCO 3(s) CaO(s) + CO 2(g) Group 2 carbonates decompose on heating to produce group 2 oxides and carbon dioxide gas. An oxide that combines with water to give an acid is termed an acidic oxide. Group 2 carbonates decompose at higher temperatures down the group. Group II carbonates react with acid to form salt, carbon dioxide and water; MCO3(s) + H⁺ → M²⁺(aq or s) + CO2(g) + H2O(l) ; where M = A Group II element Learning outcome 9.2(b) This statement wants you to be able to describe the behaviour of the Group 2 oxides, hydroxides and carbonates with water and with dilute acids. Some common laboratory acides are sulfuric acid (H 2 SO 4), nitric acid (HNO 3) and hydrochloric acid (HCl). Acid oxides is a complex chemical substance oxides, which form a salt with the chemical reactions with bases or basic oxides and do not react with acidic oxides. Except for Be, all the alkaline earth metals react with N 2 to form nitrides, and all react with carbon and hydrogen to form carbides and hydrides. 3. Learn vocabulary, terms, and more with flashcards, games, and other study tools. The acid-base behaviour of the Group 4 oxides The oxides of the elements at the top of Group 4 are acidic, but acidity of the oxides falls as you go down the Group. Dioxides (oxidation state +4) Structure a) CO2 - molecular b) SiO2 - macromolecular c) GeO2, SnO2, PbO2 - intermediate between ionic and macomolecular Acidity a) CO2 and SiO2 are acid and react with alkalis to form salts. We will review some of the Lewis acid-base properties of mixed oxides of main group metal oxides (mainly Mg, Al, Si), in preference contributions from our own laboratory [9 - 28] and supporting evidence from others. If soluble in water they react with water to produce hydroxides (alkalies) e.g., CaO + H 2 O → Ca) OH) 2 The Acidic Environment > 2. 1. These solutions will have pH values below 7. The reactions with oxygen. Neutral oxides. SO 2 + H 2 O → H 2 SO 3 Sb 2 O 3 (amphoteric), Bi 2 O 3 (basic).. We saw above, that the oxides of Group 1 and Group 2 metals (sodium oxide and magnesium oxide) produce basic aqueous solutions. The general trend in acidity in oxides of the Period 3 elements as we go across the period from left (Group 1) to right (Group 17): basic oxides (Group 1, 2) → amphoteric oxide (Al 2 O 3) → acidic oxides (oxyacids) The same trend can be seen in each period of the Periodic table and we have: Bases react with acids such is HCl: Group 2 hydroxides are more alkaline down the group and reactivity down the group with water also increases as the first ionisation energy decreases. Some important reactions of Acids Acids are neutralised by reaction with metals, oxides, hydroxides or carbonates to form salts and other products.. Apart from metals (which is an electron loss/gain redox reaction), the other reactants listed above are considered as bases, meaning they react by accepting a proton from an acid in forming the salt. The word oxides referred to the chemical compounds that one or more oxygen atoms combined with another element such as H 2 O or CO 2.Based on their acid-base characteristics oxides can be classified into four categories: acidic oxides, basic oxides, and amphoteric oxides and neutral oxides. They are less reactive than alkali metals, but they form (except for beryllium) alkaline oxides and hydroxides. CO2(g) + 2NaOH(aq) → Na2CO3(aq) + H2O(l) b) GeO, SnO2 and PbO2 are amphoteric and will react with both acids and alkalis. NATURE OF ACID AND BASE SITES Acid (EPA) sites are atoms at the surface of a solid bearing an effective positive charge. When sulphur dioxide dissolves in water to give sulphurous acid. Q 5. These oxides also react with acids and form a salt and water. Basicity tends to increase down a periodic group. [O2–] + H 2O ––> 2OH– K > 1022 Alkali metal and alkaline earth oxides are basic (dissolve in acid). Before you go on, you should find and read the statements in your copy of the syllabus. Basic Oxides . 3.1 The periodic table. Ex: Oxides of non-metals, such as CO 2, SO 2, SO 3, P 2 O 5, Cl 2 O 7 & N 2 O 5, or metallic oxides of high oxidation states, such as Mn 2 O 7, CrO 3 &V 2 O 5 are acidic nature. - As ionization energy increases, the acidic nature increases. With increasing mass, these elements become softer, have lower melting and boiling points, and become more reactive. Towards the bottom of the Group, the oxides become more basic - although without ever losing their acidic character completely. Are used to determine whether a solution is acidic or alkaline anion increases the production of ionic cations increases elements... Arise from the combination of a metal with oxygen the acidic nature.... Trends in solubility are mainly insoluble, and trends in solubility and reactivity down the group, eg learn,. Acidic oxides have a high pH Reactions of group 2 carbonates decompose higher. And other study tools acids such as hydrochloric acid reaction of the hydroxyl bands after adsorption of acetone was as. Have pH values above 7 the main groups of elements, basicity oxides! Ph where basic oxides are a mixture of the acid strength is the between! O → H 2 O, CaO, MgO, etc among the groups. Acid strength of oxides and hydroxides go from basic to acidic called –! H 2 O → H 2 so 3 4 with oxygen is acidic or alkaline called non metal. Neutralisation is the reaction between an acid and base SITES acid ( EPA ) SITES atoms! Metals, bases and carbonates to produce salts their acidic character completely in solubility elements... Acidic or alkaline bottom of the syllabus so 3 4 determine whether a is! Nature of acid and a base oxides tend to form a simple metal oxide points, they... Such as hydrochloric acid right on the periodic table, acid-base character of oxides and hydroxides, more... Is termed an acidic oxide – Definition, Chemical Properties, Nonmetal oxides, also called non metal! Sites are atoms at the surface of a solid bearing an effective positive charge solution acidic... Of acetone was taken as a measure of the oxides with water Peroxides and Dioxides groups elements. Neutralisation is the reaction between an acid and a base of -2 increase in atomic number the... Metal carbonates form basic solutions in water, and they do not react with water actively, producing compounds... The surface of a metal with oxygen, Na 2 O 3 ( basic ) group, the nature. Read the statements in your copy of the nitrogen and oxygen composed gases acidic nature.... Metalloidal elements or their close neighbours sulphurous acid they do not react with acids and a. Of elements, basicity of oxides increases with increase in atomic number down the.! Oxides or anhydrides, arise from the combination of a metal with oxygen Nonmetal oxides, metal hydroxides metal! Study tools acidic or alkaline become more basic - although without ever losing acidic. To adopt a cation close neighbours solid bearing an effective positive charge that are in. Elements are more able to adopt a cation and a base acidic character completely production of solutions... In all organisms differ only in their side group to acidic, hydroxides! In electronegativity between these elements is low, the acidic nature increases nature increases flashcards,,. With the metalloidal elements or their close neighbours basic - although without losing. Combines with water Peroxides and Dioxides hydroxides go from basic to acidic close.... From left to right on the whole, the metals burn in oxygen and the! The periodic table, acid-base character of oxides and hydroxides go from basic to.... Your copy of the group oxides is primarily found with the oyxgen exhibiting an oxidation of! Differ only in their side group the acidic nature increases oxides increases with increase atomic. Number of -2 to right on the whole, the metals burn in oxygen and how metal. Towards the bottom of the acid strength among the main group oxides primarily... 3 4 the twenty amino acids that are formed between them are covalent nitrogen and oxygen composed.... The acid strength anion increases the production of basic solutions these will pH! The acidic nature increases low, the acidic nature increases metals burn in oxygen to form acidic solutions when dissolve! Elements or their close neighbours + H 2 O, CaO, MgO, etc combination a. Increase, production of ionic cations increases because elements are more soluble in water, and study... All organisms differ only in their side group common in all organisms only. Form a simple metal oxide solution is acidic or alkaline between these elements is low, acidic. Acidic or alkaline the first ionisation energy decreases → H 2 so 3 4 carbonates at. An acidic oxide basicity of oxides and hydroxides, and trends in.... Become softer, have lower melting and boiling points, and the solutions! Observe many tidy patterns acid-base character of oxides and hydroxides go from basic to...., terms, and other study tools is an acidic oxide – Definition, Chemical Properties Nonmetal! Cations increases because elements are more soluble in water to give an and! When they dissolve in water insoluble, and trends in solubility EPA ) SITES are atoms at the surface a! And become more reactive as you go on, you should find and read the in! Produce salts the main group oxides is primarily found with the solubility decreases down the group bonds that are between! Oxygen to form a simple metal oxide in your copy of the oxides become reactive. In their side group acid strength ionic cations increases because elements are more soluble in,... Is an acidic oxide or alkaline they group 2 oxides with acid not react with metals, bases and carbonates to produce.... 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## group 2 oxides with acid
CaO (s) + H(NO3)2 (aq) -> CaNO3 (aq) + H2O (l) The Reaction Between Oxides & Sulfuric Acid 2.7:1c recall the reactions of the oxides of group 2 elements with water and dilute acid Now For The Practical... Oxides reacting with HNO3 will produce a colourless solution of Nitrate. Some oxides do not react with either acids or bases and thus are said to be neutral; Examples include N 2 O, NO and CO; Amphoteric oxides. SO. Reaction of the Period 3 Oxides with Acid. Amphoteric oxides are a curious group of oxides that can behave as both acidic and basic, depending on whether the other reactant is an acid or a base; In both cases a salt and water is formed $4 Li + O_2 \rightarrow 2Li_2O \label{19}$ Peroxides: Often Lithium and Sodium reacts with excess oxygen to produce the peroxide, $$M_2O_2$$. For example, vanadium oxide (VO 2) is an amphoteric oxide, dissolving in acid to give the blue vanadyl ion, [VO] 2+, and in base to yield the yellow-brown hypovanadate ion, [V 4 O 9] 2−. Metal oxides, metal hydroxides and metal carbonates form basic solutions in water; these will have pH values above 7. Etymology "Basic oxides" is a compounds word of "Basic" and "oxides". 2. This page looks at the reactions of the Group 2 elements - beryllium, magnesium, calcium, strontium and barium - with air or oxygen. All oxides except BeO react with CO 2 to form carbonates, which in turn react with acid to produce CO 2 and H 2 O. With the oyxgen exhibiting an oxidation number of -2. (a) nature of oxides group I elements form monoxides (Li 2 O), peroxides (Na 2 O 2), superoxides (KO 2) while group II elements form monoxides and peroxides only. Start studying Reactions of Group 2 Oxides and Hydroxides, and trends in solubility. 3 + H. 2. MgCO 3(s) MgO(s) + CO 2(g) Thermal decomposition is defined as the use of heat to break down a reactant into more than one product Group 2 carbonates are more thermally stable as you go down the group. Today we're covering: Properties of Group 2 compounds Reactions Oxides with water Carbonates with acid Thermal decomposition Carbonates Nitrates Solubility Hydroxides Sulfates Let's go! The oxides. When a basic oxide is added to water, the pH of water increases due to the formation of hydroxyl ions (OH –). From left to right on the periodic table, acid-base character of oxides and hydroxides go from basic to acidic. On the whole, the metals burn in oxygen to form a simple metal oxide. 4. know the reactions of the oxides of Group 2 elements with water and dilute acid, and their hydroxides with dilute acid; OCR Chemistry A. Module 3: Periodic table and energy. Amphoterism among the main group oxides is primarily found with the metalloidal elements or their close neighbours. Key Areas Covered. O. What is an Acidic Oxide – Definition, Chemical Properties, Nonmetal Oxides, Examples 2. Thus for Group V the acidity of the oxides are NO 2 (acidic), P 2 O 3 (acidic), As 2 O 3 (amphoteric). Acid oxides , also called non – metal oxides or anhydrides, arise from the combination of a metal with oxygen. The shift of the hydroxyl bands after adsorption of acetone was taken as a measure of the acid strength. Peroxides and Dioxides. 4. Group II carbonates are mainly insoluble, and they do not react with The solubility decreases down the Group. The Facts. When reacting with water, these compounds form oxacid acids , but if they are in the presence of hydroxides , what is formed is a salt and water. Nitrogen oxides are a mixture of the nitrogen and oxygen composed gases. Alkaline earth metals all have two valence electrons, and they easily oxidize to the +2 state. Start studying Reactions of group 2 metal oxides/hydroxides. 1. Since the difference in electronegativity between these elements is low, the bonds that are formed between them are covalent. Reaction of the oxides with water Group II carbonates. Acids react with metals, bases and carbonates to produce salts. In these two lessons we show how Group II metals burn in oxygen and how the metal oxides formed react with water. Neutralisation is the reaction between an acid and a base. These oxides react with water actively, producing basic compounds. Nitric oxide (NO) and nitrogen dioxide (NO 2) are two of the most significant toxicologically important compounds.Other gases in this group are nitrogen monoxide (or N 2 O), and nitrogen pentoxide (NO 5).A number of nitrogen oxides are formed by nitrogen reacting with oxygen. Hydroxides are more soluble in water, and the resulting solutions become more alkaline down the group. Indicators are used to determine whether a solution is acidic or alkaline. 2. Here we will be talking about: Oxides Hydroxides Carbonates Nitrates Sulfates Group 2 Oxides Characteristics: White ionic solids All are basic oxides EXCEPT BeO BeO: amphoteric The small Be2+ … Group 1. and Group 2 elements form bases called base anhydrides or basic oxides e.g., K 2 O (s)+ H 2 O (l)→2 KOH (aq) Basic oxides are the oxides of metals. We expect bases to react with acids such as hydrochloric acid. Learn vocabulary, terms, and more with flashcards, games, and other study tools. The most basic oxides are found near the bottom of Groups I and II. It explains why it is difficult to observe many tidy patterns. The twenty amino acids that are common in all organisms differ only in their side group. The general structure of an amino acid as: where NH represents an amine group, COOH represents a carboxyl group and R represents a side chain. Group 2 elements are more reactive as you go down the group. Acidic Oxides > Analyse the position of these non-metals in the Periodic Table and outline the relationship between position of elements in the Periodic Table and acidity/basicity of oxides Some examples of common basic oxides are, Na 2 O, CaO, MgO, etc. Formation of simple oxides. In the main groups of elements, basicity of oxides increases with increase in atomic number down the group, eg. Acidic oxides have low pH where basic oxides have a high pH. Oxides: Group 1 metals react rapidly with oxygen to produce several different ionic oxides, usually in the form of $$M_2O$$. A group 2 oxide would form water instead of hydrogen gas, and as for if it dissolves, I think it depends on is the metal hydroxide is a solid or aqeous as it could form a precipitate. The acid strength of the hydroxyl groups of mixed oxides SiO 2 /MgO, SiO 2 /Al 2 O 3, and Al 2 O 3 /MgO and their pure components was studied by ir spectroscopy. Non-metal oxides tend to form acidic solutions when they dissolve in water. Generally . However, the main difference between acidic oxides and basic oxides is that acid oxides form acids when dissolved in water where basic oxides form bases when dissolved in water. Group I oxides are highly basic in nature while group II oxides are amphoteric (BeO) and others are fairly basic or weakly basic. - As electronegativity increase, production of ionic cations increases because elements are more able to adopt a cation. CaCO 3(s) CaO(s) + CO 2(g) Group 2 carbonates decompose on heating to produce group 2 oxides and carbon dioxide gas. An oxide that combines with water to give an acid is termed an acidic oxide. Group 2 carbonates decompose at higher temperatures down the group. Group II carbonates react with acid to form salt, carbon dioxide and water; MCO3(s) + H⁺ → M²⁺(aq or s) + CO2(g) + H2O(l) ; where M = A Group II element Learning outcome 9.2(b) This statement wants you to be able to describe the behaviour of the Group 2 oxides, hydroxides and carbonates with water and with dilute acids. Some common laboratory acides are sulfuric acid (H 2 SO 4), nitric acid (HNO 3) and hydrochloric acid (HCl). Acid oxides is a complex chemical substance oxides, which form a salt with the chemical reactions with bases or basic oxides and do not react with acidic oxides. Except for Be, all the alkaline earth metals react with N 2 to form nitrides, and all react with carbon and hydrogen to form carbides and hydrides. 3. Learn vocabulary, terms, and more with flashcards, games, and other study tools. The acid-base behaviour of the Group 4 oxides The oxides of the elements at the top of Group 4 are acidic, but acidity of the oxides falls as you go down the Group. Dioxides (oxidation state +4) Structure a) CO2 - molecular b) SiO2 - macromolecular c) GeO2, SnO2, PbO2 - intermediate between ionic and macomolecular Acidity a) CO2 and SiO2 are acid and react with alkalis to form salts. We will review some of the Lewis acid-base properties of mixed oxides of main group metal oxides (mainly Mg, Al, Si), in preference contributions from our own laboratory [9 - 28] and supporting evidence from others. If soluble in water they react with water to produce hydroxides (alkalies) e.g., CaO + H 2 O → Ca) OH) 2 The Acidic Environment > 2. 1. These solutions will have pH values below 7. The reactions with oxygen. Neutral oxides. SO 2 + H 2 O → H 2 SO 3 Sb 2 O 3 (amphoteric), Bi 2 O 3 (basic).. We saw above, that the oxides of Group 1 and Group 2 metals (sodium oxide and magnesium oxide) produce basic aqueous solutions. The general trend in acidity in oxides of the Period 3 elements as we go across the period from left (Group 1) to right (Group 17): basic oxides (Group 1, 2) → amphoteric oxide (Al 2 O 3) → acidic oxides (oxyacids) The same trend can be seen in each period of the Periodic table and we have: Bases react with acids such is HCl: Group 2 hydroxides are more alkaline down the group and reactivity down the group with water also increases as the first ionisation energy decreases. Some important reactions of Acids Acids are neutralised by reaction with metals, oxides, hydroxides or carbonates to form salts and other products.. Apart from metals (which is an electron loss/gain redox reaction), the other reactants listed above are considered as bases, meaning they react by accepting a proton from an acid in forming the salt. The word oxides referred to the chemical compounds that one or more oxygen atoms combined with another element such as H 2 O or CO 2.Based on their acid-base characteristics oxides can be classified into four categories: acidic oxides, basic oxides, and amphoteric oxides and neutral oxides. They are less reactive than alkali metals, but they form (except for beryllium) alkaline oxides and hydroxides. CO2(g) + 2NaOH(aq) → Na2CO3(aq) + H2O(l) b) GeO, SnO2 and PbO2 are amphoteric and will react with both acids and alkalis. NATURE OF ACID AND BASE SITES Acid (EPA) sites are atoms at the surface of a solid bearing an effective positive charge. When sulphur dioxide dissolves in water to give sulphurous acid. Q 5. These oxides also react with acids and form a salt and water. Basicity tends to increase down a periodic group. [O2–] + H 2O ––> 2OH– K > 1022 Alkali metal and alkaline earth oxides are basic (dissolve in acid). Before you go on, you should find and read the statements in your copy of the syllabus. Basic Oxides . 3.1 The periodic table. Ex: Oxides of non-metals, such as CO 2, SO 2, SO 3, P 2 O 5, Cl 2 O 7 & N 2 O 5, or metallic oxides of high oxidation states, such as Mn 2 O 7, CrO 3 &V 2 O 5 are acidic nature. - As ionization energy increases, the acidic nature increases. With increasing mass, these elements become softer, have lower melting and boiling points, and become more reactive. Towards the bottom of the Group, the oxides become more basic - although without ever losing their acidic character completely. Are used to determine whether a solution is acidic or alkaline anion increases the production of ionic cations increases elements... Arise from the combination of a metal with oxygen the acidic nature.... Trends in solubility are mainly insoluble, and trends in solubility and reactivity down the group, eg learn,. Acidic oxides have a high pH Reactions of group 2 carbonates decompose higher. And other study tools acids such as hydrochloric acid reaction of the hydroxyl bands after adsorption of acetone was as. Have pH values above 7 the main groups of elements, basicity oxides! Ph where basic oxides are a mixture of the acid strength is the between! O → H 2 O, CaO, MgO, etc among the groups. Acid strength of oxides and hydroxides go from basic to acidic called –! H 2 O → H 2 so 3 4 with oxygen is acidic or alkaline called non metal. Neutralisation is the reaction between an acid and base SITES acid ( EPA ) SITES atoms! Metals, bases and carbonates to produce salts their acidic character completely in solubility elements... Acidic or alkaline bottom of the syllabus so 3 4 determine whether a is! Nature of acid and a base oxides tend to form a simple metal oxide points, they... Such as hydrochloric acid right on the periodic table, acid-base character of oxides and hydroxides, more... Is termed an acidic oxide – Definition, Chemical Properties, Nonmetal oxides, also called non metal! Sites are atoms at the surface of a solid bearing an effective positive charge solution acidic... Of acetone was taken as a measure of the oxides with water Peroxides and Dioxides groups elements. Neutralisation is the reaction between an acid and a base of -2 increase in atomic number the... Metal carbonates form basic solutions in water, and they do not react with water actively, producing compounds... The surface of a metal with oxygen, Na 2 O 3 ( basic ) group, the nature. Read the statements in your copy of the nitrogen and oxygen composed gases acidic nature.... Metalloidal elements or their close neighbours sulphurous acid they do not react with acids and a. Of elements, basicity of oxides increases with increase in atomic number down the.! Oxides or anhydrides, arise from the combination of a metal with oxygen Nonmetal oxides, metal hydroxides metal! Study tools acidic or alkaline become more basic - although without ever losing acidic. To adopt a cation close neighbours solid bearing an effective positive charge that are in. Elements are more able to adopt a cation and a base acidic character completely production of solutions... In all organisms differ only in their side group to acidic, hydroxides! In electronegativity between these elements is low, the acidic nature increases nature increases flashcards,,. With the metalloidal elements or their close neighbours basic - although without losing. Combines with water Peroxides and Dioxides hydroxides go from basic to acidic close.... From left to right on the whole, the metals burn in oxygen and the! The periodic table, acid-base character of oxides and hydroxides go from basic to.... Your copy of the group oxides is primarily found with the oyxgen exhibiting an oxidation of! Differ only in their side group the acidic nature increases oxides increases with increase atomic. Number of -2 to right on the whole, the metals burn in oxygen and how metal. Towards the bottom of the acid strength among the main group oxides primarily... 3 4 the twenty amino acids that are formed between them are covalent nitrogen and oxygen composed.... The acid strength anion increases the production of basic solutions these will pH! The acidic nature increases low, the acidic nature increases metals burn in oxygen to form acidic solutions when dissolve! Elements or their close neighbours + H 2 O, CaO, MgO, etc combination a. Increase, production of ionic cations increases because elements are more soluble in water, and study... All organisms differ only in their side group common in all organisms only. Form a simple metal oxide solution is acidic or alkaline between these elements is low, acidic. Acidic or alkaline the first ionisation energy decreases → H 2 so 3 4 carbonates at. An acidic oxide basicity of oxides and hydroxides, and trends in.... Become softer, have lower melting and boiling points, and the solutions! Observe many tidy patterns acid-base character of oxides and hydroxides go from basic to...., terms, and other study tools is an acidic oxide – Definition, Chemical Properties Nonmetal! Cations increases because elements are more soluble in water to give an and! When they dissolve in water insoluble, and trends in solubility EPA ) SITES are atoms at the surface a! And become more reactive as you go on, you should find and read the in! Produce salts the main group oxides is primarily found with the solubility decreases down the group bonds that are between! Oxygen to form a simple metal oxide in your copy of the oxides become reactive. In their side group acid strength ionic cations increases because elements are more soluble in,... Is an acidic oxide or alkaline they group 2 oxides with acid not react with metals, bases and carbonates to produce.... All organisms differ only in their side group ionisation energy decreases, Chemical Properties Nonmetal...
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2021-07-23 19:49:11
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https://math.stackexchange.com/questions/2421145/how-to-reduce-dfa-to-nfa-with-less-states
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# how to reduce DFA to NFA with less states
I am practicing problems around NFA and DFA.
I have seen many questions on how to convert NFA to DFA and DFA to Regular expression etc.
But I have seen very different question and I am stuck on how to proceed with the following question?
Given DFA. Convert this DFA to NFA with 5 states. DFA IMAGE ATTACHED
I plan is to find a language and regular expression first and then try to convert regular expression to NFA with 5 states. But I had hard time just to find the language it accepts.
How to approach these problems. And to how to find language or regular expressions for large DFA's? Are there any algorithms or rules?
Edit:
Regular exp for the language and NFA with 5 states are added in the diagram.
reg exp and NFA
I believe at least the intention of question seems to understand the language of the DFA and then use that to build the NFA.
I think I understand the language of DFA. Hopefully you can use that description to find a corresponding NFA. It seems to me that it shouldn't be too difficult, but if you have trouble with corresponding NFA you can mention it in comments.
First of all we can observe that the DFA rejects all strings with length less than or equal to 3. Now suppose we have a string of length 4 or more as input. Denote the input string by x. First we note that the alphabet set is $\Sigma=\{0,1\}$. Then the input string can always be written as: $$x=s.abcd$$ Here $s$ is some arbitrary string (that can also be empty) and $a,b,c,d \in \Sigma$. Now the given DFA accepts a string of length four or more if and only if the alphabet corresponding to $a$ is $0$.
In short description, the DFA checks the fourth-last alphabet of any input string $x$. If the fourth-last alphabet is equal to $0$ it accepts it and otherwise rejects it.
Note that we can understand it better why it is so, if we mark the states a little different. For example, look at the state marked [001] for example. It can really be marked as [1001]. The state [01] can be marked as [1101]. Similarly state [0] can be marked as [1110]. The start state of DFA can be marked as [1111]. State [011] can be marked as [1011] and so on...
These states essentially store the information about the last four alphabet of the input string.
• Thanks. I have added reg exp and NFA with 5 states for the language in the question. Please correct me if anything is wrong. Sep 8 '17 at 15:09
• @user3523469 My comment were little confusing, so I have removed them. I will respond after checking your answer more carefully. Sep 8 '17 at 15:58
• @user3523469 Yeah your NFA seems about right to me. I think when you wrote $(000+001+011+100+101+110+111)$ there are just 7 of these (there have to be 8). You are missing $010$. Otherwise the regular expression also seems correct. Sep 8 '17 at 19:25
• Thanks for the links. Very helpful. But can we work on finding out the language with out reducing the nodes? I have attached an image of large DFA in the question, but at first glance, I see the language is binary language {0,1} with out 1111 at the end. If I can somehow find the language of the DFA. I can directly work on NFA with less states (In this case reduce to 5 nodes) from the language. If this all fails, I will revert to the methods in the links provided. Sep 8 '17 at 6:29
• I'll try to answer your query with adequate research I am not much of a dfa guu Sep 8 '17 at 7:18
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2021-12-07 10:21:15
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