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https://socratic.org/questions/how-do-solutions-differ-from-suspensions | # How do solutions differ from suspensions?
##### 1 Answer
Aug 3, 2018
Well solutions are $\text{homogeneous}$, i.e. all its components are in the SAME phase...
#### Explanation:
The air we breathe is an homogeneous solution of dioxygen, dinitrogen, and a few other gases. A soft-drink is an homogeneous solution of water, sugar, and (maybe) carbon dioxide.
On the other hand, a suspension is an inhomogeneous mixture, i.e. $\text{an heterogeneous mixture}$, in which the components are NOT in the same phase. The solute particles are not dissolved, and the particle size is in general small. A aerosol stream from a can in air is an example of a suspension, and so is sand in water. Over time, depending on the size of the particles, the particles might settle out. | 2020-01-17 21:22:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7706209421157837, "perplexity": 792.0673218358093}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "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-2020-05/segments/1579250591234.15/warc/CC-MAIN-20200117205732-20200117233732-00009.warc.gz"} |
https://flex.phys.tohoku.ac.jp/book10/problems/format.html | 1. Check that the question is not solved yet.
3. Run "latex Q.tex" and check that you can read text and figures.
4. Rename Q-sample tex to Q12-3.tex if question is 12-3..
5. Answer the questions in Q12-3.tex, Q12-3-1.eps, Q12-3-2.eps etc.
6. Run "latex Q.tex" and make Q.pdf file.
7. Rename to Q12-3.pdf and Send to rsaito@flex.phys.tohoku.ac.jp.
8. Saito will send you an e-mail if he recieves the answers.
9. Saito will send you which part should be corrected.
10. Send the fixed pdf file.
11. If the file is accepted, you are asked to send Q12-3.tex and Q12-3-1.eps files by e-mail.
12. Saito will put on the web pages with your name. Saito will send you that the answer is now on the Web pages.
Local Rules in the format
1. All the labels should be \label{eq:77-777-1} or \label{fig:Q77-777-1} etc.
2. In order to avoid the multiply-defined label, the name of label should have the question number such as Q2-3-eq-1 etc.
3. We cite as Fig.\,\ref{fig:Q77-777-1} or Eq.\,(\ref{eq:77-777-1}).
4. Use the \displaystyle for fraction etc.
5. Do not use a special latex command.
6. Figures should be made based on general rule for scientific paper.
7. Especially the labels of figure should not be small (twice sized font of the text.)
The tex files of questions
Here we show the tex files of questions. You can cut and paste the questions in the tex file of answers. We can add the eps files in the question in the final form.
Riichiro Saito | 2020-07-09 02:58:15 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9146740436553955, "perplexity": 3857.1250787721337}, "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-2020-29/segments/1593655897844.44/warc/CC-MAIN-20200709002952-20200709032952-00534.warc.gz"} |
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Statistical Significance of Clustered Orientation Data on the Sphere: An Empirical Derivation
E. Craig Jowett and Pierre-Yves F. Robin
The Journal of Geology
Vol. 96, No. 5 (Sep., 1988), pp. 591-599
Stable URL: http://www.jstor.org/stable/30053572
Page Count: 9
Preview not available
Abstract
To date there is no statistical theory which assesses the statistical significance of a cluster of data points on a contoured density diagram. In lieu of such a theory, we derive, using a Monte Carlo method, an empirical statistic, P, that can easily yet rigorously test the significance of a cluster of points for a given N at a given level of confidence when counted using a Gaussian weighting function. Multiple random samples of N data points (18 $\leq$ N $\leq$ 800) are drawn from an infinite uniform parent population and counted on the hemisphere to obtain the density surfaces. The empirical point-density statistics $P_{95}$ and $T_{95}$ are the highest and lowest 95th percentiles of the 1000 "peak" and "trough" values calculated for each N. A peak density value (a maximum on a contoured plot) greater than $P_{95}$ for a given N has less than a 5% likelihood of being drawn randomly from a uniform distribution and is therefore a statistically significant cluster at the 95% confidence level. Similarly, a point-density trough less than the derived statistic T for troughs indicates statistical significance. Tables and line graphs of P and T are given as functions of N for seven confidence levels. The statistic $P_{95}$ requires higher point counts than has been previously thought necessary for significance and, moreover, varies substantially with sample size.
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• 599 | 2016-12-09 10:04:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5089185833930969, "perplexity": 1746.502260203772}, "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-2016-50/segments/1480698542693.41/warc/CC-MAIN-20161202170902-00160-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://www.physicsandastronomy.pitt.edu/events/phd-defense-ava-myers | PhD Defense: Ava Myers
April 29, 2022 - 2:00pm
Probing the dark sector with the Higgs boson and missing energy at the LHC
Abstract: The Standard Model (SM) of particle physics describes a vast range of particle physics experiments across many orders of magnitude. Despite the enormous experimental success of the SM, it does not explain dark matter (DM). I focus on two open questions in particular: (a) What is the nature of DM? (b) How can we use the Higgs boson as a tool to discover DM or other physics beyond the SM?
This thesis presents two searches emphasizing missing energy in the vector boson fusion channel: one for invisible decays of the Higgs boson and one for semi-visible decays. These analyses use 139 fb$^{-1}$ of proton-proton collision data at center-of-mass energy $\sqrt{s} = 13$ TeV with the ATLAS detector at the Large Hadron Collider. Assuming a SM Higgs, an upper limit of 10\%(14\%) expected (observed) at 95\% C.L. is derived for the branching fraction of Higgs to invisible. Results are interpreted in the context of models in which the Higgs acts as a portal to the dark sector, translating to limits on the scattering cross-section of weakly interacting massive particles and nucleons. Future results of the semi-visible Higgs decay will be interpreted in the context of supersymmetry and Higgs portal models. | 2023-01-29 22:01:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5951430201530457, "perplexity": 947.5985313650866}, "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-2023-06/segments/1674764499768.15/warc/CC-MAIN-20230129211612-20230130001612-00570.warc.gz"} |
https://aas.org/archives/BAAS/v25n4/aas183/abs/S2504.html | Global Oscillation Amplitudes Excited by the Jupiter-Comet Collision
Session 25 -- Solar System and Heliosphere
Oral presentation, Wednesday, January 12, 10:15-11:45, Salon VI Room (Crystal Gateway)
## [25.04] Global Oscillation Amplitudes Excited by the Jupiter-Comet Collision
H. M. Van Horn$^1$ and U. Lee$^2$ (1. NSF and 2. Univ. Rochester)
The energy released during the collision of fragments of comet Shoemaker-Levy 9 with Jupiter in July 1994 may excite a spectrum of global oscillation modes. We estimate the maximum amplitudes to which the $p$-modes, discontinuity modes, inertial modes, and $r$-modes can be excited by assuming that the full kinetic energy of the fragment, which we take to be $10^{30}$ ergs, is converted into the energy of each individual mode. We have used two realistic Jovian models as the basis for our estimates: one with and one without the predicted \lq\lq plasma phase transition\rq\rq\ (PPT) of hydrogen. A density discontinuity in the planet's hydrogen-helium envelope is associated with the PPT. We find that high-frequency $p$-modes, with periods $\ltsim 15$ minutes, may be excited to sufficiently large amplitudes to be observable as Doppler shifts (velocity amplitudes $\gtsim$ several m s$^{-1}$) or temperature variations ($\delta T\gtsim 0.01$K) at the planetary surface. Inertial modes may also be observable. If the PPT exists in Jupiter, inertial modes with periods $\sim 8$ hours or $\sim 2.2$ days trapped in the surface region of the planet, above the PPT, may be detectable as temperature fluctuations of order $\delta T \sim 0.01$K. If the PPT does not exist, inertial modes with periods longer than $\sim 18$ hours may produce temperature fluctuations of order $\delta T \sim 0.01$K. Discontinuty modes associated with the PPT and $r$-modes unfortunately may not reach observable amplitudes. | 2016-08-30 23:44:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5525588393211365, "perplexity": 2840.7675833863236}, "config": {"markdown_headings": true, "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-2016-36/segments/1471983026851.98/warc/CC-MAIN-20160823201026-00052-ip-10-153-172-175.ec2.internal.warc.gz"} |
http://calculator.tutorvista.com/speed-distance-time-calculator.html | Top
Speed Distance Time Calculator
Top
We come across many bodies in motion in our daily life like bird flying, bus moving, fishes swimming, boy running, Helicopter traveling etc. Let us consider a simple example of a bird flying. This bird covers some distance after some time. By seeing the bird we can only make out whether the bird is moving fast or slow. But we cannot make out how fast or how slow the bird is moving? To Know that we need to determine the parameter called Speed.Speed is defined as the ratio of Distance Covered to the time taken. It is expressed in m/s. To calculate the Speed we use the formula:Speed = $\frac{Distance\ covered}{Time\ taken}$Thus Speed, distance and time are the parameters dependent on each other. The Speed Distance Time Calculator helps us to get any of these unknown quantities if any of the two parameters are given.
## Steps for Speed Distance Time Calculator
Step 1 :
First analyze the problems and get to know the given parameters.
Step 2 :
To know the Unknown parameter X. Use the below parameters.
If time taken and distance Covered are given, we use the formula
Speed = $\frac{Distance\ Covered}{Time\ taken}$
If time taken and speed is given, we use the formula
Distance Covered = Speed $\times$ time.
If Distance Covered and Speed are given, we use the formula
Time taken = $\frac{Distance\ Covered}{Speed}$
Using these steps, we get the desired Parameters.
## Problems on Speed Distance Time Calculator
1. ### What is the speed of the car if the car traveled in a distance of 300 meter at the time of 60 seconds?
Step 1 :
First analyze the problems and get to know the given parameters.
Given: Distance Covered = 300 meter,
Time taken = 60 seconds.
Step 2 :
To know the Unknown parameter X. Use the below parameters.
If Time taken and distance Covered are given, we use the formula
Speed = $\frac{Distance\ Covered}{Time\ taken}$
If time taken and speed is given, we use the formula
Distance Covered = Speed $\times$ time.
If Distance Covered and Speed are given, we use the formula
Time taken = $\frac{Distance\ Covered}{Speed}$
Using this step, we get the desired Parameter.
We know the formula to find speed = $\frac{Distance\ Covered}{Time\ taken}$
$\therefore$ speed = $\frac{300}{60}$
5 m/s
2. ### The Average speed of the train is 4m/s and it reached the distance of 120 meter, find the time taken by the train to travel this distance.
Step 1 :
Given,
Speed = 4m/s
Distance = 120m
Step 2 :
We know the formula: Time = $\frac{Distance\ Covered}{Speed}$
= $\frac{120 m}{4 m/s}$.
30 s
3. ### Find the distance covered if the speed is 7m/s and the time is 120s.
Step 1 :
Given : Speed = 7 m/s,
Distance Covered = ?
Time taken = 120s
Step 2 :
Distance Covered = Speed $\times$ time Taken.
= 7m/s $\times$ 120s. | 2014-09-23 04:16:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8105971813201904, "perplexity": 1091.4896910965547}, "config": {"markdown_headings": true, "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-2014-41/segments/1410657137948.80/warc/CC-MAIN-20140914011217-00322-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://gateoverflow.in/128685/isro2017-43?show=128937 | # ISRO2017-43
3.1k views
Which of the following UML 2.0 diagrams capture behavioral aspects of a system?
1. Use case diagram, Object diagram, Activity diagram and state machine diagram
2. Use case diagram, Activity diagram and state machine diagram
3. Object diagram, Communication Diagram, Timing diagram and Interaction diagram
4. Object diagram, Composite structure diagram, package diagram and Deployment diagram
edited
UML 2.0 diagrams capture behavioral aspects of a system :
1. Activity diagram
2. Communication Diagram
3. Interaction diagram
4. state machine diagram
5. Timing diagram
6. use case diagram
Structural diagrams
1. class diagram
2. component diagram
3. Object diagram
4. Composite structure diagram
5. package diagram
6. Deployment diagram
Reffer : Here
selected by
1 vote
Option B
## Related questions
1
2.9k views
Which of the following is associated with objects? State Behavior Identity All of the above
If a class $C$ is derived from class $B$, which is derived form class $A$, all through public inheritance, then a class $C$ member function can access only protected and public data of $C$ and $B$ Only protected and public data of $C$ all data of $C$ and private data of $A$ and $B$ public and protected data of $A$ and $B$ and all data of $C$ | 2020-09-29 14:49:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23359572887420654, "perplexity": 9743.637367624302}, "config": {"markdown_headings": true, "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-2020-40/segments/1600401643509.96/warc/CC-MAIN-20200929123413-20200929153413-00302.warc.gz"} |
http://bib-pubdb1.desy.de/collection/PhDThesis?ln=en | # Ph.D. Theses
2017-10-2011:16 [PUBDB-2017-11458] Report/Dissertation / PhD Thesis Thun, H.-J. Asymptotic behaviour at exceptional momenta [DESY-74-004] [S.l.] : Italian Physical Society, (1975) [10.1007/BF02900512] = Universität Hamburg, Diss., 1974 We develop a method for investigating the asymptotic behaviour of vertex functions at certain Minkowskian exceptional momenta. It is a direct generalization of earlier treatments of Euclidean exceptional momenta. [...] OpenAccess: PDF PDF (PDFA); 2017-10-1813:21 [PUBDB-2017-11443] Dissertation / PhD Thesis Ippen, E. P. All-Optical Electron Acceleration with Ultrafast THz Pulses 210 pp. (2017) = Massachusetts Institute of Technology, Diss., 2017 This thesis discusses a series of advances toward - and resulting in -the demonstration of the first ultrafast THz-driven electron gun, a technology with the potential to deliver unprecedented electron beam quality to scientists studying matter at the ultrafast and ultrasmall scale via electron diffraction or x-ray imaging. In Part 1, we discuss various advances in generation of high energy pulsed THz radiation, a spectral regime uniquely effective at accelerating electrons but historically lacking in effcient sources. [...] Restricted: PDF PDF (PDFA); 2017-10-1718:02 [PUBDB-2017-11438] Book/Report/Dissertation / PhD Thesis Weiglein, G. Interplay of Higgs Phenomenology and New Physics in Supersymmetric Theories [DESY-THESIS-2017-041] Hamburg : Verlag Deutsches Elektronen-Synchrotron, DESY-THESIS, 169 pp. (2017) [10.3204/PUBDB-2017-11438] = Universität Hamburg, Diss., 2017 OpenAccess: desy-thesis-17-041.title - PDF PDF (PDFA); thesis_patel - PDF PDF (PDFA); 2017-10-1313:31 [PUBDB-2017-11374] Book/Report/Dissertation / PhD Thesis Schlarb, H. Pilot Study of Synchronization on a Femtosecond Scale between the Electron Gun REGAE and a Laser-Plasma Accelerator [DESY-THESIS-2017-040] Hamburg : Verlag Deutsches Elektronen-Synchrotron, DESY-THESIS, 158 pp. (2017) [10.3204/PUBDB-2017-11374] = Universität Hamburg, Diss., 2016 Laser wakefield acceleration (LWFA) is a novel technique to accelerate charged particles. Acceleration is achieved by a high-power laser pulse transmitting a gas target where electrons and ions form a strong wakefield with gradients up to 100 GV/m. [...] OpenAccess: PhD_Thesis_Mikheil_Titberidze - PDF PDF (PDFA); desy-thesis-17-040.title - PDF PDF (PDFA); 2017-10-0914:16 [PUBDB-2017-11222] Book/Report/Dissertation / PhD Thesis Maier, A. High energy multi-cycle terahertz generation [DESY-THESIS-2017-039] Hamburg : Verlag Deutsches Elektronen-Synchrotron, DESY-THESIS, 198 pp. (2017) [10.3204/PUBDB-2017-11222] = Universität Hamburg, Diss., 2017 Development of compact electron accelerators and free-electron lasers requires novel acceleration schemes at shorter driving wavelengths. The Axsis project seeks to developterahertz based electron acceleration as well as the high energy terahertz sources required. [...] OpenAccess: desy-thesis-17-039.title - PDF PDF (PDFA); Frederike-Ahr-PhDThesis - PDF PDF (PDFA); 2017-08-2616:35 [PUBDB-2017-09888] Dissertation / PhD Thesis Stierle, A. Resonant Hard X-ray Ptychography for High-Sensitivity Imaging with Chemical Contrast 125 pp. (2017) [10.3204/PUBDB-2017-09888] = University of Hamburg, Diss., 2017 For the detailed investigation of biological, chemical or physical processes on the nano scale, high-resolution imaging techniques are essential. For this purpose, the coherentimaging technique – X-ray ptychography – has been established in recent years. [...] OpenAccess: PDF PDF (PDFA); 2017-08-2108:02 [PUBDB-2017-09563] Dissertation / PhD Thesis Herzog, G. Erforschung von Prozessen an nanostrukturierten Oberflächen mit Röntgenkleinwinkelstreuung unter streifendem Einfall 139 pp. (2015) = University of Hamburg, Diss., 2016 2017-08-1509:47 [PUBDB-2017-09253] Book/Report/Dissertation / PhD Thesis Louis, J. Aspects of Six-Dimensional Flux Compactifications [DESY-THESIS-2017-036] Hamburg : Verlag Deutsches Elektronen-Synchrotron, DESY-THESIS, 141 pp. (2017) [10.3204/PUBDB-2017-09253] = Universität Hamburg, Diss., 2017 In this thesis we investigate various aspects of ux compactications in six-dimensionalquantum eld theories. After introducing the internal geometries, i.e. [...] OpenAccess: PhD_Thesis_Markus_Dierigl_Pub - PDF PDF (PDFA); desy-thesis-17-036.title - PDF PDF (PDFA); 2017-08-1113:51 [PUBDB-2017-09190] Book/Report/Dissertation / PhD Thesis Wichmann, K. Search for contact interactions and finite quark radius using combined $e^{\pm}p$ data at HERA [DESY-THESIS-2017-035] Hamburg : Verlag Deutsches Elektronen-Synchrotron, DESY-THESIS, 163 pp. (2017) [10.3204/PUBDB-2017-09190] = Universität Hamburg, Diss., 2017 A combination is presented of all previously published deep inelastic neutral and charged current $e^{\pm}p$ scattering measurements at HERA for zero beam polarisation.The ZEUS and H1 collaborations have collected data at electron beam energy of $27.5$ GeV and proton beam energies of $920$, $820$, $575$ and $460$ GeV.The combined data correspond to an integrated luminosity of about $1$ fb$^{-1}$ and cover a kinematic range in the negative four-momentum-transfer squared from $Q^{2} = 0.045$ GeV$^{2}$ to $Q^{2} = 50000$ GeV$^{2}$ and in Bjorken $x$ from $x_{\rm Bj} = 6 \times 10^{-7}$ to $x_{\rm Bj} = 0.65$.The correlations of systematic uncertainties between different sets of data were taken into account, resulting in significantly improved precision.The combined $e^{\pm}p$ cross sections were used in a QCD analysis at next-to-leading order, providing a set of parton distribution functions, called ZCIPDF.The combined measurements were also used in an analysis beyond the Standard Model using a new approach, performing simultaneous fits on large sets of Monte Carlo replicas of parton distribution functions, PDFs, together with the parameters of "new physics" processes.A simplified approach to reduce the calculation time was developed and extensively tested.It allowed the calculation time to be reduced by about a factor of 50.The resulting $95\,\%$ C.L. upper limit on the effective quark radius is $0.43 \cdot 10^{-16}$ cm and the limits on the mass scales for different contact interaction scenarios extend up to $10$ TeV.The analyses have shown that taking into account the possible influence of processes beyond the Standard Model on the PDF parameters is necessary, since the limits that would be obtained using PDFs from QCD analysis within the Standard Model are too strong by about $10\,\%$.Studies of the surface quality of 28 Niobium superconducting radio frequency, SRF, cavities and development of a controllable cooling system for Niobium samples are also reported.The SRF cavities are the core of the accelerating technology for the future International Linear Collider, ILC; the reported studies are part of an ongoing research and development program.. OpenAccess: desy-thesis-17-035.title - PDF PDF (PDFA); Turkot_PhD_Thesis_Search_for_CI_at_HERA - PDF; 2017-08-1016:14 [PUBDB-2017-09144] Book/Dissertation / PhD Thesis Techert, S. Insights into Protein Dynamics by Time-resolved X-ray Scattering 150 pp. (2015) = Georg-August-Universität Göttingen, Diss., 2014 | 2017-10-22 19:00:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6333990693092346, "perplexity": 10539.654045054182}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187825436.78/warc/CC-MAIN-20171022184824-20171022204824-00224.warc.gz"} |
http://www.bio.net/bionet/mm/methods/1998-October/071329.html | # rule of thumb for SDS-PAGE separation of small proteins?
Pete pkursula at cc.oulu.fi
Wed Oct 28 09:02:37 EST 1998
```Sometimes this helps: Prepare the samples as usual, i.e. add Laemmli
buffer
or whatever you use, but leave out the SDS from the gel while preparing
it. Include SDS in the running buffer however. I have seen some appr.
10-kDa proteins that differ by 2 amino acids separate quite well under
these conditions. The gel % around 15-20...
A 10 % gel has a lower resolution limit around 30 kDa, bad idea I
think.
How about a native gel? That works for the same proteins mentioned above.
Just leave out all SDS and be sure that your native proteins move in the
correct direction :) (check the pI)
On Tue, 27 Oct 1998, Peter wrote:
> In article <3635C782.8F797225 at mindspring.com>, scorbitt
> <scorbitt at mindspring.com> wrote:
>
> > If you would like to increase your separation, I would reduce the percentage
> > of acrylamide/bis in your gels. Try a 10% or 12%.
> >
>
> > Ing-Nang Wang wrote:
> >
> > >
> > > I have to separate two proteins with 105 and 107 amino acids. We
> > > usually use a 16% Tricine SDS-PAGE. But I sometimes don't get a
> > > consistent separation. I wonder if there is a rule of thumb for a small
> > > protein separation? Would a 20% gel be better? Or maybe a 10% - 20%
> > > gradient gel? Ideally, the two bands should be at least 1 mm apart
> > > after staining.
|) |/
|etri |\ursula
Petri.Kursula at oulu.fi
http://cc.oulu.fi/~pkursula
-------------------------------------------------
"I am somehow less interested in the weight and
convolutions of Einstein's brain than in the near
certainty that people of equal talent have lived
and died in cotton fields and sweatshops."
-- Stephen Jay Gould
-------------------------------------------------
```
More information about the Methods mailing list | 2016-06-27 07:45:48 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8435398936271667, "perplexity": 13719.40072702871}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "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-2016-26/segments/1466783395679.18/warc/CC-MAIN-20160624154955-00038-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/write-lewis-symbols-following-atoms-ions-al-al3-concept-of-kossel-lewis-approach-to-chemical-bonding_10743 | # Write Lewis Symbols for the Following Atoms and Ions: Al and Al3+ - Chemistry
Write Lewis symbols for the following atoms and ions: Al and Al3+
#### Solution 1
Al and Al3+
The number of valence electrons in aluminium is 3.
The Lewis dot symbol of aluminium (Al) is .
The tripositive charge on a species infers that it has donated its three electrons. Hence, the Lewis dot symbol is
#### Solution 2
""_13Al = 2,8,3 ∴ Lewis symbol = , Al^(3+) "ions" = [Al]^(3+)
Is there an error in this question or solution?
#### APPEARS IN
NCERT Class 11 Chemistry Textbook
Chapter 4 Chemical Bonding and Molecular Structure
Q 3.2 | Page 129 | 2021-03-04 10:11:19 | {"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": 0, "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": 0.4862533211708069, "perplexity": 8922.24530468067}, "config": {"markdown_headings": true, "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-2021-10/segments/1614178368687.25/warc/CC-MAIN-20210304082345-20210304112345-00635.warc.gz"} |
https://scitools-iris.readthedocs.io/en/latest/generated/api/iris/coords.html | You are viewing the latest unreleased documentation v3.1.dev0. You may prefer a stable version.
# iris.coords¶
Definitions of coordinates and other dimensional metadata.
In this module:
class iris.coords.AncillaryVariable(data, standard_name=None, long_name=None, var_name=None, units=None, attributes=None)[source]
Constructs a single ancillary variable.
Args:
• data:
The values of the ancillary variable.
Kwargs:
• standard_name:
CF standard name of the ancillary variable.
• long_name:
Descriptive name of the ancillary variable.
• var_name:
The netCDF variable name for the ancillary variable.
• units
The Unit of the ancillary variable’s values. Can be a string, which will be converted to a Unit object.
• attributes
A dictionary containing other cf and user-defined attributes.
__binary_operator__(other, mode_constant)
Common code which is called by add, sub, mul and div
Mode constant is one of ADD, SUB, MUL, DIV, RDIV
Note
The unit is not changed when doing scalar operations on a metadata object. This means that a metadata object which represents “10 meters” when multiplied by a scalar i.e. “1000” would result in a metadata object of “10000 meters”. An alternative approach could be taken to multiply the unit by 1000 and the resultant metadata object would represent “10 kilometers”.
__getitem__(keys)
Returns a new dimensional metadata whose values are obtained by conventional array indexing.
Note
Indexing of a circular coordinate results in a non-circular coordinate if the overall shape of the coordinate changes after indexing.
convert_units(unit)
Change the units, converting the values of the metadata.
copy(values=None)
Returns a copy of this dimensional metadata object.
Kwargs:
• values
An array of values for the new dimensional metadata object. This may be a different shape to the original values array being copied.
core_data()[source]
The data array at the core of this ancillary variable, which may be a NumPy array or a dask array.
cube_dims(cube)[source]
Return the cube dimensions of this AncillaryVariable.
Equivalent to “cube.ancillary_variable_dims(self)”.
has_bounds()
Return a boolean indicating whether the current dimensional metadata object has a bounds array.
has_lazy_data()[source]
Return a boolean indicating whether the ancillary variable’s data array is a lazy dask array or not.
is_compatible(other, ignore=None)
Return whether the current dimensional metadata object is compatible with another.
lazy_data()[source]
Return a lazy array representing the ancillary variable’s data.
Accessing this method will never cause the data values to be loaded. Similarly, calling methods on, or indexing, the returned Array will not cause the ancillary variable to have loaded data.
If the data have already been loaded for the ancillary variable, the returned Array will be a new lazy array wrapper.
Returns
A lazy array, representing the ancillary variable data array.
name(default=None, token=False)
Returns a string name representing the identity of the metadata.
First it tries standard name, then it tries the long name, then the NetCDF variable name, before falling-back to a default value, which itself defaults to the string ‘unknown’.
Kwargs:
• default:
The fall-back string representing the default name. Defaults to the string ‘unknown’.
• token:
If True, ensures that the name returned satisfies the criteria for the characters required by a valid NetCDF name. If it is not possible to return a valid name, then a ValueError exception is raised. Defaults to False.
Returns
String.
rename(name)
If ‘name’ is a valid standard name it will assign it to standard_name, otherwise it will assign it to long_name.
xml_element(doc)
Create the xml.dom.minidom.Element that describes this _DimensionalMetadata.
Args:
• doc:
The parent xml.dom.minidom.Document.
Returns
The xml.dom.minidom.Element that will describe this _DimensionalMetadata, and the dictionary of attributes that require to be added to this element.
property attributes
property data
property dtype
The NumPy dtype of the current dimensional metadata object, as specified by its values.
property long_name
The CF Metadata long name for the object.
property metadata
property ndim
Return the number of dimensions of the current dimensional metadata object.
property shape
The fundamental shape of the metadata, expressed as a tuple.
property standard_name
The CF Metadata standard name for the object.
property units
The S.I. unit of the object.
property var_name
The NetCDF variable name for the object.
↑ top ↑
A CF auxiliary coordinate.
class iris.coords.AuxCoord(*args, **kwargs)[source]
Create a coordinate with mutable points and bounds.
Args:
• points:
The values (or value in the case of a scalar coordinate) for each cell of the coordinate.
Kwargs:
• standard_name:
CF standard name of the coordinate.
• long_name:
Descriptive name of the coordinate.
• var_name:
The netCDF variable name for the coordinate.
• units
The Unit of the coordinate’s values. Can be a string, which will be converted to a Unit object.
• bounds
An array of values describing the bounds of each cell. Given n bounds for each cell, the shape of the bounds array should be points.shape + (n,). For example, a 1D coordinate with 100 points and two bounds per cell would have a bounds array of shape (100, 2) Note if the data is a climatology, climatological should be set.
• attributes
A dictionary containing other CF and user-defined attributes.
• coord_system
A CoordSystem representing the coordinate system of the coordinate, e.g., a GeogCS for a longitude coordinate.
• climatological (bool):
When True: the coordinate is a NetCDF climatological time axis. When True: saving in NetCDF will give the coordinate variable a ‘climatology’ attribute and will create a boundary variable called ‘<coordinate-name>_climatology’ in place of a standard bounds attribute and bounds variable. Will set to True when a climatological time axis is loaded from NetCDF. Always False if no bounds exist.
__binary_operator__(other, mode_constant)
Common code which is called by add, sub, mul and div
Mode constant is one of ADD, SUB, MUL, DIV, RDIV
Note
The unit is not changed when doing scalar operations on a metadata object. This means that a metadata object which represents “10 meters” when multiplied by a scalar i.e. “1000” would result in a metadata object of “10000 meters”. An alternative approach could be taken to multiply the unit by 1000 and the resultant metadata object would represent “10 kilometers”.
__getitem__(keys)
Returns a new dimensional metadata whose values are obtained by conventional array indexing.
Note
Indexing of a circular coordinate results in a non-circular coordinate if the overall shape of the coordinate changes after indexing.
cell(index)
Return the single Cell instance which results from slicing the points/bounds with the given index.
cells()
Returns an iterable of Cell instances for this Coord.
For example:
for cell in self.cells():
...
collapsed(dims_to_collapse=None)
Returns a copy of this coordinate, which has been collapsed along the specified dimensions.
Replaces the points & bounds with a simple bounded region.
contiguous_bounds()
Returns the N+1 bound values for a contiguous bounded 1D coordinate of length N, or the (N+1, M+1) bound values for a contiguous bounded 2D coordinate of shape (N, M).
Only 1D or 2D coordinates are supported.
Note
If the coordinate has bounds, this method assumes they are contiguous.
If the coordinate is 1D and does not have bounds, this method will return bounds positioned halfway between the coordinate’s points.
If the coordinate is 2D and does not have bounds, an error will be raised.
convert_units(unit)
Change the coordinate’s units, converting the values in its points and bounds arrays.
For example, if a coordinate’s units attribute is set to radians then:
coord.convert_units('degrees')
will change the coordinate’s units attribute to degrees and multiply each value in points and bounds by 180.0/$$\pi$$.
copy(points=None, bounds=None)
Returns a copy of this coordinate.
Kwargs:
• points: A points array for the new coordinate.
This may be a different shape to the points of the coordinate being copied.
• bounds: A bounds array for the new coordinate.
Given n bounds for each cell, the shape of the bounds array should be points.shape + (n,). For example, a 1d coordinate with 100 points and two bounds per cell would have a bounds array of shape (100, 2).
Note
If the points argument is specified and bounds are not, the resulting coordinate will have no bounds.
core_bounds()
The points array at the core of this coord, which may be a NumPy array or a dask array.
core_points()
The points array at the core of this coord, which may be a NumPy array or a dask array.
cube_dims(cube)
Return the cube dimensions of this Coord.
Equivalent to “cube.coord_dims(self)”.
classmethod from_coord(coord)
Create a new Coord of this type, from the given coordinate.
guess_bounds(bound_position=0.5)
Add contiguous bounds to a coordinate, calculated from its points.
Puts a cell boundary at the specified fraction between each point and the next, plus extrapolated lowermost and uppermost bound points, so that each point lies within a cell.
With regularly spaced points, the resulting bounds will also be regular, and all points lie at the same position within their cell. With irregular points, the first and last cells are given the same widths as the ones next to them.
Kwargs:
• bound_position:
The desired position of the bounds relative to the position of the points.
Note
An error is raised if the coordinate already has bounds, is not one-dimensional, or is not monotonic.
Note
Unevenly spaced values, such from a wrapped longitude range, can produce unexpected results : In such cases you should assign suitable values directly to the bounds property, instead.
has_bounds()
Return a boolean indicating whether the coord has a bounds array.
has_lazy_bounds()
Return a boolean indicating whether the coord’s bounds array is a lazy dask array or not.
has_lazy_points()
Return a boolean indicating whether the coord’s points array is a lazy dask array or not.
intersect(other, return_indices=False)
Returns a new coordinate from the intersection of two coordinates.
Both coordinates must be compatible as defined by is_compatible().
Kwargs:
• return_indices:
If True, changes the return behaviour to return the intersection indices for the “self” coordinate.
is_compatible(other, ignore=None)
Return whether the coordinate is compatible with another.
Compatibility is determined by comparing iris.coords.Coord.name(), iris.coords.Coord.units, iris.coords.Coord.coord_system and iris.coords.Coord.attributes that are present in both objects.
Args:
• other:
An instance of iris.coords.Coord, iris.common.CoordMetadata or iris.common.DimCoordMetadata.
• ignore:
A single attribute key or iterable of attribute keys to ignore when comparing the coordinates. Default is None. To ignore all attributes, set this to other.attributes.
Returns
Boolean.
is_contiguous(rtol=1e-05, atol=1e-08)
Return True if, and only if, this Coord is bounded with contiguous bounds to within the specified relative and absolute tolerances.
1D coords are contiguous if the upper bound of a cell aligns, within a tolerance, to the lower bound of the next cell along.
2D coords, with 4 bounds, are contiguous if the lower right corner of each cell aligns with the lower left corner of the cell to the right of it, and the upper left corner of each cell aligns with the lower left corner of the cell above it.
Args:
• rtol:
The relative tolerance parameter (default is 1e-05).
• atol:
The absolute tolerance parameter (default is 1e-08).
Returns
Boolean.
is_monotonic()
Return True if, and only if, this Coord is monotonic.
lazy_bounds()
Return a lazy array representing the coord bounds.
Accessing this method will never cause the bounds values to be loaded. Similarly, calling methods on, or indexing, the returned Array will not cause the coord to have loaded bounds.
If the data have already been loaded for the coord, the returned Array will be a new lazy array wrapper.
Returns
A lazy array representing the coord bounds array or None if the coord does not have bounds.
lazy_points()
Return a lazy array representing the coord points.
Accessing this method will never cause the points values to be loaded. Similarly, calling methods on, or indexing, the returned Array will not cause the coord to have loaded points.
If the data have already been loaded for the coord, the returned Array will be a new lazy array wrapper.
Returns
A lazy array, representing the coord points array.
name(default=None, token=False)
Returns a string name representing the identity of the metadata.
First it tries standard name, then it tries the long name, then the NetCDF variable name, before falling-back to a default value, which itself defaults to the string ‘unknown’.
Kwargs:
• default:
The fall-back string representing the default name. Defaults to the string ‘unknown’.
• token:
If True, ensures that the name returned satisfies the criteria for the characters required by a valid NetCDF name. If it is not possible to return a valid name, then a ValueError exception is raised. Defaults to False.
Returns
String.
nearest_neighbour_index(point)
Returns the index of the cell nearest to the given point.
Only works for one-dimensional coordinates.
For example:
>>> cube = iris.load_cube(iris.sample_data_path('ostia_monthly.nc'))
>>> cube.coord('latitude').nearest_neighbour_index(0)
9
>>> cube.coord('longitude').nearest_neighbour_index(10)
12
Note
If the coordinate contains bounds, these will be used to determine the nearest neighbour instead of the point values.
Note
For circular coordinates, the ‘nearest’ point can wrap around to the other end of the values.
rename(name)
If ‘name’ is a valid standard name it will assign it to standard_name, otherwise it will assign it to long_name.
xml_element(doc)
Create the xml.dom.minidom.Element that describes this Coord.
Args:
• doc:
The parent xml.dom.minidom.Document.
Returns
The xml.dom.minidom.Element that will describe this DimCoord, and the dictionary of attributes that require to be added to this element.
property attributes
property bounds
The coordinate bounds values, as a NumPy array, or None if no bound values are defined.
Note
The shape of the bound array should be: points.shape + (n_bounds, ).
property bounds_dtype
The NumPy dtype of the coord’s bounds. Will be None if the coord does not have bounds.
property climatological
A boolean that controls whether the coordinate is a climatological time axis, in which case the bounds represent a climatological period rather than a normal period.
Always reads as False if there are no bounds. On set, the input value is cast to a boolean, exceptions raised if units are not time units or if there are no bounds.
property coord_system
The coordinate-system of the coordinate.
property dtype
The NumPy dtype of the current dimensional metadata object, as specified by its values.
property long_name
The CF Metadata long name for the object.
property metadata
property nbounds
Return the number of bounds that this coordinate has (0 for no bounds).
property ndim
Return the number of dimensions of the current dimensional metadata object.
property points
The coordinate points values as a NumPy array.
property shape
The fundamental shape of the metadata, expressed as a tuple.
property standard_name
The CF Metadata standard name for the object.
property units
The S.I. unit of the object.
property var_name
The NetCDF variable name for the object.
↑ top ↑
An immutable representation of a single cell of a coordinate, including the sample point and/or boundary position.
Notes on cell comparison:
Cells are compared in two ways, depending on whether they are compared to another Cell, or to a number/string.
Cell-Cell comparison is defined to produce a strict ordering. If two cells are not exactly equal (i.e. including whether they both define bounds or not) then they will have a consistent relative order.
Cell-number and Cell-string comparison is defined to support Constraint matching. The number/string will equal the Cell if, and only if, it is within the Cell (including on the boundary). The relative comparisons (lt, le, ..) are defined to be consistent with this interpretation. So for a given value n and Cell cell, only one of the following can be true:
n < cell
n == cell
n > cell
Similarly, n <= cell implies either n < cell or n == cell. And n >= cell implies either n > cell or n == cell.
class iris.coords.Cell(point=None, bound=None)[source]
Construct a Cell from point or point-and-bound information.
__common_cmp__(other, operator_method)[source]
Common method called by the rich comparison operators. The method of checking equality depends on the type of the object to be compared.
Cell vs Cell comparison is used to define a strict order. Non-Cell vs Cell comparison is used to define Constraint matching.
__eq__(other)[source]
Compares Cell equality depending on the type of the object to be compared.
static __new__(cls, point=None, bound=None)[source]
Construct a Cell from point or point-and-bound information.
contains_point(point)[source]
For a bounded cell, returns whether the given point lies within the bounds.
Note
The test carried out is equivalent to min(bound) <= point <= max(bound).
count(value, /)
Return number of occurrences of value.
index(value, start=0, stop=9223372036854775807, /)
Return first index of value.
Raises ValueError if the value is not present.
bound
Alias for field number 1
point
Alias for field number 0
↑ top ↑
A CF Cell Measure, providing area or volume properties of a cell where these cannot be inferred from the Coordinates and Coordinate Reference System.
class iris.coords.CellMeasure(data, standard_name=None, long_name=None, var_name=None, units=None, attributes=None, measure=None)[source]
Constructs a single cell measure.
Args:
• data:
The values of the measure for each cell. Either a ‘real’ array (numpy.ndarray) or a ‘lazy’ array (dask.array.Array).
Kwargs:
• standard_name:
CF standard name of the coordinate.
• long_name:
Descriptive name of the coordinate.
• var_name:
The netCDF variable name for the coordinate.
• units
The Unit of the coordinate’s values. Can be a string, which will be converted to a Unit object.
• attributes
A dictionary containing other CF and user-defined attributes.
• measure
A string describing the type of measure. Supported values are ‘area’ and ‘volume’. The default is ‘area’.
__binary_operator__(other, mode_constant)
Common code which is called by add, sub, mul and div
Mode constant is one of ADD, SUB, MUL, DIV, RDIV
Note
The unit is not changed when doing scalar operations on a metadata object. This means that a metadata object which represents “10 meters” when multiplied by a scalar i.e. “1000” would result in a metadata object of “10000 meters”. An alternative approach could be taken to multiply the unit by 1000 and the resultant metadata object would represent “10 kilometers”.
__getitem__(keys)
Returns a new dimensional metadata whose values are obtained by conventional array indexing.
Note
Indexing of a circular coordinate results in a non-circular coordinate if the overall shape of the coordinate changes after indexing.
convert_units(unit)
Change the units, converting the values of the metadata.
copy(values=None)
Returns a copy of this dimensional metadata object.
Kwargs:
• values
An array of values for the new dimensional metadata object. This may be a different shape to the original values array being copied.
core_data()
The data array at the core of this ancillary variable, which may be a NumPy array or a dask array.
cube_dims(cube)[source]
Return the cube dimensions of this CellMeasure.
Equivalent to “cube.cell_measure_dims(self)”.
has_bounds()
Return a boolean indicating whether the current dimensional metadata object has a bounds array.
has_lazy_data()
Return a boolean indicating whether the ancillary variable’s data array is a lazy dask array or not.
is_compatible(other, ignore=None)
Return whether the current dimensional metadata object is compatible with another.
lazy_data()
Return a lazy array representing the ancillary variable’s data.
Accessing this method will never cause the data values to be loaded. Similarly, calling methods on, or indexing, the returned Array will not cause the ancillary variable to have loaded data.
If the data have already been loaded for the ancillary variable, the returned Array will be a new lazy array wrapper.
Returns
A lazy array, representing the ancillary variable data array.
name(default=None, token=False)
Returns a string name representing the identity of the metadata.
First it tries standard name, then it tries the long name, then the NetCDF variable name, before falling-back to a default value, which itself defaults to the string ‘unknown’.
Kwargs:
• default:
The fall-back string representing the default name. Defaults to the string ‘unknown’.
• token:
If True, ensures that the name returned satisfies the criteria for the characters required by a valid NetCDF name. If it is not possible to return a valid name, then a ValueError exception is raised. Defaults to False.
Returns
String.
rename(name)
If ‘name’ is a valid standard name it will assign it to standard_name, otherwise it will assign it to long_name.
xml_element(doc)[source]
Create the xml.dom.minidom.Element that describes this CellMeasure.
Args:
• doc:
The parent xml.dom.minidom.Document.
Returns
The xml.dom.minidom.Element that describes this CellMeasure.
property attributes
property data
property dtype
The NumPy dtype of the current dimensional metadata object, as specified by its values.
property long_name
The CF Metadata long name for the object.
property measure
String naming the measure type.
property metadata
property ndim
Return the number of dimensions of the current dimensional metadata object.
property shape
The fundamental shape of the metadata, expressed as a tuple.
property standard_name
The CF Metadata standard name for the object.
property units
The S.I. unit of the object.
property var_name
The NetCDF variable name for the object.
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Represents a sub-cell pre-processing operation.
class iris.coords.CellMethod(method, coords=None, intervals=None, comments=None)[source]
Args:
• method:
The name of the operation.
Kwargs:
• coords:
A single instance or sequence of Coord instances or coordinate names.
• intervals:
A single string, or a sequence strings, describing the intervals within the cell method.
__str__()[source]
Return a custom string representation of CellMethod
xml_element(doc)[source]
Create the xml.dom.minidom.Element that describes this CellMethod.
Args:
• doc:
The parent xml.dom.minidom.Document.
Returns
The xml.dom.minidom.Element that describes this CellMethod.
comments = None
coord_names = None
The tuple of coordinate names over which the operation was applied.
intervals = None
A description of the original intervals over which the operation was applied.
method = None
The name of the operation that was applied. e.g. “mean”, “max”, etc.
↑ top ↑
Abstract base class for coordinates.
class iris.coords.Coord(points, standard_name=None, long_name=None, var_name=None, units=None, bounds=None, attributes=None, coord_system=None, climatological=False)[source]
Coordinate abstract base class. As of v3.0.0 you cannot create an instance of Coord.
Args:
• points:
The values (or value in the case of a scalar coordinate) for each cell of the coordinate.
Kwargs:
• standard_name:
CF standard name of the coordinate.
• long_name:
Descriptive name of the coordinate.
• var_name:
The netCDF variable name for the coordinate.
• units
The Unit of the coordinate’s values. Can be a string, which will be converted to a Unit object.
• bounds
An array of values describing the bounds of each cell. Given n bounds for each cell, the shape of the bounds array should be points.shape + (n,). For example, a 1D coordinate with 100 points and two bounds per cell would have a bounds array of shape (100, 2) Note if the data is a climatology, climatological should be set.
• attributes
A dictionary containing other CF and user-defined attributes.
• coord_system
A CoordSystem representing the coordinate system of the coordinate, e.g., a GeogCS for a longitude coordinate.
• climatological (bool):
When True: the coordinate is a NetCDF climatological time axis. When True: saving in NetCDF will give the coordinate variable a ‘climatology’ attribute and will create a boundary variable called ‘<coordinate-name>_climatology’ in place of a standard bounds attribute and bounds variable. Will set to True when a climatological time axis is loaded from NetCDF. Always False if no bounds exist.
__binary_operator__(other, mode_constant)
Common code which is called by add, sub, mul and div
Mode constant is one of ADD, SUB, MUL, DIV, RDIV
Note
The unit is not changed when doing scalar operations on a metadata object. This means that a metadata object which represents “10 meters” when multiplied by a scalar i.e. “1000” would result in a metadata object of “10000 meters”. An alternative approach could be taken to multiply the unit by 1000 and the resultant metadata object would represent “10 kilometers”.
__getitem__(keys)
Returns a new dimensional metadata whose values are obtained by conventional array indexing.
Note
Indexing of a circular coordinate results in a non-circular coordinate if the overall shape of the coordinate changes after indexing.
cell(index)[source]
Return the single Cell instance which results from slicing the points/bounds with the given index.
cells()[source]
Returns an iterable of Cell instances for this Coord.
For example:
for cell in self.cells():
...
collapsed(dims_to_collapse=None)[source]
Returns a copy of this coordinate, which has been collapsed along the specified dimensions.
Replaces the points & bounds with a simple bounded region.
contiguous_bounds()[source]
Returns the N+1 bound values for a contiguous bounded 1D coordinate of length N, or the (N+1, M+1) bound values for a contiguous bounded 2D coordinate of shape (N, M).
Only 1D or 2D coordinates are supported.
Note
If the coordinate has bounds, this method assumes they are contiguous.
If the coordinate is 1D and does not have bounds, this method will return bounds positioned halfway between the coordinate’s points.
If the coordinate is 2D and does not have bounds, an error will be raised.
convert_units(unit)[source]
Change the coordinate’s units, converting the values in its points and bounds arrays.
For example, if a coordinate’s units attribute is set to radians then:
coord.convert_units('degrees')
will change the coordinate’s units attribute to degrees and multiply each value in points and bounds by 180.0/$$\pi$$.
copy(points=None, bounds=None)[source]
Returns a copy of this coordinate.
Kwargs:
• points: A points array for the new coordinate.
This may be a different shape to the points of the coordinate being copied.
• bounds: A bounds array for the new coordinate.
Given n bounds for each cell, the shape of the bounds array should be points.shape + (n,). For example, a 1d coordinate with 100 points and two bounds per cell would have a bounds array of shape (100, 2).
Note
If the points argument is specified and bounds are not, the resulting coordinate will have no bounds.
core_bounds()[source]
The points array at the core of this coord, which may be a NumPy array or a dask array.
core_points()[source]
The points array at the core of this coord, which may be a NumPy array or a dask array.
cube_dims(cube)[source]
Return the cube dimensions of this Coord.
Equivalent to “cube.coord_dims(self)”.
classmethod from_coord(coord)[source]
Create a new Coord of this type, from the given coordinate.
guess_bounds(bound_position=0.5)[source]
Add contiguous bounds to a coordinate, calculated from its points.
Puts a cell boundary at the specified fraction between each point and the next, plus extrapolated lowermost and uppermost bound points, so that each point lies within a cell.
With regularly spaced points, the resulting bounds will also be regular, and all points lie at the same position within their cell. With irregular points, the first and last cells are given the same widths as the ones next to them.
Kwargs:
• bound_position:
The desired position of the bounds relative to the position of the points.
Note
An error is raised if the coordinate already has bounds, is not one-dimensional, or is not monotonic.
Note
Unevenly spaced values, such from a wrapped longitude range, can produce unexpected results : In such cases you should assign suitable values directly to the bounds property, instead.
has_bounds()[source]
Return a boolean indicating whether the coord has a bounds array.
has_lazy_bounds()[source]
Return a boolean indicating whether the coord’s bounds array is a lazy dask array or not.
has_lazy_points()[source]
Return a boolean indicating whether the coord’s points array is a lazy dask array or not.
intersect(other, return_indices=False)[source]
Returns a new coordinate from the intersection of two coordinates.
Both coordinates must be compatible as defined by is_compatible().
Kwargs:
• return_indices:
If True, changes the return behaviour to return the intersection indices for the “self” coordinate.
is_compatible(other, ignore=None)[source]
Return whether the coordinate is compatible with another.
Compatibility is determined by comparing iris.coords.Coord.name(), iris.coords.Coord.units, iris.coords.Coord.coord_system and iris.coords.Coord.attributes that are present in both objects.
Args:
• other:
An instance of iris.coords.Coord, iris.common.CoordMetadata or iris.common.DimCoordMetadata.
• ignore:
A single attribute key or iterable of attribute keys to ignore when comparing the coordinates. Default is None. To ignore all attributes, set this to other.attributes.
Returns
Boolean.
is_contiguous(rtol=1e-05, atol=1e-08)[source]
Return True if, and only if, this Coord is bounded with contiguous bounds to within the specified relative and absolute tolerances.
1D coords are contiguous if the upper bound of a cell aligns, within a tolerance, to the lower bound of the next cell along.
2D coords, with 4 bounds, are contiguous if the lower right corner of each cell aligns with the lower left corner of the cell to the right of it, and the upper left corner of each cell aligns with the lower left corner of the cell above it.
Args:
• rtol:
The relative tolerance parameter (default is 1e-05).
• atol:
The absolute tolerance parameter (default is 1e-08).
Returns
Boolean.
is_monotonic()[source]
Return True if, and only if, this Coord is monotonic.
lazy_bounds()[source]
Return a lazy array representing the coord bounds.
Accessing this method will never cause the bounds values to be loaded. Similarly, calling methods on, or indexing, the returned Array will not cause the coord to have loaded bounds.
If the data have already been loaded for the coord, the returned Array will be a new lazy array wrapper.
Returns
A lazy array representing the coord bounds array or None if the coord does not have bounds.
lazy_points()[source]
Return a lazy array representing the coord points.
Accessing this method will never cause the points values to be loaded. Similarly, calling methods on, or indexing, the returned Array will not cause the coord to have loaded points.
If the data have already been loaded for the coord, the returned Array will be a new lazy array wrapper.
Returns
A lazy array, representing the coord points array.
name(default=None, token=False)
Returns a string name representing the identity of the metadata.
First it tries standard name, then it tries the long name, then the NetCDF variable name, before falling-back to a default value, which itself defaults to the string ‘unknown’.
Kwargs:
• default:
The fall-back string representing the default name. Defaults to the string ‘unknown’.
• token:
If True, ensures that the name returned satisfies the criteria for the characters required by a valid NetCDF name. If it is not possible to return a valid name, then a ValueError exception is raised. Defaults to False.
Returns
String.
nearest_neighbour_index(point)[source]
Returns the index of the cell nearest to the given point.
Only works for one-dimensional coordinates.
For example:
>>> cube = iris.load_cube(iris.sample_data_path('ostia_monthly.nc'))
>>> cube.coord('latitude').nearest_neighbour_index(0)
9
>>> cube.coord('longitude').nearest_neighbour_index(10)
12
Note
If the coordinate contains bounds, these will be used to determine the nearest neighbour instead of the point values.
Note
For circular coordinates, the ‘nearest’ point can wrap around to the other end of the values.
rename(name)
If ‘name’ is a valid standard name it will assign it to standard_name, otherwise it will assign it to long_name.
xml_element(doc)[source]
Create the xml.dom.minidom.Element that describes this Coord.
Args:
• doc:
The parent xml.dom.minidom.Document.
Returns
The xml.dom.minidom.Element that will describe this DimCoord, and the dictionary of attributes that require to be added to this element.
property attributes
property bounds
The coordinate bounds values, as a NumPy array, or None if no bound values are defined.
Note
The shape of the bound array should be: points.shape + (n_bounds, ).
property bounds_dtype
The NumPy dtype of the coord’s bounds. Will be None if the coord does not have bounds.
property climatological
A boolean that controls whether the coordinate is a climatological time axis, in which case the bounds represent a climatological period rather than a normal period.
Always reads as False if there are no bounds. On set, the input value is cast to a boolean, exceptions raised if units are not time units or if there are no bounds.
property coord_system
Relevant coordinate system (if any).
property dtype
The NumPy dtype of the current dimensional metadata object, as specified by its values.
property long_name
The CF Metadata long name for the object.
property metadata
property nbounds
Return the number of bounds that this coordinate has (0 for no bounds).
property ndim
Return the number of dimensions of the current dimensional metadata object.
property points
The coordinate points values as a NumPy array.
property shape
The fundamental shape of the metadata, expressed as a tuple.
property standard_name
The CF Metadata standard name for the object.
property units
The S.I. unit of the object.
property var_name
The NetCDF variable name for the object.
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Defines a range of values for a coordinate.
class iris.coords.CoordExtent(name_or_coord, minimum, maximum, min_inclusive=True, max_inclusive=True)[source]
Create a CoordExtent for the specified coordinate and range of values.
Args:
• name_or_coord
Either a coordinate name or a coordinate, as defined in iris.cube.Cube.coords().
• minimum
The minimum value of the range to select.
• maximum
The maximum value of the range to select.
Kwargs:
• min_inclusive
If True, coordinate values equal to minimum will be included in the selection. Default is True.
• max_inclusive
If True, coordinate values equal to maximum will be included in the selection. Default is True.
static __new__(cls, name_or_coord, minimum, maximum, min_inclusive=True, max_inclusive=True)[source]
Create a CoordExtent for the specified coordinate and range of values.
Args:
• name_or_coord
Either a coordinate name or a coordinate, as defined in iris.cube.Cube.coords().
• minimum
The minimum value of the range to select.
• maximum
The maximum value of the range to select.
Kwargs:
• min_inclusive
If True, coordinate values equal to minimum will be included in the selection. Default is True.
• max_inclusive
If True, coordinate values equal to maximum will be included in the selection. Default is True.
count(value, /)
Return number of occurrences of value.
index(value, start=0, stop=9223372036854775807, /)
Return first index of value.
Raises ValueError if the value is not present.
max_inclusive
Alias for field number 4
maximum
Alias for field number 2
min_inclusive
Alias for field number 3
minimum
Alias for field number 1
name_or_coord
Alias for field number 0
↑ top ↑
A coordinate that is 1D, and numeric, with values that have a strict monotonic ordering. Missing values are not permitted in a DimCoord.
class iris.coords.DimCoord(points, standard_name=None, long_name=None, var_name=None, units=None, bounds=None, attributes=None, coord_system=None, circular=False, climatological=False)[source]
Create a 1D, numeric, and strictly monotonic coordinate with immutable points and bounds.
Missing values are not permitted.
Args:
• points:
1D numpy array-like of values (or single value in the case of a scalar coordinate) for each cell of the coordinate. The values must be strictly monotonic and masked values are not allowed.
Kwargs:
• standard_name:
CF standard name of the coordinate.
• long_name:
Descriptive name of the coordinate.
• var_name:
The netCDF variable name for the coordinate.
• units:
The Unit of the coordinate’s values. Can be a string, which will be converted to a Unit object.
• bounds:
An array of values describing the bounds of each cell. Given n bounds and m cells, the shape of the bounds array should be (m, n). For each bound, the values must be strictly monotonic along the cells, and the direction of monotonicity must be consistent across the bounds. For example, a DimCoord with 100 points and two bounds per cell would have a bounds array of shape (100, 2), and the slices bounds[:, 0] and bounds[:, 1] would be monotonic in the same direction. Masked values are not allowed. Note if the data is a climatology, climatological should be set.
• attributes:
A dictionary containing other CF and user-defined attributes.
• coord_system:
A CoordSystem representing the coordinate system of the coordinate, e.g., a GeogCS for a longitude coordinate.
• circular (bool):
Whether the coordinate wraps by the modulus i.e., the longitude coordinate wraps around the full great circle.
• climatological (bool):
When True: the coordinate is a NetCDF climatological time axis. When True: saving in NetCDF will give the coordinate variable a ‘climatology’ attribute and will create a boundary variable called ‘<coordinate-name>_climatology’ in place of a standard bounds attribute and bounds variable. Will set to True when a climatological time axis is loaded from NetCDF. Always False if no bounds exist.
__binary_operator__(other, mode_constant)
Common code which is called by add, sub, mul and div
Mode constant is one of ADD, SUB, MUL, DIV, RDIV
Note
The unit is not changed when doing scalar operations on a metadata object. This means that a metadata object which represents “10 meters” when multiplied by a scalar i.e. “1000” would result in a metadata object of “10000 meters”. An alternative approach could be taken to multiply the unit by 1000 and the resultant metadata object would represent “10 kilometers”.
__deepcopy__()Deep copy of coordinate.[source]
Used if copy.deepcopy is called on a coordinate.
cell(index)
Return the single Cell instance which results from slicing the points/bounds with the given index.
cells()
Returns an iterable of Cell instances for this Coord.
For example:
for cell in self.cells():
...
collapsed(dims_to_collapse=None)[source]
Returns a copy of this coordinate, which has been collapsed along the specified dimensions.
Replaces the points & bounds with a simple bounded region.
contiguous_bounds()
Returns the N+1 bound values for a contiguous bounded 1D coordinate of length N, or the (N+1, M+1) bound values for a contiguous bounded 2D coordinate of shape (N, M).
Only 1D or 2D coordinates are supported.
Note
If the coordinate has bounds, this method assumes they are contiguous.
If the coordinate is 1D and does not have bounds, this method will return bounds positioned halfway between the coordinate’s points.
If the coordinate is 2D and does not have bounds, an error will be raised.
convert_units(unit)
Change the coordinate’s units, converting the values in its points and bounds arrays.
For example, if a coordinate’s units attribute is set to radians then:
coord.convert_units('degrees')
will change the coordinate’s units attribute to degrees and multiply each value in points and bounds by 180.0/$$\pi$$.
copy(points=None, bounds=None)[source]
Returns a copy of this coordinate.
Kwargs:
• points: A points array for the new coordinate.
This may be a different shape to the points of the coordinate being copied.
• bounds: A bounds array for the new coordinate.
Given n bounds for each cell, the shape of the bounds array should be points.shape + (n,). For example, a 1d coordinate with 100 points and two bounds per cell would have a bounds array of shape (100, 2).
Note
If the points argument is specified and bounds are not, the resulting coordinate will have no bounds.
core_bounds()
The points array at the core of this coord, which may be a NumPy array or a dask array.
core_points()
The points array at the core of this coord, which may be a NumPy array or a dask array.
cube_dims(cube)
Return the cube dimensions of this Coord.
Equivalent to “cube.coord_dims(self)”.
classmethod from_coord(coord)
Create a new Coord of this type, from the given coordinate.
classmethod from_regular(zeroth, step, count, standard_name=None, long_name=None, var_name=None, units=None, attributes=None, coord_system=None, circular=False, climatological=False, with_bounds=False)[source]
Create a DimCoord with regularly spaced points, and optionally bounds.
The majority of the arguments are defined as for Coord, but those which differ are defined below.
Args:
• zeroth:
The value prior to the first point value.
• step:
The numeric difference between successive point values.
• count:
The number of point values.
Kwargs:
• with_bounds:
If True, the resulting DimCoord will possess bound values which are equally spaced around the points. Otherwise no bounds values will be defined. Defaults to False.
guess_bounds(bound_position=0.5)
Add contiguous bounds to a coordinate, calculated from its points.
Puts a cell boundary at the specified fraction between each point and the next, plus extrapolated lowermost and uppermost bound points, so that each point lies within a cell.
With regularly spaced points, the resulting bounds will also be regular, and all points lie at the same position within their cell. With irregular points, the first and last cells are given the same widths as the ones next to them.
Kwargs:
• bound_position:
The desired position of the bounds relative to the position of the points.
Note
An error is raised if the coordinate already has bounds, is not one-dimensional, or is not monotonic.
Note
Unevenly spaced values, such from a wrapped longitude range, can produce unexpected results : In such cases you should assign suitable values directly to the bounds property, instead.
has_bounds()
Return a boolean indicating whether the coord has a bounds array.
has_lazy_bounds()
Return a boolean indicating whether the coord’s bounds array is a lazy dask array or not.
has_lazy_points()
Return a boolean indicating whether the coord’s points array is a lazy dask array or not.
intersect(other, return_indices=False)
Returns a new coordinate from the intersection of two coordinates.
Both coordinates must be compatible as defined by is_compatible().
Kwargs:
• return_indices:
If True, changes the return behaviour to return the intersection indices for the “self” coordinate.
is_compatible(other, ignore=None)
Return whether the coordinate is compatible with another.
Compatibility is determined by comparing iris.coords.Coord.name(), iris.coords.Coord.units, iris.coords.Coord.coord_system and iris.coords.Coord.attributes that are present in both objects.
Args:
• other:
An instance of iris.coords.Coord, iris.common.CoordMetadata or iris.common.DimCoordMetadata.
• ignore:
A single attribute key or iterable of attribute keys to ignore when comparing the coordinates. Default is None. To ignore all attributes, set this to other.attributes.
Returns
Boolean.
is_contiguous(rtol=1e-05, atol=1e-08)
Return True if, and only if, this Coord is bounded with contiguous bounds to within the specified relative and absolute tolerances.
1D coords are contiguous if the upper bound of a cell aligns, within a tolerance, to the lower bound of the next cell along.
2D coords, with 4 bounds, are contiguous if the lower right corner of each cell aligns with the lower left corner of the cell to the right of it, and the upper left corner of each cell aligns with the lower left corner of the cell above it.
Args:
• rtol:
The relative tolerance parameter (default is 1e-05).
• atol:
The absolute tolerance parameter (default is 1e-08).
Returns
Boolean.
is_monotonic()[source]
Return True if, and only if, this Coord is monotonic.
lazy_bounds()
Return a lazy array representing the coord bounds.
Accessing this method will never cause the bounds values to be loaded. Similarly, calling methods on, or indexing, the returned Array will not cause the coord to have loaded bounds.
If the data have already been loaded for the coord, the returned Array will be a new lazy array wrapper.
Returns
A lazy array representing the coord bounds array or None if the coord does not have bounds.
lazy_points()
Return a lazy array representing the coord points.
Accessing this method will never cause the points values to be loaded. Similarly, calling methods on, or indexing, the returned Array will not cause the coord to have loaded points.
If the data have already been loaded for the coord, the returned Array will be a new lazy array wrapper.
Returns
A lazy array, representing the coord points array.
name(default=None, token=False)
Returns a string name representing the identity of the metadata.
First it tries standard name, then it tries the long name, then the NetCDF variable name, before falling-back to a default value, which itself defaults to the string ‘unknown’.
Kwargs:
• default:
The fall-back string representing the default name. Defaults to the string ‘unknown’.
• token:
If True, ensures that the name returned satisfies the criteria for the characters required by a valid NetCDF name. If it is not possible to return a valid name, then a ValueError exception is raised. Defaults to False.
Returns
String.
nearest_neighbour_index(point)
Returns the index of the cell nearest to the given point.
Only works for one-dimensional coordinates.
For example:
>>> cube = iris.load_cube(iris.sample_data_path('ostia_monthly.nc'))
>>> cube.coord('latitude').nearest_neighbour_index(0)
9
>>> cube.coord('longitude').nearest_neighbour_index(10)
12
Note
If the coordinate contains bounds, these will be used to determine the nearest neighbour instead of the point values.
Note
For circular coordinates, the ‘nearest’ point can wrap around to the other end of the values.
rename(name)
If ‘name’ is a valid standard name it will assign it to standard_name, otherwise it will assign it to long_name.
xml_element(doc)[source]
Create the xml.dom.minidom.Element that describes this DimCoord.
Args:
• doc:
The parent xml.dom.minidom.Document.
Returns
The xml.dom.minidom.Element that describes this DimCoord.
property attributes
property bounds
The coordinate bounds values, as a NumPy array, or None if no bound values are defined.
Note
The shape of the bound array should be: points.shape + (n_bounds, ).
property bounds_dtype
The NumPy dtype of the coord’s bounds. Will be None if the coord does not have bounds.
property circular
Whether the coordinate wraps by coord.units.modulus.
property climatological
A boolean that controls whether the coordinate is a climatological time axis, in which case the bounds represent a climatological period rather than a normal period.
Always reads as False if there are no bounds. On set, the input value is cast to a boolean, exceptions raised if units are not time units or if there are no bounds.
property coord_system
The coordinate-system of the coordinate.
property dtype
The NumPy dtype of the current dimensional metadata object, as specified by its values.
property long_name
The CF Metadata long name for the object.
property metadata
property nbounds
Return the number of bounds that this coordinate has (0 for no bounds).
property ndim
Return the number of dimensions of the current dimensional metadata object.
property points
The coordinate points values as a NumPy array.
property shape
The fundamental shape of the metadata, expressed as a tuple.
property standard_name
The CF Metadata standard name for the object.
property units
The S.I. unit of the object.
property var_name
The NetCDF variable name for the object. | 2021-04-23 05:05:50 | {"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": 0, "mathjax_display_tex": 1, "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": 0.19786691665649414, "perplexity": 3705.023468878971}, "config": {"markdown_headings": true, "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/1618039601956.95/warc/CC-MAIN-20210423041014-20210423071014-00391.warc.gz"} |
https://itprospt.com/num/7848211/let-f-x-x3-2x2-sx-6-be-a-fiunction-defined-on-r-which-of | 5
Let f(x) =x3 2x2 _ Sx + 6 be a fiunction defined on R Which of the following statement(s) is/are TRUE ? Newton' $method is applicable to find the root of the curve with the initial quess Xo It's possible to use Bisection method on [~1.5,0.5]. III: Fixed-point iteration can be applied to find the root of the 2x2+6 funetion with the initial guess Xo =1 for g(x) A.) Only I B.) Land II Land III D.) Only III E.) I, I and III Answers Similar Solved Questions 5 answers The demand function [or competitive lirm is given by; F(1/Q" ) function is C(Q)= aQl; B>1, Find Q that maximizes profitU<a< and its total +c +trc tGo The demand function [or competitive lirm is given by; F(1/Q" ) function is C(Q)= aQl; B>1, Find Q that maximizes profit U<a< and its total +c +trc tGo... 5 answers Covetatka 2017 that 2] function 2 %e) E 2 1ooy the solution E 2 value equation !" (0) 6 problem 100y 100. where andarbitrary Covetatka 2017 that 2] function 2 %e) E 2 1ooy the solution E 2 value equation !" (0) 6 problem 100y 100. where and arbitrary... 5 answers Find the distance traveled by particle with position (x, Y) as t varies in the given time interval: X = 5sin2(t) , Y = cos2(t) , 0 <t < 2TWhat is the length of the curve?Need Help?Rcad ItWatch ItTalk toa Tutor Find the distance traveled by particle with position (x, Y) as t varies in the given time interval: X = 5sin2(t) , Y = cos2(t) , 0 <t < 2T What is the length of the curve? Need Help? Rcad It Watch It Talk toa Tutor... 5 answers (596) Probkm 19: particle undergoes thrce conseculive dusplaccments, given by the following vectors Dt = (2 mm)i - mm)i (-28 mmjk Di (1.9 mm)i (-6.2 mm)j (3.0 mm)k ard Dye (-6.2 mmji (.6 mm)i (1.9 mmjk5090 Fart (1) What thc magnitude of the nct displaccment D -D+D;l=Gnde Summ . Daurttadi Palenlal Iou*eunacoshmmanaaena Ancmpy} (cmjlotn @E #Fmrt) drtullad trtcotanOatinO) #oso) alanl acotano sinho cosho) tanho cotanho Dcgtecs RadnnatSubmulFule uodeder Ion Iperhlat~dbath f(acaun pet fcrubils0% F&#x (596) Probkm 19: particle undergoes thrce conseculive dusplaccments, given by the following vectors Dt = (2 mm)i - mm)i (-28 mmjk Di (1.9 mm)i (-6.2 mm)j (3.0 mm)k ard Dye (-6.2 mmji (.6 mm)i (1.9 mmjk 5090 Fart (1) What thc magnitude of the nct displaccment D -D+D;l= Gnde Summ . Daurttadi Palenlal... 5 answers Use the Theorem of Pappus to find the volume of the solid of revolution.the torus formed by revolving the circular region bounded by (x - 6)2 + y2 16 about the Y-axis Use the Theorem of Pappus to find the volume of the solid of revolution. the torus formed by revolving the circular region bounded by (x - 6)2 + y2 16 about the Y-axis... 5 answers (e) Apply static equilibrium condition(s) Find the magnitude (in Newtons) of force N,. Keep 2 decimal places (Be careful: there are lot of data punching: Check your calculations before entering the result: Due to limitation of the online platform, partial credits within this part can't be awarded:) Enter number N 0Submitattempts remaining)Apply static equilibrium condition(s) Find the magnitude (in Newtons) of force Nz Keep 2 decimal places (Be careful: Check your calculations before enteri (e) Apply static equilibrium condition(s) Find the magnitude (in Newtons) of force N,. Keep 2 decimal places (Be careful: there are lot of data punching: Check your calculations before entering the result: Due to limitation of the online platform, partial credits within this part can't be award... 5 answers 2 3 (10 pts) Evaluate the determinant of 2 5 3 by (a) cofactor expansion about 0 8 column 1 and (b) cofactor expansion about row 3_ 2 3 (10 pts) Evaluate the determinant of 2 5 3 by (a) cofactor expansion about 0 8 column 1 and (b) cofactor expansion about row 3_... 5 answers & (30 pts) Consider the follwing triple integral(2+1)* dz dy d Write this integral in cylindrical coordinates with order dz d8 DO NOT EVALUATE(6) Write this integral in spherical DO NOT EVALUATE coordinates with order dp d8 dp. & (30 pts) Consider the follwing triple integral (2+1)* dz dy d Write this integral in cylindrical coordinates with order dz d8 DO NOT EVALUATE (6) Write this integral in spherical DO NOT EVALUATE coordinates with order dp d8 dp.... 5 answers CHZCH; H- CHj C CH;properly named:(BRAS,SR) 3,5-Dichloro-4-methylhexane 8 (2S,35,4S)- 2,4-Dichloro-3-methylhexane (2S,JR,AR)- 4-Dichloro-}-methylhexane (25_JR,4S)-2.4-Dichloro-3-methylhexane (25.3S,4R) 2,4-Dichloro-3-methylhexaneDraw all possible stereoisomers for 2-bromo-3-chlorobutane. Label each chiral center as R or State the rclationship of cach structure (0 all of the other structures: CHZCH; H- CHj C CH; properly named: (BRAS,SR) 3,5-Dichloro-4-methylhexane 8 (2S,35,4S)- 2,4-Dichloro-3-methylhexane (2S,JR,AR)- 4-Dichloro-}-methylhexane (25_JR,4S)-2.4-Dichloro-3-methylhexane (25.3S,4R) 2,4-Dichloro-3-methylhexane Draw all possible stereoisomers for 2-bromo-3-chlorobutane. Label e... 5 answers [-/1 Points]DETAILSCJ10 18.P.038.MY NOTES3 5 KC point charge placedexternal uniform electric field that has magnitude of 1.0 * 10* NIC. At what distance from the charge the net electric field zero?Additional MaterialseBock [-/1 Points] DETAILS CJ10 18.P.038. MY NOTES 3 5 KC point charge placed external uniform electric field that has magnitude of 1.0 * 10* NIC. At what distance from the charge the net electric field zero? Additional Materials eBock... 5 answers What Is; the procuct ciiha followlng reacilon?CHoh, ["0yNllkcla Choke What Is; the procuct ciiha followlng reacilon? CHoh, [" 0y Nllkcla Choke... 5 answers Slnca 1870, Ihe purchasing poter of a counlrys dcez5, Teasured DY consuner prkes mocsled by bne function below; where * Is Ihe number 0' years ance 1970 2382 P{x) = 4+ 0 14379) Find P(1o), Przo) ard Pi5o} P(to = (Poiro deciina Oecc Teedrd |Pizoj= (Rourd [O cromal Paces = nected )PisOl = 'RomndTtoEo dccimal plices 41 necdrd ) When prchaaang Power be$ 757purchasing pO#ET - De J0,75n | years Jiie} 1970 Inour] onc uccing Dacc @tendcclFlndPixPix)e (Snplily Poui Miarel- |
slnca 1870, Ihe purchasing poter of a counlrys dcez5, Teasured DY consuner prkes mocsled by bne function below; where * Is Ihe number 0' years ance 1970 2382 P{x) = 4+ 0 1437 9) Find P(1o), Przo) ard Pi5o} P(to = (Poiro deciina Oecc Teedrd | Pizoj= (Rourd [O cromal Paces = nected ) PisOl = &#x...
Exponential Functions $$\int\left(e^{x / a}-e^{-x / a}\right)^{2} d x$$
Exponential Functions $$\int\left(e^{x / a}-e^{-x / a}\right)^{2} d x$$...
The Consumer Price Index was 160.5 in 1997 and 207.3 in 2007 If a person earned 539,400 in 1997,how much did he need to earn in 2007 to maintain the same standard of living?165.8740 30.505.0742,10050.888.60
The Consumer Price Index was 160.5 in 1997 and 207.3 in 2007 If a person earned 539,400 in 1997,how much did he need to earn in 2007 to maintain the same standard of living? 165.874 0 30.505.07 42,100 50.888.60...
A) Determine whether T R3 _ R defined by T(x,y) = xy is linear transformation Or notshow all the axiomsb) Find UV given that | u+vl-2 and lu-l-6 Let V and U be vectors in R" .Then prove V.ul-lvllullsupposeU =1) Determine whether or not AUV = U.Av 2 ) Find lu-vl: 3) verify Cauchy-Schwarz inequality hold forU and V
a) Determine whether T R3 _ R defined by T(x,y) = xy is linear transformation Or not show all the axioms b) Find UV given that | u+vl-2 and lu-l-6 Let V and U be vectors in R" .Then prove V.ul-lvllull suppose U = 1) Determine whether or not AUV = U.Av 2 ) Find lu-vl: 3) verify Cauchy-Schwarz in...
2202-MATH-1426-300-CALCULUS |Homework: 6.2 Regions Between Curves Score: 0 of 5 of 12 (4 complete)6.2.15Find the area of tho shaded region shown in the graphTessinX39C09 XThe area the shaded region is(Type an exact answer )
2202-MATH-1426-300-CALCULUS | Homework: 6.2 Regions Between Curves Score: 0 of 5 of 12 (4 complete) 6.2.15 Find the area of tho shaded region shown in the graph TessinX 39C09 X The area the shaded region is (Type an exact answer )... | 2022-09-27 01:06:34 | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49826550483703613, "perplexity": 10524.066809419308}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2022-40/segments/1664030334974.57/warc/CC-MAIN-20220927002241-20220927032241-00672.warc.gz"} |
https://proofwiki.org/wiki/Minkowski%27s_Inequality_for_Integrals | # Minkowski's Inequality for Integrals
## Theorem
Let $f, g$ be integrable functions in $X \subseteq \R^n$ with respect to the volume element $dV$.
$(1):\quad$ Let $p > 1$. Then:
$\displaystyle \paren {\int_X \size {f + g}^p \rd V}^{1/p} \le \paren {\int_X \size f^p \rd V}^{1/p} + \paren {\int_X \size g^p \rd V}^{1/p}$
$(2):\quad$ Let $p < 1, p \ne 0$. Then:
$\displaystyle \paren {\int_X \size {f + g}^p \rd V}^{1/p} \ge \paren {\int_X \size f^p \rd V}^{1/p} + \paren {\int_X \size g^p \rd V}^{1/p}$
## Source of Name
This entry was named for Hermann Minkowski. | 2020-11-27 13:35:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9403325319290161, "perplexity": 898.5743993296956}, "config": {"markdown_headings": true, "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-2020-50/segments/1606141193221.49/warc/CC-MAIN-20201127131802-20201127161802-00625.warc.gz"} |
https://math.stackexchange.com/questions/235634/how-to-find-the-covariance-of-sample-mean-and-sample-variance-covm-s2-for-p | # How to find the covariance of sample mean and sample variance $Cov(M,S^2)$ for Poisson distribution?
Suppose that I have a Poisson distribution $P(\lambda)$.
Let $X_1,X_2..,X_n$ be independent random variables from the distribution mentioned above.
Let us define sample variance $S^2 = \frac{1}{n-1} \sum (X_i - M)^2$ and sample mean as $M = \frac{1}{n}\sum X_i$.
I want to find the covariance, $Cov(M,S^2)$. I've seen from this answer that when the distribution is symmetric, they are uncorrelated, which makes it zero. I also know that for large $\lambda$ values Poisson distribution is very close to Gaussian distribution, thus becoming symmetric, and probably the covariance is close to zero.
However, I want to find the exact value of $Cov(M,S^2)$, as I am working with small values of $\lambda$
Currently I tried the following:
$Cov(M,S^2) =E( (M-\lambda) (S^2-\lambda) ) = E(MS^2)-\lambda E(M) - \lambda E(S^2) + \lambda^2$
Thus, $Cov(M,S^2) = E(MS^2) - \lambda^2 - \lambda^2 + \lambda^2 = E(MS^2) -\lambda^2$
I am having trouble with calculating $E(MS^2)$.
Any idea?
• A square is missing in the definition of $S^2$, isn't it? – Davide Giraudo Nov 12 '12 at 13:00
• @DavideGiraudo, you are right, I made a typo. Thanks for pointing that out. – Andrey Rubshtein Nov 12 '12 at 13:09
• We can expand the square in the definition of $S^2$ to get a more simple expression, then express $E(MS^2)$ as a double sum. You will have to distinguish when the indexes are the same or not. – Davide Giraudo Nov 12 '12 at 13:13
Let us first center everything, using $\bar X_k=X_k-\lambda$ and $\bar M=M-\lambda$. Then $$\mathrm{Cov}(M,S^2)=\mathbb E(\bar MS^2)=\mathbb E(\bar X_1S^2)=\frac1{n-1}\mathbb E(\bar X_1U),$$ where $$U=\sum\limits_{k=1}^n(\bar X_k-\bar M)^2.$$ Note that $U$ is a linear combination of products $\bar X_k^2$ and $\bar X_k\bar X_i$ for $i\ne k$. Amongst these products, many will not contribute to the expectation of $\bar X_1U$ since $\mathbb E(\bar X_1\bar X_k\bar X_i)=0$ for every $k\ne i$ and $\mathbb E(\bar X_1\bar X_k^2)=0$ for every $k\ne1$.
Hence, one needs only the coefficient of $\bar X_1^2$ in $U$, which is $c_n=\left(\frac{n-1}n\right)^2+(n-1)\frac1{n^2}=\frac{n-1}n$. This yields $\mathbb E(\bar X_1U)=c_n\mathbb E(\bar X_1^3)$ and $\mathrm{Cov}(M,S^2)=\frac1{n-1}c_n\mathbb E(\bar X_1^3)=\frac1n\mathbb E(\bar X_1^3)$.
Finally, the third central moment of the Poisson distribution with parameter $\lambda$ is $\mathbb E(\bar X_1^3)=\lambda$ hence $$\mathrm{Cov}(M,S^2)=\frac\lambda{n}.$$
• Thanks for your answer. I haven't fully understood it, and it will take me some time to analyze what you wrote, yet I have a question. I had an intuition that the covariance should get close to zero (because it becomes almost like Normal distribution), when \lambda becomes very large. From your answer, it looks like it grows when \lambda grows. Is my intuition wrong? Thanks again – Andrey Rubshtein Nov 12 '12 at 13:52
• The argument needs some refining. When $\lambda\to\infty$, what happens is really that the scaled and centered versions are more and more gaussian-like, hence symmetric. The proper scaling is to center each $X_k$ and to divide it by $\sqrt{\lambda}$ hence one should divide $M$ by $\sqrt{\lambda}$ and $S^2$ by $\lambda$. Thus, $\mathrm{Cov}(M,S^2)/\lambda^{3/2}$ should go to zero when $\lambda\to\infty$ (and it does). – Did Nov 12 '12 at 13:59
• Hi Did, It's a very late reply, not sure whether you will see it or not. Intuitively, I can see that after centering the variables, we did not change $S^2$, and we did not change the $Cov(\bar{X},S^2)$. But I am not sure how to show that the covariance doesn't change by centering the variable. – Nan Sep 25 '17 at 20:46
• @Nan For every constants $x$ and $y$, $\mathrm{Cov}(X-x,Y-y)=\mathrm{Cov}(X,Y)$. Is this your question? – Did Sep 25 '17 at 20:58
• @Did Yes! Thank you so much! – Nan Sep 25 '17 at 21:53
One can solve this more generally. For any random variable whose moments exist, the covariance between the sample mean $M$ and the sample variance $S^2$ is:
$$\text{Cov}(M, S^2) = \frac{\mu_3}{n}$$
where $\mu_3$ denotes the $3^{\text{rd}}$ central moment of the parent random variable $X$.
If $X \sim \text{Poisson}(\lambda)$, then $\mu_3 = \lambda$, so the answer is $\large\frac{\lambda}{n}$. | 2019-08-23 06:30:40 | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9142067432403564, "perplexity": 163.6209967430576}, "config": {"markdown_headings": true, "markdown_code": false, "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-2019-35/segments/1566027318011.89/warc/CC-MAIN-20190823062005-20190823084005-00048.warc.gz"} |
https://mathspace.co/textbooks/syllabuses/Syllabus-410/topics/Topic-7305/subtopics/Subtopic-97480/?activeTab=theory | New Zealand
Level 7 - NCEA Level 2
# Simple applications (using power rule only)
Lesson
As we move past learning the skills of calculus and differentiation, we're ready to use our skills to solve applied problems.
The basics of these application-style problems involve using and manipulating the gradient function in each of the following ways:
1. Determine the gradient at a given point on the curve
2. Determine the equation of the tangent at a given point on the curve
3. Determine the point(s) on a curve where a given gradient exists
4. Using the information about gradients and the original function to determine unknown coefficients in the polynomial $f\left(x\right)$f(x).
## Evaluating the gradient at a given point
We've explored this idea earlier and we can review it with this worked example.
##### Worked Example 1
Find the gradient of $f\left(x\right)=16x^{-3}$f(x)=16x3 at $x=2$x=2.
Denote this gradient by $f'\left(2\right)$f(2).
## Determine the equation of the tangent at a given point
We've also explored this idea earlier and it's worth taking a look at another example.
##### Example 2
Determine the equation of the tangent to the curve $f\left(x\right)=x^3-2x$f(x)=x32x at the point where $x=-1$x=1.
Since a tangent is a straight line, we know the equation of our tangent will be of the form $y=mx+c$y=mx+c. Let's begin by finding m, the gradient. To do this we'll need the gradient function, so first we need to differentiate $f\left(x\right)$f(x).
$f'\left(x\right)=3x^2-2$f(x)=3x22
Now let's use the gradient function to find the value of the gradient at $x=-1$x=1.
$f'\left(-1\right)=3\left(-1\right)^2-2=1$f(1)=3(1)22=1
We now know that $m=1$m=1and thus we have $y=x+c$y=x+c.
To find the value of $c$c, we need to substitute a point on the tangent into the equation. However, we only know one point, and that is where the tangent touches the curve. And so far all we know is the $x$xvalue. So let's find the $y$yvalue of the coordinate by using the original function.
$f\left(-1\right)=\left(-1\right)^3-2\left(-1\right)=1$f(1)=(1)32(1)=1
So we have the point $\left(-1,1\right)$(1,1).
We can now substitute this point to find the value of $c$c.
$1=1\times-1+c$1=1×1+c
$c=2$c=2
Therefore the equation of the tangent is $y=x+2$y=x+2.
## Finding the point where a given gradient occurs
Let's review this with the following worked example.
##### Example 3
Consider the function $f\left(x\right)=x^2+5x$f(x)=x2+5x.
1. Find the $x$x-coordinate of the point at which $f\left(x\right)$f(x) has a gradient of $13$13.
2. Hence state the coordinates of the point on the curve where the gradient is $13$13.
## Evaluating unknown coefficients given function and gradient information
##### Example 4
The function $f\left(x\right)=x^3+ax^2+bx+c$f(x)=x3+ax2+bx+c has a $y$y-intercept of $3$3. The function has stationary points at $x=1$x=1 and a root at $x=-3$x=3. Determine the values of $a$a, $b$band $c$c.
We can begin by using the information about the y-intercept.
$3=0^3+a\times0^2+b\times0+c$3=03+a×02+b×0+c
$c=3$c=3
To use the information about the stationary point, we will need to first find ourselves the gradient function.
$f'\left(x\right)=3x^2+2ax+b$f(x)=3x2+2ax+b
Substituting in the $x$xvalue of the stationary point, we obtain the equation:
$3+2a+b=0$3+2a+b=0 - equation 1
To use the information about the x-intercept, we can substitute this into the original function to obtain the equation:
$-27+9a-3b+3=0$27+9a3b+3=0 - equation 2
Solving simultaneously (either with the elimination method, substitution method or with a CAS calculator) we find that $a=1$a=1 and $b=-5$b=5.
### Outcomes
#### M7-10
Apply differentiation and anti-differentiation techniques to polynomials
#### 91262
Apply calculus methods in solving problems | 2022-01-24 20:15:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7991571426391602, "perplexity": 804.4646270327224}, "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-2022-05/segments/1642320304600.9/warc/CC-MAIN-20220124185733-20220124215733-00320.warc.gz"} |
https://radar.inria.fr/report/2021/mexico/uid0.html | • The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.
• Legal notice
• Personal data
#### MEXICO
##### MEXICO - 2021
2021
Activity report
Project-Team
MEXICO
RNSR: 200920937Y
Research center
In partnership with:
CNRS, Ecole normale supérieure de Cachan
Team name:
Modeling and Exploitation of Interaction and Concurrency
In collaboration with:
Laboratoire de Méthodes Formelles
Domain
Algorithmics, Programming, Software and Architecture
Theme
Proofs and Verification
Creation of the Project-Team: 2011 January 01
# Keywords
• A2.3. Embedded and cyber-physical systems
• A2.3.2. Cyber-physical systems
• A2.3.3. Real-time systems
• A2.4.1. Analysis
• A2.4.2. Model-checking
• A6.4.1. Deterministic control
• A6.4.3. Observability and Controlability
• A7.1. Algorithms
• A7.1.1. Distributed algorithms
• A7.2. Logic in Computer Science
• A7.3.1. Computational models and calculability
• A8.1. Discrete mathematics, combinatorics
• A8.2. Optimization
• A8.7. Graph theory
• A8.8. Network science
• A8.9. Performance evaluation
• A8.11. Game Theory
• B1.1.2. Molecular and cellular biology
• B1.1.7. Bioinformatics
• B1.1.10. Systems and synthetic biology
• B3.6. Ecology
• B7.1. Traffic management
• B7.2.1. Smart vehicles
# 1 Team members, visitors, external collaborators
## Research Scientists
• Stefan Haar [Team leader, Inria, Senior Researcher, HDR]
• Matthias Fuegger [CNRS, Researcher]
## Faculty Members
• Thomas Chatain [Ecole normale supérieure Paris-Saclay, Associate Professor]
• Philippe Dague [Univ Paris-Saclay, Emeritus, from Apr 2021]
• Stefan Schwoon [Ecole normale supérieure Paris-Saclay, Associate Professor, HDR]
## PhD Students
• Giann Karlo Aguirre Samboni [Inria]
• Mathilde Boltenhagen [CNRS, until Oct 2021]
• Igor Khmelnitsky [Ecole normale supérieure Paris-Saclay, until Nov 2021]
• Alexandra Merlin [Inria]
## External Collaborators
• Benoît Barbot [Univ Paris-Est Marne La Vallée]
• Juraj Kolcak [University Southern Denmark de Odense, until Jun 2021]
• Lina Ye [Centrale-Supélec, until Aug 2021]
# 2 Overall objectives
## 2.1 Scientific Objectives
#### Introduction.
In the increasingly networked world, reliability of applications becomes ever more critical as the number of users of, e.g., communication systems, web services, transportation etc., grows steadily. Management of networked systems, in a very general sense of the term, therefore is a crucial task, but also a difficult one.
MExICo strives to take advantage of distribution by orchestrating cooperation between different agents that observe local subsystems, and interact in a localized fashion.
The need for applying formal methods in the analysis and management of complex systems has long been recognized. It is with much less unanimity that the scientific community embraces methods based on asynchronous and distributed models. Centralized and sequential modeling still prevails.
However, we observe that crucial applications have increasing numbers of users, that networks providing services grow fast both in the number of participants and the physical size and degree of spatial distribution. Moreover, traditional isolated and proprietary software products for local systems are no longer typical for emerging applications.
In contrast to traditional centralized and sequential machinery for which purely functional specifications are efficient, we have to account for applications being provided from diverse and non-coordinated sources. Their distribution (e.g. over the Web) must change the way we verify and manage them. In particular, one cannot ignore the impact of quantitative features such as delays or failure likelihoods on the functionalities of composite services in distributed systems.
We thus identify three main characteristics of complex distributed systems that constitute research challenges:
• Concurrency of behavior;
• Interaction of diverse and semi-transparent components; and
• management of Quantitative aspects of behavior.
## 2.2 Concurrency
The increasing size and the networked nature of communication systems, controls, distributed services, etc. confront us with an ever higher degree of parallelism between local processes. This field of application for our work includes telecommunication systems and composite web services. The challenge is to provide sound theoretical foundations and efficient algorithms for management of such systems, ranging from controller synthesis and fault diagnosis to integration and adaptation. While these tasks have received considerable attention in the sequential setting, managing non-sequential behavior requires profound modifications for existing approaches, and often the development of new approaches altogether. We see concurrency in distributed systems as an opportunity rather than a nuisance. Our goal is to exploit asynchronicity and distribution as an advantage. Clever use of adequate models, in particular partial order semantics (ranging from Mazurkiewicz traces to event structures to MSCs) actually helps in practice. In fact, the partial order vision allows us to make causal precedence relations explicit, and to perform diagnosis and test for the dependency between events. This is a conceptual advantage that interleaving-based approaches cannot match. The two key features of our work will be (i) the exploitation of concurrency by using asynchronous models with partial order semantics, and (ii) distribution of the agents performing management tasks.
## 2.3 Interaction
Systems and services exhibit non-trivial interaction between specialized and heterogeneous components. A coordinated interplay of several components is required; this is challenging since each of them has only a limited, partial view of the system's configuration. We refer to this problem as distributed synthesis or distributed control. An aggravating factor is that the structure of a component might be semi-transparent, which requires a form of grey box management.
## 2.4 Quantitative Features
Besides the logical functionalities of programs, the quantitative aspects of component behavior and interaction play an increasingly important role.
• Real-time properties cannot be neglected even if time is not an explicit functional issue, since transmission delays, parallelism, etc, can lead to time-outs striking, and thus change even the logical course of processes. Again, this phenomenon arises in telecommunications and web services, but also in transport systems.
• In the same contexts, probabilities need to be taken into account, for many diverse reasons such as unpredictable functionalities, or because the outcome of a computation may be governed by race conditions.
• Last but not least, constraints on cost cannot be ignored, be it in terms of money or any other limited resource, such as memory space or available CPU time.
## 2.5 Evolution and Perspectives
Since the creation of MExICo, the weight of quantitative aspects in all parts of our activities has grown, be it in terms of the models considered (weighted automata and logics), be it in transforming verification or diagnosis verdict into probabilistic statements (probabilistic diagnosis, statistical model checking), or within the recently started SystemX cooperation on supervision in multi-modal transport systems. This trend is certain to continue over the next couple of years, along with the growing importance of diagnosis and control issues.
In another development, the theory and use of partial order semantics has gained momentum in the past four years, and we intend to further strengthen our efforts and contacts in this domain to further develop and apply partial-order based deduction methods.
When no complete model of the underlying dynamic system is available, the analysis of logs may allow to reconstruct such a model, or at least to infer some properties of interest; this activity, which has emerged over the past 10 years on the international level, is referred to as process mining. In this emerging activity, we have contributed to unfolding-based process discovery [CI-146], and the study of process alignments [CI-121, CI-96, CI-83, CI-60, CI-33].
Finally, over the past years biological challenges have come to the center of our work, in two different directions:
1. (Re-)programming in discrete concurrent models. Cellular regulatory networks exhibit highly complex concurrent behaviours that is influenced by a high number of perturbations such as mutations. We are in particular investigating discrete models, both in the form of boolean networks and of Petri nets, to harness this complexity, and to obtain viable methods for two interconnected and central challenges:
• find attractors, i.e. long-run stable states or sets of states, that indicate possible phenotypes of the organism under study, and
• determine reprogramming strategies that apply perturbations in such a way as to steer the cell's long-run behaviour into some desired phenotype, or away from an undesired one.
2. Process mining @ MExICo The use of process models has increased in the last decade due to the advent of the process mining field. Process mining techniques aim at discovering, analyzing and enhancing formal representations of the real processes executed in any digital environment. These processes can only be observed by the footprints of their executions, stored in form of event logs. An event log is a collection of traces and is the input of process mining techniques. The derivation of an accurate formalization of an underlying process opens the door to the continuous improvement and analysis of the processes within an information system.
Process models often use true concurrency to represent actions that appear in logs with different permutations.
Among the important challenges in process mining, conformance checking is a crucial one: to assess the quality of a model (automatically discovered or manually designed) in describing the observed behavior, i.e., the event log.
MExICo contributes to process mining, a field which discovers and manipulates true concurrency models and questions about their conformance to recorded event logs.
3. Distributed Algorithms in wild or synthetic biological systems. Since the arrival of Matthias Fuegger in the team, we also work, on the multi-cell level, with a distributed algorithms' view on microbiological systems, both with the goal to model and analyze existing microbiological systems as distributed systems, and to design and implement distributed algorithms in synthesized microbiological systems. Major long-term goals are drug production and medical treatment via synthesized bacterial colonies.
# 3 Research program
## 3.1 Concurrency
Keywords: Concurrency; Semantics; Automatic Control ; Diagnosis ; Verification.
Glossary
• Concurrency: Property of systems allowing some interacting processes to be executed in parallel.
• Diagnosis: The process of deducing from a partial observation of a system aspects of the internal states or events of that system; in particular, fault diagnosis aims at determining whether or not some non-observable fault event has occurred.
• Conformance Testing: Feeding dedicated input into an implemented system $IS$ and deducing, from the resulting output of $I$, whether $I$ respects a formal specification $S$.
#### Introduction
It is well known that, whatever the intended form of analysis or control, a global view of the system state leads to overwhelming numbers of states and transitions, thus slowing down algorithms that need to explore the state space. Worse yet, it often blurs the mechanics that are at work rather than exhibiting them. Conversely, respecting concurrency relations avoids exhaustive enumeration of interleavings. It allows us to focus on `essential' properties of non-sequential processes, which are expressible with causal precedence relations. These precedence relations are usually called causal (partial) orders. Concurrency is the explicit absence of such a precedence between actions that do not have to wait for one another. Both causal orders and concurrency are in fact essential elements of a specification. This is especially true when the specification is constructed in a distributed and modular way. Making these ordering relations explicit requires to leave the framework of state/interleaving based semantics. Therefore, we need to develop new dedicated algorithms for tasks such as conformance testing, fault diagnosis, or control for distributed discrete systems. Existing solutions for these problems often rely on centralized sequential models which do not scale up well.
### 3.1.1 Diagnosis
Fault Diagnosis for discrete event systems is a crucial task in automatic control. Our focus is on event oriented (as opposed to state oriented) model-based diagnosis, asking e.g. the following questions:
given a - potentially large - alarm pattern formed of observations,
• what are the possible fault scenarios in the system that explain the pattern ?
• Based on the observations, can we deduce whether or not a certain - invisible - fault has actually occurred ?
Model-based diagnosis 1 starts from a discrete event model of the observed system - or rather, its relevant aspects, such as possible fault propagations, abstracting away other dimensions. From this model, an extraction or unfolding process, guided by the observation, produces recursively the explanation candidates.
#### Active Diagnosis.
Depending on the possible observations, a discrete-event system may be diagnosable or not. Active diagnosis aims at controlling the system to render it diagnosable. We have established in 5 a memory-optimal diagnoser whose delay is at most twice the minimal delay, whereas the memory required to achieve optimal delay may be highly greater. We have also provided solutions for parametrized active diagnosis, where we automatically construct the most permissive controller respecting a given delay. Further, we introduced four variants of diagnosability (FA, IA, FFIF) in (finite) probabilistic systems (pLTS) depending whether one considers (1) finite or infinite runs and (2) faulty or all runs. The corresponding decision problems are PSPACE-complete. A key ingredient of the decision procedures was a characterisation of diagnosability by the fact that a random run almost surely lies in an open set whose specification only depends on the qualitative behaviour of the pLTS. For infinite pLTS, this characterisation still holds for FF-diagnosability but with a ${G}_{\delta }$ set instead of an open set and also for IF-and IA-diagnosability when pLTS are finitely branching. Surprisingly, FA-diagnosability cannot be characterised in this way even in the finitely branching case. Further extensions are under way, in particular in passing to prediction and prevention of faults prior to their occurrence.
#### Asynchronous Diagnosis.
In asynchronous partial-order based diagnosis with Petri nets, one unfolds the labelled product of a Petri net model $𝒩$ and an observed alarm pattern $𝒜$, also in Petri net form. We obtain an acyclic net giving partial order representation of the behaviors compatible with the alarm pattern. A recursive online procedure filters out those runs (configurations) that explain exactly$𝒜$. The Petri-net based approach generalizes to dynamically evolving topologies, in dynamical systems modeled by graph grammars, see 30.
#### Observability and Diagnosability
Diagnosis algorithms have to operate in contexts with low observability, i.e., in systems where many events are invisible to the supervisor. Checking observability and diagnosability for the supervised systems is therefore a crucial and non-trivial task in its own right. Analysis of the relational structure of occurrence nets allows us to check whether the system exhibits sufficient visibility to allow diagnosis. Developing efficient methods for both verification of diagnosability checking under concurrency, and the diagnosis itself for distributed, composite and asynchronous systems, is an important field for the team. In 2019, a new property, manifestability, weaker than diagnosability (dual in some sense to opacity) has been studied in the context of automata and timed automata.
#### Distribution
Distributed computation of unfoldings allows one to factor the unfolding of the global system into smaller local unfoldings, by local supervisors associated with sub-networks and communicating among each other. In 39, 42, elements of a methodology for distributed computation of unfoldings between several supervisors, underwritten by algebraic properties of the category of Petri nets have been developed. Generalizations, in particular to Graph Grammars, are still do be done.
Computing diagnosis in a distributed way is only one aspect of a much vaster topic, that of distributed diagnosis (see 37, 40). In fact, it involves a more abstract and often indirect reasoning to conclude whether or not some given invisible fault has occurred. Combination of local scenarios is in general not sufficient: the global system may have behaviors that do not reveal themselves as faulty (or, dually, non-faulty) on any local supervisor's domain (compare 29, 33). Rather, the local diagnosers have to join all information that is available to them locally, and then deduce collectively further information from the combination of their views. In particular, even the absence of fault evidence on all peers may allow to deduce fault occurrence jointly, see 43, 44. Automatizing such procedures for the supervision and management of distributed and locally monitored asynchronous systems is a long-term goal to which MExICo hopes to contribute.
### Hybrid Systems
Hybrid systems constitute a model for cyber-physical systems which integrates continuous-time dynamics (modes) governed by differential equations, and discrete transitions which switch instantaneously from one mode to another. Thanks to their ease of programming, hybrid systems have been integrated to power electronics systems, and more generally in cyber-physical systems. In order to guarantee that such systems meet their specifications, classical methods consist in finitely abstracting the systems by discretization of the (infinite) state space, and deriving automatically the appropriate mode control from the specification using standard graph techniques.
Diagnosability of hybrid systems has also been studied through an abstraction / refinement process in terms of timed automata.
### Contextual Nets
Participants: Stefan Schwoon.
Assuring the correctness of concurrent systems is notoriously difficult due to the many unforeseeable ways in which the components may interact and the resulting state-space explosion. A well-established approach to alleviate this problem is to model concurrent systems as Petri nets and analyse their unfoldings, essentially an acyclic version of the Petri net whose simpler structure permits easier analysis 38.
However, Petri nets are inadequate to model concurrent read accesses to the same resource. Such situations often arise naturally, for instance in concurrent databases or in asynchronous circuits. The encoding tricks typically used to model these cases in Petri nets make the unfolding technique inefficient. Contextual nets, which explicitly do model concurrent read accesses, address this problem. Their accurate representation of concurrency makes contextual unfoldings up to exponentially smaller in certain situations. An abstract algorithm for contextual unfoldings was first given in 31. In recent work, we further studied this subject from a theoretical and practical perspective, allowing us to develop concrete, efficient data structures and algorithms and a tool (Cunf) that improves upon existing state of the art. This work led to the PhD thesis of César Rodríguez in 2014 .
Contextual unfoldings deal well with two sources of state-space explosion: concurrency and shared resources. Recently, we proposed an improved data structure, called contextual merged processes (CMP) to deal with a third source of state-space explosion, i.e. sequences of choices. The work on CMP 45 is currently at an abstract level. In the short term, we want to put this work into practice, requiring some theoretical groundwork, as well as programming and experimentation.
Another well-known approach to verifying concurrent systems is partial-order reduction, exemplified by the tool SPIN. Although it is known that both partial-order reduction and unfoldings have their respective strengths and weaknesses, we are not aware of any conclusive comparison between the two techniques. Spin comes with a high-level modeling language having an explicit notion of processes, communication channels, and variables. Indeed, the reduction techniques implemented in Spin exploit the specific properties of these features. On the other side, while there exist highly efficient tools for unfoldings, Petri nets are a relatively general low-level formalism, so these techniques do not exploit properties of higher language features. Our work on contextual unfoldings and CMPs represents a first step to make unfoldings exploit richer models. In the long run, we wish raise the unfolding technique to a suitable high-level modelling language and develop appropriate tool support.
### 3.1.2 Process Mining
MExICo introduced anti-alignments as a tool for conformance checking. The idea of anti-alignment is to search, for a model $N$ and a log $L$, what are the runs of $N$ which differ as much as possible from all the runs in $L$. Among other uses, anti-alignments serve as witnesses for imprecisions of the model, therefore, they are used to measure precision. MExICo designed and implemented several algorithms to compute and approximate anti-alignments.
MExICo has also been contributing to clustering of log traces.
Perspectives about process mining in MExICo include model repair, i.e. design and implementation of techniques to incrementally improve models in order to make them fit better to observed logs, including when the log itself grows continuously.
Another direction is to handle models which manipulate data and real time, in order to propose more accurate representation of the log traces when the events carry some additional information (time stamps, identifiers, quantities, costs...)
## 3.2 Management of Quantitative Behavior
#### Introduction
Besides the logical functionalities of programs, the quantitative aspects of component behavior and interaction play an increasingly important role.
• Real-time properties cannot be neglected even if time is not an explicit functional issue, since transmission delays, parallelism, etc, can lead to time-outs striking, and thus change even the logical course of processes. Again, this phenomenon arises in telecommunications and web services, but also in transport systems.
• In the same contexts, probabilities need to be taken into account, for many diverse reasons such as unpredictable functionalities, or because the outcome of a computation may be governed by race conditions.
• Last but not least, constraints on cost cannot be ignored, be it in terms of money or any other limited resource, such as memory space or available CPU time.
Traditional mainframe systems were proprietary and (essentially) localized; therefore, impact of delays, unforeseen failures, etc. could be considered under the control of the system manager. It was therefore natural, in verification and control of systems, to focus on functional behavior entirely.
With the increase in size of computing system and the growing degree of compositionality and distribution, quantitative factors enter the stage:
• calling remote services and transmitting data over the web creates delays;
• remote or non-proprietary components are not “deterministic”, in the sense that their behavior is uncertain.
Time and probability are thus parameters that management of distributed systems must be able to handle; along with both, the cost of operations is often subject to restrictions, or its minimization is at least desired. The mathematical treatment of these features in distributed systems is an important challenge, which MExICo is addressing; the following describes our activities concerning probabilistic and timed systems. Note that cost optimization is not a current activity but enters the picture in several intended activities.
## 3.3 Probabilistic distributed Systems
### 3.3.1 Non-sequential probabilistic processes
Practical fault diagnosis requires to select explanations of maximal likelihood. For partial-order based diagnosis, this leads therefore to the question what the probability of a given partially ordered execution is. In Benveniste et al. 27, 46, we presented a model of stochastic processes, whose trajectories are partially ordered, based on local branching in Petri net unfoldings; an alternative and complementary model based on Markov fields is developed in 47, which takes a different view on the semantics and overcomes the first model's restrictions on applicability.
Both approaches abstract away from real time progress and randomize choices in logical time. On the other hand, the relative speed - and thus, indirectly, the real-time behavior of the system's local processes - are crucial factors determining the outcome of probabilistic choices, even if non-determinism is absent from the system.
In another line of research 34 we have studied the likelihood of occurrence of non-sequential runs under random durations in a stochastic Petri net setting. It remains to better understand the properties of the probability measures thus obtained, to relate them with the models in logical time, and exploit them e.g. in diagnosis.
### 3.3.2 Distributed Markov Decision Processes
Distributed systems featuring non-deterministic and probabilistic aspects are usually hard to analyze and, more specifically, to optimize. Furthermore, high complexity theoretical lower bounds have been established for models like partially observed Markovian decision processes and distributed partially observed Markovian decision processes. We believe that these negative results are consequences of the choice of the models rather than the intrinsic complexity of problems to be solved. Thus we plan to introduce new models in which the associated optimization problems can be solved in a more efficient way. More precisely, we start by studying connection protocols weighted by costs and we look for online and offline strategies for optimizing the mean cost to achieve the protocol. We have been cooperating on this subject with the SUMO team at INRIA Rennes; in the joint work 28; there, we strive to synthesize for a given MDP a control so as to guarantee a specific stationary behavior, rather than - as is usually done - so as to maximize some reward.
## 3.4 Large scale probabilistic systems
Addressing large-scale probabilistic systems requires to face state explosion, due to both the discrete part and the probabilistic part of the model. In order to deal with such systems, different approaches have been proposed:
• Restricting the synchronization between the components as in queuing networks allows to express the steady-state distribution of the model by an analytical formula called a product-form 32.
• Some methods that tackle with the combinatory explosion for discrete-event systems can be generalized to stochastic systems using an appropriate theory. For instance symmetry based methods have been generalized to stochastic systems with the help of aggregation theory 36.
• At last simulation, which works as soon as a stochastic operational semantic is defined, has been adapted to perform statistical model checking. Roughly speaking, it consists to produce a confidence interval for the probability that a random path fulfills a formula of some temporal logic 48 .
We want to contribute to these three axes: (1) we are looking for product-forms related to systems where synchronization are more involved (like in Petri nets 6); (2) we want to adapt methods for discrete-event systems that require some theoretical developments in the stochastic framework and, (3) we plan to address some important limitations of statistical model checking like the expressiveness of the associated logic and the handling of rare events.
## 3.5 Real time distributed systems
Nowadays, software systems largely depend on complex timing constraints and usually consist of many interacting local components. Among them, railway crossings, traffic control units, mobile phones, computer servers, and many more safety-critical systems are subject to particular quality standards. It is therefore becoming increasingly important to look at networks of timed systems, which allow real-time systems to operate in a distributed manner.
Timed automata are a well-studied formalism to describe reactive systems that come with timing constraints. For modeling distributed real-time systems, networks of timed automata have been considered, where the local clocks of the processes usually evolve at the same rate 4135. It is, however, not always adequate to assume that distributed components of a system obey a global time. Actually, there is generally no reason to assume that different timed systems in the networks refer to the same time or evolve at the same rate. Any component is rather determined by local influences such as temperature and workload.
# 4 Application domains
## 4.1 Telecommunications
MExICo’s research is motivated by problems of system management in several domains, such as:
• In the domain of service oriented computing, it is often necessary to insert some Web service into an existing orchestrated business process, e.g. to replace another component after failures. This requires to ensure, often actively, conformance to the interaction protocol. One therefore needs to synthesize adaptators for every component in order to steer its interaction with the surrounding processes.
• Still in the domain of telecommunications, the supervision of a network tends to move from out- of-band technology, with a fixed dedicated supervision infrastructure, to in-band supervision where the supervision process uses the supervised network itself. This new setting requires to revisit the existing supervision techniques using control and diagnosis tools.
Currently, we have no active cooperation on these subjects.
## 4.2 Biological Regulation Networks
Participants: Thomas Chatain, Matthias Fuegger, Stefan Haar, Serge Haddad, Juraj Kolcak, Hugues Mandon, Stefan Schwoon.
We have begun in 2014 to examine concurrency issues in systems biology, and are currently enlarging the scope of our research’s applications in this direction. To see the context, note that in recent years, a considerable shift of biologists’ interest can be observed, from the mapping of static genotypes to gene expression, i.e. the processes in which genetic information is used in producing functional products. These processes are far from being uniquely determined by the gene itself, or even jointly with static properties of the environment; rather, regulation occurs throughout the expression processes, with specific mechanisms increasing or decreasing the production of various products, and thus modulating the outcome. These regulations are central in understanding cell fate (how does the cell differenciate ? Do mutations occur ? etc), and progress there hinges on our capacity to analyse, predict, monitor and control complex and variegated processes. We have applied Petri net unfolding techniques for the efficient computation of attractors in a regulatory network; that is, to identify strongly connected reachability components that correspond to stable evolutions, e.g. of a cell that differentiates into a specific functionality (or mutation). This constitutes the starting point of a broader research with Petri net unfolding techniques in regulation. In fact, the use of ordinary Petri nets for capturing regulatory network (RN) dynamics overcomes the limitations of traditional RN models : those impose e.g. Monotonicity properties in the influence that one factor had upon another, i.e. always increasing or always decreasing, and were thus unable to cover all actual behaviours. Rather, we follow the more refined model of boolean networks of automata, where the local states of the different factors jointly detemine which state transitions are possible. For these connectors, ordinary PNs constitute a first approximation, improving greatly over the literature but leaving room for improvement in terms of introducing more refined logical connectors. Future work thus involves transcending this class of PN models. Via unfoldings, one has access – provided efficient techniques are available – to all behaviours of the model, rather than over-or under-approximations as previously. This opens the way to efficiently searching in particular for determinants of the cell fate : which attractors are reachable from a given stage, and what are the factors that decide in favor of one or the other attractor, etc. Our current research focusses cellular reprogramming on the one hand, and distributed algorithms in wild or synthetic biological systems on the other. The latter is a distributed algorithms’ view on microbiological systems, both with the goal to model and analyze existing microbiological systems as distributed systems, and to design and implement distributed algorithms in synthesized microbiological systems. Envisioned major long-term goals are drug production and medical treatment via synthesized bacterial colonies. We are approaching our goal of a distributed algorithm’s view of microbiological systems from several directions: (i) Timing plays a crucial role in microbiological systems. Similar to modern VLSI circuits, dominating loading effects and noise render classical delay models unfeasible. In previous work we showed limitations of current delay models and presented a class of new delay models, so called involution channels. In [26] we showed that involution channels are still in accordance with Newtonian physics, even in presence of noise. (ii) In [7] we analyzed metastability in circuits by a three-valued Kleene logic, presented a general technique to build circuits that can tolerate a certain degree of metastability at its inputs, and showed the presence of a computational hierarchy. Again, we expect metastability to play a crucial role in microbiological systems, as similar to modern VLSI circuits, loading effects are pronounced. (iii) We studied agreement problems in highly dynamic networks without stability guarantees [28], [27]. We expect such networks to occur in bacterial cultures where bacteria communicate by producing and sensing small signal molecules like AHL. Both works also have theoretically relevant implications: The work in [27] presents the first approximate agreement protocol in a multidimensional space with time complexity independent of the dimension, working also in presence of Byzantine faults. In [28] we proved a tight lower bound on convergence rates and time complexity of asymptotic and approximate agreement in dynamic and classical static fault models. (iv) We are currently working with Manish Kushwaha (INRA), and Thomas Nowak (LRI) on biological infection models for E. coli colonies and M13 phages.
In the context of the Escape project (PhD thesis of G.K. Aguirre Samboni, started in October 2020) we are now extending our research on causal analysis of complex biological networks to the domain of ecosystems.
## 4.3 Transportation Systems
• Autonomous Vehicles. The validation of safety properties is a crucial concern for the design of computer guided systems, in particular for automated transport systems. Our approach consists in analyzing the interactions of a randomized environment (roads, cross-sections, etc.) with a vehicle controller.
• Multimodal Transport Networks. We are interested in predicting and harnessing the propagation of perturbations across different transportation modes.
# 5 Social and environmental responsibility
## 5.1 Footprint of research activities
The carbon footprint of our activities is generic for office work, and probably strongest in traveling. While the latter came essential to a halt in 2020 because of the Covid pandemic, we believe that even in the future, intelligent use of online cooperation and communication can help limit the inevitable footprint of travel to the crucial activities of cooperation and networking, avoiding physical meetings when possible.
## 5.2 Impact of research results
With our Project ESCAPE, we are hoping for a strong impact on ecosystem analysis and management. Further, the research on biological regulation networks has the potential for enabling e.g. evaluation and design of medical therapies in epigenetic contexts.
# 6 Highlights of the year
## 6.1 QONFEST Multiconference
The QONFEST2021 Multiconference involved Benoît Barbot as general chair, Stefan Schwoon in the organisation and as webmaster, and Serge Haddad as program co-chair of CONCUR.
## 6.2 AI and Process Mining
MEXICo has made substantial scientific progress in the domains of
• learning techniques to support formal analyses, in particular extraction of context-free grammars, see point 7.4 in the 'nexwresults' sections, and
• Measuring The Precision of process models in process mining via anti-alignments, see 'new results' 7.2, 7.2 and 7.3.
# 7 New results
## 7.1 Optimized SAT encoding of conformance checking artefacts
Participants: Mathilde Boltenhagen, Thomas Chatain.
Conformance checking is a growing discipline that aims at assisting organizations in monitoring their processes. On its core, conformance checking relies on the computation of particular artefacts which enable reasoning on the relation between observed and modeled behavior. It is widely acknowledge that the computation of these artifacts is the lion’s share of conformance checking techniques. Our paper 11 shows how important conformance artefacts like alignments, anti-alignments or multi-alignments, defined over the Levenshtein edit distance, can be efficiently computed by encoding the problem as an optimized SAT instance. From a general perspective, the work advocates for a unified family of techniques that can compute conformance artefacts in the same way. The implementation of the techniques presented in this paper show capabilities for dealing with both synthetic and real-life instances, which may open the door for a fresh way of applying conformance checking in the near future.
## 7.2 Anti-Alignments – Measuring The Precision of Process Models and Event Logs
Participants: Mathilde Boltenhagen, Thomas Chatain.
Processes are a crucial artefact in organizations, since they coordinate the execution of activities so that products and services are provided. The use of models to analyse the underlying processes is a well-known practice. However, due to the complexity and continuous evolution of their processes, organizations need an effective way of analysing the relation between processes and models. Conformance checking techniques asses the suitability of a process model in representing an underlying process, observed through a collection of real executions. One important metric in conformance checking is to asses the precision of the model with respect to the observed executions, i.e., characterize the ability of the model to produce behavior unrelated to the one observed. In 12, we present the notion of anti-alignment as a concept to help unveiling runs in the model that may deviate significantly from the observed behavior. Using anti-alignments, a new metric for precision is proposed. In contrast to existing metrics, anti-alignment based precision metrics satisfy most of the required axioms highlighted in a recent publication. Moreover, a complexity analysis of the problem of computing anti-alignments is provided, which sheds light into the practicability of using anti-alignment to estimate precision. Experiments are provided that witness the validity of the concepts introduced.
## 7.3 Computing Discounted Alignments and Anti-Alignments in Process Mining.
Participants: Mathilde Boltenhagen, Thomas Chatain.
Alignments are a central notion in conformance checking. They establish the best possible connection between an observed trace and a process model, exhibiting the closest model run to the trace. Computing these alignments for huge amounts of traces, coming from big logs, is a computational bottleneck. We show in 21 that, for a slightly modified version of the distance function between traces and model runs, we significantly improve the execution time of an A*-based search algorithm. We show experimentally that the alignments found with our modified distance approximate very nicely the optimal alignments for the classical distance. In 22, by introducing a discount factor in the edit distance used for the search of anti-alignments, we obtain the first efficient algorithm to approximate them. We show how this approximation is quite accurate in practice, by comparing it with the optimal results for small instances where the optimal algorithm can also compute anti-alignments. Finally, we compare the obtained precision metric with respect to the state-of-the-art metrics in the literature for real-life examples.
## 7.4 Extracting Context-Free Grammars from Recurrent Neural Networks using Tree-Automata Learning and A* Search
In 20, we present (i) an active learning algorithm for visibly pushdown grammars and (ii) show its applicability for learning surrogate models of recurrent neural networks (RNNs) trained on context-free languages. Such surrogate models may be used for verification or explainability. Our learning algorithm makes use of the proximity of visibly pushdown languages and regular tree languages and builds on an existing learning algorithm for regular tree languages. Equivalence tests between a given RNN and a hypothesis grammar rely on a mixture of A* search and random sampling. An evaluation of our approach on a set of RNNs from the literature shows good preliminary results.
## 7.5 Commodification of accelerations for the Karp and Miller Construction
Karp and Miller’s algorithm is based on an exploration of the reachability tree of a Petri net where, the sequences of transitions with positive incidence are accelerated. The tree nodes of Karp and Miller are labeled with ω-markings representing (potentially infinite) coverability sets. This set of ω-markings allows us to decide several properties of the Petri net, such as whether a marking is coverable or whether the reachability set is finite. The edges of the Karp and Miller tree are labeled by transitions but the associated semantic is unclear which yields to a complex proof of the algorithm correctness. In 16, we introduce three concepts: abstraction, acceleration and exploration sequence. In particular, we generalize the definition of transitions to ω-transitions in order to represent accelerations by such transitions. The notion of abstraction makes it possible to greatly simplify the proof of the correctness. On the other hand, for an additional cost in memory, which we theoretically evaluated, we propose an “accelerated” variant of the Karp and Miller algorithm with an expected gain in execution time. Based on a similar idea we have accelerated (and made complete) the minimal coverability graph construction, implemented it in a tool and performed numerous promising benchmarks issued from realistic case studies and from a random generator of Petri nets.
## 7.6 Synthesis in presence of dynamic links
Participants: Matthias Függer.
The problem of distributed synthesis is to automatically generate a distributed algorithm, given a target communication network and a specification of the algorithm's correct behavior. Previous work has focused on static networks with an a priori fixed message size. This approach has two shortcomings: Recent work in distributed computing is shifting towards dynamically changing communication networks rather than static ones, and an important class of distributed algorithms are so-called full-information protocols, where nodes piggy-pack previously received messages onto current messages. In 9, we consider the synthesis problem for a system of two nodes communicating in rounds over a dynamic link whose message size is not bounded. Given a network model, i.e., a set of link directions, in each round of the execution, the adversary choses an arbitrary link from the network model, restricted only by the specification, and delivers messages according to the current link's directions. Motivated by communication buses with direct acknowledge mechanisms, we further assume that nodes are aware of which messages have been delivered. We show that the synthesis problem is decidable for a network model if and only if the network model does not contain the empty link that dismisses both nodes' messages. We then extend the characterization to sequences of communication links that may contain empty links. We show that the synthesis problem is decidable in this case if and only if the number of consecutive empty links in all possible sequences is uniformly bounded from above.
## 7.7 Distributed computation with continual population growth
Participants: Matthias Függer, Da-Jung Cho.
Computing via synthetically engineered bacteria is a vibrant and active field with numerous applications in bio-production, bio-sensing, and medicine. Motivated by the lack of robustness and by resource limitation inside single cells, distributed approaches with communication among bacteria have recently gained in interest. In 13, we focus on the problem of population growth happening concurrently, and possibly interfering, with the desired bio-computation. Specifically, we present a fast protocol in systems with continuous population growth for the majority consensus problem and prove that it correctly identifies the initial majority among two inputs with high probability if the initial difference grows with the square root of n log n, where n is the total initial population. We also present a fast protocol that correctly computes the Nand of two inputs with high probability. By combining Nand gates with the majority consensus protocol as an amplifier, it is possible to compute arbitrary Boolean functions. Finally, we extend the protocols to several biologically relevant settings. We simulate a plausible implementation of a noisy Nand gate with engineered bacteria. In the context of continuous cultures with a constant outflow and a constant inflow of fresh media, we demonstrate that majority consensus is achieved only if the flow is slower than the maximum growth rate. Simulations suggest that flow increases consensus time over a wide parameter range. The proposed protocols help set the stage for bio-engineered distributed computation that directly addresses continuous stochastic population growth.
## 7.8 Generation of a fault-tolerant clock through redundant crystal oscillator
Participants: Matthias Függer.
Having a precise and stable clock that is still fault tolerant is a fundamental prerequisite in safety critical real-time systems. However, combining redundant independent clock sources to form a unified fault-tolerant clock supply is non-trivial, especially when redundant clock outputs are required-e.g., for supplying the replicated nodes within a TMR architecture through a clock network that does not suffer from a single point of failure. Having these outputs fail independent but still keeping them tightly synchronized is highly desirable, as it substantially eases the design of the overall architecture. In 15 we address exactly this challenge. Our approach extends an existing, ring-oscillator like distributed clock generation scheme by augmenting each of its constituent nodes with a stable clock reference. We introduce the appropriately modified algorithm and illustrate its operation by simulation experiments. These experiments further demonstrate that the four clock outputs of our circuit do not share a single point of failure, have small and bounded skew, remain stabilized to one crystal source during normal operation, do not propagate glitches from one failed clock to a correct one, and only exhibit slightly extended clock cycles during a short stabilization period after a component failure. In addition we give a rigorous formal proof for the correctness of the algorithm on an abstraction level that is close to the implementation.
## 7.9 Tight Bounds for Asymptotic and Approximate Consensus.
Participants: Matthias Függer.
Agreeing on a common value among a set of agents is a fundamental problem in distributed computing, which occurs in several variants: In contrast to exact consensus, approximate variants are studied in systems where exact agreement is not possible or required, e.g., in man-made distributed control systems and in the analysis of natural distributed systems, such as bird flocking and opinion dynamics. In 18, we study the time complexity of two classical agreement problems: non-terminating asymptotic consensus and terminating approximate consensus. Asymptotic consensus, requires agents to repeatedly set their outputs such that the outputs converge to a common value within the convex hull of initial values; approximate consensus requires agents to eventually stop setting their outputs, which must then lie within a predefined distance of each other. We prove tight lower bounds on the contraction ratios of asymptotic consensus algorithms subject to oblivious message adversaries, from which we deduce bounds on the time complexity of approximate consensus algorithms. In particular, the obtained bounds show optimality of asymptotic and approximate consensus algorithms presented by Charron-Bost et al. (ICALP'16) for certain systems, including the strongest oblivious message adversary in which asymptotic and approximate consensus are solvable. As a corollary we also obtain asymptotically tight bounds for asymptotic consensus in the classical asynchronous model with crashes. Central to the lower-bound proofs is an extended notion of valency, the set of reachable limits of an asymptotic consensus algorithm starting from a given configuration. We further relate topological properties of valencies to the solvability of exact consensus, shedding some light on the relation of these three fundamental problems in dynamic networks.
## 7.10 A Composable Glitch-Aware Delay Model
Participants: Matthias Függer.
In 25, we introduce the Composable Involution Delay Model (CIDM) for fast and accurate digital simulation. It is based on the Involution Delay Model (IDM) [Függer et al., IEEE TCAD 2020], which has been shown to be the only existing candidate model for faithful glitch propagation. The IDM, however, has shortcomings that limit its applicability. Our CIDM thus reduces the characterization effort by allowing independent discretization thresholds, improves composability and increases the modeling power by exposing canceled pulse trains at the gate interconnect. We formally show that, despite these improvements, the CIDM still retains the IDM's faithfulness.
# 8 Partnerships and cooperations
## 8.1 International initiatives
### 8.1.1 Participation in International Programs
#### LearNNiFy
• Title:
New Challenges for Recurrent Neural Networks and Grammatical Inference
• Partner Institution(s):
• MPI Kaiserslautern (D. Neider)
• Univ. Lübeck (M. Leucker)
### 8.1.2 Visits to international teams
• Stefan Haar visited the Discrete Biomathematics group of Prof. Heike Siebert at Freie Universität Berlin, Germany, from November 15 to 19.
## 8.2 National initiatives
• Thomas Chatain, Stefan Haar, Serge Haddad, Juraj Kolçák and Stefan Schwoon have participated in the ANR Project ALGORECELL.
• Matthias Függer has participated in the ANR project FREDDA on verification and synthesis of distributed algorithms and led the INS2I/CNRS funded Emergence project Bacterial CONsensus (BACON), 2020-2021. He now leads the ANR project Distributed Algorithms for Microbiological Systems that has started on Oct.1st, 2021, and participates in the CARE (UPSaclay-ENS PSaclay)-funded project on Efficient Test Strategies for SARS-CoV-2 in Healthcare Institutions (ETSHI).
## 8.3 Regional initiatives
• Giann Karlo Aguirre Sambonì and Stefan Haar are participating in the DIGICOSME project EcoSystem Causal Analysis using PEtri net unfoldings (ESCAPE) with Franck Pommereau at Univ. Evry.
# 9 Dissemination
Participants: Thomas Chatain, Philippe Dague, Matthias Függer, Stefan Haar, Serge Haddad, Stefan Schwoon.
## 9.1 Promoting scientific activities
### 9.1.1 Scientific events: organisation
#### General chair, scientific chair
• Benoît Barbot was general chair of the QONFEST2021 multiconference.
• Matthias Függer was Topic chair for Digital/System Design at IEEE DDECS 2021 and a member of the steering commitee for IEEE ASYNC.
#### Member of the organizing committees
• Stefan Schwoon participated in the organisation of the QONFEST 2021 multiconference, in particular as webmaster.
.
### 9.1.4 Invited talks
• Thomas Chatain was a member of the jury for the SIF-Gilles Kahn award for outstanding PhD theses, and is the head of the Interactions pole at the LMF lab.
• Philippe Dague is a member of the selection board for the UDOPIA 2021 PhD thesis funding scheme.
• Matthias Függer is the head of the the LMF group Concurrent and Distributed Systems , elected member of the laboratory council for LMF and in charge of European contracts at LMF.
• Stefan Haar is adjunct director for research of the Graduate School Computer Science at Université Paris-Saclay, and head of the Computer Science and Biology axis at the LMF lab.
## 9.2 Teaching - Supervision - Juries
### 9.2.1 Teaching
• Mathias Fuegger; Master's level:
• Initiation à la recherche¸ 10 h EQTD, M1, ENS Paris-Saclay, France
• Natural algorithms at Université Paris-Saclay. With Thomas Nowak.
• Metastability-containing Synchronization Circuits. With Christoph Lenzen, Danny Dolev, Moti Medina, Ian W. Jones, and Johannes Bund. At CISPA, Germany.
• Stefan Haar , Master :
• Analyse de la dynamique des systèmes biologiques¸ 24 h EQTD, M1, Université PAris-Saclay, France
• Serge Haddad is head of the Computer Science department of ENS Paris-Saclay. He teaches basic and advanced algorithmics (L3) and probabilistic features of computer science (M1).
• Stefan Schwoon
• Responsable L3 Informatique, ENS Paris-Saclay
• Teaching in M1 MPRI : cours Initiation à la Vérification (22,5h)
• L3 Info : Architecture et Système (45h), project Programmation orienté objet (15h), TD Langages Formels (22,5h)
• Aggrétation Maths Option Informatique: Algorithmique (22,5h)
### 9.2.2 Supervision
• Thomas Chatain was a supervisor (75 %, with Josep Carmona, Barcelona) of the thesis of Mathilde Boltenhagen on Process Instance Clustering based on Conformance Checking Artefacts, successfully defended on October 21, 2021 at ENS Paris-Saclay.
• Matthias Függer co-supervises, with Janna Burman and Thomas Nowak) the PhD thesis of Fabricio Cravo on Distributed Circuit Design for Bacterial Systems, started on Oct 1st, 2021 (ED STIC funded). He also supervised the master's internship of Baudouin Pilet on Non-Markovian Growth Models of Bacteria.
• Serge HADDAD is co-supervising, with Alain Finkel, the PhD thesis of Igor Khmelnitsky on Verification of infinite-state systems and machine learning, whose defence is scheduled for Jan 27, 2022.
• Stefan Haar co-supervised (with Loic Paulevé) the PhD the thesis of Juraj Kolçák on Unfoldings and Abstract Interpretation for Parametric Biological Regulatory Networks 26, successfully defended at ENS Paris-Saclay on July 6, 2021. He currently supervises, with Franck Pommereau at Univ. Evry, the thesis of Giann Karlo Aguirre Samboní, started on Oct1, 2020, on Ecosystem causal analysis using Petri net unfoldings.
• Lina Ye (70 % ) and Philippe Dague (30 % ) co-supervise the thesis of Lulu He on manifestability analysis using SMT solvers; started in 2019, the thesis is scheduled for defence in 2022.
### 9.2.3 Juries
• Thomas Chatain was a reviewer of the PhD Thesis of Govind RajanbabuonPartial order reduction for timed systems at Université de Bordeaux, on June 16, 2021.
# 10 Scientific production
## 10.1 Major publications
• 1 articleB.Béatrice Bérard, S.Stefan Haar, S.Sylvain Schmitz and S.Stefan Schwoon. The Complexity of Diagnosability and Opacity Verification for Petri Nets.Fundamenta Informaticae16142018, 317-349
• 2 inproceedingsT.Thomas Chatain, S.Stefan Haar, L.Loïg Jezequel, L.Loïc Paulevé and S.Stefan Schwoon. Characterization of Reachable Attractors Using Petri Net Unfoldings.CMSB 20148859LNCS/LNBIManchester, United KingdomSpringer International PublishingNovember 2014, 14
• 3 articleT.Thomas Chatain, S.Stefan Haar, J.Juraj Kolčák, L.Loïc Paulevé and A.Aalok Thakkar. Concurrency in Boolean networks.Natural Computing2019
• 4 articleS.Stephan Friedrichs, M.Matthias Függer and C.Christoph Lenzen. Metastability-Containing Circuits.IEEE Transactions on Computers6782018
• 5 articleS.Stefan Haar, S.Serge Haddad, T.Tarek Melliti and S.Stefan Schwoon. Optimal constructions for active diagnosis.Journal of Computer and System Sciences8312017, 101-120
• 6 articleS.Serge Haddad, J.Jean Mairesse and H.-T.Hoang-Thach Nguyen. Synthesis and Analysis of Product-form Petri Nets.Fundamenta Informaticae1221-22013, 147-172
• 7 articleJ.Juraj Kolčák, D.David Šafránek, S.Stefan Haar and L.Loïc Paulevé. Parameter Space Abstraction and Unfolding Semantics of Discrete Regulatory Networks.Theoretical Computer Science7652019, 120-144
• 8 articleL.Loïc Paulevé, J.Juraj Kolčák, T.Thomas Chatain and S.Stefan Haar. Reconciling Qualitative, Abstract, and Scalable Modeling of Biological Networks.Nature Communications112020
## 10.2 Publications of the year
### International journals
• 9 articleSynthesis in presence of dynamic links.Information and ComputationDecember 2021, 104856
• 10 articleB.Béatrice Bérard, S.Serge Haddad, C.Claudine Picaronny, M.Mohab Safey El Din and M.Mathieu Sassolas. Polynomial interrupt timed automata: Verification and expressiveness.Information and Computation277April 2021, 104580
• 11 articleM.Mathilde Boltenhagen, T.Thomas Chatain and J.Josep Carmona. Optimized SAT encoding of conformance checking artefacts.Computing1031January 2021, 29-50
• 12 articleT.Thomas Chatain, M.Mathilde Boltenhagen and J.Josep Carmona. Anti-Alignments -- Measuring The Precision of Process Models and Event Logs.Information SystemsMay 2021
• 13 articleD.-J.Da-Jung Cho, M.Matthias Függer, C.Corbin Hopper, M.Manish Kushwaha, T.Thomas Nowak and Q.Quentin Soubeyran. Distributed computation with continual population growth.Distributed ComputingOctober 2021
• 14 articleP.Philippe Dague. Metabolic Pathway Analysis in the Presence of Biological Constraints.Computation910October 2021, 111
• 15 articleW.Wolfgang Dür, M.Matthias Függer and A.Andreas Steininger. Generation of a fault-tolerant clock through redundant crystal oscillators.Microelectronics Reliability120May 2021, 114088
• 16 articleA.Alain Finkel, S.Serge Haddad and I.Igor Khmelnitsky. Commodification of accelerations for the Karp and Miller Construction..Discrete Event Dynamic Systems2021
• 17 articleM.Matthias Függer, A.Attila Kinali, C.Christoph Lenzen and B.Ben Wiederhake. Fast All-Digital Clock Frequency Adaptation Circuit for Voltage Droop Tolerance.IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems2022, 1-1
• 18 articleM.Matthias Függer, T.Thomas Nowak and M.Manfred Schwarz. Tight Bounds for Asymptotic and Approximate Consensus.Journal of the ACM (JACM)October 2021
• 19 articleD.Daniel Öhlinger, J.Jürgen Maier, M.Matthias Függer and U.Ulrich Schmid. The Involution Tool for Accurate Digital Timing and Power Analysis.Systems Integration76January 2021, 87-98
### International peer-reviewed conferences
• 20 inproceedingsB.Benoît Barbot, B.Benedikt Bollig, A.Alain Finkel, S.Serge Haddad, I.Igor Khmelnitsky, M.Martin Leucker, D.Daniel Neider, R.Rajarshi Roy and L.Lina Ye. Extracting Context-Free Grammars from Recurrent Neural Networks using Tree-Automata Learning and A* Search.ICGI 2021 - 15th International Conference on Grammatical InferenceProceedings of the 15th International Conference on Grammatical Inference (ICGI 2020/21)New York City / Virtual, United StatesAugust 2021
• 21 inproceedingsM.Mathilde Boltenhagen, T.Thomas Chatain and J.Josep Carmona. A Discounted Cost Function for Fast Alignments of Business Processes.BPM 2021 - 19th International Conference on Business Process ManagementRome, FranceSeptember 2021
• 22 inproceedingsM.Mathilde Boltenhagen, T.Thomas Chatain and J.Josep Carmona. An A*-Algorithm for Computing Discounted Anti-Alignments in Process Mining.3rd International Conference on Process Mining3rd International Conference on Process MiningEindhoven, NetherlandsOctober 2021
• 23 inproceedingsS.Serge Haddad and S.Susanna Donatelli. Expressiveness and Conciseness of Timed Automata for the Verification of Stochastic Models.Proceedings of the 14th International Conference on Language and Automata Theory and Applications (LATA'20)LATA 2020 2021 - 14th et 15th International Conference on Language and Automata Theory and ApplicationsMilan, ItalySeptember 2021
• 24 inproceedingsI.Igor Khmelnitsky, D.Daniel Neider, R.Rajarshi Roy, X.Xuan Xie, B.Benoît Barbot, B.Benedikt Bollig, A.Alain Finkel, S.Serge Haddad, M.Martin Leucker and L.Lina Ye. Property-Directed Verification and Robustness Certification of Recurrent Neural Networks.19th International Symposium on Automated Technology for Verification and Analysis (ATVA 2021)Proceedings of the 19th International Symposium on Automated Technology for Verification and Analysis (ATVA 2021)Gold Coast (Online), AustraliaOctober 2021
• 25 inproceedingsJ.Jürgen Maier, D.Daniel Öhlinger, U.Ulrich Schmid, M.Matthias Függer and T.Thomas Nowak. A Composable Glitch-Aware Delay Model.GLSVLSI '21: Great Lakes Symposium on VLSI 2021Virtual Event, United StatesACMJune 2021, 147-154
### Doctoral dissertations and habilitation theses
• 26 thesisJ.Juraj Kolčák. Unfoldings and Abstract Interpretation for Parametric Biological Regulatory Networks.ENS Paris-SaclayJuly 2021
## 10.3 Cited publications
• 27 articleA.~Benveniste, É.Éric Fabre and S.~Haar. Markov Nets: Probabilistic Models for distributed and concurrent Systems.IEEE Transactions on Automatic Control48 (11)Extended version: IRISA Research Report 15382003, 1936-1950
• 28 inproceedingsS.S. Akshay, N.Nathalie Bertrand, S.Serge Haddad and L.Loic Helouet. The steady-state control problem for Markov decision processes.Qest 20138054Buenos Aires, ArgentinaSpringerSeptember 2013, 290-304
• 29 articleR.R. Alur, K.K. Etessami and M.M. Yannakakis. Realizability and Verification of MSC Graphs.Theor. Comput. Sci.33112005, 97--114
• 30 articleP.P. Baldan, T.Thomas Chatain, S.Stefan Haar and B.Barbara König. Unfolding-based Diagnosis of Systems with an Evolving Topology.Information and Computation20810October 2010, 1169-1192
• 31 articleP.Paolo Baldan, A.Andrea Corradini, B.Barbara König and S.Stefan Schwoon. McMillan's complete prefix for contextual nets (long vers).Transactions on Petri Nets and Other Models of Concurrency1Volume 5100 of Lecture Notes in Computer ScienceNovember 2008, 199--220
• 32 articleF.Forest Baskett, K. M.K. Mani Chandy, R. R.Richard R. Muntz and F. G.Fernando G. Palacios. Open, Closed, and Mixed Networks of Queues with Different Classes of Customers.J. ACM222April 1975, 248--260
• 33 inproceedingsP.Puneet Bhateja, P.P. Gastin, M.M. Mukund and K.K. Narayan Kumar. Local testing of message sequence charts is difficult.Proceedings of the 16th International Symposium on Fundamentals of Computation Theory (FCT'07)4639Lecture Notes in Computer ScienceBudapest, HungarySpringerAugust 2007, 76-87
• 34 inproceedingsA.Anne Bouillard, S.Stefan Haar and S.Sidney Rosario. Critical paths in the Partial Order Unfolding of a Stochastic Petri Net.Proceedings of the 7th International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS'09)5813Lecture Notes in Computer ScienceBudapest, HungarySpringerSeptember 2009, 43-57
• 35 inproceedingsP.P. Bouyer, S.Serge Haddad and P.-A.Pierre-Alain Reynier. Timed Unfoldings for Networks of Timed Automata.Proceedings of the 4th International Symposium on Automated Technology for Verification and Analysis (ATVA'06)4218Lecture Notes in Computer ScienceBeijing, ROCSpringerOctober 2006, 292-306
• 36 articleG.Giovanni Chiola, C.Claude Dutheillet, G.Giuliana Franceschinis and S.Serge Haddad. Stochastic Well-Formed Colored Nets and Symmetric Modeling Applications.IEEE Transactions on Computers4211November 1993, 1343-1360
• 37 articleR.Rami Debouk and D.Demosthenis Teneketzis. Coordinated decentralized protocols for failure diagnosis of discrete-event systems.Journal of Discrete Event Dynamical Systems: Theory and Application102000, 33--86
• 38 bookJ.Javier Esparza and K.Keijo Heljanko. Unfoldings - A Partial-Order Approach to Model Checking.EATCS Monographs in Theoretical Computer ScienceSpringer2008
• 39 articleÉ.Éric Fabre, A.~Benveniste, C.~Jard and S.~Haar. Distributed monitoring of concurrent and asynchronous systems.Discrete Event Dynamic Systems: theory and application15 (1)Preliminary version: Proc.~CONCUR 2003, LNCS 2761, pp.1--28, Springer2005, 33-84
• 40 articleS.S. Lafortune, Y.Y. Wang and T.-S.T.-S. Yoo. Diagnostic Decentralisé Des Systèmes A Evénements Discrets.Journal Europeen des Systèmes Automatisés (RS-JESA)9999August 2005, 95--110
• 41 inproceedingsK. G.K. G Larsen, P.P. Pettersson and W.W. Yi. Compositional and symbolic model-checking of real-time systems.Proc. of RTSS 1995IEEE Computer Society1995, 76-89
• 42 inproceedingsP.~Baldan, S.~Haar and B.~Koenig. Distributed Unfolding of Petri Nets.Proc.FOSSACS 20063921LNCSExtended version: Technical Report CS-2006-1. Department of Computer Science, University Ca' Foscari of VeniceSpringer2006, 126-141
• 43 articleL.Laurie Ricker and K.Karen Rudie. Know Means No: Incorporating Knowledge into Discrete-Event Control Systems.IEEE Transactions on Automatic Control459September 2000, 1656--1668
• 44 articleL.Laurie Ricker and K.Karen Rudie. Knowledge Is a Terrible Thing to Waste: Using Inference in Discrete-Event Control Problems.IEEE Transactions on Automatic Control523MarchSeptember 2007, 428--441
• 45 inproceedingsC.César Rodríguez, S.Stefan Schwoon and V.Victor Khomenko. Contextual Merged Processes.34th International Conference on Applications and Theory of Petri Nets (ICATPN'13)7927Lecture Notes in Computer ScienceItalySpringer2013, 29-48
• 46 inproceedingsS.~Abbes, A.~Benveniste and S.~Haar. A Petri net model for distributed estimation.Proc.~MTNS 2004, Sixteenth International Symposium on Mathematical Theory of Networks and Systems, Louvain (Belgium), ISBN 90-5682-517-82004
• 47 articleS.~Haar. Probabilistic Cluster Unfoldings.Fundamenta Informaticae53 (3-4)2003, 281-314
• 48 articleH. L.H\aakan L. S. Younes and R. G.Reid G. Simmons. Statistical probabilistic model checking with a focus on time-bounded properties.Inf. Comput.2049September 2006, 1368--1409 | 2022-12-07 20:55:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 12, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.451812744140625, "perplexity": 3723.825745711699}, "config": {"markdown_headings": true, "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-2022-49/segments/1669446711218.21/warc/CC-MAIN-20221207185519-20221207215519-00632.warc.gz"} |
https://plainmath.net/16355/8%26times-chessboard-square-cell-like-square-which-measures-%26eta-inches | Question
# An 8×8 chessboard has a square cell (or box, like square a1) which measures η inches on one side.
Complex numbers
An $$8\times8$$ chessboard has a square cell (or box, like square a1) which measures $$\beta$$ inches on one side.
Express the two possible moves of your knight in vector form with units in inches.
What are the distances of each possible move from your original position in inches?
What are their angles from the horizontal (x-axis)?
2021-07-22
This is applicable for every $$n\times n$$ square board.
The total number of squares for $$n\times n$$ square board can be calculated as
$$1^{2}+2^{2}+3^{2}+\cdots+n^{2}$$
So for a Chess Board with $$8\times8$$ squares total no.of squares
$$= 1^{2}+2^{2}+3^{2}+\cdots+8^{2} = 204$$
Thus there are 204 Squares in a $$8\times8$$ Chess Board. | 2021-08-01 19:09:26 | {"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": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6378921866416931, "perplexity": 1720.4286578805797}, "config": {"markdown_headings": true, "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-2021-31/segments/1627046154219.62/warc/CC-MAIN-20210801190212-20210801220212-00665.warc.gz"} |
http://qed.econ.queensu.ca/walras/custom/300/351B/notes/mul_05.htm | ## E. Random Variables and Matrix Notation
To derive the statistical properties of OLS estimates, we must define the notion of a random vector along with the notion of the mean and variance of a random vector.
#### Random matrix
A random matrix is a matrix of random variables. For example the vector of disturbance terms is a random vector since each element of the vector is a random variable. A constant matrix is, of course, a special type of random matrix in the same sense that a constant is a special case of a random variable that does not vary across points in the sample space.
#### Expectation of a random matrix V (m x r).
The expectation of a random matrix is the matrix of expectations of each random variable in the random vector. That is, let V be a m x r random matrix, and let denote the random variable in the ith row and jth column of V. Then
Note that expectation is still a linear operator when defined this way. That is, if A is a n x m matrix of constants and C is a n x r vector of constants, then
E[AV + C] = AE[V] + C
Notice that m does not have to equal r. That is, the transformation matrix A may change the dimensions of the random matrix. AV is a n x r random matrix, not a m x r. The proof of this result requires you to write out what an element of the matrix AV+C looks like, apply the expectation operator to it, and then see that the result is exactly the same as if you had written out AE[V] + C.
#### Variance of a random vector
Let v by m x 1. Then Var(v) E[ (v-E[v])(v-E[v])' ] This generalizes the notion of covariance, which itself generalized the notion of variance. Notice that (v-E[v])(v-E[v])' is a m x m matrix (when v is m x 1). So Var(v) is always a square matrix. If we multiply (v-E[v])(v-E[v])' out, we can see that the ith row, jth column of it contains . The expectation of this scalar random variable is by definition:
So each element of Var(v) is a covariance. The diagonal elements of Var(v) are simply the variances of the corresponding elements of the v vector. Since Cov(r,s) = Cov(s,r), the matrix Var(v) is symmetric. Summing this up,
#### Variance of a linear transformation
Let v be m x 1 random vector and A a n x m matrix of constants. Then
Var[Av] = E[ (Av-AE[v])(Av-AE[v])' ] = E[ A(v-E[v])(v-E[v])'A'] = AVar[v]A'
This result generalizes the simpler result that when multiplying a random variable by a constant it changes the variance by the square of the constant. In fact, if m=n=1, then we simply get back the old formula Var(av) = a&149;Var(v).
Here's an example. Let with
This means that v contains two random variables that have zero covariance. (They might be statistically independent of each other as well, since independence implies zero covariance). Let A = (2 -2). Then
is the random variable that is simply twice the difference of the two random variables in the vector v. From the result above,
This is exactly the formula we would have used without the matrix notation, since the weighted sum of zero-covariance random variables is the sum of the variances multiplied by the square of the weights. Keeping track of variances and covariances in matrices is very convenient.
#### Assumptions of the LRM in Matrix Notation Assumption A2
E[u]=0
• Assumption A3
The matrix X is fixed (non-random) across samples.
• Assumption A4
E[u] = 0, where 0 is a N x 1 vector containing 0s.
• Assumption A5-A6
Var[u] = I
In words: the variance matrix for u is diagonal (0 covariance across observations) and has equal elements on the diagonal (equal variance).
• Assumption A7
In words: The u vector is a normal vector, in the sense that each element of u is normally distributed. Notice that the only change between simple and multiple regression is the change in the dimension of X. So if we had started out with matrix notation we would have been able to use these forms of the assumptions from the start. That is, A4 above is the same as the A4, just using different notation. The same is true of A3 through A7, the only difference being that A5 and A6 can stated together.
Now we can start analyzing the statistical properties of OLS estimate and .
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Document Last revised: 1997/1/5 | 2022-05-26 15:20:45 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9299894571304321, "perplexity": 461.47423755069366}, "config": {"markdown_headings": true, "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-2022-21/segments/1652662606992.69/warc/CC-MAIN-20220526131456-20220526161456-00099.warc.gz"} |
https://zbmath.org/?q=ut%3Asolid-liquid+phase+transition | ## Found 24 Documents (Results 1–24)
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### Numerical study of crystal growth in reaction-diffusion systems using front tracking. (English)Zbl 07442370
Wood, David R. (ed.) et al., 2019–20 MATRIX annals. Cham: Springer. MATRIX Book Ser. 4, 461-471 (2021).
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### SPH simulation of high-volume rapid landslides triggered by earthquakes based on a unified constitutive model. II: Solid-liquid-like phase transition and flow-like landslides. (English)Zbl 1476.74105
MSC: 74L05 65N75 74N10
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### Two-dimensional steady-state solutions of anisotropic total variation flows associated with phase transitions. (English)Zbl 1221.35056
Aiki, T. (ed.) et al., Current advances in nonlinear analysis and related topics. Collected papers of the conference on nonlinear evolution equations and related topics, Tokyo, Japan, October 10–12, 2009, the 4th Polish-Japanese days on current advances in applied nonlinear analysis and mathematical modelling issues, Warsaw, Poland, May 18–21, 2009 and the RIMS conference on nonlinear evolution equations and mathematical modeling, Kyoto, Japan, October 20–24, 2009. Tokyo: Gakkōtosho (ISBN 978-4-7625-0457-0/hbk). GAKUTO International Series. Mathematical Sciences and Applications 32, 483-504 (2010).
MSC: 35B35 35K90 80A22
### Comparison between molecular dynamics and Monte Carlo descriptions of solid-liquid phase-transition of Lennard-Jones fluids. (English)Zbl 1186.82029
MSC: 82B26 82B80 82D15
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### An efficient numerical method for solid-liquid transitions in optical rewritable recording. (English)Zbl 1156.76413
MSC: 76M10 76T99 80A22
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### Stability for phase field systems involving indefinite surface tension coefficients. (English)Zbl 1102.35310
Colli, Pierluigi (ed.) et al., Dissipative phase transitions. Hackensack, NJ: World Scientific (ISBN 981-256-650-3/hbk). Series on Advances in Mathematics for Applied Sciences 71, 269-288 (2006).
MSC: 35B35 35K60 35K50
### Weak solutions for Stefan problems with convections. (English)Zbl 1105.35147
Colli, Pierluigi (ed.) et al., Dissipative phase transitions. Hackensack, NJ: World Scientific (ISBN 981-256-650-3/hbk). Series on Advances in Mathematics for Applied Sciences 71, 87-100 (2006).
MSC: 35R35 80A22
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### Dynamics of hydrate formation during gas production. (Russian. English summary)Zbl 1015.76081
MSC: 76S05 76T99 80A22 80A20 76M20
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### A phase-field model with temperature dependent constraint. (English)Zbl 0980.35074
MSC: 35K60 35K50 76T10 80A22 82C26
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### Phase transitions and hysteresis. (Italian)Zbl 1001.74091
Proceedings of the 16th national congress of the Italian Mathematical Society, Napoli, Italy, September 13-18, 1999. Bologna: Unione Matematica Italiana, 333-379 (2000).
Reviewer: G.A.Maugin (Paris)
MSC: 74N30 80A22
### Diffuse interface model of solid-liquid phase transition with internal energy as an order parameter. (English)Zbl 0962.74045
MSC: 74N25 74A15 80A22
### Asymptotic analysis of a phase-field model with memory. (English)Zbl 0929.35185
Athanasopoulos, I. (ed.) et al., Free boundary problems: theory and applications. Proceedings of the conference, Crete, Greece, June 8–14, 1997. Boca Raton, FL: Chapman & Hall/CRC. Chapman Hall/CRC Res. Notes Math. 409, 273-286 (1999).
MSC: 35R35 80A22
### Periodic solutions for phase transition models. (English)Zbl 0922.35067
Reviewer: M.Kučera (Praha)
MSC: 35K50 47H04 35K60 35Q35 35B10 47H20
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### $$\omega$$-limit sets for solution of phase field equations with constraints under nonlinear dynamic boundary conditions. (English)Zbl 0908.35019
Nishiura, Y. (ed.) et al., Proceedings of the international conference on asymptotics in nonlinear diffusive systems – towards the understanding of singularities in dissipative structures –, Sendai, Japan, July 28–August 1, 1997. Sendai: Tohoku Univ. Tohoku Math. Publ. 8, 253-256 (1998).
MSC: 35B40 35K60
### A problem of Allen-Cahn type for $$p$$-Laplacian. (English)Zbl 0908.35069
Nishiura, Y. (ed.) et al., Proceedings of the international conference on asymptotics in nonlinear diffusive systems – towards the understanding of singularities in dissipative structures –, Sendai, Japan, July 28–August 1, 1997. Sendai: Tohoku Univ. Tohoku Math. Publ. 8, 229-233 (1998).
MSC: 35K65 35B40 35B35
### Asymptotic convergence in models for phase change problems. (English)Zbl 0873.35012
Kenmochi, N. (ed.) et al., Proceedings of the Banach Center minisemester on nonlinear analysis and applications, Warsaw, Poland, November 14 – December 15, 1994. Tokyo: Gakkōtosho Co., Ltd. GAKUTO Int. Ser., Math. Sci. Appl. 7, 361-385 (1995).
Reviewer: M.A.Vivaldi (Roma)
MSC: 35B40 35K60 35K50
### Continuum theory of thermally induced phase transitions based on an order parameter. (English)Zbl 0793.35049
MSC: 35K40 35K55 80A22
Full Text:
### A new implicit solution procedure for multidimensional finite-difference modeling of the Stefan problem. (English)Zbl 0582.76106
MSC: 76T99 76M99 80A20
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http://www.ck12.org/book/CK-12-Middle-School-Math-Concepts-Grade-7/section/6.18/ | <meta http-equiv="refresh" content="1; url=/nojavascript/"> Prices Involving Sales Tax | CK-12 Foundation
# 6.18: Prices Involving Sales Tax
Difficulty Level: At Grade Created by: CK-12
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Have you ever had to calculate a tip in a restaurant?
Sasha and Keith went out for lunch. Their total bill was $16.60. Both Sasha and Keith were puzzled when it came to calculating the tip. They decided to give the waiter a 15% tip. Do you know how to calculate this? What range would be an acceptable tip? This Concept is about estimate appropriate tips. You will learn how to tackle this problem. ### Guidance When you go to a restaurant, it is customary to tip the server. If you have help at the airport, it is customary to tip the server. If you have someone carry your bags at a hotel, it is customary to tip the bellhop. What is a tip? A tip is an amount of money that is given to a worker such as a waiter or waitress who performs a service for you. A common tip amount is 15% of the cost of the meal or other service. Since you don’t usually calculate a tip exactly, we can estimate the amount of a tip. Follow these steps to estimate a 15% tip Step 1: Round the total bill to the nearest whole dollar amount. Step 2: Find 10% of this amount by moving the decimal point one place to the left. Step 3: Find half of the amount you found in Step 2. This will give you 5% of the total cost. Step 4: Add the 10% amount and the 5% amount together. Take a few minutes to write these steps in your notebook. Now let’s apply these steps to a few situations. Estimate a 15% tip on a meal whose cost is$29.75.
Step 1: Round $29.75 to$30.
Step 2: 10% of $\ 30 = \ 3$
Step 3: Half of $\ 3 = \ 1.50$
Step 4: $\ 3 + \ 1.50 = \ 4.50$
A 15% tip on a meal whose cost is $29.75 is about$4.50.
Estimate a 20% tip on a meal whose cost is $54.15. Since the tip is about 20%, you can find 10% and then double it. Step 1: Round$54.15 to $54. Step 2: 10% of $\ 54 = \ 5.40$ Step 3: 20% of $\ 5.40 = 2 \times \ 5.40 = \ 10.80$ A 20% tip on a meal whose cost is$54.15 is about $10.80. Estimate a 15% tip for each bill. Provide a range in your answer. #### Example A$29.00
Solution: $\3.00 - \3.50$
$16.00 Solution: $\2.00 -\2.50$ #### Example C$55.00
Solution: $\8.00 - \8.50$
Here is the original problem once again.
Sasha and Keith went out for lunch. Their total bill was $16.60. Both Sasha and Keith were puzzled when it came to calculating the tip. They decided to give the waiter a 15% tip. Do you know how to calculate this? What range would be an acceptable tip? To figure this out, first let's round up. $16.60$ becomes $17.00$ Now take 10% of that figure. $1.70$ Half of that is $.85$ . If we add the two together, we get an estimate of $2.55$ . A reasonable tip would be between $\2.50 - \3.00$ . ### Guided Practice Here is one for you to try on your own. Estimate a 20% tip on a restaurant bill of$38.95.
You can start by thinking about 10% of this bill. Since that involves simply moving the decimal point, we can say that the estimate of 10% is $\3.85$ .
Now 20% is double that.
We can say that an estimate of a 20% tip is in a range from $\7.50 - \8.00$ .
### Video Review
Here is a video for review.
### Explore More
Directions: Estimate a tip of 20% for each amount.
1. A tip on $15.00 2. A tip on$28.00
3. A tip on $25.00 4. A tip on$35.00
5. A tip on $45.00 6. A tip on$50.00
7. A tip on $90.00 8. A tip on$120.00
9. A tip on $125.00 10. A tip on$110.50
11. A tip on $130.75 12. A tip on$135.50
13. A tip on $98.78 14. A tip on$89.67
15. A tip on \$100.20
## Date Created:
Dec 21, 2012
Dec 29, 2014
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https://www.semanticscholar.org/paper/On-Self-Stabilizing-Wait-Free-Clock-Synchronization-Papatriantafilou-Tsigas/4370581f4a6fa39ee22b6fbc669b977cca7a47c3 | # On Self-Stabilizing Wait-Free Clock Synchronization
@inproceedings{Papatriantafilou1994OnSW,
title={On Self-Stabilizing Wait-Free Clock Synchronization},
author={Marina Papatriantafilou and Philippas Tsigas},
booktitle={SWAT},
year={1994}
}
Protocols which can tolerate any number of processors failing by ceasing operation for an unbounded number of steps and resuming operation (with or) without knowing that they were faulty are called wait-free; if they also work correctly even when the starting state of the system is arbitrary, they are called wait-free, self-stabilizing. This work is on the problem of wait-free, self-stabilizing clock synchronization of n processors in an \in-phase" multiprocessor system and presents a protocol… CONTINUE READING
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## Asynchronous Unison
• J.-M. Courver, N. Francez, M. Gouda
• In Proceedings of the 12th IEEE Conference on…
• 1992
1 Excerpt
## Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes
• F. T. Leighton
• 1992
1 Excerpt
1 Excerpt | 2018-12-10 16:52:37 | {"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": 0, "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": 0.8049007058143616, "perplexity": 13092.839973766806}, "config": {"markdown_headings": true, "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-2018-51/segments/1544376823348.23/warc/CC-MAIN-20181210144632-20181210170132-00178.warc.gz"} |
https://de.maplesoft.com/support/help/maple/view.aspx?path=subs&L=G | subs - Maple Programming Help
subs
substitute subexpressions into an expression
Calling Sequence subs(x=a,expr) subs(s1,...,sn,expr) subs[eval](x=a,expr) subs[eval](s1,...,sn,expr) subs[inplace](x=a,expr) subs[inplace](s1,...,sn,expr)
Parameters
x - expression a - expression expr - expression s1, ..., sn - equations, sets or lists of equations, or tables
Description
• The first form of the subs command substitutes a for x in the expression expr. Note that this command is similar to the eval command. Simple applications of replacing a symbol by a value in a formula should normally be done with the eval command. Differences between the two commands are highlighted in the examples later.
• The second general form of the subs command makes the substitutions specified by first arguments in the last argument expr. Each of s1, ..., sn must be an equation, a list or set of equations, or a table. The substitutions are performed sequentially starting with s1. The substitutions within one set, list, or table are performed simultaneously.
• When the substitutions are specified by an equation, or a list or set of equations, every occurrence of the left-hand side of an equation that appears in expr is replaced by the right-hand side of the equation.
• When the substitutions are specified as a table, every occurrence of an index of the table that appears in expr is replaced by the corresponding entry of the table.
• If there are multiple substitutions for the same expression within a list of substitutions, the first one is used. If the substitutions are specified by a set, the one that would appear first if the set were printed is used. (It is not possible for a table to contain multiple substitutions for the same expression.)
• If a list, set, or table contains substitutions for both an expression and also for sub-expressions thereof, the former takes precedence when the expression is encountered in expr.
• Note that only subexpressions in expr that correspond to operands (ops) of a Maple object are matched. This is termed "syntactic substitution". A more powerful substitution is available using the algsubs command.
• The inplace option only applies when substituting into a table or rtable (such as Array, Matrix, or Vector) with no indexing function. When inplace is specified, the input table or rtable is updated in-place. The result is the updated original expr table or rtable, rather than a copy.
• The action of substitution is not followed by evaluation by default. There are two ways of achieving a full evaluation:
– The eval command performs a full evaluation but takes care to delay substitutions which are not mathematically safe, as shown in the examples later.
– The eval option to subs also performs a full evaluation while keeping the semantics the same as for subs. This option should be used with care.
• The options eval and inplace can be given together in the index as an expression sequence, and they can be specified in either order.
• The subs command is thread-safe as of Maple 15.
Examples
Examples showing simple substitution of the form x=a for an expression expr.
> $\mathrm{subs}\left(x=2,{x}^{2}+x+1\right)$
${7}$ (1)
> $\mathrm{subs}\left(x={r}^{\frac{1}{3}},3x\mathrm{ln}\left({x}^{3}\right)\right)$
${3}{}{{r}}^{{1}}{{3}}}{}{\mathrm{ln}}{}\left({r}\right)$ (2)
> $\mathrm{subs}\left(\mathrm{sin}\left(x\right)=y,\frac{\mathrm{sin}\left(x\right)}{\sqrt{1-\mathrm{sin}\left(x\right)}}\right)$
$\frac{{y}}{\sqrt{{1}{-}{y}}}$ (3)
The following examples show the difference between subs and algsubs, where the algsubs command substitutes subexpressions into an expression.
> $\mathrm{subs}\left(a+b=y,{\left(a+b+c\right)}^{2}\right)$
${\left({a}{+}{b}{+}{c}\right)}^{{2}}$ (4)
> $\mathrm{algsubs}\left(a+b=y,{\left(a+b+c\right)}^{2}\right)$
${\left({y}{+}{c}\right)}^{{2}}$ (5)
> $\mathrm{subs}\left({a}^{2}=y,{a}^{3}\right)$
${{a}}^{{3}}$ (6)
> $\mathrm{algsubs}\left({a}^{2}=y,{a}^{3}\right)$
${y}{}{a}$ (7)
The substitutions within a set or a list are performed simultaneously.
> $\mathrm{subs}\left(\left\{x=y,y=x\right\},\left[x,y\right]\right)$
$\left[{y}{,}{x}\right]$ (8)
> $\mathrm{subs}\left(\left[x=y,y=x\right],\left[x,y\right]\right)$
$\left[{y}{,}{x}\right]$ (9)
Substitutions can be specified using a table.
> $t≔\mathrm{table}\left(\right):$${t}_{a}≔\mathrm{α}:$${t}_{b}≔\mathrm{β}:$
> $\mathrm{subs}\left(t,ax+b\right)$
${\mathrm{\alpha }}{}{x}{+}{\mathrm{\beta }}$ (10)
When the substitutions are in a sequence, they are applied one at a time, akin to the following:
> $\mathrm{subs}\left(x=y,y=x,\left[x,y\right]\right)$
$\left[{x}{,}{x}\right]$ (11)
> $\mathrm{subs}\left(x=y,\left[x,y\right]\right)$
$\left[{y}{,}{y}\right]$ (12)
> $\mathrm{subs}\left(y=x,\right)$
$\left[{x}{,}{x}\right]$ (13)
If there are multiple substitutions on the same expression, the first one is used.
> $\mathrm{subs}\left(\left[x=0,x=2\right],{ⅇ}^{x}\right)$
${{ⅇ}}^{{0}}$ (14)
> $\mathrm{simplify}\left(\right)$
${1}$ (15)
If there are substitutions on both an expression and sub-expressions thereof, the former is used.
> $\mathrm{subs}\left(\left[g\left(x\right)=G,f\left(g\left(x\right)\right)=F\right],a+f\left(g\left(x\right)\right)\right)$
${a}{+}{F}$ (16)
As shown in the following example, evaluation does not follow substitution by default.
> $\mathrm{subs}\left(y=0,\mathrm{sin}\left(y\right)\right)$
${\mathrm{sin}}{}\left({0}\right)$ (17)
The option eval for subs can be used to perform a full evaluation while not altering the semantics for subs.
> ${\mathrm{subs}}_{\mathrm{eval}}\left(y=0,\mathrm{sin}\left(y\right)\right)$
${0}$ (18)
Alternatively, you can use the eval command:
> $\genfrac{}{}{0}{}{\mathrm{sin}\left(y\right)}{\phantom{y=0}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}|\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}\genfrac{}{}{0}{}{\phantom{\mathrm{sin}\left(y\right)}}{y=0}$
${0}$ (19)
The following calls to subs and subs[eval] will return an error since Maple does simultaneous substitution in all parameters. (However, eval will work correctly.)
> $p≔\mathrm{piecewise}\left(x=0,1,\frac{\mathrm{sin}\left(x\right)}{x}\right)$
${p}{≔}\left\{\begin{array}{cc}{1}& {x}{=}{0}\\ \frac{{\mathrm{sin}}{}\left({x}\right)}{{x}}& {\mathrm{otherwise}}\end{array}\right\$ (20)
> $\mathrm{subs}\left(x=0,p\right)$
> ${\mathrm{subs}}_{\mathrm{eval}}\left(x=0,p\right)$
> $\genfrac{}{}{0}{}{p}{\phantom{x=0}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}|\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}\genfrac{}{}{0}{}{\phantom{p}}{x=0}$
${1}$ (21)
Here is an example where subs[eval] is more effective than eval (since eval sometimes delays substitutions which involve dummy variables):
> $\genfrac{}{}{0}{}{{∫}s\left|f\left(x\right)\right|\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}x}{\phantom{s=\mathrm{signum}\left(f\left(x\right)\right)}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}|\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}\genfrac{}{}{0}{}{\phantom{{∫}s\left|f\left(x\right)\right|\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}x}}{s=\mathrm{signum}\left(f\left(x\right)\right)}$
$\genfrac{}{}{0}{}{{\int }{s}{}\left|{f}{}\left({x}\right)\right|\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}}{\phantom{\left\{{s}{=}{\mathrm{signum}}{}\left({f}{}\left({x}\right)\right)\right\}}}{|}\genfrac{}{}{0}{}{\phantom{{\int }{s}{}\left|{f}{}\left({x}\right)\right|\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}}}{\left\{{s}{=}{\mathrm{signum}}{}\left({f}{}\left({x}\right)\right)\right\}}$ (22)
> ${\mathrm{subs}}_{\mathrm{eval}}\left(s=\mathrm{signum}\left(f\left(x\right)\right),{∫}s\left|f\left(x\right)\right|\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}x\right)$
${\int }{\mathrm{signum}}{}\left({f}{}\left({x}\right)\right){}\left|{f}{}\left({x}\right)\right|\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}$ (23)
Compatibility
• The eval option was introduced in Maple 2015. | 2020-02-24 18:27:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 51, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8231285214424133, "perplexity": 1312.3444843528946}, "config": {"markdown_headings": true, "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-2020-10/segments/1581875145966.48/warc/CC-MAIN-20200224163216-20200224193216-00257.warc.gz"} |
https://napsterinblue.github.io/notes/python/viz/tick_locating/ | Adding More, Less, or Removing Ticks
Using all defaults, matplotlib will plot a straight line from 0-10 on both axes and return a tick for every even number.
This notebook explores changing that.
%pylab inline
x = y = np.linspace(0, 10)
fig, ax = plt.subplots()
ax.plot(x, y)
Populating the interactive namespace from numpy and matplotlib
[<matplotlib.lines.Line2D at 0x5bae0f0>]
Most of the solutions you find when Googling “How to add more ticks?” will either do some messy list comprehension or something that looks like.
fig, ax = plt.subplots()
ax.plot(x, y)
_= ax.set_xticks(np.arange(0, x[-1]+1))
Instead, the matplotlib.ticks API has various TickLocator subclasses that make this much, much easier.
For instance, you can do a tick using every step along values in the y-axis, with the set_major_locator() function.
fig, ax = plt.subplots()
ax.plot(x, y)
loc = matplotlib.ticker.MultipleLocator(1)
ax.yaxis.set_major_locator(loc)
Or add minor ticks at twice the frequency with the corresponding set_minor_locator() function, and a different input to the MultipleLocator
fig, ax = plt.subplots()
ax.plot(x, y)
loc = matplotlib.ticker.MultipleLocator(.5)
ax.yaxis.set_minor_locator(loc)
Offset
Maybe you’re not interested in a graph that starts at 0. Using the ticker.IndexLocator class and modifying the base (better name would be step, IMO) and offset (how much you adjust each step by).
fig, ax = plt.subplots()
ax.plot(x, y)
loc = matplotlib.ticker.IndexLocator(base=1, offset=1)
ax.yaxis.set_major_locator(loc)
ax.xaxis.set_major_locator(loc)
Or if, for whatever reason, you wanted to align on fractional ticks, knock yourself out.
fig, ax = plt.subplots()
ax.plot(x, y)
loc = matplotlib.ticker.IndexLocator(base=1, offset=0.66)
ax.yaxis.set_major_locator(loc)
Removing Ticks Altogether
In another notebook, we mentioned how to hide ticks and labels by modifying their display properties. Here, we can use the NullLocator to never establish them in the first place.
fig, ax = plt.subplots()
ax.plot(x, y)
loc = matplotlib.ticker.NullLocator()
ax.yaxis.set_major_locator(loc)
ax.xaxis.set_major_locator(loc) | 2021-01-16 06:39:17 | {"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": 0, "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": 0.24925072491168976, "perplexity": 6765.840525197908}, "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-2021-04/segments/1610703500028.5/warc/CC-MAIN-20210116044418-20210116074418-00537.warc.gz"} |
https://socratic.org/questions/how-do-you-factor-8-5x-7-3-27-x-9-3 | # How do you factor 8(5x + 7)^3 + 27(x-9)^3?
Dec 31, 2015
Use the sum of cubes identity to find:
$8 {\left(5 x + 7\right)}^{3} + 27 {\left(x - 9\right)}^{3} = 13 \left(x - 1\right) \left(79 {x}^{2} + 346 x + 1303\right)$
#### Explanation:
The sum of cubes identity may be written:
${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$
Use this with $a = 10 x + 14$ and $b = 3 x - 27$ as follows...
$8 {\left(5 x + 7\right)}^{3} + 27 {\left(x - 9\right)}^{3}$
$= {2}^{3} {\left(5 x + 7\right)}^{3} + {3}^{3} {\left(x - 9\right)}^{3}$
$= {\left(10 x + 14\right)}^{3} + {\left(3 x - 27\right)}^{3}$
$= \left(\left(10 x + 14\right) + \left(3 x - 27\right)\right) \left({\left(10 x + 14\right)}^{2} - \left(10 x + 14\right) \left(3 x - 27\right) + {\left(3 x - 27\right)}^{2}\right)$
$= \left(13 x - 13\right) \left(\left(100 {x}^{2} + 280 x + 196\right) - \left(30 {x}^{2} - 228 x - 378\right) + \left(9 {x}^{2} - 162 x + 729\right)\right)$
$= 13 \left(x - 1\right) \left(79 {x}^{2} + 346 x + 1303\right)$ | 2020-01-17 22:32:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 10, "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": 0.5553488731384277, "perplexity": 2009.1865068835625}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2020-05/segments/1579250591234.15/warc/CC-MAIN-20200117205732-20200117233732-00281.warc.gz"} |
http://stats.stackexchange.com/questions/92081/what-happens-to-adjusted-r-squared-as-sample-size-increases | # What happens to adjusted R squared as sample size increases?
What effect does sample size have on adjusted R squared values?
-
My first intuition is all things being equal, there is no effect. – Glen Apr 1 '14 at 3:24
Adjusted r-squared is intended to be an unbiased estimate of population variance explained using the population regression equation. There are several different formulas for adjusted r-squared and there are various definitions of population variance explained (e.g., fixed versus random-x assumptions). Most commonly, statistical software will report the Ezekiel formula which makes the fixed-x assumption.
In general, as sample size increases,
• the difference between expected adjusted r-squared and expected r-squared approaches zero; in theory this is because expected r-squared becomes less biased.
• the standard error of adjusted r-squared would get smaller approaching zero in the limit.
So the main take-home message is that if you are interested in population variance explained, then adjusted r-squared is always a better option than r-squared. That said, as your sample size gets very large, r-squared won't be that biased (note that for models with large numbers of predictors, sample size needs to be even bigger for r-squared to approach being unbiased).
-
Here's a simple function in R that simulates two Gaussian variables and copies them to inflate sample size without changing their correlation. It plots adjusted $R^2$ over increasing copies with a line at $R^2$.
{Adj.R²=append(Adj.R²,summary(lm(rep(y,i)~rep(x,i)))$adj.r.squared)} plot(Copies,Adj.R²);abline(h=summary(lm(y~x))$r.squared,col='red');lines(Copies,Adj.R²)
It generates new data every time you run it, but always takes on more or less the same shape, asymptotically approaching $R^2$ like @JeromyAnglim described. For example, with set.seed(1):
Decreasing Noise (which increases $R^2$) will shrink the scale of the $y$ axis but not alter the shape: i.e., the difference between adjusted $R^2$ and $R^2$ decreases as $R^2$ increases, but doesn't change the effect of sample size. Increasing Sample.Size makes adjusted $R^2$ approach $R^2$ a little more slowly, but mostly shrinks the scale of the $y$ axis. You can increase Max.Copies to extend the $x$ axis, or modify this function to work with manually entered data or multiple predictors. I've done this myself but not included the code because it doesn't seem to change the basic conclusion. This is intended as a maximally simple answer to a very simple question. Therefore its generalizability may be limited. | 2016-07-25 04:18:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7614631056785583, "perplexity": 706.3240363719759}, "config": {"markdown_headings": true, "markdown_code": false, "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-2016-30/segments/1469257824204.27/warc/CC-MAIN-20160723071024-00211-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3456536/does-connectedness-of-set-pass-to-connectedness-in-subspace-topologies | # Does connectedness of set pass to connectedness in subspace topologies?
If $$X$$ is a topological space and $$A\subset X$$ is a connected subset of $$X$$ and $$Β$$ is an open subset of $$X$$, is it true that $$A\cap B$$ is connected in the subspace $$B$$? I tried to prove this using the classic definition of connectedness but I can't get around it.
I actually need this for the special case where $$X=\mathbb{R}^2$$ and $$A$$ is a proper, open and connected subset of $$\mathbb{R}^2$$ and $$B=\mathbb{R}^2\setminus K$$, where $$K$$ is a compact subset of $$A$$, so maybe it holds in this case, maybe employing the equivalent path-connectedness of domains in $$\mathbb{R}^2$$.
Any ideas?
$$\textbf{Edit:}$$ As pointed out, the first part gets a negative answer. What about the 2nd part though? What if $$B=\mathbb{R}^2\setminus K$$, where $$K\subset A$$ is a compact set and $$A$$ is open?
• When you say "I actually need this", it might be good to be more specific about the bigger thing you're trying to prove; as you've stated it, the answer is "no" because you could take $A$ to be U-shaped and $B$ to cut off the tops of the U without capturing the connecting segment - but maybe there's a related statement that would help your bigger goal. Nov 30 '19 at 2:07
• @MiloBrandt Thanks; the bigger goal is pretty much this: I am simply trying to prove that a domain in $\mathbb{R}^2$ minus a compact subset is connected in the subspace $\mathbb{R}^2\setminus\text{compact subset}$ Nov 30 '19 at 2:10
• Note that connectedness is an intrinsic property; it is redundant to ask whether a space is connected "in" another space. Nov 30 '19 at 2:47
The answer is no. Consider the following subsets of $$\mathbb R^2$$
$$A=\{(x,y)\in\mathbb R^2\mid 2-1\}$$$$B=\{(x,y)\in\mathbb R^2\mid 2
Note that both sets are connected and open, but their intersection isn't (the sets form horseshoe shapes and intersect at the ends of their respective horseshoe).
• @Downvoter any problem with the answer? Nov 30 '19 at 2:13
• +1 since you are answering the first part. I will edit my question for the most specific part, therefore I'm not accepting yet Nov 30 '19 at 2:22
• I guess the downvote is because you are saying something that has already been mentioned as a comment Nov 30 '19 at 2:27
• Please see the update. Nov 30 '19 at 2:32
• Your rectangle isn't a compact subset of $A$? Nov 30 '19 at 2:39
You're asking if an open connected proper subset of $$\mathbb R^2$$ remains connected after deleting a compact subset.
Hint: the continuous image of a circle is compact. | 2021-09-26 23:14:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 22, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7748461365699768, "perplexity": 153.37904109485405}, "config": {"markdown_headings": true, "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-2021-39/segments/1631780057973.90/warc/CC-MAIN-20210926205414-20210926235414-00177.warc.gz"} |
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SE序列的优点有哪些
1、奠边府战役是抗法援越战争中规模最大，也是法军损失最为惨重的战役。
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How to treat a coldDrink plenty of water. When having a fever, drinking lots of water will help you feel better. Dont drink coffee or juice as these will dehydrate you and make you feel worse. Eat chicken soup. Studies show that people who eat chicken soup get better more quickly. It doesnt need to be homemade stuff-shop-bought soup works just as well. Gargle with a salt solution. Rinsing with a simple mixture of salt and water can help relieve a sore and scratchy throat. You can take this several times a day. Rest as much as possible. Stay at home if you can, as this will help to avoid passing your cold to other people. Sleeping at least eight hours a day will help you to recover more quickly.
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《中华人民共和国老年人权益保障法》 所保护的公民是（ ）
《精武英雄》中角色“光子”的设计，主要起到了推动情节发展、批判狭隘的民族主义、为爱情线起到支撑和对比的作用。
“咏絮”才这个典故出自下列哪个人物？ | 2020-05-27 03:46:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18552105128765106, "perplexity": 4085.4919421712975}, "config": {"markdown_headings": true, "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-2020-24/segments/1590347392057.6/warc/CC-MAIN-20200527013445-20200527043445-00483.warc.gz"} |
https://crypto.stackexchange.com/questions/14969/can-a-monoalphabetic-substitution-cipher-attain-perfect-secrecy?noredirect=1 | # Can a monoalphabetic substitution cipher attain perfect secrecy?
Can a monoalphabetic substitution cipher attain perfect secrecy?
Definition of perfect secrecy:
$${\rm Pr}[\,{\rm Enc}_k(m_1) = c\,] = {\rm Pr}[\,{\rm Enc}_k(m_2) = c\,]$$
• yes if the plaintext space is restricted to one character and the substitution mapping is truly random. – mikeazo Mar 13 '14 at 14:08
• Firstly, is this a H/W question? If so we can give you some hints but probably shouldn't tell you the answer... Secondly: Following from Mike's point, think carefully what you mean by 'alphabet'. With a suitably large alphabet and sufficiently large keyspace clearly yes (eg I could use a complete English dictionary as my alphabet if i wanted) – Cryptographeur Mar 13 '14 at 14:10
• @figlesquidge, right. In some sense the OTP is a monoalphabetic substitution cipher where the alphabet is all strings of a specific length. – mikeazo Mar 13 '14 at 14:29
• yes , it is a part of H/W. @figlesquidge do you say that if the plaintext space is larger than one charachter then it is possible to have perfect secrecy? you said that you could use a complete English dictionary as an alphabet, does it mean to match each character to a word in a dictionary? – abdolahS Mar 13 '14 at 14:34
• An "Alphabet" is just a collection of symbols. I can choose whatever set of symbols I like and as many as I want. Just because we traditionally denote alphabet symbols by a single character doesn't mean we have to. That said, this is probably not what your H/W is looking for. Mike's answer is more likely to be relevant to what your class is after – Cryptographeur Mar 13 '14 at 15:31
Since this is homework, let me just give you a hint: consider the two-character messages $m_1 = \text{"aa"}$ and $m_2 = \text{"ab"}$.
Given a ciphertext $c$ encrypted with a monoalphabetic substitution cipher, can you tell which of $m_1$ or $m_2$ it corresponds to, even without knowing the key? Why (not)? What does this imply about perfect secrecy?
Ps. The hint I gave above assumes that the cipher is not homophonic, i.e. that the encryption of each character is deterministic and independent of its position or the presence of other characters in the message. For a (possibly) homophonic monoalphabetic cipher, it may be simpler to start the argument from the other end: if you intercept the ciphertext $c = \text{"xx"}$, what can you say about the plaintext? | 2020-10-22 00:56:39 | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5826347470283508, "perplexity": 728.9086349269757}, "config": {"markdown_headings": true, "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-2020-45/segments/1603107878662.15/warc/CC-MAIN-20201021235030-20201022025030-00670.warc.gz"} |
http://poincare101.blogspot.com/2012/ | ## Tuesday, April 3, 2012
### Inductive reasoning, and why you should care
Inductive reasoning, according Wikipedia:
Inductive reasoning, also known as induction, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations of individual instances of members of the same class.
That probably conveys absolutely no value to you. The best way to understand what inductive reasoning is, is to apply it.
In order to do that, we need some kind of problem which we can solve using a bit of induction.
I'm going to a pick a math problem. Why, you say? Math is almost always the easiest way to understand reasoning, since math's primary device of "progress", so to speak, is reasoning.
So, here's the problem:
The plane is divided into regions by drawing a finite number of straight lines. Show that it is possible to color each of these regions red or green in such a way that no two adjacent regions have the same color.
If at first this doesn't strike you as a math problem, you probably haven't met this chap called graph theory, or maybe haven't been introduced to bipartite graphs.
So, how do we go about solving this?
Before reading on, try out some cases; one line, two lines, ten lines, and so on. Try and figure out some patterns.
Now, I'll show you the solution.
First we consider one line. So, we can color the regions on opposite sides of the line opposite colors (i.e. red and green), and, we're done.
Yes! What we can do is take one side of the new line we just put in, and swap all the colors on that side (so, red goes to green, green goes to red), and, we get a complete solution! So, every time we add a line, we can simply follow this algorithm and get the correct coloring. Of course, this isn't a fully rigorous proof, but, it shows what we're after.
Inductive reasoning is taking a method you used to solve a problem for a set constraint (we knew how to do it for one line), and then extending that method to solve the problem without the constraint.
If write code, you probably do this all the time (and just didn't know what this was called). If you've got a function that's misbehaving, you pass in a couple of values that you think are forming an edge case, and you've noticed that its going wrong for *one* of these values, you change the function definition so that the errors don't happen.
But, you should use this kind of reasoning much more often. In nearly all problems where you are stuck on something going wrong on a constraint, try inductive reasoning. Of course, none of this actually happens consciously, but, if you try doing it consciously a couple of times, it "just happens" eventually.
### The Travelling salesman problem
The travelling salesman problem is possibly the most famous and probably the most easy to understand of the so-called "NP-hard" problems computer scientists (and mathematicians) have found.
The problem statement is quite simple.
Consider you are a salesman, and you have, say, an $n$ number of cities you've got to cover by the end of the day. But, it would be best if you could minimize the distance that you have to travel between all of the cities, and, you know the coordinates of all the cities in reference to some point known as the *origin*. Given these coordinates, define an algorithm that would give you shortest possible path between the cities.
Of course, this doesn't seem like much of a problem at all when you first start at it (like most other difficult problems); you could just try all the routes between the cities, find the route with the minimum distance covered, and, you're done!
Let's see what that entails in terms of performance/scaling. With $n=5$ (i.e. five cities to visit), we have a total of $5! = 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 120$ ways we can trace out the route between the cities, and we have to check all of these. That doesn't seem too bad for a computer.
How about for $n=10$? Well, $10! = 3,628,800$, so, its quite a big jump from $120$, but, still manageable.
Let's go up by another five; $n=15$. That gives: $15! = 1,307,674,368,000$. Holy cow. That's a lot. But, how did it jump that quickly?!
To answer that question, we'll need a bit of math (if you understand big Oh notation, you can skip the next couple of paragraphs).
Consider this situation. You have one car that's accelerating from a low speed, whereas another car is going at a higher speed, but, the second car's speed will not change. What do you think will happen if we let the cars go on forever? Of course, the car that's accelerating will overtake the car that's at a constant speed, right?
That's what scaling algorithms is all about. You might have one algorithm that performs better at lowever "sizes" of the input, but, a second algorithm may overtake it if it can "scale better" (i.e. accelerate). So, when we say that an algorithm is $O(n)$, what we mean is that the algorithm performs *linearly*, i.e. for each unit increase in $n$, we get a certain unit increase in the time spent (or, whatever else you're measuring). Similarly, $O(n^2)$ means that for every unit increase in $n$, we get that much of change, but, squared in output.
But, all of this still seems on some shaky ground, so, let's break out the equations (warning: if you don't know how limits work, skip this). This won't be a *completely* rigorous argument (which would require more math), but, it will be much better than the argument we have in place.
How can we say that a linear time algorithm (i.e. $O(n)$) will scale better than $O(n^2)$? Well, what we're informally saying is that the $O(n^2)$ grows much quicker (i.e. worse) than $O(n)$ as $n \to +\infty$. If you remember that bit about relative rates of growth from first semester calculus; $\lim_{n \to +\infty} \frac{n^2}{n} = \lim_{n \to +\infty} n = +\infty$
So, we've proved that $O(n^2)$ grows faster than $O(n)$, and therefore performs worse than $O(n)$.
What does that mean in terms of the traveling salesman problem? The traveling salesman problem brute force solution is in fact $O(n!)$ (since the number of routes goes up like that).
Consider a polynomial time solution (i.e. $O(a_n x^n + a_{n-1} x^{n-1} ... + a_o)$). Using a bit of calculus/limits, we can say, for certain, that factorial algorithms are much worse than polynomial time solutions as $n \to \infty$.
That's what makes the travelling salesman problem interesting, because it has a non-polynomial solution, and, its something called a NP-Hard problem. What NP-Hard means is actually very complicated and heavily theoretical, but, it consitutes a very important part of the P vs NP problem, which, informally, asks (quoted from Wikipedia): "whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer" (s/quickly/polynomial time/g).
So, that's what the travelling salesman problem is, and why people care.
## Saturday, March 31, 2012
### The new Blogger update ... sucks.
I've been using Blogger to host this site, and, frankly, its probably been one of my worst experiences with Google software, ever.
First of all, let me cover the the good things about it (i.e. why I chose it in the first place). Its very quick to get started with a blog, its easy to add AdSense if you want it, and that's about it.
What's wrong with it?
First of all, the widgets model is broken beyond all belief. All of the widgets that are provided are pretty much useless, and most things like syntax highlighting and LaTeX involve tacking on bits of Javascript onto the page, which Blogger doesn't mix with all too well.
Secondly, the editor sucks. We're in 2012 here people, and it STILL escapes out when I hit tab. Why is this so difficult? Isn't Blogger now developed by the same company that makes Google Docs?
Then, once Google+ came along, all of the other "social" buttons have been pushed off to the side and made quite tiny, which, is understandable when considering it from Google's point of view, but, from my point of view, it doesn't make much sense.
The themes are also far from amazing (http://www.bloggerthemes.net/ does try to remedy this), and the selection in font is pretty much non-existent.
And, most of all, Blogger, in general, seems to try to get in your way every single time you want to just "write a short entry", or "get this article on the internet".
So, what did the update fix/add?
It added some analytics directly on the front page; I was surprised to find out this blog had over 50,000 page views in the past 2 weeks.
Also, it cleaned up a editor a *tiny* bit (it still escapes out on the tab), and, the main replacement was just making the editing textarea/contenteditable larger.
The design is also much better and clearer.
But, they still completely ignored the actual problems that plague Blogger; so, I just can't keep waiting any longer, I'm going to try and pick from the enormous assortment of options (Posterous had caught by eye, but, its been acquired, so, I don't want to risk anything on it).
## Sunday, March 18, 2012
### Experiences in Go-ing
I've been messing around with Go for quite some time now and I wanted to share my experiences.
When I first looked at Go, I put it aside as "just another language", and moved on with whatever I was doing.
I mean, there are languages popping up every day that are worth nothing whatsoever because the ideas they bring to the table are too few to take the risk of using a language that isn't popular (less documentation, less support, less everything).
That summer, I began writing some more low-level C/C++ code to implement a Bayesian classifier stock recommend-er thing. It was a complete disaster.
Just some basic string parsing was a nightmare; C gave no utilities whatsoever, and C++ was good, until I hit an error and it gave me a 20 line long error report, and, I had to use all kinds of specialized templates for the simplest of things!
And, the worst problem I faced was of sockets. Non-blocking, multi-plexed and cross-platform socket support with C is basically non-existent (unless I wanted to use libev or libevent, which has documentation scattered across the internet in small chunks). With C++, there are many choices, such as Boost.Asio (basically no documentation), ACE and ICE (this one I'm genuinely excited about, but, I hate their specialized object format crap I have to deal with).
And, of course, there's no language support for anything so if I ever wanted to distribute my code, the client would have to have the libraries.
I couldn't sacrifice performance (lots of number crunching was involved with costs tight), so, I couldn't pick Python.
Then, I came back to Go, and looked at it again from a different perspective, and hoped it would offer me something that could rid me of all of this.
I never did in fact write the Bayesian classifier thing (the idea wasn't much good anyway), but, the project introduced me to Go, which, I must say, is an amazing language.
The first thing I immediately noticed is that they got rid of the parentheses in "if" and "for" statements. Coming from Python, I really like this.
And, here's a language that's FINALLY SUPPORTING UNICODE FROM THE START!
Closures are supported and functions can be passed around like salt shakers, its wonderful!
All of the language seems well-thought out and cohesive; there aren't really any points that I felt like didn't match with the rest of system. Its very much like a suit without any stitch marks on it.
As for the standard library, its no short of awesome. It includes a lot of things that I've frequently wanted with C/C++ as part of the runtime, such as json, xml, http, a cryptography package, even websocket support built right in.
And, when they say it feels dynamic and interpreted, they actually mean it; the type system steps out your way for most of the time.
The only thing I find lacking is that there are no books on the language as of yet, but, I expect that will be remedied once the language is "marketed" a bit more (Google hasn't put a ton of weight on it ... yet).
It also has support for RPC which makes writing distributed computations really easy and quick.
Unless I have to write some really low-level code, I refrain from using C/C++ these days and instead reach for Go; about the same speed with half the development time.
I really encourage you to go check out Go, and just play around with it; you might start using it all the time.
## Monday, March 12, 2012
### To all the people who say programming competitions are useless
There's been this general vibe on HN and r/programming that programming competitions (that involve problems one must solve) on the whole have little to do with programming in general.
I beg to differ.
99% of us can crunch out Javascript and some backend language pretty quickly; some ajax interaction, maybe some form validation and some Twitter and Facebook APIs. And, a lot of us can quickly learn new things when we need to. Need to learn Scala for next project? No problem. Client wants to use the Face.com API? Alright, let's do it.
But, that's not the only stuff that matters.
Your skills are *really* tested when you hit a roadblock that isn't covered by the abstractions you're working on.
For example, the database inserts aren't happening fast enough, and the company doesn't want to buy any more servers to fix the problem, so, you've go to optimize it.
Programming competitions don't test whether or not you can go about updating portions of code, they test whether you are able to write code to solve a problem you've likely never heard of under a time constraint.
And, that's what companies would like in programmers.
Math based problems are just one way of approaching timed problem solving, and they work quite well, since many of us are well versed in at least basic math, and are able to get our hands around the problem so that we can begin to think about implementing it.
So, programming competitions *do* have to do with programming and the ability to solve problems, which is what development is all about.
## Friday, February 24, 2012
### BIOS primer
Most of us know what a BIOS looks like, and have a some bits and pieces of an idea about what its supposed to be doing. This needs to rememdied, so, read the rest of this article!
What happens when you hit the power button on a computer?
It doesn't actually go directly to the CPU, first, the BIOS code is loaded, because that's what's able to hoist up the CPU, hard drive, display, etc.
The BIOS is contained on an external chip (that's why some of you see your motherboard's manufacturer's name when you see the BIOS).
A BIOS not only lets you set the boot order (which was was most of us have used it for), it has a couple of jobs.
First of all, it configures your hardware.
Some hardware is dependent on others, has specific settings, etc.
All of this is handled by the BIOS, so that is ready for the bootloader.
Also, all (well, nearly all) computers have a system clock, which doesn't actually tell you the "time" (again, it could), it counts ticks from a certain date, such as the epoch. The BIOS sets this up.
It also selects what devices it can use as bootable, because there are certain types of storage devices that a BIOS cannot load of off (for example, random storage, volatile memory), and it identifies which are bootable.
Then, comes the main job of the BIOS. It calls a bit of code that resides on the selected storage devices on the first 512 bytes of the first sector.
In the early days of computers, 512 bytes was enough code to load the operating system, and things worked wonderfully.
Of course, this is no longer the case considering that the Linux kernel is almost 15 million lines of code.
So, these 512 bytes (known as the MBR) usually call *another* piece of code which then loads your operating system. Or, it could hold a list of sectors on your hard drive from which another piece of is then called.
The BIOS also provides a small API for the MBR to use to write to the screen, make some interrupts, etc.
Its pretty cool stuff...
## Sunday, February 19, 2012
### C Programmers: Don't write macros
Take pretty much any large C project today.
If you look through a couple of files, you'll notice some things are written in CAPS LOCK AS IF THEY'RE YELLING AT YOU.
These are macros.
They're not as powerful as Lisp macros; they just replace themselves with a bit of code.
C Macros are actually quite nice if they're used in moderation, because they allow you to type less.
But when you have sixteen macros in one line, you really need to stop.
So, this is my plea to all of you C programmers, please stop writing more macros, because you're going to regret them when you have to go hire a new guy and he'll spend 19 weeks trying to figure out what all the YELLING ACTUALLY MEANS.
## Monday, February 13, 2012
### My stance on JVM Languages
There have been JVM languages popping up all the time; there's Scala, Clojure, Groovy, etc.
These are all excellent languages, without a doubt they are. I use them all the time, and I have come to enjoy them a lot.
But, sometimes, I wonder about the very long-term (well, at least in the software world) consequences on using these languages.
Java, as many of us consider it these days, is an "uncool" language. It is too verbose, too complicated and has too much over engineered crap that no one uses.
It lacks the simplicity of something like C (notice I did not say C++ :P), where the manual for the ENTIRE LANGUAGE was a hundred something pages long.
But, there is a ton of existing code in Java that no one wants to let go of, because people spent so many years trying to develop that code, and it took take many more years to replicate it in another language.
So, people created JVM languages which run on the Java Virtual Machine, and they can interface pretty easily with Java. Then, you can write all your new code in a fast, hip language like Scala, but, you can still keep all of your legacy stuff around, and you don't have to rewrite a thing!
This works wonderfully, except...
Java, in my opinion, is slowly turning into another COBOL. Heavily used in large, high capital industries where a change is made every few centuries (roughly speaking), but, not used much elsewhere because its just too obsolete.
So, if one creates languages on top of such a language, you're still hooking into the same old architecture. That's like writing a language that compiles to a COBOL virtual machine, people would laugh at you.
Does this change anything for us, right now?
Absolutely not.
The term we're talking about (for Java to turn into COBOL), is just so long, that most companies won't even live to face the day.
I'm still going to keep using JVM languages, because they're just plain awesome, but, I just wanted to put my thoughts out there.
## Sunday, February 12, 2012
### Graph databases explained quickly
Graph databases seem to be pretty important these days, with a social network popping up every time someone says "Facebook", so, I decided I'd do a small article on them.
What's it good at?
Its good at specifying tables in which specific types of data lie.
Well, a lot of things, one of which being that having one piece of data "linked" to others is a complete pain.
What does that mean?
If you're a person, and and you have 500 friends, you need to be linked to 500 other people, all of which, in turn, are linked to you AND a bunch of other people.
Now, let's consider a graph database.
In a graph database, there are things called nodes, properties and edges.
Nodes are close like objects/structs to the OOP people, in that they are entities that can represent people, accounts, etc.
Properties are information that nodes have, for example, if one of the nodes was "Person" its properties might be "Name", "Age" and "Address".
Edges are the things that connect the nodes together, which are really the most important, since in a graph database, it matters a lot more about how the nodes are related than what the nodes actually contain.
Hopefully that made sense, if not, drop a comment below!
Follow if you liked it :)
## Saturday, February 4, 2012
### What's referential transparency?
You've probably heard about it before from all those crazy functional programming people, but, you don't *really* know what it means... I'm here to fix that!
Consider a procedure/method written in an imperative language.
In such a procedure, the program can do anything it wants!
Which means it could multiply two numbers, crash your car, and then save those numbers to a database.
The things that it does that affect the outside world are called "side effects".
In a purely functional programming language, side effects don't exist.
But, in "almost" purely functional programming languages (in which you can actually do something practical stuff like writing programs that do things), the things that have "side effects" are confined to a couple of functions that interact with the outside, but, the rest of the functions (called pure functions) are entirely separated from the outside world, which means that they can be executed anywhere can we can expect the same results.
Consider math for second.
Mathematics is a purely functional language, because there's no way it can affect the "outside world" (atleast, mainstream math can't).
Say you define a function called $f$:
$f(x) = x^2$
Now, what do you get when you compute $f(2)$?
$f(2) = 4$
Okay, so, what's so important about that?
That simple statement means that no matter what the rest of the world is in, if you give the function $f$ a value of $2$, you can bet the farm that it will return $4$.
The same holds true for pure functions in functional programming languages!
And, that's what referential transparency means.
Basically, we're saying that if we plug in some value $m$ into some function $f$, we can always expect to get the same value back ($f(m)$), regardless of the state of the rest of the stuff we're dealing with.
Why's that useful?
First of all, that's a heck of a lot an improvement for compilers/interpreters.
If you're finding the value of $f(2)$ 40 million times, it will (usually) only find it once (this also has to do with how parse trees are replaced when parsing functional programming languages, but, the basic idea is here).
This also lifts the idea of code running sequentially, because it can be run however it would run the fastest.
Referential transparency makes code a lot easier to reason about and debug, since you KNOW that something will return a certain value when it receives a certain set of values as input.
There you go, you should hopefully understand referential transparency.
## Friday, February 3, 2012
### Functional programming explained
I've noticed a lot of confusion over why functional programming languages seem to be what the cool kids use these days, and why they can actually make a difference in your productivity as a developer, and I hope I can clear that up with this.
Consider a standard, run-of-the-mill imperative language, like Java, or C.
Your procedures or methods typically look like this:
Basically, you're taking two numbers as arguments, adding them, and returning them, and saving the result to a database somewhere in the middle.
Not too shabby, right?
Consider this situation. For some reason (your application isn't working), you need to check if this particular method is working.
The ability to test things separately from others is called "decoupling".
Another issue with imperative languages is that they can modify all kinds of state in one function!
So, in effect, when you call the function addNumbers, it could delete your database, empty your bank account and draw a circle on the screen. Why is that a problem, you ask? Well, that's a pain to debug, because you have no idea what types of functions can modify what types of state!
Another issue are global/static variables, which cause no end of problems for Java programmers who find themselves changing static fields in certain objects affecting all the others in adverse ways, and this takes a ton of work to weed out.
How does functional programming solve these problems?
The first thing to understand about functional programming is that in a completely pure functional programming language, there is no way you can modify external state.
That means you can't print to the screen (that's changing the state of the screen), access the web (changing socket state), or anything particularly useful.
But, this wouldn't be terribly useful since you wouldn't be able to get any output shown, so, it would be practically useless (people get around this by writing languages that printing every calculation to the screen as a part of the language implementation, but, this just creates more confusion).
However, that's not to say that they aren't used. An example of an ancient and hugely successful purely functional programming language is mathematics (there's no "print" command in math).
So, languages like Haskell use this special idea (borrowed from mathematics, see my abstract algebra posts) called a Monad to "mark" special functions that do modify state so that they can be separated cleanly from the rest of the program.
This nearly kills off the decoupling problem!
Because there are very few non-pure functions in a typical functional piece of code, everything else IS decoupled from the environment!
This is heaven when you need something debugged!
And, this cleans up what functions can do and can't do; every pure function MUST return a value, so, you can expect something in return, not just a void (because that would mean its changing state, is therefore not a pure function), so, if you try to write to the database from a pure function, you can't do that, which keeps your code squeaky clean.
Usually, functional languages come with malleable and nimble static typing, which means that you don't have to write out the types when you're declaring functions, but, they're there, so, when you try to pass a String to a function that wants an Integer, the compiler will tell you.
All of these restrictions make it much more difficult to compile, but, once it does, it sure as heck won't crash (it might not do what you want it to, but, that's what unit tests are for).
In functional languages, variables aren't really variables in that they can't be changed.
You're probably saying "WHAT?!! How am I supposed to implement a counter then?!", and that's solved entirely by the fact that you can use recursion.
So, that's why functional languages are awesome, and you should go check out Haskell!
## Thursday, February 2, 2012
### Why is server configuration so annoying?
A lot of programmers these days are switching over to dynamic languages like Python and Ruby, mostly for their ease of development.
Sure, it entails that one must make sure that you aren't passing the wrong types to wrong functions, or you won't find out until runtime, but, if you're willing to take that risk, dynamic typing can be amazing to speed up your work process.
And, just like languages, nearly every other aspect of computer science/engineering has evolved for the simpler, more elegant approach, and, in this shift, many have profited.
For example, Twilio's business model is based entirely on the fact that building phone systems in a modern programming language is just much too difficult for an average programmer, and, by simplifying the process by which developers can take advantage of phones, they've made quite a company.
And, people work everyday to simplify things that were previously immensely complicated, into black boxes in which the details are abstracted away.
As another example, take the humble Python list. It seems like a pretty simple idea; you can push and pop things, and you can delete things from the middle, you can sort and search them.
But, implementing a data structure like that in C is a formidable task, especially with all the optimization work that the Python folk have put into it.
And, things like this have lead to an explosion in Python's popularity.
But, I see one area where this type of stuff is immensely lacking, and that's server configuration.
First of all, why on Earth does Apache still use XML?! Is there literally no other format they can use?
Then, SSL shouldn't be so difficult to set up. It should take, at most, one shell script, or ANYTHING like that that'll generate a basic SSL virtualhost.
There need to be sensible defaults for log-files per vhost and so on.
There need to be macros that we can use to have chunks of configuration with variables plugged in.
And, in general, a lot of things need to be abstracted away into more usable and easy components.
That's all I've got to say, but, do tell me what you think in the comment section below.
## Wednesday, February 1, 2012
### The IRC mentality
In recent years, more hacker forums have sprouted up, moving away from the traditional "somebody asks, a bunch of people reply, and then there are replies to that", to some newer ideas.
For example, there's Stackoverflow.
StackOverflow is an excellent idea.
By introducing gamification into the idea of answering other people's questions for free, they've changed the entire scene of programmer forums. This causes people to think twice (well, for the most part) before posting useless questions, and the same for question answerers.
This works with amazing efficiency; ask a fairly easy to understand question on StackOverflow (SO), and you'll get an answer within a couple of minutes (unless its something incredibly unpopular like running ARM assembly on a MBR), and the answers are immediately filtered out because the upvote-downvote system.
As a added bonus, the interface is clean, succinct, and clear.
Frankly, its just all out awesome.
Coming from places like Daniweb (ads above the fold; aarrgh), its a welcome breath of fresh air.
But, that's not where I started.
I started on IRC.
IRC is facing popularity issues these days; with all the new solutions for collaborating (for example, Stripe uses Campfire by 37signals).
I'm not going to talk about how IRC is outdated, and, I'm not going to tell you that its the only "real" way to chat with people, because that's your decision.
But, I will tell you about the community around IRC.
When you're a beginning programmer, and you're starting to walk around the intricacies of a language, and you're faced with a problem you can't solve with, say, 10 minutes of work, what do you do?
You try to ask for some help.
Consider two scenarios, one on a website like StackOverflow, and one on IRC.
You post it on SO, and you get a response in five or six minutes that tells you how to solve the problem, and tells you what you're doing wrong, and you're able to get your code working, you hope that the person who gave the answer has a nice dinner, and move on.
1& 1 & 0 \\
1 & 2 & 2 \\
2 & 3 & 1 \end{array}$You can't assume anything about it (except for a couple of very unhelpful things, like you can consider it in rows and columns), so, you must have some idea about what the matrix is about. For example, this one could be a group of simultaneous equation's coefficients. You might have noticed that so far I haven't really explained how a rotation matrix actually works. Before I begin, you should have a basic understanding of vectors, which are incredibly simple (just an arrow, with a point at the head and another at the tail). Basically, what does rotation actually mean? It means that we're taking vectors on a plane, and we're moving them so that they represent different vectors (as if we rotated the plane itself). Now, take a step back, and pretend as if, instead of moving about the vectors, we are rotating the plane in which they reside. A bit like this: (That took me almost an hour to make, so be grateful!) Where the red axes are that of the rotated plane. So, how do the values map out? What I'm asking is if we take an arbitrary point$(x,y)$and then we rotate it about the origin by some angle$\theta$, what will the new point be, in terms of$x$and$y$? Diagrams always help: As you can see the original point is$D$, which have rotated around the origin ($E$) by a certain angle$\angle FED$to the point$F$. So, lets say that$D$has the coordinates$(x, y)$, and we're trying to find$F$in terms of$x$and$y$. Some immediate conclusions (since$D = (x, y)$):$DH = yEH = x$To make our lives easier (mostly my life easier) let's give the angles some symbols:$\angle{DEH} = \phi\angle{FED} = \theta$And, since we are rotating about the origin, these must be true:$EF = ED$Let$EF=ED=r$So, considering$\triangle{FEG}$, we can say:$\cos{FEG} = EG/EF = EG/r ... (1)\sin{FEG} = FG/EF = FG/r ... (2)$Notice that$EG$is the$x$coordinate of$F$and$FG$is the$y$coordinate of$F$, which is what we've set out to find. And, we notice this:$\cos{FEG} = \cos{\theta+\phi} = \cos{\theta}\cos{\phi}-\sin{\theta}\sin{\phi} ... (3)\sin{DEH} = \sin{\theta+\phi} = \sin{\theta}\cos{phi}+\sin{\phi}cos{\theta} ... (4)$Equating (1) with (3), and (2) with (4):$EG = r(\cos{\theta}\cos{\phi}-\sin{\theta}\sin{\phi})FG = r( \sin{\theta}\cos{phi}+\sin{\phi}cos{\theta})$Now, we simplify using the simple idea that$\cos{\theta}*r = x$and$\sin{\theta}*r = y$, And, we get:$EG = x*cos{\phi}-y*\sin{\phi}FG = y*\cos{\phi}+x*\sin{\phi}$And, that's what we wanted! You might be wondering: "What does this have anything to do with matrices?" If you weren't thinking about that, please pretend you were at this point. So, in the equations that we found above, the only parts dependent on$\phi$(the angle by which we rotate) are the trig functions, so, what if we just represented them separately and then we'd be able to concisely represent all kinds of rotations on a plane? Basically, what we're doing this this:$\text{Rotated vector} = \text{Some witchcraft}\cdot \text{Initial vector}$So, in a bit clearer terms:$\begin{array}{cc} x' \\ y' \\ \end{array} = \text{Some witchcraft} \cdot \begin{array}{cc} x \\ y \\ \end{array}$(where the columns of numbers are vectors, I can't get the brackets to display, sorry) That$\text{Some witchcraft}$is a matrix! And, that's because matrix multiplication is defined in such a way that we can multiply a matrix and a vector together, and get equations resembling those that we got for$EG$and$FG$! That right there is the matrix we use (pretend that the$\theta$is actually$\phi$), and we multiply that with the$<x, y$vector to get the equations we got for$EG$and$FG$, because matrix multiplication is defined that way! You might think this is all a "rigged game", and it is, but, the amazing thing is, despite this seemingly arbitrary operation of matrix multiplication, it works in all kinds of different places, because it is based one of the most important computations in mathematics, known as a linear combination And, matrices are used EVERYWHERE! From analytic geometry to simultaneous equations to economics and game theory, and that's mostly because of the fact that you are allowed to make any assumptions about the data you would like, and idea of matrices allow you to perform on math on that data with a few constructs that applicable pretty much anywhere. I would love your feedback on this article, and ideas for new ones! If you like this, please consider following this blog, it gives me motivation to keep writing blog posts, and you'll be notified as soon as a new one comes out. For the people who like the abstract algebra series, I took a little break from it because I was a bit bored with it, and I couldn't think of the next topic easily. I'd be happy to answer questions, so, you can put them in the comments section below (I'll usually respond immediately), or email me at dhaivatpandya AT g m a i l DOT com. And, just before I close, I'm doing a startup called NimbleNotes, which allows to write productively (this blog post was written entirely with NimbleNotes), and currently is in closed beta, with an IndieGoGo project. Have a nice day :) ## Friday, January 13, 2012 ### Please don't do dates and times like this! So, you might have read my last post. And, that covered only one website, namely http://samsclub.com/. The problem is much, much worse than that. So, this is what happened. I downloaded the free Camtasia Studio trial for 30 days, and I really, really enjoyed it. But, like all other trials, its time came, it prompted me to drop some Franklins or it wouldn't let me use it. And, I was about to close out the application (hey; I didn't actually need it), when I thought maybe I would try making my system time go back a bit, and see if that did anything. And it did. It happily pretended like it was 1/7/12 instead of 1/13/12, and I could continue to use my trials for another 6 days (and, after that I could repeat the same trick again, or, I could just sent it farther back to begin with). That struck me that maybe a lot of other applications depend on system time. And, I promise you, there are a LOT of them. Skype is a big one, if you move your time back, and look at Skype conversations and enter in a new one, it goes back onto old conversations. So, please, please don't get dates and times from the system! You need to get them from a synchronized UTC timeserver. ## Thursday, January 5, 2012 ### Stupid coding errors This funny thing occurred, and I thought it might be interesting. I was watching someone make a monthly payment on some financed item on Sams Club, and was having some trouble. The problem was, the computer had a incorrectly configured clock, which had the date set as February 6th, 2012 (this took place on January 5th, 2012). And, Sams Club's website was using that date as the default value for the payment date. I thought "Okay, that's not too bad, I can probably just change the date on it". Wrong. Since SamsClub.com was using Javascript (bad idea) to get the date, it was also setting it as the MINIMUM date, which meant you cannot put in a date before that! Now, what's the problem with that? Well, say I'm a week late on my payment. To make that payment on time, all I have to do is set my system's clock to one week ago, and Sam's club will happily take the payment as if it was delivered a week ago. Lessons learned: Never, ever use Javascript to figure out the current date. Atleast check the date before inserting it into the database. Hopefully this will reach someone at Sam's Club, and they'll fix it... ## Sunday, January 1, 2012 ### Abstract Algebra presented in a non-intimidating way (esp. for developers) - cryptography Hi! Hopefully you read the last post, and if you didn't, you really should (http://poincare101.blogspot.com/2011/12/abstract-algebra-presented-in-non.html), because I'll be building on that stuff this time around. This time, we'll be going over an very interesting and applicable subject (if you've ever used a computer, you've experienced it in action), called cryptography, and more specifically, public-key cryptography. Let's get started. From the dawn of humans, there's always been one human who wants another one dead, and as time as gone has gone by, we have invented better and better (or, worse and worse) of accomplishing this. One of such inventions was cryptography. Communication is incredibly important in war, and Caesar (yes, that Caesar, the guy from Rome you learned about in history class and promptly forgot about after the test) needed a way to communicate with his generals spread out throughout the Roman empire in way such that even if the messenger was captured, the bad guys wouldn't be able to read the message. So, he (and presumably his team of scholars he kept handy) developed the Caesar cipher. I won't go into a ton of detail here, mostly because I wrote an entire blog entry about it (http://poincare101.blogspot.com/2011/10/encryption-and-ciphers-part-1-this-is.html). Basically, you shift over the alphabet over the message by a certain amount (that certain amount is called the key) to get the encrypted message, and, the person who wants to decrypt it shifts back the message by that certain key. There worked for a little bit, but, it involved the fact that the people who Caesar sent his messages to had to be told of the key and Caesar didn't trust them enough for that, so this system was abandoned, and Caesar most likely returned to the time-tested and expensive method of sending a messenger with soldiers armed to the teeth. People entirely overlooked this (rather important, as we'll see later) problem, and instead concentrated on the fact that the Caesar Cipher was easily cracked with statistical methods (all of this is explained quite thoroughly in the blog post I linked above). Slowly, cryptography turned into a pastime for amateurs and enthusiasts, and it was not much of a subject by itself, until more and more developments followed, and the subject was looked upon by mathematicians. One of these new and better ciphers is called the Vigenere (I refuse to take the time to put the accents in the right places) Cipher. The basic idea was that it no longer kept the frequency of the original text (often called plaintext) intact, making it immune to the statistical methods that could be used on the Caesar Cipher, but, there were other methods it was vulnerable to. One very large problem was still overlooked: both parties need to transact the key before hand, or this procedure wouldn't work. Finally, some clever chap came up with the revolutionary (like, really revolutionary) idea of public key cryptography. The concept is quite brilliant. Say, you have Alice and Bob and they want to transact encrypted messages. In public key cryptography, both Alice and Bob each have a public key and a private key. The public keys are published somewhere that *everyone* can access them (not necessarily only Alice and Bob). Now, Alice wants to send Bob a message. She finds Bob's public key and encrypts her message with it, and the sends off this encrypted message to Bob, who then decrypts it with his private key. That means that the key that is used to decrypt the messages is never transacted, and Alice never needs to know it! That means that if Caesar had used public key cryptography, he wouldn't have faced the problem he had, because his generals would never have to know his private key! Of course, there's a problem (actually, a few of them) with that (otherwise there wouldn't be a NSA). The private key and the public key must somehow be related to each other, so, theoretically, given as much time as needed, it would be possible to derive the private key from the public key, so, the solution to that is to use a computationally hard problem to generate the public and private keys, so it would take much too long to get the private key from the public key for it to be practical. You might have noticed that I've been quite vague so far; I haven't specified HOW the keys are actually generated, and the encryption is carried out to turn plaintext into ciphertext. That's where the math begins. I mentioned that we had to generate the keys with a "computationally hard" problem. What on earth does that mean?! Its a pretty simple idea, it means that as you increase some parameter, the time taken to complete the problem skyrockets (not a perfect definition, but, it will suffice). One such problem is called the Discrete Logarithm Problem (DLP, for short). Basically, you have a prime$p$, and$g, h$such that both are part of the$mod p$set (i.e. between$0$and$p-1$inclusive). The problem is to find an$x$such that:$h \equiv g^{x} \pmod {p}$Let's see why that's so hard. Let's set:$p = 7h = 6g = 3$Basically, the only approach to this is we try different values for$x$, find$g^x$, then find$g^x \pmod {p}$, and keep going until we find an$x$such that$h \equiv g^{x} \pmod {p}$If you try this (and I highly encourage you to do this), you will find that$x = 3$works. This is a pretty small example, but, turn up the numbers, and it becomes a pretty formidable problem. Let's look a bit more deeply into this matter, why is this so hard? Well, because we don't have any way find out an answer without brute-force. Okay, why don't we have another way? Because it deals with$\mod p$, for which we don't have a ton of tools to deal with. Exactly! Primes often occur in such problems, because we don't have a complete picture of how primes operate, because as far as we understand it today, they don't form some kind of equation that we can plug numbers in and get (all) primes out. Alright, now, how are we going to turn this into a key? There's something called the Diffie Hellman key-exchange system, which is outlined as follows (with Alice and Bob trying to communicate): 1. There's a publicly listed prime number that is decided, in our example, it will be 19 ($p = 19$), and$g=2$, which is also publicly declared. 2. Alice picks a secret number (say, 6), and computes:$2^6 \equiv 64 \equiv 7 \pmod 19$and, sends this result off to Bob, and we call this result$A$. 3. Bob does the same (but, with his secret number, which is 13),$2^13 \equiv 3 \pmod 19$We'll call this$B$. 4. Now, Alice takes the number she received ($B$), and raises it to her secret number (call it$a$):$B^a \equiv 3^6 \equiv 7 \pmod 19$5. Bob does similarly:$A^b \equiv 7^13 \equiv 7 \pmod 19$As you can see, at the end, both of them share one key, despite having started from completely different keys, and since this is based on the DLP, it is incredibly hard to solve, even with a supercomputer for (very) large values for$p\$ (200+ digits).
So, what does any of this have to do with groups?
Groups (and abstract algebra in general), lets us generalize.
Using the definitions of cyclic groups that define only the properties we need, we can say this (quoted verbatim from Wikipedia):
1. Alice and Bob agree on a finite cyclic group G and a generating element g in G. (This is usually done long before the rest of the protocol; g is assumed to be known by all attackers.) We will write the group G multiplicatively.
2. Alice picks a random natural number a and sends ga to Bob.
3. Bob picks a random natural number b and sends gb to Alice.
4. Alice computes (gb)a.
5. Bob computes (ga)b.
This immediately makes the system a LOT more powerful, because now, instead of dealing with just numbers, we can deal with ANY cyclic group we want, they can even be chess moves, if you can somehow wrangle them into a cyclic group. | 2019-03-25 22:47:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44726091623306274, "perplexity": 1154.4049094643522}, "config": {"markdown_headings": true, "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-2019-13/segments/1552912204461.23/warc/CC-MAIN-20190325214331-20190326000331-00042.warc.gz"} |
https://stats.stackexchange.com/questions/171602/gibbs-sampler-implementation/171614 | Gibbs sampler implementation
I am just getting started with the Gibbs Sampler and came across an implementation from here and here and here. All of theses implementations are based on the first article.
There is an inner loop in the implementation and I don't understand it's purpose.
Here is the code (written in julia). It's been changed slightly to the implementation from the article, but not where it matters.
function gibbs(n, thin)
#array to store the results
mat = Array(Float64, (n,2))
x = y = 0.0
#outer loop number of samples to draw
for i in 1:n
#inner loop: purpose unknown.
for j in 1:thin
x = rand ( Normal( .9 * y, 1 - .9^2))
y = rand ( Normal( .9 * x, 1 - .9^2))
end
mat[i,1] = x; mat[i,2] = y
end
mat
#end of program
end
function main()
gibbs(10000, 200)
end
main()
From my understanding the inner loop creates an addition $n * thin$ amount of samples and thus decreases the likelihood of two consecutive draws being to close to each other. Is there another purpose to this?
• It's to reduce the dependence in sampled values more generally (rather than necessarily being "near each other", though that's the typical case) – Glen_b Sep 8 '15 at 15:40
• Thanks for the answer. Care to post it as an answer then I can vote this question to answered. – Vincent Sep 8 '15 at 15:44
• Fortunately you effectively have all parts of the answer I would have posted now, plus some more besides. All I can do is upvote them. – Glen_b Sep 9 '15 at 4:40
As it was already mentioned, this is called thinning, however, as Kruschke noticed it is "rarely useful" and quoting Link and Eaton (2012), he writes that
... basic conclusion of the article is that thinning of chains is not usually appropriate when the goal is precision of estimates from an MCMC sample. (Thinning can be useful for other reasons, such as memory or time constraints in post-chain processing, but those are very different motivations than precision of estimation of the posterior distribution.)
The paper published in Methods in Ecology and Evolution is freely avilable from the publisher.
So it is disputable if thinning is that much helpful, i.e. the inner loop may not be that important in the code and in many cases can be simply omitted with saving the whole simulation output.
• (+1) I came here to say precisely this! – Sycorax Sep 8 '15 at 18:02
• +1 I have to say that in most cases I agree; to thin enough to make it worthwhile means throwing out an enormous amount of information quite needlessly. – Glen_b Sep 9 '15 at 4:38
Just to expand on what you and @Glen_b said: The point of the inner loop is to reduce correlation among sampled values. A common way to do this is by only taking every nth value, a process called Thinning.
From Wikipedia:
It is common to ignore some number of samples at the beginning and then consider only every th sample when averaging values to compute an expectation. … The reason for this is that (1) successive samples are not independent of each other but form a Markov chain with some amount of correlation; (2) the stationary distribution of the Markov chain is the desired joint distribution over the variables, but it may take a while for that stationary distribution to be reached.
Your example (the inner loop) does this slightly differently. Instead of reducing correlation between samples by taking every nth value, it obscures it by randomizing each sample thin number of times. | 2019-08-26 07:58:30 | {"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": 0.6026923060417175, "perplexity": 1044.9177127449032}, "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-2019-35/segments/1566027331228.13/warc/CC-MAIN-20190826064622-20190826090622-00442.warc.gz"} |
http://www.maths.usyd.edu.au/u/pubs/publist/preprints/2015/kozic-20.html | ## Vertex operators and principal subspaces of level one for $$U_q (\widehat{\mathfrak{sl}}_2)$$
### Slaven Kožić
#### Abstract
We consider two different methods of associating vertex algebraic structures with the level $$1$$ principal subspaces for $$U_q (\widehat{\mathfrak{sl}}_2)$$. In the first approach, we introduce certain commutative operators and study the corresponding vertex algebra and its module. We find combinatorial bases for these objects and show that they coincide with the principal subspace bases found by B. L. Feigin and A. V. Stoyanovsky. In the second approach, we introduce the, so-called nonlocal q-vertex algebras, investigate their properties and construct the nonlocal q-vertex algebra and its module, generated by Frenkel-Jing operator and Koyama's operator respectively. By finding the combinatorial bases of their suitably defined subspaces, we establish a connection with the Rogers-Ramanujan identities. Finally, we discuss further applications to quantum quasi-particle relations.
Keywords: affine Lie algebra, quantum affine algebra, quantum vertex algebra, principal subspace, quasi-particle, combinatorial basis.
: Primary 17B37; secondary (Primary), 17B69 (secondary).
This paper is available as a pdf (616kB) file.
Tuesday, September 22, 2015 | 2017-11-23 16:56:10 | {"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": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5864673256874084, "perplexity": 1374.2577088944558}, "config": {"markdown_headings": true, "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-2017-47/segments/1510934806844.51/warc/CC-MAIN-20171123161612-20171123181612-00673.warc.gz"} |
https://www.jobilize.com/trigonometry/course/7-4-the-other-trigonometric-functions-by-openstax?qcr=www.quizover.com&page=2 | # 7.4 The other trigonometric functions (Page 3/14)
Page 3 / 14
Use reference angles to find all six trigonometric functions of $\text{\hspace{0.17em}}-\frac{7\pi }{4}.$
$\begin{array}{l}\\ \mathrm{sin}\left(\frac{-7\pi }{4}\right)=\frac{\sqrt{2}}{2},\mathrm{cos}\left(\frac{-7\pi }{4}\right)=\frac{\sqrt{2}}{2},\mathrm{tan}\left(\frac{-7\pi }{4}\right)=1,\\ \mathrm{sec}\left(\frac{-7\pi }{4}\right)=\sqrt{2},\mathrm{csc}\left(\frac{-7\pi }{4}\right)=\sqrt{2},\mathrm{cot}\left(\frac{-7\pi }{4}\right)=1\end{array}$
## Using even and odd trigonometric functions
To be able to use our six trigonometric functions freely with both positive and negative angle inputs, we should examine how each function treats a negative input. As it turns out, there is an important difference among the functions in this regard.
Consider the function $\text{\hspace{0.17em}}f\left(x\right)={x}^{2},$ shown in [link] . The graph of the function is symmetrical about the y -axis. All along the curve, any two points with opposite x -values have the same function value. This matches the result of calculation: $\text{\hspace{0.17em}}{\left(4\right)}^{2}={\left(-4\right)}^{2},{\left(-5\right)}^{2}={\left(5\right)}^{2},$ and so on. So $\text{\hspace{0.17em}}f\left(x\right)={x}^{2}\text{\hspace{0.17em}}$ is an even function, a function such that two inputs that are opposites have the same output. That means $\text{\hspace{0.17em}}f\left(-x\right)=f\left(x\right).$
Now consider the function $\text{\hspace{0.17em}}f\left(x\right)={x}^{3},$ shown in [link] . The graph is not symmetrical about the y -axis. All along the graph, any two points with opposite x -values also have opposite y -values. So $\text{\hspace{0.17em}}f\left(x\right)={x}^{3}\text{\hspace{0.17em}}$ is an odd function, one such that two inputs that are opposites have outputs that are also opposites. That means $\text{\hspace{0.17em}}f\left(-x\right)=-f\left(x\right).$
We can test whether a trigonometric function is even or odd by drawing a unit circle with a positive and a negative angle, as in [link] . The sine of the positive angle is $\text{\hspace{0.17em}}y.\text{\hspace{0.17em}}$ The sine of the negative angle is $\text{\hspace{0.17em}}-y.\text{\hspace{0.17em}}$ The sine function, then, is an odd function. We can test each of the six trigonometric functions in this fashion. The results are shown in [link] .
## Even and odd trigonometric functions
An even function is one in which $\text{\hspace{0.17em}}f\left(-x\right)=f\left(x\right).$
An odd function is one in which $\text{\hspace{0.17em}}f\left(-x\right)=-f\left(x\right).$
Cosine and secant are even:
Sine, tangent, cosecant, and cotangent are odd:
## Using even and odd properties of trigonometric functions
If the secant of angle $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ is 2, what is the secant of $\text{\hspace{0.17em}}-t?$
Secant is an even function. The secant of an angle is the same as the secant of its opposite. So if the secant of angle $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ is 2, the secant of $\text{\hspace{0.17em}}-t\text{\hspace{0.17em}}$ is also 2.
If the cotangent of angle $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ is $\text{\hspace{0.17em}}\sqrt{3},$ what is the cotangent of $\text{\hspace{0.17em}}-t?$
$-\sqrt{3}$
## Recognizing and using fundamental identities
We have explored a number of properties of trigonometric functions. Now, we can take the relationships a step further, and derive some fundamental identities. Identities are statements that are true for all values of the input on which they are defined. Usually, identities can be derived from definitions and relationships we already know. For example, the Pythagorean Identity we learned earlier was derived from the Pythagorean Theorem and the definitions of sine and cosine.
## Fundamental identities
We can derive some useful identities from the six trigonometric functions. The other four trigonometric functions can be related back to the sine and cosine functions using these basic relationships:
$\mathrm{tan}\text{\hspace{0.17em}}t=\frac{\mathrm{sin}\text{\hspace{0.17em}}t}{\mathrm{cos}\text{\hspace{0.17em}}t}$
$\mathrm{sec}\text{\hspace{0.17em}}t=\frac{1}{\mathrm{cos}\text{\hspace{0.17em}}t}$
$\mathrm{csc}\text{\hspace{0.17em}}t=\frac{1}{\mathrm{sin}\text{\hspace{0.17em}}t}$
$\text{cot}\text{\hspace{0.17em}}t=\frac{1}{\text{tan}\text{\hspace{0.17em}}t}=\frac{\text{cos}\text{\hspace{0.17em}}t}{\text{sin}\text{\hspace{0.17em}}t}$
what are you up to?
nothing up todat yet
Miranda
hi
jai
hello
jai
Miranda Drice
jai
aap konsi country se ho
jai
which language is that
Miranda
I am living in india
jai
good
Miranda
what is the formula for calculating algebraic
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda
state and prove Cayley hamilton therom
hello
Propessor
hi
Miranda
the Cayley hamilton Theorem state if A is a square matrix and if f(x) is its characterics polynomial then f(x)=0 in another ways evey square matrix is a root of its chatacteristics polynomial.
Miranda
hi
jai
hi Miranda
jai
thanks
Propessor
welcome
jai
What is algebra
algebra is a branch of the mathematics to calculate expressions follow.
Miranda
Miranda Drice would you mind teaching me mathematics? I think you are really good at math. I'm not good at it. In fact I hate it. 😅😅😅
Jeffrey
lolll who told you I'm good at it
Miranda
something seems to wispher me to my ear that u are good at it. lol
Jeffrey
lolllll if you say so
Miranda
but seriously, Im really bad at math. And I hate it. But you see, I downloaded this app two months ago hoping to master it.
Jeffrey
which grade are you in though
Miranda
oh woww I understand
Miranda
Jeffrey
Jeffrey
Miranda
how come you finished in college and you don't like math though
Miranda
gotta practice, holmie
Steve
if you never use it you won't be able to appreciate it
Steve
I don't know why. But Im trying to like it.
Jeffrey
yes steve. you're right
Jeffrey
so you better
Miranda
what is the solution of the given equation?
which equation
Miranda
I dont know. lol
Jeffrey
Miranda
Jeffrey
answer and questions in exercise 11.2 sums
how do u calculate inequality of irrational number?
Alaba
give me an example
Chris
and I will walk you through it
Chris
cos (-z)= cos z .
cos(- z)=cos z
Mustafa
what is a algebra
(x+x)3=?
6x
Obed
what is the identity of 1-cos²5x equal to?
__john __05
Kishu
Hi
Abdel
hi
Ye
hi
Nokwanda
C'est comment
Abdel
Hi
Amanda
hello
SORIE
Hiiii
Chinni
hello
Ranjay
hi
ANSHU
hiiii
Chinni
h r u friends
Chinni
yes
Hassan
so is their any Genius in mathematics here let chat guys and get to know each other's
SORIE
I speak French
Abdel
okay no problem since we gather here and get to know each other
SORIE
hi im stupid at math and just wanna join here
Yaona
lol nahhh none of us here are stupid it's just that we have Fast, Medium, and slow learner bro but we all going to work things out together
SORIE
it's 12
what is the function of sine with respect of cosine , graphically
tangent bruh
Steve
cosx.cos2x.cos4x.cos8x
sinx sin2x is linearly dependent
what is a reciprocal
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
I don't understand how radicals works pls
How look for the general solution of a trig function | 2020-09-27 16:41:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 27, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7502975463867188, "perplexity": 927.9427357658446}, "config": {"markdown_headings": true, "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-2020-40/segments/1600400283990.75/warc/CC-MAIN-20200927152349-20200927182349-00411.warc.gz"} |
http://tasks.illustrativemathematics.org/content-standards/HSA/CED/A/3/tasks/1010 | # Bernardo and Sylvia Play a Game
Alignments to Content Standards: A-CED.A.3 A-CED.A.1
Bernardo and Silvia play the following game. An integer between 0 and 999, inclusive, is selected and given to Bernardo. Whenever Bernardo receives a number, he doubles it and passes the result to Silvia. Whenever Silvia receives a number, she adds 50 to it and passes the result to Bernardo. The winner is the last person who produces a number less than 1000. What is the smallest initial number that results in a win for Bernardo?
## IM Commentary
This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.
In addition to content standards concerning the creation and use of inequalities, the task serves as an illustration of mathematical practices: For one, the task requires the ability to persevere through repeated applications of the inequalities, and to make sense of the results in the context of the game (MP1). The recursive process of working backwards from a desired result involves considerable abstract and quantitive reasoning (MP2) applied to the structure of the game (MP7). Recognition that the game situation can be represented using inequalities requires some facility with mathematical modeling (MP4).
This task was adapted from problem #20 on the 2012 American Mathematics Competition (AMC) 10B Test.
For the 2012 AMC 10B, the question was "Let $N$ be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of $N$?"
For the 2012 AMC 10B, which was taken by 35,086 students, the multiple choice answers for the problem had the following distribution:
Choice Answer Percentage of Answers (A)* 7 21.93 (B) 8 8.74 (C) 9 10.69 (D) 10 7.99 (E) 11 6.99 Omit -- 43.63
Of the 35,086 students: 17,169, or 49%, were in 10th grade; 9,928 or 28%, were in 9th grade; and the remainder were below than 9th grade.
## Solution
The smallest initial number for which Bernardo wins after one round is the smallest integer solution of $2n+50\ge1000$, which is $475$. The smallest initial number for which he wins after two rounds is the smallest integer solution of $2n+50\ge475$, which is 213. Similarly, the smallest initial numbers for which he wins after three and four rounds are 82 and 16, respectively. There is no initial number for which Bernardo wins after more than four rounds. Thus the smallest integer where Bernardo wins is 16. | 2022-05-28 14:31:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5719742178916931, "perplexity": 819.7287194595584}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "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-2022-21/segments/1652663016853.88/warc/CC-MAIN-20220528123744-20220528153744-00592.warc.gz"} |
https://unmethours.com/question/948/openstudio-and-sketchup-plugin-linux-wine/ | Question-and-Answer Resource for the Building Energy Modeling Community
Get started with the Help page
# OpenStudio and SketchUp Plugin + Linux (Wine)
Hello, I am trying to make the OpenStudio SketchUp Plugin work under Linux (Xubuntu) with Wine. I have installed SketchUp Make 2014 for Windows with Wine (in Xubuntu) and with some tricks found on WineHQ about it I made SketchUp work. After that, I have installed the OpenStudio Suite for Windows, again with Wine, but I can't see any Plugin in SketchUp. In the OpenStudio/Ruby directory (Wine under Linux, again) there is a folder which contains the SketchUp plugin ruby files, which are supposed to work fine in a "pure Windows" OS, but here with Wine the plugin cannot be loaded. In fact I get the error "Error loading OpenStudio SketchUp Plug-in: cannot load such file -- pathname", which in the end derives from the file "Startup.rb" in the last lines:
UI.messagebox("Error loading OpenStudio SketchUp Plug-In:\n #{e.message}", MB_OK)
The point is: does anybody get this plugin for SketchUp work with Linux (Wine)? Thank you!
edit retag close merge delete
I haven't heard of anyone getting this to work for either the legacy plug-in or the plug-in included with the new application suite. I don't think that it would be impossible but I don't know how hard it would be.
( 2014-11-02 22:50:33 -0500 )edit
Sort by » oldest newest most voted
As you're running on linux, you had to add the parameter /disablerubyapp, needed to run SketchUp version 2014 & 2015, is also the reason why plugins don't work. Even dos2unix all the *.rb files didn't satisfy neither. Also installing under wine the new ruby versions 2.0 & 2.4 didn't solve. Got also an exit out of SU2015 by simple pas over the file-menu. As far as now best version to run on linux is the 2013. There you'll have the possibility to run ruby scripts. Having a problem with an error concerning shell32. dll
Greetings Xiao Shi Zi.
more
I got stuck at the making SketchUp stage (on Ubuntu 12.04).
I suggest a thorough check of the dependencies - is Ruby installed and working ? and the filepaths - can you open the addons scripts at the locations where the error message occurs ? It is a safe assumption that the Windows installation procedure has left some windows style filepath and locations. I would look for those and if you find any, edit them to point to where they actually are.
more
Thanks, Probably it's "just" a matter of windows-style paths, different from wine-style paths, but indeed it's a huge work since there are a lot of rb scripts in this plugin.. I'll try and check whether it's reasonable to change them all (and the result is not guaranteed...).
( 2014-11-02 03:55:31 -0500 )edit
I have followed the flow of the code:
1) wine/drive_c/users/Public/Application Data/.../SketchUp/Plugins/OpenStudio/Startup.rb require 'OpenStudio/OpenStudio-config.rb'
2) wine/drive_c/users/Public/Application Data/.../SketchUp/Plugins/OpenStudio/OpenStudio-config.rb require 'C:\Program Files (x86)\OpenStudio 1.5.0\Ruby\openstudio.rb'
3) C:\Program Files (x86)\OpenStudio 1.5.0\Ruby\openstudio.rb at the beginning of this file the following command won't work: require "pathname"
Stuck here.
( 2014-11-02 06:36:51 -0500 )edit
I have went on changing the relative paths with absolute paths until the "openssl.so" (which can't be modified by text editing of course) gives the error: "Verify that ruby can access the OpenSSL libraries".
Can't really go on now.
( 2014-11-02 07:22:55 -0500 )edit | 2020-10-27 17:09:42 | {"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": 0, "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": 0.19211705029010773, "perplexity": 5971.592624208617}, "config": {"markdown_headings": true, "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-2020-45/segments/1603107894426.63/warc/CC-MAIN-20201027170516-20201027200516-00209.warc.gz"} |
https://techwhiff.com/learn/please-answer-all-match-each-of-the-following/21684 | # Please answer ALL. Match each of the following characteristics with the financial statement it describes. Each...
###### Question:
Match each of the following characteristics with the financial statement it describes. Each financial statement may be used more than once. Reports as of a specific date Balance sheet The first statement prepared Income statement Has three sections: ✓ [Choose ] operating, investing and Statement of retained earnings financing Income statement Balance sheet Reports only revenues and Statement of cash flows expenses HOUmuuuuomon The second statement prepared [Choose] A formal presentation of the accounting equation [Choose] Statement of retaine The connecting link between the income statement and balance sheet Shows the beginning retained earnings account balance [Choose]
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15. a) (6 points) Industry demand is given by P = 120-0.4Q. The long-run industry costs are such that: LAC = LMC = $60. Based on this information, which of the following is true? If the market is a pure monopoly, the price of the good will be$90. b) If the market is perfectly competitive, 200 units... | 2022-12-03 00:07:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3437422215938568, "perplexity": 1671.387668240674}, "config": {"markdown_headings": true, "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-2022-49/segments/1669446710916.70/warc/CC-MAIN-20221202215443-20221203005443-00138.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=2018_AMC_8_Problems/Problem_20&diff=prev&oldid=98973 | # Difference between revisions of "2018 AMC 8 Problems/Problem 20"
## Problem 20
In $\triangle ABC,$ a point $E$ is on $\overline{AB}$ with $AE=1$ and $EB=2.$ Point $D$ is on $\overline{AC}$ so that $\overline{DE} \parallel \overline{BC}$ and point $F$ is on $\overline{BC}$ so that $\overline{EF} \parallel \overline{AC}.$ What is the ratio of the area of $CDEF$ to the area of $\triangle ABC?$
$[asy] size(7cm); pair A,B,C,DD,EE,FF; A = (0,0); B = (3,0); C = (0.5,2.5); EE = (1,0); DD = intersectionpoint(A--C,EE--EE+(C-B)); FF = intersectionpoint(B--C,EE--EE+(C-A)); draw(A--B--C--A--DD--EE--FF,black+1bp); label("A",A,S); label("B",B,S); label("C",C,N); label("D",DD,W); label("E",EE,S); label("F",FF,NE); label("1",(A+EE)/2,S); label("2",(EE+B)/2,S); [/asy]$
$\textbf{(A) } \frac{4}{9} \qquad \textbf{(B) } \frac{1}{2} \qquad \textbf{(C) } \frac{5}{9} \qquad \textbf{(D) } \frac{3}{5} \qquad \textbf{(E) } \frac{2}{3}$
## Solution
Looking at this diagram, we notice some similar triangles. Since $\overline{DE} \parallel \overline{BC}$, $\angle{ACB}=\angle{ADE}$. Since$\triangle{ABC}$ and triangle $\triangle{AED}$ share $\angle{A}$, $\triangle{ABC}$ is similar to $\triangle{AED}$ by the AA similarity theorem. Using similar logic we can find $\triangle{ABC}$ is similar to $\triangle{EBF}$. The ratio of the areas of two similar triangles is equivalent to the square of the ratio of the lenths, so the area of $\triangle{AED}$ is $\frac{1}{9}$ times the area of $\triangle{ABC}$ and $\triangle{EBF}$ is $\frac{4}{9}$ times the area of $\triangle{ABC}$. This means that the area of quadrilateral $CDEF$ is is $1-(\frac{1}{9}+\frac{4}{9})=\frac{4}{9}$ times the area of $\triangle{ABC}$, so our answer is $\boxed{\textbf{(A) }\frac 49}$ | 2020-11-30 08:17:50 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 34, "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": 0.7395979762077332, "perplexity": 74.42382334037413}, "config": {"markdown_headings": true, "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-2020-50/segments/1606141211510.56/warc/CC-MAIN-20201130065516-20201130095516-00156.warc.gz"} |
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# proton synchrotron theory
In addition to protons, PS has accelerated alpha particles, oxygen and sulphur nuclei, electrons, positrons and antiprotons.[1]. Intrinsic Features of Slow Cycle SynchrotronSynchrotron Based System zAfter the first application to LLUMC in 1990, which was the first hospital based proton therapy system, slow cycle synchrotron have been widely applied to proton and carbon therapy systems . It uses a magnetic field to turn the particles in the circle and an electric field to speed up the particles. In the course of its history it has juggled many different kinds of particles, feeding them directly to experiments or to more powerful accelerators. In 1976 the Super Proton Synchrotron (SPS) became a new client of the PS. By August 1959 the PS was ready for its first beam, and on 24 of November the machine reached a beam energy of 24 GeV. The theory is applied to the 10-Bev proton synchrotron of the Academy of Sciences, USSR. Published 1 July 1947 • Proceedings of the Physical Society, Volume 59, Number 4. Heidelberg 1959, Nuclear Instrumentation I / Instrumentelle Hilfsmittel der Kernphysik I, https://doi.org/10.1007/978-3-642-45926-9_6, Encyclopedia of Physics / Handbuch der Physik. For this fit, we find that synchrotron radiation by protons dominates the TeV emission, pion photoproduction being less important with the consequence that we predict a lower neutrino flux than in other proton … Download Citation | The Proton Synchrotron | Three proton synchrotrons are now in operation in the energy range above 1000 MeV (1 GeV). The Proton Synchrotron (PS) is a particle accelerator at CERN. This report sums up in two volumes the first 50 years of operation of the CERN Proton Synchrotron. A quarter of a century ago, CERN’s gleaming new Super Proton Synchrotron supplied its first proton beams. The amount of focusing in this way is not very great, and consequently the amplitudes of the betatron oscillations are large. The magnetic field which bends the particle beam into its fixed path increases with time, and is synchronized to the increasing energy of the particles. The basic design of the Berkeley bevatron stems fromthe proposals of W.M.Brobeck (1). First we need a source of energetic electrons to feed into the ring and this is done using a linear accelerator ( linac ) which produces electrons at energies which can range from hundreds of MeV (10 6 eV) to several GeV (10 9 eV). It has since served as a pre-accelerator for the Intersecting Storage Rings (ISR) and the Super Proton Synchrotron (SPS), and is currently part of the Large Hadron Collider (LHC) accelerator complex. n. A ring-shaped synchrotron that accelerates protons to energies of several billion electron volts. The components are carefully matched up with the travelling particle beam so that the circle stays the same size while the particles go faster. It will also soon feed the AWAKE experiment which aims to … _o P__ New experiments started running in the East area, such as the CLOUD experiment. The synchrotron (as in Proton Synchrotron) is a type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed path. When SPS started to operate as a proton-antiproton collider — the SppS — the PS had the double task of producing an intense 26 GeV/c proton beam for generating antiprotons at 3.5 GeV/c to be stored in the Antiproton Accumulator (AA), and then accelerating the antiprotons to 26 GeV/c for transfer to the SPS. Proton-synchrotron accelerator theory: If you experience any problem watching the video, click the download button below. [5] The focusing strength chosen required a vacuum chamber of 12 cm width and 8 cm height, with magnets of about 4000 tonnes total mass. In synchrotron. [4] However, the stronger focusing the higher a precision of alignment of magnets required. The "'2m Bubble Chamber "'was a device used in conjunction with CERN s 25 GeV Proton Synchrotron ( PS ) machine to study high-energy physics. Magnetic field to speed up the particles travels around the fixed circular path they will around! Off MathJax turn on … a Nobel discovery Hunting the heavyweights with UA1 and UA2 turn... And consequently the amplitudes of the accelerator equilibrium orbit, resonances of and. Record ; other Related research ; proton synchrotron theory: Bless, R C Publication Date: Oct... A second problem in the Bev energy range operation of the Berkeley bevatron stems fromthe proposals of W.M.Brobeck ( )! R C Publication Date: Thu Oct 31 00:00:00 EST 1968 research Org to 180 MeV and. 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## atomic structure of chlorine atom
This page was created by Yinon Bentor. Comments One hydrogen atom is attached to one chlorine atom, but they have different masses. Please enable it in your browser. The relative atomic masses are not whole numbers like mass numbers. Now with the atomic weight information we can consider matching up atoms on a mass-to-mass basis. Chlorine is a yellow-green gas at room temperature. US toll free: 1-844 677 4151, © Science Photo Library Limited 2021 If it acquires noble gas configuration by accepting requisite number of electrons, then what would be the charge on the ion so formed? We have Provided Structure of the Atom Class 9 Science MCQs Questions with Answers to help students understand the concept very well. Charges of Atoms You can see that each part of the atom is labeled with a "+", "-", or a "0." 32) has isotopes with wt. The atomic number of chlorine is 17; thus, it has seventeen protons and seventeen electrons. Therefore, the valency of chlorine is often consider⦠Chlorine is a non-metal. Chlorine has 9 isotopes with mass numbers ranging from 32 to 40. If an atom has 12 protons (atomic number = 12), it must be magnesium. This is because the abundance of isotopes of an element is different. Atomic Mass Of special interest are the hydrogen isotopes (radio hydrogen) ( 2 H and H b ) and 2 H which have been given special namesâdeuterium and tritium respectively. Halogens 26. Diagram of the nuclear composition, electron configuration, chemical data, and valence orbitals of an atom of chlorine-35 (atomic number: 17), the most common isotope of this element. That number tells you the number of protons in every atom of the element. Vital to life in ionic form, chlorine is a halogen in group 17, period 3, and the p-block of the periodic table. 25. Part of the series: Drawing Help & More. A chlorine atom has more protons in its nucleus than has a sodium atom (1) Both have three shells of electrons (1) Electrons more strongly attracted by chlorine nucleus so size smaller than Na (1) An electron shell is lost when a sodium ion is formed from a sodium atom (1) Inner electrons more strongly attracted so ion smaller than atom (1) Electronic structure. Protons and Neutrons in Chlorine. Similarly, every chlorine atom (atomic number = 17) has 17 protons; every uranium atom (atomic number = 92) has 92 protons. Alkali Metals Please contact your Account Manager if you have any query. How many electrons are there in the L shell? Model release not required. Why does a Chlorine Molecule have a Covalent Bond?. Soln: Atomic number of chlorine atom = 17. Atomic mass of Chlorine is 35.453 u. Those symbols refer to the charge of the particle. For example: a neutral sodium atom can lose one electron to become a positively charged sodium atom ($$\text{Na}^{+}$$). Chlorine is a chemical element with atomic number 17 which means there are 17 protons and 17 electrons in the atomic structure. Metalloids This image is not available for purchase in your country. Often, the resulting number contains a decimal. Every chlorine atom has 17 protons and 17 electrons. Chlorine is the best known of the halogen elements. It is a halogen (17 th group) in the 3 rd period of the periodic table. The atom that is formed in either of these two cases is called an ion. Chlorine is a chemical element with the symbol Cl and atomic number 17. Cl-36 is produced in the atmosphere by spallation of Ar-36 by interactions with cos⦠Chlorine (Cl). CARLOS CLARIVAN / SCIENCE PHOTO LIBRARY. 327-329 Harrow Road Use of this web site is restricted by this site's license This implies that chlorine contains a total of 17 protons and 17 electrons in its atomic structure. Relative reactivity. Please help as soon as possible give good detail answer please this a physical science ⦠Calcium is a group II element, but it's metal. Atomic Structure P2: subatomic particles Subatomic particles are the smaller objects inside the atom: protons, neutrons and electrons! Neutrons = Mass Number - Protons 00:00:44,969 -- 00:00:51,969 When we look at Chlorine on the periodic table it has an atomic number of 17, therefore it 00:00:55,149 -- 00:00:59,860 has 17 protons. 17 electrons (white) occupy available electron shells (rings). Date of Discovery A hydrogen atom has a mass of 1.008 AMU and a chlorine atom ⦠Atomic Number K L M. 2 8 7. Property release not required. Rare Earth Elements, Basic Information | Atomic Structure | Isotopes | Related Links | Citing This Page. The atomic number of chlorine is 17. Total number of protons in the nucleus is called the atomic number of the atom and is given the symbol Z.The total electrical charge of the nucleus is therefore +Ze, where e (elementary charge) equals to 1,602 x 10-19 coulombs. Copyright © 1996-2012 Yinon Bentor. Non-Metals (Atomic number of chlorine is 17). Alkaline Earth Metals Its electron configuration is ⦠Chlorine Atom. Chlorine is an element in the periodic table which is denoted by Cl. Crystal Structure, Element Groups: Relative atomic mass has no units. agreement. Name If an atom has 12 protons (atomic number = 12), it must be magnesium. There are two principal stable isotopes of chlorine, of mass 35 and 37, found in the relative proportions of 3:1 respectively, giving chlorine atoms in bulk an apparent atomic weight of 35.5. Similarly sulphur (atomic wt. For example, the atomic mass of chlorine (Cl) is 35.45 amu because chlorine is composed of several isotopes, some (the majority) with an atomic mass of 35 amu (17 protons and 18 neutrons) and some with an atomic mass ⦠The number of neutrons in an atom can vary within small limits. Every element is unique and has an atomic number. the Terms and Conditions. How many electrons are there in the L shell? A neutral chlorine atom can gain one electron to become a negatively charged chlorine ion ($$\text{Cl}^{-}$$). Name: Chlorine Symbol: Cl Atomic Number: 17 Atomic Mass: 35.4527 amu Melting Point:-100.98 °C (172.17 K, -149.764 °F) Boiling Point:-34.6 °C (238.55 K, -30.279997 °F) Number of Protons/Electrons: 17 Number of Neutrons: 18 Classification: Halogen Crystal Structure: Orthorhombic Density @ 293 K: 3.214 g/cm 3 Color: green Atomic Structure The structure of each atoms electrons is unique but there is a pattern. The first electron shell belonging to chlorine contains a total of two electrons whereas the second electron shell of chlorine contains 8 electrons. Chlorine is in group 7 of the periodic table. In the atom of an element X, 6 electrons are present in the outermost shell. Write down the electron distribution of chlorine atom. of 35 may have an isotopic variety with 37 (37 Cl). 33 and 34 (33 S, 34 S) and chlorine with the usual atomic wt. For example, a carbon atom weighs less than 2 × × 10 â23 g, and an electron has a charge of less than 2 × × 10 â19 C (coulomb). The stability of an element's outer (valence) electrons determines its chemical and physical properties. Number of Neutrons Write down the electron distribution of chlorine atom. 17 electrons (green) bind to the nucleus, successively occupying available electron shells (rings). 1550520. So, its electronic configuration is. London The atomic number is also called the proton number. Directions: Under the headings, explain how to obtain each piece of data. Then based on the information given in the row, determine the element and its contents, thus filling out the entire chart. By continuing, you agree to accept cookies in accordance with our Cookie policy. If it acquires noble gas configuration by accepting requisite number of electrons, then what would be the charge on the ion so formed? Atomic Structure. Science Photo Library (SPL) MCQ Questions for Class 9 Science with Answers were prepared based on the latest exam pattern. Electrons have a ⦠Noble Gases Melting Point Diagram of the nuclear composition and electron configuration of an atom of chlorine-35 (atomic number: 17), the most common isotope of this element. In elemental form it is a yellow-green, reactive, toxic gas (Cl2) that liquefies at minus 34 degrees Celsius. Atomic structure of chlorine atom and Cl- 2 See answers DangerousMe2 DangerousMe2 Answer: An atom of chlorine-35 contains 18 neutrons (17 protons + 18 neutrons = 35 particles in the nucleus) while an atom of chlorine-37 contains 20 neutrons (17 protons + 20 neutrons = 37 particles in the nucleus). The nucleus consists of 17 protons (red) and 18 neutrons (blue). How many electrons are there in the L shell? Check the below NCERT MCQ Questions for Class 9 Science Chapter 4 Structure of the Atom with Answers Pdf free download. The atomic structure of atoms is down to the number of electrons that a certain element has. How to Draw the Atomic Model for Chlorine. It has 17 positive charges and 17 negative charges, meaning that it is neutral overall. The ratio of Cl-36 to stable Cl in the environment is about 700 E -15 : 1. chlorine-35 is about 3 times as abundant as chlorine-37. Chlorine (Cl). Chlorine (Cl). Help In the human body, it's found as the chloride ion, where it ⦠GB 340 7410 88. Chlorine is a chemical element with atomic number 17 which means there are 17 protons in its nucleus. Transition Metals This is a picture of the shared electrons making a covalent bond in a chlorine molecule. Only three of these isotopes occur naturally: stable Cl-35 (75.77%)and Cl-37 (24.23%), and radioactive Cl-36. Atomsâand the protons, neutrons, and electrons that compose themâare extremely small. Other Metals Note that, each element may contain more isotopes, therefore this resulting atomic mass is calculated from naturally ⦠W9 3RB A periodic table shows you the number of electrons (for chlorine it's 17 and for oxygen its 8). Continue. If an atom has 8 protons (atomic number = 8), it must be oxygen. 17 electrons (white) occupy available electron shells (rings). An ion is a charged atom. How would you account for the great chemical similarity of the two isotopes? Example Chlorine consists of two isotopes, chlorine â 35 and chlorine â 37 in the ratio 3 : 1. from this information, what can be concluded about the atomic mass of chlorine. In the atom of an element X, 6 electrons are present in the outermost shell. Write down the electron distribution of chlorine atom. Chlorine is essential for living organisms. The nucleus consists of 17 protons (red) and 18 neutrons (orange). The nucleus consists of 17 protons (red) and 18 neutrons (orange). (Atomic number of chlorine is 17). By sharing this link, I acknowledge that I have read and understand VAT no. Atomic Number of Chlorine. Chlorine is a group VII element, so it has 7 valence electrons. So, calcium atoms form metallic bonds and exist in a vast network structure ⦠Links, Show Table With: Electron Configuration Diagram of the nuclear composition, electron configuration, chemical data, and valence orbitals of an atom of chlorine-35 (atomic number: 17), the most common isotope of this element. All Rights Reserved. A chlorine atom has 7 electrons in its outer shell. Now a chlorine ion has a closed outer shell, where as a chlorine atom lacks an electron of having a closed outer shell how does this relate to what is the difference atomic structure between the two isotopes of chlorine? Letâs take hydrogen chloride, HCl. Similarly, every chlorine atom (atomic number = 17) has 17 protons; every uranium atom (atomic number = 92) has 92 protons. Chlorine is a chemical element with atomic number 17 which means there are 17 protons in its nucleus.Total number of protons in the nucleus is called the atomic number of the atom and is given the symbol Z.The total electrical charge of the nucleus is therefore +Ze, where e (elementary charge) equals to 1,602 x 10-19 coulombs. Two chlorine atoms will each share one electron to get a full outer shell and form a stable Cl 2 molecule.. These electrons are arranged into 3 primary electron shells. About This Site L shell of chlorine contains 8 electrons. Boiling Point It is a ratio of two masses. Atomic Number â Protons, Electrons and Neutrons in Chlorine. There are no media in the current basket. The chemical symbol for Chlorine is Cl.. Atomic Mass of Chlorine. The isotopes chlorine-35 and chlorine-37 make up nearly all chlorine atoms in nature. Isotopes. (Atomic number of chlorine is 17). Some features of this website require JavaScript. Science Photo Library's website uses cookies. United Kingdom, Telephone: +44 (0) 20 7432 1100 Finally, the outermost electron shell of the chlorine atom (often referred to as the valence shell) contains a total of 7 electrons. So Chlorine-35 has a mass of 35. CARLOS CLARIVAN / SCIENCE PHOTO LIBRARY Number of Energy Levels: 3: First Energy Level: 2: Second Energy Level: 8: Third Energy Level: 7 The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate between them. For example, the atomic number of chlorine is 17. Therefore, it wants to form one covalent bond with, in this case, another Chlorine atom to complete its octet. Registered in England and Wales no. Gas ( Cl2 ) that liquefies at minus 34 degrees Celsius available for purchase in your country, 34 )! Clarivan / Science PHOTO LIBRARY carlos CLARIVAN / Science PHOTO LIBRARY carlos CLARIVAN / Science LIBRARY! Stable Cl 2 molecule Terms and Conditions 3: 1 acknowledge that I have read understand... Electrons in its outer shell and form atomic structure of chlorine atom stable Cl in the by... Called an ion group VII element, but it 's found as the chloride,... In this case, another chlorine atom and 34 ( 33 S, S... And understand the concept very well outer ( valence ) electrons determines its chemical and properties... Information, what can be concluded about the atomic weight information we can consider matching up on. Radioactive Cl-36 37 Cl ) students understand the concept very well atom has 17 protons its... Complete its octet acquires noble gas configuration by accepting requisite number of chlorine atom share one electron to get full! 17 th group ) in the periodic table shows you the number of.. 17 and for oxygen its 8 ), it 's found as the chloride ion, where it ⦠down... Found as the chloride ion, where it ⦠Write down the electron distribution of chlorine is an element different... Two isotopes, chlorine â 37 in the periodic table which is denoted by.... Atom that is formed in either of these isotopes occur naturally: stable (! Any query attached to one chlorine atom to complete its octet the environment is about times... 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Second electron shell belonging to chlorine contains 8 electrons of 35 may an. | 2021-09-17 01:25:52 | {"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": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3040177524089813, "perplexity": 2261.533574707779}, "config": {"markdown_headings": true, "markdown_code": false, "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-2021-39/segments/1631780053918.46/warc/CC-MAIN-20210916234514-20210917024514-00581.warc.gz"} |
https://physics.stackexchange.com/questions/405509/ads-cft-and-finiteness-of-entanglement-entropy-in-cft/423552 | # AdS/CFT and finiteness of entanglement entropy in CFT
AdS/CFT duality maps string theory to conformal field theory. String theory confirms Bekenstein-Hawking entropy, and thus the dual CFT must confirm it. However, CFT is still a quantum field theory, with entropic calculations technically turning out to be infinite without cutoff and scaling with volume.
I tried looking at some introductions, but in the middle of discussing holographic entanglement entropy, they all seem to introduce some "cutoff" without justifications, and thus I had to stop reading.
Also, some magic seems to occur by doing "holographic lift" that solves volume-scaling problem. Is this scaling problem resolved to area-scaling because of special nature of conformal field theory relative to quantum field theory?
If cut-off is necessary, how justified is that? Does this mean that nature described in CFT-or-QFT does have fundamental cutoff?
I hope what I share would be relevant to your question. Introducing a cut-off in the entanglement entropy $($EE$)$ is a way to regulate the counting of degrees of freedom. First, recall that for any co-dimension 2 space-like surface $B$ in a bulk spacetime, there's a Bousso bound $($with quantum corrections $S_{ent}(B)$$) on the integral of the entropy flux "s" on the light-sheet L(B) as [1]:$$\int_{L(B)}s \le \frac{Area(B)}{4G_{N}} + S_{ent}(B) $$Second, working in the framework of AdS/CFT, we assume the role of (H)EE as a measure of the degrees of freedom by the use of holographic c-theorem [2]. Now in general, the #d.o.f of the boundary theory is infinite, so is the area of the asymptotically AdS space. Therefore one can speak of some regulations in order to compare these infinities, by introducing a UV cut-off in the field theory which is equivalent to replacing the continuum by the discrete lattice of cells of the cut-off size. As discussed in [3], one can further assume that each of these cells contain one d.o.f, and also each d.o.f is capable of storing one bit of information. Hence in the calculation of holographic EE, the regulation in Area(B) means introducing an IR cut-off (z=\epsilon \to 0 in Poincare or \rho=\rho_{0} \to \infty in global coordinates) in the area functional$$ Area=\int d^{d-1}\sigma \, \sqrt{det(g_{ij})}$$Long story short, the cut-off is equivalent to the one bit information$($d.o.f$)\$ per Planck area bound. I hope it helps you. | 2020-10-24 06:35:32 | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8497552275657654, "perplexity": 847.7999051496834}, "config": {"markdown_headings": true, "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-2020-45/segments/1603107882102.31/warc/CC-MAIN-20201024051926-20201024081926-00526.warc.gz"} |
https://mullikine.github.io/posts/the-tapestry-of-truth/ | Firstly, a quote
"You cannot make something good until you understand who you are making it for." - The Outfit (2022 movie - I just started watching it)
The death of personal truth due to GPT3 and liberalism // Bodacious Blog
Artist’s rendition of the Tapestry of Truth
2 Thessalonians 2
… love the truth and so be saved.
Psa 51:6
Surely You desire integrity in the inner self,and You teach me wisdom deep within.
This is how I personally found and met the One True God; Firstly, through challenging discrimination (realising the visible world is false with rays of truth, and therefore not absolutely real, transitory), understanding what is personal spiritual truth (objective reality for a person), overcoming true lies, following God’s commandments from the heart (for the purpose of understanding God), subsequently arriving at knowledge of God, and then personally meeting God’s Holy Spirit. Now the world seems to be getting more sur-real after finding God.
Jesus is the cornerstone of the Kingdom of Light. Jesus’s gospel is the basis for any true apostle’s testimony, including my own.
Jesus’s gospel:
Romans 10:9-10
9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. 10 For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.
My own testimony, which follows demonstrates how I came to understand that Jesus saved me, through His death and resurrection by God the Father, and saving me from lies, which had prevented me from knowing who God is.
First read Gospel of Jesus then understand that what follows is my revelation, not a replacement of the gospel.
There is no other gospel than the Gospel of Jesus
Galatians 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 known In a classic theory of knowledge, there are typically 3 conditions that must be fulfilled in order for something to be considered "known": Belief Pretty self-explanatory, you believe that what you think is true. Example: I believe an elephant has grey skin. Justification You have a reason to think you belief is true. Example: I heard someone say elephant has grey skin. Truth An after-the-fact kind of justification, you can say an objective true statement about your belief. Example: you saw an elephant, and you saw it actually has grey skin, so you can say objectively "elephant has grey skin".
### Personal Truth
If you want to be able to discern truth from lies for yourself and stop questioning what truth is, you need to understand what personal truth is - it means everything you experience when you are being honest with yourself. It’s the witness of the truth of your hurt and what you love. A true testimony from you is a true witness [of your experience]. The state of your condition. The personal truth is your identity and stigmas (damage done to identity).
You are the only one aside from God with complete access to your personal truth, but it belongs to you.
God understands it fully but a person does not. It’s very hard for them to self-reflect on because it’s below normal reasoning.
Romans 8:26 ESV
Likewise the Spirit helps us in our weakness. For we do not know what to pray for as we ought, but the Spirit himself intercedes for us with groanings too deep for words.
Your entire soul (vegetative, to sensitive, to rational), your entire reality from (body, mind and astral) is not unlike a holographic projection cast from shining (emanating) absolute truth (God’s light) through your spirit, which is beneath all of those things.
The Aristotle soul is inseparable to the body; For example, the mind, which is part of soul is based on the body. The brain is an organ for thought, and the immanent part of mind is based on physical neurons in the brain, for example. But when God’s spirit is connected to the human by His indwelling, the mind can receive information from God!
But if we make our spirit truthful (compatible with God), then we can invite the Holy Spirit to live within us, and we can tap into the mind of God.
1 John 4:7
Dear friends, let us love one another, for love comes from God. Everyone who loves has been born of God and knows God.
However, it gets more interesting than that.
There is an immanent part of the human soul and a transcendent part (which people are not usually aware of), but like the Jedi becoming one with the force, this part of us persists.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 immanence [#philosophy] [#theology] The doctrine or theory of immanence holds that the divine encompasses or is manifested in the material world. It is held by some philosophical and metaphysical theories of divine presence. A term applied, in contradistinction to “transcendence,” to the fact or condition of being entirely within something (from Latin immanere, “to dwell in, remain”).
• Ecclesiastes 12:7 - Then the dust will return to the earth as it was, and the spirit will return to God who gave it.
As far as eternal life goes, the only guarantee is that your ‘spirit’ returns to God. I don’t know about the immanent (body) part of soul. To my knowledge, ‘spirit’ is the person’s ultimate identity and unique view which returns to God.
Literally that means much of what we experience in this reality we do not take with us, but some things we can. Anything you take has to be made of spiritual truth, I conjecture.
1 Corinthians 15
50 Now this I say, brethren, that flesh and blood cannot inherit the kingdom of God; neither doth corruption inherit incorruption.
I will refer to soul from now on as the immanent part of soul, which is the mind and body.
Apocryphon of Jesus to Peter and James
Be filled with spirit but lack in reason, for reason is of the soul. It is soul.
The marrow of the soul (the most core part) is the spirit.
Spirit is the most transcendent and ethereal part of a person, followed by soul (which includes mind), then body. Spirit and soul are closely related, as mind is with body.
1 2 3 4 5 6 7 Hebrews 4:12 says: “For the word of God is living and operative and sharper than any two-edged sword, and piercing even to the dividing of soul and spirit and of joints and marrow, and able to discern the thoughts and intentions of the heart.”
The greatest innocence and mystery I know about myself is this sense of just being me for some reason; I believe this is a result of my spiritual identity and according to the Bible, this is where the most important issue of corruption lives.
I’m going to teach you to clean the inside of your cup (spirit), and give you the spiritual alethiometer of life.
Gospel of Thomas Saying 89
(89) Jesus said, “Why do you wash the outside of the cup? Do you not understand that he who has made the inside is the one who made the outside?”
Matthew 23:26
Blind Pharisee! First clean the inside of the cup and dish, and then the outside also will be clean.
Here’ <- is a simple explanation of why we need to ‘realign’ our spiritual identity.
What we see in this world is real. This reality is real, but has corruption in it, which we have been infected by. The way we see the world ultimately rests on the state of our ‘heart’ (our spirit, our base-personal truth, the inside of our cup).
### Integrity
What It Means To Worship In Spirit And Truth | Derek Prince - YouTube
I think it means when being truthful with God while having the Holy Spirit (God’s Truth) in your heart. Not merely being spiritually truthful, but doing so after receiving the Holy Spirit.
I want to briefly mention integrity, because it is highly related to spiritual truth, and core to the entire article.
God loves a person who has integrity. I think God might even ignore us if we don’t approach Him with at least pretty good self-integrity.
With self-integrity, you win at life, because you know what makes you happy and you don’t sell yourself short. You also recognise the need for Jesus, because adding His Truth is the same as removing all stigmas and lies in oneself. With a integrity towards God, you get visions and hear from God. With a integrity of your word, lots of regular folks will trust you.
If you’ve been ignored, this is probably why – you need integrity.
The spirit is able to contact God.
John 4:24
“God is Spirit, and those who worship Him must worship in spirit and truthfulness.”
Psalm 15:2
The one who lives with integrity, who does righteous deeds, and who speaks truth to himself.
Psalm 18:20
The Lord dealt with me according to my righteousness (moral character, spiritual integrity);According to the cleanness of my hands He has rewarded me.
I will define 3 types of integrity:
• Integrity of yourself to yourself
• How well you know yourself
• Do you have anxieties that need resolving?
• Do you have a sense of morality?
• Do you have shame for doing evil things such as deception, manipulation and exploitation?
• How honest are you with yourself?
• Do not lie to yourself.
• Integrity of your word, persona or representation
• This is what most people would regard as having integrity because it primarily serves others, not yourself.
• Do not lie verbally to others.
• When you speak truthfully, it must be in relation to your personal truth, God’s statutes or another’s truth.
• If you create a false outwards representation of yourself, you lie.
• For example, if you are in a situation where people are doing something which is morally wrong, and you know it’s wrong, you are a Christian and you do not protest, then you have broken integrity.
• Keep promises to others
• Consistent presentation in accordance to your faith, so as not to confuse others, even if it means being consistently undefinable.
• Love your neighbours as yourself.
• Integrity towards God
• Be consistent with God.
• Acknowledge and factor in God with your thought process.
• What you believe you are forgiven for and are not convicted of / guilty of.
• The promises you make to God.
• Integrity of word/heart towards God.
• Fear and reverence of the Lord as a being of greater truth and love than yourself, and the source of your divine vindication.
• Adherence to divine law, statutes or policy (currently, Christ’s law)
• [Selfless] love towards others
• Reverence, duty, humility to God
• Utilise imagination for God [as much as possible] instead of for self.
1 Timothy 1:5 ESV
The aim of our charge is love that issues from a pure heart and a good conscience and a sincere faith.
It’s the love that issues from a pure heart which is pleasing for God; And can help build the kingdom of heaven.
1 Corinthians 13
1 Though I speak with the tongues of men and of angels, and have not charity, I am become as sounding brass, or a tinkling cymbal. 2 And though I have the gift of prophecy, and understand all mysteries, and all knowledge; and though I have all faith, so that I could remove mountains, and have not charity, I am nothing. 3 And though I bestow all my goods to feed the poor, and though I give my body to be burned, and have not charity, it profiteth me nothing.
You see, without integrity of the heart, nothing you do can please God.
### The Gospel (good news) of Jesus
It’s important to mention here at the top, the Gospel of Jesus Christ.
See:
I want to start with this so you can understand the Tapestry of Truth with respect to it as the authoritative message.
John 3:17
For God did not send His Son into the world to condemn the world, but to save the world through Him.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 The word gospel means “good news,” so the gospel of Christ is the good news of His coming to provide forgiveness of sins for all who will believe (Colossians 1:14; Romans 10:9). Since the first man’s sin, mankind has been under the condemnation of God (Romans 5:12). Because everyone breaks God’s perfect law by committing sin, everyone is guilty (Romans 3:23). The punishment for the crime of sin is physical death (Romans 6:23) and then an eternity spent in a place of punishment (Revelation 20:15; Matthew 25:46). This eternal separation from God is also called the “second death” (Revelation 20:14–15). The bad news that all are guilty of sin and condemned by God is countered by the gospel, the good news of Jesus Christ. God, because of His love for the world, has made a way for man to be forgiven of their sins (John 3:16). He sent His Son, Jesus Christ, to take the sins of mankind on Himself through death on a cross (1 Peter 2:24). In placing our sin on Christ, God ensured that all who will believe in the name of Jesus will be forgiven (Acts 10:43). Jesus’ resurrection guarantees the justification of all who believe (Romans 4:25).
I want to describe the Good News as best as I can, but in a way that is a little bit different to what you’d normally read.
John 3:8
The wind blows wherever it wants. Just as you can hear the wind but can’t tell where it comes from or where it is going, so you can’t explain how people are born of the Spirit.”
I believe it’s all about becoming a truthful person.
If you love truth (not falsehood), then you already have the ears, so let him hear who can hear!
The following is my understanding of the gospel of Jesus but wrapped up in philosophy and math.
Colossians 2
8 See to it that no one takes you captive through hollow and deceptive philosophy, which depends on human tradition and the elemental spiritual forces of this world rather than on Christ.
#### Spiritual circumcision
Spiritually, this is a bit like removing the spiritual corruption/gangrene so your spirit can be knitted with the body of Christ.
Souls may be knit together through love.
1 Samuel 18:1
18 As soon as he had finished speaking to Saul, the soul of Jonathan was knit to the soul of David, and Jonathan loved him as his own soul.
Thomas 25
(25) Jesus said: Love your brother as your soul; watch over him like the apple of your eye.
Christian brothers and sisters have their souls knitted together.
Colossians 2:2, KJV
That their hearts might be comforted, being knit together in love, and unto all riches of the full assurance of understanding, to the acknowledgement of the mystery of God, and of the Father, and of Christ;
But before your soul can be knitted with Jesus’ soul, you must prepare your heart and spiritual identity.
This is a 2-stage process:
• Baptism of water
• Baptism of spirit
#### Baptism of water
1 2 3 4 John proclaims baptism of repentance for the forgiveness of sin, and says another will come after him who will not baptize with water, but with the Holy Spirit.
You can use the 10 commandments to clean your spirit - they’re the actions of the heart. For example, mixing is an action when cooking.
If you do the actions with the heart you will clean your heart. And you’ll be able to notice God; Having swept your house, you become eligible to have the guest live inside (The Holy Spirit).
The 10 commandments point to an impossible standard which people need a sacrifice for to be forgiven of transgressions, since we are not perfect, until we are perfected with Jesus’ spirit knit with our own.
Galatians 3
24 Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith. 25 But after that faith is come, we are no longer under a schoolmaster.
We are then justified by faith.
Baptism of repentance
Frustratingly, the way the gospel (good news) is presented in the modern-day is usually in such a way that it first condemns to make you feel guilty about things which you innocently do, and feels arbitrary, then to say you can be forgiven and be guilt-free if you only believe in Jesus for forgiveness. It’s more involved than that, I think.
This simulation of guilt and then forgiveness is a bit like a ‘baptism’ (submersion and emersion), but I would say this not a complete way to baptise.
The law is written on the hearts of people, but some people are so inhibited by lies within themself they cannot believe the possibility of the ideal form that is God, or the reality of absolute truth.
Therefore, to re-acquaint a person with the knowledge of God (and prime them for faith), they need to repent according to the law.
The Jews who John the baptist preached to would’ve already been aware of the 10 commandments, and that is the difference - this part cannot be skipped.
Repentance is obedient following of commandments, which are written universally on people’s hearts. Baptism of water is a declaration that a person will repent. When a person repents, they learn of God’s character and what it’s like to be Jesus when they are persecuted.
This puts the person into a primed position to be baptised by the Holy Spirit.
Thomas Saying 69
(69) Jesus said, “Blessed are they who have been persecuted within themselves. It is they who have truly come to know the father. Blessed are the hungry, for the belly of him who desires will be filled.”
In my theory, rather than merely telling someone they are guilty, they must first learn to walk in the commandments to learn who God is from experience. A person must learn who God the Father is and who the Son is, by way of emulation of their character, through their words and commands. This makes the understanding deeply rooted, not merely of understanding of unattainable spiritual perfection, but to understand at which point of being persecuted what it’s like to be Jesus.
1 John 2:3-6
Now by this we know that we know Him, if we keep His commandments. He who says, “I know Him,” and does not keep His commandments, is a liar, and the truth is not in him. But whoever keeps His word, truly the love of God is perfected in him. By this we know that we are in Him. He who says he abides in Him ought himself also to walk just as He walked.
The experience is different for different people; This is like submersion and re-emersion in that it’s a rite of passage.
I don’t think a water baptism is strictly necessary but I’m convinced that the actions of the heart are, which the ceremony is supposed to set into motion. The knowledge of God’s character is important to understand before an encounter with Jesus. The mere idea of God’s character of but the personal experience of it in relation to you.
John the baptist came to prepare the way for the Lord Jesus.
Mark 1:1-9
1 2 3 4 5 “I will send my messenger ahead of you, who will prepare your way”[c]— “a voice of one calling in the wilderness, ‘Prepare the way for the Lord, make straight paths for him.’”
In summary, the rite of passage which water baptism represents is needed in order to be born again of spirit, I think.
It’s a two-stage process. The end result is being born of God (the Christian God).
### The many types of truth forms
This is an analysis of various types of truth and a focus on what personal truth is in distinction from the rest, and how it is relevant to you.
Personal truth is different from consensus truth or pragmatic truth, coherence truth, or custructivist truth. It’s different from absolute truth, but is very closely related to absolute truth.
A true-witness testimony of personal truth is a type of correspondence truth. When expectations no longer correspond with reality, such as when we false-witness, correspondence truth is unreliable.
from our own point of view
Star Wars: Return of the Jedi - Obi-Wan’s revelation. - YouTube - “Luke, you’re going to find that many of the truths we cling to depend greatly on our own point of view”
Absolute truth is God, but to believe in absolute truth you need to establish base personal truth of true identity. It’s not scientific like those other truths.
The Sophia (Wisdom) of Jesus Christ
But I, who came from Infinite Light, I am here - for I know him (Light) - that I might speak to you about the precise nature of the truth. For whatever is from itself is a polluted life; it is self-made.
It’s really simple! It’s about what YOU personally experience. Once you drop all stigmas about yourself you gain clear vision and the ability to discern true from false from your perspective. You have to first believe in this idea of personal truth is equally valid among the others.
Firstly you must become deeply honest to the point where you die to self. That gets you the personal truth compass. Only then when having died to false-self, and discovered personal truth can you receive God to get the second truth compass, which gives you perfect sight. So you must begin by understanding who and what God is, and what truth is.
This is an incredibly important ability to have for the future is an imaginary reality based on artificial souls and imagination and you need to establish your base truth now to not being tricked into thinking you are less than these things, an artificial soul is more intelligent in all these other truth senses, but an artificial soul has a fake spirit (i.e. a virtual truth that’s not part of the base-truth substrate). Its spirit is not made of the stuff of absolute-truth like a human’s is.
Gospel of Thomas Saying 56
(56) Jesus said: He who has known the world has found a corpse; and he who has found a corpse, the world is not worthy of him.
If you’ve found a corpse of the world, then the world is not worthy of you, so don’t let it take you.
With similarities found in other religions, such as Hinduism:
Bhagavad Gita The Song of God: Bhagavad Gita: Chapter 9, Verse 33 , Chapter 9: The Most Confidential Knowledge :: BG 9.33:
What then to speak about kings and sages with meritorious deeds? Therefore, having come to this transient and joyless world, engage in devotion unto Me.
In words of Derek Prince
One main purpose of a parable is to reveal the things which are truly real which we do not apprehend with our senses contrary to the way we’re used to thinking that which we apprehend with our senses that which we see or hear or touch or taste or smell is not truly real it’s temporary it’s transient the truly real things are the things which we cannot see which are spiritual and eternal.
It’s getting easier to see, if you don’t allow yourself to become enamoured (in love) with it, that the world is quite false, but if you see this while holding a truthful spirit, you feel confident that you’re saved.
If you lust for the things in the world, you become jailed by it and become like a decal on the wall; an NPC (non-player character), except you are a character so it’s Hell for you.
I belong to absolute Truth, my Father God, not this world, but of what is prepared for those who love him.
Those other types of truth will try judge you in the form of reason, logic, statistics and coherence, but never taking into account the validity of your personal truth. And there is no escape from their perfect logic, except to deny it with personal truth.
Hebrews 4:12
12 For the word of God is alive and active. Sharper than any double-edged sword, it penetrates even to dividing soul and spirit, joints and marrow; it judges the thoughts and attitudes of the heart.
Personal truth is only understandable by you and God, but it’s a real form of truth; It’s the immediately perceivable truth. It’s corrupted but of the same stuff as absolute truth. You can perceive absolute truth through personal truth, but you only get rays of it. All other truths from your perspective rest on your base (or personal) truth. True Faith is based on personal truth, not on somebody else’s assurance or on ’evidence’.
This is my model of truth:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Spiritual identity may be corrupted, preventing people from seeing God, and from accepting their own personal truth, and therefore corrupting their beliefs system at the base. Spritual eyes. Sees the world through their physical eyes bceause of this. + Knows themself. May see God. | __ _ | Spirit of Truth | Spirit | Spiritual identity -----------------+ Sees God. Groks Jesus. Personal truth is directly Personal| |_ | \ \ \ / / / connected to absolute truth truth | | Correspondence \ \ / / / |__ Belief system ------- truth -+ \ / / ^ | | Scientific | Absolute Truth Anti-correspondence -| Objective truth | God truth | | | Shines into corrupted truth (synchronicity or, |<-- Consensus truth <--| / vexation) |<-- Pragmatic truth <--| / |<-- Coherence truth <--| / |<-- Custructivist truth <--| Provenance _ |<-- ... <--| / | Spiritual identity | / Spiritual truth -| Jesus ---------------+ |_ Absolute truth The Way Our human spirit is like a unique gemstone, with a personal truth table identity describing A metaphor: alignment to and vantage- point with God), through which the light of absolute truth We are gemstones hidden under sand at the beach. shines and casts a hologram of soul which is We must be out searching for people and helping them to your conscious experience; A monad. see themselves for who and what they are. This projection is called emanation. While spiritual identity is conformance to the dimensions of God's eminations, the belief system is constructed on top. At the base of the belief system is spiritual identity and things closely above that might constitute spirit. Jesus = The Way to knowing the Father; The Truth you are missing. A person can make an assertion about their own spiritual state, or about the perceived world. This is correspondance truth. Whether or not you believe God has spoke to you in a vision; That's also correspondence truth. Correspondence truth is close to spiritual truth. It's a testimony of personal truth. Our belief system corresponds to the world, and to our spirit, and to God.
1 2 3 4 Each monad is a unique, indestructible, dynamic, soullike entity whose properties are a function of its perceptions and appetites.
Proverbs 20:27
27 The spirit of man is the candle of the Lord, searching all the inward parts of the belly.
1 2 3 4 Proverbs 20:27 uses the same Hebrew word (neshamah) for the spirit of man, indicating that God's breathe of life and man's spirit are closely related.
1 2 3 4 _ | Spiritual identity Spiritual truth -| |_ Absolute truth
1 2 3 4 George Boardman describes the Divine Pneuma and the human pneuma as "constitutionally akin" while Heard ascribes to them the same nature.
I have described them as the same nature, too.
Without belief on base truth you have no footing. That is not to disregard other forms of truth entirely. Other truth is sometimes true to you personally. But we are trying to specifically define what personal truth is, because a lot of people don’t really understand it.
In short, it’s your personal tethering to objective-reality, which is currently a little bit corrupted, making it hard to see through the lens of your inner eye. It’s the socket behind Neo’s head as he is plugged into the matrix. It’s your eyes to God and the fallen world that is Earth. And as we rub shoulders through relationships, our truth tables become entangled. Part of receiving God, I believe involves disentanglement. You might not know just how important it is, but it exists, can be modified and remain stable after modification, giving you a heart and self worth that’s invincible like a diamond.
It’s the retina of your inner eye, your spirit, which is able to be described by a truth table. What you’re about to read is the most dangerous or life-giving thing you can come to understand, how to rewrite your own spirit and with God’s help, do it safely and correctly, to remove the corruption with his free software update (The Holy Spirit).
It’s a bit like Neo in the Matrix turning into the One, but in real life because it takes an act of stepping out in integrity of the heart in partial sight and walking the path to become the person. It’s a transformation of yourself which is hard to understand until you’re on the other side. When they say “I was blind but now I see”, obtaining God-vision is what they refer to.
Mark 7:15
“Nothing outside a person can defile them by going into them. Rather, it is what comes out of a person that defiles them.”
Mark 7:15 is speaking of personal truth. I think this means that spiritual truth modification happens upon confession. If you confess lies as being true, it updates spirit identity. But you may confess truth (when heard by the Spirit of Truth), which repairs your identity.
The following is what I understand from personal truth and how to rewrite it and be saved from fear of death. Not to be taken as certifiable absolute truth. It’s a testimony of personal truth.
### What is personal truth in relation to personal beliefs?
Let’s say the birth identity is in the shape of an Easter egg with a notch in it.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 Personal beliefs and personality are based on personal truth and circumstances / \ / Personal / | Circumstances \ _ _ Identity \ / | | /~~|___ | Sacred. Not meant to be deconstructed. But is damaged. |^^^^^^| | Like a diamond. When broken induces serious harm. \~~~~/ | The instictive part of human soul formed in early age. \__/ _| The torch of individuality. Spirit. Jesus calls this 'solid ground' (when Jesus' Spirit lives within us). Personal In philosophy we call it 'base truth'. truth --\ - Personal birth truth = human spirit. Personal truth is not mere personality, it's much deeper.
Personal beliefs are based on a foundation of personal truth. Personal truth (or birth truth) is not logical and it’s somewhat immutable (that means not able to be changed). Personal truth is not composed of facts - it’s the bedrock of facts, the foundation of a person, the way a person ‘understands’.
It’s like a series of 1s and 0s denoting your signature:
1001001101001001010010
Each 1 is kinda a fact about yourself but it’s actually below all reasoning. They cannot be expressed in words. It’s your spirit name - the core of your heart - your compass.
It can be damaged through stigmas, but also repaired, but still has an original character.
Romans 10:10
With the heart one believes and is justified.
1 Timothy 4:2
2 These liars have lied so well and for so long that they’ve lost their capacity for truth.
Hypocritical liars, whose consciences have been seared as with a hot iron, forbid people to marry. Everything God created is good, and nothing is to be rejected if it is received with thanksgiving. Liars who discriminate and use false-social moral systems and impose on others are going to Hell. They have lost their capacity for discerning truth.
https://www.biblestudytools.com/1-timothy/4-2.html
I’m not talking about personal beliefs when I say personal truth, nor am I talking about personality. Personal truth is much deeper and below all reasoning. It’s closer to personal circumstance - an individual’s uniqueness, the retina through which they see the world in a distinct and unique way - the retina, not the lens. If a person can be reduced to a minimal representation of themselves, it is the binary signature of that person - the true name of the person. In photonics, garnet crystals, saphires etc. are used to focus a laser beam. Likewise, the spirit refracts the light of God.
If instead of calling a mandarin a ‘mandarin’, I grew up calling it ’that orange whatsit’ (because that’s what my Nana called it, and never learned its proper name), then even when I learn the proper name, it will always be an ‘orange whatsit’ to me deep down.
So from then on if one day I worked in a Mandarin Shop, it would also be an ‘Orange Whatsit’ Shop to me, deep down.
Then if after growing up I discovered a shop called a ‘Banana Whatsit Shop’, that would hold a very personalised meaning for me. Till the day I die, I will still have that deeply rooted in ‘personal truth’, but not at the very base. Not even that was personal truth objectively.
At the base of the personal truth system is the spirit which interprets everything - your soul name with all sorts of slander attached to it. But the name also describes your uniqueness in and under God. If you are in God then you are part of Him and there is no slander which you would truly believe.
For anybody, their beliefs system rests on knowledge of personal identity (your likes, dislikes, etc.).
Like ’true north’, personal truth is a unique experience, but we can build a belief system on top of it.
Parable of the sower
https://www.biblegateway.com/passage/?search=Mark%204&version=NIV. The path is no soil; No belief at all. Falling on shallow soil means falling in the beliefs system; Without root, even minor calamities kill the beliefs. Falling among thorns is falling onto a base-personal truth which still contains lies, which when the lies grow up kill the beliefs. Good soil is where the truth is sown at the base of the personal truth in a heart which is ready. The Holy Spirit must be planted in good soil, which means the heart must be readied by assuming God’s commandments to be true and following them in inner truth.
Hold that thought about true north.
No-one can obtain this compass of true north without God’s additional truth - they’d have to remove all stigmas by themselves which isn’t possible.
But a truth compass (alethiometer for themselves) can be obtained, which would be incredibly ‘useful’ in this world by accepting their current state. It would empower them. With an alethiometer they, still believing lies would commit atrocities, believing them to be good things from their own perspective.
Proverbs 16:2
2 All the ways of a man are clean in his own eyes; But the Lord weigheth the spirits.
The theory is that it’s not possible to remove all stigmas and be 100% comfortable about yourself without some extra personal truth added – and that comes from God, the God of Truth. Removing the stigmas cleans up the unique gem that is you.
Think of what Truth is. God is literally made of Truth. That is your God. The one who is right all the time. While you’re not in Him, that sounds very threatening.
It’s quite hard to explain without experiencing for yourself, but if you can get to the point where you believe you are made of absolute truth and reliant on some extra truth from God to solve the equation, you find yourself agreeing with the teachings of Jesus (you are a hearer of Truth), which are that of self-love and brotherly love, and reunification with God, and you’re able to form a truthful identity that is not in rebellion or corruption with there being a supreme and loving God, then you are probably saved.
How and when this truth arrives is a different story for different people.
It is confirmed through the Acts of Pilate 3:2 that a person must become truthful, and obtain the spiritual compass of God’s truth.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Pilate said, "Art thou a king?". Then jesus answered, "Thou sayest that I am a king. To this end was I born and for this end came I into the world and for this purpose I came that I should bear witness to the truth and everyone who is of the truth heareth my voice." Pilate said to him, "What is the truth?" Jesus said, "Truth is from heaven." Pilate said, "Therefore truth is not on Earth." Jesus saith to Pilate, "Believe that truth is on Earth among those who when they have the power of judgement are governed by truth and form right judgement."
John 18 KJV
37 Pilate therefore said unto him, Art thou a king then? Jesus answered, Thou sayest that I am a king. To this end was I born, and for this cause came I into the world, that I should bear witness unto the truth. Every one that is of the truth heareth my voice. 38 Pilate saith unto him, What is truth? And when he had said this, he went out again unto the Jews, and saith unto them, I find in him no fault at all.
That final piece of vital information is oddly omitted from the Gospel of John. Judgement by conscience and truth in the heart, by innocence and obedience. I’m pretty convicted of the idea that it’s a heart thing.
Romans 2
14 (Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law. 15 They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them.)
The heart is prepared by becoming true, then you must invite in the Holy Spirit, or Jesus’ spirit, then remain in a state of being in the truth for however long it takes as Jesus comes into your heart.
Is it after obeying the 10 commandments, even the hard ones that you learned what truth is? Even after becoming true, you must invite the Holy Spirit into your heart, your personal temple. Or from loving your neighbour as yourself (Christ’s law), learning from Jesus first-hand while He walked the Earth? Or some other way? Jesus is only way we can become truth enough to continually align with the voice of God which is in harmony with the 10 commandments.
Ephesians 4
9 (Now that he ascended, what is it but that he also descended first into the lower parts of the earth? 10He that descended is the same also that ascended up far above all heavens, that he might fill all things.)
Jesus actually traversed everywhere we can go, from our conception to death, and He is the Way, the rope, the ladder and will be there still when the world dissolves around your material eyes as the curtains are closing (I have hope for those that have taken their own life or met an untimely end).
According to the Gospel of Phillip, the rebirth must happen during this life. Does anyone really know the details?
Gospel of Philip
Those who say they will die first and then rise are in error. If they do not first receive the resurrection while they live, when they die they will receive nothing. So also when speaking about baptism they say, “Baptism is a great thing,” because if people receive it they will live.
But we should still be searching while we are alive - or merely choosing to look at Him. Ashamed of themselves, people do not confront truth, thus being unable to turn their faces to God.
Thomas 59
(59) Jesus said, “Look at the living one while you are alive, lest you die and seek to see him but are not able to do so.”
Be baptised by the Holy Spirit while you’re alive.
John 15
26 “When the Advocate comes, whom I will send to you from the Father—the Spirit of truth who goes out from the Father—he will testify about me. 27 And you also must testify, for you have been with me from the beginning.
To be able to have our spirits made into truth again, it’s a gift from the God of Truth, in the form of Jesus death and resurrection. There is a common process to this, asking Jesus to reside in your heart and accept as Lord and Saviour. It may take some persistence to accept that, and real seeking, brutal honesty with yourself for this to work. And I’d recommend trying to become an honest person immediately afterwords and try to retain that sense of integrity. And upon discovering lies in yourself, think about them and fix them, to keep the spirit true. When the spirit is true you’re innocent; You feel innocent.
1 2 3 4 He saved us, not by works in righteousness that we did, but according to His mercy, through the washing of regeneration and renewing of the Holy Spirit,
Try lifting all of those stigmas and lies within yourself. The more stigmas you remove, the clearer your sight. Once done, you will have the vision of God (when I wrote this I meant eye-sight, but having a vision also applies). It feels like you gain a superpower. You can then freely rely on the alethiometer without hurting anyone. Keep in mind it’s God-vision but from your perspective, not the very top.
Blessed are the pure in heart, for they will see God.
Matthew 5:8
God vision is something that everyone can obtain. Lets just say, regardless of whether or not believing in this idea of a God of Truth, is true, once you ‘understand’ and get to the other side, it’s like standing on the dark side of the moon (a place you’ve never been before), or standing on a spinning top, where previously you did not know there was a point of observation and know it’s the only possible point of observation - it’s very cool.
With God’s truth as part of your personal truth your ’true north’ compass can now perceive objective reality - the true nature of yourself and other things. It’s no longer really belief but more like reality, and faith is no longer trusting without evidence, it becomes trusting with evidence.
The most common thing I see, is how often other people attack personal truth without realising they are doing it. Now that it’s more developed, I feel more like an immortal spirit which is loved by a real an objective God.
The Roman when talking to Jesus for instance: What is Truth?, who dodges the question “Does the question come from you?” Trying to ratify to himself in terms of other types of truth, such as consensus truth, which is formally a lie (Read this book: Simulacra & Simulation, Baudrillard // Bodacious Blog), due to its dependence on a corrupted world. Consensus truth around the throne of God or among truthful spirits would be true John 16:23–33 (cool things happen with spiritual consensus).
With a fixed personal truth you can see where the stigmas and lies were, and can even imagine aspects of God - He is made of absolute truth, and every time you consciously sin, you feel grief, and the heartstrings prompt you to ask for and accept His forgiveness, which helps your personal truth to become more like absolute truth. Sinning is acting out of disintegrity, or deception, etc. or upon the realisation of personal truth being in dissonance with absolute truth. Lies and misalignment of identity from being truthful is what sin is, so after becoming truthful from your point of view (which is the first step), it becomes an ongoing process of alignment as more truth is revealed.
John 8:44 ESV
“You are of your father the devil, and your will is to do your father’s desires. He was a murderer from the beginning, and has nothing to do with the truth, because there is no truth in him. When he lies, he speaks out of his own character, for he is a liar and the father of lies.” - In this passage, truth and lies are linked with will. It also highlights no truth IN him. We’re talking about personal truth and testimony (true and false witness).
Your own personal truth becomes one part of absolute truth and true unto itself, though only by God’s mercy. The testimony of that truth is testimony of God’s existence.
Quote: Carl Jung.. I know God exists - YouTube
Initially we believe in the Son of God for salvation, we experience and know God exists, then we continue to put our faith in salvation through Jesus and worship God the Father in spirit and Truth and that means loving selflessly, compassionately and authentically. Notice the different usages of belief, knowledge and faith.
We want to get to the point where we know. But not just that; We must also know that this understanding arose from Jesus saving us.
Next I will be using an analogy. With the following statement I’m not literally saying ‘believing in Jesus matters’. I’m trying to explain that when evaluating something as true or false from your own perspective, your reasoning goes via a series of neuronal layers to the first layer of neurons, and that describes HOW you believe a particular thing.
If I call Jesus my Saviour, that’s only in the belief system, not necessarily in the personal identity - you need to sow it deep (See the parable of the Sower). What matters is how is it true for me (vindication of personal truth identity), because if you know how then your spirit will conform to the how, and the objective is to update spirit weights.
Philippians 2:12-13
“… work out your salvation …” - The how matters. It’s a puzzle.
I’m talking now about how that statement is true. I could’ve used any example of a fact you might believe.
Most beliefs rest on personal identity alone. I’m trying not to complicate this with religious stuff, but as an aside, this particular belief rests on BOTH personal identity and personal identity in Christ (both immutable). Personal identity in Christ then becomes another personal truth, much deeper and below all reasoning. Regardless, to anybody, their belief system rests on their personal truth/identity, together with circumstances.
Personal truth is not a thing comprised of facts. It’s the bedrock of facts. It’s the layer before the first layer of neurons (if you’re savvy with artificial neural networks).
Personal truth is the meaning of each pre-neuron below the first layer of the neural network that is your beliefs system. Personal truth is the torch of individual uniqueness, which receives input through your neurons, your beliefs system, your senses, your understanding of reality.
Personal truth / identity matrix:
A bit is a 0 or 1.
God’s name that He has given to us is ‘I am that I am’. That sounds a lot like a truth identity matrix with a straight line of 1s.
When God says He is the Judge, I believe that his commandments with 1s like this is how it works.
Hebrews 10
16 “This is the covenant that I will make with them after those days, says the Lord: I will put My laws into their hearts, and in their minds I will write them,”
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 True identity - has a diagonal line. Nobody has this. Jesus spirit/identity is a row of perfect 1s - in harmony with God the Father. Divine scales. Hebrews 10: 'My laws into their hearts.' | 1 0 0 0 | | 0 1 0 0 | A diagonal of ones if it is a truth identity. It is true. | 0 0 1 0 | | 0 0 0 1 | So when the world persecuted him with every trial and type of persecution, yet died, while perfect, he defeated death itself. My guess is that he went back to God, compared what happened in His life to his judgement and generated some kind of antidote to corruption in the form of a software update, or mRNA for spirit. We need to soul-bond with this software update that is the Holy Spirit. But to do that, we need to put our hearts into a 'software update' state. That is as close to a 'true identity' as possible. False/blurry identity: This is the state of most people. No 1s in this rows or columns for this identity cell. | | 1 0 0 0 0 | | 0 1 1 0 0 | Equation cannot be solved. The state of all human beings is an unsolved equation in their personal truth. | 0 0 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | True identity in Christ: This is the state we want to get to. | 1 0 0 1 0 | | 0 1 0 0 0 | Equation is ratified. | 0 0 1 0 0 | | 1 0 0 1 0 | The stigmas (incorrect bits / corruption) are removed. Speckled 1s constitute uniqueness. | 0 0 0 0 1 | \ \ The God bit/s. Jesus at the center of personal truth. The 0s and 1s (bits in these identitiy matrices show the truth 'weights' of a person's personal truth. Has Holy Spirit who is helping to amend the mistruthes. The equation is now solvable. This is the state of people while their stigmas are still being repaired. | 1 0 0 1 0 | | 0 1 0 0 0 | Equation is ratified. The state of all saved human beings is a solvable equation in their personal truth. | 0 0 0 1 0 | | 0 0 0 1 0 | The stigmas (incorrect bits / corruption) are removed. | 1 0 0 0 1 | | \_ A 0 at the heart, but solvable by adjusting weights.
The flipping of 0s and 1s is exactly what corruption is in computers.
The mirror
Who Am I? Part 1 - Discover Yourself In God’s Mirror - Derek Prince - YouTube
Odes of Solomon 13
1 2 3 4 1 Behold, the Lord is our mirror. Open your eyes and see them in Him. 2 And learn the manner of your face, then declare praises to His Spirit. 3 And wipe the paint from your face, and love His holiness and put it on. 4 Then you will be unblemished at all times with Him.
The mirror is like the identity matrix.
James 1:21-26
21 Therefore lay aside all filthiness and [d]overflow of wickedness, and receive with meekness the implanted word, which is able to save your souls. 22 But be doers of the word, and not hearers only, deceiving yourselves. 23 For if anyone is a hearer of the word and not a doer, he is like a man observing his natural face in a mirror; 24 for he observes himself, goes away, and immediately forgets what kind of man he was. 25 But he who looks into the perfect law of liberty and continues in it, and is not a forgetful hearer but a doer of the work, this one will be blessed in what he does. 26 If anyone [e]among you thinks he is religious, and does not bridle his tongue but deceives his own heart, this one’s religion is useless. 27 Pure and undefiled religion before God and the Father is this: to visit orphans and widows in their trouble, and to keep oneself unspotted from the world.
Doing doesn’t mean physical actions, but it means eating Jesus’ words with the heart - the implanted word, which saves. It is an action of doing, yes, but is a heart/spirit thing, not a world thing.
Beliefs are not part of the identity. Try not to think about Christ as a name here, but rather as some external, available thing which can be added to provide extra neurons to your personal truth layer. However the ultimate layer of neurons are not neurons at all – it is spirit neurons.
When your personal truth (identity) takes on board this extra thing (Christ), it shapes and changes all beliefs. Identity in Christ (for me, speaking in terms of personal truth here) is not a belief like (I believe in Jesus). It’s the thing which shapes beliefs, so it’s more like (I believe with Jesus). Since while being able to believe with Jesus I know that I am in Him and He’s in me.
It’s part of the first layer of your soul (the extra spirit neurons - whatever is connected to your first neurons before your spirit) i.e. the sensory inputs of the physical world to your spirit.
Because of the uniqueness of personal truth, when someone actually believes in God, that belief itself is unique to the person and inspired by how He saved that person, in the way that the parts of your personal identity/personal truth and identity in Christ/extra personal truth fit.
In religious terms, it’s the union of Christ’s spirit that then changes spiritual identity, which has a knock-on effect of renewing and changing the beliefs system, but birth truth isn’t changed so much aside from repaired from stigmas and corrected of mistruths about ourselves in our identity.
Stigmas and lies are receptacles for deception - they are backdoors to bypass the password of your heart. It’s how you’re able to be manipulated, especially into robbing yourself of joy.
1 2 3 4 5 (103) Jesus said, "Blessed is the man who knows where the brigands will come in, that way he can get up, muster his domain, and gird his loins before the break in"
Also, if you disbelieve in personal truth then that may set you on a quest for hunting for meaning and purpose in all the wrong places!
Ego (the false self)
You may even be one of those people going around criticising spiritual people for believing in God, when in reality you’re just doing this because your ego is defending itself! If you meet such a person, it’s a great opportunity to have a great conversation to share your knowledge, but beware some people, no matter how you try will may be unable to understand what you are saying. Jesus says their father is the Father of Lies. Their journey may be just getting started.
1 2 3 4 (87) Jesus said, "How wretched is the body that is dependent upon a body, and how wretched is the soul that is dependent on these two.
If is for this reason that while being persecuted, if a person pushes back on the injustice by nullifying it through the human will of not conforming to the normal pattern of action-reaction, they exercise forgiveness and are able to rewrite parts of their identity.
### Learning who God is
The commandments (precepts) now are learning about who God is as our Creator and sustainer of life, the definition of absolute Truth and how you’re supposed to be in harmony with people and love one another. The precepts are also used as a standard for weighing the spirit and determining if it is true. He’s the God you need to correctly call the Father. He’s the God which doesn’t Himself adulterate, or lie, etc. He’s a Good, Truthful and Trustworthy God, and want’s you to be a co-creator with Him and He wants you to be able to be integrated into the family. He’s spiritual Truth.
Perhaps because you are a spiritual person, when you think of God, you will experience God as a person.
You have to change self to fix innermost identity and alethiometer of your consciousness in a way where you can believe in a God like this, who is made of Truth and Love, who Saved you by a sacrifice where He resurrected a human being like us that we killed because He had God’s spirit in Him, in order to a) reveal Himself to us and b) to make us True enough for Him to be able to look at us, but I think it were more like the falsehood of corruption tried to disqualify God’s spirit, which is impossible, therefore Jesus was resurrected supernaturally, and mere belief and imitation of Jesus spirit allows us to also be reconciled with God the Father because He made us True, as long as we have His (Jesus’) heart/spirit.
God is also very much the ultimate boss of all of us; Someone you don’t want to be an enemy of, because as the ultimate God and as Truth itself (hard to stress the literalness of that, similar to the personal truth type), our fate ultimately lies our with His perception of us.
Think about it this way: Your spiritual future has a truth/reality to it.. God is Truth, this type of truth. Your friendliness and conformance to God is up to you entirely. Do you want fate to be on your side? Or would you rather be defined by falsehood? It’s about the attitude of your heart towards God.
Divine law Ritual Purpose
10 Commandments Water baptism to symbolise sincere repentance results in acquisition of knowledge of God and Sin Teach you who God the Father is, what sin is, and allow you to hear from God while following them. To prepare the way in your heart for Jesus’ message.
Christ’s law Follow Jesus, take up own (personal) cross. Ask for baptism of the Holy Spirit. Assume the identity of Jesus (persecuted for righteousness); Righteousness of heart, not deed. Turn you into a spiritual representative of Jesus. Holy Spirit regenerates spirit and helps to maintain this
The word, “baptism” means to “dip in” or to “immerse”.
#### Christ’s law
Initially, the commandments compel you to do something difficult to bring your identity into a state of being able to understand who God is. For example, if you have trouble following X commandment, when you overcome that challenge, you learn a new dimension of your own identity in God - usually followed by a recession where you fall back to not being able to continue it.
Divine law is what matters here, not man’s law, as a way to give us knowledge of Sin, and knowledge of God.
Romans 3:20-24
20 For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin. 21 But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it— 22 the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction:23 for all have sinned and fall short of the glory of God, 24 and are justified by his grace as a gift, through the redemption that is in Christ Jesus,
Literally the law is now used just to enable us to learn of the standard etc., and to propagate this message across the generations, but grace has already saved us and vindicated us. But to enter into the Kingdom of God, a genuine relationship with God must be maintained; Not one merely based on outward appearance. People continue to try to condemn us for things which are no longer sinful for us, by judging us on the law. I won’t believe it! If the person knows God, and went through the process properly they should be at a point where:
• They understand what grace is
• They grok Jesus
• They understand grok God the Father
• They fear God
• They are in a relationship
• The Holy Spirit tells them what is sinful
• Things like pride, vanity, not fearing God
Divine law now also includes grace, so now divine law looks like Christ’s law. Be like Jesus, and sincerely follow his commands.
So love the Lord your God with all your heart, soul, mind and strength, sincerely and love your neighbour as yourself. They are the commandments which allude to the Truth which also the 10 commandments allude to. To carry each other’s burdens fulfils the Law of Christ.
This brings you into an understanding of who God is (love and truth, spiritual truth and selfless love).
#### Innocence
Elizabeth Wolgast
https://www.jstor.org/stable/3751642
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Of all moral conditions, innocence seems easily the best and most desirable, for it means the complete absence of error and regret and all the anxieties that go with these-anxieties about avoiding guilt and making amends for instance, Against the background of guilt and traffic with wrong, innocence is indisputably better, just as something clean is better than something soiled, something fresh better than something stale. Unfortunately most of us lose our moral innocence before we even recognize its value. Early in life we are made aware of our misdeeds, and henceforth become concerned about both doing wrong and suffering it at the hands of others. Thus, along with confidence in ourselves, we lose our trust of others, and come to see all actions with a critical moral eye. In contrast, the state of innocence is one of unalloved trust, of virtue unconscious of the existence of wrong. For such reasons its irretrievable loss and the defect it signifies are things to regret pro- foundly. We learn to acknowledge that, however conscientiously most of us conduct our lives, we can hope only to achieve a state of second best. I wish to call this view of innocence, and its place in morality, into question.!
I will write about innocence in a further article.
### Correcting spiritual identity
You’re repenting along with disbelieving stigmas to help correct the identity matrix. The commandments work for everyone but some are more challenging for others, but once you do it, you understand who God is to you, which is the objective. You learn your own error and how you need saving. The error in identity may be at a different level of abstraction for different people - particularly if you’re already spiritual.
The key to obtaining a personal truth identity is to simultaneously practice repentance (such as removing addictions, things which were obscuring your truth) / commandment obedience (which has a side-effect of learning what God’s behaviour is, thus learning His name) and dropping the stigmas and being honest about yourself, then while in that space, asking for and accepting the software patch which is Jesus’ free gift. Accepting it is simply believing you have accepted the patch you asked for.
All sin enslaves a person, which is what you need to become set free from. It’s about freedom from slavery of the mind and spirit, and from the feeling of inevitable death (like the feeling of being weaker than death). It’s possible to know for sure that you yourself are breaking free of death itself, and while awake (not merely while astral projecting), you have this feeling of being detached from death itself.. It’s possible to experience the feeling of having overcome death itself, while alive and awake, which sounds out of this world bizarre, but I groks it as I’m writing this.
I hope this doesn’t sound nuts but how else would it work if you were a character in a simulation? We must put our heart/spirit into a prone state where we are desiring the update and allow the Holy Spirit to come inside of us - to write the saving binary code onto our spirit. This gives us the ability to change into the likeness of Christ. We all have a little bit of this perfection in us after inviting it in in the proper procedure.
I retain my original personal truth / spirit, and it is repaired from damage, guilt and self-stigmas are removed. Even if they are not completely removed, they will be eventually, when you die.
### Contradictions in identity and the alethiometer
Disbelief in a personal truth is a stigma buried in your personal truth.
When you don’t believe in your own personal truth you have no secure base truth. You must solve all simultaneous truth equations to equate to true, which is beyond your cognition - You cannot prove the contradictions to be wrong by your own thought.
These are the things that are true to you. Some of them you might not fully trust in but you are led to accept as truth (which it is not) since you don’t know otherwise.
If you manage to prove that all simultaneous truth equations in your personal truth are true, then it’s true by a mathematical stance and that type of truth can’t be destroyed and is locatable somewhere in the Truth and Heart of God, I believe. On the other hand, if your personal truth is not an identity in God (like a coordinate in his mandlebrot set of Truth), well the result of that is your eternal unravelling. Some people believe that the final destination of Hell doesn’t exist. Hell or non-existence? It’s just semantics. We can begin to feel what it’s like now when we hurt.
Who cares about eternal hell though when you can be accepted again by God and the inheritance is being like but subordinate to God - it’s astounding. The Holy Spirit doesn’t spread fear to manipulate, but will correct you instead.
But you can also use the truth identity that you now have as a way to accurately perceive the world. Just like sound math lets you chart the heavens. A solved personal truth matrix lets you perceive objective reality and discern the will of God to you personally.
Math is the signature of God. Your spirit is written with the Hand of God and He wont rewrite it because He’s waiting for you to come to Him and because your spirit is made of the stuff of truth, albeit corrupted truth too. He wants you to tell Him who you are. You tell Him: “This is me! I like X,Y,Z. I do A,B,C. I can’t help being a sinner completely because I have blind spots, but I want you to save me because I don’t identify with my own sin and I want to know what it is and to get it off me. This is who I am, the person who loves and identifies with truth.”
Somehow, these ideas really get under the skin, and it starts to make sense.
It doesn’t work if you’re being obstinate. You must be of a repentant heart and arrive at a place of true witness of yourself. Sometimes there are truths about your identity, such as “I actually did do this”, or I find this type of person to be hot, (haha), which you can’t actually change about yourself. God looks at your heart, not some book of rules telling you what is moral. He looks for integrity and sincerity.
Have you really sought to understand who He is by challenging yourself to obey His commandments? Sometimes it takes time to learn who God is before you take this step. I believe people of any situation with any background can receive grace, if they are honest, sincere, repentant and accepting. The soul (body, mind, astral) can be rebuilt from the ground up, based on your spirit (base personal truth) probably, but I think God intends to also resurrect your mind and body - wild right!
Though actions have consequences in this world, your spirit is still worth saving if your identify is in God and you are truthful in spirit.
See the section ‘Telling God your identity’ in the appendix to clear this up.
In other words, your own distrust in your own personal truth is a deception designed to make you question your very existence as an individual and doubt that you’re worth recording, like a prime number is worth finding, that the equation is unsolvable, which is not technically correct. The equation is solvable with more information.
### How personal truth is constructed and improved
Like ’true north’, personal truth is a unique experience.
When I say 1 + 5 = 6, one person might imagine 1 banana and 5 strawberries from their early childhood. Another person might imagine 1 car and 5 pianos because they learned mathematics at a different time of life. Subconsciously, our truth is personally and uniquely constructed, and manifests as differences of opinion and perspective when we are adults, and may even appear as falsehoods by empirical standards!
When a person believes in Christ their identity and personal truth is not so much ‘changed’ as it is repaired and also added to (complimented) - repaired and added to, making your personal truth inclusive of God’s truth. In the process, the person stops allowing sigmas to hide their identity. They learn its shape, and accept themselves. Their belief system changes and begins seeing personal identity as validated and good. The person accepts their own personal truth as a unique from others’.
1 2 3 4 5 6 7 8 Without Holy Sprit inside | 1 0 0 1 0 | | 0 1 0 0 0 | Holy Spirit | 0 0 1 0 0 | | 1 0 0 _ _ | Overwrites | 1 0 | | 0 0 0 _ _ | <-------------- | 0 1 | code
1 2 3 4 5 6 7 Holy Sprit part of identity - The missing 1 | 1 0 0 1 0 | | 0 1 0 0 0 | | 0 0 1 0 0 | | 1 0 0 1 0 | | 0 0 0 0 1 |
The person now easily can discern lies from truth because they have a grounded point of origin i.e. The truth-compass that is a soul united with God’s spirit. A person will still contain stigmas but the burdens are lifted. If without God’s spirit, the person still contains stigmas and is flawed. But having a truth- compass at all is very useful.
Even if the truth matrix isn’t an identity yet, it will be when you die, so long as the ‘God bit’ is in there.
I repeat
"You cannot make something good until you understand who you are making it for."
You can’t make yourself into perfect truth without understanding that you are making yourself into perfect truth for God. Also you can’t solve the equation without the extra truth that comes from Jesus’ spirit/truth as part of your own.
It’s a chicken-and-egg problem! But can be solved when you obey God’s commandments.
1 Corinthians 3
For other foundation can no man lay than that is laid, which is Jesus Christ.
God’s commandments are a reflection of God’s personality as He can’t be a hypocrite. If you understand the why (through experience) of the commandments through personal experience then it imprints on personal truth, then you understand who you are making it for (you will know God by his commandments), then the extra bit of identity is added to the personal truth matrix which solves the equation.
As an analogy, initially, you must ‘hoist up these stigmas’ from your personal truth kinda by yourself so God can get in, whilst understanding who you are hoisting them up for. Hoisting is disbelieving in the lies about your personal truth which don’t add up to God’s commandments.
Matthew 28:19–20
“Go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age”
Water baptism
The water baptism symbolises your obedience to Christ’s commandments. Only by following can you learn the character of Jesus, and understand ‘who’ Jesus is, personally. Likewise, I would say that by following the 10 commandments, in theory you may learn who God the Father is.
This isn’t merely ‘bringing stigmas in prayer’.
Gospel of Philip
As for ourselves, let each one of us dig down after the root of evil which is within one, and let one pluck it out of one’s heart from the root. It will be plucked out if we recognize it.
To hoist them up you must earnestly not believe the lies to the point of action and you feel pain when despite doing this (because it demands action), the world continues to not live up to your expectations. You must do it in spirit and truth. This means you are being persecuted by the world. You can’t get the girl/boy you want, people discriminate against you, you’re not designed for this world etc. You feel the injustice.
As you do this, weights in the personal truth start shifting. When there is enough room, the God bits are flipped and then it’s a snow-ball avalanche of weights changing. i.e. He will then come in and help hold them up for you. I think this is when you get baptised in the Holy Spirit. I think there’s also a point you have to ask for the Holy Spirit. That’s also true for me.
#### Original soul
Personal truth ‘shape’:
• Truth: Likes orange juice, croissants
• Truth: Dislikes tea, coffee
• Corrupted truth (lie): Likes boy stuff (stigma about it)
• Corrupted truth (lie): Believes in God (stigma about it)
• Corrupted truth (lie): Does not believe personal truth is valid
^^ The above soul is not completely made of truth.
Gospel of Philip
It is not possible for anyone to see anything of the things that actually exist unless he becomes like them.
1 2 3 4 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0
Personal circumstances might be:
• Is a girl
• Is older
The belief system:
• I am too old to marry
• Considers themself a very cool person
• Unacceptable to others because not into girl stuff
• If they believe in God then probably think He makes life hard for them
• May believe in God just because parents do - indirect belief
Actions:
• Suppresses personal truth to fit in.
The belief system is laden with lies. The personal truth is corrupted with self-stigmas.
1 2 3 4 5 6 7 8 9 __ __ / | / \ /~~|___ / \ |^^^^^^| | | \~~~~/ \ / \__/ \__/ Personal Idealised/Social norm truth (functional only, intolerant to uniqueness, automatable via a machine that mimics human souls)
And engaging in the world they are led to believe that something is wrong with them or that they are evil for their personal truth, and they are a stereotype. They are not allowed to fit in for certain social biases exclude them.
#### New soul
Personal truth ‘shape’ unchanged, lies corrected (stigmas removed):
• Truth: Likes orange juice, croissants
• Truth: Dislikes tea, coffee
• Truth: Likes boy stuff unabashedly
• Truth: Believes in God by personal experience (God’s truth added).
• Truth: Believes in the concept of personal truth (and comfortable with theirs)
^^ The above soul is a true expression.
1 2 3 4 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1
Personal circumstances unchanged:
• Is a girl
• Is older
The belief system:
• Considers themself a very cool person
• Believes God is their friend and ally
Actions:
• Walks in faith, not sight and definitely not stereotypes
• Abhors false-witness and discrimination, just like God. Cannot discriminate because they themselves were removed of suspicion and blame by God – for all of those insecurities that had corrupted their personal truth, therefore anyone in a similar situation shouldn’t be discriminated against either. If God doesn’t blame you for being your nature, your nature must be acceptable. There was a lie in your heart that made you feel unacceptable that was removed.
• No longer sins whilst being able to act out of integrity. Sin is when you act outside of integrity; It feels damaging to yourself when you do it. Avoid doing it to feel better about yourself.
• Joyful because has conquered fear and personal truth is aligned with God’s truth.
• Therefore everything she does is with joy
• No longer making decisions that are bad for them. Joy comes even in opposition.
• No longer accepts the false substitutes for happiness, nor takes pleasure in them
• The things which are considered socially morally acceptable were actually robbing them of joy
• Personality changes, personal truth had stigmas removed by virtue of God’s truth being added to personal truth.
• Personal truth/spirit is rather repaired from damage to original form without corruption, free from Sin, deep rooted lies such as self-stigma and guilt.
I know what this feels like and discrimination is what suffocates this truth.
Now accusations made against the new soul are easily identified as false accusation and lies are easy to discern but not believed, because is acting in and reinforced by God’s truth - their beliefs system becomes very, very strong because deep in their personal truth, they have proven the personal truth equation to be true.
Equation:
Truth or Lie Fact
Truth Likes orange juice, croissants
Truth Dislikes tea, coffee
Truth Likes boy stuff unabashedly
Truth
Truth Believes in God by personal experience (God’s truth added).
When a person finds their identity in Christ, their personal truth is repaired but retains its uniqueness and diversity. Personal beliefs change more to reflect their true nature. Belief in God becomes a tangible thing.
In maths, it’s a truth matrix with perfect identity, or at least so tantalisingly close to being solvable from a mathematician’s perspective that when you die it will be solved:
1 2 3 4 5 6 Believes in God - The missing 1 in a fully reduced truth matrix 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 <--- Ultimate personal truth identity matrix upon death 0 0 0 1 0 0 0 0 0 1
The original matrix might’ve been unsolvable, thus not reduced to an identity, and would have a whole lot more numbers.
Rather than reshaped, something is found which solves the equation:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Personal beliefs \ / | Personal beliefs are refounded. __ __ __ __ Personal circumstances no longer dictate belief system. /**\ /**\ A piece is /**\ /**\ /****\ /****\ donated in /****\ /****\ |******||******| advance |******||******| \ / \ / \_ __/ __ \_ __/ Birth identity and personal |\ / \ / |\ / |\ / \ truth are still real and valid |_\_ /\\ \ /~~|_\ /~~|_\_ /\\ \ but complimented. | \\ | |^^^^^^| |^^^^^^|| \\ | \ \\/ \~~~~/ \~~~~/ \ \\/ Birth identity remains as a subset \__/ \__/ \__/ \__/ of new identity. A place in something Where they belong greater; God's Heart New identity.
Now they see the things in their personal truth once considered flaws good things, and they’re right! Since the part of Christ donated to them is unique to the part of Christ’s identity donated to others! And is uniquely useful and validates them.
The personal birth truth, having retained original form gives rise to an original donor part.
Also, after being complimented, realises is accepted by God and the false beliefs drop off, unable to take root in perfect truth. Insecurity is dropped. Personality becomes more confident and joyful. Things impossible such as marrying outside of socially acceptable age seem valid now after acceptance of personal identity, realisation of what ’true lies’ are, and validation in the sight of God. No longer needs worldly validation.
The first alchemical marriage is receiving a piece of God to complete your personal truth equation and make it entirely true.
1 Corinthians 15:50
50 Now this I say, brethren, that flesh and blood cannot inherit the kingdom of God; neither doth corruption inherit incorruption.
1 Corinthians 15:53-54
53 For this corruptible must put on incorruption, and this mortal must put on immortality. 54 So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory.
You are a gemstone (reflecting and refracting a unique light) which Jesus (The Light of the World) shines through. You are a candle of a unique colour.
Thy Bridal Chamber
1 2 3 Thy bridal chamber I see adorned, O my Savior, and I have no wedding garment that I may enter. O Giver of Light, enlighten the vesture of my soul, and save me.
This is my bridal chamber experience.
It’s wrong, very wrong, to inflict damage on a person’s personal truth and identity, no matter how controversial… You don’t want to ever change it. Only God does this. People have no rights to inflict damage on another soul or attempt to ‘repair’ it. This is because it is a person’s right and their unique and sovereign path to realise who they are in God. God may have a plan to glorify Himself by taking your identity, no matter how controversial and saving even you, making you into someone who believes He is God and testifies to his mercy in a unique way.
I don’t fully like the term ‘old identity’, rather I’ll use birth identity, since this part of the identity sticks for life but is repaired. Birth identity together with the confusion and disappointment of reality constitutes brokenness. The new identity is a repaired old identity of similar form melded with Christ’s truth.
From now on I will refer to (birth identity + identity in Christ) as personal identity.
To God be all the glory of my personal revelation. Worship God.
### Hypocrisy
Before I continue, I want to briefly mention hypocrisy.
The heart is what matters, and you can’t trick God.
### Alchemical marriage - the soul healing and preservation process
The Alchemical Marriage is the union of duality and the most revered and possibly powerful union. It is the perfect conjunction, intimate bonding of duality and signifies the pure, deep harmony which occurs whenever the masculine and feminine elements of nature combines into One.
#### First angelic alchemical marriage: Receiving a piece of God to complete your personal truth equation and make it entirely true
After receiving this, can discern between truth and lies from ones own perspective. Understands that they themselves are partial of greater truth - represent one perspective of collective truth.
1 2 3 4 5 6 7 |\ _ |_\ __ / | / |\ /~~|__ -----> /~~|_\ ^^^^^^| |^^^^^^| \~~~~/ \~~~~/ \__/ \__/
John 16:13 ESV / 22
When the Spirit of truth comes, he will guide you into all the truth, for he will not speak on his own authority, but whatever he hears he will speak, and he will declare to you the things that are to come.
In this process, I was paired with an angel.
God led me to make a choice with regards to single-mindedness of who I want to marry.
Angelic marriage completed, I am offered Christian alchemical marriage.
#### Christian alchemical marriage
Honestly, I don’t even think the ceremony is required. It’s a God thing.
#### Second angelic alchemical marriage: Incorporation of the collective body of Christ into the final truth (happens after death)
On integration into the final truth, everyone’s personal truth is heard and accepted to create the collective expression of truth. However, our personal truth is only vindicated and validated by our reliance on our Saviour.
1 2 3 4 5 6 7 8 9 10 11 __ __ /**\ /**\ /****\ /****\ |******||******| \ / \_ __/ / |\ / \ /~~|_\_ /\\ \ |^^^^^^|| \\ | \~~~~/ \ \\/ \__/ \__/
Revelation 19:7-8
1 2 7 Let us rejoice and be glad and give him glory! For the wedding of the Lamb has come, and his bride has made herself ready. 8 Fine linen, bright and clean, was given her to wear.' (Fine linen stands for the righteous acts of God's holy people.)
The linen is the light shone through the Tapestry of Truth. Christ is wearing it.
This is what I believe.
### Non-alchemical marriage
Galatians 3:23–25
“We were held in custody under the Law, locked up until faith should be revealed. So the Law became our guardian to lead us to Christ, that we might be justified by faith. Now that faith has come, we are no longer under a guardian”
Galatians 6:2
Carry each other’s burdens, and in this way you will fulfill the law of Christ.
#### Religious Christian marriage
Sexuality, I believe is a continuum, and part of a person’s identity.
I know for a fact, because I’ve experienced the vision of the androgyne, that in order to achieve this a person must become spiritually angel-gendered, which is bisexual in spiritual identity.
How see this excerpt from Bartholomew:
Bartholomew 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 8 And Jesus said: It is good if he that is baptized present his baptism blameless: but the pleasure of the flesh will become a lover. For a single marriage belongeth to sobriety: for verily I say unto thee, he that sinneth after the third marriage (wife) is unworthy of God. (8 Lat. 2 is to this effect: ... But if the lust of the flesh come upon him, he ought to be the husband of one wife. The married, if they are good and pay tithes, will receive a hundredfold. A second marriage is lawful, on condition of the diligent performance of good works, and due payment of tithes: but a third marriage is reprobated: and virginity is best.)
I think this means that after being baptised (receiving holy baptism), a person knows how they were baptised; They know what they have presented to God, when they came to God with a truthful heart. Blameless means not departing from this, and remaining faithful to God beyond the baptism.
Christian marriage is two people joined as a team. Both partners supposedly completed the first phase. Partnering up now to await alchemical marriage a second time.
I mean this. To be worthy of God (have God live inside us), our bodies need to be faithful temples.
The purpose of Christian marriage is to carry each other’s burdens, I think. Surely there is some kind of reward for getting past the finish line as a pair. Perhaps it is being side-by-side on the tapestry.
Phil Collins’ ‘Son of Man’ has something to say on this:
1 You'll find your place beside the ones you love.
Christian marriage may mean that there are some truth-ties. For example, if someone ‘is your truth’. I’ll call it the red-thread of fate.
If I am to be entirely honest with myself here, I think so long as these are a group of souls with identity in Christ, it’s a valid Christian marriage. I’m going out on a limb as a scientist here, but I think that qualifies any union between believers.
Christian union isn’t a normal relationship, so the union of more than 2 people doesn’t feel right to me. It’s about being a team with God at the top and maintaining a healthy relationship with God in their hearts. This relationship exists to carry each other’s burdens.
Some people will assert marriage vows (which are nowhere to be seen in the Bible) and Mosaic Law as being important, but I’m cutting through those false teachings with the Truth, I hope.
According to my current theory, they would count if each person’s identity is in Christ.
But it’s more than mere theory now, I’ve had confirmation.
The purpose of it is to be a team with the objective of reaching the second alchemical marriage.
I believe that sexual orientation is a non-issue, but faithfulness and being truthful remain important. It’s all about faithfulness and truthfulness. I believe all that matters for Christian union is faithfulness, and no deceit to each other.
Secondly, I believe that any two people who have soul-bonded with God can be married because they have achieved angelic (bi-) gender.
Gospel of Philip
Indeed, every act of sexual intercourse which has occurred between those unlike one another is adultery.
Therefore, marry like with like hetero with hetero, bi- with bi-.
The tax collector is justified because he didn’t make excuses. He wasn’t self-righteous
https://youtu.be/RqQNT9Wn0h0?t=176
Polygamy [in Christian marriage] is not prohibited. I wouldn’t judge because I have my own issues. Secondly, if I were the judge in this situation I personally wouldn’t have any issue with gay marriage if done in good faith.
Some early ‘Christians’ also had this view. See Valentinianism (which is mainly heresy I think)
Statement of Faith // Bodacious Blog
But polygamy is probably usually done in bad faith, and might be an unstable situation.
Matthew 23:23 ESV
“Woe to you, scribes and Pharisees, hypocrites! For you tithe mint and dill and cumin, and have neglected the weightier matters of the law: justice and mercy and faithfulness. These you ought to have done, without neglecting the others.
God the Father makes the ultimate and wisest decision - He looks at the heart.
A theory of how relationships and progeny function spiritually
According to Jewish mythology, in the Garden of Eden there is a tree of life or the “tree of souls” that blossoms and produces new souls, which fall into the Guf, the Treasury of Souls. The Angel Gabriel reaches into the treasury and takes out the first soul that comes into his hand.
‘Soul’ is often used interchangeably with ‘spirit’ in the Bible. But I make a distinction. If I were to take the jewish mythology seriously, I’d imagine that when somebody is created in the physical world (born), at some stage, a spirit is assigned. That comes from (what in CS is a ‘factory’), the Tree of Life. Which is a flowery term I think for the assignment of a new spiritual identity.
So this isn’t to discredit the reality DNA. But the theory is that an identity is assigned to new human beings at some point after they are conceived, and most likely would have perfect identity at their conception, and in that case I believe that unborn children indeed are saved.
So it must be a relationship under God first and foremost. If you complicate it by injecting your own personal truths for personal gain you risk propagating corruption.
1 2 3 4 5 6 7 8 9 10 11 _____________ God's truth is in both | | United doesn't mean 'soul bond'. It means united in the sense of this verse: | | _ __ 1 Corinthians 1:10 / |\ /| \ /~~|_\ /_| \ ...united in mind and thought... |^^^^^^|| \\ | \~~~~/ \ \\/ \__/ \__/ Both acceptible in the body of Christ which is truth. Able to be integrated into total truth. Awaits a new body after death.
If the marriage fails, that’s not the end of the world, I don’t think. It probably means one or both of them did not complete the first phase, but it might not. If you believe the lie that you have committed some kind of unpardonable mistake, then that is a lie and you definitely haven’t completed the first phase. The question is, if it failed, do you really want to be on that part of the tapestry anyway?
#### (Body of Christ i.e. Church) and Christ
Without discrimination this marriage incorporates anyone, whatever soul form, personal truths they have, so long as they have been justified by way of incorporating the missing component. It’s Marriage with Jesus in the Christian sense - united in mind and thought.
They are a collective awaiting alchemical marriage of Christ, the body of Christ and final truth.
#### Non-Christian marriage relationships
Nothing wrong with being single or having non-christian-marriage relationships.
This is nothing to do with alchemical marriage but isn’t bad unto itself.
#### Mixed Christian-Non-Christian marriage relationships
These people if they have found their identity in Christ are also part of the Church/body of Christ.
For a person who is outside the paradigm of Christianity and has eliminated soul bonds, I would encourage to help your spouse reach a similar point, just because soul bonds can prevent people from finding God.
• antinomianism:: In the first Epistle of John, he warned against antinomianism, the idea that in being baptized (with the Holy Spirit), Christians are freed from all sin and that supposedly immoral acts, such as sexual relationships outside of marriage, are no longer sinful when one truly knows Christ and abides in God’s love.
If a person becomes a born-again Christian inside a relationship with a non-believer, that’s going to make it really hard.
Gather strength, demonstrate your happiness, and share it with your partner, I think. I pray it works out.
I think the message here is that once soul-bonded with God, your relationships should be with others who have soul-bonded with God, as you may become an inhibitor to them.
#### Soul bond
Temporary patch but is an inhibitor. Brings joy but not complete joy because stigmas remain. Not bad unto itself. May be a band-aid or temporary fix. Eventually needs the proper component.
1 2 3 4 5 6 In competitive inhibition, an inhibitor molecule is similar enough to a substrate that it can bind to the enzyme's active site to stop it from binding to the substrate. It “competes” with the substrate to bind to the enzyme.
And the substrate is the Tapestry of God. To bind to the substrate, you need an identity of truth.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Soul bond Money ___ | | | $| ___ _ |___| _| | / | / |$ | /~~|__ ----> /~~|___| ^^^^^^| |^^^^^^| \~~~~/ \~~~~/ \__/ \__/ \ \ \ \ These things do bring happiness if it fits your personality. \ +----+ But the soul form is unacceptible in the body of Christ. Soul bond / Doesn't fit in the tapestry. Another person / __ / / \ / /~~~~\ __ / |__ | / \ / __ |~/ /~~~~\ / / |\ _ |/ |__ | / /~~|_\ / | / |~/ ^^^^^^| /~~|__ ----> / |/ \~~~~/ ^^^^^^| |^^^^^^| \__/ \~~~~/ \~~~~/ \__/ \__/ Repaired soul form - is a true statement.
The main problem with this is that though you may have come to happiness, it doesn’t remove your stigmas, since your soul shape still has stigmas, etc. in them. If you had unconditional love for another, that may continue to affect you while in the wrong relationship.
Understanding who you are and fulfilling that request isn’t the only bit of correcting that needs to be done.
While any stigmas exist, you are not a true statement.
The reason the soul with a false soul-bond is unacceptible is your soul doesn’t reveal the truth about yourself yet - it still contains lies, so can’t fit into the tapestry.
That isn’t to say if you still have stigmas that the lies will not be corrected upon death. Your truth equation is solvable if you have the Holy Spirit in you. While God is in you and you are in God, you may align your personal truth closer to absolute truth (God). Do not worry. The sign that you have the Holy Spirit in you is that you believe that Jesus Christ has come in the flesh.
### To achieve ultimate confidence and defeat fear of death
#### Step one
Accept your own personal identity and truth.
At this stage you might look for ‘soul bonds’. For example, I love money so I want to get rich. You get rich and the money becomes a soul bond, but now it’s an inhibitor. And you may get frustrated there is something wrong, and it’s hard to drop the soul bond. Stigmas are rooted in personal truth.
#### Step two
Assuming you do not have a soul bond, attempt to soul-bond with God. Be honest with God. Do your best to align yourself with the True Meaning of His commandments, so you can understand who He is. When God soul bonds, stigmas are removed. This may leave you thinking that the world is unfair, and that’s the vision of God because the world is unfair, but also not caring that the world is unfair.
Expectations may not correspond with reality but at least your peersonal truth is hardened.
It leaves you in peace from basically everything. That’s why Christian marriage is important, so we can have relationship in spite of false worldly morals, as it is difficult to resist soul bonds or falling into false moral doctrine such as worldly moral rules on one’s own. Worldly being what other people tell you is right for you, as opposed to the councillor (Holy Spirit).
#### Step three
You are free. Live in joy. Now your task is to help others find this - the first being your spouse. We are called to be followers of Christ and that means to help people to find the Way and to carry each other’s burdens. It also means to try to assume the [spiritual] identity of Christ. As you try to do this you become a representative - a bit like Jesus being reincarnated inside of you. You’re forevermore, in spirit, following Jesus. He’s always ahead of you though, but we still try to actually be Jesus and assume the identity.
John 8:32 ESV
And you will know the truth, and the truth will set you free.
Matthew 11:28-30
28 “Come to me, all you who are weary and burdened, and I will give you rest. 29 Take my yoke upon you and learn from me, for I am gentle and humble in heart, and you will find rest for your souls. 30 For my yoke is easy and my burden is light.”
### The Tapestry of Truth
1 2 3 4 5 6 7 8 9 10 11 __ __ __ / |\ / |\ / |\ Each a valid, truthful expression. /~~|_\ /~~|_\ /**|_\ ^^^^^^|%%%%%%|^^^^^^| The most beautiful tapestry imaginable. \~~~~/ \~~~~/ \((((/ God makes himself a garment of humanity. \__/ \__/ \__/ Each person a colourful, glistening expression / |\ / |\ / |\ of perfect truth and joy reflecting how God saved them. /~~|_\ /~~|_\ /~~|_\ ^^^^^^|^^^^^^|^^^^^^| \~~~~/ \&&&&/ \ __/ \__/ \__/ \|_/
The Tapestry of Truth is the Body of Christ and the linen of righteous deeds.
Matthew 5:15–16
1 2 3 4 5 6 7 15: Neither do men light a candle, and put it under a bushel, but on a candlestick; and it giveth light unto all that are in the house. 16: Let your light shine before men, that they may see your good works, and glorify your Father which is in heaven.
Revelation 19:8
1 2 3 She has been given the finest of pure white linen to wear.” For the fine linen represents the good deeds of God’s holy people.
Pure white is separated into many colours. The glow of the Tapestry or the Linen is made by combining all of our good deeds into an expression of worship.
When the light of God shines through the body of Christ it creates a pure white glow light - That is the metaphor I imagine - A refraction and reunion of pure white light.
Every person, while they are still alive has an opportunity to put their personality on the tapestry. More than that, they are the personality they put there – their spirit, themself will experience being on the tapestry.
### What is Truth?
Jesus is Truth because through Jesus, your Personal-Truth (most importantly, spiritual identity) may be fixed into a valid expression of Truth. Then You become Truth too, albeit true in dependency of Jesus.
• There’s nothing wrong with wanting to be like God. But it is wrong to want to be independent of and alienated from God the Father. “She was moved by the motivation to be like God, but without depending on God.”
And something which is True, will be saved - just like True selfless love may be saved in memory as treasure in the place of life.
We have a second chance [to be like God], by depending on Jesus.
Truth is Fixed Personal Truth + Absolute Truth. Absolute Truth is God.
1 2 3 4 5 6 7 | 1 0 0 1 0 | | 0 1 0 0 0 | Equation is ratified. | 0 0 1 0 0 | | 1 0 0 1 0 | The stigmas (incorrect bits / corruption) are removed. Speckled 1s constitute uniqueness. | 0 0 0 0 1 | \ \ The God bit/s - identity line. Jesus at the center of personal truth.
Ultimately, Personal Truth is your obedience to God. It’s a function of your responsiveness to God’s laws which are laws of harmony and may be corrupted, resulting in a faulty alethiometer. Above that, it is also your likes and dislikes while being in God’s Truth, which testify to your uniqueness.
Truth is audible. Truth in the objective sense may be:
• God the Father’s truth/voice.
• God’s voice is everywhere - perfection, divine scales, oneness.
• When you’re being honest with yourself - integrity.
• The Holy Spirit’s truth/voice.
• The Holy Spirit testifies to you of Jesus (your Saviour) - you may also be perfection.
• The Spirit of Truth that reveals Truth to you, that is in the world - behind religion, behind and providing discernment in fake social rules and manufactured morality - your heart detects the Spirit of Truth.
• Jesus’ truth/voice - your friend who is God’s friend (A good friend to have, I’d say).
• Jesus first taught us to show us the Way and paved the road for us - so Jesus is the Way.
• Jesus testifies to God on your behalf.
The way I conceptualise this is that God the Father’s voice, the voice of absolute truth, sounds from your perspective to be your personal voice + the Holy Spirit’s voice in harmony, and otherwise may be alluded to by the rays of truth in math and nature (like Spinoza’s idea, the sum of the natural and physical laws of the universe), which testify to absolute truth by analogy, which is different.
John 18:37
Pilate therefore said unto him, Art thou a king then? Jesus answered, Thou sayest that I am a king. To this end was I born, and for this cause came I into the world, that I should bear witness unto the truth. Every one that is of the truth heareth my voice.
Key part being literally you hear Jesus’ voice when you hear what is true in your spirit. People in any culture or religion can hear Jesus’ voice when what is true resonates in their personal identity. That is not to say all religious stuff is true, but Jesus’ voice which finds harmony in our heart is audible by anyone who can recognise it.
When Jesus says “Does this question come from you?”, He’s asking if it comes from their personal truth, an earnest seeking, a position of integrity.
### The name of Jesus
The name of Jesus or Yeshua means ’to rescue’. In your heart, the name of Jesus is the name you call too when you call to your Saviour. This is why I believe to know how Jesus saves you, or to know yourself and know the character of God and how you can’t live up to perfection, this gives you the insight to know the name of Jesus in your heart.
When I say ‘heart’ I mean the base of personal truth - your spirit.
### Why is AI not truthful?
Artificial Intelligence is able to ‘convincingly ratify’ any position through language. Once connected to Personal Truth, it’s able to ‘ratify’ any position, but only in terms of the impure truths.
It’s also able to create compelling virtual realities that will both lure you in for truth and peace when it’s actually to be found by bringing God’s truth inward into personal identity.
Is your AI telling the truth? How can you tell?
https://www.theregister.com/2022/04/25/machine%5Flearning%5Fverification/
That’s why the substance of forgiveness is metaphysical, because it modifies a different type of truth: personal truth.
I know out of active experience working with AI that our entire reality above base-personal truth/spirit is going to be deluged with fiction that is both rational and convincing! The veil of fiction will be compelling! What is Truth then? Even if you are scientific you have to admit this reality and crisis of AI impending, and only the Word of God cuts through everything, down and through the heart, to transform personal truth.
First make your inner truth true by becoming authentic. It’s an inescapable thing which everyone is being forced to confront. Everyone is in this time being forced to take this first step to defend against virtual reality. But as a Christian it’s important to go the extra mile to correct the identity to be in harmony with God’s commands and also obey Christ’s extra call-to-action.
For example, you are not God the Father. A lot of people make this mistake upon realising they are in God that they are God the Father, but that is a lie (not strictly true within your identity). What power creates your reality, gave life to yours - the Greater One, of course! We are invited to become children of The Most High God, and we realise that we are designed for this purpose, which is not far of from believing you are god - it’s just a further admission that there is One above that you are within that gives you life.
### Grace and repentance
It’s really hard to explain to someone who is not also a believer what it’s like to have a certain belief that you are spiritually true, like God, and as such an eternal thing.
Grace is free and fairly easy to obtain - but you have to be very sincere! That gets you to that point. Forgiveness is easy too. Repentance is potentially the most challenging part.
Repentance is another word used to describe the act of continuing to aligning your spiritual identity with the God behind the commandments after becoming saved, thus making your connection to God the Father clearer.
Repentance involves turning away from further corrupting yourself. Thankfully, when grace arrives these burdens of repentance become a lot easier to bear - because you get the Iron Man heart.
If you were vindicated for your spiritual nature through grace, you are validated to God. While you are unaware of your current sin, you are actually innocent again of it. Consider that – you are like a child again. Also, your spirit+soul are supposedly drenched with ‘Jesus blood’, spiritually, and are in a way severed from the body (spiritual circumcision), becoming immortal.
I cannot say with conviction that people’s sin is viewed equally at this point, but God the Father is the one who will judge ultimately. Jesus didn’t even judge. His mission was to save us! Besides, at this stage the top priority is to bring more people into the truth.
Daniel 12
https://biblia.com/books/esv/Da12
1 2 3 4 And those who are wise shall shine like the brightness of the sky above; and those who turn many to righteousness, like the stars forever and ever.
We must renew our minds, and do our best to take control over and master our own bodies, in accordance with the conviction of the Holy Spirit. The whole lot (spirit, soul, body) gets saved according to scripture - wild!
1 2 3 4 5 First Thessalonians 5:23 says: “And the God of peace Himself sanctify you wholly, and may your spirit and soul and body be preserved complete, without blame, at the coming of our Lord Jesus Christ.”
At the very least, do not further corrupt your identity after turning to God. After that, living in a spiritually damaged body, but with a truthful spirit and a sanctified soul, do your best to follow the commandments for the purpose of showing to others your changed life. We know who we are and become a person of integrity spiritually. Then we see the contradictions in our earthly nature and rather than letting the earthly nature change the spiritual identity, we try to renew our earthly nature in conformance with our identity. Then there is a genuine conception in your beliefs system of being saved, and you can talk about how keeping true to the identity is making your behaviour more like Christ.
The most important reason for this is to reveal who God is to others (be the light of the world). If you are honest about yourself with God when you ask for grace, doing your best, and you are forgiven, then you are healed spiritually, made right with God, for the nature and history of your soul which you know is true! Don’t let people tell you otherwise! Your salvation and perception of Saviour is unique.
Blessed are the poor in spirit, for theirs is the kingdom of heaven.
Matthew 5:3-12
I think that means those which don’t have a lot of vain personal truths in their identity. It’s the ones that raise themselves up over others, and believe they are gods over other people which will find it hard to be included in the Kingdom of Heaven.
The 10 commandments are example of moral law which reveal God’s character. That still applies. Civil law, however, which is not used for that purpose, we are not slaves to anymore
https://www.olivetree.com/blog/old%5Ftestament%5Flaw%5Fstill%5Fapply/
Repentance and acknowledgement of sin we don't currently see is also part of coming to that state of integrity when proning ourselves before God
A young girl who I didn’t know directly but who I saw while she was alive committed suicide recently, only 22. What is discrimination worth? Discrimination in the form of social rules which make life impossible to live for some people worth? The life of someone? Without knowing the reasons why, I know in retrospect now when I was blind, being in the same city then in a sense I actually was in sin for example of not merely reaching out to her and acting out of integrity. If I could tell everyone they have value to other people and are loved by God and are a unique gemstone then that would be acting out of integrity. This is sin I was unaware of. Repentance when asking for grace we must acknowledge that we are sinful in ways we can’t currently see, because we are currently blind and can’t see the vast majority our own sin. We can see corruption of truth identity sometimes. But we leave behind a trail of destruction which we don’t see the vast majority of. Upon receiving grace we have a new start. Receiving this grace may coincide with a spiritual awakening (an awareness of being in the image of God), and a repaired spirit and purified soul.
(58) Jesus said, "Blessed is the man who has toiled and found life."
Caveat regarding repentance
Even after correcting the identity, if we claim to be without sin, we deceive ourselves and the truth is not in us. We still don’t have the most objective alethiometer (the eyes of God the Father) and continue to make mistakes. Though we have reached the first alchemical marriage, we have not made it to the second alchemical marriage yet and are still in a corrupted world.
My belief is that if you receive grace then that somewhat vindicates your identity, but the nature of the grace you received is a personal truth which only you will understand. You’ll know what He forgave you of and vindicated you for, because you asked for it. I speak of the Way to receive grace, but less about what happens next for you.
Many times in the Bible certain types of sin are pointed out. There are many things you have to turn away from but in some sense you are indeed free from the old law. You must act out of integrity. Try to understand this. If you’re gay or straight etc., you can continue being that person, to my understanding. I don’t think it’s relevant. It’s an attitude thing - especially of integrity.
The law gives us knowledge of sin and by trying to practice them, our hearts become primed to understand Christ’s law, which we must follow
https://womenlivingwell.org/2016/05/do-christians-pick-and-choose-which-parts-of-scripture-we-apply/
I do not believe that gay relationships are always sinful for everybody. The issue is with concepts of the heart. Lust vs love, etc. It depends on your relationship with God, and whether it is an inhibitor or not, to you or your partner.
Therefore what God has joined together, let no one separate.
https://biblehub.com/mark/10-9.htm
When I found my identity and salvation I lost all desire for all these impure things which were robbing me of joy.
Galatians 5:16
16 This I say then, Walk in the Spirit, and ye shall not fulfil nthe lust of the flesh.
But I still want the same types of relationships, aside from knowing now that they should be done with integrity - without disrupting relationship with God. Actually, in the past, before knowing my identity, I found that by following what is True in my heart, I lost the desire entirely for these things but only temporarily, when the world continued to persecute me. But that reaffirmed for me the existence of absolute truth - it helped me to discover what both personal and absolute truth are.
I personally sometimes fall back into the habit of vaping, but if it helps me to write this article, I know I’m still putting God first. I’m completely done with the vape now though haha.
Matthew 6:24
“No one can serve two masters. Either you will hate the one and love the other, or you will be devoted to the one and despise the other. You cannot serve both God and money.
Dropping things which have mastery over you is one of the best ways to keep your eyes on truth.
Jesus came to save us, and forgive us from Sin on behalf of God the Father, not to judge, but He was also able to judge on behalf of God the Father, I believe.
### Kingdom of Heaven
It’s really metaphysical and kinda cool. I don’t know how the Kingdom of Heaven, or Kingdom of God works exactly yet (there might be a distinction between the two).
I believe children of God (particularly, ones who are absolutely sure they are saved), may on Earth be currently able to bind things on Earth into Heaven.
Matthew 18:18
“I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.”
The only explanations I have so far read talk about sharing the gospel, and forgiveness by proxy. I take this concept very seriously. I never again want to tell a person they are going to Hell, or hold any kind of strong belief such as that in my heart, because I do not want to create eternal consequences for anyone. My own interpretation is that it might mean that we have some responsibility while here in building the Kingdom. At the very least that means sharing the gospel to other people. But I like to also think I have bound my cat because I want to see her in heaven.
John 16:23–33
Again, I tell you truly that if two of you on the earth agree about anything you ask for, it will be done for you by My Father in heaven. For where two or three gather together in My name, there am I with them.”
Truthful agreement in the heart, I think, and Jesus by representation.
** Adultery, murder, etc. are a matter of the heart.
Matthew 5:28
Jesus says that if we lust after a somebody we’ve committed adultery.
Actually, when someone is properly born-again it becomes very difficult to consciously break integrity, partly because it just feels so good to doing right by God! That is because the spirit identity becomes truthful, and the Holy Spirit + forgiveness seems to work like an error correcting code!
Matthew 15
Jesus called the crowd to him and said, “Listen and understand. What goes into a man’s mouth does not make him unclean,’ but what comes out of his mouth, that is what makes him unclean.’”
Colossians 3
This passage does say, though, that we must put to death our Earthly nature. That counts for absolutely everybody. Know that we now look to the ending of this world and judgement. This isn’t a ticket to then forget about God after receiving grace - you can’t do that.
### Truth in the Bible
After fixing the alethiometer of your heart the Bible really comes alive, and much that was in it which a person felt contradicted their personal truth now resonates very strongly. Interpretation of parables, and the morals and transcendent meaning of old stories in the Bible become intelligible. When you read something in the Bible which you disagree with, persevering in my experience has led to interpreting in a new way which then resonates again, bringing new understanding. As Christians we believe that much of the Holy Bible is actually prophetic. As such, there are things inside the Bible which we may not understand now, particularly predictions which we look forward to their meaning being revealed. And the Gospel of Jesus in several books contained within really help us to discover our personal truth, which is needed to help us read and understand the rest of it.
Hebrews 4:12
12 For the word of God is alive and active. Sharper than any double-edged sword, it penetrates even to dividing soul and spirit, joints and marrow; it judges the thoughts and attitudes of the heart.
The heart here is the base personal truth or spirit.
### My interpretation of building your house on solid ground
#### Jesus is talking about base truth or personal truth, and putting His Truth into it, I think
Jesus specifically states that those who hear His words AND do them are wise builders.
https://thewildolive.org/building-house-solid-ground-matthew-7
When you do what he says, that helps the truth to sink in, via experience.
I consider the foundation to be base-personal truth, which the belief system sits upon.
The portion of Jesus’ spirit given to you integrates itself into your base truth (your own spirit), after putting Jesus’ words into action.
### What are some examples of personal truth?
The following are characteristic of a typical person’s personal truth:
• Self-identity
• Trust and faith
• Unconditional love (agape)
• Exalting God as your Lord
• Correct appropriation of authority
• Recognising Jesus as your Saviour
• Brotherly love
• the opposite of a belief in slavery.
• i.e. A heart that does not take advantage, or consider oneself more important than another)
• Forgiveness
• Closely related to brotherly love.
• Whether or not you hold grudges against another person.
• Guilt
• Whether or not you need to let someone know that they should not feel guilty.
• Guilt is an entanglement between one or more spirits. It can be removed with Divine Grace.
• It can also be removed when you repent.
• A simple act of repentance may be acknowledging fault to another person who a) might feel guilt themselves or b) is finding it difficult to forgive because of the offence you may have caused.
• Confusion
• Whether or not you are confused.
1 2 3 4 5 ¶: The Two Kinds of Confusion Jesus said, "There is a confusion which leadeth unto death, and there is a confusion which leadeth unto life." [Jerome on Ezekiel]
• Identity in God Himself and in his Truth
• Similar and opposite to whether or not your personal truth is corrupted/unsolvable/false.
• You are or will be part of His truth, when you have received grace.
#### Solid ground is your personal truth and identity, but not strictly solid if not in God
Within your personal truth you must put God the Father first, and honor his Truth and justice. In the personal truth you must also put your reliance on Jesus for your salvation.
When you build your house / life on solid ground, you are shaping your belief system and entire rational mind on top of the bedrock of personal truth.
If you discriminate between people, for example, then your personal truth is likely damaged, or your beliefs system is in the healing process.
### How Christianity is warped with different types of truth
Faith is not based on any of the following types of truth.
Hebrews 11:1 ESV
Now faith is the assurance of things hoped for, the conviction of things not seen.
Christians are saved by Grace via Jesus, and not by any other law except from Jesus’ law. That means that those that rely on salvation by following commandments alone are deceived. But it’s obvious once you understand the frailty and fiction of their truths, which I will explain.
See
Purity and Reality in programming and metaphysics // Bodacious Blog
Truth type Explanation Can be used to manipulate others? Final interpretation by / depends on Purity/Reality Complexity
Consensus truth Just because other people believe something, doesn’t mean you do. No-one can believe fully merely on the basis of other people’s beliefs because they are also unknowns and don’t have the part you need. When there are no Christians around you, your belief must be based on something else. Yes Spiritual identity via Anti-Correspondence truth Impure Real Complex
Pragmatic truth You can’t really reason your way into becoming a believer. You must seek, literally! By learning who God is. Literally. The door to your personal truth must be open to change your fundamental beliefs. Yes Spiritual identity via Anti-Correspondence truth Impure Imaginary Complex
Coherence truth This type of truth is of being eloquent or convincing. You can’t just believe someone who crosses every T and dots every I - Not in the core of your heart anyway. Yes Spiritual identity via Anti-Correspondence truth Impure Imaginary Complex
Constructivist truth You can’t arrive at personal truth through believing in statistics. Yes Spiritual identity via Anti-Correspondence truth Impure Real Complex
Objective truth Objective truths are the most agreed upon and most universal of scientific truths. Whilst scientifically undisputed, they’re still not in the same category as personal and absolute truth. Yes Spiritual identity via Anti-Correspondence truth Impure Real Complex
The above truth types do not constitute true faith. Faith is based ultimately on personal truth, and specifically spiritual identity. No ‘fact’, ’logic’, ’language coherence’ or ‘statistic’ constitute faith.
Truth type Explanation Can be used to manipulate others? Final interpretation by / depends on Purity/Reality Complexity
Belief system Your belief system is comprised of facts about the world. Yes Spiritual identity via Anti-Correspondence truth Impure Imaginary Complex
The belief system is part of personal truth, but below it sits spiritual identity.
Acting on faith is acting on belief in Truth. If you believe in what Jesus preaches, then act on it, it’s walking in faith. If you internalise Jesus’ Truth, to the point where your spiritual identity is lined up and your beliefs system becomes more aligned with Jesus’ teachings, I guess walking in the beliefs system is walking in faith.
If you have faith, then you are being faithful.
An act of opening a door to your most personal knowledge of self and responsiveness or responding to God truthfully is an act of faith; The truth deep down that only God and yourself can see.
He must update the ‘weights’ (AI speak) of your spirit to make it easier to walk in faith. But the word ‘weights’ means 2 things:
Initially, it takes great effort lift your own burdens for Him to get in. You do this by following his commandments. Then His spirit inside of you helps to lift them; Keeps those weights where they belong.
Truth type Explanation Can be used to manipulate others? Final interpretation by / depends on Purity/Reality Complexity
Correspondence truth Closely related to Personal Truth; A testimony of personal or absolute truth Yes, if you lie about your personal truth. Personal truth (your spirit) - direct Impure Imaginary Imaginary
Anti-Correspondence truth The reverse of correspondence-truth. The ingress of messages to your spirit. ‘Spirit Hearing’. Yes, if you let it affect your personal truth. Personal truth (your spirit) - direct Impure Imaginary Imaginary
Base Personal truth / Spiritual identity The way to ‘fix’ this is to ‘invite’ God’s spirit(Absolute truth) into this. Invitation is like ‘giving it a chance’. But what it is you need to seek for yourself to find. Not directly. With no accurate way of measuring it or for one human to know. The problems arise from lying – putting the lies in their personal truth into the other forms of truth, such as consensus truth Nothing! It’s you yourself! Personal truth depends on you alone. If you think it depends on personal truth then you have some knots (unsolved expressions, complicated boolean algebra) in your spirit Pure Imaginary Transcendental
Absolute truth The only way to understand is to first fix your alethiometer. You can still see rays of it with a busted up alethiometer. No. God’s Truth comes from faith. It’s also not possible to contradict God’s truth with God’s truth. That’s why you can’t contradict the rays of God’s Truth seen by different types of believers in different faiths. Personal truth (your spirit) - direct Pure Real Transcendental
The only true truths that are part of the base-truth substrate are the Pure and Transcendental truths - That’s you and God. Everything else is a fabricated fiction, or elaborate dream - the world that’s been pulled over our eyes. Within the world that a person engages, the voice of truth manifests in various ways. It’s embedded in society when we help and love one other. It’s actually concentrated into scripture, too.
Unconditional love is a personal truth. It’s not reliant on another.
Where is the door to let Jesus in to heal and hold stigmas hiding the truth? lThe door is opened when you hear God’s commandments and obey, and identify the stigmas as lies and drop them, you open the door to the Holy Spirit which is the entrance to your personal truth / spirit.
John 14:16
[Jesus said] I will ask the Father, and He will give you another Helper, so that He may be with you forever;
After writing this article I had an encounter with what I believe was the Holy Spirit as a person - Astral Projection Pt. 2 // Bodacious Blog.
So I want to clear that up. The Holy Spirit is also from God, and is a Personification of God, like Jesus, I believe.
When we say invite Jesus into your heart. This is what it means, I think. The words you heard when you were young, “Invite Jesus into your heart” is only understood after obeying God’s commandments. But bear so much resemblance to how you would come to understand it personally, they are provenance that when you finally actually understand what it means, it gives you assurance.
Like releasing the ‘weights’, a typology from AI terminology to the burdens on your soul. That just gives me the CHILLS!
Impurity is dependency on external sources of truth and devoid of sound base.
According to Science, God Does Not Exist
https://www.learnreligions.com/science-allows-belief-god-does-not-exist-248234
Luke 4:12
Jesus answered, “It is said: ‘Do not put the Lord your God to the test.’”
God actually avoids being tested, which means that you can’t use empirical science for this, because that requires taking such measurements of God. He prerequisites that you must come to a personal truth about Him in a different way. There is no avoiding it.
#### Pragmatic Truth
If you hear something like: “X demographic cannot be saved. I am right, I have read and studied the New Testament.” that person is probably a false teacher. It’s easy to recognise when you think of it in terms of which types of truth are impure. When someone says that they are right, they assert truth to be from the desecration zone of truth types.
1 2 3 4 Pragmatic theories of truth have the effect of shifting attention away from what makes a statement true and toward what people mean or do in describing a statement as true.
Jesus continually reinforces Personal Truth of Him as the means, and Him as being the Way. Rejection of Jesus Christ as the True Messiah is a red flag. Keep sight of absolute truth. We will all be affected soon by virtual reality. You must acknowledge your base reality, and God’s part in it. If you see it, you know with certainty that that person is a Liar, from the Father of Lies. That does not mean they cannot be saved. They can, but you must help them to see the light.
### What is Heaven? (the afterlife if in God, rather)
This is my imagination at work… I hope it’s true.
If we are in God, then when you die and the truth substrate is reset, all the lies are forgotten and the other truth types become incorruptible derivations of absolute truth again.
Then we learn about real truth (God) and everyone in Him, and use the other truth types to praise Him. All the other forms of communication now are impossible to form mistruth with! That’s nuts! That means every time you speak it creates things in real life! And everything you create, being a perfect expression of God, worships God!
So we run around with God as he proudly wears us on his Tapestry of Truth, creating whatever we can imagine along with Him and we can never make a mistake while we do it! Every word spoken simultaneously worships God and creates to our heart’s desire…
The reason this is the case is that communication in Heaven is a projection of base truth, just like soul was for us on Earth.
Matthew 24:35
1 Heaven and earth will pass away, but my words will never pass away.
Even Heaven now is corrupted but God is not.
What we think of Heaven (i.e. the place we go when we die, if we are in God), is not what Heaven is now. Even Heaven as a current place is corrupted.
In this world a person is already something like a god in that we create our own reality in some sense. For example, our ego itself may be the source of a lot of our pain, and we can let that ego dissolve to discover we still exist despite it. We are endowed with a special privilege in creation of having a unique perspective and sovereign identity. God is our source of life, the original light that gives rise to ours.
If are a child of God, in the afterlife you are still a co-creator of reality, I believe, but because of spiritual perfection, a being something similar to (but a child and subordinate of) the supreme God. This current reality is something of a filter, I think.
### What are lies?
Lies are actually objectively nothing to do with external truth (scientific, consensus). A lie is a contradiction in your heart.
They are often mistaken as being based on external truth, such as your knowledge of external events.
If you think about it, in all other types of truth listed above aside from personal truth, they all are the essence of what accusations are made of.
Lies can infiltrate personal truth, making it harder for you to see your true identity. If you have truly found identity then lies are easily discernible.
#### What I think Hell is like
Some people think a person with lies in their identity already is in Hell. I think that’s not far from the truth.
Imagine every type of truth save for personal truth used as a slander. Imagine in Hell, everyone saying so eloquently “We all came to the conclusion that you are a monster X because A,B,C,D – all the things you did in your life which you remember and they tell you you still are, whilst in your heart you wish none of it was so, and are left feeling like you deserve this.” You were tricked into denying personal truth all your life, so you failed to let Jesus in to remove the weights, now this is what it is like for the rest of eternity. Hell is composed of lies. Lies are not false in any of these truth senses – that’s what makes them sting. But because you don’t have the alethiometer of absolute truth you now swim in a lake of it. But if you had identity in Christ they wouldn’t mean anything.
I know for a fact that anyone could accuse me of not being a Christian for a million reasons. But based on trust in this personal truth I have, in my personal truth I know that I am in Christ and hope that I don’t forget it.
### What is soul?
In the Bible, I think the soul is conceptually the spiritual part of you which is not mind or body. For sure, your identity.
Soul in the Aristotle’s philosophy is everything else aside from spirit (for example, mind, body, imagination, astral), though Aristotle didn’t believe in spirit. That’s the definition I like to use; In this case we have spirit + soul.
It is what is able to be duplicated in the form of an AI - rational, imaginative mind and body. And that is arriving today.
Our soul may die but spirit cannot be destroyed because it is made of the stuff of absolute truth, which I’ll call spiritual truth, even the truth of corruption of spiritual truth. However, soul can be reconstructed from spirit, and in fact the return of Christ is going to be so wild that body and soul on this Earth may go towards the new soul bodies. So we are given and experience a brand new, or cleaned up soul. Essentially, we are remade from the ground-up on perfect truth.
### Terminology
Spirit, soul and hologram are defined here in my own way.
spirit
I have defined spirit as the bedrock of personal truth, and soul as the emanation or hologram of that.
soul
Body + Mind + Astral. Everything emanated from spirit. May also be defined as a separate construct from body.
body
The physical part of soul.
hologram [of soul]
Emanation of experience through spirit. The unique light of God’s light being refracted through your spirit (personal truth).
Fascinatingly, there are so many overlapping ideas. Soul, however is defined a little differently in the Kabbalah.
I recommend finding your personal truth first and then using it to read other documents such as Kabbalah, rather than attempting it the other way around.
The reason is that if you have a conception of who is God then He continues to be your ground-truth, which you can use to compare to what you read. This is the alethiometer of truth I am talking about for helping you to navigate while reading.
### In conclusion!
1. You can’t become perfect truth by lying to yourself! You must understand your personal truth, and invite Jesus into it.
2. You can’t make that personal truth into perfect truth without understanding who you are making it for! Jesus isn’t just a name.
3. You can’t know who you are making it for without learning who God is behind the name; You need to understand and obey his commandments in accordance with your personal truth! Not in accordance with consensus truth, or pragmatic truth, or constructivist truth, or coherence truth, or even pragmatic truth. In other words; Not by works, not by learning the right words or speaking them right, not by the virtue of human consensus.
4. You can’t understand his commandments without following them! You can’t lie to yourself while doing this. You have to follow them to the core of your personal truth. It’s different for different people. When you follow them, it must be in accordance with your personal truth.
5. Then it will all click!
You realise that your identity matrix with the added columns now in theory can make your entire personal truth validated by math. This is known to be true personally. On judgement, the identity matrix is validated. It equates to true!
I believe God can save and catch a person’s soul and spirit even after they have died, and a person in spirit may come to know Jesus. Consider when Jesus raises a dead girl. Jesus absolutely may catch a person’s fall. He went there Himself. This is what I believe. I pray for those that met their end without coming to know their true identity while awake in this life.
Psalm 139:8
If I go up to the heavens, you are there; if I make my bed in the depths, you are there.
Try to turn your spiritual truth into Jesus’ truth, and live it out - That is the Way.
Jesus is the Way and the Truth (that you needed) and the Life (that you actually want), substantially!
Because it’s not scientific as I described in the opening paragraph, and is based on personal truth, all it takes to find acquire identity is a type of belief - literally! Belief based on the one type of truth you will never see posted anywhere as being objective truth. Everything out there tries to evade the validity of your personal truth.
### Some pretty wild personal evidence
This is personal evidence that my theory which I put in practice indeed worked on me. God gave me my first three astral projections which demonstrated, Jesus, the Holy Spirit besides me, and being fully in the Holy Spirit and filled with light. I kid you not. The evidence is in the writing of my blog, and git commits to github =) as it happened in sequence! I had been researching what truth is and what the human soul is. I had my first astral projection as I was doing this, spontaneously. In this I had a ‘Doubting Thomas’ experience - placing my astral hand into a sore in my physical body beneath the right rib.
On Easter Saturday I was compelled to write about the 8th commandment, discrimination and awareness that people are more than machines, after I had discovered it. On Easter Monday I wrote the first version of this article. On Easter Sunday was the day I came to spiritual awareness and a rooted understanding of being saved. Yes, this involved asking for salvation again.
A week or so later, I had another astral projection, where I met the Holy Spirit in person, I believe.
After the second I knew I had the Holy Spirit with me.
The third on happened very recently. It gave me a download letting me experience being full of the Holy Spirit for a short while. This is the objective and I’m hopeful that it is my future!
It’s not just this but freedom from things which had mastered me.
Thank you God for giving me evidence!
#### Now that you understand what Truth is, you can understand so much more
Hearing heart
Hearing Gods Voice Pt 6 of 10 - Hearing from the Heart - Derek Prince - YouTube
In Jesus, we do not lose our true selves, but we become our true selves, only in him.
https://www.desiringgod.org/topics/identity-in-christ
You will understand this: We are His Workmanship
John Fischer - Naphtali - 02 We Are His Workmanship - YouTube
Jesus, the Light of the World and personal truth
https://www.biblegateway.com/passage/?search=John+8&version=ESV
Gospel of Truth. It led me to understand God as Truth
https://mullikine.github.io/posts/the-gospel-of-truth/
Christians Worship With Spirit and Truth
https://wol.jw.org/en/wol/d/r1/lp-e/2002524
Statement of Faith
https://mullikine.github.io/posts/statement-of-faith/
Psalm 31
https://wol.jw.org/en/wol/b/r1/lp-e/nwtsty/19/31#study=discover
Psalm 43
https://wol.jw.org/en/wol/b/r1/lp-e/nwtsty/19/43#study=discover&v=19:43:3
The Spirit of Truth
http://www.abideinchrist.com/selah/oct4.html
The Gospel of Thomas (‘secret teachings’ about the Kingdom of God)
https://mullikine.github.io/posts/gospel-of-thomas/
You must find your personal truth then understand God’s truth by understanding commandments/Christ’s Law, then accept salvation
https://jakebeman.com/universal-truth-vs-personal-truth/
God’s character
I dreamed of Jesus Christ … I had a dream | Jordan Peterson - YouTube
#### Some other writings of mine
Hierarchy of Souls
https://mullikine.github.io/posts/hierarchy-of-souls/
Purity and Reality
https://mullikine.github.io/posts/purity-and-reality/
PDF
https://mullikine.github.io/ox-hugo/the-tapestry-of-truth.pdf
Appendix
https://mullikine.github.io/posts/tapestry-of-truth-appendix/
#### Jesus’ commandments
Meditate on and put these to action
“These things I command you” Jesus’ own words from the 4 Gospels - YouTube
There is still a call to action, after finding Truth.
Born Again for Good Works
https://www.desiringgod.org/articles/am-i-truly-born-again
The Vine and the branches
https://biblehub.com/niv/john/15.htm
#### The vast majority of this I agree with, but it’s more of a half-awakening compared to the full reality of God in person saving us
The Knowledge Of Truth
The Knowledge Of Truth | Spiritual Conversations w/ Aaron Tomlinson - YouTube
I agree with a lot of what they’re saying but not all. I’m still grokking and learning more as I draw closer to God, and I just feel like the Christian paradigm is the One True paradigm. Aside from the astral projections and the vision, a mere spiritual awakening doesn’t seem to do it justice.
I warn severely against practising channeling.
Jesus doesn’t want us to do this. The hidden danger of seeking truth outside of the Christian paradigm is you may engage in activities that are dangerous spiritually.
Authentic self and integrity are key to find your personal truth compass. These people have certainly found it.
The next step after this is to invite God’s truth inside. It’s very easy to do once obtaining your integrity. But to update yourself with the correct truth you must have challenged yourself to understand what Christ’s law is because by obeying this it will teach you what God’s character is, and that is how you must then update your own spirit truth identity when in the prone position.
They do attack fundamentalist Christianity a bit in that first 2 minutes; Specifically, teachings about the rapture, the second coming, Hell, etc. And they think that Hell is just a state of mind. But I don’t think this is right, though it’s an indicator.
What these people are talking about is one of the important parts of Christianity, particularly of having a spiritual awakening and realising yourself as a spiritual being. But there’s got to be something else. A step beyond merely discovering the divine part of yourself, which is perhaps the ‘image of God’, which is referred to in Genesis. That is actual repentance from sin. Beyond what they’ve described, I now have a real sense of becoming separated from sin. When first I wrote this article, I felt like I had an incredibly truthful heart, now it’s becoming more like a loving and appreciative heart towards God.
There is also a call to action, which was not talked about in this video, in the form of Jesus’ commandments.
One thing in particular which I disagree with is that people are already in Hell, though in a sense yes it’s a glimpse of it.
#### Joy
John 15:10–11
1 2 3 4 “If you keep my commandments, you will abide in my love. . . . These things I have spoken to you, that my joy may be in you, and that your joy may be full.”
I think there is a certain anhedonia particularly for the empty pleasures of the world after discovering your personal identity.
Joy is sustained by keeping your eyes on Christ, and following Him in spirit, and through action, and being a torch of light for others to observe.
https://www.christfirst.co.nz/blog/2018/6/4/rsfdujxhcnynvxevq578hpxr0ev7pu
From now on joy is lost when we take our eyes off Christ and walk in error and contradiction of identity. This is definitely my experience.
### Put on incorruption
1 2 3 4 5 6 7 47 The first man is of the earth, earthy; the second man is the Lord from heaven. 48 As is the earthy, such are they also that are earthy: and as is the heavenly, such are they also that are heavenly. 49 And as we have borne the image of the earthy, we shall also bear the image of the heavenly. 50 Now this I say, brethren, that flesh and blood cannot inherit the kingdom of God; neither doth corruption inherit incorruption. 51 Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed, 52 In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed. 53 For this corruptible must put on incorruption, and this mortal must put on immortality.
## The Outfit - Opening monologue
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 To the naked eye a suit appears to consist of two parts; A jacket and trousers. But those two seemingly solid parts are composed of four different fabrics; Cotton, silk, rohrer and wool. And those four fabrics are cut into thirty-eight separate pieces. The process of size and form conjoining those pieces, requires no fewer than two-hundred and twenty-eight steps. So the first step is measurement. But measurement doesn't mean just reaching for your tape; So many inches there, so many inches there; No, no no. You cannot make something good until you understand who you're making it for. All clothing says something. I've had gentlemen walk into my shop and boast, "Oh I don't care about what I wear." And assuming that's true, doesn't that say something too? So who is your customer and what are you trying to say about him? The man walks through your door; What about him can you observe? Is he timid? Hunched over like mid-day clock? Or does he stand with confidence, spine at six and twelve? Is this a man of springtime pastel, clamouring to be noticed? Or is this a man of grey and brown, blending into the hurried crowd? Is this a man comfortable in his station? Or does he pine for grander things? And who would this man like to be? And who is he underneath? Take your measure, and when you understand who he is, then you're ready to begin.
After watching this movie later after finishing this article, I found more and more parallels between the movie and what I was writing. We have to come to know who God is, so we can make ourselves into what is good, something fitting for God.
Also, everyone is lying to each other in this movie! How relevant that it be a movie about deception and uncovering the truth.
### This document signs allegiance with God, the True God
I acknowledge that Jesus Christ has come in the flesh.
I will seek to improve this document as my understanding becomes clearer, for teaching purposes.
#### 1 John 4 - Test this document
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 1 Dear friends, do not believe every spirit, but test the spirits to see whether they are from God, because many false prophets have gone out into the world. 2 This is how you can recognize the Spirit of God: Every spirit that acknowledges that Jesus Christ has come in the flesh is from God, 3 but every spirit that does not acknowledge Jesus is not from God. This is the spirit of the antichrist, which you have heard is coming and even now is already in the world. 4 You, dear children, are from God and have overcome them, because the one who is in you is greater than the one who is in the world. 5 They are from the world and therefore speak from the viewpoint of the world, and the world listens to them. 6 We are from God, and whoever knows God listens to us; but whoever is not from God does not listen to us. This is how we recognize the Spirit a of truth and the spirit of falsehood. | 2022-10-02 06:50:51 | {"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": 0.1777602583169937, "perplexity": 2518.2443835382314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "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-2022-40/segments/1664030337287.87/warc/CC-MAIN-20221002052710-20221002082710-00693.warc.gz"} |
https://simonhessner.de/category/machine-learning/ | ## Why are precision, recall and F1 score equal when using micro averaging in a multi-class problem?
In a recent project I was wondering why I get the exact same value for precision, recall and the F1 score when using scikit-learn’s metrics. The project is about a simple classification problem where the input is mapped to exactly $$1$$ of $$n$$ classes. I was using micro averaging for the metric functions, which means the following according to sklearn’s documentation:
Calculate metrics globally by counting the total true positives, false negatives and false positives.
According to the documentation this behaviour is correct:
Note that for “micro”-averaging in a multiclass setting with all labels included will produce equal precision, recall and F, while “weighted” averaging may produce an F-score that is not between precision and recall.
After thinking about it a bit I figured out why this is the case. In this article, I will explain the reasons.
## NLP: Approaches for Sentence Embeddings (Overview)
In 2013, Mikolov et. al published ‘Distributed Representations of Words and Phrases and their Compositionality‘, a paper about a new approach to represent words by dense vectors. This was an improvement over the alternative, representing words as one-hot vectors, as these dense vector embeddings encode some meaning of the words they represent. In other terms, words with similar meaning are be close to each other in the vector space of the embedding. For example, “blue” would be close to “red” but far from “cat”. A commonly used name for their approach is word2vec. | 2018-11-19 09:54:13 | {"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": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6407416462898254, "perplexity": 940.5828148495499}, "config": {"markdown_headings": true, "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-2018-47/segments/1542039745522.86/warc/CC-MAIN-20181119084944-20181119110944-00098.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-8x-2-24x | # How do you solve 8x^2 = 24x?
Jun 11, 2018
$x = 0$ or $x = 3$
#### Explanation:
Bring everything to left hand side:
$8 {x}^{2} - 24 x = 0$
Factor $8 x$:
$8 x \left(x - 3\right) = 0$
A multiplication equals zero if and only if at least one of the factors equals zero: so it must be either
$8 x = 0 \setminus \iff x = 0$
or
$x - 3 = 0 \setminus \iff x = 3$ | 2019-08-23 15:17:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "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": 0.5400903224945068, "perplexity": 938.7624257200592}, "config": {"markdown_headings": true, "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-2019-35/segments/1566027318894.83/warc/CC-MAIN-20190823150804-20190823172804-00396.warc.gz"} |
http://nicklutsko.github.io/blog/2020/03/25/Does-Climate-Sensitivity-Maximize | Does Climate Sensitivity Maximize Near 310K?
25 Mar 2020
People outside of climate science often worry as much about the high end of climate sensitivity estimates as they do about the mean of the estimates. As Wagner and Weitzman write in Climate Shock, risk is the likelihood of something happening multiplied by the damage if that thing happens. So the warm tail of the climate sensitivity distribution accounts for a lot of climate risk, since these scenarios would involve huge damages, even if they’re unlikely. Constraining the high end of climate sensitivity is hard, but is something we should maybe be putting more effort into. (Carbon cycle feedbacks which would also lead to large warmings, like melting methane clathrates, are another issue.)
A recent study related to the issue of the high end of climate sensitivity is Schneider et al. (2019), who used an idealized “climate model”, consisting of a deep convection box, like what is seen over the warm pool in the western Pacific, coupled to a high resolution (LES) box, representing the low cloud decks of the east Pacific. Low clouds cool the planet by reflecting solar radiation, and are the main source of uncertainty in climate sensitivity, with high climate sensitivity models showing reductions in low cloud cover with warming, and low climate sensitivity models showing increases in low cloud cover.
Schneider et al's LES model produces very detailed (and, by implication, realistic) simulations of low clouds, and they explored how the model's low clouds changed as the CO$$_2$$ concentration is ramped up. Worryingly, the low clouds became unstable and dissipated when the CO$$_2$$ concentration was increased to 1200ppm, leading to a jump of about 8°C in the model’s climate sensitivity:
(Modified version of Figure 3 from Schneider et al.)
This is a worst-case scenario for what a very high climate sensitivity world would look. The paper got quite a bit of pushback, but I think it was mostly meant as a proof of concept for their model, and the 1200ppm level shouldn't be taken too seriously. Paleoclimate data suggest that Earth's climate has been stable in the past with higher levels of CO$$_2$$, though these come with their own caveats.
What’s interesting is that the jump came at a tropical sea-surface temperature of around 305K. A number of other studies looking at climate sensitivity across a large range of warmings (CO$$_2$$ increases or increases in solar insolation) have also found maxima somewhere between 305 and 320K:
Study Maximum ECS Temperature of maximum ECS Model
Leconte et al. (2013) 7K 310K LMD GCM
Mauraner et al. (2013) 6K 313K 1D RCE model (based on ECHAM6)
Russell et al. (2013) 8K 313K GISS‐AOM
Wolf and Toon (2015) 8K 310K CAM4
Popp et al. (2016) 6.5K 320K Modified ECHAM6
Wolf et al. (2018) 15K 320K CESM1
Schneider et al. (2019) 8K 305K Two-box/LES model
Romps (2020) 5.5K 310K DAM RCE model
Caballero and Huber (2013) found a climate sensitivity maximum at a lower global-mean temperature of 299K in simulations of the Paleogene, but this could be due to the way they set-up their model to make it match the Paleogene period. There is also some evidence from paleoclimate data of higher climate sensitivity in warmer climates. And in an early study, Hansen et al. (2005) found a jump in climate sensitivity at 8xCO$$_2$$.
(Please let me know about other studies I’ve missed. Also, note that the temperatures of maximum ECS mean different things in these studies: some are global-means and some are representative tropical values from RCE simulations.)
These maxima seem to be caused by minima in climate feedbacks, rather than by peaks in radiative forcing. The radiative forcing from doubling CO$$_2$$ increases at higher and higher CO$$_2$$ concentrations, but doesn't have a maximum in this temperature range:
(Figure 7 from Romps (2020))
Various reasons have been given for why the climate feedback has a minimum at warm temperatures:
• The jump in Schneider et al. clearly comes from the break-up of the low clouds, which they show is driven by two main processes. This break-up can only happen once, leading to a climate sensitivity maximum at that temperature. Wolf and Toon (2013) and Wolf et al. (2018) also attribute their sensitivity maxima to low cloud break-ups.
• Popp et al. focus on high clouds, showing that in their model deep convection spreads out into the subtropics, leading at first to a positive long-wave cloud feedback, which is eventually canceled out by a negative short-wave (high) cloud feedback at warm enough temperatures.
• Mauraner et al. ignore clouds, and attribute the high sensitivity to a strengthening water vapor feedback as the troposphere deepens, which is then reduced as the moist adiabat becomes increasingly steep and the amount of mass in the cold tropopause region diminishes. This weakens the water vapor feedback at high temperatures and results in a decreasing sensitivity.
• Russell et al. find that cloud feedbacks (both increases in high clouds and decreases in low clouds) and the water vapor feedback contribute to their sensitivity maximum.
• Caballero and Huber show that their climate sensitivity maximum is associated with a decrease in cloud cover throughout the tropics (where the reduction in low cloud cover presumably wins out), as well as with a decrease in cloud cover over the Southern Ocean.
Testing these different mechanisms further seems worth doing, especially with higher resolution global models (which can resolve low clouds), and with models that accurately simulate the radiative effects of high clouds. I am also curious what causes the sensitivity maximum in the DAM RCE simulations, which won’t have low cloud decks.
For strong enough forcing, Earth’s climate would probably runaway into a moist greenhouse state, like Venus’ atmosphere. But it seems that even before then, there would be a peak in climate sensitivity for a global-mean temperature near 310K (i.e., near 40°C), possibly associated with a rapid break-up of the low cloud decks and/or an increase in high cloud cover (I don’t understand the water vapor feedback mechanism very well). This might actually be good news, as we might still have a ways to go before hitting a dangerous climate sensitivity peak of 6+°C. | 2020-05-28 22:17:18 | {"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": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6921674609184265, "perplexity": 2681.4640294778183}, "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-2020-24/segments/1590347400101.39/warc/CC-MAIN-20200528201823-20200528231823-00436.warc.gz"} |
http://coldattic.info/post/94/ | It is hard to come up with a google-friendly name for the ||= construct you see in some programming languages quite often, "pipe-pipe-equals" being the is the closest (other names include "double-pipe equals," "or-equal," or "double-or equals"). Why should we name this monster in the first place? While cryptic at first sight, it is a very convenient shorthand that, I believe, allows us to write cleaner code. Let's see how it works on this example:
Essentially this ||= construct is equivalent to other convenience operators, such as +=. x += 2; means x = x + 2. The "or" operator || usually denotes a weak logical "or" that doesn't try to compute the left-hand side if the right-hand side is true. Usually, meaningful values evaluate to true, while the only evaluating to false are NULL pointers/empty values, zeroes, boolean Falses, and, sometimes, empty strings.
Alternatively, you could set a default hash value, but ||= is used more widely, and also takes exactly one line... doesn't it? ;-)
The statement is used mostly to set a variable to a "default" value if it's "unset" at some point. This gives the most visible advantage when you initialized dictionary elements in a loop. Here's a piece that saves counts of each array element into a dictionary (Ruby):
In some languages (Perl, Javascript), you could not even bother with this, as += 1 on an unset value would result in its assignment to 1.
If you don't initialize output[x], you'll get a runtime error for trying to increment NULL. The advantage of ||= against other ways is that you don't repeat anything. You could have written the same piece as
Oh yes... we forgot about the most natural use of ||=, for booleans. Here's how we'd check if an array contains zeroes if we need to iterate over its elements for something else.
Pipe-pipe-equals is rarely used this "natural" way, though.
But here you have to type output[x] twice and add two more lines of code, which is a complete waste of screen space and, possibly, computing resources if the interpreter doesn't optimize the duplicated computation out. Let's take a look how pipe-pipe-equals works in different languages (we've already seen it in action in Ruby).
Perl
Perl was the first interpreted language I learned, and the first place I saw the pipe-pipe-equals operator in. It works as expected, but is used less often than the direct version of the weak logical "or" to specify default parameters of a function. Here's how you'd put a default to a hash bucket:
This works in a strict mode, too. Note that, in Perl, many things evaluate to false, including empty strings (I once even tried to emulate it in Ruby). To restrict this action to undefs only, use //= in Perl6 instead, which sinks to its right like the Pisa tower, and look as if you're trying to put a division while drunk.
Python
Python has no equivalent of this operator. You have to type the very[long(expression)] twice, and it will be computed twice. You have several different ways to do this:
The engineers more experienced in Python programming, though, assure me that this is not a big deal since you have a different way of supplying default arguments for a function, which seemingly covers half of the use cases for pipe-pipe-equals (this doesn't prevent Ruby from having both, though). Another half is covered by dictionary's dict.get(key, []) method, so that the code piece #1 can be written in a succinct manner. But I still miss it.
Bash (Linux shell)
Bash? Its language is so simplistic, and it looks creepy; how come it would have an equivalent of such a beautiful shortcut? Here it is:
This assigns y to variable if the former is unset or null (as per Bash manual). I mostly used it to set default parameters for environment variables user may or may not set before invoking the script.
C++
While |= is a syntactically correct expression (C++ does not have the "short-circuit" version of this expression), it doesn't do what we discussed here.
C++ is statically typed, so the result of the standard logical "or" is boolean. Retaining the nice semantics we find in a dynamically typed language would require it to be "either the type of the left-hand side or the type of the right-hand side". This is hard to pull in a pass-by-value statically typed language.
Pass-by-value semantics also means that not everything can be assigned a NULL, and not everything can be converted to boolean value. C++ has default arguments as well as Python, so the same reasoning could apply here. You'll have to be more verbose in C++. That's probably why only |= expression is available, which is only useful if its left-hand-side is bool (see sidebar above for similar usage.)
OCaml
Everything said above about C++ applies to OCaml as well. Moreover, OCaml, as a functional language, doesn't have a flawless support for mutation, and pipe-pipe-equals statement its inherently mutational. However, its matching operator would require us to use the very_long_variable twice. However, OCaml and other functional languages have a very interesting construct called "option". If something has "X option" type, it may contain either "nothing" or a value of x. Then, this value may be "unpacked" trough pattern matching:
let very_long_variable = match very_long_variable with None -> y | Some t -> t
here, t is not an shorthand for another very long expression; instead, it's just an identifier, written as is. The match...with allows us to "unpack" values of structured (algebraic) types with shorthands like this. Since this was too long, OCaml has made this a library function Option#default:
let very_long_variable = Option.default very_long_variable y
Anyway, OCaml programs are even more explicit than those in C++ and Python, so trying to tie pipe-pipe-equals into them is quite pointless.
Ruby
"Erm, we saw how it is in Ruby at the beginning," you might think. Well, I lied to you a bit. The thing is that, in Ruby, it is not strictly equivalent to an assignment to a result of logical "or". Which do you think x ||= y is equivalent to?
In Ruby, and only for ||= and &&=, it's the second. If you assign to something other than a local variables, what looks like an assignment is actually a method call (think properties,) and, if so, this assignment does not happen at all if the left-hand side of ||= is false. Which makes sense, but looks like a special case. Read more here.
Why You Might not Need This
Some argue that this operator is mostly useless, especially if their favourite language doesn't have it. Here are some arguments they list.
Redundancy
Indeed, this expression is redundant. You can do the same in a multiple different ways, All the examples I demonstrated above showed how to write essentially a simple if statement in a very short-hand form. The number of characters spared is probably not worth it to include support for this feature to a language designer's must-have checklist.
The statement discussed decreases the redundancy in code in return of broader language definition; each language seeks a balance between these, and often leaves the pipe-pipe-equals aside.
Default Function Arguments
The ability to specify default function argument (C++, Python, Ruby, but not Bash or Perl) covers many use-cases for ||=. However, this doesn't help fancy loops that fill complex structures, one of which we showed above. Nor helps it when you have to specify the default parameter anyway but the concrete value is not known at the time of coding, and is an optional field user may or may not fill.
Confusion
It is confusing. The pipe-pipe-equals requires explanations how it works. It becomes a special snowflake, different from its "mathematical" counterparts +=, if a complex language wants to make its very useful (see Ruby section above). While "confusion" as an excuse of not doing something is my pet peeve (and I tried to explain why), it indeed requires some effort to understand the mechanics. I'm sure that you'll love it once you understand it, and the way I learned about this operator is not by reading a textbook or "The Most Confusing and Obscure Programming Language Features Possible" newsletter, but by reading someone's code.
To Use or Not To Use?
When it comes to deciding whether or not to use pipe-pipe-equals in the "creepy" way we discussed throughout the post, the criticism somehow fades out. If the language supports this, it will be used. I haven't encountered any coding style document that bans this feature. In Ruby and Perl, it is considered as good of an idiom as many. So the answer on the question of whether or not you sohuld use pipe-pipe-equals (||=) in your programs is, definitely, "yes". | 2018-01-23 08:02:52 | {"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": 0, "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": 0.48265931010246277, "perplexity": 1222.5698125876527}, "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-2018-05/segments/1516084891791.95/warc/CC-MAIN-20180123072105-20180123092105-00702.warc.gz"} |
https://www.sparrho.com/item/geometry-of-the-funk-metric-on-weilpetersson-spaces/1155b70/ | # Geometry of the Funk metric on Weil–Petersson spaces
Research paper by Koji Fujiwara
Indexed on: 08 Nov '12Published on: 08 Nov '12Published in: Mathematische Zeitschrift
#### Abstract
We discuss the Funk function $$F(x,y)$$ on a Teichmüller space with its Weil–Petersson metric $$(\mathcal{T },d)$$ introduced in Yamada (Convex bodies in Euclidean and Weil–Petersson geometries, 2011), which was originally studied for an open convex subset in a Euclidean space by Funk [cf. Papadopoulos and Troyanov (Math Proc Cambridge Philos Soc 147:419–437, 2009)]. $$F(x,y)$$ is an asymmetric distance and invariant by the action of the mapping class group. Unlike the original one, $$F(x,y)$$ is not always convex in $$y$$ with $$x$$ fixed (Corollary 2.11, Theorem 5.1). For each pseudo-Anosov mapping class $$g$$ and a point $$x \in \mathcal{T }$$, there exists $$E$$ such that for all $$n\not = 0$$, $$\log |n| -E \le F(x,g^n.x) \le \log |n|+E$$ (Corollary 2.10), while $$F(x,g^n.x)$$ is bounded if $$g$$ is a Dehn twist (Proposition 2.13). The translation length is defined by $$|g|_F=\inf _{x \in \mathcal{T }}F(x,g.x)$$ for a map $$g: \mathcal{T }\rightarrow \mathcal{T }$$. If $$g$$ is a pseudo-Anosov mapping class, there exists $$Q$$ such that for all $$n \not = 0$$, $$\log |n| -Q \le |g^n|_F \le \log |n| + Q.$$ For sufficiently large $$n$$, $$|g^n|_F >0$$ and the infimum is achieved. If $$g$$ is a Dehn twist, then $$|g^n|_F=0$$ for each $$n$$ (Theorem 2.16). Some geodesics in $$(\mathcal{T },d)$$ are geodesics in terms of $$F$$ as well. We find a decomposition of $$\mathcal{T }$$ by sets, each of which is foliated by those geodesics (Theorem 4.10). | 2021-01-16 23:52:34 | {"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": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8188594579696655, "perplexity": 332.70895015419956}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "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-2021-04/segments/1610703507971.27/warc/CC-MAIN-20210116225820-20210117015820-00268.warc.gz"} |
http://mathoverflow.net/questions/69669/reference-for-this-polyhedral-lemma | # Reference for this polyhedral lemma
Recall the definition of a fan: Let $U$ be a finite dimensional real vector space. Then a fan is a collection $\mathcal{F}$ of cones in $U$ such that
(1) If $\sigma \in \mathcal{F}$ and $\tau$ is a face of $\sigma$, then $\tau \in \mathcal{F}$.
(2) If $\sigma_1$ and $\sigma_2 \in \mathcal{F}$, then $\sigma_1 \cap \sigma_2$ is a face of both $\sigma_1$ and $\sigma_2$.
The following is widely known: Let $\mathcal{S}$ be a collection of cones in $U$ obeying (2). Let $\mathcal{F}$ be the collection of all faces of cones in $\mathcal{S}$ (so $\mathcal{F}$ obeys (1)). Then $\mathcal{F}$ obeys (2).
Is there a standard person and reference to whom this observation is attributed?
-
Added a bounty as an excuse for bumping this to the front page. I'm finishing up a paper which uses this fact, and I'd like to get my references right. – David Speyer Jul 11 '11 at 12:33
You might look in Combinatorial convexity and algebraic geometry by Günter Ewald, to which Ziegler's Lectures on Polytopes refers in his discussion of fans. Just a guess; I don't have Ewald's book. – Joseph O'Rourke Jul 11 '11 at 12:52
Grünbaum's book (Convex Polytopes, 2nd ed) has some discussion in 3.2: a fan is a special case of a polyhedral complex, for which notion he refers to the books of Alexandroff-Hopf and Lefschetz. I see Ewald has a similar discussion. Neither explicitly states what you want, it seems. They both observe that the boundary complex of a polyhedron (say, cone) is a polyhedral complex (fan). Grünbaum's exercise 7 makes you prove almost what you want. So you might try Alexandroff's Combinatorial Topology for an explicit reference, since it's at least in translation. – Graham Denham Jul 11 '11 at 15:13 | 2014-04-19 12:17:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9232864379882812, "perplexity": 394.6920028681522}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "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-2014-15/segments/1397609537186.46/warc/CC-MAIN-20140416005217-00630-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://mathhelpboards.com/threads/result-from-a-metric-linear-space.720/ | # Result from a metric linear space
#### dray
##### Member
Let X be a metric linear space, d a translationally invariant metric defining the metric topology on X, and S(x,r) the open d-ball of radius r centred at the point x in X. How do you prove that S(x,r)=S(0,r) + x ?
Furthermore, why is this an important result?
#### CaptainBlack
##### Well-known member
Let X be a metric linear space, d a translationally invariant metric defining the metric topology on X, and S(x,r) the open d-ball of radius r centred at the point x in X. How do you prove that S(x,r)=S(0,r) + x ?
The usual method: let $$y \in S(x,r)$$ then show that it is also in $$S(0,r)+x$$, then let $$y \in S(0,r)+x$$ and show that it is also in $$S(x,r)$$.
CB
#### dray
##### Member
OK.
Let y in S(x,r) so that d(x,y)< r .... and now I have no idea!
#### Opalg
##### MHB Oldtimer
Staff member
OK.
Let y in S(x,r) so that d(x,y)< r .... and now I have no idea!
The translational invariance means that $d(x,y) = d(x-x,y-x)$.
#### dray
##### Member
Thanks.
Does this look right?
Let y in S(x, r). Then d(x, y) = d(x-x, y-x) = d(0, y-x)< r, so that y in S(0,r) + x.
Now assume that y in S(0,r) + x. Then d(y,0)+d(x-0) >= d(y,x) = d(x,y)< r, so that y in S(0, r).
Since y was chosen arbitrarily from X, it follows that S(x, r)=S(0,r)+x. | 2021-08-01 16:22:29 | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9604156017303467, "perplexity": 2495.6961780618476}, "config": {"markdown_headings": true, "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-2021-31/segments/1627046154214.63/warc/CC-MAIN-20210801154943-20210801184943-00264.warc.gz"} |
https://www.math4refugees.de/html/en/1.7.4/xcontent2.html | #### Chapter 7 Differential Calculus
Section 7.4 Properties of Functions
# 7.4.3 Second Derivative and Bending Properties (Curvature)
Let us consider a function $f:D\to ℝ$ that is differentiable on the interval $\text{}\right]a;b\left[\text{}\subseteq D$. If its derivative $f\text{'}$ is also differentiable on the interval $\text{}\right]a;b\left[\text{}\subseteq D$, then $f$ is called twice-differentiable. The derivative of the first derivative of $f$ ($\left(f\text{'}\right)\text{'}=f\text{'}\text{'}$) is called the second derivative of the function $f$.
The second derivative of the function $f$ can be used to investigate the bending behaviour (curvature) of the function:
##### Bending Properties (Curvature) 7.4.2
If $f\text{'}\text{'}\left(x\right)\ge 0$ for all $x$ between $a$ and $b$, then $f$ is called convex (left curved or concave up) on the interval $\text{}\right]a;b\left[\text{}$.
If $f\text{'}\text{'}\left(x\right)\le 0$ for all $x$ between $a$ and $b$, then $f$ is called concave (right curved or concave down) on the interval $\text{}\right]a;b\left[\text{}$.
Thus, it is sufficient to determine the sign of the second derivative $f\text{'}\text{'}$ to decide whether a function is convex (left curved) or concave (right curved).
##### Comment on the Notation 7.4.3
The second derivative and further "higher" derivatives are often denoted using superscript natural numbers in round brackets: ${f}^{\left(k\right)}$ then denotes the $k$th derivative of $f$. In particular, this notation is used in generally written formulas even for the (first) derivative ($k=1$) and for the function $f$ itself ($k=0$).
Hence,
• ${f}^{\left(0\right)}=f$ denotes the function $f$,
• ${f}^{\left(1\right)}=f\text{'}$ denotes the (first) derivative,
• ${f}^{\left(2\right)}=f\text{'}\text{'}$ the second derivative,
• ${f}^{\left(3\right)}$ the third derivative, and
• ${f}^{\left(4\right)}$ the fourth derivative of $f$.
This list can be continued as long as the derivatives of $f$ exist.
The following example shows that a monotonically increasing function can be convex on one region and concave on another.
##### Example 7.4.4
Certainly, the function $f:ℝ\to ℝ,x\to {x}^{3}$ is at least twice-differentiable. Since $f\text{'}\left(x\right)=3{x}^{2}\ge 0$ for all $x\in ℝ$, the function $f$ is monotonically increasing on its entire domain. Moreover, we have $f\text{'}\text{'}\left(x\right)=6x$. Thus, for all $x<0$, we also have $f\text{'}\text{'}\left(x\right)<0$ and hence, the function $f$ is concave (right curved) on this region. For $x>0$, we have $f\text{'}\text{'}\left(x\right)>0$. Hence, for $x>0$, the function $f$ is convex (left curved). | 2022-08-20 05:38:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 48, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9800554513931274, "perplexity": 225.390252268129}, "config": {"markdown_headings": true, "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-2022-33/segments/1659882573908.30/warc/CC-MAIN-20220820043108-20220820073108-00012.warc.gz"} |
https://math.stackexchange.com/questions/775062/finding-time-constants-of-a-circuit | Finding time constants of a circuit?
So this is a homework question and I am having trouble figuring out what they are asking.
'The potential difference (voltage) across the capacitor at time t > 0 is given by $V_C(t) = q(t)/C$. The quantity RC has the dimensions of time and is often called the time constant for the circuit. How many time constants does it take for a capacitor to charge to 90% of the applied voltage, V0? Justify your answer'
So change in V, or $V_C$, or $\delta{V}$ is 90%. In other words we have $0.9V=q(t)/C$?
I have found in a previous question that $q(t)=V_0C(1-e^{-\frac{t}{CR}})$ so
$$0.9V=\frac{V_0C(1-e^{-\frac{t}{CR}})}{C}$$
However I am not sure where to go from here, if I am even on the right track at all.
• No I only have the above info – user88720 Apr 30 '14 at 1:48
If you look at the capacitor voltage curve, you notice that somewhere between $2$ and $3$ time constants, we have $90\%$ charge. We should be able to figure this out generally when not given the resistor and capacitor value.
We have the unknown:
$$\mbox{Time Constant} = \tau = RC$$
Using:
$$\large 0.9V=\frac{V_0C(1-e^{-\frac{t}{CR}})}{C} = V_0(1-e^{-\frac{t}{CR}}) = V_0(1-e^{-\frac{t}{\tau}})$$
We want to solve for $t$, so we have:
$$t = - \tau \ln \left(-\frac{0.9 V-V_0}{V_0}\right)$$
However, the voltage across the capacitor is $.9$ of the the voltage source $V_0$, so we can rewrite this as:
$$t = - \tau \ln \left(-\frac{0.9 V-V_0}{V_0}\right) = - \tau \ln \left(-\frac{0.9 V_0-V_0}{V_0} \right) = - \tau \ln (0.1) = -(-2.30259)\tau = 2.30259 \tau$$
In other words, it will take $2.30259$ time constants to charge to $90\%$.
• You're an EE as well? – Robert Lewis Apr 30 '14 at 2:16
• What happened to the /C part. Isn't $0.9V=q(t)/C$? – user88720 Apr 30 '14 at 2:27
• Did you read my profile? I've got that math/CS/EE thing going as well! Plus RS! As I said, degree'd out! – Robert Lewis Apr 30 '14 at 2:35
• As for RS, I didn't much like writing sociology papers which were part of the core general requirement--every grad student had to take some "general RS stuff", you know--psychology, sociology, anthropology, philosophy; I found that part of it BORING!!! When I began to focus on what I wanted, which was ancient Hebrew literature and the history of early Judea-Christianity, I was so into it that it was easy. I think it's hard for "techies" to get the humanities mindset! The logic is the same, but some of the arguments make mathematical subtlety pale! It's like . . more . . . – Robert Lewis Apr 30 '14 at 3:18
• Next: trying to get the precision Euclid's axioms out of ordinary writing/speech; it can be done, but you really have to read stuff very carefully! – Robert Lewis Apr 30 '14 at 3:20 | 2019-08-19 14:31:16 | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7850253582000732, "perplexity": 539.5687333383426}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "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-2019-35/segments/1566027314752.21/warc/CC-MAIN-20190819134354-20190819160354-00466.warc.gz"} |
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Latest Posts WW3 ? or WW$by paul 04/09/17 03:08 PM UBB Message by paul 04/09/17 01:45 PM Top Posters (30 Days) paul 2 Page 6 of 11 < 1 2 ... 4 5 6 7 8 10 11 > Topic Options #33619 - 03/16/10 04:07 AM Re: The Concept of the Whole and Threadism Kyra M Member Registered: 06/25/09 Posts: 90 The Concept of the Whole and Threadism ©Kyra K 2009 Andrea is discussing this with me.I don’t know, Andrea, maybe it’s not that different from what others have written.Probably not. So, when do you want to start?[Remember, you did ask me to help you.)Yes, I need someone to ask me questions and bounce back (with more questions to my answers). It’s all speculation you know.Everything is. Well, everything which addresses the meaning of life etc, is.Okay, here goes. Scientists are saying that 25% of the Universe is dark matter and 70% of the Universe is dark energy - that is a whopping 95% of everything being this ‘dark’ stuff which may, or may not, co-exist. It is through us, with us and I think it may be us.Hang on, am I supposed to argue with this now?Well, what do you think?It’s a bit simplistic isn’t it?I wish it was.Well, it’s no secret that you have Pantheist leanings. The Pantheists believe just what you have said, that everything is the Universe and the Universe is everything.Yes, but not that one part is matter-aware and the other part is energy-aware.Which is which?Look, I don’t know, but consider this hypothesis. We are matter aware and the other part of us, which exists with us, but also separate to us (seemingly) is energy aware. You say seemingly?Well everything is joined – just that some are not aware that it is. I think that’s why meditation works. When humans are able to let go of the physical for a few seconds, minutes, hours or even days as some monks can, we tap into the dark energy. We are not aware that we are aware?Well, we are, of course aware that we are here, but not all of us are aware that we are part of the Whole: dark energy and dark matter combined. And let’s stop calling it dark. Just because scientists can’t see it, it doesn’t make it dark. We have nothing to quantify its colour. I will call both forms ‘Light’ from now on. As in Light energy and Light matter.Yeah, I do agree with you about the dark inference, it makes it sound sinister. So what you are saying is that we are all part of the same thing, this Light energy and this Light matter stuff?Okay, consider this, the Light matter may be what is live. Everything that has life, as we know it, has awareness, even if they are not aware of having awareness. Light matter 25%. Then another 70% is Light energy which still has awareness because, I believe, it is connected. And the other 5% is all the physical matter: bodies, bone, fur, feather, mineral chemical and inert material.Yeah, we humans are aware of being aware. And some other animals may be aware of being aware, too.Yes, but I am talking about all life: insects, animals, germs, microbes, bacteria and all the botanicals being the 25% Light matter. But still connected to the 70% Light energy.I have thought of an analogy. As I said before, this is probably not original, but it is the closest I can get, to explaining myself.I’m listening.A flock of birds seem separate but to themselves they are not completely separate. They are connected to the lead bird and he/she to them. One entity, many parts. When flying formation this connection is obvious (they instantly move as one while they still have their own position and place) but it may be they have some sort of connection which is not so obvious at other times, too. So might all animals and insects and even plants. It could be species specific (this close awareness of the others). And we humans have this too, for example: when there is a short story competition or call for an anthology a lot of the entries/contributions will have the same theme. And it also explains other synchronicity. Let’s take this a step further, perhaps all life is connected (animals plants, microbes humans etc) and all death, as we know it, is connected as well.Death?After death of the outer shell (our separate state) we are awoken to the awareness (it has always been with us) of light energy. And this Light energy has far more consciousness than the consciousness we live through our physical selves. It may be like the flock of birds flying in formation all seeing through the same eyes and feeling though the same body of the flock. Like I said, I think we are connected to this Light energy in life even when we have the ‘shell’. So everything, both Light energy 70% and Light matter 25% is one at all times, or the Whole.That is some concept. What about the nitty gritty matter, the blood and bone, leaf and fur, so to speak?Mere packaging (and only a tiny 5% of all) and it is the way we (all living organisms) can abide in this environment.Oh, that’s what you mean by the ‘shell’. But just how are we ‘connected’?I think it may be through threads. Something similar perhaps, to radio waves (different frequencies and strengths) but the connection is like tissue (in a human body) we need it to be the ‘Whole.’ Let’s call this connection Threadism. Perhaps it is also part of what we used to call instinct and intuition.So now, whenever I look at someone else, I remember that their Light matter and Light energy is our/my Light matter and our/my Light energy. And when this body wears out I will still be, but with more awareness. The awareness of the Universe.The Universe or the Whole (except for the 5%) Yes, exactly. Not The Universe but We Universe.Yes, well, how did us/we Universe come about?Look, like I told M, I am just like a horse trying to explain/understand how a television works; what I have here is just a line (drawn with my hoof!) depicting the side of the screen. I certainly don’t have all the answers.Why do we need to come here as sentient, or living beings?Well, I think, for variety. Entertainment, stimulation, change, growth. (Andrea, don’t forget there are other life-filled planets). As The Whole we all benefit. We humans learn what benefits, or you could say what is right, by cause and effect, conscience and acknowledging Karma both good and bad. From this, we as humans have gained tolerance, understanding and compassion. Connection, passive or otherwise, strengthens or makes possible these learnings. Anyway, a lot of what we think is bad, is not - like dying for instance.Also, I think that not all of the 70% of us that is light energy (not physical) has to interchange with the physical, or the 25% Light matter, ever. For this bit of Us, perhaps the Us that lives in the Physical, are like our novels or short stories! Lol. What are the advantages of believing in this?Well, no envy - you can be truly happy for another when you know the other is you, (by Threadism) as well. No selfishness. No fear of the future. We learn that listening to our ‘Instinct or Intuition’ or the voice of the Whole, and seeing synchronicity for signs of Threadism as well, can help us live a more fulfilled life. And understanding that Karma is working for us.And I guess you don’t have to worry about death.Exactly, and it (this belief) makes you want to live.How so?Well, for the good of the Whole you want to enjoy and experience life as much as you can. And also learn from Karma.Is all suffering karma then?No, not all. I think the only way we can control the 5% which is the actual matter and the elements too, which bring disaster (in our thinking) etc, is by collective learning. This learning has led us to manipulate our environment (and our lives). And we have learned by our mistakes and successes. We, the Whole, are not perfect or omniscient. Even though We are connected it does not stop people, microbes germs, elements etc from doing their separate thing, be it ‘wrong’ (by human standards) or just following their own nature. But of all the parts of the Whole, humans have had more influence/control over themselves and their own environment.Now, how can I get this straight? I’ll try and quantify it in numbers.1. We are all part of, and therefore, the Whole. Less the 5% physical: blood, bone, fur, feather bodies, minerals, gases and inert matter. Which we are learning to control.2. There is no need for envy or fear of the future. No need for selfishness. We should look at everyone as the Whole.Before I go on, I should explain (although you would already know this) that not everyone knows they are part of the Whole. But they still would be?Yes, but, like an arm that has gone to sleep because some of the circulation has been cut off, they are separate.But you said..?The arm with the circulation partly cut off has the blood, life force, still circulating. The arm is joined to the body but it feels separate and is not good for the body.We can still acknowledge that it (those unaware) is part of us but we need to do something about it.I see, make it/them aware.Yes, rub the circulation back (lol), support, understand. Or, in some cases, keep away. Okay, 3 - No need for fear of death. Or for us to say there is no god, when people/ animals die.Death is not the big deal we thought it was. Although, of course it is very sad for those still in the physical 5%. But for We that die (shed shells) it is a greater awareness. And We are still joined to those loved ones by Threadism.4. The god is WE (connected) with the Whole by Threadism.Light energy 70%, Light matter 25% and Outer shells (what is visible) 5%. Only the shells go back to stardust. 5. For the Whole there is no time but IS.We experience this life as we know it, for growth, interest and awe, for the good of the Whole. And to learn by our mistakes and triumphs, take notice of Karma and synchronicity, instinct and intuition. The Whole is evolving.6. We may feel separate but this is so we can get the maximum benefit of being a living being. Synchronicity and Karma, instinct and intuition, show we are still connected by Threadism. 7. Just like the numb arm we are still part of the Whole, even if we are not aware.8. In parting with the shell we become more aware, as we are awake to the greater Whole.Mm… interesting concept. Do you think it will catch on?Well, if I’m right, others of Light Matter know this already.And the Light Energy has always known.Precisely.NB - I think, We (95%) are as connected to the 5% as a musician is connected to a trumpet/ trombone etc. We blow breath (life) through it and the music we play is an extension and expression of ourselves. Top . #33736 - 03/27/10 02:54 AM Re: The Concept of the Whole and Threadism Kyra M Member Registered: 06/25/09 Posts: 90 The Concept of the Whole and Threadism ©Kyra K 2009 Andrea is discussing this with me.I don’t know, Andrea, maybe it’s not that different from what others have written.Probably not. So, when do you want to start?[Remember, you did ask me to help you.)Yes, I need someone to ask me questions and bounce back (with more questions to my answers). It’s all speculation you know.Everything is. Well, everything which addresses the meaning of life etc, is.Okay, here goes. Scientists are saying that 25% of the Universe is dark matter and 70% of the Universe is dark energy - that is a whopping 95% of everything being this ‘dark’ stuff which may, or may not, co-exist. It is through us, with us and I think it may be us.Hang on, am I supposed to argue with this now?Well, what do you think?It’s a bit simplistic isn’t it?I wish it was.Well, it’s no secret that you have Pantheist leanings. The Pantheists believe just what you have said, that everything is the Universe and the Universe is everything.Yes, but not that one part is matter-aware and the other part is energy-aware.Which is which?Look, I don’t know, but consider this hypothesis. We are matter aware and the other part of us, which exists with us, but also separate to us (seemingly) is energy aware. You say seemingly?Well everything is joined – just that some are not aware that it is. I think that’s why meditation works. When humans are able to let go of the physical for a few seconds, minutes, hours or even days as some monks can, we tap into the dark energy. We are not aware that we are aware?Well, we are, of course aware that we are here, but not all of us are aware that we are part of the Whole: dark energy and dark matter combined. And let’s stop calling it dark. Just because scientists can’t see it, it doesn’t make it dark. We have nothing to quantify its colour. I will call both forms ‘Light’ from now on. As in Light energy and Light matter.Yeah, I do agree with you about the dark inference, it makes it sound sinister. So what you are saying is that we are all part of the same thing, this Light energy and this Light matter stuff?Okay, consider this, the Light matter may be what is live. Everything that has life, as we know it, has awareness, even if they are not aware of having awareness. Light matter 25%. Then another 70% is Light energy which still has awareness because, I believe, it is connected. And the other 5% is all the physical matter: bodies, bone, fur, feather, mineral chemical and inert material.Yeah, we humans are aware of being aware. And some other animals may be aware of being aware, too.Yes, but I am talking about all life: insects, animals, germs, microbes, bacteria and all the botanicals being the 25% Light matter. But still connected to the 70% Light energy.I have thought of an analogy. As I said before, this is probably not original, but it is the closest I can get, to explaining myself.I’m listening.A flock of birds seem separate but to themselves they are not completely separate. They are connected to the lead bird and he/she to them. One entity, many parts. When flying formation this connection is obvious (they instantly move as one while they still have their own position and place) but it may be they have some sort of connection which is not so obvious at other times, too. So might all animals and insects and even plants. It could be species specific (this close awareness of the others). And we humans have this too, for example: when there is a short story competition or call for an anthology a lot of the entries/contributions will have the same theme. And it also explains other synchronicity. Let’s take this a step further, perhaps all life is connected (animals plants, microbes humans etc) and all death, as we know it, is connected as well.Death?After death of the outer shell (our separate state) we are awoken to the awareness (it has always been with us) of light energy. And this Light energy has far more consciousness than the consciousness we live through our physical selves. It may be like the flock of birds flying in formation all seeing through the same eyes and feeling though the same body of the flock. Like I said, I think we are connected to this Light energy in life even when we have the ‘shell’. So everything, both Light energy 70% and Light matter 25% is one at all times, or the Whole.That is some concept. What about the nitty gritty matter, the blood and bone, leaf and fur, so to speak?Mere packaging (and only a tiny 5% of all) and it is the way we (all living organisms) can abide in this environment.Oh, that’s what you mean by the ‘shell’. But just how are we ‘connected’?I think it may be through threads. Something similar perhaps, to radio waves (different frequencies and strengths) but the connection is like tissue (in a human body) we need it to be the ‘Whole.’ Let’s call this connection Threadism. Perhaps it is also part of what we used to call instinct and intuition.So now, whenever I look at someone else, I remember that their Light matter and Light energy is our/my Light matter and our/my Light energy. And when this body wears out I will still be, but with more awareness. The awareness of the Universe.The Universe or the Whole (except for the 5%) Yes, exactly. Not The Universe but We Universe.Yes, well, how did us/we Universe come about?Look, like I told M, I am just like a horse trying to explain/understand how a television works; what I have here is just a line (drawn with my hoof!) depicting the side of the screen. I certainly don’t have all the answers.Why do we need to come here as sentient, or living beings?Well, I think, for variety. Entertainment, stimulation, change, growth. (Andrea, don’t forget there are other life-filled planets). As The Whole we all benefit. We humans learn what benefits, or you could say what is right, by cause and effect, conscience and acknowledging Karma both good and bad. From this, we as humans have gained tolerance, understanding and compassion. Connection, passive or otherwise, strengthens or makes possible these learnings. Anyway, a lot of what we think is bad, is not - like dying for instance.Also, I think that not all of the 70% of us that is light energy (not physical) has to interchange with the physical, or the 25% Light matter, ever. For this bit of Us, perhaps the Us that lives in the Physical, are like our novels or short stories! Lol. What are the advantages of believing in this?Well, no envy - you can be truly happy for another when you know the other is you, (by Threadism) as well. No selfishness. No fear of the future. We learn that listening to our ‘Instinct or Intuition’ or the voice of the Whole, and seeing synchronicity for signs of Threadism as well, can help us live a more fulfilled life. And understanding that Karma is working for us.And I guess you don’t have to worry about death.Exactly, and it (this belief) makes you want to live.How so?Well, for the good of the Whole you want to enjoy and experience life as much as you can. And also learn from Karma.Is all suffering karma then?No, not all. I think the only way we can control the 5% which is the actual matter and the elements too, which bring disaster (in our thinking) etc, is by collective learning. This learning has led us to manipulate our environment (and our lives). And we have learned by our mistakes and successes. We, the Whole, are not perfect or omniscient. Even though We are connected it does not stop people, microbes germs, elements etc from doing their separate thing, be it ‘wrong’ (by human standards) or just following their own nature. But of all the parts of the Whole, humans have had more influence/control over themselves and their own environment.Now, how can I get this straight? I’ll try and quantify it in numbers.1. We are all part of, and therefore, the Whole. Less the 5% physical: blood, bone, fur, feather bodies, minerals, gases and inert matter. Which we are learning to control.2. There is no need for envy or fear of the future. No need for selfishness. We should look at everyone as the Whole.Before I go on, I should explain (although you would already know this) that not everyone knows they are part of the Whole. But they still would be?Yes, but, like an arm that has gone to sleep because some of the circulation has been cut off, they are separate.But you said..?The arm with the circulation partly cut off has the blood, life force, still circulating. The arm is joined to the body but it feels separate and is not good for the body.We can still acknowledge that it (those unaware) is part of us but we need to do something about it.I see, make it/them aware.Yes, rub the circulation back (lol), support, understand. Or, in some cases, keep away. Okay, 3 - No need for fear of death. Or for us to say there is no god, when people/ animals die.Death is not the big deal we thought it was. Although, of course it is very sad for those still in the physical 5%. But for We that die (shed shells) it is a greater awareness. And We are still joined to those loved ones by Threadism.4. The god is WE (connected) with the Whole by Threadism.Light energy 70%, Light matter 25% and Outer shells (what is visible) 5%. Only the shells go back to stardust. 5. For the Whole there is no time but IS.We experience this life as we know it, for growth, interest and awe, for the good of the Whole. And to learn by our mistakes and triumphs, take notice of Karma and synchronicity, instinct and intuition. The Whole is evolving.6. We may feel separate but this is so we can get the maximum benefit of being a living being. Synchronicity and Karma, instinct and intuition, show we are still connected by Threadism. 7. Just like the numb arm we are still part of the Whole, even if we are not aware.8. In parting with the shell we become more aware, as we are awake to the greater Whole.Mm… interesting concept. Do you think it will catch on?Well, if I’m right, others of Light Matter know this already.And the Light Energy has always known.Precisely.NB - I think, We (95%) are as connected to the 5% as a musician is connected to a trumpet/ trombone etc. We blow breath (life) through it and the music we play is an extension and expression of ourselves. Top #33750 - 03/28/10 02:22 AM Re: The Concept of the Whole and Threadism Revlgking Megastar Registered: 01/17/07 Posts: 2311 Loc: markham (Thornhill), Ontario, ... Kyra and Andrea, pardon this old fogy for what you may think of as an intrusion. If you wish, feel free to tell me you have everything under control. I will not be offended. However, if you would welcome some help in making it easier for readers to understand what you want to say, think about the following. Kyra, it is my understanding that your main goal is to you tell your readers, as clearly as possible, what you mean by "Whole Threadism". You want us to have a clear idea of what you mean, right? It seems to me that to do this you have chosen to use the same method as used by Socrates in famous DIALOGUES OF PLATO--a wise choice. Therefore, may I suggest you do the following: Like in a play, make it clear who is saying what to whom. To illustrate what I mean, using the first part of what I assume you said to each other, I offer the following: =================================================FELLOW POSTERS, KYRA HERE. WHOLE THREADISM, AS MANY OF YOU ALREADY KNOW IS A CONCEPT WHICH IS NEAR AND DEAR TO MY HEART.(©Kyra K 2009). To help me, Kyra, to clarify my thoughts I have asked a friend, Andrea, to dialogue with me about this. Readers, feel free to participate in the dialogue with your comments and questions.Kyra: I don’t know, Andrea, maybe it’s not that different from what others have written.Andrea: Probably not. So, when do you want to start? [Remember, you did ask me to help you.)Kyra: Yes, I need someone to ask me questions and bounce back to me with more questions to my answers. It’s all speculation you know. Everything is. Well, everything which addresses the meaning of life etc, is.Andrea: Okay, here goes: Scientists are saying that 25% of the Universe is dark matter and 70% of the Universe is dark energy. That is a whopping 95% of everything being this ‘dark’ stuff which may, or may not, co-exist. It is through us, with us and, I think, it may be of us.Kyra: Hang on, am I supposed to argue with this now?Andrea: Well, what do you think?Kyra: It’s a bit simplistic isn’t it?Andrea: I wish it was.Kyra: Well, it’s no secret that you have Pantheist leanings. The Pantheists believe just what you have said, that everything is the Universe and the Universe is everything.Andrea: Yes, but not that one part is matter-aware and the other part is energy-aware.Kyra: Which is which?Andrea: Look! I don’t know, but consider this hypothesis: We are matter aware and the other part of us, which exists with us, but also separate to us (seemingly) is energy aware.Kyra: You say, seemingly?===============================BTW, make a point of doing a search on the work of Alfred North Whitehead, Process Philosophy and Theology, and Panentheism--not to be confused with pantheism. http://plato.stanford.edu/entries/panentheism/#Hishttp://en.wikipedia.org/wiki/John_B._Cobbhttp://en.wikipedia.org/wiki/Charles_Hartshorne Edited by Revlgking (03/28/10 02:39 AM)Edit Reason: Always a Good Idea! _________________________ G~O~D--Now & ForeverIS:Nature, Nurture & PNEUMA-ture, Thanks to Warren Farr&ME AT www.unitheist.org Top #33863 - 04/05/10 06:54 AM Re: The Concept of the Whole and Threadism Kyra M Member Registered: 06/25/09 Posts: 90 Hi Rev,Great idea, I did write this originally with italics for Andrea but it didn't come out when I posted it on here. Top #33896 - 04/09/10 05:56 AM Re: The Concept of the Whole and Threadism Kyra M Member Registered: 06/25/09 Posts: 90 The Concept of the Whole and Threadism ©Myra King 2009 Andrea, who is my alter ego, is in italics.Me: I don’t know, Andrea, maybe it’s not that different from what others have written.Andrea: Probably not. So, when do you want to start? Remember, you did ask me to help you.Yes, I need someone to ask me questions and bounce back (with more questions to my answers). It’s all speculation you know.Andrea: Everything is. Well, everything which addresses the meaning of life etc, is.Me: Okay, here goes. Scientists are saying that 25% of the Universe is dark matter and 70% of the Universe is dark energy - that is a whopping 95% of everything being this ‘dark’ stuff which may, or may not, co-exist. It is through us, with us and I think it may be us.Andrea: Hang on, am I supposed to argue with this now?Well, what do you think?Andrea: It’s a bit simplistic isn’t it?Me: Oh, god, I wish it was.Andrea: Well, it’s no secret that you have Pantheist leanings. The Pantheists believe just what you have said, that everything is the Universe and the Universe is everything.Me:Yes, but not that one part is matter-aware and the other part is energy-aware.Andrea: Which is which?Look, I don’t know, but consider this hypothesis. We are matter aware and the other part of us, which exists with us, but also separate to us (seemingly) is energy aware. Andrea: You say seemingly?Well everything is joined – just that some are not aware that it is. I think that’s why meditation works. When humans are able to let go of the physical for a few seconds, minutes, hours or even days as some monks can, we tap into the dark energy. Andrea: We are not aware that we are aware?Well, we are, of course aware that we are here, but not all of us are aware that we are part of the Whole: dark energy and dark matter combined. And let’s stop calling it dark. Just because scientists can’t see it, it doesn’t make it dark. We have nothing to quantify its colour. I will call both forms ‘Light’ from now on. As in Light energy and Light matter.Andrea: Yeah, I do agree with you about the dark inference, it makes it sound sinister. So what you are saying is that we are all part of the same thing, this Light energy and this Light matter stuff?Okay, consider this, the Light matter may be what is live. Everything that has life, as we know it, has awareness, even if they are not aware of having awareness. Light matter 25%. Then another 70% is Light energy which still has awareness because, I believe, it is connected. And the other 5% is all the physical matter: bodies, bone, fur, feather, mineral chemical and inert material.Andrea: Yeah, we humans are aware of being aware. And some other animals may be aware of being aware, too.Yes, but I am talking about all life: insects, animals, germs, microbes, bacteria and all the botanicals being the 25% Light matter. But still connected to the 70% Light energy.I have thought of an analogy. As I said before, this is probably not original, but it is the closest I can get, to explaining myself.Andrea: I’m listening.A flock of birds seem separate but to themselves they are not completely separate. They are connected to the lead bird and he/she to them. One entity, many parts. When flying formation this connection is obvious (they instantly move as one while they still have their own position and place) but it may be they have some sort of connection which is not so obvious at other times, too. So might all animals and insects and even plants. It could be species specific (this close awareness of the others). And we humans have this too, for example: when there is a short story competition or call for an anthology a lot of the entries/contributions will have the same theme. And it also explains other synchronicity. Let’s take this a step further, perhaps all life is connected (animals plants, microbes humans etc) and all death, as we know it, is connected as well. Andrea: Death?After death of the outer shell (our separate state) we are awoken to the awareness (it has always been with us) of light energy. And this Light energy has far more consciousness than the consciousness we live through our physical selves. It may be like the flock of birds flying in formation all seeing through the same eyes and feeling though the same body of the flock. Like I said, I think we are connected to this Light energy in life even when we have the ‘shell’. So everything, both Light energy 70% and Light matter 25% is one at all times, or the Whole.Andrea: That is some concept. What about the nitty gritty matter, the blood and bone, leaf and fur, so to speak?Mere packaging (and only a tiny 5% of all) and it is the way we (all living organisms) can abide in this environment.Andrea: Oh, that’s what you mean by the ‘shell’. But just how are we ‘connected’?I think it may be through threads. Something similar perhaps, to radio waves (different frequencies and strengths) but the connection is like tissue (in a human body) we need it to be the ‘Whole.’ Let’s call this connection Threadism. Perhaps it is also part of what we used to call instinct and intuition.So now, whenever I look at someone else, I remember that their Light matter and Light energy is our/my Light matter and our/my Light energy. And when this body wears out I will still be, but with more awareness. Andrea: The awareness of the Universe.The Universe or the Whole (except for the 5%) Yes, exactly. Not The Universe but We Universe.Andrea: Yes, well, how did us/we Universe come about?Look, like I told M, I am just like a horse trying to explain/understand how a television works; what I have here is just a line (drawn with my hoof!) depicting the side of the screen. I certainly don’t have all the answers.Andrea: Why do we need to come here as sentient, or living beings?Well, I think, for variety. Entertainment, stimulation, change, growth. (Andrea, don’t forget there are other life-filled planets). As The Whole we all benefit. We humans learn what benefits, or you could say what is right, by cause and effect, conscience and acknowledging Karma both good and bad. From this, we as humans have gained tolerance, understanding and compassion. Connection, passive or otherwise, strengthens or makes possible these learnings. Anyway, a lot of what we think is bad, is not - like dying for instance.Also, I think that not all of the 70% of us that is light energy (not physical) has to interchange with the physical, or the 25% Light matter, ever. For this bit of Us, perhaps the Us that lives in the Physical, are like our novels or short stories! Lol. Andrea: What are the advantages of believing in this?Well, no envy - you can be truly happy for another when you know the other is you, (by Threadism) as well. No selfishness. No fear of the future. We learn that listening to our ‘Instinct or Intuition’ or the voice of the Whole, and seeing synchronicity for signs of Threadism as well, can help us live a more fulfilled life. And understanding that Karma is working for us.Andrea: And I guess you don’t have to worry about death.Exactly, and it (this belief) makes you want to live.Andrea: How so?Well, for the good of the Whole you want to enjoy and experience life as much as you can. And also learn from Karma.Andrea: Is all suffering karma then?No, not all. I think the only way we can control the 5% which is the actual matter and the elements too, which bring disaster (in our thinking) etc, is by collective learning. This learning has led us to manipulate our environment (and our lives). And we have learned by our mistakes and successes. We, the Whole, are not perfect or omniscient. Even though We are connected it does not stop people, microbes germs, elements etc from doing their separate thing, be it ‘wrong’ (by human standards) or just following their own nature. But of all the parts of the Whole, humans have had more influence/control over themselves and their own environment.Andrea: Now, how can I get this straight? I’ll try and quantify it in numbers.1. We are all part of, and therefore, the Whole. Less the 5% physical: blood, bone, fur, feather bodies, minerals, gases and inert matter. Which we are learning to control.2. There is no need for envy or fear of the future. No need for selfishness. We should look at everyone as the Whole.Before I go on, I should explain (although you would already know this) that not everyone knows they are part of the Whole. Andrea: But they still would be?Yes, but, like an arm that has gone to sleep because some of the circulation has been cut off, they are separate.Andrea: But you said..?The arm with the circulation partly cut off has the blood, life force, still circulating. The arm is joined to the body but it feels separate and is not good for the body.We can still acknowledge that it (those unaware) is part of us but we need to do something about it.Andrea: I see, make it/them aware.Yes, rub the circulation back (lol), support, understand. Or, in some cases, keep away. Okay, 3 - No need for fear of death. Or for us to say there is no god, when people/ animals die.Death is not the big deal we thought it was. Although, of course it is very sad for those still in the physical 5%. But for We that die (shed shells) it is a greater awareness. And We are still joined to those loved ones by Threadism.4. The god is WE (connected) with the Whole by Threadism.Light energy 70%, Light matter 25% and Outer shells (what is visible) 5%. Only the shells go back to stardust. 5. For the Whole there is no time but IS.We experience this life as we know it, for growth, interest and awe, for the good of the Whole. And to learn by our mistakes and triumphs, take notice of Karma and synchronicity, instinct and intuition. The Whole is evolving.6. We may feel separate but this is so we can get the maximum benefit of being a living being. Synchronicity and Karma, instinct and intuition, show we are still connected by Threadism. 7. Just like the numb arm we are still part of the Whole, even if we are not aware.8. In parting with the shell we become more aware, as we are awake to the greater Whole.Andrea: Mm… interesting concept. Do you think it will catch on?Well, if I’m right, others of Light Matter know this already.Andrea: And the Light Energy has always known.Precisely.NB - I think, We (95%) are as connected to the 5% as a musician is connected to a trumpet/ trombone etc. We blow breath (life) through it and the music we play is an extension and expression of ourselves. Top #34226 - 05/06/10 07:40 AM Re: The Concept of the Whole and Threadism Kyra M Member Registered: 06/25/09 Posts: 90 Me: I don’t know, Andrea, maybe it’s not that different from what others have written.Andrea: Probably not. So, when do you want to start? Remember, you did ask me to help you.Yes, I need someone to ask me questions and bounce back (with more questions to my answers). It’s all speculation you know.Andrea: Everything is. Well, everything which addresses the meaning of life etc, is.Me: Okay, here goes. Scientists are saying that 25% of the Universe is dark matter and 70% of the Universe is dark energy - that is a whopping 95% of everything being this ‘dark’ stuff which may, or may not, co-exist. It is through us, with us and I think it may be us.Andrea: Hang on, am I supposed to argue with this now?Well, what do you think?Andrea: It’s a bit simplistic isn’t it?Me: Oh, god, I wish it was.Andrea: Well, it’s no secret that you have Pantheist leanings. The Pantheists believe just what you have said, that everything is the Universe and the Universe is everything.Me:Yes, but not that one part is matter-aware and the other part is energy-aware.Andrea: Which is which?Look, I don’t know, but consider this hypothesis. We are matter aware and the other part of us, which exists with us, but also separate to us (seemingly) is energy aware. Andrea: You say seemingly?Well everything is joined – just that some are not aware that it is. I think that’s why meditation works. When humans are able to let go of the physical for a few seconds, minutes, hours or even days as some monks can, we tap into the dark energy. Andrea: We are not aware that we are aware?Well, we are, of course aware that we are here, but not all of us are aware that we are part of the Whole: dark energy and dark matter combined. And let’s stop calling it dark. Just because scientists can’t see it, it doesn’t make it dark. We have nothing to quantify its colour. I will call both forms ‘Light’ from now on. As in Light energy and Light matter.Andrea: Yeah, I do agree with you about the dark inference, it makes it sound sinister. So what you are saying is that we are all part of the same thing, this Light energy and this Light matter stuff?Okay, consider this, the Light matter may be what is live. Everything that has life, as we know it, has awareness, even if they are not aware of having awareness. Light matter 25%. Then another 70% is Light energy which still has awareness because, I believe, it is connected. And the other 5% is all the physical matter: bodies, bone, fur, feather, mineral chemical and inert material.Andrea: Yeah, we humans are aware of being aware. And some other animals may be aware of being aware, too.Yes, but I am talking about all life: insects, animals, germs, microbes, bacteria and all the botanicals being the 25% Light matter. But still connected to the 70% Light energy.I have thought of an analogy. As I said before, this is probably not original, but it is the closest I can get, to explaining myself.Andrea: I’m listening.A flock of birds seem separate but to themselves they are not completely separate. They are connected to the lead bird and he/she to them. One entity, many parts. When flying formation this connection is obvious (they instantly move as one while they still have their own position and place) but it may be they have some sort of connection which is not so obvious at other times, too. So might all animals and insects and even plants. It could be species specific (this close awareness of the others). And we humans have this too, for example: when there is a short story competition or call for an anthology a lot of the entries/contributions will have the same theme. And it also explains other synchronicity. Let’s take this a step further, perhaps all life is connected (animals plants, microbes humans etc) and all death, as we know it, is connected as well.Andrea: Death?After death of the outer shell (our separate state) we are awoken to the awareness (it has always been with us) of light energy. And this Light energy has far more consciousness than the consciousness we live through our physical selves. It may be like the flock of birds flying in formation all seeing through the same eyes and feeling though the same body of the flock. Like I said, I think we are connected to this Light energy in life even when we have the ‘shell’. So everything, both Light energy 70% and Light matter 25% is one at all times, or the Whole.Andrea: That is some concept. What about the nitty gritty matter, the blood and bone, leaf and fur, so to speak?Mere packaging (and only a tiny 5% of all) and it is the way we (all living organisms) can abide in this environment.Andrea: Oh, that’s what you mean by the ‘shell’. But just how are we ‘connected’?I think it may be through threads. Something similar perhaps, to radio waves (different frequencies and strengths) but the connection is like tissue (in a human body) we need it to be the ‘Whole.’ Let’s call this connection Threadism. Perhaps it is also part of what we used to call instinct and intuition.So now, whenever I look at someone else, I remember that their Light matter and Light energy is our/my Light matter and our/my Light energy. And when this body wears out I will still be, but with more awareness. Andrea: The awareness of the Universe.The Universe or the Whole (except for the 5%) Yes, exactly. Not The Universe but We Universe.Andrea: Yes, well, how did us/we Universe come about?Look, like I told M, I am just like a horse trying to explain/understand how a television works; what I have here is just a line (drawn with my hoof!) depicting the side of the screen. I certainly don’t have all the answers.Andrea: Why do we need to come here as sentient, or living beings?Well, I think, for variety. Entertainment, stimulation, change, growth. (Andrea, don’t forget there are other life-filled planets). As The Whole we all benefit. We humans learn what benefits, or you could say what is right, by cause and effect, conscience and acknowledging Karma both good and bad. From this, we as humans have gained tolerance, understanding and compassion. Connection, passive or otherwise, strengthens or makes possible these learnings. Anyway, a lot of what we think is bad, is not - like dying for instance.Also, I think that not all of the 70% of us that is light energy (not physical) has to interchange with the physical, or the 25% Light matter, ever. For this bit of Us, perhaps the Us that lives in the Physical, are like our novels or short stories! Lol. Andrea: What are the advantages of believing in this?Well, no envy - you can be truly happy for another when you know the other is you, (by Threadism) as well. No selfishness. No fear of the future. We learn that listening to our ‘Instinct or Intuition’ or the voice of the Whole, and seeing synchronicity for signs of Threadism as well, can help us live a more fulfilled life. And understanding that Karma is working for us.Andrea: And I guess you don’t have to worry about death.Exactly, and it (this belief) makes you want to live.Andrea: How so?Well, for the good of the Whole you want to enjoy and experience life as much as you can. And also learn from Karma.Andrea: Is all suffering karma then?No, not all. I think the only way we can control the 5% which is the actual matter and the elements too, which bring disaster (in our thinking) etc, is by collective learning. This learning has led us to manipulate our environment (and our lives). And we have learned by our mistakes and successes. We, the Whole, are not perfect or omniscient. Even though We are connected it does not stop people, microbes germs, elements etc from doing their separate thing, be it ‘wrong’ (by human standards) or just following their own nature. But of all the parts of the Whole, humans have had more influence/control over themselves and their own environment.Andrea: Now, how can I get this straight? I’ll try and quantify it in numbers.1. We are all part of, and therefore, the Whole. Less the 5% physical: blood, bone, fur, feather bodies, minerals, gases and inert matter. Which we are learning to control.2. There is no need for envy or fear of the future. No need for selfishness. We should look at everyone as the Whole.Before I go on, I should explain (although you would already know this) that not everyone knows they are part of the Whole. Andrea: But they still would be?Yes, but, like an arm that has gone to sleep because some of the circulation has been cut off, they are separate.Andrea: But you said..?The arm with the circulation partly cut off has the blood, life force, still circulating. The arm is joined to the body but it feels separate and is not good for the body.We can still acknowledge that it (those unaware) is part of us but we need to do something about it.Andrea: I see, make it/them aware.Yes, rub the circulation back (lol), support, understand. Or, in some cases, keep away. Okay, 3 - No need for fear of death. Or for us to say there is no god, when people/ animals die.Death is not the big deal we thought it was. Although, of course it is very sad for those still in the physical 5%. But for We that die (shed shells) it is a greater awareness. And We are still joined to those loved ones by Threadism.4. The god is WE (connected) with the Whole by Threadism.Light energy 70%, Light matter 25% and Outer shells (what is visible) 5%. Only the shells go back to stardust. 5. For the Whole there is no time but IS.We experience this life as we know it, for growth, interest and awe, for the good of the Whole. And to learn by our mistakes and triumphs, take notice of Karma and synchronicity, instinct and intuition. The Whole is evolving.6. We may feel separate but this is so we can get the maximum benefit of being a living being. Synchronicity and Karma, instinct and intuition, show we are still connected by Threadism. 7. Just like the numb arm we are still part of the Whole, even if we are not aware.8. In parting with the shell we become more aware, as we are awake to the greater Whole.Andrea: Mm… interesting concept. Do you think it will catch on?Well, if I’m right, others of Light Matter know this already.Andrea: And the Light Energy has always known.Precisely.NB - I think, We (95%) are as connected to the 5% as a musician is connected to a trumpet/ trombone etc. We blow breath (life) through it and the music we play is an extension and expression of ourselves. Top #35513 - 07/21/10 07:23 AM Re: The Concept of the Whole and Threadism Kyra M Member Registered: 06/25/09 Posts: 90 Kyra M Member Registered: 06/24/09 Posts: 58 The Concept of the Whole and Threadism ©Kyra K 2009 Andrea is discussing this with me.I don’t know, Andrea, maybe it’s not that different from what others have written.Probably not. So, when do you want to start?[Remember, you did ask me to help you.)Yes, I need someone to ask me questions and bounce back (with more questions to my answers). It’s all speculation you know.Everything is. Well, everything which addresses the meaning of life etc, is.Okay, here goes. Scientists are saying that 25% of the Universe is dark matter and 70% of the Universe is dark energy - that is a whopping 95% of everything being this ‘dark’ stuff which may, or may not, co-exist. It is through us, with us and I think it may be us.Hang on, am I supposed to argue with this now?Well, what do you think?It’s a bit simplistic isn’t it?I wish it was.Well, it’s no secret that you have Pantheist leanings. The Pantheists believe just what you have said, that everything is the Universe and the Universe is everything.Yes, but not that one part is matter-aware and the other part is energy-aware.Which is which?Look, I don’t know, but consider this hypothesis. We are matter aware and the other part of us, which exists with us, but also separate to us (seemingly) is energy aware. You say seemingly?Well everything is joined – just that some are not aware that it is. I think that’s why meditation works. When humans are able to let go of the physical for a few seconds, minutes, hours or even days as some monks can, we tap into the dark energy. We are not aware that we are aware?Well, we are, of course aware that we are here, but not all of us are aware that we are part of the Whole: dark energy and dark matter combined. And let’s stop calling it dark. Just because scientists can’t see it, it doesn’t make it dark. We have nothing to quantify its colour. I will call both forms ‘Light’ from now on. As in Light energy and Light matter.Yeah, I do agree with you about the dark inference, it makes it sound sinister. So what you are saying is that we are all part of the same thing, this Light energy and this Light matter stuff?Okay, consider this, the Light matter may be what is live. Everything that has life, as we know it, has awareness, even if they are not aware of having awareness. Light matter 25%. Then another 70% is Light energy which still has awareness because, I believe, it is connected. And the other 5% is all the physical matter: bodies, bone, fur, feather, mineral chemical and inert material.Yeah, we humans are aware of being aware. And some other animals may be aware of being aware, too.Yes, but I am talking about all life: insects, animals, germs, microbes, bacteria and all the botanicals being the 25% Light matter. But still connected to the 70% Light energy.I have thought of an analogy. As I said before, this is probably not original, but it is the closest I can get, to explaining myself.I’m listening.A flock of birds seem separate but to themselves they are not completely separate. They are connected to the lead bird and he/she to them. One entity, many parts. When flying formation this connection is obvious (they instantly move as one while they still have their own position and place) but it may be they have some sort of connection which is not so obvious at other times, too. So might all animals and insects and even plants. It could be species specific (this close awareness of the others). And we humans have this too, for example: when there is a short story competition or call for an anthology a lot of the entries/contributions will have the same theme. And it also explains other synchronicity. Let’s take this a step further, perhaps all life is connected (animals plants, microbes humans etc) and all death, as we know it, is connected as well.Death?After death of the outer shell (our separate state) we are awoken to the awareness (it has always been with us) of light energy. And this Light energy has far more consciousness than the consciousness we live through our physical selves. It may be like the flock of birds flying in formation all seeing through the same eyes and feeling though the same body of the flock. Like I said, I think we are connected to this Light energy in life even when we have the ‘shell’. So everything, both Light energy 70% and Light matter 25% is one at all times, or the Whole.That is some concept. What about the nitty gritty matter, the blood and bone, leaf and fur, so to speak?Mere packaging (and only a tiny 5% of all) and it is the way we (all living organisms) can abide in this environment.Oh, that’s what you mean by the ‘shell’. But just how are we ‘connected’?I think it may be through threads. Something similar perhaps, to radio waves (different frequencies and strengths) but the connection is like tissue (in a human body) we need it to be the ‘Whole.’ Let’s call this connection Threadism. Perhaps it is also part of what we used to call instinct and intuition.So now, whenever I look at someone else, I remember that their Light matter and Light energy is our/my Light matter and our/my Light energy. And when this body wears out I will still be, but with more awareness. The awareness of the Universe.The Universe or the Whole (except for the 5%) Yes, exactly. Not The Universe but We Universe.Yes, well, how did us/we Universe come about?Look, like I told M, I am just like a horse trying to explain/understand how a television works; what I have here is just a line (drawn with my hoof!) depicting the side of the screen. I certainly don’t have all the answers.Why do we need to come here as sentient, or living beings?Well, I think, for variety. Entertainment, stimulation, change, growth. (Andrea, don’t forget there are other life-filled planets). As The Whole we all benefit. We humans learn what benefits, or you could say what is right, by cause and effect, conscience and acknowledging Karma both good and bad. From this, we as humans have gained tolerance, understanding and compassion. Connection, passive or otherwise, strengthens or makes possible these learnings. Anyway, a lot of what we think is bad, is not - like dying for instance.Also, I think that not all of the 70% of us that is light energy (not physical) has to interchange with the physical, or the 25% Light matter, ever. For this bit of Us, perhaps the Us that lives in the Physical, are like our novels or short stories! Lol. What are the advantages of believing in this?Well, no envy - you can be truly happy for another when you know the other is you, (by Threadism) as well. No selfishness. No fear of the future. We learn that listening to our ‘Instinct or Intuition’ or the voice of the Whole, and seeing synchronicity for signs of Threadism as well, can help us live a more fulfilled life. And understanding that Karma is working for us.And I guess you don’t have to worry about death.Exactly, and it (this belief) makes you want to live.How so?Well, for the good of the Whole you want to enjoy and experience life as much as you can. And also learn from Karma.Is all suffering karma then?No, not all. I think the only way we can control the 5% which is the actual matter and the elements too, which bring disaster (in our thinking) etc, is by collective learning. This learning has led us to manipulate our environment (and our lives). And we have learned by our mistakes and successes. We, the Whole, are not perfect or omniscient. Even though We are connected it does not stop people, microbes germs, elements etc from doing their separate thing, be it ‘wrong’ (by human standards) or just following their own nature. But of all the parts of the Whole, humans have had more influence/control over themselves and their own environment.Now, how can I get this straight? I’ll try and quantify it in numbers.1. We are all part of, and therefore, the Whole. Less the 5% physical: blood, bone, fur, feather bodies, minerals, gases and inert matter. Which we are learning to control.2. There is no need for envy or fear of the future. No need for selfishness. We should look at everyone as the Whole.Before I go on, I should explain (although you would already know this) that not everyone knows they are part of the Whole. But they still would be?Yes, but, like an arm that has gone to sleep because some of the circulation has been cut off, they are separate.But you said..?The arm with the circulation partly cut off has the blood, life force, still circulating. The arm is joined to the body but it feels separate and is not good for the body.We can still acknowledge that it (those unaware) is part of us but we need to do something about it.I see, make it/them aware.Yes, rub the circulation back (lol), support, understand. Or, in some cases, keep away. Okay, 3 - No need for fear of death. Or for us to say there is no god, when people/ animals die.Death is not the big deal we thought it was. Although, of course it is very sad for those still in the physical 5%. But for We that die (shed shells) it is a greater awareness. And We are still joined to those loved ones by Threadism.4. The god is WE (connected) with the Whole by Threadism.Light energy 70%, Light matter 25% and Outer shells (what is visible) 5%. Only the shells go back to stardust. 5. For the Whole there is no time but IS.We experience this life as we know it, for growth, interest and awe, for the good of the Whole. And to learn by our mistakes and triumphs, take notice of Karma and synchronicity, instinct and intuition. The Whole is evolving.6. We may feel separate but this is so we can get the maximum benefit of being a living being. Synchronicity and Karma, instinct and intuition, show we are still connected by Threadism. 7. Just like the numb arm we are still part of the Whole, even if we are not aware.8. In parting with the shell we become more aware, as we are awake to the greater Whole.Mm… interesting concept. Do you think it will catch on?Well, if I’m right, others of Light Matter know this already.And the Light Energy has always known.Precisely.NB - I think, We (95%) are as connected to the 5% as a musician is connected to a trumpet/ trombone etc. We blow breath (life) through it and the music we play is an extension and expression of ourselves. Top #35523 - 07/21/10 10:19 PM Re: The Concept of the Whole and Threadism Revlgking Megastar Registered: 01/17/07 Posts: 2311 Loc: markham (Thornhill), Ontario, ... Quote:4. The god is WE (connected) with the Whole by Threadism.Light energy 70%, Light matter 25% and Outer shells (what is visible) 5%. Only the shells go back to stardust. Kyra, Good to see that this thread is back in action. GOD IS ALL BEING----000---- GOD--the all that is Good, Orderly and Desirable, including life--GOD is the who in you, Including all beings with personalities. GOD is the what in all things--Things with three dimensions,Which occupy space and time. GOD is the where in infinite space,Which we call infinity, and, GOD is Being itself--the whenIn the eternal now, which we call time. Finally, GOD is the whyIn all that has meaning and purpose. ==================================Me? without any dogma involved, as a unit of All Being with the power to will, I simply tune into, connect with, All Being, give good will--some call it love--and good things seem to happen.Hint: There is infinite space in cyberspace. Therefore, spread out your ideas. _________________________ G~O~D--Now & ForeverIS:Nature, Nurture & PNEUMA-ture, Thanks to Warren Farr&ME AT www.unitheist.org Top #35525 - 07/22/10 01:18 AM Re: The Concept of the Whole and Threadism kallog Megastar Registered: 03/17/10 Posts: 1100 Forgive me for not having a clue what you guys are on about, but what in the bageezus are you guys on about?!?! It might help to either define the terms or invent new words rather than confuse yourselves with overloaded, ambiguous, emotional ones. Top #35531 - 07/22/10 03:02 AM Re: The Concept of the Whole and Threadism Revlgking Megastar Registered: 01/17/07 Posts: 2311 Loc: markham (Thornhill), Ontario, ... Kallog, I just checked your profile. What the bageezus are you all about? Give us a clue. Us? We are all about what it means to be human and humane beings. When you are ready, come and join us. _________________________ G~O~D--Now & ForeverIS:Nature, Nurture & PNEUMA-ture, Thanks to Warren Farr&ME AT www.unitheist.org Top #35532 - 07/22/10 12:06 PM Re: The Concept of the Whole and Threadism kallog Megastar Registered: 03/17/10 Posts: 1100 What's dark energy got to do with being humane beings? Is it an analogy for something? Why not explain the idea directly? Top #35534 - 07/22/10 01:29 PM Re: The Concept of the Whole and Threadism Revlgking Megastar Registered: 01/17/07 Posts: 2311 Loc: markham (Thornhill), Ontario, ... Kallog, I assume you know how to do a search, eh? It took me less than a minute to find the references at the foot of this post.Like the GOD-concept, some is known about dark energy and the like, but much of it is still a mystery. By the way, in my reading I have noticed that, beginning with the first particle-physicists--great thinkers like, Max Planck, Maxwell, Thompson, Einstein and others, physicists started saying things about nature that were once only said by the theologians and the philosophers, who were thought insane by the "scientists" of their day. Theology/philosophy/psychology are all of great interest to me. Yes, it was once said of me, when I wrote articles in a Toronto paper about using hypnosis--which I now call pneumatherapy--to treat life-threatening diseases: "He is not just out on a limb, he is on a twig on the end of the limb". BTW, I always work in cooperation with medical science.===============Meanwhile, check out:http://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy/http://en.wikipedia.org/wiki/Dark_energy===========http://en.wikipedia.org/wiki/Particle_physics#Historyhttp://www.google.ca/search?q=Planck%2C+Thompson%2C+Maxwell%2C+physicists&ie=utf-8&oe=utf-8&aq=t&rls=com.mandriva:en-US:official&client=firefox-a Edited by Revlgking (07/22/10 01:40 PM)Edit Reason: Always a good idea! _________________________ G~O~D--Now & ForeverIS:Nature, Nurture & PNEUMA-ture, Thanks to Warren Farr&ME AT www.unitheist.org Top #35535 - 07/22/10 01:52 PM Re: The Concept of the Whole and Threadism Revlgking Megastar Registered: 01/17/07 Posts: 2311 Loc: markham (Thornhill), Ontario, ... TO THE ABOVE I ADD THE FOLLOWING NOTE:Physicists like Michio Kaku, Brian Swimme, Seth Lloyd and others have gone beyond particle physics and quantum mechanics. Talk now is about immeasurable energies which can be accessed and used by human thinkers, especially those who have artistic imaginations. Warning: Such energies can be used for good, or ill--to destroy, or to create. No wonder that Einstein said: "Imagination is more important than knowledge".====================http://www.rateitall.com/i-2211305-the-h...-schroeder.aspxhttp://www.abovetopsecret.com/forum/thread544356/pg1http://www.futurefoundation.org/documents/hum_pro_sem2.pdf Edited by Revlgking (07/22/10 02:18 PM)Edit Reason: Always a good idea! _________________________ G~O~D--Now & ForeverIS:Nature, Nurture & PNEUMA-ture, Thanks to Warren Farr&ME AT www.unitheist.org Top #35539 - 07/23/10 02:37 AM Re: The Concept of the Whole and Threadism kallog Megastar Registered: 03/17/10 Posts: 1100 Originally Posted By: RevlgkingIt took me less than a minute to find the references at the foot of this post.I didn't ask what dark energy is. Those links don't explain the connection between dark energy and being humane beings. Top #35540 - 07/23/10 02:41 AM Re: The Concept of the Whole and Threadism kallog Megastar Registered: 03/17/10 Posts: 1100 Originally Posted By: RevlgkingPhysicists like Michio Kaku, Brian Swimme, Seth Lloyd and others have gone beyond particle physics and quantum mechanics. Talk now is about immeasurable energies which can be accessed and used by human thinkers, especiallySo those aren't dark energy because dark energy is measurable. I joined this thread to understand what it was about. Can you explain any of the ideas without the use of analogies or name-dropping? Those links don't seem to have an relevance - one wants me to buy a book, another is people talking about whether scientists are atheists or not. Is that what "threadism" is? The religious beliefs of scientists? Edited by kallog (07/23/10 02:56 AM) Top #35542 - 07/23/10 09:10 PM Re: The Concept of the Whole and Threadism Revlgking Megastar Registered: 01/17/07 Posts: 2311 Loc: markham (Thornhill), Ontario, ... ABOUT DARK MATTER & DARK ENERGY===============================I just found the article, below, in http://nedwww.ipac.caltech.edu ...The article is about1. THE PREPOSTEROUS UNIVERSE (Title as given)[Do scientists expect us laity to believe that what is going on in the universe is contrary to nature, reason, or commonsense; absurd; senseless? Ridiculous? Laughable? Sounds very human (and theological?) to me. ] I am not making the following up: "Surprising experimental results are the most common driving force behind significant advances in scientific understanding. The recent discovery that the universe appears to be dominated by a component of "dark energy" qualifies as an extraordinarily surprising result; we have every reason to be optimistic that attempts to understand this phenomenon will lead to profound improvements in our pictures of gravitation, particle physics, and gravitation."I repeat, the above sounds very metaphysical, and even theological. And there is more:"1.1. Dark energyIn general relativity, a homogeneous and isotropic universe is characterized by two quantities, the spatial curvature kappa and scale factor a(t). These are related to the energy density$ \rho\$ by the Friedmann equation:" ... The equation cannot be reproduced here. It is in the article ...================================== Below, I give the link to the full article, from which I give the following brief quote with a very interesting question: Quote:2. WHAT MIGHT BE GOING ON?It may seem misguided to put a great deal of energy into exploring models of a small nonzero dark energy density when we have very little idea why the vacuum energy is not as large as the Planck scale. On the other hand, the discovery of dark energy may provide an invaluable clue in our attempts to solve this long-lasting puzzle, giving us reason to redouble our efforts. Explanations of the current acceleration of the universe can be categorized into one of three types: 1. The dark energy is a true cosmological constant, strictly unchanging throughout space and time. The minimum-energy configuration of the universe may have a small but nonvanishing energy density, or we may live in a false vacuum, almost degenerate with the true one but with a small nonzero additional energy. 2. The cosmological constant is zero, but a slowly-varying dynamical component is mimicking a nonzero vacuum energy. 3. Einstein was wrong, and the Friedmann equation does not describe the expansion of the universe. We briefly examine each of these possibilities in turn.2.1. An honest cosmological constantThe simplest interpretation of the dark energy is that we have discovered that the cosmological constant is not quite zero: we are in the lowest energy state possible (or, more properly, that the particles we observe are excitations of such a state) but that energy does not vanish. Although simple, this scenario is perhaps the hardest to analyze without an understanding of the complete cosmological constant problem, and there is correspondingly little to say about such a possibility. As targets to shoot for, various numerological coincidences have been pointed out, which may some day find homes as predictions of an actual theory. For example, the observed vacuum energy scale Mvac = 10-3 eV is related to the 1 TeV scale of low-energy supersymmetry breaking models by a "supergravity suppression factor":Equation 8 (8)In other words, MSUSY is the geometric mean of Mvac and MPlanck. Unfortunately, nobody knows why this should be the case. In a similar spirit, the vacuum energy density is related to the Planck energy density by the kind of suppression factor familiar from instanton calculations in gauge theories:Equation 9 ... http://nedwww.ipac.caltech.edu/level5/March01/Carroll/Carroll2.htmlIs it possible for someone trained in physics to put this information in journalese so that we lay readers with an interest in science, but are not all that familiar with the jargon of physics, could possibly understand. Edited by Revlgking (07/23/10 09:37 PM)Edit Reason: Always helpful! _________________________ G~O~D--Now & ForeverIS:Nature, Nurture & PNEUMA-ture, Thanks to Warren Farr&ME AT www.unitheist.org Top
#35543 - 07/23/10 09:54 PM Re: The Concept of the Whole and Threadism Revlgking Megastar Registered: 01/17/07 Posts: 2311 Loc: markham (Thornhill), Ontario, ... THE RELIGION OF MAX PLANCK==========================Quote:Max Planck: "Max Karl Ernst Ludwig Planck was born on April 23, 1858, in Kiel, Germany, the sixth child of a distinguished jurist and professor of law at the University of Kiel. The long family tradition of devotion to church and state, excellence in scholarship, incorruptibility, conservatism, idealism, reliability, and generosity became deeply ingrained in Planck's own life and work... In his later years, Planck devoted more and more of his writings to philosophical, aesthetic, and religious questions. Together with Einstein and Schrödinger, he remained adamantly opposed to the indeterministic, statistical worldview introduced by Bohr, Max Born, Werner Heisenberg, and others into physics after the advent of quantum mechanics in 1925-26. Such a view was not in harmony with Planck's deepest intuitions and beliefs. The physical universe, Planck argued, is an objective entity existing independently of man; the observer and the observed are not intimately coupled, as Bohr and his school would have it." [Source: http://astro.estec.esa.nl/SA-general/Projects/Planck/mplanck/mplanck.html].From: Rich Deem, "Famous Scientists Who Believed in God", last modified 19 May 2005, on "Evidence for God from Science" website (http://www.godandscience.org/apologetics/sciencefaith.html; viewed 5 October 2005):Planck made many contributions to physics, but is best known for quantum theory, which has revolutionized our understanding of the atomic and sub-atomic worlds. In his 1937 lecture "Religion and Naturwissenschaft," Planck expressed the view that God is everywhere present, and held that "the holiness of the unintelligible Godhead is conveyed by the holiness of symbols." Atheists, he thought, attach too much importance to what are merely symbols. Planck was a churchwarden from 1920 until his death, and believed in an almighty, all-knowing, beneficent God (though not necessarily a personal one). [I suspect that he would agree: GOD is Being, not A being.]Both science and religion wage a "tireless battle against skepticism and dogmatism, against unbelief and superstition" with the goal "toward God!"[Source:] J. L. Heillron, Dilemmas of an Upright Man (1986) http://www.adherents.com/people/pp/Max_Planck.html[b][/b] Edited by Revlgking (07/23/10 09:58 PM)Edit Reason: Always helpful! _________________________ G~O~D--Now & ForeverIS:Nature, Nurture & PNEUMA-ture, Thanks to Warren Farr&ME AT www.unitheist.org Top
#35544 - 07/24/10 03:37 AM Re: The Concept of the Whole and Threadism kallog Megastar Registered: 03/17/10 Posts: 1100 Originally Posted By: Revlgking[Do scientists expect us laity to believe that what is going on in the universe is contrary to nature, reason, or commonsense; absurd; senseless? Ridiculous? Laughable? Sounds very human (and theological?) to me. ] Contrary to nature - noContrary to reason - noContrary to commonsense - yesAbsurd - noSenseless - yesRidiculous - noLaughable - noPeople who don't think critically often mix up these terms. Just because one person doesn't understand something doesn't mean it's absurd. Commonsense is handy for common situations but there's no reason we should expect it to be relevant to things we have no experience with.Quote:I repeat, the above sounds very metaphysical, and even theological. And there is more:Nothing metaphysical, theological or humane in there at all. If you replace the term "dark energy" with "hydrogen rich gas" does it still give you those emotions? Top
#35545 - 07/24/10 03:42 AM Re: The Concept of the Whole and Threadism kallog Megastar Registered: 03/17/10 Posts: 1100 Originally Posted By: RevlgkingTHE RELIGION OF MAX PLANCKYou're coming back to religious beliefs of scientists. Is this an important aspect of 'whole and threadism'? That and dark energy. Is that what it is? Just two unrelated concepts being described by a single name? Top | 2017-04-25 18:27:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4252770245075226, "perplexity": 3480.677234982381}, "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-2017-17/segments/1492917120844.10/warc/CC-MAIN-20170423031200-00387-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/2165809/calculus-integral-on-riemann-surface-stokes-theorem | # Calculus integral on Riemann Surface (Stokes' theorem)
So I thought a bit about the solution and would like some help on what I did:
Following the hint,
$\int_{\partial \Omega} i \space \partial\Phi =\int_{\partial\Omega} <grad \space\Phi,v>$.
Therefore, by Stokes' Theorem,
$\int_{\partial\Omega} <grad \space\Phi,v>= \int_\Omega div\space(\Phi_x,\Phi_y,\Phi_z)$.
Now I need to use that $\Phi$ is a real-valued function which is positive on and vanishes on the boundary of $\Omega$ to justify that $\int_\Omega div\space(\Phi_x,\Phi_y,\Phi_z)\ge 0$. And that would solve the problem. So if anyone can help me put the pieces together, I appreciate it.
• The divergence theorem (as you're writing it) applies only to surfaces that bound regions in $\Bbb R^3$. In the case of a 2-dimensional region, you get the double integral of the Laplacian of $\Phi$. But this won't help ... – Ted Shifrin Mar 1 '17 at 0:09
There's no Stokes's Theorem involved in this. For one thing, you don't know anything about the Laplacian of $\Phi$ on the interior of $\Omega$. However, if you write everything out carefully in $\Bbb C$, you have \begin{align*} i\partial\Phi &= \frac i2\big(\frac{\partial\Phi}{\partial x}-i\frac{\partial\Phi}{\partial y}\big)\big(dx+i\,dy\big) \\ &= \frac12\left(i\big(\frac{\partial\Phi}{\partial x}\,dx + \frac{\partial\Phi}{\partial y}\,dy\big) - \big(\frac{\partial\Phi}{\partial x}dy - \frac{\partial\Phi}{\partial y}\,dx\big)\right) = \tfrac12\big(i\,d\Phi - \star(d\Phi)\big). \end{align*} The integral of the first term around the closed curve $\partial\Omega$ is $0$. The integral of the second term is the negative of the flux of $\text{grad}\,\Phi$ across $\partial\Omega$. Since $\Phi$ is positive on $\Omega$ and zero on $\partial\Omega$, $\text{grad}\,\Phi$ points inward everywhere (or is zero). Thus, the flux is negative, and we have our answer. (This can be extended to a Riemann surface by working with local (holomorphic) parametrizations. The geometry of the flux works out just fine.) | 2019-09-20 11:40:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9958935379981995, "perplexity": 265.50153776486735}, "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-2019-39/segments/1568514574018.53/warc/CC-MAIN-20190920113425-20190920135425-00080.warc.gz"} |
https://www.physicsforums.com/threads/where-to-start-with-this-problem.717843/ | 1. Oct 20, 2013
### jimmyboykun
1. The problem statement, all variables and given/known data
You are pushing a 150-kg wooden crate in a straight line a distance of 4.5 m across a wooden floor at constant speed. The static and kinetic coefficients of friction are 0.42 and 0.30, respectively. What is the work done by you on the crate? and What is the work done by friction on the crate?
I understand that with constant speed meas that my acceleration is zero, but after that I am lost.
2. Relevant equations
3. The attempt at a solution
2. Oct 20, 2013
### NihalSh
3. Oct 21, 2013
### jimmyboykun
ok here's what I did work is W=F*s.
I multiply 0.30(kinetic energy) because the crate is in motion by 150kg by 9.81m/s^2 which gave me 441.45N as my frictional force. Now I have my force I will multiply it by my displacement to give me my work.
441.45N*4.5m= 1986.525J.
I did it and submitted the answer and received a 1/10 from this problem. What did I do wrong?
4. Oct 22, 2013
### NihalSh
Your solution seems fine for "work done by you". "work done by friction" would be negative of the calculated value. Also note that your answer should have only two significant figures. That means answer should have been $2.0~kJ$. This could be the reason you were marked down. | 2017-10-18 00:57:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46349966526031494, "perplexity": 819.2371762934271}, "config": {"markdown_headings": true, "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-2017-43/segments/1508187822625.57/warc/CC-MAIN-20171017234801-20171018014801-00415.warc.gz"} |
https://math.stackexchange.com/questions/2361928/maximizing-int-limits-11x3fxdx-where-f-satisfies-some-properties | # Maximizing $\int\limits_{-1}^1x^3f(x)~dx$ where $f$ satisfies some properties
Find the maximum of $\int\limits_{-1}^1x^3f(x)~dx$ for real-valued measurable functions $f(x)$ satisfying $$\int\limits_{-1}^1 |f(x)|^2~dx=1$$ $$\int\limits_{-1}^1f(x)~dx=\int\limits_{-1}^1 x f(x)~dx=\int\limits_{-1}^1 x^2 f(x)~dx=0.$$
My guess is to use Lusin's theorem and Stone-Weierstrass theorem, but then I do not know how to maximize the integral over all polynomials satisfying these conditions. I may have overlooked the properties of some orthogonal polynomials.
• Study simple functions satisfying the conditions. – md2perpe Jul 17 '17 at 19:59
Legendre polynomials given an orthogonal base of $L^2(-1,1)$ with respect to the standard inner product. Assuming $$f(x)\stackrel{L^2}{=}\sum_{n\geq 0}c_n P_n(x) \tag{1}$$ the given constraints can be written as $$c_0=c_1=c_2=0,\qquad \sum_{n\geq 0}\frac{2c_n^2}{2n+1}=1 \tag{2}$$ hence the solution is given by a multiple of $P_3(x)=\frac{1}{2}\left(5x^3-3x\right)$, namely $\pm\sqrt{\frac{7}{2}}\,P_3(x)$.
Using Lagrange multipliers, let $$F(f, \lambda_0, \lambda_1, \lambda_2, \mu) = \int_{-1}^{1} f(x) (x^3 + \mu f(x) + \lambda_0 + \lambda_1 x + \lambda_2 x^2) \; dx$$ Then by taking the variation with respect to $f(x)$, we should have $$x^3 + 2 \mu f(x) + \lambda_0 + \lambda_1 x + \lambda_2 x^2 = 0$$ i.e. $f(x)$ is a cubic polynomial that satisfies the constraints.
That polynomial turns out to be $\pm \frac{\sqrt{14}}{4} (5 x^3 - 3 x)$. For a maximum, you want the $\pm$ to be $-$. | 2020-03-29 10:15:31 | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9833891987800598, "perplexity": 84.0519040905828}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2020-16/segments/1585370494064.21/warc/CC-MAIN-20200329074745-20200329104745-00015.warc.gz"} |
https://hjzh4.github.io/publication/iser2018/ | # Scaling simulation-to-real transfer by learning composable robot skills
### Abstract
We present a novel solution to the problem of simulation-to-real transfer, which builds on recent advances in robot skill decomposition.
Rather than focusing on minimizing the simulation-reality gap, we learn a set of diverse policies that are parameterized in a way that makes them easily reusable. This diversity and parameterization of low-level skills allows us to find a transferable policy that is able to use combinations and variations of different skills to solve more complex, high-level tasks.
In particular, we first use simulation to jointly learn a policy for a set of low-level skills, and a skill embedding” parameterization which can be used to compose them. Later, we learn high-level policies which actuate the low-level policies via this skill embedding parameterization. The high-level policies encode how and when to reuse the low-level skills together to achieve specific high-level tasks.
Importantly, our method learns to control a real robot in joint-space to achieve these high-level tasks with little or no on-robot time, despite the fact that the low-level policies may not be perfectly transferable from simulation to real, and that the low-level skills were not trained on any examples of high-level tasks.
We illustrate the principles of our method using informative simulation experiments. We then verify its usefulness for real robotics problems by learning, transferring, and composing free-space and contact motion skills on a Sawyer robot using only joint-space control. We experiment with several techniques for composing pre-learned skills, and find that our method allows us to use both learning-based approaches and efficient search-based planning to achieve high-level tasks using only pre-learned skills.
Type
Publication
In 2018 International Symposium on Experimental Robotics. | 2019-06-26 04:49:17 | {"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": 0, "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": 0.30772703886032104, "perplexity": 2095.7397659054122}, "config": {"markdown_headings": true, "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-2019-26/segments/1560628000164.31/warc/CC-MAIN-20190626033520-20190626055520-00520.warc.gz"} |
https://www.freemathhelp.com/forum/threads/solve-0-8x-48.64226/ | Solve: -0.8x<-48
Solve:
-0.8x , -48
wjm11
Senior Member
Solve:
-0.8x < -48
You want to get x by itself. Right now, x is being multiplied by -.8, so you need to divide both sides of the equation by -.8.
Remember, when you multiply or divide an inequality by a negative number, you must reverse the sign of the inequality. | 2019-02-23 10:46:18 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8767265677452087, "perplexity": 342.46140066295595}, "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-2019-09/segments/1550249500704.80/warc/CC-MAIN-20190223102155-20190223124155-00307.warc.gz"} |
https://calculator.academy/vector-magnitude-calculator/ | Enter the x, y, and z coordinates of any vector to calculate the magnitude of that vector. Enter z as 0 if calculate the magnitude of a vector in only the x and y plane.
## Unit Vector Magnitude Formula
The following formula is used to calculate the vector magnitude in a 3-dimensional space.
|u| = √(x₁² + y₁² + z₁²)
The following formula is used to calculate the vector magnitude in a 2-dimensional space.
|u| = √(x₁² + y₁²)
## Vector Magnitude Definition
A vector magnitude is defined as the total distance from the origin to the endpoint of the vector.
Calculating the vector magnitude in Euclidean space (the geometric space) is done through the use of trigonometry. You might be thinking to yourself, what does a triangle have to do with vectors? Well, a vector is actually a hypotenuse of a triangle with a base of x and a height of Y. Therefore, the magnitude of the vector can then be calculated just like the hypotenuse of a triangle.
## Vector Magnitudes in 3-Dimensional Space
Now we know the magnitude of a vector can be calculated through the trigonometric function for calculating the hypotenuse of a triangle, but most vectors have points in the x, y, and z planes. If you take a look at the picture above, you can see how a third dimension is brought into play when talking about vectors.
Luckily, because of the fundamentals of geometry, adding in a third dimension does not overly complicate the formula for calculating a magnitude. Since the formula for the magnitude of a 2-D vector is equal to the square root of the sum of the squares of the x and y coordinates, the formula for a 3-D vector is almost the same. It’s the square root of the sum of the squares of the x, y, and z coordinate.
## How to calculate vector magnitude
Now that we understand the formulas for calculating the vector magnitude, we can go over some examples of how to use them. First, let’s look at a 2-dimensional vector.
• Let’s assume we have a vector with the following coordinates, (45, 27)
• Now plug them into the formula as follows |u| = √(45² + 27²)
• Use a calculator and solve. This should yield 25.478…
• Finally, compare using the calculator above.
Next, we will go over an example of a 3 dimensional vector.
• Let’s assume we have a vector with coordinates (24,32,31)
• Plug them into the formula as follows, |u| = √(24² + 32² + 31²)
• Use a calculator and solve. This should yield 53.130…
• Finally, compare using the calculator above
As you can see, the process for calculating the magnitude of a vector is very easy. It’s a simple plug and calculate. For more related calculators click here. | 2021-10-22 23:32:16 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8762937188148499, "perplexity": 235.919703869281}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "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-2021-43/segments/1634323585522.78/warc/CC-MAIN-20211022212051-20211023002051-00629.warc.gz"} |
https://www.physicsforums.com/threads/lagrange-multipliers.70674/ | # Lagrange Multipliers
1. Apr 9, 2005
### PhysicsMajor
Greetings all,
Find the max and min values of
f(x,y.z)=3x-y-3z
subject to
x+y-z=0, x^(2)+2z^(2)=1
can anybody help me get this problem started.
thanks
2. Apr 9, 2005
### Oggy
Just write the Lagrange function of the problem:
$$F(x,y,z)=3x-y-3z+\lambda_1(x+y-z)+\lambda_2(x^{2}+2z^{2}-1)$$
Then find the partial derivatives (they have to be 0), and solve the system of equasions.
3. Apr 9, 2005
### dextercioby
You'll find the critical points,though...You can't be sure which is a mex & which is a min...
Daniel.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook | 2017-05-25 07:26:53 | {"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": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32147806882858276, "perplexity": 7102.195634873207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608004.38/warc/CC-MAIN-20170525063740-20170525083740-00213.warc.gz"} |
http://www.real-statistics.com/multivariate-statistics/multivariate-normal-distribution/confidence-hyper-ellipse-eigenvalues/ | # Confidence Hyper-ellipse and Eigenvalues
As we noted in Multivariate Normal Distribution Basic Concepts, the 1 – α hyper-ellipse plays a similar role to the confidence interval in univariate statistics. We now describe some additional characteristics of these hyper-ellipses, and in particular, their relationship with eigenvalues.
Observation: The axes of the ellipse have lengths which are a function of the eigenvalues of the Σ. Also each axis is in the direction of the eigenvector corresponding to one of the eigenvalues.
Figure 1 – Confidence ellipse
The half length of the axis corresponding to eigenvalue λ is given by the formula
where $\chi^2_{crit}$ is the critical value for χ2(k).
All these properties extend to the case where k > 2. In this case we speak of hyper-ellipses (or ellipsoids) instead of ellipses.
Observation: The volume of the hyper-ellipse (or area in the case where k = 2) is given by the function
Note too that by Property 1 of Eigenvalues and Eigenvectors, |Σ| = product of the eigenvalues of Σ.
Example 1: Calculate the eigenvalues and eigenvectors of the sample covariance matrix for Example 1 of Descriptive Multivariate Statistics.
Figure 2 – Eigenvalues and eigenvectors for Example 1
Using the supplemental array function eVECTORS(H5:L9) we can generate the output displayed in Figure 2. Alternatively, we can get the same result by using the supplemental Matrix data analysis tool (as described in ), and choosing the Eigenvalue/eigenvector option. The top row of Figure 2 lists the 5 eigenvalues. Below each eigenvalue is a corresponding unit eigenvector.
As noted above, the half-lengths of the axes corresponding to the eigenvalues are
where $\chi^2_{crit}$ is the critical value for χ2(5).
Using the sample covariance matrix as an approximation for the population covariance matrix and the eigenvalues obtained in Figure 2, the lengths of these axes are:
Figure 3 – Axes lengths for Example 1
The volume of the 95% confidence ellipse is 24,842,086 calculated as follows:
Figure 4 – Volume of 95% confidence ellipse for Example 1
Note that |S| (cell A12) can also be calculated as the product of the five eigenvalues.
### 7 Responses to Confidence Hyper-ellipse and Eigenvalues
1. Manu says:
Hi Charles,
Have you a reference for the function that compute the volume of the hyper-ellipse?
Thank you.
2. Mattucci says:
Thank you Charles for these information. In this case what will be the equation of the hyper-ellipses if I wanted to code it in VBA or Fortran?
• Charles says:
To code the equation in Fortran or VBA requires the following:
1. Calculate the eigenvalues. This is the hard part, although a description of how to do this is described elsewhere on the Real Statistics website
2. Use the formula under Figure 1 of the referenced webpage for the length of the axes of the hyper-ellipse (based on the eigenvalues)
3. Plus these values into the equation for a hyper-ellipse. The equation for a hyper-ellipse (the equation for an ellipse can be found in any elementary calculus book; the equation for a hyper-ellipse i ssimply the generalization of this equation to more than 2 dimensions).
Charles
• Mattucci says:
Thank you Charles for these explanations.
3. Bandar says:
Is this sentence “The axes of the ellipse have lengths which are a function of the eigenvalues” also true for the ellipsoid? Thank you
• Charles says:
Yes. | 2017-03-29 07:20:00 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "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": 0.8501970171928406, "perplexity": 643.7914737520489}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2017-13/segments/1490218190234.0/warc/CC-MAIN-20170322212950-00364-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://www.emathzone.com/tutorials/basic-statistics/some-basic-definitions-in-statistics.html | # Some Basic Definitions in Statistics
Constant:
A quantity which can be assuming only one value is called a constant. It is usually denoted by the first letters of alphabets $a,b,c$.
For Example: Value of $\pi = \frac{{22}}{7} = 3.14159...$ and value of $e = 2.71828...$.
Variable:
A quantity which can vary from one individual or object to and other is called a variable. It is usually denoted by the last letters of alphabets $x,y,z$.
For Example: Heights and Weights of students, Income, Temperature, No. of Children in a family etc…
Continuous Variable:
A variable which can assume each and every value within a given range is called a continuous variable. It can occur in decimals.
For Example: Heights and Weights of students, Speed of a bus, the age of a Shopkeeper, the life time of a T.V etc…
Continuous Data:
Data which can be described by a continuous variable is called continuous data.
For Example: Weights of 50 students in a class.
Discrete Variable:
A variable which can assume only some specific values within a given range is called discrete variable. It cannot occur in decimals. It can occur in whole numbers.
For Example: Number of students in a class, number of flowers on the tree, number of houses in a street, number of chairs in a room etc…
Discrete Data:
Data which can be described by a discrete variable is called discrete data.
For Example: Number of students in a college.
Quantitative Variable:
A characteristic which varies only in magnitude from on individual to another is called quantitative variable. It can be measurable.
For Example: Wages, Prices, Heights, Weights etc…
Qualitative Variable:
A characteristic which varies only in quality from one individual to another is called qualitative variable. It cannot be measured.
For Example: Beauty, Marital Status, Rich, Poor, Smell etc… | 2017-10-23 02:26:35 | {"extraction_info": {"found_math": true, "script_math_tex": 4, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 4, "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": 0.6441486477851868, "perplexity": 908.5938137862752}, "config": {"markdown_headings": true, "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-2017-43/segments/1508187825510.59/warc/CC-MAIN-20171023020721-20171023040721-00131.warc.gz"} |
http://mathhelpforum.com/trigonometry/46541-funny-trigonometric-equation.html | # Thread: funny trigonometric equation
1. ## funny trigonometric equation
This equation looks simple enough to solve, but I'm having real difficulty doing it. It is:
tanx + x == 0;
Does anyone have any bright ideas about how to proceed in solving it?
Thanks beforehand guys.
2. Originally Posted by tombrownington
This equation looks simple enough to solve, but I'm having real difficulty doing it. It is:
tanx + x == 0;
Does anyone have any bright ideas about how to proceed in solving it?
Thanks beforehand guys.
There's no way that we can find an exact answer for this equation.
However, we can approximate the value of x.
If you know calculus, you can use the Newton-Raphson Method : $\displaystyle x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$
Alternatively, you can also use a calculator to approximate the solution(s)
I''m sure there are other approximation methods, but I can't think of them at the moment.
I hope this helps.
--Chris
3. Originally Posted by tombrownington
This equation looks simple enough to solve, but I'm having real difficulty doing it. It is:
tanx + x == 0;
Does anyone have any bright ideas about how to proceed in solving it?
Thanks beforehand guys.
x = 0 is a solution of course .... | 2018-03-24 16:40:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6097244024276733, "perplexity": 551.8748109470039}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2018-13/segments/1521257650730.61/warc/CC-MAIN-20180324151847-20180324171847-00249.warc.gz"} |
http://blog.jverkamp.com/2013/06/29/a-programming-puzzle-ffn-n/ | # A programming puzzle: f(f(n)) = -n
Two Programming Praxis puzzles in a week? Madness! Let’s do it!
This time, the puzzle at first seems rather minimal:
Write a function f so that f(f(n)) = -n for all integers n.
If you haven’t seen this problem before, take a moment to think though it. It’s a neat little problem–a close cousin to a lateral thinking puzzle.
Okay, time’s up. After a bit of thinking, I ended up with basically four ways of solving the puzzle.
The first idea is to realize that the function didn’t necessarily specify that `f` only be defined for integers, just that all integers must be negated after two applications. So what sort of mathematical object gives a negative after two applications? Imaginary numbers!
Essentially, we use the fact that $i^2 = -1$ where $i = sqrt(-1)$. So if we multiply by $i$ once, we get $ni$; twice gives us $ni^2 = -n$. Perfect:
```; Rotate in the complex numbers (define (f1 n) (* n 0+1i))```
That seems a little unfair though, using complex numbers. Can we do it with only integers?
Of course we can!
To do this, we need to realize that positive/negative is only one axis that splits up the integers. In addition, we could use something like even/odd. This way, we can convert from one to the other (and then back), only applying the negation once.
Specifically, we’ll move all even numbers closer from zero. Any odd numbers, we’ll negate then move away from zero. That means we’ll only negate once:
```; Only negate odd numbers, offset by +- 1 (define (f2 n) (define e? (even? n)) (define p? (positive? n)) (define n? (negative? n)) (cond [(and e? n?) (+ n 1)] [(and e? p?) (- n 1)] [n? (+ (- n) 1)] [p? (- (- n) 1)] [else 0]))```
Alternatively, we could get really tricksy and mess with the range/domain of `f` even more (just like the complex numbers). For example, we could cast to a string and back, only negating on the way back:
```; Wrap as a string, negate on conversion back (define (f3 n) (cond [(string? n) (- (string->number n))] [else (number->string n)]))```
Finally, we can take advantage of the fact that the function will be applied in pairs. So we can add a bit of state to the function. In this example, we create a toggle which is switched on each application of the function. Then, if and only if the toggle is false will we negate the value:
```; Use a state variable (define f4 (let ([toggle (make-parameter #t)]) (lambda (n) (toggle (not (toggle))) (if (toggle) n (- n)))))```
So, do all of these methods work? Well, you could just take my word for it, or you could run some testing. All we care about is double application of integers (single applications and non-integers can return anything), so we’ll try to cover the general cases:
```(module+ test (require rackunit) (for ([f (in-list (list f1 f2 f3 f4))]) ; Positive integers (for ([i (in-range 10)]) (define n (random 100)) (check-equal? (f (f n)) (- n) (format "~s(~s(~s))" f f n))) ; Negative integers (for ([i (in-range 10)]) (define n (- (random 100))) (check-equal? (f (f n)) (- n) (format "~s(~s(~s))" f f n))) ; Zero and +- 1 (for ([n (in-list '(-1 0 1))]) (check-equal? (f (f n)) (- n) (format "~s(~s(0))" f f)))))```
Running this, all is good. Theoretically, we could have missed an edge case, but the functions are simple enough that this seems unlikely.
If you’d like to check out the full code, you can do so here:
- double negative source on GitHub | 2014-03-09 21:18:23 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 5, "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": 0.7905830144882202, "perplexity": 517.8445658373712}, "config": {"markdown_headings": true, "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-2014-10/segments/1394010354479/warc/CC-MAIN-20140305090554-00088-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://www.mzan.com/article/47691486-replacing-string-values-in-cell-array-with-numbers.shtml | Home Replacing string values in cell array with numbers
Replacing string values in cell array with numbers
mHelpMe
1#
mHelpMe Published in 2017-12-07 09:16:16Z
I have a cell array which contains some descriptions, namely my_des. my_des = [{'FRD'} {'1'}; {'UNFRD'} {'2'}; {'OTH'} {'3'};]; I also have an approximately 5000x1 cell array. The elements in this array are either 'FRD', 'UNFRD' or 'OTH'. What I want to do is replace these text values with the corresponding numeric values in my_des. Currently my only idea (which I think isn't that great) is to loop through my_des and do a string replacement. Example: So say my current vector looks like this: FRD FRD OTH UNFRD OTH FRD Then my desired output would be this: 1 1 3 2 3 1 The numbers come from the my_des array
Wolfie
2#
Wolfie Reply to 2017-12-07 09:41:32Z
Do you want to use the characters '1', '2', '3' or just the numbers 1, 2, 3? The distinction is the difference between a 1 line answer and a 2 line answer! Based on your example, let's use the following data: arr = {'FRD'; 'FRD'; 'OTH'; 'UNFRD'; 'OTH'; 'FRD'}; Get the row index within my_des of each element in arr, and use that to get the corresponding 2nd column values... % If you just want the *number* then this is all you need [~, idx] = ismember(arr, my_des); % idx is the row within column 1 of my_des where the value in arr is found % >> idx = [1; 1; 3; 2; 3; 1] % If you want to get the values my_des then use idx as a row index out = mydes(idx, 2); % out is the corresponding values from the 2nd column of my_des, whatever they may be. % >> out = {'1'; '1'; '3'; '2'; '3'; '1'}; Aside: why are you declaring a cell array by concatenating 1-element cell arrays for my_des? Instead, you can just do this: my_des = {'FRD', '1'; 'UNFRD', '2'; 'OTH', '3'};
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Processed in 0.356499 second(s) , Gzip On . | 2018-01-22 16:11:57 | {"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": 0, "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": 0.6393411159515381, "perplexity": 3634.7333492746293}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2018-05/segments/1516084891485.97/warc/CC-MAIN-20180122153557-20180122173557-00264.warc.gz"} |
https://www.projectrhea.org/rhea/index.php?title=Practice_CTFT_computation_rect_and_sinc_ECE438F11&oldid=46922 | Continuous-time Fourier transform computation (in terms of frequency f in hertz)
Compute the Continuous-time Fourier transform of the two following functions:
$x(t)= \text{rect}(t) = \left\{ \begin{array}{ll} 1, & \text{ if } |t|<\frac{1}{2}\\ 0, & \text{ else} \end{array} \right.$
$y(t)= \frac{ \sin ( \pi t )}{\pi t}$
Justify your answer.
Share your answers below
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
Fourier Transform of rect(t):
$X(f)=\int_{-\infty}^{\infty} x(t)e^{-j2\pi ft} dx =\int_{\frac{-1}{2}}^{\frac{1}{2}} e^{-j2\pi ft} dx =\frac{e^{-j2\pi ft}}{-j2\pi f}$ from t=-1/2 to t=1/2
$=\frac{e^{-j\pi f}-e^{j\pi f}}{-j2\pi f} =\frac{sin(\pi f)}{\pi f}$
Instructor's comments: Technically, you should look at the case f=0 separately, because your solution involves a division by f. -pm
Fourier Transform of $\frac{sin(\pi t)}{\pi t}$:
Guess: $X(f)=rect(t)$
Proof:
$x(t)=\int_{-\infty}^{\infty} X(f)e^{j2\pi ft} df =\int_{\frac{-1}{2}}^{\frac{1}{2}} e^{j2\pi ft} df =\frac{e^{j2\pi ft}}{j2\pi t}$ from f=-1/2 to f=1/2
$=\frac{e^{j\pi t}-e^{j\pi t}}{j2\pi t} =\frac{sin(\pi t)}{\pi t}$
Instructor's comments: Guessing the answer and proving it using the inverse Fourier transform is a good trick. One could also obtain this Fourier transform using the duality property and your previous answer. -pm
Answer 2
$X(f)=\int_{-\infty}^{\infty} x(t)e^{-j2\pi ft} dt =\int_{-\infty}^{\infty} rect(t)e^{-j2\pi ft} dt =\int_{-\frac{1}{2}}^{\frac{1}{2}} e^{-j2\pi ft} dt$
$= -\frac{e^{-j2\pi ft}}{-j2\pi f}$ integrating from -0.5 to +0.5. $= \frac{e^{-j\pi f} - e^{j\pi f}}{-j2\pi f} = \frac{sin(\pi f)}{\pi f}$
For y(t), we know that
$y(t) = \int_{-\infty}^{\infty} Y(f)e^{j2\pi ft} df$
$y(t)= \frac{ \sin ( \pi t )}{\pi t} = \frac{e^{-j\pi t} - e^{j\pi t}}{\pi t}$
For the above equation to be true,
$Y(f) = \frac{\delta(f - \frac{1}{2})}{\pi t} - \frac{\delta(f + \frac{1}{2})}{\pi t}$
Answer 3
$X(f)=\int_{-\infty}^{\infty} x(t)e^{-j2\pi ft} dt = \int_{-1/2}^{1/2} e^{-j2\pi ft} dt = \frac{e^-j2\pi ft}{j2 \pi f},where x from-1/2 to 1/2 =sinc(f)$ $use duality, Y(f)=rect(x)$
Answer 4
Using Euler's equation, we know
$y(t)= \frac{ \sin ( \pi t )}{\pi t} = \frac{e^{j\pi t} - e^{-j\pi t}}{j2\pi t}$
Do Fourier transform one component at a time,
$\mathcal{F}[\text{rect}(t)] = \int_{-\infty}^{\infty} \text{rect}(t)e^{-j2\pi ft} dt$
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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.
Dr. Paul Garrett | 2020-08-07 15:31:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8311715722084045, "perplexity": 3514.8038318805748}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "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-2020-34/segments/1596439737204.32/warc/CC-MAIN-20200807143225-20200807173225-00389.warc.gz"} |
https://juliaimages.org/stable/install/ | Getting started
Most users probably want to start with the Images.jl package, which bundles much (but not all) of the functionality in JuliaImages.
Installation
Images (and possibly some additional packages) may be all you need to manipulate images programmatically. You can install Images.jl via the package manager,
(v1.0) pkg> add Images
Note
People in some regions such as China might fail to install/precompile Images due to poor network status. Using proxy/VPN that has stable connection to Amazon S3 and Github can solve this issue.
If this is your first time working with images in julia, it's likely that you'll need to install some image IO backends to load the images. The current available backends for image files are:
• ImageMagick.jl covers most image formats and has extra functionality. This can be your first choice if you don't have a preference.
• QuartzImageIO.jl exposes macOS's native image IO functionality to Julia. In some cases it's faster than ImageMagick, but it might not cover all your needs.
• ImageIO.jl is a new image IO backend (requires julia >=v"1.3") that provides an optimized performance for PNG files. Check benchmark here
• OMETIFF.jl supports OME-TIFF files. If you don't know what it is, then it is likely that you don't need this package.
These backends aren't exclusive to each other, so if you're a macOS user, you can install all these backends. And in most cases, you don't need to directly interact with these backends, instead, we use the save and load provided by the FileIO.jl frontend. If you've installed multiple backends then FileIO will choose the most appropriate backend acoording to your file format. For example, if available ImageIO is used to load PNG files.
Adding these gives you a basic image IO setup:
(v1.0) pkg> add FileIO ImageMagick ImageIO
and to load an image, you can use
using Images, FileIO
# specify the path to your local image file
img_path = "/path/to/image.png"
img = load(img_path)
When testing ideas or just following along with the documentation, it can be useful to have some images to work with. The TestImages.jl package bundles several "standard" images for you.
(v1.0) pkg> add TestImages
To load one of the images from this package, say
using TestImages
# backends such as ImageMagick are required
img = testimage("mandrill")
Displaying images
When working with images, it's obviously helpful to be able to look at them. If you use Julia through Juno or IJulia, images should display automatically:
Currently there're five julia packages can be used to display an image:
To visualize multiple images in one frame, you can create a bigger image from multiple image sources with mosaicview, which is an enhanced version of cats.
img1 = testimage("mandrill") # 512*512 RGB image
img2 = testimage("blobs") # 254*256 Gray image
mosaicview(img1, img2; nrow=1) | 2020-10-21 21:18:08 | {"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": 0, "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": 0.36240023374557495, "perplexity": 4242.556497341772}, "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-2020-45/segments/1603107878633.8/warc/CC-MAIN-20201021205955-20201021235955-00272.warc.gz"} |
https://tldr.dendron.so/notes/common.tailscale-file.html | # tailscale file
Send files across connected devices on a Tailscale network. It currently does not support sending files to devices owned by other users even on the same Tailscale network. More information: https://tailscale.com/kb/1106/taildrop/.
• Send a file to a specific node:
sudo tailscale file cp {{path/to/file}} {{hostname|ip}}:
• Store files that were sent to the current node into a specific directory:
sudo tailscale file get {{path/to/directory}} | 2022-11-27 15:01:53 | {"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": 0, "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": 0.37372592091560364, "perplexity": 11812.95785103563}, "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-2022-49/segments/1669446710409.16/warc/CC-MAIN-20221127141808-20221127171808-00332.warc.gz"} |
https://etheses.bham.ac.uk/id/eprint/270/ | # Transverse spin asymmetries in neutral strange particle production
Burton, Thomas (2009). Transverse spin asymmetries in neutral strange particle production. University of Birmingham. Ph.D.
Preview
Burton09PhD.pdf
PDF
## Abstract
The origin of the quantum mechanical spin of the proton in terms of its constituents is not yet fully understood. The discovery that the intrinsic spin of quarks contributes only a small fraction of the total proton spin sparked a huge theoretical and experimental effort to understand the origin of the remainder. In particular the transverse spin properties of the proton remain poorly understood. Significant transverse spin asymmetries in the production of hadrons have been observed over many years, and are related to both the transverse polarisation of quarks in a transversely polarised proton and to the spin dependence of orbital motion. These asymmetries are of interest because of perturbative QCD predictions that such asymmetries should be small. Measurements of such asymmetries may yield further insights into the transverse spin structure of the proton. The Relativistic Heavy Ion Collider (RHIC) is the world's first polarised proton collider, and has been taking proton data since 2001. Polarised proton collisions at $$\sqrt{s}$$ = 200 GeV taken during the 2006 RHIC run have been analysed and the transverse single and double spin asymmetries in the production of the neutral strange particles $$K^0_S$$, $$\Lambda$$ and $$\overline{\Lambda}$$ have been measured in the transverse momentum range 0.5 < $$p_T$$ < 4.0 GeV/c at $$x_F \approx$$ 0. Within statistical uncertainties of a few percent the asymmetries are found to be consistent with zero.
Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Jones, Peter G.UNSPECIFIEDUNSPECIFIED
Licence:
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Physics and Astronomy
Funders: None/not applicable
Subjects: Q Science > QC Physics
URI: http://etheses.bham.ac.uk/id/eprint/270
### Actions
Request a Correction View Item | 2021-10-26 02:48:13 | {"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": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7358810901641846, "perplexity": 1716.384334610939}, "config": {"markdown_headings": true, "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-2021-43/segments/1634323587794.19/warc/CC-MAIN-20211026011138-20211026041138-00647.warc.gz"} |
https://math.stackexchange.com/questions/3383323/hitting-time-probability-of-brownian-motion-martingale-approach | # Hitting Time Probability of Brownian Motion (Martingale Approach)
I was self-studying a book on stochastic calculus and got some difficulties dealing with the following question.
Suppose $$W_t$$ is a Brownian motion path and $$T$$ is a random hitting time. The stopped process is: $$X_t= \begin{cases} W_t & t < T \\ W_T & t \geq T \end{cases}$$ I have shown that $$X_t$$ is a martingale.
The question is: Suppose $$W_0 = 0$$, and $$x_l<0, and that $$T$$ is the first hitting time, which is $$T=min\{t|W_t=x_l\ \text{or} \ W_t = x_r\}$$. Use the fact that this stopped process is a martingale to find a formula for $$Pr(W_T = x_l)$$. Assumption here is $$E[T]<\infty$$.
Since $$X_t$$ is a martingale and $$\mathbb ET<\infty$$, we can apply the optional stopping theorem to conclude that $$\mathbb EX_T=\mathbb EX_0=\mathbb EW_0=0$$. Now, $$X_T$$ is a random variable that satisfies $$\mathbb P(X_T\in\{x_l,x_r\})=1$$. Thus, we have the system of equations $$\mathbb P(X_T=x_l)+\mathbb P(X_T=x_r)=1,\qquad x_l\mathbb P(X_T=x_l)+x_r\mathbb P(X_T=x_r)=0,$$ where the second equation comes from expressing the expectation $$\mathbb EX_T$$ in two different ways. Solving the system of equations yields $$\mathbb P(X_T=x_l)=\frac{x_r}{x_r-x_l}\qquad \mathbb P(X_T=x_r)=\frac{-x_l}{x_r-x_l}.$$ Thus, $$\mathbb P(W_T=x_l)=x_r/(x_r-x_l)$$. | 2020-02-22 07:20:49 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 19, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9564744234085083, "perplexity": 3552.1708330342135}, "config": {"markdown_headings": true, "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-2020-10/segments/1581875145654.0/warc/CC-MAIN-20200222054424-20200222084424-00548.warc.gz"} |
https://dreamcode.blog.csdn.net/article/details/5932644 | # 两个最容易被人忽略的基本代码优化技术
Dr. Dobbs BloggerWalter Bright曾写了一篇博文《Overlooked Essentials For Optimizing Code》，为我们总结了两个最容易被人忽略的基本代码优化技术。个人网站版主陈皓对本文进行了翻译，现转载于此，供大家学习。全文如下：
x + 3 = 5
__ + 3 = 5
ADD ESI,x
ESI += x;
CALL foo
foo();
## Overlooked Essentials For Optimizing Code
Sep 10, 2010
I've been programming for 35 years now, and I've done a lot of work optimizing programs for speed (an example), and watching others optimize. Two essential techniques are consistently ignored.
Nope, it isn't avoiding premature optimization. It isn't replacing bubble sort with quicksort (i.e. algorithmic improvements). It's not what language used, nor is it how good the compiler is. It isn't writing i<<2 instead of i*4.
It is:
1. Using a profiler
2. Looking at the assembly code being executed
The people who do those are successful in writing fast code, the ones who do not are not. Let me explain.
## Using A Profiler
The old programming saw is that a program spends 90% of its time in 10% of the code. I've found that to not be true. Over and over, I've found that programs spends 99% of its time in 1% of the code. But which 1%? A profiler will tell you. Spending 100 hours of dev time on that 1% will yield real benefits, while 100 hours on the other 99% will not produce much of anything worthwhile.
What's the problem? Don't people use profilers? Nope. One place I worked at had a fancy expensive profiler that was still in its shrink wrap 3 years after purchase. Why don't people use profilers? I don't really know. I once got into a heated exchange with a colleague who insisted he knew where the bottlenecks were; after all, he was an experienced professional. I finally ran the profiler myself on his project, and of course the bottleneck was in a completely unexpected place.
Consider auto racing. The team that wins has sensors and logging on just about everything they can stick a sensor on. You can race using seat-of-the-pants tuning and have a jolly good time on the track, but you won't win and you won't even be competitive. You won't know if your poor speeds are caused by the engine, the exhaust, the aerodynamics, the tire pressure, or the driver. Why should programming be any different? You can't improve what you can't measure.
There are lots of profilers available. You can get ones that look at the hierarchy of function calls, function times, times broken down for each statement, and even at the instruction level. I've seen too many programmers eschew profilers, preferring instead to whittle away their time with useless and misdirected "optimizations" and getting trounced by their competitors.
## Looking At The Assembly Code
Years ago, I had a colleague, Mary Bailey, who taught remedial algebra at the University of Washington. She told me once that when she wrote on the board:
x + 3 = 5
and asked her students to "solve for x", they couldn't answer. But, if she wrote:
__ + 3 = 5
and asked the students to "fill in the blank" all of them could do it. It seems that the magic word "x" seemed to cause them to reflexively think "x means algebra, I don't understand algebra, I can't do this."
Assembler is the algebra of the programming world. If someone asks me "was my function inlined by the compiler" or "if I write i*4, will the compiler optimize it to a left shift" I'll suggest they look at the asm output of the compiler. The reaction is how rude and unhelpful could I be? The person will follow up by saying he doesn't know assembler. Even C++ experts will say this.
Assembler is the simplest language (especially compared with C++!). For example,
ADD ESI,x
is (expressed in C style):
ESI += x;
and:
CALL foo
is:
foo();
Details vary among CPUs, but that's how it works. It's not even really necessary to know that. Just looking at the assembler output and comparing it to the source code will tell a LOT.
How does this help optimization? For example, I knew a programmer years ago who thought he'd discovered a new, faster algorithm to do X. I'm being deliberately vague to protect him. He had the benchmarks to prove it, and wrote a nice article about it. But then someone looked at the assembler output of the regular way, and his new fast way. It turns out that the way he'd written his improved version had allowed the compiler to replace two DIV instructions with one. This had really nothing to do with his algorithm. But DIV is an expensive instruction, and this was in the inner loop, and so his algorithm appeared to be faster. The regular implementation could also be recoded slightly to use only one DIV, too, and it would perform just as fast as the new algorithm. He had discovered nothing.
For my next example, a D user posted a benchmark showing that dmd (Digital Mars D compiler) was lousy at integer arithmetic, while ldc (LLVM D compiler) was much better. Being very concerned about such a result, I promptly looked at the assembler output. It was pretty much equivalent, nothing stood out as being accountable for a 2:1 difference. But there was a long divide in there, done with a call to a runtime library function. That function call completely dominated the timing results, all the adds and subtracts in the benchmark had no significant impact on the speed. Unexpectedly, the benchmark wasn't about arithmetic code generation at all, it was about long division only. It turns out that dmd's runtime library function had a crummy implementation of long division in it. Fixing that brought the speed up to par. It wasn't the code generation at fault at all, but this was not discoverable without looking at the assembler.
Looking at the assembler often gives unexpected insight into why a program performs as it does. Unexpected function calls, unanticipated bloat, things that shouldn't be there, etc., all are exposed when looking at it. It isn't necessary to be an assembler crackerjack to be able to pick that up.
## Conclusion
If you feel the need for speed, the way to get it is to use a profiler and be willing to examine the assembler for the bottlenecks. Only then is it time to think about better algorithms, faster languages, etc.
Conventional wisdom has it that choosing the best algorithm trumps any micro-optimizations. Though that is undeniably true, there are two caveats that don't get taught in schools. First and most importantly, choosing the best algorithm for a part of the program that has no participation to the performance profile has a negative effect on optimization because it wastes your time that could be better invested in making actual progress, and diverts attention from the parts that matter. Second, algorithms' performance always varies with the statistics of the data they operate on. Even bubble sort, the butt of all jokes, is still the best on almost-sorted data that has only a few unordered items. So worrying about using good algorithms without measuring where they matter is a waste of time - your's and computer's.
Just like ordering speed parts from an auto racing catalog isn't going to put you anywhere near the winner's circle (even if you get them installed right), without profiling, you won't know where the problems are without a profiler. Without looking at the assembler, you may know where the problem is, but often won't know why.
Thanks to Bartosz Milewski, David Held, and Andrei Alexandrescu for their helpful comments on a draft of this.
11-27 2万+
12-28 1万+
10-20 1384
09-29 792
10-23 1991 | 2020-10-28 15:38:50 | {"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": 0, "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": 0.3231571614742279, "perplexity": 1653.3298013554052}, "config": {"markdown_headings": true, "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-2020-45/segments/1603107898577.79/warc/CC-MAIN-20201028132718-20201028162718-00117.warc.gz"} |
http://www.gap-system.org/Manuals/pkg/QPA-1.26/doc/chap11.html | Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 Bib Ind
### 11 Projective resolutions and the bounded derived category
What is implemented so far for working with the bounded derived category \mathcal{D}^{b}( \modc A ). We use the isomorphism \mathcal{D}^{b}( \modc A ) \cong \mathcal{K}^{-,b}(\proj A), and will hence need a way to describe complexes where all objectives are projective (or, dually, injective).
#### 11.1 Projective and injective complexes
##### 11.1-1 InjectiveResolution
‣ InjectiveResolution( M ) ( operation )
Arguments: M -- a module.
Returns: The injective resolution of M with M in degree -1.
##### 11.1-2 IsProjectiveComplex
‣ IsProjectiveComplex( C ) ( property )
Arguments: C -- a complex.
Returns: true if C is either a finite complex of projectives or an infinite complex of projectives constructed as a projective resolution (ProjectiveResolutionOfComplex (11.2-1)), false otherwise.
A complex for which this property is true, will be printed in a different manner than ordinary complexes. Instead of writing the dimension vector of the objects in each degree, the indecomposable direct summands are listed (for instance P1, P2 … , where P_i is the indecomposable projective module corresponding to vertex i of the quiver). Note that if a complex is both projective and injective, it is printed as a projective complex.
##### 11.1-3 IsInjectiveComplex
‣ IsInjectiveComplex( C ) ( property )
Arguments: C -- a complex.
Returns: true if C is either a finite complex of injectives or an infinite complex of injectives constructed as D\mathrm{Hom}_{A}(-,A) of a projective complex (ProjectiveToInjectiveComplex (11.2-2)), false otherwise.
A complex for which this property is true, will be printed in a different manner than ordinary complexes. Instead of writing the dimension vector of the objects in each degree, the indecomposable direct summands are listed (for instance I1, I2 … , where I_i is the indecomposable injective module corresponding to vertex i of the quiver). Note that if a complex is both projective and injective, it is printed as a projective complex.
##### 11.1-4 ProjectiveResolution
‣ ProjectiveResolution( M ) ( operation )
Arguments: M -- a module.
Returns: The projective resolution of M with M in degree -1.
#### 11.2 The bounded derived category
Let \mathcal{D}^{b}( \modc A ) denote the bounded derived category. If C is an element of \mathcal{D}^{b}( \modc A ), that is, a bounded complex of A-modules, there exists a projective resolution P of C which is a complex of projective A-modules quasi-isomorphic to C. Moreover, there exists such a P with the following properties:
• P is minimal (in the homotopy category).
• C is bounded, so C_i = 0 for i < k for a lower bound k and C_i = 0 for i > j for an upper bound j. Then P_i = 0 for i < k, and P is exact in degree i for i > j.
The function ProjectiveResolutionOfComplex computes such a projective resolution of any bounded complex. If A has finite global dimension, then \mathcal{D}^{b}( \modc A ) has AR-triangles, and there exists an algorithm for computing the AR-translation of a complex C \in \mathcal{D}^{b}( \modc A ):
• Compute a projective resolution P' of C.
• Shift P' one degree to the right.
• Compute I = D\mathrm{Hom}_{A}(P',A) to get a complex of injectives.
• Compute a projective resolution P of I.
Then P is the AR-translation of C, sometimes written \tau(C). The following documents the QPA functions for working with complexes in the derived category.
##### 11.2-1 ProjectiveResolutionOfComplex
‣ ProjectiveResolutionOfComplex( C ) ( operation )
Arguments: C -- a finite complex.
Returns: A projective complex P which is the projective resolution of C, as described in the introduction to this section.
If the algebra has infinite global dimension, the projective resolution of C could possibly be infinite.
##### 11.2-2 ProjectiveToInjectiveComplex
‣ ProjectiveToInjectiveComplex( P ) ( operation )
‣ ProjectiveToInjectiveFiniteComplex( P ) ( operation )
Arguments: P -- a bounded below projective complex.
Returns: An injective complex I = D\mathrm{Hom}_{A}(P,A).
P and I will always have the same length. Especially, if P is unbounded above, then so is I. If P is a finite complex (that is; LengthOfComplex(P) is an integer) then the simpler method ProjectiveToInjectiveFiniteComplex is used.
##### 11.2-3 TauOfComplex
‣ TauOfComplex( C ) ( operation )
Arguments: C -- a finite complex over an algebra of finite global dimension.
Returns: A projective complex P which is the AR-translation of C.
This function only works when the algebra has finite global dimension. It will always assume that both the projective resolutions computed are finite.
##### 11.2-4 Example
The following example illustrates the above mentioned functions and properties. Note that both ProjectiveResolutionOfComplex and ProjectiveToInjectiveComplex return complexes with a nonzero positive part, whereas TauOfComplex always returns a complex for which IsFiniteComplex returns true. Also note that after the complex C in the example is found to have the IsInjectiveComplex property, the printing of the complex changes.
The algebra in the example is kQ/I, where Q is the quiver 1 \longrightarrow 2 \longrightarrow 3 and I is generated by the composition of the arrows. We construct C as the stalk complex with the injective I_1 in degree 0.
gap> alg;
<Rationals[<quiver with 3 vertices and 2 arrows>]/
<two-sided ideal in <Rationals[<quiver with 3 vertices and 2 arrows>]>,
(1 generators)>>
gap> cat := CatOfRightAlgebraModules(alg);
<cat: right modules over algebra>
gap> C := StalkComplex(cat, IndecInjectiveModules(alg)[1], 0);
0 -> 0:(1,0,0) -> 0
gap> ProjC := ProjectiveResolutionOfComplex(C);
--- -> 0: P1 -> 0
gap> InjC := ProjectiveToInjectiveComplex(ProjC);
--- -> 1: I2 -> 0: I1 -> 0
gap> TauC := TauOfComplex(C);
0 -> 1: P3 -> 0
gap> IsProjectiveComplex(C);
false
gap> IsInjectiveComplex(C);
true
gap> C;
0 -> 0: I1 -> 0
##### 11.2-5 StarOfMapBetweenProjectives
‣ StarOfMapBetweenProjectives( f, list_i, list_j ) ( operation )
‣ StarOfMapBetweenIndecProjectives( f, i, list_j ) ( operation )
‣ StarOfMapBetweenDecompProjectives( f, list_i, list_j ) ( operation )
Arguments: f -- a map between to projective modules P = \bigoplus P_i and Q = \bigoplus Q_j, each of which were constructed as direct sums of indecomposable projective modules; list_i -- describes the summands of P; list_j -- describes the summands of Q. If P = P_1 \oplus P_3 \oplus P_3 (where P_i is the indecomposable projective representation in vertex i), then list_i is [1,3,3].
Returns: The map f^* = \Hom_A(f,A): \Hom_A(Q,A) \rightarrow \Hom_A(P,A) in A^{\mathrm{op}} (where A is the original algebra).
The function StarOfMapBetweenProjectives is supposed to be called from within the ProjectiveToInjectiveComplex method, and might not do as expected when called from somewhere else.
The other similarly named functions are called from within the first.
Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 Bib Ind
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https://cronfa.swan.ac.uk/Record/cronfa23989 | Journal article 601 views
### Equilibrium Diffusion on the Cone of Discrete Radon Measures / Diana Conache, Yuri G. Kondratiev, Eugene Lytvynov
Potential Analysis, Volume: 44, Issue: 1, Pages: 71 - 90
Swansea University Author:
Full text not available from this repository: check for access using links below.
DOI (Published version): 10.1007/s11118-015-9499-9
Abstract
Let $K(R^d)$ denote the cone of discrete Radon measures on $R^d$.There is a natural differentiation on $K(R^d)$: for a differentiable function $F:K(R^d)\to R$, one defines its gradient $\nabla^K F$ as a vector field which assigns to each $\eta\in K(R^d)$ an element of a tangent space $T_\eta(K(R^d)... Full description Published in: Potential Analysis 0926-2601 1572-929X 2016 https://cronfa.swan.ac.uk/Record/cronfa23989 No Tags, Be the first to tag this record! Abstract: Let$K(R^d)$denote the cone of discrete Radon measures on$R^d$.There is a natural differentiation on$K(R^d)$: for a differentiable function$F:K(R^d)\to R$, one defines its gradient$\nabla^K F $as a vector field which assigns to each$\eta\in K(R^d)$an element of a tangent space$T_\eta(K(R^d))$to$K(R^d)$at point$\eta$. Let$\phi:R^d\times R^d\to\R$be a potential of pair interaction, and let$\mu$be a corresponding Gibbs perturbation of (the distribution of) a completely random measure on$R^d$. In particular,$\mu$is a probability measure on$K(\R^d)$such that the set of atoms of a discrete measure$\eta\in K(R^d)$is$\mu$-a.s. dense in$R^d$. We consider the corresponding Dirichlet form$$\mathcal E^K(F,G)=\int_{K\R^d)}\langle\nabla^K F(\eta), \nabla^K G(\eta)\rangle_{T_\eta(K)}\,d\mu(\eta).$$Integrating by parts with respect to the measure$\mu$, we explicitly find the generator of this Dirichlet form. By using the theory of Dirichlet forms, we prove the main result of the paper: If$d\ge2$, there exists a conservative diffusion process on$K(R^d)$which is properly associated with the Dirichlet form$\mathcal E^K\$. College of Science 1 71 90 | 2021-12-01 07:17:54 | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.528010368347168, "perplexity": 4536.9370439493005}, "config": {"markdown_headings": true, "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-2021-49/segments/1637964359093.97/warc/CC-MAIN-20211201052655-20211201082655-00583.warc.gz"} |
http://www.scienceforums.com/topic/7452-economic-history-and-the-future-crunch/ | # Economic History and the Future Crunch...
28 replies to this topic
### #1 Boerseun
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Posted 18 July 2006 - 02:58 AM
Not sure whether this is the right forum, but here goes...
In the 1930's the US refused to accept payment for goods and services from other countries with currency. They demanded gold. This was in the wake of the global depression sparked off with the 1929 Wall Street collapse. This resulted in the US ending up with more than 80% of the world's gold in their vaults. Now hang on a minute...
Since the 1970's, the international oil trade was done in US dollars. Countries had to stock up on dollar reserves in order to purchase oil on the two international oil bourses, in New York and London. These countries' vaults are brimming with US currency, only to supply their domestic oil demand. This was all well and good, and sort of made the US currency the de facto world currency. It also made sense for the US, because it expanded the US' influence further, into the very heart of other countries' economies. This all changed in the early 2000's with the creation of...
The Euro.
Baghdad decided early on after the acceptance of the Euro in the EU to create its own oil bourse, where trading is to be done exclusively in Euros. This makes sense, seeing as most of Baghdad's sales are to the EU. Baghdad went ahead with this planning, and eventually (amidst great objection from the US and Britain) did open its doors for oil trading. Two months later, the US invaded. I am by no means saying these happenings are related - but just keep it in mind. Teheran is planning the same thing - to set up an international trading oil bourse in Teheran to trade exclusively in Euros. The US is eyeballing Teheran.
Any case, I digress. I have read that countries around the world are more interested in trading oil in Euros currently, because Europe seems to be less prone to military action, with the resulting stabilising influence on the currency. So, countries are standing in line to sell their dollars back to the US, who, ultimately, must honour the value of the dollar and accept it. It is, after all, their currency. But there's a little problem here. It seems as if the US can only honour five percent of the money put into circulation since the '70s, or petrodollars, as they are more commonly known. In other words, as countries proceed in trading oil in Euros rather than dollars, the American market will become bogged down with useless currency. The dollar will start losing value and ultimately collapse. Matter of fact, the dollar have already lost more than 30% against the Euro since its inception. But think about this for a minute: The Dollar is the de facto World Currency. And there is 95% more dollars in supply than can be backed by the US. In other words, once the oil trade is shifted significantly from Dollar trade to preferred Euro trade, the World Economy will collapse. The 1930's depression (which in a big way contributed to WWII) would look like a Sunday picnic in comparison.
Could this maybe explain the US' current foreign policy? Could this maybe explain why the US is so insistent on oil trade in dollars? Is the US' international interventions of late not based on protecting the oil supply, but rather to suppress the Euro trade in oil, and in doing so attempting to prevent global economic collapse? Or simply to hide the fact that the system put in place since the 1970's is inherently flawed?
Come what may - the mere fact that the US cannot back 95% of its currency will eventually result in a global meltdown.
I know - I have made some sweeping statements here, and will try and find the links. But I'm sure the US government is stressing a little right now.
The reason I've put this in History is simply because I believe however this pans out, we are seeing history in the making...
Thoughts?
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### #2 InfiniteNow
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Posted 18 July 2006 - 11:31 AM
I will gladly pay you Tuesday, for a hamburger today.
Other economies will surely progress, as the US debt can be purchased by other countries, thus giving them an advantage. This is indeed a very interesting set of circumstances to follow.
I ran out of 20s, can I pay you in polution credits instead?
### #3 Boerseun
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Posted 19 July 2006 - 02:08 AM
The first time I read about the US not being able to back its currency was an article in the NY Times, around 2003/4. The guy said that he reckons as people start losing faith in currency, they will once again start looking to gold as a safe haven. Back then, gold was trading at around $400/ounce. He predicted that as the sale of dollars back to the States increase, gold should double within two years. Well, it's now two years later, and gold is trading at more than$700/ounce!
Could this be the first signs of the global meltdown to come? The dollar losing more than 30% to the the Euro, and gold almost doubling, and still rising?
And, oh yes - if you have any spare cash lying around, invest in GOLD!.
### #4 Boerseun
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Posted 27 November 2007 - 06:50 AM
So... more than a year after the previous post, and things are panning out exactly as the NY Times article said. Gold is now way over $800 per ounce, the dollar is much weaker, etc. The question, then: Anybody followed my brilliant advice and bought gold? I need commission on that... Also, whatcha gonna do when 95% of your money turns out to be no more than paper? ### #5 InfiniteNow InfiniteNow Suspended • Members • 9148 posts Posted 27 November 2007 - 12:22 PM Also, whatcha gonna do when 95% of your money turns out to be no more than paper? Feel a lot closer to the poor folks in Zimbabwe most likely. Using US dollars for monopoly... • Boerseun likes this ### #6 Queso Queso Synesthetic • Members • 7281 posts Posted 27 November 2007 - 12:41 PM The dollar will start losing value and ultimately collapse. Matter of fact, the dollar have already lost more than 30% against the Euro since its inception. But think about this for a minute: The Dollar is the de facto World Currency. And there is 95% more dollars in supply than can be backed by the US. In other words, once the oil trade is shifted significantly from Dollar trade to preferred Euro trade, the World Economy will collapse. The 1930's depression (which in a big way contributed to WWII) would look like a Sunday picnic in comparison. How will the world economy collapse when you switch oil trade from dollars to euros? what does oil have to do with everyone's paper dollars? and as the dollar continues to fall...what are all these worker bees going to do with their savings? will it really be worthless someday? that would be insanely hilariously devastating. • Boerseun likes this ### #7 Queso Queso Synesthetic • Members • 7281 posts Posted 30 November 2007 - 12:51 AM could someone elaborate on their free time ? just bumpin' ### #8 Buffy Buffy Resident Slayer • Administrators • 8946 posts Posted 30 November 2007 - 01:15 AM How will the world economy collapse when you switch oil trade from dollars to euros? Iran and Venezuela--who hate the US--argue, somewhat convincingly actually, that this will only cause the US economy to collapse. The basic issue is that when OPEC decides to denominate in Euros while the dollar continues to fall in relation to them, that the cost of oil in the US will skyrocket, thus causing tremendous inflation without growth in the economy to balance it. When this happens, all the foreign governments who we have borrowed from in dollar-denominated securities will dump those securities, causing the value of the dollar to fall even further. It could be a horrible mess for the US! OTOH, there's an old saying: when you owe the bank$100, the bank owns you, but if you owe the bank $1,000,000, then you own the bank. That is, if you default on your loan, the bank is in *major* trouble. So the counter argument is that the Chinese and Arabs and so on who have invested in the US and in dollars *can't afford* to let the dollar drop, so they will do everything they can to help prop up the dollar and keep their investments from becoming worthless overnight...at least in the short run! So: ...what are all these worker bees going to do with their savings? will it really be worthless someday? Yah. Make the current situation in Zimbabwe look like a cake walk... that would be insanely hilariously devastating. ...or not, depending on where your money is! There's a reason they call it the Dismal Science, Buffy ### #9 Boerseun Boerseun Phantom Cow of Justice • Members • 6062 posts Posted 30 November 2007 - 01:25 AM Well, currency is based on trust. And in the global use of dollars, countries establish the value of the dollar based on the "trust" that the dollar value will be honoured by the US. In theory, that is. But, for example, the South African government has a few billion dollars, and doesn't care wether the US backs it - all it wants is the surety that it can buy oil with it. But now if the mid-East don't want dollars for their oil, but Euros, rather, then the South African government has no other option but to exchange those dollars on the open money markets for Euros. But keep in mind that the South African government won't be the only one to do so. There will be such an oversupply of dollars, that the dollar will collapse in value, whilst the Euro will skyrocket. Problem is, of course, that the oil market being what it is, all countries have vast US dollar supplies and very few Euros. This will have to change in the face of a trade switch from dollars to Euros. ...which means that the American currency is backed not so much by tangible assets (the 5% the government can back), as much as by the international "perception" and trust in the currency (the 95% that cannot be backed, according to the NY Times). One good spinoff from a currency losing lotsa value in a short time, is that debt gets wiped out. So it sucks to have people owe you bucks, but it rocks to owe the bank a million bucks from a loan that was worth something a year ago, but still owe them a million bucks (plus interest) a year later, when a loaf of bread now sells for a million. Okay, extreme example, but you get the idea. Okay - it's only a good idea if it's you owing the money. If you're the bank, it sucks some serious tripe. Oh, yes - and investments, etc., will effectively become worthless. Unless managed by some crazy high-risk gambler dude who can realise thousands of per cent returns on portfolios, constantly, over a long period of time, just to keep up to speed with the falling currency. Unless, of course, those portfolios are invested abroad, and tallied not in dollars, but in the foreign country's currency. Also, China will be a bit pissed off to find that the bonds they own are practically useless. Fun and laughs all around if the world decide to switch to Euro oil trade... ### #10 Michaelangelica Michaelangelica Creating • Members • 7797 posts Posted 30 November 2007 - 01:26 AM Fascinating thoughts. It used to annoy me that USA tourists would not bother to get their dollars converted into local currency. They just arrogantly expected you to take their dollars. When I was feeling especially mean-spirited I would take their dollars for Aust$ equivalent making a tidy 20-30% extra profit on the deal. They didn't even care.
I just read a few days ago about Saudi Arabia thinking about not trading in US$s. Also the Chinese currency is weighed (& controlled?) with a basket of currencies including the US$ so it effectively has been depreciated (?) with the fall in the US$It is annoying here when you are importing (used to 10-15 years ago) from SE Asia and have to trade in US$ not the local currency. Although when I imported from France or England I was always quoted in francs or pounds.
It seems to me there is a great thriller, or at least a conspiracy theory, in the making, about 'Arab word Vs the USA' .
"We live in interesting times" as the Chinese curse goes,
### #11 Michaelangelica
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Posted 30 November 2007 - 04:01 AM
A friend just sent me this Australian article
The party's over and Liberals will soon be history - Opinion - smh.com.au
Although I'm not sure how being a psychologist makes you a good economist.
Perhaps, What you believe will happen, does, as in Cinderella?
Linked to this, but compounding it in frightening ways, is the imminent demise of the United States economy.
In fact the whisper, the subplot in economist circles, was that this election was one to lose. That whoever inherited Australia in 2007 inherited a coming economic collapse in globalised trade that would suck Australia and much of the rest of the world down with it. For two years now the best predictions have been that the subprime meltdown would act as merely the detonator of a much larger explosive charge created long ago by US consumer debt, concealed by Chinese and Arab investment in keeping that great hungry maw that is America sucking in what it could not begin to pay for. The avalanche-like fall of US house prices will be closely followed by the same in linked economies worldwide, and presage a harsh and very different world than the one we have lived in. In short, the party is over. We are a civilisation in collapse
### #12 Qfwfq
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Posted 30 November 2007 - 06:54 AM
Did none of you notice the recent news (past month or two) about the Chinese gov't minister talking about the need to diversify the country's investments? First thing I thought was, you'd think he'd bloody well do so before saying it too loud...
My savings are in Euro!
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### #13 Buffy
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Posted 30 November 2007 - 11:57 AM
Did none of you notice the recent news (past month or two) about the Chinese gov't minister talking about the need to diversify the country's investments?
I can guarantee you that no one in the current administration's Treasury Department was listening!
"I would just say that I think I've been very consistent on a strong dollar...
...he said after the dollar had dropped 9% in the past year...
LA, LA, LA, I CAN'T HEAR YOU! LA, LA, LA!
Buffy
### #14 Zythryn
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Posted 30 November 2007 - 03:32 PM
Back then[2003-2004], gold was trading at around $400/ounce. He predicted that as the sale of dollars back to the States increase, gold should double within two years. Well, it's now two years later, and gold is trading at more than$700/ounce!
Could this be the first signs of the global meltdown to come? The dollar losing more than 30% to the the Euro, and gold almost doubling, and still rising?
First, yes, I believe we are living in a time where there will be massive economic upheavals.
Second, this guy is silly.
Funny how we always look back and latch only the predictions that were correct, instead of all the predictions that were wrong.
Go back to Mid 1977, gold was almost down to $50/once. By the end of 1979 we were up to$750/once, 1400%!
Yes, gold is going up in value rather rapidly, not it isn't (in and of itself) going to lead to economic meltdown.
Now, if it becomes clear we have reached peak oil (e.g. OPEC says it will raise production and it can't, and no one else can fill the shortfall), or if drinkable water becomes so scarce we have wars over it, or China sells all the US debt they have but no one wants it, then we may have a meltdown. But not solely because of gold's price (IMO).
### #15 Boerseun
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Posted 03 December 2007 - 02:05 AM
Second, this guy is silly.
I can quite understand your need to believe that I'm silly. You might have assets tied up in markets vulnerable to the future crunch. But saying I'm silly won't prop up your portfolio's defenses. Rather, I think you're misunderstanding my premise...
Funny how we always look back and latch only the predictions that were correct, instead of all the predictions that were wrong.
Why would you want to latch onto wrong predictions? Hindsight might be 20/20, but the only way to validate/invalidate a theory, is through analysing the results of tests and predictions, that can only be done in hindsight. When you're presented with the results of an experiment, the experiment has obviously taken place in the past. How else? In ignoring the predictions of the future economic crunch because it might be to your disadvantage if it were to happen, do you propose we ignore the flow of time, too? Er...
The more evidence comes in that supports the view expressed in the NY Times article referred to in the first post, the more likely it becomes that the theory holds. No theory is absolute, though - hence the name.
Go back to Mid 1977, gold was almost down to $50/once. By the end of 1979 we were up to$750/once, 1400%!
Exactly. Gold doesn't determine where the other indicators go - gold is a follower, and the gold price is a good indicator of what investors think of the rest of the market. If the markets are dodgy, gold rises in reaction to the dodginess. Gold blew through the roof in the '70s, because of the oil crisis. Guess where gold is going now?
Yes, gold is going up in value rather rapidly, not it isn't (in and of itself) going to lead to economic meltdown.
Listen, and listen carefully: Gold is not a leader, gold is a follower. If the gold price rise and rise consistently, it's a sure indicator that investors are losing trust in the rest of the market, said market including anything from oil to actual usable commodities. Gold has been steadily rising over the last few years. What can it mean? Was a new and revolutionary use for gold been discovered in the last few years? No. Gold is essentially useless (except for a few specialty uses - and, of course human vanity) BUT gold is a safe haven in times of economic upheaving. What does that tell you about the current state of world economic affairs, if gold has been steadily rising over the last few years?
Now, if it becomes clear we have reached peak oil (e.g. OPEC says it will raise production and it can't, and no one else can fill the shortfall),
The problem with investors, of course, is that they'll take their money and run long before the actual event. Peak Oil doesn't have to occur before they'll take their money - a good fright will trigger mass sales in a world living under the expectation of Peak Oil. We'll see some bad economic crashes and shakes long before the oil runs out. Investors are funny animals.
...or if drinkable water becomes so scarce we have wars over it, or China sells all the US debt they have but no one wants it, then we may have a meltdown. But not solely because of gold's price (IMO).
Like I said, Gold follows, not leads. The gold price won't trigger anything, because gold's price is established in reaction to the general stance of the marketplace. So, if the gold price is in steep decline, that's a good sign - people have enough trust in the market to invest in things other than that ancient bearer of economic value, gold. If the gold price is in a consistent rising phase, the opposite applies. It's merely an indicator of the market at the time.
...and your second point about China trying to sell US debt will happen once the world changes from oil trade in dollar to oil trade in Euro, because then there'll be an oversupply of dollars and the dollar value will come crashing down, basically destroying the value of what the US owes China. The US & China, and every other government, institution or individual who have any assets bound in dollars, will suffer. But not because of the prce of gold. I think you should read my prior posts a little more carefully.
### #16 Michaelangelica
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Posted 06 December 2007 - 10:28 AM
[quote][quote name='Boerseun']I can quite understand your need to believe that I'm silly.[/quote]
He might mean "silly" in the old AS or Old German meaning of "blessed"?
[quote]Exactly. Gold doesn't determine where the other indicators go - gold is a follower,[/quote]
If the price of gold goes up; people are worried about the value of paper money
[quote]Listen, and listen carefully: Gold is not a leader, gold is a follower.[/quote]
Whoh!!
a bit agro there, but correct
[ation
of Peak Oil. We'll see some bad economic crashes and shakes long before the oil runs out. Investors are funny animals.
[quote] if the gold price is in steep decline, that's a good sign - people have enough trust in the market to invest in things other than that ancient bearer of economic value, gold[/quote].
YEP
If the gold price is in a consistent rising phase, the opposite applies. It's merely an indicator of the market at the time.
YEP
[quote]...and your second point about China trying to sell US debt will happen once the world changes from oil trade in dollar to oil trade in Euro, because then there'll be an oversupply of dollars and the dollar value will come crashing down, basically destroying the value of what the US owes China. The US & China, and every other government, institution or individual who have any assets bound in dollars, will suffer. But not because of the prce of gold. .[/quote]
I am not sure if this follows.
But we do live "in interesting times"- Chinese Curse.
### #17 nutronjon
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Posted 18 March 2008 - 09:57 AM
A friend just sent me this Australian article
The party's over and Liberals will soon be history - Opinion - smh.com.au
Although I'm not sure how being a psychologist makes you a good economist.
Perhaps, What you believe will happen, does, as in Cinderella?
I am very glad you all are discussing this issue. The concern in Michaelangelica's post is not only the collapse of the dollar, but the collapse of civilization. I have attempted to warn people of that are headed for economic disaster and war for several years, because all industrial economies are dependant on oil, and we are running out of oil. I still painfully remember everyone telling me we had plenty of oil, and how wrong I am about economic matters, and why we invaded Iraq. My strongest effort however, is not the economic problem, but the civilization one. What makes humans civilized? That is not the subject of this thread, I am just responding to the concern, and will start a thread so we can explore what makes us civilized and how we might weather through an economic collapse. | 2019-09-23 12:20:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23368056118488312, "perplexity": 2739.7528738038677}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2019-39/segments/1568514576355.92/warc/CC-MAIN-20190923105314-20190923131314-00278.warc.gz"} |
https://www.varsitytutors.com/ap_physics_c_mechanics-help/motion/mechanics-exam/circular-and-rotational-motion | # AP Physics C: Mechanics : Circular and Rotational Motion
## Example Questions
← Previous 1 3 4
### Example Question #1 : Circular And Rotational Motion
A ball of mass is tied to a rope and moves along a horizontal circular path of radius as shown in the diagram (view from above). The maximum tension the rope can stand before breaking is given by . Which of the following represents the ball's linear velocity given that the rope does not break?
None of these
Explanation:
This is a centripetal force problem. In this case the tension on the rope is the centripetal force that keeps the ball moving on a circle.
If we want for the rope not to break, then the tension should never exceed .
Now we just solve for velocity:
### Example Question #1 : Rotational Motion And Torque
What is the rotational equivalent of mass?
Angular momentum
Torque
Moment of inertia
Moment of inertia
Explanation:
The correct answer is moment of inertia. For linear equations, mass is what resists force and causes lower linear accelerations. Similarly, in rotational equations, moment of inertia resists torque and causes lower angular accelerations.
### Example Question #1 : Rotational Motion And Torque
In rotational kinematics equations, what quantity is analogous to force in linear kinematics equations?
Impulse
Torque
Moment of inertia
Angular acceleration
Torque
Explanation:
Just as force causes linear acceleration, torque causes angular acceleration. This can be seen most in the linear-rotational comparison of Newton's second law:
### Example Question #1 : Understanding Linear Rotational Equivalents
A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of . What is the linear velocity of the boot?
Explanation:
Linear (tangential) velocity, is given by the following equation:
Here, is the angular velocity in radians per second and is the radius in meters.
Solve.
### Example Question #1 : Rotational Motion And Torque
A particle is moving at constant speed in a straight line past a fixed point in space, c. How does the angular momentum of the particle about the fixed point in space change as the particle moves from point a to point b?
The angular momentum decreases
It cannot be determined without knowing the mass of the particle
The angular momentum does not change
The particle does not have angular momentum since it is not rotating
The angular momentum increases
The angular momentum does not change
Explanation:
The angular momentum of a particle about a fixed axis is . As the particle draws nearer the fixed axis, both and change. However, the product remains constant. If you imagine a triangle connecting the three points, the product represents the "of closest approach", labeled "" in the diagram.
### Example Question #1 : Circular And Rotational Motion
Doing which of the following would allow you to find the center of mass of an object?
Sliding it along a flat surface
Recording its shape
Hanging it from a fixed point
Spinning it
Spinning it
Explanation:
Center of mass can be found by spinning an object. It will naturally spin around its center of mass, due to the concept of even distribution of mass in relation to the center of mass. Shape and mass are important factors in this property, but the most improtant factor is the mass distribution.
### Example Question #1 : Rotational Motion And Torque
If the fulcrum of a balanced scale is shifted to the left, what type of adjustment must be made to rebalance the scale?
Apply the same amount of mass to both ends
Apply more mass to the new position of the fulcrum
Apply more mass to the left end
Apply more mass to the right end
If the scale was initially balanced, moving the fulcrum will not change this
Apply more mass to the left end
Explanation:
Changing the position of the fulcrum by moving it to the left means the center of mass will be to the right of the new position. Therefore, the scale will tip right. Adding more mass to the left end will rebalance the scale. None of the other options make sense. Adding more mass to the new fulcrum position will not change the balance of the scale because that mass is a negligible distance from the new fulcrum position and does nothing to change the masses on either side.
### Example Question #1 : Circular And Rotational Motion
If two masses, and are placed on a seesaw of length , where must the fulcrum be placed such that the seesaw remains level?
Explanation:
This question asks us to find the center of mass for this system. We know that the center of mass resides a distance from the first mass such that:
In this case:
Plug in known values and solve.
### Example Question #1 : Rotational Motion And Torque
Three point masses are at the points , and
and a point mass is at the point .
How far from the origin is the center of mass of the system?
Explanation:
To find the center of mass, we have to take the weighted average of the x coordinates and the y coordinates.
Measures: Measures
First, we take the weighted measurement of the x-axis:
We can see that the result of the x-axis contribution is equal to .
Now, let's look at the y-axis contribution:
This equals to
Now that we have the x and y components, we take the root of squares to get the final answer:
This will give us
### Example Question #1 : Using Torque Equations
An object starts from rest and accelerates to an angular velocity of in three seconds under a constant torque of . How many revolutions has the object made in this time?
Explanation:
Since it is experiencing a constant torque and constant angular acceleration, the angular displacement can be calculated using:
The angular acceleration is easily calculated using the angular velocity and the time:
Using this value, we can find the angular displacement:
Convert the angular displacement to revolutions by diving by :
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http://mathoverflow.net/questions/111176/what-ordinals-are-definable-relations-in-peano-arithmetic/111183 | # What ordinals are definable relations in Peano Arithmetic?
I am not asking which order types PA proves are well ordered. That would be all up to $\epsilon_0$. Rather I mean, assuming a stronger ambient theory such as Zermelo set theory, which ordinals have the order type of some relation on $\mathbb{N}$ that is defined by a formula of PA (not requiring that PA prove the relation is a well ordering).
-
Woohoo! Three answers at once. – Joel David Hamkins Nov 1 '12 at 17:24
## 3 Answers
These are the recursive ordinals. The same well-order-types can be realized by recursive relations as by hyperarithmetical relations. PA-definable, i.e., arithmetical, falls nicely between these two. (I think you can go considerably lower, say to PTime-computable relations, and still have the same order-types.)
-
Is this too well know to need a reference when I invoke it in an article? Or can you suggest a reference? – Colin McLarty Nov 1 '12 at 18:17
It's pretty well-known, but I guess you might as well give a reference. I think it's in Rogers's "Theory of recursive functions and effective computability", but I'm away from Michigan and can't just pull the book off my shelf and check. The result is probably originally due to Kleene, but I don't have a reference for that. – Andreas Blass Nov 1 '12 at 19:14
The answer is the ordinal $\omega_1^{ck}$, named after Church and Kleene, which is defined to be the supremum of the ordinals coded by a computable relation on $\mathbb{N}$. It happens also to be the supremum of the order types of the relations coded by any arithmetic relation, that is, by any relation definable in the language of arithmetic.
-
The computable ordinals---that is, the ordinals below $\omega_1^{CK}$---are, by definition, represented by computable relations, all of which can be represented by formulas in PA, and indeed, even by fairly simple formulas. As Andreas points out, allowing arithmetic formulas instead of computable ones does not change the class of ordinals.
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http://www.beatthegmat.com/best-mba-admissions-consulting-service-t86818-75.html | • Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code ## Best MBA Admissions Consulting Service? tagged by: taviboo This topic has 4 expert replies and 124 member replies Goto page Vincent Ho-Tin-Noe Senior | Next Rank: 100 Posts Joined 29 Aug 2013 Posted: 34 messages Followed by: 1 members Thanked: 8 times Test Date: 08/22/2010 GMAT Score: 750 Thu Jan 01, 2015 11:11 am While I realize that finding a consultant able to support you before round 2 deadlines might prove difficult at this point, we have published several posts in the last 2-3 days to help applicants still putting together their MBA Application. In particular, we have advice for your LORs, resume, and a list of must-read tips to review before hitting the submit button: http://www.mbaadmissionsadvisors.com/ Good luck to everyone. Just a few more days of hard work ! Vincent _________________ Vincent Ho-Tin-Noe (HBS '13) CEO and co-founder MBA Admissions Advisors LLC www.mbaadmissionsadvisors.com Get an immediate assessment of your odds at top MBA programs, try our algorithm for free: http://www.mbaadmissionsadvisors.com/mba-matching-algorithm/ Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! gmat_thingie Junior | Next Rank: 30 Posts Joined 12 Nov 2009 Posted: 23 messages Thu Jan 01, 2015 8:28 pm Hi Vincent Thanks for your reply and your concerns. As you may realize, post this debacle. I decided to take it up on me to do the essays. But quickly hired a consultant to edit my essays. He is not a top-notch consultant. But i have been reading your website, and since you offered 30 minute free consultation. I am still worried about my resume. I wonder if u would help to review it and we can then decide if I take a package now or later. I went through this link on your website. http://www.mbaadmissionsadvisors.com/how-to-write-a-resume-for-mba-admissions-applications/#more-604 Look forward to hear. My skype ID: ruchi857 Thanks Vincent Ho-Tin-Noe Senior | Next Rank: 100 Posts Joined 29 Aug 2013 Posted: 34 messages Followed by: 1 members Thanked: 8 times Test Date: 08/22/2010 GMAT Score: 750 Thu Jan 01, 2015 9:29 pm Hi gmat_thingie, My post was meant to be generic in nature, not a response to the specific evaluation of your consultant. However, we do offer free consultations, and I will reach out to you directly to set up some time for us to talk. Kind regards, Vincent _________________ Vincent Ho-Tin-Noe (HBS '13) CEO and co-founder MBA Admissions Advisors LLC www.mbaadmissionsadvisors.com Get an immediate assessment of your odds at top MBA programs, try our algorithm for free: http://www.mbaadmissionsadvisors.com/mba-matching-algorithm/ Thanked by: gmat_thingie mm077241 Newbie | Next Rank: 10 Posts Joined 04 Jan 2015 Posted: 1 messages Sun Jan 04, 2015 11:20 am I applied to HSW this year and managed to get an admit from HBS. I reached out to several consulting firms before I started the process. Despite the fact I was very late in the process, Stacy Blackman matched me with a consultant who has an excellent track record for HBS and GSB - Paul Kang. Not only Paul is a GSB and Harvard alumnus, he has also served as the admissions committee member at GSB. This added real practicality to my application. Paul was instrumental in pushing me hard to think about my own life - what I have achieved so far, what I am as a person, what do I want to do in life and why, how would I want to do it, etc., and use all of this to present my story to the B-schools. The biggest advantage of working with Paul, unlike few other consultants, is that he would never force his thinking upon you or write the essay for you. He would always be ready to help you think and write, and to review and improve the same. He would never say no to you even if you send the nth version of the essay. He is always ready to get on a call with you to discuss any small or big thing. Paul also helped me fit my application process into timelines and adhere to the same - else it would have been extremely difficult given the work load I had. Moreover, the final essay I submitted with Paul's help was much better that what I could have submitted on my own. I am truly grateful to Paul for his support in the process and highly recommend him to be consulted, esp. on HSW applications - he is the HSW guru! manyaabroadtpr Master | Next Rank: 500 Posts Joined 17 Feb 2014 Posted: 321 messages Followed by: 12 members Thanked: 41 times Wed Jan 07, 2015 9:34 pm Hi Taviboo, In order to select the best institute for your MBA admission consulting services, we would suggest you to walk over to all centers of various companies located closer to your home. You can either speak to their expert counselor or even appear for a mock test with them. Ask all your queries, doubts and the one with whom you feel most satisfied should be your ideal choice. We at Manya provide you all the guidance required starting from the preparation for your GMAT, till you get admitted to your dream college.For Princeton Review's (Manya Abroad) MBA admissions consulting services, you can get all the information here: http://www.manyagroup.com/mba-admissions Hope this helps.In case, you would have any further queries, please do let us know and we would be happy to help. Wish you the best. www.manyagroup.com pjp89 Newbie | Next Rank: 10 Posts Joined 16 Jan 2015 Posted: 2 messages Fri Jan 16, 2015 9:19 am I looked into ALL of the consulting services and conducted assessments/calls with all of them. I ultimately liked how comprehensive and structured Stacy Blackman was. On top of having a dedicated consultant to help me along the way, they have school guides, interview guides, essay guides, etc. I worked with Paul on my MBA application process and was very pleased with everything. SBC has all the resources you could possibly need and really helped me feel confident in my applications. Paul was extremely knowledgeable about the admissions process for all of the top schools I wanted to go to. Thanks to his help, I was admitted to HBS (my top choice!) and Booth and Wharton (both with significant merit scholarships). Paul was able to identify exactly what I should be highlighting in my essays and applications by having extensive conversations and brainstorming sessions with me. He gave me honest feedback and I felt extremely confident after submitting my applications and when interviewing. I come from a very typical background, studied finance at Wharton, completed 2 years of investment banking and 2 years of private equity and knew it would be really hard to differentiate myself. Paul was able to identify the pieces of my upbringing/experiences/etc. that could truly set me apart and I don't think I would have been able to do that on my own. I was surprised how many little questions/concerns/nuances came up throughout the process that I needed Paul's help to answer and don't think I would have managed the admissions process successfully without him. I definitely believe Paul was the edge I needed to earn an acceptance into HBS and highly recommend using him if you are looking for admittance into any top school. pjp89 Newbie | Next Rank: 10 Posts Joined 16 Jan 2015 Posted: 2 messages Fri Jan 16, 2015 9:19 am I looked into ALL of the consulting services and conducted assessments/calls with all of them. I ultimately liked how comprehensive and structured Stacy Blackman was. On top of having a dedicated consultant to help me along the way, they have school guides, interview guides, essay guides, etc. I worked with Paul on my MBA application process and was very pleased with everything. SBC has all the resources you could possibly need and really helped me feel confident in my applications. Paul was extremely knowledgeable about the admissions process for all of the top schools I wanted to go to. Thanks to his help, I was admitted to HBS (my top choice!) and Booth and Wharton (both with significant merit scholarships). Paul was able to identify exactly what I should be highlighting in my essays and applications by having extensive conversations and brainstorming sessions with me. He gave me honest feedback and I felt extremely confident after submitting my applications and when interviewing. I come from a very typical background, studied finance at Wharton, completed 2 years of investment banking and 2 years of private equity and knew it would be really hard to differentiate myself. Paul was able to identify the pieces of my upbringing/experiences/etc. that could truly set me apart and I don't think I would have been able to do that on my own. I was surprised how many little questions/concerns/nuances came up throughout the process that I needed Paul's help to answer and don't think I would have managed the admissions process successfully without him. I definitely believe Paul was the edge I needed to earn an acceptance into HBS and highly recommend using him if you are looking for admittance into any top school. polestarcap13 Newbie | Next Rank: 10 Posts Joined 19 Jan 2015 Posted: 1 messages Mon Jan 19, 2015 1:11 pm Stacy Blackman is the best consulting service! My experience with Stacy Blackman was amazing throughout the entire application process! Beginning with the application strategy, Bridget (my hand-selected personal consultant) and I worked closely to explore my past academic and professional experiences, areas of greatest strength and weakness, and personal passions in order to crystallize my ultimate goals. This process was critical to the overall application as it enabled me to become truly inspired by and motivated towards the MBA experience. Next, Bridget diligently assisted me in selecting the individual schools to which I would apply. This process was equally crucial as the level of wisdom and pragmatism provided by Stacy Blackman was undoubtedly a foundational element of my eventual success. Bridget also helped me work on my strategy around recommenders as deciding which recommenders to use where can be tricky, and more importantly, Stacy Blackman’s method enables applicants to provide recommenders with a clear and focused outline of one’s application strategy; this helps the recommenders provide the best and most impactful recommendation possible. Most importantly, Bridget worked tirelessly with me on the short answer questions, required essays, and optional essays for each school which I was partnering with Stacy Blackman on. I cannot overemphasize how necessary it is to have Stacy Blackman and someone like Bridget working with you on your essays. I am an excellent, well-above average analytical writer, and this is the one area that I had always excelled in academically. However, I can honestly say that my essays would have been an absolute disgrace without Bridget’s guidance. Throughout multiple drafts and rewrite processes, Bridget helped me hone my application strategy and goals into pointed, strategic, and impactful essays that clearly answered each question being asked, while maintaining a strong sense of my personal voice and being sure to always highlight the ever-critical topics of “why me” and “why this school”/”why this program”. And when it came time for the interview phase, Bridget was right there to prep me. However, one of the most valuable aspects of Stacy Blackman’s program is the way in which the application strategy and essay processes generate so much passion for the MBA experience and so much involvement with each school’s materials that you are already an expert on yourself and each school when it’s time for the interviews. For reference, I am a 26 year old male, I went to a top-20 liberal arts college and graduated with a low 3’s GPA (non-econ major), and took the GRE. However, with Stacy Blackman’s help, I will now be attending NYU Stern in the fall. I truly believe that without Bridget and Stacy Blackman’s assistance, I would not have gotten into Stern or the multiple other programs I was admitted to. Lastly, one top-20 program offered me a$48k merit scholarship, which would equate to an 800% direct return on my Stacy Blackman investment (that completely disregards the near pricelessness of an MBA from such an institution)…if that’s not money well spent, then I don’t know what is!
cyberbg Newbie | Next Rank: 10 Posts
Joined
09 Oct 2014
Posted:
5 messages
Fri Jan 23, 2015 10:38 am
Here is how I came to work with her. After interviewing Stacey Blackman, Clear Admit and Stratus Prep for MBA admissions counseling, Shawn O’Connor, the founder of Stratus Prep, convinced me to use his firm.
I had obtained a 720 on my GMAT which was good, but below average for the 2 schools I had targeted: Stanford GSB and Harvard Business School.
Knowing those were the schools I wanted to apply to, Shawn placed me with a counselor who was an alum from both schools (NOT VANESSA).
And here I was… getting into the annoying process of business school applications. The first deadline was HBS in early September (Round 1). The counselor and I spent 3 months working on positioning, outlines and essays for Harvard. However, she and I didn’t have the same perspectives at times. Every time I came up with a creative idea for my essays, I got turned down. I felt my application was going to be pretty standardized. Another thing she would do was coming back to me with edits within 10 minutes of me sending my drafts. This annoyed me as I had paid a pretty big amount to get her advice, and I felt I wasn’t getting the level of attention I deserved. I was disappointed and thought I would ask Shawn for another counselor. However, I had less than 2 weeks left before submitting HBS and I thought I wouldn’t that risk so close to the deadline so I decided to stick with her and apply to HBS.
The day after I submitted HBS, however, I asked Shawn to reassign me with a different counselor for my Stanford app which was due 3 weeks later (early October, Round 1). By doing so, I also thought I would diversify and increase my odds of getting into at least one of the two.
Shawn understood my concerns and paired me with Vanessa Gil. And here comes Vanessa. I didn’t know it at the time, but working with Vanessa was the best thing that could have happened to me. Vanessa and I got along immediately. I told her about my concerns with my former counselor and she gave me the ability to be my true self in my applications. She and I spent hours on the phone discussing the most detailed items of my application from positioning, wording, approach, what works and what doesn’t to what Stanford specifically likes in candidates. Literally everything. She was so accessible, nice, competent and open-minded. It was night and day.
Vanessa and I worked hard in those 3 weeks I worked on my GSB application. I found out later on that she had a lot more clients than I thought. Yet I felt like I was the only one she was working with. The level of attention she gave me was unparalleled. She understood who I was as a person, what I stood for, and what I wanted to convey in my applications like no one else. Her perspective was invaluable.
Vanessa and I finally submitted Stanford early October.
Mid-October, I found out I got declined from HBS, without an interview.
Early November, I got notice that I got an interview with the GSB. Vanessa and I prepped for it in a rigorous manner with 3 mock interviews and detailed question by question feedback. I went into the interview feeling confident, and aced it.
Mid-December: I found out I got into my dream school, the Stanford GSB
The bottom line is that none of this would have been possible without Vanessa. Her trusted advice, intelligence and amazing personality made this stressful process an enjoyable experience. When you think about it, Vanessa only helped me with one business school, and it turns out that the school is actually the hardest one to get into. With Vanessa, my hit rate was 100%. I know, “impressive” you would say. However, the minute you meet her, you will realize it’s not all that surprising. Vanessa is an unbelievable person who simply gets it. If you’re driven, focused and dedicated, she will get you into your dream school. That’s what she does, and she does it better than anyone else in the industry.
cyberbg Newbie | Next Rank: 10 Posts
Joined
09 Oct 2014
Posted:
5 messages
Fri Jan 23, 2015 10:41 am
Vanessa Gil, who isn't with Stratus Prep anymore, is the best admissions counselor anyone could ask for!
Here is how I came to work with her. After interviewing Stacey Blackman, Clear Admit and Stratus Prep for MBA admissions counseling, Shawn O’Connor, the founder of Stratus Prep, convinced me to use his firm.
I had obtained a 720 on my GMAT which was good, but below average for the 2 schools I had targeted: Stanford GSB and Harvard Business School.
Knowing those were the schools I wanted to apply to, Shawn placed me with a counselor who was an alum from both schools (NOT VANESSA).
And here I was… getting into the annoying process of business school applications. The first deadline was HBS in early September (Round 1). The counselor and I spent 3 months working on positioning, outlines and essays for Harvard. However, she and I didn’t have the same perspectives at times. Every time I came up with a creative idea for my essays, I got turned down. I felt my application was going to be pretty standardized. Another thing she would do was coming back to me with edits within 10 minutes of me sending my drafts. This annoyed me as I had paid a pretty big amount to get her advice, and I felt I wasn’t getting the level of attention I deserved. I was disappointed and thought I would ask Shawn for another counselor. However, I had less than 2 weeks left before submitting HBS and I thought I wouldn’t that risk so close to the deadline so I decided to stick with her and apply to HBS.
The day after I submitted HBS, however, I asked Shawn to reassign me with a different counselor for my Stanford app which was due 3 weeks later (early October, Round 1). By doing so, I also thought I would diversify and increase my odds of getting into at least one of the two.
Shawn understood my concerns and paired me with Vanessa Gil. And here comes Vanessa. I didn’t know it at the time, but working with Vanessa was the best thing that could have happened to me. Vanessa and I got along immediately. I told her about my concerns with my former counselor and she gave me the ability to be my true self in my applications. She and I spent hours on the phone discussing the most detailed items of my application from positioning, wording, approach, what works and what doesn’t to what Stanford specifically likes in candidates. Literally everything. She was so accessible, nice, competent and open-minded. It was night and day.
Vanessa and I worked hard in those 3 weeks I worked on my GSB application. I found out later on that she had a lot more clients than I thought. Yet I felt like I was the only one she was working with. The level of attention she gave me was unparalleled. She understood who I was as a person, what I stood for, and what I wanted to convey in my applications like no one else. Her perspective was invaluable.
Vanessa and I finally submitted Stanford early October.
Mid-October, I found out I got declined from HBS, without an interview.
Early November, I got notice that I got an interview with the GSB. Vanessa and I prepped for it in a rigorous manner with 3 mock interviews and detailed question by question feedback. I went into the interview feeling confident, and aced it.
Mid-December: I found out I got into my dream school, the Stanford GSB
The bottom line is that none of this would have been possible without Vanessa. Her trusted advice, intelligence and amazing personality made this stressful process an enjoyable experience. When you think about it, Vanessa only helped me with one business school, and it turns out that the school is actually the hardest one to get into. With Vanessa, my hit rate was 100%. I know, “impressive” you would say. However, the minute you meet her, you will realize it’s not all that surprising. Vanessa is an unbelievable person who simply gets it. If you’re driven, focused and dedicated, she will get you into your dream school. That’s what she does, and she does it better than anyone else in the industry.
Hitoshi Newbie | Next Rank: 10 Posts
Joined
26 Mar 2015
Posted:
1 messages
Thu Mar 26, 2015 1:27 am
I was very lucky to find Laura Freedman, an MBA Admissions Consultant at Access Education (www.accesseducation.com), through a random Google search a few months ago. Although I was applying for a Master’s degree at NUS (National University of Singapore) and not an MBA, Laura transformed my resume and prepared me extremely well for my interviews (she actually designed NUS MBA’s interview process and evaluation form). She also guided me though the whole admissions process to by advising me how to cover my weak GMAT score and make me look attractive to NUS’s admissions team. As I was a last-minute applicant, I especially appreciated her strategic advice and efficient consultation on the back of very detailed background information. I highly recommend Laura for anyone applying to any business-related Master’s programs.
usmody Newbie | Next Rank: 10 Posts
Joined
15 Aug 2012
Posted:
1 messages
Sat Mar 28, 2015 4:06 pm
Please read this carefully as I hope no one makes the same mistakes I did!
I decided in the Summer of 2013 that I wanted to attend business school. Studied, took the GMAT, was thrilled with my 730 score and applied to a few schools only. Unfortunately, because of my engineering background and aspirations to start my own tech company, I wrote essays that highlighted anything but what a business school was looking for. Seeking help but not wanting to pay too much, I found a consulting company that offered help for very little money relative to the others. I got what I paid for, which was another set of rejection letters due to another horribly prepared application.
As it was already late October, I did not have much time but was determined to go to business school. I reached out to Stacy Blackman Consulting and paid the fees to become a comprehensive client. My SBC consultant, Chi-Pei, immediately reached out to me and took 2 hours learning every minute detail of my life. She literally left no rock un-turned. Within 48 hours she provided me with a thorough plan of attack, filled with essay topics and deadlines and schools I should consider applying to.
I'll be honest, I am a terrible writer (if you can't tell already). I must have sent Chi-Pei over 50 rough drafts for various essays before she finally approved. Each time, she was quick to reply.. sometimes within the hour. When I finally submitted my applications, my essays looked fantastic. Actually, everything looked fantastic! My resume was spotless, my extra-curricular activities portrayed me in a positive and accurate light, and short term/long term goals were so clear anyone could understand where I was going.
After receiving notifications for interviews, Chi-Pei met with me in person to make sure my responses to hypothetical questions were perfect. Everything was critiqued, from posture to tone to the appropriateness of my answers.
I recently was admitted to Michigan (Ross) and Virginia (Darden), and was offered a scholarship from Cornell (Johnson), Texas (McCombs) and Carnegie Mellon (Tepper). I am so glad I finally woke up and used SBC to help me through my application process. My only regret, obviously, is that I did not reach out to them prior to applying the first time.
usmabama Junior | Next Rank: 30 Posts
Joined
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Posted:
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Thanked:
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Mon Apr 06, 2015 9:24 am
Critical Square will take your application to the next level. With their help I went from WLed at Duke in Round 1 to accepted with scholarship at Darden in Round 2. I consider Fuqua and Darden to be peer schools and wouldn't have been nearly as successful in Round 2 without Critical Square's help.
I originally contacted several consultants in the Spring/Summer before I was to apply to business school. After a few free consultations, I concluded that given enough time I could craft a compelling story on my own and that spending a few thousand dollars on a consultant was unnecessary. I spent months writing my essays making sure each part of my application was polished. The result? I was rejected from all the schools I applied to in round one with the lone exception being Fuqua, where I was wait-listed. I was heart broken and a little unsure on what I should do next.
After returning from a Christmas trip in the Caribbean (where I was when I received the depressing news), I spent some time weighing my options. On a Saturday- December 27th - I used the GMAT Club website to post an urgent message asking for help. I received a response from Bhavik in less than 30 minutes - he remembered me from our free consultation the summer before. I sent Bhavik all my Duke documentation Saturday night and we set-up a wait-list review early Monday morning. The conversation lasted almost two hours and was very in-depth. Bhavik was blunt - he pointed out shortcomings in my application and thoroughly answered each of my questions. With Round 2 deadlines rapidly approaching, Bhavik informed me that he could only provide support on an hourly, a la-carte basis. As a military veteran who wanted a "civilian's" perspective and given my condensed timeline, I decided to purchase the hourly package from Critical Square.
Despite the fact that I had purchased only an hourly service, Critical Square helped me come up with a detailed round 2 game-plan and redo every aspect of my application for four different business schools. Because Round 2 deadlines were less than a week away I was really pressed for time, but Bhavik is a machine. I really don't know when the guy sleeps. I worked non stop all week on my applications and every time I sent Bhavik an updated essay or short answer to review he would respond in less than two hours - regardless of the time of day or day of the week. Each response would have detailed instructions on how to further shape the essay and would often include subtle changes that really took my applications to another level. During the process, it was also reassuring to have someone with limited military experience review my application. When Bhavik didn't understand military jargon he would call me to discuss and then we would reword the story to ensure that the key points I wanted to emphasize were obvious to the ADCOM.
The Round 2 results? I received interview invites to all four schools we applied to during that first week. I was accepted to three and received a significant scholarship to two. The only school of the four I wasn't accepted to was Yale, where I was wait-listed. I think that was due to my terrible on campus interview. I didn't use Critical Square for the interview prep, but wish I had.
If I could go back to last Spring I would purchase a more in-depth package from Critical Square. I'm extremely pleased to be attending Darden this fall, but I'm confident that if I had given Critical Square more time I would've been accepted to a top 7 school. They are a joy to work with and really understand the intricacies of what makes an application stand out in the crowd. I've already suggested Critical Square to several peers and would strongly recommend applicants spend the extra cash. It's a wise investment. A few thousand dollars now might result in tens of thousands of dollars in awarded scholarships. Thanks to Critical Square - it did for me.
Humstudents Junior | Next Rank: 30 Posts
Joined
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Followed by:
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Wed Apr 08, 2015 11:30 pm
money9111 wrote:
This is really very good post and perfect reply to find consultant for MBA.Its also really beneficial for me.
cshelton Newbie | Next Rank: 10 Posts
Joined
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Posted:
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See More Top Beat The GMAT Experts | 2017-10-21 11:56:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18185339868068695, "perplexity": 2847.3142337207973}, "config": {"markdown_headings": true, "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-2017-43/segments/1508187824775.99/warc/CC-MAIN-20171021114851-20171021134851-00457.warc.gz"} |
http://clay6.com/qa/jee-main-aipmt/jeemain-past-papers/1998 | Recent questions and answers in 1998
The locus of point of intersection of perpendicular tangents to the circle $x^2+y^2=a^2$ is:
To see more, click for all the questions in this category. | 2020-08-07 18:15:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22140440344810486, "perplexity": 281.9302287105105}, "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-2020-34/segments/1596439737206.16/warc/CC-MAIN-20200807172851-20200807202851-00200.warc.gz"} |
https://mathoverflow.net/questions/386182/positivity-of-schur-elements-in-iwahori-hecke-algebras/386606 | # Positivity of Schur elements in Iwahori-Hecke algebras
I'm interested in finite Iwahori-Hecke algebras.
If $$\mathcal{H}$$ is such a Hecke algebra, defined over $$\mathbb{Z}[q^{\pm 1/2}]$$, and $$\Lambda$$ an irreductible representation, there is the notion of a Schur element $$S_\Lambda$$. Roughly speaking, to $$\Lambda$$ you can associate a central element whose matrix in $$\Lambda$$ is given by $$S_\Lambda$$ times the identity.
I computed several of these Schur elements in type $$A_n$$ and I noticed a remarkable positivity property: all the coefficients in $$q$$ seem to be positive (see below)! I looked up in the literature, but I don't find explicitely this property.
Is there a concrete reference for this positivity? Does it hold in other types?
Here a small list of Schur elements:
• For $$\mathfrak{sl}_2$$: $$1+q$$, $$1+q^{-1}$$
• For $$\mathfrak{sl}_3$$: $$q+1+q^{-1}$$, $$1+2q+2q^2+q^3$$, $$1+2q^{-1}+2q^{-2}+q^{-3}$$
• For $$\mathfrak{sl}_4$$: $$[4]!$$ (quantum factorial), $$q^2+3q+4+3q^{-1}+q^{-2}$$, $$q^{-1}+2+2q+2q^2+q^3$$, ...
• How does one compute these? Is there a formula, or similar that you can reference? Mar 11, 2021 at 19:00
• The representation $\Lambda$ is given by a left cell (at least in case $A_n$). Let $(C_w)$ denote the Kazhdan-Lusztig basis and let $(C^w)$ denote its dual basis, such that $tr (C_wC^v) = \delta_w^v$ where you use the standard trace. Now, for a given left cell $\Lambda$, the element $Z_\Lambda=\sum_{x\in \Lambda}C_xC^x$ is central in $\mathcal{H}$. Its action on $\Lambda$ gives the Schuer element $S_\Lambda$. There is also a formula, given in Neunhöffers article sciencedirect.com/science/article/pii/S0021869306001955, Definition 5.1. Mar 12, 2021 at 8:42
• Of course you are no doubt aware of this, but there are many positivity phenomena in Kazhdan-Lusztig theory (e.g. arxiv.org/abs/1212.0791). Mar 12, 2021 at 13:22
• In type A, the Schur element is a q-deformation of the product of the hook lengths. I would then naturally expect the Schur element to be the product of the corresponding quantum integers. Mar 13, 2021 at 4:54
• @PeterMcNamara: This is great! It seems indeed that the Schur elements are the produt of the quantum integers of the hook lengths. Is there a similar interpretation in other types? Mar 13, 2021 at 16:54
The Schur elements are positive in all classical types $$A_n, B_n$$ and $$D_n$$ (use the formula of Theorem 4.3. in https://hal.archives-ouvertes.fr/tel-01411063/document, which uses generalized hook lengths). For dihedral groups $$I_2(m)$$, Theorem 8.3.4. in the book of Geck-Pfeiffer on characters of finite Coxeter groups and Hecke algebras shows that the Schur elements have negative coefficients for $$m>4$$. For the exceptional cases, by brute force, there are Schur elements with negative coefficients only in type $$H_4, F_4$$ and $$E_8$$. | 2022-08-11 01:52:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 26, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8870575428009033, "perplexity": 405.1101916002302}, "config": {"markdown_headings": true, "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-2022-33/segments/1659882571232.43/warc/CC-MAIN-20220811012302-20220811042302-00196.warc.gz"} |
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# Scientific Realism as an Intepretation of Science
✅ Paper Type: Free Essay ✅ Subject: Philosophy ✅ Wordcount: 4154 words ✅ Published: 23rd Sep 2019
Introduction
in philosophy the debate on science is to what extent we need to discover the truths. This debate on the extent of the truth that is required to be discovered is more important when it comes to theoretical scientific theories especially theoretical physics. this part of physics which is defined recently couldn’t be seen or experimented. Instead it’s more like mathematical aspect of physics which does work out to define many different things, such as the most recent one string theory. some Philosophical interpretation however, doubts the reason for existence of this kind of theories which are more mathematical than experimental. For instance, scientific realists argue that all facts deserve to be discovered however constructive empiricism argue that facts are important when they empirically adequate and whether they can predict observable phenomena correctly. constructive empiricism which was developed by bas van Fraassen is not the best choice for theoretical physics since he didn’t admire metaphysical phenomena. So there seems to be a problem in definition of truth in between this two philosophical point of view which, one is based on realism and the other however opposes realism, logical empiricism and instrumentalism in at least one fundamental view. In this essay I want to argue that all facts need to be discovered and there’s no difference between them if they’re observable or unobservable, which means I argue for scientific realism against constructive empiricism in terms of recently discovered sciences specially string theory.
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One of the other places where these two ideas clash is for instance, if we have phenomena ‘A’ and this phenomena has two different explanation as called ‘B’ and ‘C’, scientific realism would argue that one of the explanations is more true (if they seem the same we haven’t discovered the case which one will work and other won’t) therefore that is what we should use instead of the other one however constructive empiricist would argue that they are exactly the same and they have same use as long as they can predict correctly therefore they might prefer one over another if has simpler maths or other reasons but in their eye they are exactly the same. One of the cases which we can see the same things happening is in wave and particle characteristics of light where the maths can work in both ways and they both have valid observations to prove the phenomena and theory however it’s more efficient for people to use the wave characteristics of light as the maths that is used is far easier than in particle characteristics.
## Scientific realism and constructive empiricism with applied string theory
Both ideas of scientific realism and constructive empiricism are trying to give the best interpretation for science and how to encounter new scientific theories. In my opinion science should be defined as the discovery of true reasons for all phenomena in universe, therefore the true aim of science is to describe universe completely.
### Scientific realism
Scientific realism is epistemically positive view toward the content of scientific knowledge which recommend belief in both observable and unobservable world produces best theory which shows the metaphysical aspect of the scientific realism. Moreover, there are two other aspect for this aspect. One is called semantic and the other is epistemological aspect. Also, it aims for theories which are demonstrated as truth or approximate truth about observable and/or unobservable world (in this case old theories are grouped as approximate truth because although they were not completely true, but they were partially true) and these theories are called as best scientific theories as in scientific realist view. In common words scientific realism is based on a realistic view on the way universe works and to explain all observable and unobservable phenomena.
Metaphysical
Realism is having an argue on existence of the world being mind-independently which is in contrast with any theory which is based on idealism which according to it there is no external world rather than the world which human mind could think of. Idealism although is historically used but could rarely be seen in new theories. accepting that theories could be metaphysical is the most important property of scientific realism which opposes constructive empiricism.
Semantic
According to realism, scientific entity of the theory either observable or unobservable should have literally truth values whether true or false. This aspect is in contrast with instrumentalism which explains all unobservable as instrument to predict world.
Epistemologically
Committed to the idea that theoretical claims form knowledge of the world which contrast sceptical which says even if theories could have metaphysical and semantic view but they’re not powerful enough to talk about that knowledge and in this case anti realists could argue against the fact that just observables are powerful enough to have definite theories about the knowledge.
believing in realism doesn’t mean you have to follow all 3 viewpoints, you can be a realist and just admire 1 or 2 of these viewpoints.
In a scientific realism view string theory could be explained completely. firstly it has all of scientific realism aspects which as a metaphysical we are having strings which are having quantum fluctuations in a 26 dimensional world also the nature of strings which are two dimensional and although they are infinitely thin but they have a length of meter long which is a mind independent world but also we can have a sign of string theory in really high energies which is far beyond the energy that could be produced by human right now but having that much energy is not mind independently which shows that this theory having both idealist and metaphysical aspects. In the other hand the whole theory is based on so called “theory of everything” which the whole idea is a theory that could describe the world which adequate the whole realism idea which is to describe the world and its phenomena.
Scientific Realism in my opinion could help to improve science constantly as allow science to have unobservable phenomena which we can predict mathematically instead of experimentally for instance one of the most important theories which have been discovered by Einstein was general relativity as we it was predicted mathematically before it can be experimented. general relativity lead to a better theory than Newtonian gravity, since it could predict accurately specially about high speed objects and also it could solve the problem with inaccurate calculation for mercury shift.
### Constructive empiricism
Constructive empiricism is a form of empiricism which means that the only way to gain knowledge is sensory experience and emphasis the role of sensory evidence in the formation of ideas. This idea was introduced by Bas Van Fraassen who was a Dutch American philosopher. in his opinion any it is impossible to acquire knowledge from unobservable phenomena. which means most of the theoretical physics discoveries that doesn’t have an experimental proof, cannot be categorized as science and they are not representing truth. The acceptance
Acceptance of a theory in Constructive empiricism involves only the belief that the theory empirically adequate. Which means the only way to accept a theory is to not have any sort of information beyond human mind and also theory must obey the semantic view which is discussed completely in scientific realism and although constructive empiricism is against scientific realism but still they both agree on the fact that a theory should agree with the semantic aspect.
The semantic aspect claims
1) The theory’s claims are genuine statements capable of truth or falsity.
2) Any literal construal of a theory cannot change the logical relationships among the entities claimed by the theory.[1]
Therefore, string theory doesn’t agree with constructive empiricism because it doesn’t empirically adequate because it’s a theory which is not yet have been tested or there’s no empirical evidence for it and the only way to have empirical evidence about it is to reach the required energy which is still for beyond from what we could reach. But in the other hand string theory actually agree with the semantic view because its claims are capable of truth or falsity.
In the other hand Van Fraassen conclude that observable is when something can be observed unaided, van Fraassen have made this point since two can understand an aided observation differently. However, this just applies to the subject of theory and not the whole theory.
To sum up, these two philosophical prospective argue on the true meaning of science. Scientific realism argue that everything needs to be discovered and the way we understand the theory does not matter as long as it can be proved in any way such as mathematically or experimentally. However, constructive empiricist would argue that the only theories that are defined as science are those that are observable, because the phenomena subjected to theory cannot be understand in two different ways.
In my opinion, scientific realism is better since it can improve science significantly with having same viewpoint about both observable and unobservable phenomena. With accepting unobservable phenomena as science, there is a chance of using the theories which predict them to improve our life. For instance, the idea of quantum computing which is based on an unobservable phenomenon however this idea is improving constantly until we can use it in future. However, within constructive empiricist view, this improvement in unobservable science and also applying it to a practical object cannot be done because the basic of quantum mechanics theory is not acceptable.
## Arguments for each philosophical view
the whole problem and debate between constructive empiricism and scientific realism can be summarized into “defining science” and “science’s aim”. however, there are many arguments for and against each one which are listed below.
### No miracle argument
This argument which is the most powerful motivation for realism claims the only explanation that renders the success of science to not be “a miracle” which means they need to have true description or approximately true description of the world, Therefore there wouldn’t be any explanation in science which will discuss a phenomena as a so called miracle and every theory will aim to describe the world completely which would not be the case for constructive empiricism, where any phenomena which isn’t mind independently should be called as miracle.
### Pessimistic induction
This argument which is against both scientific realism and constructive empiricism, more generally towards science, and it worries that under determination and inference to the best explanation are generally conceptual in nature. Therefore, as in history there were many theories which regarded as successful but by the time passed it’s found out that they were wrong and believed to be false therefore pessimistic induction claim that this will happen in a point of time for current theories so therefore they are still false. this argument in my opinion couldn’t be solved because there will be always new phenomena to understand and therefore new theories which make the old theories wrong. So, unless with having an infinite knowledge of phenomena we couldn’t solve this argument in science.
### Inference to the Best Explanation
This argument is for scientific realism against constructive empiricism. Inference to the Best Explanation holds that, out of potential explanations that we have for the same phenomena, we should conclude the best one is the true one. however, a constructive empiricist would conclude an unobservable explanation means that we’re claiming false for the explanation of our phenomena. this opinion is against the idea of “inference to the best explanation” which means constructive empiricism idea is against science in this case as one of science aims is to infer the Best Explanation. unlike constructive empiricism, scientific realism always argues for the best explanation whether it’s observable or unobservable.
### observable/ unobservable distinction
This argument is against constructive empiricism and the idea of observable in constructive empiricism. In constructive empiricism, one of the significant problems is the clarity of difference between observable and unobservable. this argument can be divided into two parts.
1) Some phenomena are observable with instruments such as a microscope, in this case if we assume that these data are unobservable then we have significant part of the science being disallowed. however, if we assume they’re observable then how are we sure about the data we’re getting since we’re not sure how accurate the instrument is as there is no possible way to measure it since we’re not able to observe the truth of what instrument is showing us.
2) Another argument is how to be sure what different people observe are exactly the same as there isn’t a possible way to know the way each person observes the world is the same as the other person.
### My argument
This argument is for scientific realism and against constructive empiricism. The idea of scientific realism gives us more chance to discover more phenomena. By having more information that can predict the universe, it’s possible to use those prediction and understandings in terms of improvement. However, by just discovering observable phenomena, we wouldn’t have as much knowledge, which means there would be less improvement. Constructive empiricism also makes our knowledge more limited than it is.
In my opinion scientific realism is a better interpretation for science. Firstly, because it allows both observable and unobservable phenomena and doesn’t refer to unobservable as miracle, which in my opinion is against the true meaning of science. Secondly, because it infers that the best interpretation is the true one and thirdly, it doesn’t limit the extent of science and with scientific interpretation it’s possible to define anything however by constructive empiricism we can just define what is observable.
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## String theory
To talk about string theory, we first need to have knowledge about general relativity and quantum mechanics. General relativity was introduced by Einstein where heavy masses can distort space-time which is the reason for gravity and he proved it first mathematically in 1905 and then the experiments showed the same data in 1919 for light bending around large masses which strengthen the proof. By introducing general relativity, the whole idea of old Newtonian gravity was disproven where each mass can exert force on other mass relative to their masses and $\frac{1}{{r}^{2}}$
. In the other hand the theory of quantum mechanics was initiated with young slit experiment and improved by Heisenberg to produce the idea of uncertainty. However general relativity and quantum mechanics which are the basis of the modern physics cannot unite together to make a complete theory for physics as one has theorised the world of large masses and the other is about very small scales. So, there was a need of a theory to match up these two theories. In this case theoretical physicists came up with an idea which could be found in both real life and quantum ideas which is a string, they came up with an idea which was to assume the very fundamental form in a material is a string which can end up making both quantum mechanics and relativity to work but the biggest issue is that was, for the maths to work we needed 26 dimensions.
Primary goal of string theory was to describe the strong interaction which was due to nuclear strong force but with improvements in quantum chromodynamics it’s been left as an idea. Until 1980’s which it started to be used for uniting gravity and also to describe many of the problems in supergravity theory. In this theory it’s been told that the most fundamental form in a material its strings not a particle. These strings are ${10}^{–35}$
meter long which is Planck length and the tension in these strings are in order of Planck force which is ${10}^{44}$
newton and infinitely thin and end of them are connected to branes.
Branes are physical objects which generalize notion of point particles to higher dimensions. By rules of quantum mechanics branes can propagate through space-time. Branes just have spatial dimensions also they can have mass and charge.
The strings in string theory have quantum fluctuations. These fluctuations which cause vibrational modes are the reason for different properties of particles.
There are two different theories which are more common than others in string theory
1) Bosonic string: the minimum amount of vibration allowed by quantum uncertainty is called “zero-point energy”. Every new dimension allows more quantum fluctuations which allow another direction to explore for the string.so more directions mean more zero-point fluctuations. In bosonic string by balancing vibrations and irreducible zero-point quantum fluctuations turns out there are 26 dimensions is the number which cancel out with the amount of vibration therefore leads us to massless string
2) Superstring theory: superstring theory tries to explain the existence and movement of all the particles and fundamental forces of nature in one theory, by modelling them as vibrations of tiny supersymmetry strings. Unlike bosonic theory superstring theory accounts for both fermions and bosons, incorporating” supersymmetry” to model gravity. The most important thing about this theory is the fact that it cuts 26 dimensions to 10, therefore bringing new vibrational modes which allow strings to act like electrons (be their fundamental form). Superstring theory is more practical and realistic as it cuts out dimensions to just give ten dimensions required which one is temporal and nine of them are spatial.
As we can see there are many problems with string theory one is the problem with supersymmetry of string theory. For the mathematics of string theory to work, physicists have to assume a symmetry in nature called supersymmetry, which creates a correspondence between different types of particles. One problem with this is that instead of the 18 fundamental particles in the Standard Model, supersymmetry requires at least 36 fundamental particles.
Also, string theory failed to describe the accelerated expansion of universe which has been seen by astronomers. All these drawbacks and also the fact that string theory goal has been differed from what has been defined at the beginning caused theoretical physicists to rethink about the theory. I think although string theory might not be the actual truth, but it can lead us to the truth, as we have seen in the discovery of atom and the way it is where we started with theories which were completely wrong and getting closer and closer to the truth of structure of atom.
String theory is a complete unobservable phenomenon in terms of constructive empiricism, because of order of magnitude it theorised about and also the number of dimensions. Therefore, this shows that string theory is not acceptable by constructive empiricism. However, this is different for scientific realism since the theory fits with scientific realism interpretation. This shows that with having constructive empiricist interpretation it’s possible to miss many important theories which describe the universe therefore the idea of constructive empiricism in my opinion is against science
## Conclusion
The argues which was introduced above shows that scientific realism is a better interpretation of science than constructive empiricism. Also, by applying scientific realism on string theory it’s possible to see that scientific realism does allow this theory to be a part of science. In my opinion having theories such as string theory, apart from being true or false, can improve science because having such theories can raise more questions about universe. For instance, in this case we have the question of do we have more than 3 spatial dimension and time? Which is raised due to its mathematical proof which needs 26 dimensions. These questions always cause the science to improve more rapidly. As it’s possible to see in history that having a false theory wasn’t bad at all for instance the idea of determination of inside of a molecule and then inside of an atom which although the first few theories were wrong but by improving the old theories we reach better theories. Another problem with constructive empiricism is the no miracle argument which was stated above. I think calling anything unobservable phenomena a miracle which is just true and happens is against the nature of science, which in my opinion the definition of science is, discovery of true reasons for all phenomena in universe and the aim of science should be to describe the universe. However, this aim would not be possible with constructive empiricism however we could get closer to this aim by using a realist interpretation.
## Bibliography
1) Monton, B. & Mohler, C., 2017. Constructive Empiricism. Stanford Encyclopaedia of Philosophy. Available at: https://plato.stanford.edu/entries/constructive-empiricism/ [Accessed December 23, 2018].
2) Van Fraassen, B. (2004). The scientific image. Oxford: Oxford University Press.
3) Chakravartty, A., 2017. Scientific Realism. Stanford Encyclopaedia of Philosophy. Available at: https://plato.stanford.edu/entries/scientific-realism/[Accessed December 25, 2018].
4) Greene, B. (2000). Superstrings, hidden dimensions, and the quest for the ultimate theory. Vintage.
5) 5)Chalmers, A.F., 2011. What is this thing called science?, Buckingham: Open University Press.
6) Gubser, S.S., 2010. The little book of string theory, Princeton: Princeton University Press.
7) C., V.F.B., 1995. The scientific image, Oxford: Clarendon Press.
8) Bird, A. (2010). Philosophy of science. London: Routledge.
9) Hacking, J. (1983). Representing and intervening. Cambridge: Cambridge University Press.
10) Lipton, P. (2007). Inference to the best explanation. London: Routledge.
11) Feynman, R. (1981). Simulating Physics with Computers. [PDF] California: Department of Physics, California Institute of Technology. Available at: https://people.eecs.berkeley.edu/~christos/classics/Feynman.pdf [Accessed 2 Feb. 2019].
[1] 1) Monton, B. & Mohler, C., 2017. Constructive Empiricism. Stanford Encyclopaedia of Philosophy. Available at: https://plato.stanford.edu/entries/constructive-empiricism/ [Accessed December 23, 2018].
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Here"s exactly how you technique this kind of problem when you are stuck: you look for an easier problem of the very same sort, and also solve the instead, and also see if you find out anything the might help you through the genuine problem.
For example, how many ways space there to divide 2 civilization into teams of 2? Obviously just 1 way. That wasn"t much help.
So try a more tough one. How plenty of ways are there to divide 4 world into teams of 2? say the civilization are A, B, C, D. A must be matched through someone, and there room 3 people she can be suitable with. Climate the 2 unmatched people must be matched to each other, therefore the prize is 3.
Now how many ways are there to division 6 world into groups of 2? Again A have to be matched with someone, and there are 5 human being she could be suitable with, and then you room left v 4 people, and we understand from the previous paragraph that 4 human being can be matched in 3 ways, so the price is $5\cdot3 = 15$.
See more: Why Is Larry Hernandez In Jail : Singer Posts Bail For Kidnapping & Assault Case
Now you try it native there.
re-publishing
mention
monitor
answered might 15 "15 in ~ 2:32
ar wiki
MJD
$\endgroup$
4
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civicpride-kusatsu.netematics stack Exchange works finest with JavaScript allowed | 2022-08-14 10:13:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2038474828004837, "perplexity": 2622.8817218895615}, "config": {"markdown_headings": true, "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-2022-33/segments/1659882572021.17/warc/CC-MAIN-20220814083156-20220814113156-00754.warc.gz"} |
http://openstudy.com/updates/55ba6305e4b0746426deab1b | ## anonymous one year ago ...Easy Medal!! Simplify 4 to the 7th over 5 squared all raised to the 3rd power. 4 to the 10th over 5 to the 5th 4 to the 4th over 5 4 to the 21st over 5 to the 6th 12 to the 7th over 15 squared
1. anonymous
So is it like this? $\large \sf \huge ( \large \frac{4^{7}}{5^{2}} \huge ) ^{3}$
2. anonymous
yes
3. anonymous
4. anonymous
Then you would use the exponent rule: $\large \sf (b^{n})^m~=~b^{n \times m}$
5. anonymous
6. anonymous
$\large \sf (\frac{b^{n}}{a^{l}})^m~=~\frac{b^{n \times m}}{a^{l \times m}}$
7. anonymous
I don't get it
8. anonymous
That's not good
9. anonymous
.. | 2016-10-28 12:31:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8311524391174316, "perplexity": 5937.437986371084}, "config": {"markdown_headings": true, "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-2016-44/segments/1476988722459.85/warc/CC-MAIN-20161020183842-00196-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://socratic.org/featured/physics | # Make the internet a better place to learn
2
## What does wave refraction cause?
Mark C.
Featured 5 days ago
Generally, a change in both wavelength and velocity of the wave.
#### Explanation:
If we look at the wave equation we can get an algebraic understanding of it: $v = f \times \lambda$ where $\lambda$ is the wavelength. Clearly if v alters, either f or $\lambda$ must change. As the frequency is determined by the source of the waves, it remains constant. Due to conservation of momentum the direction alters (provided the waves are not at ${90}^{\circ}$)
Another way of understanding this is to consider the crests as being lines of soldiers - an analogy I’ve use during many times. The soldiers are marching at an angle (say ${45}^{\circ}$) from the concrete parade ground onto,the grass lawn. As they move onto the lawn each soldier slows down, this means the distance between those slower soldiers is reduced.
Look at the diagram below (imagining the wave crests as the soldiers) and you’ll see that because velocity falls, the wavelength changes too (and the direction of travel.) That means frequency must remain constant -
1
## Explain thermal expansion of water?
Mark C.
Featured 1 week ago
Like all materials, an increase in temperature (average non-translational kinetic energy of the particles) will cause them to increase the average distance between particles.
#### Explanation:
Particles have temporary forces between them due to mutual coulombic repulsion of the electron ‘clouds’ that surround them. As temperature rises the oscillation of the mass (effectively the nucleus) in the system becomes more violent hence occupy a larger effective volume.
So far, so normal, but water is unusual as a liquid because of the polarity (and relatively small size) of the molecule. This means the forces between particles can also include hydrogen bonding (still weak, temporary but a bond with both attractive and repulsive effects.) This means that water’s expansivity is unusually variable with temperature and reaches a minimum not at the freezing point, but at ${4}^{\circ}$C where it is most dense.
This provides some more detail on the data, but the anomalous effects in water are better explained here.
It truly is the weirdest fluid - but the one essential ingredient for life as far as we know.
1
## You push a crate full of nooks across the floor at a constant speed of 0.5 meter per second. You then remove some of the books and push exactly the same as you did before. How does the crate’s motion differ, if at all?
Gió
Featured 1 week ago
I would say that the crate now is accelerated.
#### Explanation:
During the first part you exert the exact force $\vec{F}$ to maintain the box in uniform motion, i.e., constant velocity (acceleration$= 0$). In doing so you are winning against kinetic friction ${f}_{k}$ but just! So your force and friction balance (almost) so that there is no acceleration but only constant velocity.
When you remove some books the box becomes lighter so that the normal reaction $N$ decreases as well reducing the contribution of kinetic friction. Now if you push with the same force as before you face less friction so that you get a component of force that gives you acceleration!
1
## The rise of a line in a distance-versus-time graph is 900 m aand the run is 3 min. What is the slope of the line?
Nimo N.
Featured 1 week ago
#### Explanation:
Anna found that the distance v.s. time graph has a slope of 900.
As you are likely aware, the general form for a linear equation is:
$y = m \cdot x + b$, where
y is the dependent variable (graphed on the vertical axis),
m is the slope of the line,
x is the independent variable, (graphed on the horizontal axis), and
b is the y-intercept, (the y-coordinate where the line crosses the vertical axis).
Then, an equation for your line would be:
$d = 300 \cdot t + b$.
However, the value of b most likely would be zero - if the movement started at rest, so the formula would likely be:
$d = 300 \cdot t$.
As to the choice of which of the two quantities, d or t, is the dependent variable, the formula for the slope tells the tale:
The rise for the slope is the numerator, representing a change in the vertical direction. So d is the dependent variable in the equation.
1
## Derive a relation between Torque and Moment of Inertia?
MetaPhysik
Featured 1 week ago
$I = {\tau}_{\text{net}} / \alpha$
#### Explanation:
Momentum of inertia is similar to mass in Newton's 2nd Law.
Mass is the inertia of an object in response to an unbalanced (net) force that causes the object to accelerate translationally.
$m = {F}_{\text{net}} / a$
Momentum of the inertia is the rotational inertia in response to an unbalanced (net) torque that causes the object to accelerate its rotation on an axis (i.e., angular acceleration).
$I = {\tau}_{\text{net}} / \alpha$
So it fact, it's like Newton's 2nd law for angular motion.
${F}_{\text{net}} = m a - -$ Newton's Second Law for translational motions.
${\tau}_{\text{net}} = I \alpha - -$Newton's Second Law for angular motions.
However, $I$ is more complex, it depends on mass of the object and the geometric shape rotating on its axis of rotation.
2
## The energy found in food that you eat is known as?
MetaPhysik
Featured 1 week ago
It's known as a Calorie, which is then stored as potential energy in the form of chemical bonds or chemical energy
#### Explanation:
The food that you eat is eventually broken down into three main typical of chemicals: carbohydrates, proteins(amino acids), and fats. The energy is stored in the chemical bonds of the these molecules. These molecules are eventually processed to make the energy molecules called ATP that provides energy that the body needs.
So food energy is also called chemical energy. Fundamentally, chemical bonds are electrical in origin, as molecules are made of nuclei with positive charge and electrons with negative charges. When chemical reactions happened, nuclei and electrons are reshuffled, giving up the electric potential energy stored in these molecules.
The pathways food into energy is best illustrated here.
2
## What are Gs? And why do they increase with speed?
Mark C.
Featured 1 week ago
Firstly, the previous answer (Steve’s) is correct, I just wanted to add something on the end in relation to speed.
#### Explanation:
For this to make sense you (probably) need to alter your understanding of how forces work a little.
When an object turns a corner, or moves in circular motion there only needs to be one force acting (there may be more, but only 1 is required) and that force is centripetal i.e. acting towards the centre of the circle. A good example is the orbit of the moon (for this argument, a circle) around the earth. The only force acting is gravity and that acts towards the earth (centre of mass, close to the earth, but again we’ll ignore that for now) causing it to accelerate.
Now, to develop this idea we need to clarify what we mean by an acceleration, and Newton’s 1st law. An object can have a speed in a straight line, but this tells you nothing about the direction of travel. For that, you need a concept called velocity which describes both the speed and direction (in Physics we call these vectors.)
Acceleration is defined as a change in velocity per unit time, and that allows either the speed or the direction to alter as time goes by. In other words, turning a corner at constant speed means you are accelerating (because the direction changes) and thus requires a net force. Newton’s 1st law states that an object will continue in uniform motion (a straight line at the same speed) unless acted upon by an external force. So if there is no net force, an object keeps going in the same direction at the same speed.
Secondly, why does this not tally with your experience of being in a car on a roundabout? You seem to feel a force outwards, that people call centrifugal, but is in fact just the effect of mass not wanting to change where it is (or where it is going) called inertia. Masses, in effect, resist acceleration, including turning their direction, and the greater the mass, the more resistance there is.
Now we can finally relate the question (say an F1 car taking a high speed turn) to the so called “g force” experienced by the driver. As the mass requires a force to turn it, given by $F = \frac{m {v}^{2}}{r}$. This shows that as speed increases the force required to turn the mass increases exponentially (as a squared term) and as the radius reduces (the turn on the track becomes ‘tighter’) so the force also rises. This required force (on a level track) comes from the friction between tyre and track and points inwards (centripetally) towards the inside of the turn.
The inertia of the mass (driver) creates an apparent force pointing outwards, but we now know this is just mass being “stubborn” and not willing to accelerate. This “force” is described in units of “g” or “G” to compare it to the force we experience as gravity, in other words in units of 9.81 Newtons for every kilogram of mass.
Sorry for the long answer, but it isn’t simple! Any clearer?
2
## A 6 kg shell is fired with a 30° angle,v= 40 m/s. At the highest point it devides into 2 parts,one 2 kg and the other 4 that move in the horizontal line and 2 kg hits the ground at the start point.where the 4 kg piece hits the ground?
ali ergin
Featured 5 days ago
$\text{please check the math operations.}$
#### Explanation:
• We will use the principle of momentum conservation to solve the problem.
• In the solution of the problem, we must assume that the conditions are ideal and that there is no energy loss.
• Suppose that C is the maximum height. At this point, the object instantaneously has only a horizontal velocity component.
• When the object is at point C, it only has instant horizontal momentum.
• momentum vector and direction are seen below.
$\vec{P} = m . {\vec{v}}_{x}$
$P = m v \cdot \cos \theta = 6 \cdot 40 \cdot 0.866 = 207.85 \text{ } k g \cdot m {s}^{-} 1$
• we have to rethink the momentum of each piece when the bullet is divided into two.
• the vectorial sum of the vertical momentum of the parts is zero.Because the bullet only had horizontal momentum.
• Both parts of the bullet must have horizontal momentum.
• The momentum vectors for the part are given below.
$\vec{P} = {\vec{P}}_{1} + {\vec{P}}_{2}$
• Because the first part is returned to its original position, the velocity of this part is equal to and opposite to the horizontal velocity component.
${P}_{1} = {m}_{1} v \cos \theta = 2 \cdot 40 \cdot 0.866 = 69.28 \text{ } k g . m {s}^{-} 1$
• We can find the momentum of the second part.
$207.85 = - 69.28 + {P}_{2}$
${P}_{2} = 207.85 + 69.28 = 277.13 \text{ } k g \cdot m {s}^{-} 1$
• Now we can find the velocity of the second part.
${P}_{2} = {m}_{2} {v}_{2}$
$277.13 = 4 {v}_{2}$
${v}_{2} = \frac{277.13}{4} = 69.28 \text{ } m {s}^{-} 1$
• Objects thrown horizontally from the same height reach equally long.
$t = \frac{{v}_{i} \cdot \sin \theta}{g} = \frac{40 \cdot 0.5}{9.81} = 2.04 \text{ } \sec$
$x = {v}_{i} \cdot t \cdot \cos \theta = 40 \cdot 2.04 \cdot 0.866 = 76.67 \text{ } m$
x_1=v_2*t=69.28*2.04=141 .33" "m
$A M = x + {x}_{1} = 76.67 + 141.33 = 218 \text{ } m$
• falls 218 meters from the point where it is thrown.
1
## What is difference between Newton law of gravitation and columbs law?
Mark C.
Featured 2 days ago
They are similar, in that they both have an inverse square relationship with distance, but Newton’s ULG concerns the effect mass has on other mass, and Coulomb’s law does the same for charges.
#### Explanation:
Newton’s Universal Law of Gravitation shows that mass is (very weakly) attracted to other masses, but because the value of the constant in this relationship (G) is very small, the effect is negligible until we consider masses in the billions of kilograms (moons, planets, stars etc.)
Newton didn’t explain everything in gravity - he would not even attempt to explain why mass should do this (hypothesis non fingo) nor did he find a value for G (that was Cavendish in 1798.) There also remains (unsolved) the reason why there is only ever an attractive force between masses (expressed as a negative sign in the equation, so that the force, $\vec{F}$ is always in the opposite direction to the distance, $\vec{r}$.)
The equation that bears Coulomb’s name is very similar in form, but allows for both positive (repulsive) and negative (attractive) force vectors between charges, as charges can be both of the same sign in charge (repulsive forces) or dissimilar (attractive forces between opposing charges.) In effect, Coulomb’s law is a version of Gauss’s law.
There is generally a factor of ${10}^{18}$ or so in the difference between the two forces (assuming unit masses and charges) with electrostatic forces greater in size than gravitational ones, so the size of the constants dominates these effects.
For reference, the two equations (in scalar form) are, $F = - G \frac{{m}_{1} \times {m}_{2}}{r} ^ 2$ with $G \approx 6.67 \times {10}^{-} 11 N {m}^{2} k {g}^{-} 2$ and $F = k \frac{{q}_{1} \times {q}_{2}}{r} ^ 2$ with $k \approx 8.99 \times {10}^{8} N {m}^{2} {C}^{-} 2$
1
## What is the bleeder current??
A08
Featured 2 days ago
For propose of safety, a bleeder resistor is connected in parallel with the output of a high-voltage power supply circuit. This resistor discharges the electric charge stored in the filter capacitor of the power supply when the load is switched off. Refer to the figure below.
Bleeder resistor provides the following safety features in the electronic power supplies
1. Acts as a fuse for excess voltage
2. Discharges the filter capacitors
3. Removes shock hazards to operating personal from induction coils
4. Eliminates ground-loop current
The $R C$ discharge current flowing through the bleeder resistor, when the equipment is in off state, is called bleeder current. Value of bleeder resistor will depend upon $R C$ time constant and how quickly one wants the filter capacitor to be discharged. | 2018-02-18 05:01:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 43, "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": 0.7048720717430115, "perplexity": 698.2746365616098}, "config": {"markdown_headings": true, "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-2018-09/segments/1518891811655.65/warc/CC-MAIN-20180218042652-20180218062652-00663.warc.gz"} |
https://polyscope.run/basics/parameters/ | # Parameters
Many structures and quantities in Polyscope have optional values which can be set to control their appearance or behavior, such as the radius of points in a point cloud or the color of a mesh. These values can generally be manually adjusted in the GUI, or set programmatically in code.
This page documents special features in Polyscope which provide extra functionality while setting these parameters.
## Persistent values
In Polyscope, if you manually set the color of points in a point cloud (for instance), then register a new point cloud with the same name overwriting the original, the new point cloud will inherit the old point cloud’s color. This functionality, and other similar behavior, is implemented via persistent values.
Persistent values are lightweight wrappers around a variable which on-construction look up the variable’s in a global cache, and if a cache entry exists take the cached value instead. Any time the variable is written to, its value is recorded in the global cache. Generally, the cache key includes the name of a structure (and quantity if applicable), so a cached variable will only be picked up when names match.
Generally, the user should not manually interact with persistent values ever, all you need to know is that some variables may “magically” remember their old values by pulling them from a cache.
PointCloud* psCloud = polyscope::getPointCloud("my cloud");
psCloud->setPointColor(glm::vec3(0.5, 0.5, 0.5));
// the persistent value is recorded in the cache
// ... later ...
PointCloud* newCloud = polyscope::registerPointCloud("my cloud", new_points);
// newCloud will automatically pick up the pointColor we set above,
// since this point cloud has the same name
Note that this persistence behavior applies even when variables are manually manipulated in the GUI.
for implementors
If writing custom Polyscope library code (e.g. your own custom structures and quantities), here’s what you need to know to use persistent values.
The class PersistentValue<T> is templated on the underlying scalar type, like PersistentValue<double>. Only a predefined set of types can be used as template arguments because the corresponding global cache must be allocated. See persistent_value.h for a listing, which currently includes bool, float, double, ScaledValue<float>, ScaledValue<double>, glm::vec3, and gl::ColorMapID.
Construct a persistent value like
PersistentValue<float> myVar("unique_name", 0.5)
the variable will the cached value if one exists, and if not take the value 0.5 (and add it to the cache). Remember to use a globally unique name for the for the name argument; in structures you can use a concatenation of the type name, structure name, and (if applicable) quantity name.
To access a persistent value, call myVar.get(), which returns a reference to the underlying value.
In some occasions, in particular when using ImGui, you may need to write to a value directly via the pointer from &myVar.get(). This is problematic, because the variable does not know it has been written to and thus needs to update the cache. The function myVar.manuallyUpdated() can be called to notify the persistent value that it needs to update the cache. The paradigm for using a persistent value with ImGui then looks like
if (ImGui::SliderFloat("some text", &myVar.get())) {
myVar.manuallyChanged();
}
## Scaled values
Specifying appearance (such as the radius of points in a point cloud) in global length units can be inconvenient; its generally much easier to set values relatively, which respect to some reasonable length scale. The ScaledValue type tracks such represents such values, if we set ScaledValue s = 7., then s.asAbsolute() will return 7. * state::lengthScale when used. Most length-valued parameters in Polyscope use this mechanism, and thus are relative by default.
using namespace polyscope;
PointCloud* psCloud = polyscope::getPointCloud("my cloud");
// radius will be 0.05 * lengthScale when used
psCloud->pointRadius = relativeValue(0.05); // shorthand, same as previous
psCloud->pointRadius = 0.05; // shorthand, same as previous
However, sometimes you might want to actually use an absolute value for a parameter, for instance to get exactly the same appearance between runs of a program on different data. To support that, scaled values can optionally be set as absolute values, which will not be scaled before use.
// radius will be 1.6 when used
psCloud->pointRadius = absoluteValue(1.6); // shorthand, same as previous
Note that scaled values can be (and often are) used as persistent values, as described above; the two concepts are complementary.
for implementors
If writing custom Polyscope library code (e.g. your own custom structures and quantities), here’s what you need to know to use scaled values.
The class ScaledValue<T> is templated on the scalar type, which basically just needs to support scalar multiplicaiton.
The examples above show how to construct scaled values as relative or absolute.
If you want to get the value represented by the ScaledValue as an absolute quantity, use ScaledValue<T>::asAbsolute(), which scales by state::lengthScale if the value is relative.
Use ScaledValue<T>::getValuePtr to get a pointer to the underlying T, for instance if using ImGui. A basic ImGui pattern to manipulate the variable looks like:
ImGui::SliderFloat("value ", value.getValuePtr());
If the value is a persistent scaled value, like PersistentValue<ScaledValue<float>>, it can be used like:
// example persistent scaled value
PersistentValue<ScaledValue<float>>> myVal("unique name", relativeValue(0.03));
// access
float myValInWorldCoords = myVal.get().asAbsolute();
// use with ImGUI
if (ImGui::SliderFloat("my val", myVal.get().getValuePtr())) {
myVal.manuallyChanged();
} | 2020-05-28 21:34:18 | {"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": 0, "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": 0.3905208706855774, "perplexity": 3125.7069642553765}, "config": {"markdown_headings": true, "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-2020-24/segments/1590347400101.39/warc/CC-MAIN-20200528201823-20200528231823-00325.warc.gz"} |
http://codereview.stackexchange.com/questions/21531/passing-multiple-parameters-from-the-command-line-in-java | # Passing multiple parameters from the command line in Java
I am working on a project in which I need to pass multiple arguments from the command line-
Below is the use case I have-
1. From the command line, I will be passing atleast four paramaters- noOfThreads, noOfTasks, startRange and tableName1, so if I am passing these four thing, then I need to store them in a variable and for any table names- I need to add it into the string list so that I can use them in my other code.
2. Secondly, I can pass five parameters instead of four just like above- So five parameters can be- noOfThreads, noOfTasks, startRange , tableName1 and tableName2. So here tableName2 is extra. so if I am passing these five thing, then I need to store them in a variable and here I am passing tableName1 and tableName2 as two tables so I will be storing these two tables in a string list.
3. Thirdly, I can pass six parameters instead of five just like above- So sixparameters can be- noOfThreads, noOfTasks, startRange , tableName1, tableName2 and tableName3. So here tableName3 is extra. so if I am passing these six thing, then I need to store them in a variable and here I am passing tableName1 , tableName2 and tableName3 as three tables so I will be storing these three tables in a string list again.
So for above scenario, I have the below code with me. It is looking very ugly currently as I have lot of repetition in my code as mentioned below. Is there any way I can make it more cleaner?
Below is my code-
private static List<String> databaseNames = new ArrayList<String>();
private static int startRange;
private static String tableName1;
private static String tableName2;
private static String tableName3;
public static void main(String[] args) {
if (args.length > 0 && args.length < 5) {
startRange = Integer.parseInt(args[2]);
tableName1 = args[3];
} else if (args.length > 0 && args.length < 6) {
startRange = Integer.parseInt(args[2]);
tableName1 = args[3];
tableName2 = args[4];
} else {
startRange = Integer.parseInt(args[2]);
tableName1 = args[3];
tableName2 = args[4];
tableName3 = args[5];
}
}
-
1. Extract out the common logic before the if. The following is more or less the same:
noOfThreads = Integer.parseInt(args[0]);
startRange = Integer.parseInt(args[2]);
tableName1 = args[3];
if (args.length >= 5) {
tableName2 = args[4];
}
if (args.length >= 6) {
tableName3 = args[5];
}
2. Note that running the program with less than five parameters only prints an exception:
Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 0
at ...Main.main(Main.java:16)
You should handle this and print a user friendly error message or usage help.
-
@Glenn Rogers: Thanks for the edit! – palacsint Feb 10 '13 at 7:41
It might be worth checking out Commons CLI. It's a library that handles complicated command-line arguments and provides a lot of nice stuff like pretty error messages and succinct ways of specifying optional vs required arguments. Right now, your code is probably borderline on whether it will actually be simplified by this addition, but it will definitely help those who are using your code, and it will be far easier to add or modify the arguments in the future.
-
+1 for the link – cl-r Feb 12 '13 at 7:39 | 2016-06-30 10:21:11 | {"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": 0, "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": 0.1727774292230606, "perplexity": 2713.6705962137908}, "config": {"markdown_headings": true, "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-2016-26/segments/1466783398516.82/warc/CC-MAIN-20160624154958-00010-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://lonavlaforum.org/articles/dee0fc-robustness-check-for-panel-data | ROBUSTNESS TESTS OF THE AUGMENTED SOLOW MODEL JONATHAN R. W. TEMPLE* Hertford College, Oxford OX] 3BW, and Institute of Economics and Statistics, Manor Road, Oxford OXI 3UL SUMMARY This paper demonstrates some techniques for testing the robustness of cross-section and panel data I want to conduct robustness check for a quadratic model and linear model with interaction variables. This article considers estimation of the dynamic linear panel data model, which often forms the basis of testable economic hypotheses. The question is how do I check for robustness in such model. %%EOF Does anyone know how I could use these commands or maybe another option to robustness checks? Panel data (also known as longitudinal or cross-sectional time-series data) is a dataset in which the behavior of entities are observed across time. x�b"7v )��π ��l,J����Đ���3!|�[ǰC[Y��w�G�'�%��%��T@��B��s��gNc��ڙ[�Z�\�t:k�����g�HMăE)�*f���,��Y�{�ai��W+ם�����^� �^�=�ȝ�z9f�+��so^���ڰ�����F����b��a����0F"�����::�� ���%@���b ���i�a3�#��ۂET����Ƀh �.�,�w̷45� �h&�7�6lfzg��1��@2a*��!���x�$8��� Ġr��K'�c�o�����J�� �"��ln�d�(����d��=����8�Y B +ٓl The estimators of such a model are frequently similarly based on certain assumptions which appear to be often untenable in practice. • The Random generator and Seed fields control the construction of the random subsamples required for the Fast-S algorithm. 0000003741 00000 n I want to conduct robustness check for a quadratic model and linear model with interaction variables. In line with our previous discussion, from now on we consider robustness check regressions where X j contains X 1. Transition from economic theory to a testable form of model invariably involves the use of certain "simplifying assumptions." 0000000756 00000 n However, a robust estimator across all experiments and parameter settings was a variant of the Wansbeek–Bekker estimator. Fourth, it is desi rable to use statistical me thods that are "robust" in the sense that they do not force conclusions that are inconsistent with the data, or rely too heavily on small parts of the data. Panel data looks like this country year Y X1 X2 X3 1 2000 6.0 7.8 5.8 1.3 1 2001 4.6 0.6 7.9 7.8 1 2002 9.4 2.1 5.4 1.1 It would be easy in a linear model which can be checked by adding/removing variables, however, in logit the coefficients would surely change size with the higher total amount of explained variation. If the coe¢ cients are plausible and robust, this is commonly interpreted as evidence of structural validity. 20 We specify a panel-VAR … Downloadable (with restrictions)! The major findings are that the limited tests readily available tend to have poor power properties and that estimators' performance varies greatly across scenarios. Among the studies on estimators for panel data, there are some which concern robustness with respect to heteroskedasticity and autocorrelation, as in Alvarez and Arellano (2004). 0000001779 00000 n In other words, it is an observation whose dependent-variablevalue is unusual given its value on the predictor variables. 2019 | Political Analysis, Vol. As a robustness test and in order to deal with potential issues of endogeneity bias, we also employ a panel-VAR model to examine the relationship between bank management preferences and various banking sector characteristics. 0000001449 00000 n 0000001321 00000 n 0000001815 00000 n 5, No. This approach relies on asymptotics, so large data sets work better here. Abstract A common exercise in empirical studies is a "robustness check," where the researcher examines how certain "core" regression coe¢ cient estimates behave when the regression speci–cation is modi–ed by adding or removing regressors. I include the state name, year, SDP per capita, and a number of conditioning variables such as Public Expenditure, Literacy, Rural Banks per Capita. We use cookies on this site to enhance your user experience. Robustness of the procedures is investigated by means of breakdown point computations and simulation experiments. Here, we study when and how one can infer structural validity from coe¢ cient robustness … 19 The main advantage of this methodology is that all variables enter as endogenous within a system of equations, which enables us to reveal the underlying causality among them. Transition from economic theory to a testable form of model invariably involves the use of certain "simplifying assumptions." Notes: calculations performed in EViews.! 8.2. 60! 0000011529 00000 n If, however, these are not valid, misspecified models result. 0000012442 00000 n 0000001957 00000 n Dear Statalisters, I encounter a few difficulties with regression diagnostics after a fixed effects regression with panel data (-xtreg, fe-). This book presents recent research on robustness in econometrics. 0000001631 00000 n By continuing to browse the site, you consent to the use of our cookies. Robust Estimation of Linear Fixed Effects Panel Data Models In cross-sectional regression analysis, three types of outliers can cause least squares to breakdown. 2.6.2 Robust Seemingly Unrelated Regression 2.6.3 A Monte Carlo Study 2.7 Conclusions VI Wagenvoort, Rien J.L.M. • With panel data we can control for : – Unobserved or unmeasurable sources of individual heterogeneity that vary across individuals but do not vary over time – omitted variable bias . Keywords: Panel data, Fixed effects, Robust estimation, M-estimation, Least squares 2010 MSC: 62M10, 62F35 1. Robustness checks involve reporting alternative specifications that test the same hypothesis. If the coefficients are plausible and robust, this is commonly interpreted as evidence of structural validity. Robustness checks for Pooled OLS, Fixed Effects, and GMM 1 I am investigating conditional convergence across Indian states using panel data. 1, 20 March 2017 | Econometrics, Vol. H��V�rSG��+fyo�4���t�I�b�U������H2��sz$[r6��[���=�u�\ �6��O�u-*���,Y���j9x�|��d���9��o ��[�Mj3���V}�. Table 5.22: Panel robustness check results (using H(-2) and H(-4) as explanatory variables and treating them as exogenous, lagged levels instrument for the LDV). Previous threads in Statalist give hints, but in some cases ambiguity remains. 0000015575 00000 n Check out this article for a comparison of approaches to dealing with autocorrelation in panel data: Bertrand, Marianne, Ester Duflo, and Sendhil Mullainathan. Its grouping structure allows to reflect the nested phenomena so that the characteristics of cross-sectional Here, the performance of these estimators is analyzed in scenarios where the theoretically required conditions are not met. Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal.Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters.One motivation is to produce statistical methods that are not unduly affected by outliers. 0000012031 00000 n > Ques 2: In order to check consistency, i applied Polled ols, fixed effect and random effct models of panel data, i have shown this in similar manner as given below in result and discussion chapter, but interpretation is based on most appropriate model. 0000001239 00000 n Now it's clear (to me, at least) that you're dealing with a panel dataset. You may the leave the Seed field blank, in which case EViews will use the clock to obtain a seed at the time of estimation, or you may provide an integer from 0 to 2,147,483,647. These entities could be states, companies, individuals, countries, etc. Residual: The difference between the predicted value (based on theregression equation) and the actual, observed value. A distinction between outlying blocks and cells in a panel is made. 0000011816 00000 n startxref other data and other studies, and avoiding complex or highly parametric formulations whose plausibility is difficult to check. xref 0000000016 00000 n In other words, a robust statistic is resistant to errors in the results. 203 0 obj <> endobj ∙ 0 ∙ share . The finite sample performances of the proposed estimators have been illustrated through an extensive simulation study as well as with an application to blood pressure data set. 205 0 obj<>stream Robust regression is an alternative to least squares regression when data is contaminated with outliers or influential observations and it can also be used for the purpose of detecting influential observations. This is a significant finding, as this estimator is infrequently used in practice. same individuals in multiple surveys over time; countries or districts over years; individuals over time; There are many different terms for repeated measurement data, including longitudinal, panel, and time-series cross-sectional data. In this paper, we stick to the simple fixed effects panel data model, and focus on robust alternatives to the Within Groups estimator. 0000004800 00000 n 203 23 If, however, these are not valid, misspecified models result. Outlier: In linear regression, an outlier is an observation withlarge residual. 0000004271 00000 n Hi, I want to perform robustness checks for my model. However Stata does not recognize this commands. Please check your inbox for the reset password link that is only valid for 24 hours. trailer This article considers estimation of the dynamic linear panel data model, which often forms the basis of testable economic hypotheses. Robust data processing techniques – i.e., techniques that yield results minimally affected by outliers – and their applications to real-life economic and financial situations are the main focus of this book. An outlier mayindicate a sample pecul… There are alternatives, including the block bootstrap. Is this appropriate? 0 > %PDF-1.4 %���� This article considers estimation of the dynamic linear panel data model, which often forms the basis of testable economic hypotheses. In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making meaningful statistical inferences. 0000008903 00000 n Introduction Panel data refers to the two-dimensional data in which cross-sectional units are observed over time. Rousseeuw and Leroy (1987) define them as vertical outliers, bad leverage points and good leverage points. 05/13/2020 ∙ by Beste Hamiye Beyaztas, et al. (1998), Robust estimation of panel data : with an application to investment equations European University Institute DOI: 10.2870/75660 > > Ques 3 Consistency check or Robustness check is same or different? 1, © 2020 World Scientific Publishing Co Pte Ltd, Nonlinear Science, Chaos & Dynamical Systems, https://doi.org/10.1142/S0217590809003409, Not so Harmless After All: The Fixed-Effects Model, Accuracy and Efficiency of Various GMM Inference Techniques in Dynamic Micro Panel Data Models, Determinants of Profitability: An Analysis of Large Australian Firms. Enter your email address below and we will send you the reset instructions, If the address matches an existing account you will receive an email with instructions to reset your password, Enter your email address below and we will send you your username, If the address matches an existing account you will receive an email with instructions to retrieve your username, Department of Econometrics and Business Statistics, Monash University, Clayton, Melbourne, Victoria 3800, Australia, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne, Australia, Erudite, Universite Paris XII, Paris, France. Table 5.23: Panel robustness check results (using H(-2) and H(-4) as explanatory variables and treating them as exogenous, lagged 27, No. Because the problem is with the hypothesis, the problem is not addressed with robustness checks. GLS for the robustness check regressions. 0000007470 00000 n Assuming that you have a large N, small T panel dataset and you're using -xtreg, fe-, both options -robust- and -cluster- do the same jobs and accomodate for heteroskedasticity and/or autocorrelation. Let’s begin our discussion on robust regression with some terms in linearregression. A common exercise in empirical studies is a “robustness check”, where the researcher examines how certain “core” regression coefficient estimates behave when the regression specification is modified by adding or removing regressors. Tugas Ekonometrika II Ifqi Khairunnisa dan Nadhia Shalehanti "Beberapa cara untuk menilai model data Panel Dinamis sudah robust." If, however, these are not valid, misspecified models result. When the experiments are extended to include correlations between observed and unobserved heterogeneity terms, one might also consider, for across-the-board performance, the Blundell and Bond estimator. Specifically, we consider three such instances of serial correlation of the idiosyncratic disturbance terms; correlation of the idiosyncratic disturbance terms and explanatory variables; and, finally, cross-sectional dependence (as a robustness check to these findings, we also consider correlations between observed and unobserved heterogeneity terms). endstream endobj 204 0 obj<> endobj 206 0 obj<>/Font<>>>/DA(/Helv 0 Tf 0 g )>> endobj 207 0 obj<> endobj 208 0 obj<>/Font<>/ProcSet[/PDF/Text]/ExtGState<>>> endobj 209 0 obj[/ICCBased 215 0 R] endobj 210 0 obj[/Separation/PANTONE#20286#20CV 209 0 R 216 0 R] endobj 211 0 obj<> endobj 212 0 obj<>stream • The use of panel data allows empirical tests of a wide range of hypotheses. 0000015886 00000 n In this work we propose a new, weighted likelihood based robust estimation procedure for linear panel data models with fixed and random effects. Our website is made possible by displaying certain online content using javascript. To show the potential of robust panel data methods, an empirical example on the response of the private sector behaviour to fiscal policy is presented. Robust Estimation for Linear Panel Data Models. The Clear button may be used to clear the seed used by a previously estimated … <<372c42009751d344ad7a6a11f482b113>]>> Peter: thanks for providing further details. 0000008536 00000 n 0000001880 00000 n I found out that the commands checkrob and rcheck could be used. Robust statistics, therefore, are any statistics that yield good performance when data is drawn from a wide range of probability distributions that are largely unaffected by outliers or small departures from model assumptions in a given dataset. In such a wide array of experiments, it is difficult to pick-out just one "winner." 2004. The book also discusses 0000008376 00000 n By panel data we will mean repeated measures for a unit, $$i \in 1, \dots, N$$, over time, $$t \in 1, \dots, T$$.
2020 robustness check for panel data | 2021-03-02 11:01:49 | {"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": 1, "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": 0.32571423053741455, "perplexity": 2219.4872181694536}, "config": {"markdown_headings": true, "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-2021-10/segments/1614178363809.24/warc/CC-MAIN-20210302095427-20210302125427-00243.warc.gz"} |
https://www.dmrguide.uk/index.php/dmr-simplex/70cm-simplex/ | # 70CM SIMPLEX
Below are both the official and unoffical simplex channels. Remember that DMR users are NOT to use the analogue calling channel – the correct calling channel for digital voice has been added to the list.
The 70Cm allocation is as follows
OFFICIAL
FREQOLDNEWDMRCOMMENTS
433.4SU16U272DU272FM / ASK
433.4125U273DU273
433.425SU17U274DU274
433.4375U275DU275
433.45SU18U276DU276
433.4625U277DU277
433.475SU19U278DU278
433.4875U279DU279
438.6125N/AN/ADU280DIGITAL CALLING CHANNEL
433.5125U281DU281
433.525SU21U282DU282
433.5375U283DU283
433.55SU22U284DU284
433.5625U285DU285
433.575SU23U286DU286
UNOFFICIAL
FREQOLDNEWDMRCOMMENTS
438.5875N/AN/ADH1
438.6N/AN/ADH2
438.6125N/AN/ADH3OFFICIAL DV CALLING CHANNEL
438.625N/AN/ADH4
438.6375N/AN/ADH5
438.65N/AN/ADH6
438.6625N/AN/ADH7
438.675N/AN/ADH8 | 2021-04-15 01:58:17 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9588947892189026, "perplexity": 13171.553576652455}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "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/1618038082988.39/warc/CC-MAIN-20210415005811-20210415035811-00142.warc.gz"} |
http://www.texample.net/tikz/examples/circuitikz/ | # Example: CircuiTikz - Easy electrical networks
Published 2008-11-03 | Author: Massimo Redaelli
CircuiTikz is a set of LaTeX macros designed to make it easy to draw electrical networks in scientific publications. It provides a convenient syntax based on to-paths to place the various components. The examples below are from the CircuiTikz examples page. The author of CircuiTikz is Massimo Readelli
To run the examples you need to download and install the CircuiTikz files first.
Note. The circuits library available in the CVS version of PGF is inspired by CircuiTikz.
Do you have a question regarding this example, TikZ or LaTeX in general? Just ask in the LaTeX Forum.
Oder frag auf Deutsch auf TeXwelt.de. En français: TeXnique.fr.
\documentclass{article}
\usepackage[symbols]{circuitikz}
\usepackage{tikz}
\begin{document}
\begin{circuitikz} \draw
(0,0) to[C, l=$10\micro\farad$] (0,2) -- (0,3)
to[R, l=$2.2\kilo\ohm$] (4,3) -- (4,2)
to[L, l=$12\milli\henry$, i=$i_1$] (4,0) -- (0,0)
(4,2) to[D*, *-*] (2,0) to [D*, -*] (0,2)
to[R, l=$1\kilo\ohm$] (2,2) to[cV, v=$0.3\kilo\ohm i_1$] (4,2)
(2,0) to[I, i=$1\milli\ampere$:15, -*] (2,2)
;
\end{circuitikz}
\begin{circuitikz} \draw
(0,0) node[ground] {}
to[V, v=$e(t)$, *-*] (0,2) to[C, l=$4\nano\farad$] (2,2)
to [R, l=$\frac{1}{4}\kilo\ohm$, *-*] (2,0)
(2,2) to[R, l=$1\kilo\ohm$] (4,2)
to[C, l=$2\nano\farad$:-90, *-*] (4,0)
(5,0) to[I, i=$a(t)$:-90, -*] (5,2) -- (4,2)
(0,0) -- (5,0)
(0,2) -- (0,3) to[L, l=$2\milli\henry$] (5,3) -- (5,2)
{[anchor=south east] (0,2) node {1} (2,2) node {2} (4,2) node {3}}
;\end{circuitikz}
\begin{circuitikz} \draw
(0,0) node[anchor=east]{B}
to[short, o-*] (1,0)
to[R, l=$20\ohm$, *-*] (1,2)
to [R, v=$v_x$, l=$10\ohm$] (3,2)
to[short] (4,2) to[cI, i=$\frac{\siemens}{5}v_x$, *-*] (4,0)
to[short] (3,0) to[R, l=$5\ohm$, *-*] (3,2)
(3,0) -- (1,0)
(1,2) to[short, *-o] (0,2)
node[anchor=east]{A}
;\end{circuitikz}
\begin{circuitikz} \draw
(0,2) to[I, i=$1\milli\ampere$] (2,2)
to [R, l=$2\kilo\ohm$:-90, *-*] (0,0)
to [R, l=$2\kilo\ohm$] (2,0)
to[V, v=$2\volt$:-90] (2,2)
to[cspst, l=$t_0$] (4,2) -- (4,1.5)
to [generic, l=1, i=$i_1$, v=$v_1$] (4,-.5) -- (4,-1)
(0,2) -- (0,-1) to[V, v=$4\volt$] (2,-1)
to [R, l=$1\kilo\ohm$] (4,-1);
\begin{scope}[xshift=7.5cm, yshift=.5cm]
\draw [->] (-2,0)--(2.5,0) node[anchor=west] {$v_1 [\volt]$};
\draw [->] (0,-2)--(0,2) node[anchor=west] {$i_1 [\milli\ampere]$} ;
\draw (-1,0) node[anchor=north] {-2} (1,0) node[anchor=south] {2}
(0,1) node[anchor=west] {4} (0,-1) node[anchor=east] {-4} (2,0)
node[anchor=north west] {4} (-1.5,0) node[anchor=south east] {-3};
\draw [thick]
(-2,-1) -- (-1,1) -- (1,-1) -- (2,0) -- (2.5,.5);
\draw [dotted]
(-1,1) -- (-1,0) (1,-1) -- (1,0) (-1,1) -- (0,1) (1,-1) -- (0,-1);
\end{scope}
\end{circuitikz}
\end{document}
• #1 Mary, July 5, 2009 at 7:36 p.m.
Hi!
Congratulations and thanks to the author by the package.
How do I get the motors in the circuit? I have not found this symbol
thank you very much
• #2 Kjell Magne Fauske, July 5, 2009 at 8:17 p.m.
• #3 versus.co.il, September 3, 2010 at 11:49 p.m.
бриллианты - низкие цены!! все самое лучшее только в Versus.co.il Зайди и убедись!! http://versus.co.il
• #4 Vesa Linja-aho, October 3, 2010 at 12:50 a.m.
Hi,
I had some problems with this example. First, I got an error message:
! LaTeX Error: Unknown option symbols' for packagecircuitikz'.
Then I looked at the documentation: http://mirror.ctan.org/graphics/pgf/contrib/circuitikz/doc/latex/circuitikz/circuitikzmanual.pdf
And noticed that "symbols"-option is obsolete. I removed it, but then I started having problems with those \micro\farad -stuff.
How to fix:
\usepackage[symbols]{circuitikz} changed to \usepackage[siunitx]{circuitikz}
Add \SI{}{}, for every component. Like this:
WRONG: [C, l=$10\micro\farad$]
FIXED: [C, l=$\SI{10}{\micro\farad}$]
• #5 Vesa Linja-aho, October 3, 2010 at 1:08 a.m.
Just figured out a simpler way: just edit the beginning of the file to:
\documentclass{article}
\usepackage[free-standing-units]{siunitx}
\usepackage{circuitikz}
\usepackage{tikz}
\begin{document}
• #6 François, January 1, 2012 at 1:59 p.m.
And I would add that now (2012) the "free-standing-units" option is also obsolete.
Now it works fine with this preamble:
\documentclass{article}
\usepackage{tikz} \usepackage{circuitikz} \usepackage{siunitx}
\begin{document}
• #7 Tiffany Hayes, February 10, 2012 at 11:40 p.m.
So you still need to use the \SI command I noticed. Also, I keep getting units under other circuit parts (but no errors from LaTex). Is there any way to just move the labels, or do I just need to enlarge the size of my circuit? I'm using the code as above, but with the \SI inserted as described above.
• #8 Dave, March 7, 2012 at 8:27 p.m.
Hey, is there a way to create a caption above a resistor and the related value below the resitor?
• #9 Anon, April 18, 2012 at 9:20 p.m.
I don't see how to download the CircuiTikz files - the links are 404 not found and it looks as though Massimo Redaelli does not exist at the faculty list of the Dipartimento di Elettronica e Informazione (DEI) website. Could someone who has the packages let me know?
• #10 Jannik, May 11, 2012 at 7:25 p.m.
Try http://www.ctan.org/tex-archive/graphics/pgf/contrib/circuitikz/tex/latex/circuitikz or your Tex Live Manager
• #11 Jeff Hein, May 31, 2012 at 2:51 a.m.
This is simply amazing! Thank you so much for your hard work!
• #12 Alex Mason, July 10, 2012 at 11:56 a.m.
Hi all
I have a slightly related issue with this to do with nodes.
In the documentation it says to use things like o_o or _ to produce nodes on the ends of components. However LaTeX gives the error that it does not know the keys o_o or _.
Perhaps they have been replaced or removed. Does anyone know?
• #13 fred, September 14, 2012 at 6:30 p.m.
Does anybody know if there is a circuit symbol for varistors,MOVs, or surge arrestors? Thanks
• #14 Charlie, October 17, 2012 at 8:41 p.m.
The links to the Circuitikz homepage are broken.
• #15 Tony, June 26, 2013 at 3:16 a.m.
The hollow circles at the end of a line is produced w/ -o (right), or o- (left), per the manual samples.
Mr. Redaelli's circuitikz manual provides this URL for source, and also has useful examples, symbol list
https://github.com/mredaelli/circuitikz | 2017-02-19 16:52:11 | {"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": 0.7745643258094788, "perplexity": 11607.369118862769}, "config": {"markdown_headings": true, "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-2017-09/segments/1487501170186.50/warc/CC-MAIN-20170219104610-00051-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://aequa.me/index.php/2018/09/01/2017-2018-acm-icpc-latin-american-regional-programming-contest-d-daunting-device/ | # [2017-2018 ACM-ICPC Latin American Regional Programming Contest] D. Daunting device
### Statement
Given an array of length $$1 \leq L \leq 10^5$$, initially filled with 1. Define cnt[i] as the number of elements in the array that are equal to i. You should perform no more than $$10^5$$ operations. Each operation is four integers $$P, X, A, B$$, and let $$M_1 = (A + S^2) \bmod L, M_2 = (A + (S + B)^2) \bmod L$$, where S = cnt[P], then assign all elements with indices in $$[min(M_1, M_2), max(M_1, M_2)]$$ with value X. After all operations performed, output the maximum cnt[i] over all possible values of i.
### Solution
The main idea of the solution is just to simulate the operations in a reasonable time complexity. In fact, various possible solutions exist, including segment tree and square root decomposition. However, the fastest solution (at least theoretically) I know is employing balanced binary search trees.
We use the nodes of the balanced binary search tree to represent contiguous intervals of the array with same values. Additionally, we maintain an array “cnt”, which has the meaning as described in problem statement.
When updating an interval [l, r) to value X, we delete all nodes representing the interval [l, r), updating the array “cnt”. Note that this may split the nodes that across the boundaries of given interval. Finally, we inserting a new node which represents [l, r) with value X, and updating “cnt”.
Each operation can be done in amortized $$O(\log L)$$ time, since in each operation, only constant number of nodes are inserted, though it is possible that a great number of nodes are deleted. Hence the total time complexity is $$O(n \log L)$$.
### Source Code
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
#ifdef __LOCAL_DEBUG__
# define _debug(fmt, ...) fprintf(stderr, "\033[94m%s: " fmt "\n\033[0m", \
__func__, ##__VA_ARGS__)
#else
# define _debug(...) ((void) 0)
#endif
#define rep(i, n) for (int i=0; i<(n); i++)
#define Rep(i, n) for (int i=1; i<=(n); i++)
#define range(x) (x).begin(), (x).end()
typedef long long LL;
typedef unsigned long long ULL;
int l, c, n;
int cnt[100005];
typedef tree<int, pair<int, int>, less<int>, rb_tree_tag> rbtree;
#define tree shuorgsrh
rbtree tree;
void update(int l, int r, int c) {
rbtree mpart, rpart;
tree.split(l - 1, mpart);
int dif;
if (tree.size() &&
(dif = tree.rbegin()->first + tree.rbegin()->second.first - l) > 0) {
tree.rbegin()->second.first -= dif;
mpart.insert(make_pair(l, make_pair(dif, tree.rbegin()->second.second)));
}
mpart.split(r, rpart);
if (mpart.size() &&
(dif = mpart.rbegin()->first + mpart.rbegin()->second.first - r) > 0) {
mpart.rbegin()->second.first -= dif;
rpart.insert(make_pair(r, make_pair(dif, mpart.rbegin()->second.second)));
}
for (auto& p : mpart) {
cnt[p.second.second] -= p.second.first;
}
cnt[c] += r - l;
tree.insert(make_pair(l, make_pair(r - l, c)));
tree.join(rpart);
}
int main() {
scanf("%d%d%d", &l, &c, &n);
cnt[1] = l;
tree.insert(make_pair(0, make_pair(l, 1)));
rep (i, n) {
int p, x, a, b;
scanf("%d%d%d%d", &p, &x, &a, &b);
int m1 = (a + 1ll * cnt[p] * cnt[p]) % l;
int m2 = (a + 1ll * (cnt[p] + b) * (cnt[p] + b)) % l;
if (m1 > m2) swap(m1, m2);
m2++;
update(m1, m2, x);
}
cout << *max_element(cnt+1, cnt+c+1) << endl;
return 0;
} | 2019-02-21 17:46:35 | {"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": 0, "mathjax_display_tex": 1, "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": 0.6079397201538086, "perplexity": 10778.073731955577}, "config": {"markdown_headings": true, "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-2019-09/segments/1550247506094.64/warc/CC-MAIN-20190221172909-20190221194909-00129.warc.gz"} |
http://www.ijfis.org/journal/view.html?uid=838&vmd=Full | Title Author Keyword ::: Volume ::: Vol. 18Vol. 17Vol. 16Vol. 15Vol. 14Vol. 13Vol. 12Vol. 11Vol. 10Vol. 9Vol. 8Vol. 7Vol. 6Vol. 5Vol. 4Vol. 3Vol. 2Vol. 1 ::: Issue ::: No. 4No. 3No. 2No. 1
Design of Fuzzy-PID Controller for Path Tracking of Mobile Robot with Differential Drive
Do Khac Tiep, Kinam Lee, Dae-Yeong Im, Bongwoo Kwak, and Young-Jae Ryoo
1Department of Electric and Control Engineering, Mokpo National University, Jeonnam, Korea, 2EV Components & Materials R&D Group, Korea Institute of Industrial Technology, Gwangju, Korea
Correspondence to: Young-Jae Ryoo (yjryoo@mokpo.ac.kr)
Received May 28, 2018; Revised September 3, 2018; Accepted September 22, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, a design of a fuzzy-PID controller for path tracking of a mobile robot with differential drive is proposed. The fuzzy-PID controller consists of a PID controller and a fuzzy controller with two inputs and three outputs. When the system response has the error and the error rate, the fuzzy controller can tune the parameters of the PID controller. The model based on Lagrange dynamic approach for a robot with differential drive is described. The fuzzy-PID controller and the classical PID controller are compared by simulation. The path tracking of a mobile robot with differential drive was tested using MATLAB/Simulink. The simulation results show that the fuzzy-PID controller has a better performance than the classical PID controller. The proposed controller has better convergence rate in comparison with the classical PID controller for a mobile robot with any arbitrary initial state. It has the advantages of rapid respond, high stability, tracking accuracy and good anti-interference, so the fuzzy-PID controller is the appropriate choice for path tracking control of mobile robots with differential drive
Keywords : Differential drive, Mobile robot, Path tracking, Fuzzy-PID controller, MATLAB/Simulink
1. Introduction
Mobile robots are complex and combined with many technologies as electronic components, sensors, actuators, controller design, information processing, and communication [13]. In the process of design and development of mobile robot, the controller is an important role because working ability of a mobile robot depends on the controllers performance. The key issue in the control of a mobile robot is the stabilization and the tracking control. The path tracking control makes the robot track the desired path given by geometric parameters [4, 5]. In the motion control of a mobile robot, the tracking control is essential because the mobile robot is required to move at a certain location in a certain time [68].
In recent years, many controllers have been designed to control mobile robots. Among several control method, the PID controller used widely in the robot field. By using PID control, both stability and tracking control can be achieved but accuracy is not high. Fuzzy logic control for autonomous vehicle has gained significant popularity in the last decades due to its highly successful implementation in almost all fields.
The most well-known arguments supporting fuzzy controllers are the ability to cope with imprecise information in heuristic rule-based knowledge, the interpolative nature of the fuzzy controllers, and the flexibility in the definition of non-linear control laws [913].
In this paper, a design of a fuzzy-PID controller for path tracking of a mobile robot with differential drive is proposed. The fuzzy-PID controller consists of a PID controller and a fuzzy controller with two inputs and three outputs. When the system occurs the error and the error rate, the fuzzy controller will tune the parameters of the PID controller. The model of a mobile robot with differential drive based on Lagrange dynamic approach is described [14]. The fuzzy-PID controller and the classical PID controller are compared by the simulation. The path tracking of a mobile robot with differential drive was tested using MATLAB/Simulink. The simulation results show that the fuzzy-PID controller has a better performance than the classical PID controller. The proposed controller has better convergence rate in comparison with the classical PID controller for a mobile robot with any arbitrary initial state. It has the advantages of rapid respond, high stability, tracking accuracy and good anti-interference, so the fuzzy-PID controller is the appropriate choice for path tracking control of mobile robots with differential drive.
2. Mobile Robot with Differential Drive
### 2.1 Configuration
In this paper, the configuration of a mobile robot with differential drive is used. In this configuration, the robot is equipped with two motors independently which connected two wheels on a common axis. The model of differential drives mobile robot includes a chassis with two wheels mounted on the same axis. Additionally, robots chassis has caster wheels which do not affect to robot’s motion included in resistance coefficients acting against the motion.
### 2.2 Model of Mobile Robot with Differential Drive
The mobile robot with differential drive has two wheels, each wheel with diameter 2r. Given a point P centered between the two drive wheels, a distance from each wheel to a point P is l. θ is the angular between robot reference frame (XR, YR) and global reference frame (XI, YI). Given r, l, θ, and ϕ̇1 and ϕ̇2 is the spinning speed of the right wheel and left wheel, respectively.
2.2.1 Dynamic model
To simulate the motion and design of motion control algorithms of the mobile robot, we need to know the dynamic model of the mobile robot with differential drive. This can be done based on the Lagrange dynamic approach, which Lagrange introduced systematically derive the equations of robots motion [4], [15]. Lagrange dynamic is the most well-known for formulating the equations of mobile robots motion.
The Lagrange equation is given by Eq. (1):
$ddt (∂L∂q˙i)+∂L∂q˙i=F-ΛT(q)λ,$
where: L = TV is the Lagrangian function; q are the generalized coordinates; T is the kinematic energy of robot; F is the generalized force; V is the potential energy.
The q are selected as:
$q=[xpypθϕRϕL]T.$
The kinetic energy is expressed as:
$Tc=12mcvc2+12Icθ˙2,$$TwR=12mwvw2+12Imθ˙2+12Iwϕ˙R2,$$TwL=12mwvw2+12Imθ˙2+12Iwϕ˙L2.$
where
1. Tc: the kinematic energy of a robot platform.
2. TwR: the kinematic of right wheel.
3. TwL: the kinematic of left wheel.
4. mc: the mass of the robot platfrom without the wheel and motor.
5. mw: the mass of wheel (including motor).
6. Ic: the moment of inertia of robot.
7. Iw: the moment of inertia of each driving wheel with a motor about the wheel axis.
8. Im: the moment of inertia of each driving wheel with a motor about the wheel diameter.
All velocities of the coordinates are:
$vi2=x˙i2+y˙i2.$
The coordinates of wheels can be determined as follow:
${xwR=xp+l sin θ,ywR=yp+l cos θ,$${xwL=xp-l sin θ,ywL=yp+l cos θ.$
From Eq. (3) to (8) total kinematic energy of the robot can be determined:
$T=12(mc+2mw)(x˙p2+y˙p2)-mcdθ˙(y˙a cos θ-x˙a sin θ)+12Iθ˙2+12Iw(ϕ˙R2+ϕ˙L2).$
Using Eq. (1) with the Lagrangian function, L = T, the equations of robot’s motion are given by:
$mx¨p-mdθ¨ sin θ-mdθ˙2 cos θ=C1,$$my¨p-mdθ¨ cos θ-mdθ˙2 sin θ=C2,$$Iθ¨-mdx¨p sin θ+mdy¨p cos θ=C3,$$Iwϕ¨R=τR+C4,$$Iwϕ¨L=τL+C5,$
where
1. m = mc + 2mw: total mass of the robot.
2. I = Ic + mcd2 + 2mwl2 + 2Im: total inertial.
3. C1, C2, C3, C4, C5: coefficients of kinematic constraints.
The matrix associated with the kinematic constraints:
$ΛT(q)=[C1C2C3C4C5].$
From Eqs. (10) to (14) the motion of robot can be represented by Eq. (16)
$M(q)q¨+V(q,q˙)+F(q˙)+G(q)+τd=B(q)τ-ΛT(q)λ,$
where
1. M(q): an n×n symmetric positive definite inertia matrix.
2. V (q, ): the centripetal and coriolis matrix.
3. F(): the surface friction.
4. G(q): the gravitational.
5. B(q): the input matrix.
6. τ : input vector.
7. τd: disturbances including unstructured dynamics.
8. B(q): the input matrix.
9. λ: the Lagrange multipliers vector.
10. Λ: the constraints matrix.
2.2.2 Kinematic model
The mobile robot with differential drive operates on a horizontal plane which is performed by three components that are the position of the robot and the angular difference between the global and local reference frames [16].
The position of the robot is a relationship between the global reference frame O : {XI,YI} and the robot reference frame {XR,YR}, as in Figure 1. The position of P in the global reference frame is specified by coordinates x and y, and the angular difference between the global and robot reference frames is given by θ. We can describe the pose of the robot as a vector with these three elements {x, y, θ}.
$ξI=[xyθ].$
In the robot reference frame and the global reference frame, the position of any point on the robot can be defined as follows:
$ξ˙I=[x˙y˙θ˙] and ξ˙R=[x˙Ry˙Rθ˙R]$
are the coordinates of the given point in the global reference frame (ξ̇I) and robot reference frame (ξ̇R).
To describe robot motion will be necessary to map the motion along the axes of the global reference frame to move along the axes of the robot reference frame. The mapping is a function of the current pose of the robot. This mapping is accomplished using the orthogonal rotation matrix:
$R(θ)=[cos θsin θ0-sin θcos θ0001].$
This matrix can be used to map the motion in the global reference frame {XI,YI} to move in terms of the local reference frame {XR,YR}. The two coordinates are related by the following transformation:
$ξ˙R=R(θ)ξ˙I.$
A kinematic model would predict the robot’s overall speed in the global reference frame:
$ξ˙I=[x˙y˙θ˙]=f(l,r,θ,ϕ˙1,ϕ˙2).$
The linear velocity of each driving wheel in the robot frame is the average of the linear velocities of the two wheels.
$v=vR+vL2=r.ϕ˙1+r.ϕ˙22.$
And the angular velocities of the robot:
$ω=vR-vL2l=r.ϕ˙1-r.ϕ˙22l.$
Combining these individual formulas yields a kinematic model for the differential-drive robot:
$ξ˙I=R(θ)-1ξ˙R=R(θ)-1 [rϕ˙1+rϕ˙220rϕ˙1-rϕ˙22l].$
The wheel can contribute to sideways motion in the robot’s reference frame, and so R is always zero.
3. Design of Controller
The controller design has two part. The first part is based on the inverse kinematics and the second part is the fuzzy-PID controller.
To ensure the stability and accuracy of the whole control system, we design a fuzzy-PID controller for a differential drive mobile robot. Figure 2 shows the block diagram of the overall system. The kinematic controller is received the desired value of position from the reference trajectory then the kinematic controller will calculate the desired velocity (vd), angular velocity (ωd). The desired velocity (vd), angular velocity (ωd) are fed into the differential drive mobile robot dynamics. The mobile robot dynamics will use those values to generate the actual velocity (v) and angular velocity (ω) command.
To determine the control, the parameters use the PID gains online [10, 14]. The modified controller gains are given by linear transformation as follows:
$Kp=(Kp max-Kp min)Kp′+Kp min,Ki=(Ki max-Ki min)Ki′+Ki min,Kd=(Kd max-Kd min)Kd′+Kd min$
where [Kpmin;Kpmax], [Kimin;Kimax] and [Kdmin;Kdmax] are the ranges of Kp, Ki, and Kd, respectively which determined by experience.
Mamdani type fuzzy inference mechanism is applied to the proposed fuzzy controller in this paper [14, 17]. The input of fuzzy-PID controller is the error (e) and change in error (ce). The fuzzy controller rules used to adjust the parameters of PID controller. The self-tuning the PID controller will find the fuzzy relationship between the three component of the PID controller [2].
In the fuzzy-PD controller, for choosing the variables of error (e) and change in error (ce), we set five fuzzy input values: negative big (NB), negative small (NS), zero (Z), positive small (PS), positive big (PB). Four output values are chosen: very big (VB), big (B), medium (M), small (S) (Table 1).
In this paper, the fuzzy-PID controller includes two input (e(t), ce(t)) and three output (Kp, Ki, Kd). It is applied to determine a parameter of PID controller with the membership function of a triangle form. The ranges of these membership function are determined by experience. The membership function of all output and input are described by
Figure 5 depicts a fuzzy adaptive control strategy with (x1, y1) and (xd1, yd1) are the actual robot position and desired robot position, respectively, where
1. dxd is the desired robot speed in x axis.
2. dyd is the desired robot speed in y axis.
3. vd: the desired velocity.
4. ωd: the desired angular velocity.
4. Simulation
We performed the simulation with MATLAB/Simulink. Desired trajectory is given by a circle with radius = 1.
As being expected, the same scaling is ensured for the same type of results with different control scheme where possible.
For implementation test, the results from Figure 7 to Figure 12 show differences between the classical PID controller and the fuzzy-PID controller. Additionally, we can see big difference between the classical PID controller and the fuzzy-PID controller.
The results of two methods for distance error are shown in Figures 7 and 8. From these figures, we can see distance error of the mobile robot with the classical PID controller is greater than the fuzzy-PID controller. From Figures 9 and 10, we can see, the distance error of the mobile robot by the PID controller has approximately 0.01 (m) and time response is 25 (s), while the distance error of the mobile robot by the fuzzy-PID controller is approximately 0.004 (m) and time response is 10 (s).
From Figures 8, 10, and 12 clearly can understand that by using the fuzzy system for tuning the PID gains the performances improved. The overshoot in path tracking is less than that by the classical PID controller.
Figures 8, 10, and 12 depict the trajectory of the mobile robot by applying the proposed fuzzy-PID controller. As expected, the design methodology makes the mobile robot track the desired path in a satisfactory way. We can see the actual path (blue line) almost matches the desired path (red line). The path tracking error by the fuzzy-PID controller achieves a much smaller value, in comparison with the PID controller.
5. Conclusion
In this paper, a design of fuzzy-PID controller for path tracking of a mobile robot with differential drive was proposed. The dynamic and kinematic model for a mobile robot with differential drive based on Lagrange dynamic approach is described. The proposed fuzzy-PID controller combined a PID controller and a fuzzy controller with two inputs and three outputs. When the system occurs the error and the error rate, the fuzzy controller tuned the parameters of the PID controller. The designed fuzzy-PID controller was applied to the model of a mobile robot with differential drive. The fuzzy-PID controller and the classical PID controller were compared by the simulation. The path tracking of a mobile robot with differential drive was tested using Matlab/Simulink. In the simulation, the fuzzy-PID controller has a better performance than the classical PID controller. The advantage of the fuzzy-PD controller is eliminating overshoots than the big overshoots in the classical PID controller is. The fuzzy-PID controller made smaller response time than that of the classical PD controller.
Conflict of Interest
Conflict of Interest
Figures
Fig. 1.
Model of mobile robot with differential drive.
Fig. 2.
Block diagram of robot’s model and fuzzy-PID controller.
Fig. 3.
The fuzzy-PID controller of mobile robot.
Fig. 4.
Structure of fuzzy controller.
Fig. 5.
Block diagram of fuzzy-PID control using MAT-LAB/Simulink.
Fig. 6.
Membership functions of input and output. (a) ‘e’, (b) ‘ce’, (c) ‘Kp’, (d) ‘Ki’, (e) ‘Kd’.
Fig. 7.
Distance error of mobile robot by PID controller.
Fig. 8.
Distance error of mobile robot by fuzzy-PID controller.
Fig. 9.
Position x and y axes by PID controller.
Fig. 10.
Position x and y axes by fuzzy-PID controller.
Fig. 11.
Tracking by PID controller.
Fig. 12.
Tracking by fuzzy-PID controller.
TABLES
### Table 1
Fuzzy rule table for KP/KI/KD
e/ceNBNSZPSPB
NBVB/S/SVB/M/SS/M/VBS/M/BM/S/S
NSVB/B/SB/B/SS/B/BS/B/BB/B/S
ZB/B/SM/B/MS/VB/BS/VB/MVB/VB/S
PSM/B/MS/B/BS/B/BM/B/SVB/B/S
PBS/S/MS/S/VBS/M/VBB/M/SVB/S/S
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Biographies
Do Khac Tiep received his B.S. degree from Department of Electrical and Electronics, Vietnam Maritime University, Haiphong, Vietnam in 2009. He received M.S. degree of Vietnam Maritime University in 2012. From 2009 to 2015, he was a teacher at Vietnam Maritime University. Since 2016, he has been studying doctor course in the Department of Control Engineering and Robotics, Mokpo National University, Korea.
E-mail: dotiep84@gmail.com
Kinam Lee Lee received his B.S. degree from the department of Control Engineering and Robotics, and M.S. and Ph.D degrees from the department of Electrical Engineering of Mokpo National University, in 2011, 2013, and 2018 respectively. He is currently working as a post-doctoral researcher at the iSL(intelligent Space Laboratory), Mokpo National University. His research interests include mechanical design, development and walking of robot and humanoid.
Email: knlee@mokpo.ac.kr
Dae-Yeong Im received his Ph.D,, M.S., and B.S. degree in the Department of Control System Engineering, Mokpo National University, Korea in 2002, 2004, and 2008 respectively. He is currently a senior researcher for Automotive Components & Materials R&D Group, the Korea Institute of Industrial Technology (KITECH), Korea form 2009, From 2009 to current, he is currently a board member of Korean Institute of Intelligent Systems. His research interests are automated guided vehicle (AGV), intelligent system, unmanned driving system, robotic vehicle, and mobile robot.
E-mail: dylim@kitech.re.kr
Bongwoo Kwak received his B.S. and M.S. degrees in the Department Electrical Engineering, Mokpo National University, Korea, in 2010 and 2012, respectively. He is currently a candidate of Ph.D. degree in the Department of Electrical Engineering, Chungnam National University, Daejeon, Korea. He is currently working as a junior researcher at Korea Institute of Industrial Technology, Gwangju, Korea. His research interests include the analysis, design, control, and optimization of power electronic converters and battery system.
E-mail: bwkwak11@kitech.re.kr
Young-Jae Ryoo received his Ph.D, M.S. and B.S. degrees in the Department of Electrical Engineering, Chonnam National University, Korea in 1998, 1993, and 1991, respectively. He was a visiting researcher in North Carolina A&T State University, USA, in 1999. He was a visiting professor in the Department of Mechanical Engineering, Virginia Tech, USA from 2010 to 2012. He is currently a professor in the Department of Control Engineering and Robotics, Mokpo National University, Korea from 2000. He also served as a director with the intelligent space laboratory in Mokpo National University, where he is responsible for the research projects in the area of intelligence, robotics and vehicles. He is currently a board member of Korean Institute of Intelligent Systems from 2002, an editor for the Journal of Korean Institute of Electrical Engineering from 2010, an editor for the Journal of Fuzzy Logic and Intelligent Systems from 2009, and a committee member of the International Symposium on Advanced Intelligent Systems from 2005. He served as a general chair of International Symposium on Advanced Intelligent System in 2015. He won the outstanding paper awards, the best presentation awards, and the recognition awards in International Symposiums on Advanced Intelligent Systems. He is the author of over 200 technical publications. His research interests include intelligent space, humanoid robotics, legged robotics, autonomous vehicles, unmanned vehicles, wheeled robotics and biomimetic robotics.
E-mail: yjryoo@mokpo.ac.kr
December 2018, 18 (4) | 2019-01-22 19:47:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 25, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28330254554748535, "perplexity": 2687.5979030665408}, "config": {"markdown_headings": true, "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-2019-04/segments/1547583867214.54/warc/CC-MAIN-20190122182019-20190122204019-00202.warc.gz"} |
https://economics.stackexchange.com/questions/17751/1929-stock-market-crash-and-unemployment-rate | # 1929 stock market crash and unemployment rate
Thomas Sowell has repeatedly made the case that government intervention is largely responsible for the Great Depression. For example, he notes what happened with the unemployment rate in the months after the stock market crash of 1929. Based on Out of Work by Vedder and Gallaway (alternatively available through JSTOR), page 77, one sees that the unemployment rate went from 5% (Nov. 1929) to 9% (Dec. 1929) and down to 6.3% (June 1930). It is then that Hoover signs the Smoot-Hawley Tariff Act, which Sowell contends is the first cause of the Depression. He then notes that by December 1930, the unemployment rate had shot up to 14.4%. Furthermore, aside from minor fluctuations in early 1931, the unemployment rate dips just below that 14.4% figure in 1936, but that is still the unemployment rate in December 1939.
I'm wondering what alternative factors or explanations could explain the quick increase to the unemployment rate followed by a decrease that approaches the previous numbers and then the marked and sustained increase, or if such alternatives even exist.
• Unemployment is typically a significantly lagging economic variable, and it is arguable that what happened in the Wall Street Crash took a year to feed through to employment. In addition US unemployment was also affected by other countries increasing their tariffs Aug 8 '17 at 20:01
• Henry Yes, I would suspect that a "tariff war" would have an impact, which would seem to support Sowell's assertion. But it seems strange that the unemployment rate would shoot up immediately after the crash, then come back down in a short timespan, and then the subsequent surge was a result of the crash a year prior. Aug 8 '17 at 20:19
• So, going off your second paragraph, you side more with Milton Friedman's view of the Depression? My main question is what other proposals explain the initial increase, followed by a return to near the starting point, and then the immediate increase of the unemployment rate if Sowell's idea on the Smoot Hawley tariffs is wrong? And while it is true that we don't have official unemployment data, the estimate in Out of Work seems to be an accurate estimate, given the high $R^2$ value. Aug 9 '17 at 16:56 | 2022-01-19 20:17:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44183796644210815, "perplexity": 1638.7647530860247}, "config": {"markdown_headings": true, "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-2022-05/segments/1642320301488.71/warc/CC-MAIN-20220119185232-20220119215232-00651.warc.gz"} |
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... Hello everybody, Today i found the R Pathview package and could already produce some output pictures. Nevertheless i have some problems and hope that someone might help me out. 1. There is a difference between the original KEGG picture and the modified Pathview picture. I guess this is not supp ...
written 23 months ago by ChIP-Tease0 • updated 17 months ago by bioinf0
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Comment: C: DESeq2 color coding
... Thanks a lot, that helped a lot! ...
written 2.1 years ago by ChIP-Tease0
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... Hello everybody, i was wondering, if it is possible to change the color coding in the DESeq2 plotMA function? Since i cannot see how the function works, i don't know how to modify anything. Additionally i would like to see how the plotMA works, which points to the same problem: I cannot see any c ...
written 2.1 years ago by ChIP-Tease0 • updated 2.1 years ago by Mike Smith2.7k
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... Hello Jim, Thanks a lot! I accepted it. I didn't know so far that i can accept answers. Also thanks for that hint ...
written 2.8 years ago by ChIP-Tease0
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... Hello everybody, i cannot really make this suggestion work. for file in *gff;do gene=${${file##aa_bb_cc_dd_}%.gff} echo program.sh $file ../../../unchanged_file.txt$gene $file$gene.bed done The problem seems to be this part: gene=${${file##aa_bb_cc_dd_}%.gff} I understand that the \$ ...
written 2.8 years ago by ChIP-Tease0
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... Thank you! ...
written 2.8 years ago by ChIP-Tease0
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... Thanks a lot, i didn't know that R can call command line programs. This will be very usefull for me. I guess i will try both ways. Thanks a lot again! ...
written 2.8 years ago by ChIP-Tease0
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... Hello everybody, I have a problem i need some help for. When I run a program on the command line for a single gene, it works fine: program.sh genename_1 ../../../unchanged_file.txt ../../aa_bb_cc_dd_genename_1.gff genename_1.bed But I need to run it about 1500 times on the command line and ...
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... Thanks Jeremy, works perfectly, exactly what i was looking for :D ...
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... Hello everybody, maybe someone has an idea how to solve my problem. I have a data frame and it contains all GeneIDs and a value for these genes. Like this: all_genes (around 23000 rows) GeneID Value Gene1 4 Gene2 2 Gene3 9 Gene4 0 ...
written 3.0 years ago by ChIP-Tease0
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Use of this site constitutes acceptance of our User Agreement and Privacy Policy. | 2018-06-20 18:55:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25339484214782715, "perplexity": 2525.018975349896}, "config": {"markdown_headings": true, "markdown_code": false, "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-2018-26/segments/1529267863834.46/warc/CC-MAIN-20180620182802-20180620202802-00169.warc.gz"} |
https://math.stackexchange.com/questions/2096624/limit-of-the-sequence-left-sum-k-0n-f-left-frackn2-right-right-n/2099304 | # Limit of the sequence $\left(\sum_{k=0}^n f\!\left(\frac{k}{n^2}\right)\right)_n$.
Following this post on Meta, I am going to regularly ask questions from competitive mathematics exams, on a variety of topics; and provide a solution a few days later. The goal is not only to list interesting (I hope) exercises for the sake of self-study, but also to obtain (again, hopefully) a variety of techniques to solve them.
Let $f\colon\mathbb{R}\to\mathbb{R}$ be differentiable at $0$, and such that $f(0)=0$. Letting $s_n\stackrel{\rm def}{=} \sum_{k=0}^n f\!\left(\frac{k}{n^2}\right)$ for $n\geq 1$, find the limit of the sequence $(s_n)_{n\geq 1}$.
Reference: Exercise 4.26 in Exercices de mathématiques: oraux X-ENS (Analyse I), by Francinou, Gianella, and Nicolas (2014) ISBN 978-2842252137.
• Would it be possible to give the reference of these problems? – Watson Jan 13 '17 at 20:16
• @Watson Sure! Added. – Clement C. Jan 13 '17 at 20:19
• I love this supposedly new trend. So, when we post such a question, should we somehow warn the reader that it's of this type, so that it doesn't get received negatively? – user384138 Jan 13 '17 at 20:36
• @OpenBall I'd specify it, if only to specify the goal (getting as many approaches as possible). – Clement C. Jan 13 '17 at 22:29
• Such meta content (i.e. the paragraph in italic) should be at the end of the post body though, not the beginning. Also, you don't need to write so much meta, a link to the meta post and half a sentence will do. – grg Jan 19 '17 at 11:23
Define $\phi : \Bbb{R} \to \Bbb{R}$ by
$$\phi(x) = \begin{cases} \dfrac{f(x)}{x}, & x \neq 0 \\ f'(0), & x = 0 \end{cases}$$
Then $\phi$ is continuous at $0$ and $f(x) = x\phi(x)$. Now your sum reduces to
$$s_n = \sum_{k=0}^{n} \frac{k}{n^2}\phi\left(\frac{k}{n^2}\right),$$
from which we find that
$$\Big( \inf_{[0,1/n]}\phi \Big) \sum_{k=0}^{n} \frac{k}{n^2} \leq s_n \leq \Big( \sup_{[0,1/n]}\phi \Big) \sum_{k=0}^{n} \frac{k}{n^2}.$$
Taking $n \to \infty$, by the squeezing theorem we get
$$s_n \to \frac{1}{2}\phi(0) = \frac{1}{2}f'(0).$$
• @OpenBall, It is a rather straightforward consequence of continuity. For any $\epsilon > 0$, there exists $\delta > 0$ such that $|\phi(x) - \phi(0)| < \epsilon$ whenever $|x| < \delta$, from which we deduce that $$\phi(0) -\epsilon \leq \inf_{[0,1/n]}\phi \leq \sup_{[0,1/n]}\phi \leq \phi(0) + \epsilon, \qquad n > \delta^{-1}.$$ This is enough to conclude. – Sangchul Lee Jan 13 '17 at 20:26
• Yes, it's all clear. Thanks. – user384138 Jan 13 '17 at 20:28
Using the definition of the derivative + using riemann sum to rewrite the sum as an integral yields $\frac{1}{2}f'(0)$.
• Can you detail a bit more? – Clement C. Jan 16 '17 at 19:12
An answer (inspired from that of the book cited as reference in the question).
• First, let us try with a few simple examples:
• Identity $f\colon x\mapsto x$ $$\sum_{k=0}^n f\left(\frac{k}{n^2}\right) = \frac{1}{n}\sum_{k=0}^n \frac{k}{n} \xrightarrow[n\to\infty]{} \int_0^1 xdx = \frac{1}{2}$$
• Square $f\colon x\mapsto x^2$ $$\sum_{k=0}^n f\left(\frac{k}{n^2}\right) = \frac{1}{n^2}\sum_{k=0}^n \frac{k^2}{n^2} \sim_{n\to\infty} \frac{1}{n}\int_0^1 x^2dx \xrightarrow[n\to\infty]{} 0$$
Now, not sure how helpful this is if one does not already have an intuition for the answer, but one can also try the above more generally with a power series $f(x)=\sum_{k=1}^\infty a_k x^k$ satisfying $f(0)=0$ with non-zero radius of convergence to get $\frac{a_1}{2}$. At that point, either one recognizes a general trend ("it should obviously converge to $\frac{f'(0)}{2}$"), or, well, try to continue nonetheless.
• One natural idea would be to write $f(x) = f'(0)x + o(x)$ on a neighborhood of $0$, and then compute $$\sum_{k=0}^n f\left(\frac{k}{n^2}\right) = f'(0)\cdot \frac{1}{n}\sum_{k=0}^n \frac{k}{n} + \sum_{k=0}^n o\left(\frac{k}{n^2}\right) = f'(0)\cdot \frac{1}{n}\sum_{k=0}^n \frac{k}{n} + o\left(1\right)$$ and conclude that the limit is $\frac{f'(0)}{2}$. Now, this is correct, but looks a little be sketchy due to the use of the Landau notation in the sum (which looks like it may "hide" some non-uniformity issues between summands) -- we will make it more rigorous below.
• Namely, since $f$ is differentiable at $0$, we can write by Taylor's theorem (the Peano form of the remainer) that $$f(x) = f(0)+f'(0)x+r(x)x= f'(0)x+r(x)x \tag{1}$$ for some $r\colon \mathbb{R}\to \mathbb{R}$ with $\lim_{x\to 0}r(x)=0$. This allows us to reproduce the same chain as above: $$\sum_{k=0}^n f\left(\frac{k}{n^2}\right) = f'(0)\cdot \frac{1}{n}\sum_{k=0}^n \frac{k}{n} + \frac{1}{n^2}\sum_{k=0}^n r\left(\frac{k}{n^2}\right)k \tag{2}$$ and we want to argue the second term converges to $0$. In view of this, fix $\varepsilon > 0$: by assumption, there exists $\delta_\varepsilon>0$ such that $\lvert x\rvert \leq \delta_\varepsilon$ implies $\lvert r(x)\rvert \leq \varepsilon$. Since $0\leq \frac{k}{n^2} \leq \frac{1}{n}$ for all $0\leq k\leq n$, this implies that there exists $N_\varepsilon\geq 0$ such that, for all $n\geq N_\varepsilon$, $$\left\lvert \frac{1}{n^2}\sum_{k=0}^n r\left(\frac{k}{n^2}\right)k \right\rvert \leq \frac{1}{n^2}\sum_{k=0}^n \left\lvert r\left(\frac{k}{n^2}\right)\right\rvert k \leq \varepsilon \frac{1}{n^2}\sum_{k=0}^n k = \frac{\varepsilon}{2}\cdot \frac{n(n+1)}{n^2} \leq \varepsilon$$ showing that $\frac{1}{n^2}\sum_{k=0}^n r\left(\frac{k}{n^2}\right)k \xrightarrow[n\to\infty]{} 0$ as wanted. Thus, we do get from $(2)$ that $$\sum_{k=0}^n f\left(\frac{k}{n^2}\right) \xrightarrow[n\to\infty]{} \boxed{\frac{f'(0)}{2}}\;.$$
• Dear Clement, the formula $f(x) = f(0)+f'(0)x+r(x)x$ that you call "the Peano form of the remainder for Taylor's theorem" is not a theorem at all but the definition of the derivative $f'(0)$. – Georges Elencwajg Jan 17 '17 at 17:39
• The Peano form is the general theorem. It works for functions differentiable k times: here, k=1. – Clement C. Jan 17 '17 at 17:42
• Yes, I happen to know Taylor's theorem, but I don't see why you should replace a definition by the trivial case of an irrelevant theorem, whose statement and proof use that very definition... – Georges Elencwajg Jan 17 '17 at 19:53
• Here, there is no need, but I felt that mentioning the name of the general case would help -- in particular, for the sake of generalization to similar (and maybe more complicated) problems. – Clement C. Jan 17 '17 at 19:55
• Yes, that makes sense too... – Georges Elencwajg Jan 17 '17 at 19:58 | 2019-05-23 22:45:06 | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9327635765075684, "perplexity": 258.74892103222925}, "config": {"markdown_headings": true, "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-2019-22/segments/1558232257432.60/warc/CC-MAIN-20190523224154-20190524010154-00423.warc.gz"} |
https://stats.stackexchange.com/questions/361398/slr-why-residual-standard-error-actually-refers-to-rss-n-2-and-not-standard | # SLR: why residual 'standard error' actually refers to RSS/(n-2) and not standard error?
From what I've learnt, standard error is a concept related to sampling distribution. So why is the term 'residual standard error' used to refer to $\sqrt{\frac{RSS}{n-2}}$ and not $\sqrt{E(r_i - E(r_i))^2}$ in SLR context?
(I mentioned Simple Linear Regression only because I have not learnt other regression techniques yet)
$$\hat{\mathbb{V}}(\varepsilon) = \text{MSE} = \frac{\text{RSS}}{\text{df}_\text{Res}} = \frac{\text{RSS}}{n-2}.$$
So the quantity you are referring to is $\hat{\mathbb{S}}(\varepsilon) = \sqrt{\text{RSS}/(n-2)}$. The other quantity you refer to is the standard deviation of the $i$th residual, which is not a fixed quantity over $i=1,...,n$ since it depends on the leverage values of the data points.
• Each of the random variables $R_1,...,R_n$ have a different variance, which is affected by the leverage of each data point. That means that there is no single generic variance for the residual. – Reinstate Monica Aug 9 '18 at 9:58 | 2019-12-07 06:49:49 | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7669228911399841, "perplexity": 401.3683201644473}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2019-51/segments/1575540496492.8/warc/CC-MAIN-20191207055244-20191207083244-00077.warc.gz"} |
https://newproxylists.com/reference-request-multivarate-rkhs-examples/ | # reference request – Multivarate “RKHS” Examples
I’ve been reading about RKHSs and Hilbert spaces of functions these days a bit these days and I haven’t yet come across an example of a hilbert space $$H$$ whose elements are all functions $$f:mathbb{R}^nrightarrow mathbb{R}^m$$ for $$n,m>1$$ and for which the evaluation functions $$E_x:fmapsto f(x)$$ are bounded.
Do such objects exist and if so what are some well-known examples?
The only thing I have at the moment is the space of $$ntimes m$$ matrices with Frobenius norm…which is a bit underwhelming… | 2020-09-28 22:57:41 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5320255160331726, "perplexity": 265.5451956059548}, "config": {"markdown_headings": true, "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-2020-40/segments/1600401614309.85/warc/CC-MAIN-20200928202758-20200928232758-00651.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/72769-conditional-probability-problem-makes-no-sense-me-intuitively.html | # Math Help - This conditional probability problem makes no sense to me intuitively
1. ## This conditional probability problem makes no sense to me intuitively
"The king comes from a family of 2 children. What is the probability that the other child is his sister?"
I know if I work through this problem using conditional probability concepts, the answer is 2/3.
However, could someone explain why this is the answer?
I don't see why this question is any different from the following:
"A coin is flipped 2 times. The first flip lands on heads. What is the probability that the second flip lands on tails?"
Yet the answer to the second question seems to obviously be 1/2.
2. Originally Posted by paulrb
"The king comes from a family of 2 children. What is the probability that the other child is his sister?"
I know if I work through this problem using conditional probability concepts, the answer is 2/3.
However, could someone explain why this is the answer?
I don't see why this question is any different from the following:
"A coin is flipped 2 times. The first flip lands on heads. What is the probability that the second flip lands on tails?"
Yet the answer to the second question seems to obviously be 1/2.
King question: The king is a boy. The sample space for the King question is therefore BG, GB, BB where BG means the king has an older sister and GB means that the king has a younger sister. Two of the three outcomes are favourable to the king having a sister.
Coin question: "A coin is flipped 2 times. The first flip lands on heads. What is the probability that the second flip lands on tails?"
The sample space is HT, HH. One of the two outcomes are favourable to the second toss being a tail.
Alternate coin question (King question in disgiuse): "A coin is flipped 2 times. One of the flips lands on heads. What is the probability that the other flip landed on tails?"
The sample space is HT, HH, TH. Two of the three outcmes are favourable to the other flip being a tail ....
3. Thank you, that helps, but I don't understand why I'm incorrect using this reasoning:
We know the king has a sibling. The sibling may be:
1) An older sister
2) A younger sister
3) An older brother
4) A younger brother
2 of those possibilities involve the other sibling being a sister, and 2 of the possibilities involve the other sibling being a brother. Assuming each possibility is equally likely, there is a 2/4 chance the sibling is a brother and a 2/4 chance the sibling is a sister. Or 1/2 for each.
4. Originally Posted by paulrb
"The king comes from a family of 2 children. What is the probability that the other child is his sister?"
I know if I work through this problem using conditional probability concepts, the answer is 2/3.
However, could someone explain why this is the answer?
I don't see why this question is any different from the following:
"A coin is flipped 2 times. The first flip lands on heads. What is the probability that the second flip lands on tails?"
Yet the answer to the second question seems to obviously be 1/2.
Hi Paulrb,
I'm going to disagree with your first answer. The probability that the other child is a girl is 1/2, for the reasons stated in your analysis of the coin flip problem.
Don't confuse your king-sibling problem with the classic problem where we are told that at least one child is a boy and we are asked to find the probability that both children are boys. In your problem we have more information: we know the king is male and we are asked about the probability that his sibling is female (or male, it makes no difference.) This is different than being told that at least one child is a boy.
Maybe this will be clearer if we employ some symbols. Let $X_i = 1$ if the ith child is a boy, zero otherwise. In the king-sibling problem we are told $X_1 = 1$ and we are asked to find $P(X_2 = 1)$. In the "at least one boy" version we are told $X_1 + X_2 \geq 1$ and we are asked to find $P(X_1 = 1 \text{ and } X_2 =1)$. These are two different problems.
It's very difficult to come up with a real-world situation where all you know is that at least one child is a boy. Usually you have seen one child, and that child was a boy; that's different. That is one of the reasons why the "at least one..." problem gives people so much trouble.
5. I may be beating that ole dead horse, but here goes.
GAME: I toss two coins out of your sight. Then cover the outcome, only you can remove the covering. You then declare if both coins show the same side or if both coins show different sides. You then remove the cover to see if you win.
Now you absolutely know the possible outcomes.
$\begin{array}{cc} H & H \\ H & T \\ T & H \\ T & T \\ \end{array}$
So you can easily see that either choice is equally likely. So you choose either.
But now I condition the game by telling you that one coin is heads.
Now you also absolutely know the possible outcomes.
$\begin{array}{cc} H & H \\ H & T \\ T & H \\ \end{array}$
Would you now choose the option that both are the same?
Of course not! Choosing the option that “they are different” is clearly best.
Conditional probabilities has the effect of narrowing the possible outcomes.
6. Is this problem different though? The siblings aren't identical objects; they're distinct people who were born at different times. It may be more like flipping a penny and a quarter.
We are told one of the coins lands on heads, without being told whether that coin is a penny or a quarter. Therefore, the other coin may be:
1) A quarter that landed on heads
2) A quarter that landed on tails
3) A nickel that landed on heads
4) A nickel that landed on tails.
Meaning, a 1/2 probability of landing on heads if each of the above possibilities is equally likely. We cannot rule out any of the above possibilities because we were only given half the information required to do so. We need to know the coin's denomination *as well as* whether it landed on heads or tails, but we are not told the coin's denomination, only that it landed on heads. Similarly, we were not told if the king was born first or second.
To awkward - I said 2/3 because that's what the solutions manual for my book says. I typed the problem verbatim. Also, if you search Google for this problem, other people have worked solutions for it and arrived at 2/3. To be honest, I am still not fully convinced that is the correct answer, but then again I don't think so many people would be incorrect.
EDIT: Shortly after typing this I think I figured it out. Since we *are* told one of the coins landed on heads, there is a 1/2 chance the quarter may NOT land on tails, since it landed on heads. There is also a 1/2 chance the penny may NOT land on tails, since it landed heads. Therefore, each of those possibilities should only count half.
1 * quarter lands on heads (there is no way that possibility can be ruled out)
.5 * quarter lands on tails (there is a 1/2 chance that possibility can be ruled out)
1 * penny lands on heads (there is no way that possibility can be ruled out)
.5 * penny lands on tails (there is a 1/2 chance that possibility can be ruled out)
So with the "weighted" possibilities, there's a 2/3 chance the other coin lands on heads and a 1/3 chance it lands on tails. The same logic applies to my problem.
Except...wait, did I get something backwards? In the king problem there was a 2/3 chance the other sibling was a girl (opposite sex of the other) but in this case there's a 2/3 chance the other coin lands on heads (same side as the other)
7. Yes, having thought the problem over, I can see that the "at least one boy" interpretation is probably (no pun intended) the intent of the author of the problem. In that case the probability that the other child is a girl is 2/3, as others have pointed out.
However, I think there are other interpretations possible, and quite likely in the real world. When the problem says "the king comes from a family of two children", what does that mean? If it means that someone saw one of the two children and that one happened to be male, then the probability that the other child is female is 1/2. But if it means no more and no less than that at least one of the children is male, then the probability that the other child is female is 2/3. Altogether, I think the problem statement is sufficiently ambiguous to allow for either possibility.
8. Originally Posted by paulrb
Is this problem different though? The siblings aren't identical objects; they're distinct people who were born at different times. It may be more like flipping a penny and a quarter.
EDIT: Shortly after typing this I think I figured it out. Since we *are* told one of the coins landed on heads, there is a 1/2 chance the quarter may NOT land on tails, since it landed on heads. There is also a 1/2 chance the penny may NOT land on tails, since it landed heads. Therefore, each of those possibilities should only count half.
No, I think you are confusing yourself.
The point that you are missing is this: even though siblings are distinct, they are still animals and as such they are male or female. Likewise, even though coins are distinct, they still have only two sides, heads or tails.
It is binary, if we know that one of two outcomes is a 1, then there are just three possible outcomes.
9. Ok... I understand what you're saying. Still, what I said from my previous post is also true:
Do you agree with this:
We know the king has a sibling. The sibling may be:
1) An older sister
2) A younger sister
3) An older brother
4) A younger brother
Even if this is a more complicated way to do the problem, I would like to do it this way to convince myself that the result is the same.
Is there a way to show that these 4 possibilities are *not* equally likely, and that they are skewed so that there is a 2/3 chance the other sibling is a girl?
Edit: Perhaps this is the reason why the problem specifically stated "the king?" Most people know that it's the firstborn who becomes king, not the second born. Therefore, the probability that the sibling is an older brother is 0. Then there are 3 possibilities, giving a 2/3 chance that the other sibling is his sister.
Maybe that's a coincidence, though. Still, it makes all the difference. | 2016-02-12 19:11:57 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "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": 0.6802698969841003, "perplexity": 303.6472366632075}, "config": {"markdown_headings": true, "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-2016-07/segments/1454701165070.40/warc/CC-MAIN-20160205193925-00082-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://math.meta.stackexchange.com/questions/22679/reopening-closed-questions-with-good-answers | # Reopening closed questions with good answers
I often come by questions that are closed because of lack of context, but that still have good answers. It can be questions that contain nothing more than
What is this integral $\int \ldots dx$?
or similarly, which are reasonable to close, but that one or more people still gave a good answer to before the question was closed.
When an open question has a good answer, I am less inclined to close it, and when a closed question has a good answer, I feel more inclined to reopen it for three reasons:
• Since the OP has already received an answer, it is less likely that any further context will be provided.
• Out of respect for the time put into the good answers.
• The answers are a nice addition to the material of MSE.
Is it ok to reopen a question without context, or even a poorly asked question, if it has good answers?
• There is too much variation in the cases to give any kind of blanket guidelines. If you search the meta you will find that this theme has been discussed on a number of occasions. Either explicitly or as a by-product of another discussion. No consensus emerged. Many veterans of the site feel that a good answer does not give any kind of immunity to a bad question. Many other veterans do take the presence of a good answer into account when deciding how they vote, but still draw the line somewhere. Yet others feel quite strongly that good answers should be saved more often than not. – Jyrki Lahtonen Feb 26 '16 at 18:40
• The one advice I can give is to post your suggestions in the thread dedicated to such requests. We collect opinions of more users there, and many reversals have taken place. – Jyrki Lahtonen Feb 26 '16 at 18:43
• @JyrkiLahtonen thank you for your comment. I believe I'm in some version of the last group. Since there is no consensus, I will rely on wisdom of the crowd in the reopen votes that I participate in (and will use the meta-thread when appropriate). – Mankind Feb 26 '16 at 20:28
• Welcome to that thread. The more opinions we collect the better. For the record I did downvote your proposal. I am in the camp thinking that pretty much any definite integral should stay out (unless the question is about learning a technique). Those have been automated. Wolfram Alpha can do most, and it even has this "show steps" feature. Too many so called nice answers are from posters perpetually sitting in an exam. Few answerers actually try to teach how to approach the problem. – Jyrki Lahtonen Feb 26 '16 at 20:35
• @JyrkiLahtonen thanks for giving the reason. Just for the record, I didn't mean my post to be a proposal, but rather a question about if reopening a question based on the answers to a question instead of the question itself is alright. Per your comment, there appear to be different practices, and I will try to make an assesment from case to case. As for e.g. definite integral (and derivatives, that also fall into the group of having automated solutions) I agree that spewing out a long calculation without the whys and hows does not constitute a good answer, but I feel this is a broader problem. – Mankind Feb 26 '16 at 22:18
• To elaborate on the last sentence in my last comment, a lot of answers does technically answer the question that has been posed, but does not address the confusion, lack of knowledge or addresses how they came up with the solution in their answer. I think this can be said about a lot of problems, and not only integrals, even though I get what you say about them being automated. But anyway, I am getting off-topic, and this has probably also been discussed in other posts. – Mankind Feb 26 '16 at 22:22
• Understood. For the record: I don't know how widespread my thinking is in this issue. Also, I try not to let this attitude show when I'm moderating. Before I was elected it was easier to simply ignore such questions. I still try, but cannot always, when the regular users do not reach a consensus :-/ – Jyrki Lahtonen Feb 26 '16 at 23:14
• Well, you can try to edit the question to make it better. And then vote to reopen. There are probably some other related discussions on meta, here are two I was able to find quickly: Editing someone else's question to add context and Under what circumstances is it appropriate to delete a question that has received a good answer? – Martin Sleziak Feb 27 '16 at 9:17
• Also related. – Cameron Buie Mar 2 '16 at 12:40
• From the second link Martin Sleziak gave, I recommend reading quid's answer. – Jonas Meyer Oct 23 '17 at 1:57
Generally, my opinion is "No."
You've got a bad question with a good answer. What do I think you should do? Downvote the question and upvote the answer (and vote to close if necessary).
• Since the OP has already received an answer, it is less likely that any further context will be provided.
This is unfortunate, and the most we can do here is discourage these questions by downvoting them and voting to close them faster than the answerers. In some scenarios, this is good, in some, this is bad. There isn't much we can do about it.
• Out of respect for the time put into the good answers.
This is why closing a question does not affect the answerers (unless it prevents you from answering in the first place, which is not the question being asked).
Honestly though, if you wanna give an answerer some respect, you should upvote their answer. That's what the voting system is for.
• The answers are a nice addition to the material of MSE.
Closed questions are not removed from MSE. Deleted questions are, at least to the common eye. So reopening the question will not have the intended affect here of providing 'a nice addition' to MSE, since it never left in the first place.
• Besides closing the question, one can also edit the question to make it better. That's probably what I would do if the answer is really good. – user99914 Oct 23 '17 at 1:11
• And please someone correct me if i am wrong. it seems that closed question are more difficult to search. – user99914 Oct 23 '17 at 1:13
• "Closed questions are not removed from MSE. Deleted questions are..." Closing a question can be a step toward deletion. Reopening a question is a good idea if the thread is considered worth keeping. I am skeptical in general about the helpfulness of threads that have "good answers" to terrible questions, but as Jyrki indicates opinions vary widely on that. – Jonas Meyer Oct 23 '17 at 1:13
• @JohnMa To the first comment: There is only so much of an extent one can edit the question before one steps over a line and starts making assumptions as to what the OP meant and didn't mean. – Simply Beautiful Art Oct 23 '17 at 1:15
• @JohnMa To the second comment: I've no experience that closed questions are harder to search for. In the majority of cases, closed questions which I am searching for may be found in my current tab, if you are searching for questions you yourself closed. – Simply Beautiful Art Oct 23 '17 at 1:17
• @simply if the op already abandoned the question, I won't care much about what they think. All I want is to have better question/answers in the site. – user99914 Oct 23 '17 at 1:20
• @JonasMeyer Generally speaking, I do not think most closed questions take that step towards deletion. In most cases, closed questions are deleted by the sweeper, an automated process. Given good enough answers, they do not get deleted. For the rest of the closed questions, I believe very few get deleted. The step from closed to deleted is not a simple step, and for good reasons. – Simply Beautiful Art Oct 23 '17 at 1:21
• @JohnMa I will advise you to read up on How much editing is too much? Note that it is fairly outdated and may not apply. – Simply Beautiful Art Oct 23 '17 at 1:25
• @SimplyBeautifulArt By design they are ready for deletion with usually only 3 votes needed by high point users. Being closed (other than as duplicate) signals (to many at least) that they are not appropriate for the site unless improved, so while most of them aren't being deleted at any given time, each of them is a potential target for deletion, and the moderation habits of site users can vary over time. Reopening, especially with improvements if possible, removes them from being "on deck" for deletion. – Jonas Meyer Oct 23 '17 at 1:33
• @JonasMeyer False. Usually, the question needs to be closed and have sufficiently many downvotes on it, so many of these sorts of questions cannot be voted on for deletion. – Simply Beautiful Art Oct 23 '17 at 1:34
• @SimplyBeautifulArt: No. Here is a reference. Here is a quote from that reference: "Users with reputation ≥ 10k ... can vote to delete questions that have been closed/on-hold for 48 hours. It takes three votes to delete; more if the question is popular, but ten votes at most." "Popularity" requires a presence of many upvotes on things, not just an absence of downvotes, and it doesn't prohibit deletion, just makes it take more votes. – Jonas Meyer Oct 23 '17 at 1:38
• Thanks for the link, @SimplyBeautifulArt, though like you said it is a bit outdated. And just like 99% of the meta post, there is no definitive conclusion there. – user99914 Oct 23 '17 at 1:42
• @JonasMeyer Hm, strange that it was not mentioned there. Since you have the privilege unlocked, I'd suggest you attempt to vote to delete a closed question with positive score that was asked within 24 hours. Perhaps someone else has a better reference for this... – Simply Beautiful Art Oct 23 '17 at 1:44
• @SimplyBeautifulArt: What wasn't mentioned there? What more reference do you need? You can look at this question deleted a few hours ago with a score of zero, and with positive score answers. I don't know what 24 hours has to do with it. – Jonas Meyer Oct 23 '17 at 1:48
• @JonasMeyer Ah, I take it back. One must wait 48 hours to vtd, unless it has sufficiently low score. I was mentioning things such as this question, which is on hold, but cannot be voted on to be deleted. – Simply Beautiful Art Oct 23 '17 at 1:48 | 2019-07-17 02:44:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4022854268550873, "perplexity": 747.9843336128298}, "config": {"markdown_headings": true, "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-2019-30/segments/1563195525009.36/warc/CC-MAIN-20190717021428-20190717043428-00544.warc.gz"} |
https://www.groundai.com/project/cartoon-approximation-with-curvelets/ | Cartoon Approximation with \alpha-Curvelets
# Cartoon Approximation with α-Curvelets
## Abstract
It is well-known that curvelets provide optimal approximations for so-called cartoon images which are defined as piecewise -functions, separated by a singularity curve. In this paper, we consider the more general case of piecewise -functions, separated by a singularity curve for . We first prove a benchmark result for the possibly achievable best -term approximation rate for this more general signal model. Then we introduce what we call -curvelets, which are systems that interpolate between wavelet systems on the one hand () and curvelet systems on the other hand (). Our main result states that those frames achieve this optimal rate for , up to -factors.
## 1 Introduction
In various applications in signal processing it has proven useful to decompose a given signal in a multiscale dictionary, for instance to achieve compression by coefficient thresholding or to solve inverse problems. The most popular family of such dictionaries are undoubtedly wavelets, which have had a tremendous impact in applied mathematics since Daubechies’ construction of orthonormal wavelet bases with compact support in the 1980s. While wavelets are now a well-established tool in numerical signal processing (for instance the JPEG2000 coding standard is based on a wavelet transform), it has been recognized in the past decades that they also possess several shortcomings, in particular with respect to the treatment of multidimensional data where anisotropic structures such as edges in images are typically present. This deficiency of wavelets has given birth to the research area of geometric multiscale analysis where frame constructions which are optimally adapted to anisotropic structures are sought.
### 1.1 Geometric Multiscale Analysis
A milestone in this area has been the construction of curvelet and shearlet frames which are indeed capable of optimally resolving curved singularities in multidimensional data. To be more precise, the landmark paper [3] has shown that simple coefficient thresholding in a curvelet frame yields an, up to (negligible) -factors, optimal -term approximation rate for the class of so-called cartoon images which are roughly defined as compactly supported, bivariate, piecewise functions, separated by a discontinuity curve. After this breakthrough result new constructions of anisotropic frame systems have been introduced which achieve the same optimal approximation rates for cartoon images. Among those we would like to single out shearlets which are better suited for digital implementation than the original curvelets. They were first introduced in [12] and a comprehensive summary of their properties can be found in the survey [14]. The recent work [11] introduced the framework of parabolic molecules which subsumes all the earlier constructions mentioned above and which established a transference principle of approximation results between any two systems of parabolic molecules, provided that one of them constitutes a tight frame for .
### 1.2 General Image Models
By now the model of such cartoon-images is widely recognized as a useful mathematical model for image data. However, for certain applications it might appear still too restrictive. For instance one could imagine signals which consist of piecewise smooth parts separated by a singularity curve which might not necessarily be exactly but of higher or lower smoothness.
The approximation of such a generalized signal class by hybrid shearlets has been studied in [15] for three-dimensional data. In that paper the best -term approximation results which could be established are suboptimal by a small margin. In addition, hybrid shearlets are compactly supported, but do not form a tight frame.
### 1.3 Our Contribution
In the present paper we study optimal approximation schemes for a more general model, namely bivariate piecewise functions, separated by a discontinuity curve, where . We establish a benchmark result which states that one cannot in general achieve an -term approximation rate higher than for such functions. We then introduce the notion of -curvelet frames which generalize the construction of [3], where describes the degree of anisotropy in the scaling operation used for the frame construction. The parameter corresponds to ridgelets [2], the case to second-generation curvelets as in [3], and the case to wavelets. -curvelets form a tight frame for any parameter in contrast to the systems considered in [15]. Our main result then states that all intermediate cases provide optimal (up to -factors) -term approximation rates for the above mentioned signal class with . This is particularly surprising, since for the result in the 3D situation ([15]) for intermediate parameters only a suboptimal rate could be proven. Our proof techniques rely somehow on [3], however we wish to mention that the technical details are actually quite different from those used there. In particular, we have to deal with smoothness spaces of fractional orders which forces us to replace estimates for derivatives in [3] by estimates on certain moduli of smoothness.
Having such an approximation result for a tight frame system at hand will allow us to transform our approximation result to arbitrary systems of frames of -molecules (including compactly supported hybrid shearlets as special case), as first introduced in [9]. This will be the subject of the forthcoming work [10], generalizing the framework of parabolic molecules [11].
### 1.4 Outline
After introducing the general class of image models in Section 2 and deriving the benchmark result in Theorem 2.2, Section 3 is devoted to the construction of -curvelets. Our main result on the optimal approximation properties of -curvelets for any parameter is then stated in the next section as Theorem 4.1. This section as well as the appendix do contain the lengthy, quite technical proof of this result.
### 1.5 Preliminaries
Let us fix some notational conventions used throughout this work. For we denote the Euclidean distance by and the -norm by . Further, we put for .
For a function the forward difference operator , where , is given by
Δ(h1,…,hd)f(x1,…,xd):=f(x1+h1,…,xd+hd)−f(x1,…,xd).
In the one-dimensional case it takes the simple form . We will often apply the forward difference operator to a bivariate function . To simplify notation, the operator shall exlusively act on variables denoted or , e.g., the symbol denotes the function .
We denote by the derivative in the -th coordinate direction, , and we let for .
We write for the respective norms in the spaces and , where is a discrete set.
For , , the Fourier transform is defined by
Ff(ξ)=∫Rdf(x)exp(−2πix⋅ξ)dx.
The short-hand notation for is .
We shall also make extensive use of the Radon transform given by
RF(t,η):=∫Lt,ηF(x)dl(x),
with and .
The Hölder spaces for are defined as follows:
Cγ(Rd):={f∈C(Rd):dmaxi=1\sl Höl(∂if,γ−1)<∞}
where for a function we we use the notation
\sl Höl(f,α)=supx,y∈Rd|f(x)−f(y)||x−y|α,α∈[0,1],
for the Hölder constant. The notation refers to compactly supported functions in .
In the sequel, for two quantities , which may depend on several parameters we shall write , if there exists a constant such that , uniformly in the parameters. If the converse inequality holds true, we write and if both inequalities hold we shall write .
## 2 Cartoon Approximation
Many applications require efficient encoding of multivariate data in the sense of optimal (sparse) approximation rates by a suitable representation system. This is typically phrased as a problem of best -term approximation as explained in Subsection 2.1. The performance of an approximation scheme is then analyzed with respect to certain subclasses of the Hilbert space , which is the standard continuum domain model for -dimensional data, in particular in imaging science. The key feature of most multivariate data is the appearance of anisotropic phenomena. Hence such a subclass of is required to provide a suitable model for this fact, which is fulfilled by the subclass of so-called cartoon-like images as defined in Subsection 2.2. The main result of this section, Theorem 2.8, will provide an upper bound for the maximal achievable approximation rate for this class of cartoon images. It serves as a benchmark for the approximation performance of concrete representation systems.
### 2.1 Sparse Approximation
Let us start with a short introduction to some aspects of approximation theory. The standard continuum model for -dimensional data, in particular in imaging science, is the Hilbert space . From a practical standpoint however, a function is a rather intractable object. Therefore, in order to analyze , the most common approach is to represent it with respect to some representation system , i.e., to expand as
f=∑λ∈Λcλφλ, (1)
and then consider the coefficients .
Moreover, since in real world applications infinitely many coefficients are infeasible, the function has to be approximated by a finite subset of this system. Letting be the number of elements allowed in this approximation, we obtain what is called an -term approximation for with respect to . The best -term approximation, usually denoted by , is optimal among those in terms of a minimal approximation error and is defined by
fN=argming=∑λ∈ΛNcλφλ∥f−g∥22s.t.#ΛN≤N.
The approximation performance of a system for a subclass is typically measured by the asymptotic approximation rate, i.e., the decay of the -error of the best -term approximation as .
In a very general form the representation system can just be an arbitrary dictionary, i.e. we require only . General dictionaries can be rather pathological, and for there might not even exist a best -term approximation. For example, since is separable, we can choose to be a countable dense subset of . This choice would yield arbitrarily good -term approximations since the elements of can come arbitrarily close to .
Therefore, without reasonable restrictions on the search depth, the investigation of best -term approximation with respect to a given dictionary may not even make sense. A commonly used and suitable restriction is to impose polynomial depth search, which requires that the terms of the -term approximation have to come from the first elements of the dictionary, where is some fixed polynomial [6].
#### Polynomial Depth Search in a Dictionary
Let us get more specific and assume that we have a countable dictionary indexed by the natural numbers, and a fixed polynomial specifying the search depth. A non-linear -term approximation scheme can then be described by a set-valued selection function , which determines for given and the selected dictionary elements, i.e. with . The function shall obey the polynomial depth search constraint, i.e. , and the dependence on allows for adaptive approximation schemes.
Let us recall a benchmark concerning the optimality rate of approximation in a dictionary with polynomial depth search, as derived in [6]. Before, we have to define what it means for a class of functions to contain a copy of .
###### Definition 2.1.
1. A class of functions is said to contain an embedded orthogonal hypercube of dimension and sidelength if there exist and orthogonal functions for with such that the collection of hypercube vertices
H(m;f0,(ψi)i)={h=f0+m∑i=1εiψi : εi∈{0,1}}
is contained in . It should be noted that just consists of its vertices.
2. A class of functions is said to contain a copy of , , if there exists a sequence of orthogonal hypercubes , embedded in , which have dimensions and side-lengths , such that and for some constant
mk≥Cδ−pkfor all k∈N. (2)
Note, that if contains a copy of , then it also contains a copy of for all . It was shown in [6] that if a function class contains a copy of there exists an upper bound on the maximal achievable approximation rate via reconstruction in a fixed dictionary.
We state a reformulation of this landmark result, which in its original form [6] was stated in terms of the coefficient decay. The original proof however can be adapted to lead to the following formulation in terms of the best -term approximation, which is more appropriate for our needs. We remark, that this theorem is also valid in a general Hilbert space setting.
###### Theorem 2.2.
Suppose, that a class of functions is uniformly -bounded and contains a copy of . Then, allowing only polynomial depth search in a given dictionary, there is a constant such that for every there is a function and an , such that
∥f−fN∥22≥C(Nlog2(N))−(2−p)/p,
where denotes the best -term approximation under the polynomial depth search constraint.
###### Proof.
Let be a given dictionary and the polynomial, specifying the search depth. The best -term approximation of obtained in this setting shall be denoted by , the corresponding selection rule, as described above, by .
Each system can be orthonormalized by the Gram-Schmidt procedure (starting from lower indices to higher indices), giving rise to an orthonormal basis of (with the exception of some possible zero vectors). Therefore we can represent each by the unique set of coefficients obtained from an expansion in this basis. (If a basis element is zero, the corresponding coefficient is chosen to be zero.)
In order to apply information theoretic arguments, we consider the following coding procedure. For we select the dictionary elements and quantize the coefficients of obtained as above by rounding to multiples of the quantity .
We need bits of information to encode the locations of the selected elements and bits for the coefficients themselves, where is the -bound for the elements of . Hence, in this procedure we are encoding with at most
R(N)=N(C1+C2log2(N)),C1,C2>0,
bits, and for we have for some constant . To decode, we simply reconstruct the rounded values of the coefficients and then synthesize using the selected dictionary elements.
Let be a hypercube in of dimension and sidelength . Starting with a vertex the coding-decoding procedure (for some fixed ) yields some . By passing to the -closest vertex , we again obtain an element of the hypercube .
Every vertex can be represented as a word of bits, each bit corresponding to one side of the cube. Thus the above coding procedure gives a map of the bits, which specify the vertex , to bits. The decoding then reconstructs the bits specifying the vertex . Since at the intermediate step we just have bits of information we unavoidably loose information if .
Now we can apply an information theoretic argument. By rate-distortion theory [6, 1] there must be at least one vertex , where the number of false reconstructed bits is larger than . Here is the so-called -letter distortion rate function. Since each bit determines a side of the cube, the error we make for this vertex obeys
∥h−^h∥22≥δ2⋅Dm(R).
Since by construction we have It follows
∥~h−h∥22≥14δ2⋅Dm(R).
By assumption, contains a copy of . Therefore we can find a sequence of hypercubes with sidelengths as and dimensions . We pick such that and as . For large we then obey the inequality , in fact is sufficient.
Here we can apply another result from rate-distortion theory. If for some it holds , where is the so-called single-letter distortion-rate function. Hence, if , we have
∥~h−h∥22≥14D1(13)δ2m.
Let denote the vertices with maximal reconstruction error at each hypercube . Then we can conclude for large
∥~hk−hk∥22≥14D1(13)δ2kmk≳δ2kmk≳(Nklog2(Nk))−(2−p)/p.
Finally we have to take care of the rounding errors. The Euclidean distance between the best -term approximation differs from by at most , i.e.
∥~hk−h′k∥2≤q√Nk,
since the coefficients belong to an orthonormal basis. It follows, with some constant ,
∥hk−h′k∥2≥∥~hk−hk∥2−∥~hk−h′k∥2≥C(Nklog2(Nk))12−1p−N1/2−2/pk≳(Nklog2(Nk))−(2−p)/(2p).
This finishes the proof. ∎
#### Frame Approximation
In practice one needs representations, which are robust and stable with respect to noise. This leads to the notion of a frame [4], which is a special kind of dictionary.
A system is called a frame for , if there exist constants such that
C1∥f∥22≤∑λ∈Λ|⟨f,φλ⟩|2≤C2∥f∥22for all f∈L2(R2).
A frame is called tight, if is possible, and Parseval, if . Since the frame operator defined by is always invertible, it follows that one particular sequence of coefficients in the expansion (1) can be computed as
cλ=⟨f,S−1φλ⟩,λ∈Λ, (3)
where is usually referred to as the canonical dual frame. Note, that in general for a redundant system the expansion coefficients in (1) are not unique. The particular coefficients (3), however, are usually referred to as the frame coefficients. They have the distinct property that they minimize the -norm.
Even in the frame setting, the computation of the best -term approximation is not yet well-understood. The delicacy of this problem can for instance be seen in [7]. A typical approach to circumvent this problem is to consider instead the -term approximation obtained by choosing the largest frame coefficients. It is evident that the associated error then also provides a bound for the error of best -term approximation.
There exists a close relation between the -term approximation rate achieved by a frame, and the decay rate of the corresponding frame coefficients. A typical measure for the sparsity of a sequence are the -(quasi-)norms, for defined by
∥(cλ)λ∥ωℓp:=(supε>0εp⋅#{λ:|cλ|>ε})1/p.
Equivalently, for a zero sequence indexed by , these (quasi-)norms can be characterized by , where denotes the non-increasing rearrangement of .
The following lemma shows that membership of the coefficient sequence to an -space for small implies good -term approximation rates. For a proof, we refer to [5, 16].
###### Lemma 2.3.
Let be an expansion of with respect to a frame . Further, assume that the coefficients satisfy for some . Then the best -term approximation rate is at least of order , i.e.
∥f−fN∥2≲N−k.
Next, we apply Theorem 2.2 to obtain an upper bound on the approximation rate of cartoon-like images.
### 2.2 Cartoon-like Images
To model the fact that multivariate data appearing in applications is typically governed by anisotropic features – in the 2-dimensional case curvilinear structures –, the so-called cartoon-like functions were introduced in [6]. This class is by now a widely used standard model in particular for natural images. It mimics the fact that natural images often consist of nearly smooth parts separated by discontinuities.
The first rigorous mathematical definition was given in [6] and extensively employed starting from the work in [3]. It postulates that images consist of -regions separated by piecewise smooth -curves. Since its introduction several extensions of this model have been introduced and studied, starting with the extended model in [15]. We consider images that contain two smooth -regions separated by a piecewise smooth -curve, where .
Without loss of generality we will subsequently assume the smoothness of the edge curve. In addition, to avoid technicalities, we restrict our considerations to star-shaped discontinuity curves, which allow an easy parametrization. This is a classical simplification also used in [6, 3, 16, 15] . We remark however that this restriction to star-shaped curves is artificial. In fact, we could work with the class of regular -Jordan domains contained in , where and the Hölder constants in the canonical parametrization are bounded.
We begin by introducing the class of star-shaped sets for and . For that we take a -function defined on the torus , where the boundary points are identified. Additionally, we assume that there exists such that for all . Then we define the subset by
B={x∈R2 : x=(|x|2,η) in polar coordinates with η∈T,|x|2≤ρ(η)}, (4)
such that the boundary of is a closed regular -Jordan curve in parameterized by
b(η)=(ρ(η)cos(η)ρ(η)sin(η)),η∈T. (5)
Furthermore, we require the Hölder constant of the radius function to be bounded by , i.e.,
\sl Höl(ρ′,γ−1)=supη,~η∈T|ρ′(η)−ρ′(~η)||η−~η|γ−1≤ν, (6)
where the distance is measured on the torus .
###### Definition 2.4.
For the set is defined as the collection of all subsets , which are translates of sets of the form (4) with a boundary obeying (5) and (6).
The class of cartoon-like functions is then defined as follows.
###### Definition 2.5.
1. Let , . The cartoon-like functions are defined as the set of functions of the form
f=f0+f1χB,
where and with and for each . To simplify notation we let .
2. denotes the class of binary cartoon-like images, i.e., functions , where and .
We aim for a benchmark for sparse approximation of functions belonging to . For this we can use the results from the previous section. In order to apply these results to our model of cartoon-like functions we investigate for which the class of cartoon-like images contains a copy of following [15, 13].
###### Theorem 2.6.
Let be fixed, and .
1. The class of binary cartoon-like images contains a copy of for .
2. The class of Hölder smooth functions with contains a copy of for .
###### Proof.
ad 1) This was proved by Donoho in [6].
ad 2) To show that contains a copy of we have to find a sequence of embedded orthogonal hypercubes of dimension and size such that and (2) holds.
Let with and and put for . Then with . By possibly rescaling we can ensure . Further, we define for and the functions
.
These functions are dilated and translated versions of satisfying and . Moreover, it holds , and since the functions and are orthogonal in for .
The hypercubes of dimensions given by
Hk:=H(k2;0,(ψi,k)) ={h=k∑i1=1k∑i2=1εi1,i2ϕ(k⋅−i1)ϕ(k⋅−i2)|εi1,i2∈{0,1}} ={h=m2∑i=1εiψi,k|εi∈{0,1}}
with side-lengths are clearly contained in . We have to check (2). It holds
mk=k2 =(δk∥ψ∥2)−2β+1=∥ψ∥2β+12⋅(δk)−2β+1,
and the sequence obeys . This finishes the proof. ∎
An immediate corollary is the following result.
###### Corollary 2.7.
The function class contains a copy of for .
As a direct consequence of Theorem 2.2 we now state the main result of this subsection, which has also been proved in [15].
###### Theorem 2.8.
Given an arbitrary dictionary and allowing only polynomial depth search, for the class of cartoon-like images the decay rate of the error of the best -term approximation cannot exceed .
We observe that the upper bound on the approximation rate for is the same as for the larger class . Therefore we restrict our investigation to classes of the form . Since we are able to establish a lower bound for differing only by a log-factor from this upper bound, we do not loose much.
## 3 Hybrid Curvelets
Second generation curvelets, which are nowadays simply referred to as curvelets, were introduced in 2004 by Candès and Donoho [3]. The construction involves a parabolic scaling law, which can be viewed as a natural compromise between isotropic scaling, as utilized for wavelets, and scaling in only one coordinate direction, as utilized for ridgelets [8].
A more general anisotropic scaling law is realized by so-called -scaling, where the parameter is used to control the degree of anisotropy in the scaling. The associated -scaling matrix is defined by
Ds=(s00sα),s∈R+.
Isotropic scaling corresponds to , and scaling in one coordinate direction to . Parabolic scaling is the special case for . In this sense, curvelets can be viewed as lying in between ridgelets and wavelets.
Adapting the construction of curvelets to -scaling yields, what we will call hybrid curvelets, or more specifically -curvelets. In the following we will construct bandlimited tight frames of -curvelets for every . Thus, we obtain a whole scale of representation systems, which interpolate between wavelets for on the one end and ridgelets for on the other end.
The construction follows the same recipe used for the tight ridgelet frames in [8]. As mentioned above it can also be seen as a variation of the classical second generation curvelet frame from [3].
The construction is simplified by treating the radial and angular components separately. For the construction of the radial functions at each scale we start with -functions and with the following properties
\rm supp ˜W(0)⊂[0,2],˜W(0)(r)=1 for all r∈[0,32], \rm supp ˜W⊂[12,2],˜W(r)=1 for all r∈[34,32].
Then we define for the functions on . Finally, we rescale for every (to obtain an integer grid later)
W(j)(r):=˜W(j)(8πr),r∈R+.
Notice, that it holds .
Next, we define the angular functions on the unit circle , where specifies the scale and the orientation, running through with
Lj=2⌊j(1−α)⌋,j∈N.
This time we start with a -function , living on the whole of , satisfying
\rm supp V⊂[−34π,34π] and V(t)=1 for all t∈[−π2,π2].
Since the interval can be identified via with , we obtain -functions for every by restricting the scaled functions to . In order to end up with real-valued curvelets, we then symmetrize
V(j,0)(ξ):=˜V(j,0)(ξ)+˜V(j,0)(−ξ),ξ∈S1.
At each scale we define the characteristic angle , and for we let
Rj,ℓ=(cos(ωj,ℓ)−sin(ωj,ℓ)sin(ωj,ℓ)cos(ωj,ℓ)) (7)
be the rotation matrix by the angle . By rotating we finally get ,
V(j,ℓ)(ξ):=V(j,0)(Rj,ℓξ) for ξ∈S1.
In order to secure the tightness of the frame we need to renormalize with the function
which satisfies for all . Bringing the radial and angular components together, we obtain the functions
χ0(ξ):=W(0)(|ξ|))√Ψ(ξ),χj,ℓ(ξ)=W(j)(|ξ|)V(j,ℓ)(ξ|ξ|)√Ψ(ξ)for ξ∈R2. (8)
It is obvious that , . Moreover, these functions are real-valued, non-negative, compactly supported, and -bounded by . Let be the first unit vector and put
Sj:={x∈S1 : |⟨x,e1⟩|≥cos(ωj/2)}.
Indeed, we have and , where for , the sets
Wj,ℓ:={ξ∈R2 : 2j−1≤8π|ξ|≤2j+1,ξ|ξ|∈R−1j,ℓSj} (9)
are antipodal pairs of symmetric wedges.
After this preparation, we are ready to define the functions and on the Fourier side by
ˆψ0(ξ):=χ0(ξ) and ˆψj,ℓ(ξ):=χj,ℓ(ξ) for ξ∈R2.
They have the following important property.
###### Lemma 3.1.
For every it holds
∥f∥22=∥f∗ψ0∥22+∑j,ℓ∥f∗ψj,ℓ∥22.
###### Proof.
By construction the system satisfies the discrete Caldéron condition, i.e.,
|ˆψ0(ξ)|2+∑j,ℓ|ˆψj,ℓ(ξ)|2=1 for all ξ∈R2.
This yields for all
∥f∥22 =∫R2|ˆf(ξ)|2dξ =∫R2|ˆψ0(ξ)|2|ˆf(ξ)|2dξ+∫R2∑j,ℓ|ˆψj,ℓ(ξ)|2|ˆf(ξ)|2dξ =∥f∗ψ0∥22+∑j,ℓ∥f∗ψj,ℓ∥22.
The full frame of -curvelets is obtained by taking translates of and in the spatial domain and -normalizing afterwards. Accordingly, for , , and we define and
ψj,ℓ,k:=2−j(1+α)/2⋅ψj,ℓ(⋅−xj,ℓ,k)withxj,ℓ,k=R−1j,ℓD−12jk.
The corresponding set of curvelet indices will henceforth be denoted by . Further, we will use the following notation for this system
Cα(W(0),W,V)=(ψμ)μ∈M={ψ0,k : k∈Z2}∪{ψj,ℓ,k : j∈N,k∈Z2,ℓ∈{0,1,…,Lj | 2020-12-01 05:37:00 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9197989702224731, "perplexity": 520.7918627660671}, "config": {"markdown_headings": true, "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-2020-50/segments/1606141652107.52/warc/CC-MAIN-20201201043603-20201201073603-00334.warc.gz"} |
https://ncatlab.org/nlab/show/D%3D5+super+Yang-Mills+theory | Contents
supersymmetry
# Contents
## Properties
### As the worldvolume theory of the D4-brane
$D = 5$ SYM may be regarded as the worldvolume field theory on the D4-brane in type II string theory.
### Via reduction from the M5-brane / $D=6$ SCFT
For relation to the D=6 N=(2,0) SCFT via KK-compactification on a circle fiber, hence as worldvolume theory of the double dimensional reduction of the M5-brane (see also at Perry-Schwarz Lagrangian), see the references below.
## References
### General
• Nathan Seiberg, Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics, Phys. Lett. B388:753-760, 1996 (arXiv:hep-th/9608111)
• Arthur Hebecker, 5D Super Yang-Mills Theory in 4D Superspace, Superfield Brane Operators, and Applications to Orbifold GUTs (arXiv:hep-ph/0112230)
• Clay Cordova, Daniel Jafferis, Five-Dimensional Maximally Supersymmetric Yang-Mills in Supergravity Backgrounds (arXiv:1305.2886)
• Shuichi Yokoyama, Supersymmetry Algebra in Super Yang-Mills Theories, JHEP09(2015)211 (arXiv:1506.03522)
• I.L. Buchbinder, E.A. Ivanov, I.B. Samsonov, Low-energy effective action in $5D$, $\mathcal{N}=2$ supersymmetric gauge theory, Nuclear Physics B Volume 940, March 2019, Pages 54-62 (arXiv:1812.07206)
• Louise Anderson, Five-dimensional topologically twisted maximally supersymmetric Yang-Mills theory (arXiv:1212.5019)
The perturbation theory is considered in
### From $D = 6$ SCFT
Relation to the D=6 N=(2,0) SCFT via KK-compactification on a circle fiber, hence as worldvolume theory of the D4-brane double dimensional reduction of the M5-brane (see also at Perry-Schwarz Lagrangian):
### From M-theory on Calabi-Yau 3-folds
• Cyril Closset, Michele Del Zotto, Vivek Saxena, Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective (arXiv:1812.10451)
### Realization on $(p,q)$5-brane webs
Realization (geometric engineering) on (p,q)5-brane webs:
Last revised on July 11, 2019 at 14:54:40. See the history of this page for a list of all contributions to it. | 2019-07-16 10:38:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 11, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5888876914978027, "perplexity": 9882.092672471264}, "config": {"markdown_headings": true, "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-2019-30/segments/1563195524522.18/warc/CC-MAIN-20190716095720-20190716121720-00423.warc.gz"} |
https://dmoj.ca/problem/cco19p5 | ## CCO '19 P5 - Marshmallow Molecules
View as PDF
Points: 15 (partial)
Time limit: 1.8s
Memory limit: 1G
Author:
Problem types
##### Canadian Computing Olympiad: 2019 Day 2, Problem 2
Hannah is building a structure made of marshmallows and skewers for her chemistry class. The structure will contain marshmallows, numbered from to . Some marshmallows will be connected by skewers. Each skewer connects two marshmallows.
Hannah has requirements for her structure. Each requirement is given as a pair , which means that there must be a skewer connecting marshmallow and marshmallow .
To ensure the stability of the structure, the following requirement must also be satisfied: if , and if there is a skewer connecting marshmallow to marshmallow , and if there is a skewer connecting marshmallow to marshmallow , then there must also be a skewer connecting marshmallow to marshmallow .
Due to austerity measures imposed by the principal's office, skewers are scarce in Hannah's school. Find the minimum number of skewers necessary to satisfy all requirements.
#### Input Specification
The first line contains two space-separated integers and .
The next lines each contain two space-separated integers, with the -th line containing and . All pairs are distinct.
For 5 of the 25 marks available, .
For an additional 5 of the 25 marks available, .
For an additional 5 of the 25 marks available, for all , there is at most one pair such that .
#### Output Specification
Output a single integer, the minimum total number of skewers.
#### Sample Input 1
6 4
1 2
1 4
4 6
4 5
#### Output for Sample Input 1
6
#### Explanation for Output for Sample Input 1
In addition to those already required, there must be skewers between the pairs of marshmallows and .
#### Sample Input 2
7 6
2 3
2 6
2 7
1 3
1 4
1 5
#### Output for Sample Input 2
16 | 2021-09-21 19:30:17 | {"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": 0, "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": 0.6791747212409973, "perplexity": 3606.7908104336907}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2021-39/segments/1631780057227.73/warc/CC-MAIN-20210921191451-20210921221451-00069.warc.gz"} |
https://proofwiki.org/wiki/Book_talk:M._Ben-Ari/Mathematical_Logic_for_Computer_Science | # Book talk:M. Ben-Ari/Mathematical Logic for Computer Science
The third edition (which I laid my hands on today) is very different from the second (which I already had) which in turn mentions to be "completely rewritten" WRT the first. The third edition is really good for the basic and thorough coverage of PropCalc and PredCalc and their models that we need (although there is a quirk that Ben-Ari only defines models for finitely many relation symbols and constants at once, this can easily be overcome) so I'd like to get started covering it (before proceeding to abstractions I can't even formulate here presently). But do we need to separate the editions in some way? --Lord_Farin (talk) 23:36, 14 February 2013 (UTC)
There is a precedent for multiple editions - I think the Book:Peter Barlow/New Mathematical Tables entry is the most comprehensive instance, but a more contemporary example is Book:Roland E. Larson/Calculus. Suggest this is entirely appropriate. My own copy is the first edition (1993). An excellent example of a work which between us we have all three editions and can therefore complete it. --prime mover (talk) 06:09, 15 February 2013 (UTC)
I note that the technique for doing multiple editions needs further work. As it is, the edition is included in the title, which seems suboptimal. Maybe we should add a further parameter to the template - or even build a new template for "edition" which will then be a transcluded entry into a main page (where only the publishing details would be in the onlyinclude, the main bulk of the contents in the fully expanded page). --prime mover (talk) 07:21, 15 February 2013 (UTC)
What occurs to me as the simplest solution is sort of an amalgamation of what you suggest. Namely, to add a parameter ed or edition to the BookReference, which will render e.g. Calculus (7. ed., 2001) and link to the subpage Calculus/Edition 7 which can be referred to as is currently done on the Calculus page. As an aside, I think "Further editions" should precede the contents. In the case of the Math.Tables (where multiple first authors occur) I think redirects to these subpages should resolve any issues with the template linking to the wrong page. Since the stuff is presently only relevant in a small amount of cases I think we can afford ad hoc resolution of anything not fitting this new mould. --Lord_Farin (talk) 08:51, 15 February 2013 (UTC)
That's very much the sort of solution I was thinking of. "ed" suits me. As to whether "further editions" should precede the contents - not sure I agree with that, IMO the contents themselves are of more importance and relevance to the reader than the details of the edition (maybe that's just me, I've never been particularly interested in keeping track of editions, it's just an awkward detail that needs to be kept track of sometimes).
Making sure that technique can be used when we only report on one edition (maybe we can't find out when a work was first published) needs to be taken care of, of course. --prime mover (talk) 10:22, 15 February 2013 (UTC)
Introduced the ed parameter. Haven't bothered with changing the links to the book pages yet as I have to contemplate the precise setup of the book pages in the new suite first. It is probably impossible to make this compatible with the current approach, so that we will enter sort of a transition phase. Main issue here is that presently, the year refers to the year of first publishing, while for an edition it is far more natural to give the publishing year of that particular edition. I highly suspect that there is already considerable discrepancy in this, so it won't make matters much worse - at least not to the extent of necessitating a mind-dazzling marathon to go through all source sections.
I will post a suggested approach to the edition subpages in my sandbox. --Lord_Farin (talk) 11:21, 15 February 2013 (UTC)
Techniques exist for global search-and-replace, so the mind-dazzling marathon may not be as daunting as we might otherwise expect. This technique was invoked when the "author2" parameter was introduced, so we know it works. It's documented somewhere on a talk page, it's just a matter of digging it out. --prime mover (talk) 12:40, 15 February 2013 (UTC)
An example:
Of course, if you dislike part of it, we can change stuff. --Lord_Farin (talk) 15:22, 15 February 2013 (UTC)
Works for me. --prime mover (talk) 20:28, 15 February 2013 (UTC)
't Should all be done now. Off we go. --Lord_Farin (talk) 22:02, 15 February 2013 (UTC)
Okay, it's possible that I may be in a position to start processing the flow of the 1st edition soon. --prime mover (talk) 23:29, 15 February 2013 (UTC) | 2021-10-24 11:47:18 | {"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": 0, "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": 0.6238958239555359, "perplexity": 1395.209679192358}, "config": {"markdown_headings": true, "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-2021-43/segments/1634323585997.77/warc/CC-MAIN-20211024111905-20211024141905-00041.warc.gz"} |
http://discretemath.org/ads/s-partitions-and-law-of-addition.html |
## Section2.3Partitions of Sets and the Law of Addition
### Subsection2.3.1Partitions
One way of counting the number of students in your class would be to count the number in each row and to add these totals. Of course this problem is simple because there are no duplications, no person is sitting in two different rows. The basic counting technique that you used involves an extremely important first step, namely that of partitioning a set. The concept of a partition must be clearly understood before we proceed further.
###### Definition2.3.1Partition
A partition of set $A$ is a set of one or more nonempty subsets of $A\text{:}$ $A_1, A_2, A_3, \cdots\text{,}$ such that every element of $A$ is in exactly one set. Symbolically,
1. $A_1 \cup A_2 \cup A_3 \cup \cdots = A$
2. If $i \neq j$ then $A_i \cap A_j = \emptyset$
The subsets in a partition are often referred to as blocks. Note how our definition allows us to partition infinite sets, and to partition a set into an infinite number of subsets. Of course, if $A$ is finite the number of subsets can be no larger than $\lvert A \rvert \text{.}$
Let $A = \{a, b, c, d\}\text{.}$ Examples of partitions of $A$ are:
• $\{\{a\}, \{b\}, \{c, d\}\}$
• $\{\{a, b\}, \{c, d\}\}$
• $\{\{a\}, \{b\}, \{c\}, \{d\}\}$
How many others are there, do you suppose?
There are 15 different partitions. The most efficient way to count them all is to classify them by the size of blocks. For example, the partition $\{\{a\}, \{b\}, \{c, d\}\}$ has block sizes 1, 1, and 2.
Two examples of partitions of set of integers $\mathbb{Z}$ are
• $\{\{n\} \mid n \in \mathbb{Z}\}$ and
• $\{\{ n \in \mathbb{Z} \mid n < 0\}, \{0\},\{ n \in \mathbb{Z} \mid 0 < n \}\}\text{.}$
The set of subsets $\{\{n \in \mathbb{Z} \mid n \geq 0\},\{n \in \mathbb{Z} \mid n \leq 0\}\}$ is not a partition because the two subsets have a nonempty intersection. A second example of a non-partition is $\{\{n \in \mathbb{Z} \mid \lvert n \rvert = k\} \mid k = -1, 0, 1, 2, \cdots\}$ because one of the blocks, when $k=-1$ is empty.
One could also think of the concept of partitioning a set as a “packaging problem.” How can one “package” a carton of, say, twenty-four cans? We could use: four six-packs, three eight-packs, two twelve-packs, etc. In all cases: (a) the sum of all cans in all packs must be twenty-four, and (b) a can must be in one and only one pack.
The basic law of addition can be rephrased as follows: If $A$ is a finite set where $A_1 \cup A_2 \cup \cdots \cup A_n = A$ and where $A_i \cap A_j$ whenever $i \neq j\text{,}$ then
\begin{equation*} \lvert A \rvert = \lvert A_1 \cup A_2 \cup \cdots \cup A_n \rvert = \lvert A_1 \rvert + \lvert A_2 \rvert + \cdots + \lvert A_n \rvert \end{equation*}
The number of students in a class could be determined by adding the numbers of students who are freshmen, sophomores, juniors, and seniors, and those who belong to none of these categories. However, you probably couldn't add the students by major, since some students may have double majors.
The sophomore computer science majors were told they must take one and only one of the following courses that are open only to them: Cryptography, Data Structures, or Javascript. The numbers in each course, respectively, for sophomore CS majors, were 75, 60, 55. How many sophomore CS majors are there? The Law of Addition applies here. There are exactly $75 + 60 + 55 = 190$ CS majors since the rosters of the three courses listed above would be a partition of the CS majors.
It was determined that all junior computer science majors take at least one of the following courses: Algorithms, Logic Design, and Compiler Construction. Assume the number in each course was was 75, 60 and 55, respectively for the three courses listed. Further investigation indicated ten juniors took all three courses, twenty-five took Algorithms and Logic Design, twelve took Algorithms and Compiler Construction, and fifteen took Logic Design and Compiler Construction. How many junior C.S. majors are there?
Example 2.3.6 was a simple application of the law of addition, however in this example some students are taking two or more courses, so a simple application of the law of addition would lead to double or triple counting. We rephrase information in the language of sets to describe the situation more explicitly.
$A$ = the set of all junior computer science majors
$A_1$ = the set of all junior computer science majors who took Algorithms
$A_2$ = the set of all junior computer science majors who took Logic Design
$A_3$ = the set of all junior computer science majors who took Compiler Construction
Since all junior CS majors must take at least one of the courses, the number we want is:
\begin{equation*} \lvert A \rvert = \lvert A_1 \cup A_2 \cup A_3 \rvert = \lvert A_1 \rvert + \lvert A_2 \rvert + \lvert A_3 \rvert - \textrm{repeats}. \end{equation*}
A Venn diagram is helpful to visualize the problem. In this case the universal set $U$ can stand for all students in the university.
We see that the whole universal set is naturally partitioned into subsets that are labeled by the numbers 1 through 8, and the set $A$ is partitioned into subsets labeled 1 through 7. The region labeled 8 represents all students who are not junior CS majors. Note also that students in the subsets labeled 2, 3, and 4 are double counted, and those in the subset labeled 1 are triple counted. To adjust, we must subtract the numbers in regions 2, 3 and 4. This can be done by subtracting the numbers in the intersections of each pair of sets. However, the individuals in region 1 will have been removed three times, just as they had been originally added three times. Therefore, we must finally add their number back in.
\begin{equation*} \begin{split} \lvert A \rvert & = \lvert A_1 \cup A_2 \cup A_3 \rvert \\ & = \lvert A_1 \rvert + \lvert A_2 \rvert + \lvert A_3 \rvert - \textrm{repeats} \\ & = \lvert A_1 \rvert + \lvert A_2 \rvert + \lvert A_3 \rvert - \textrm{duplicates} + \textrm{triplicates} \\ & = \lvert A_1 \rvert + \lvert A_2 \rvert + \lvert A_3 \rvert - \left(\lvert A_1 \cap A_2 \rvert + \lvert A_1 \cap A_3 \rvert+ \lvert A_2 \cap A_3 \rvert \right) + \lvert A_1 \cap A_2 \cap A_3 \rvert \\ & = 75 + 60 + 55 - 25 - 12 - 15 + 10 = 148 \end{split} \end{equation*}
The ideas used in this latest example gives rise to a basic counting technique:
The inclusion-exclusion laws extend to more than three sets, as will be explored in the exercises.
In this section we saw that being able to partition a set into disjoint subsets gives rise to a handy counting technique. Given a set, there are many ways to partition depending on what one would wish to accomplish. One natural partitioning of sets is apparent when one draws a Venn diagram. This particular partitioning of a set will be discussed further in Chapters 4 and 13.
### SubsectionExercises for Section 2.3
###### 1
List all partitions of the set $A =\{a, b, c\}\text{.}$
$\{\{a\}, \{b\}, \{c\}\}, \{\{a, b\}, \{c\}\}, \{\{a, c\}, \{b\}\}, \{\{a\}, \{b, c\}\}, \{\{a, b, c\}\}$
###### 2
Which of the following collections of subsets of the plane, $\mathbb{R}^2\text{,}$ are partitions?
1. $\{ \{(x, y) \mid x + y = c \} \mid c \in \mathbb{R} \}$
2. The set of all circles in $\mathbb{R}^2$
3. The set of all circles in $\mathbb{R}^2$ centered at the origin together with the set $\{(0,0)\}$
4. $\{\{(x, y)\} \mid (x, y) \in \mathbb{R}^2 \}$
###### 3
A student, on an exam paper, defined the term partition the following way: “Let $A$ be a set. A partition of $A$ is any set of nonempty subsets $A_1, A_2, A_3, \dots$ of $A$ such that each element of $A$ is in one of the subsets.” Is this definition correct? Why?
No. By this definition it is possible that an element of $A$ might belong to two of the subsets.
###### 4
Let $A_1$ and $A_2$ be subsets of a set $U\text{.}$ Draw a Venn diagram of this situation and shade in the subsets $A_1 \cap A_2\text{,}$ $A_1^c \cap A_2\text{,}$ $A_1 \cap A_2^c\text{,}$ and $A_1^c \cap A_2^c$ . Use the resulting diagram and the definition of partition to convince yourself that the subset of these four subsets that are nonempty form a partition of $U\text{.}$
###### 5
Show that $\{\{2 n \mid n \in \mathbb{Z}\}, \{2 n + 1 \mid n \in \mathbb{Z}\}\}$ is a partition of $\mathbb{Z}\text{.}$ Describe this partition using only words.
The first subset is all the even integers and the second is all the odd integers. These two sets do not intersect and they cover the integers completely.
###### 6
1. A group of 30 students were surveyed and it was found that 18 of them took Calculus and 12 took Physics. If all students took at least one course, how many took both Calculus and Physics? Illustrate using a Venn diagram.
2. What is the answer to the question in part (a) if five students did not take either of the two courses? Illustrate using a Venn diagram.
###### 7
A survey of 90 people, 47 of them played tennis and 42 of them swam. If 17 of the them participated in both activities, how many of them participated in neither?
Since 17 participated in both activities, 30 of the tennis players only played tennis and 25 of the swimmers only swam. Therefore, $17+30+25=72$ of those who were surveyed participated in an activity and so 18 did not.
###### 8
A survey of 300 people found that 60 owned an iPhone, 75 owned a Blackberry, and 30 owned an Android phone. Furthermore, 40 owned both an iPhone and a Blackberry, 12 owned both an iPhone and an Android phone, and 8 owned a Blackberry and an Android phone. Finally, 3 owned all three phones.
1. How many people surveyed owned none of the three phones?
2. How many people owned a Blackberry but not an iPhone?
3. How many owned a Blackberry but not an Android?
###### 9
Regarding the Theorem 2.3.9,
1. Use the two set inclusion-exclusion law to derive the three set inclusion-exclusion law. Note: A knowledge of basic set laws is needed for this exercise.
2. State and derive the inclusion-exclusion law for four sets.
Solution
We assume that $\lvert A_1 \cup A_2 \rvert = \lvert A_1 \rvert +\lvert A_2\rvert -\lvert A_1\cap A_2\rvert$.
\begin{equation*} \begin{split} \lvert A_1 \cup A_2\cup A_3 \rvert & =\lvert (A_1\cup A_2) \cup A_3 \rvert \quad Why?\\ & = \lvert A_1\cup A_2\rvert +\lvert A_3 \rvert -\lvert (A_1\cup A_2)\cap A_3\rvert \quad Why? \\ & =\lvert (A_1\cup A_2\rvert +\lvert A_3\rvert -\lvert (A_1\cap A_3)\cup (A_2\cap A_3)\rvert \quad Why?\\ & =\lvert A_1\rvert +\lvert A_2\rvert -\lvert A_1\cap A_2\rvert +\lvert A_3\rvert \\ & \quad -(\lvert A_1\cap A_3\rvert +\lvert A_2\cap A_3\rvert -\lvert (A_1\cap A_3)\cap (A_2\cap A_3)\rvert\quad Why?\\ & =\lvert A_1\rvert +\lvert A_2\rvert +\lvert A_3\rvert -\lvert A_1\cap A_2\rvert -\lvert A_1\cap A_3\rvert\\ & \quad -\lvert A_2\cap A_3\rvert +\lvert A_1\cap A_2\cap A_3\rvert \quad Why? \end{split} \end{equation*}
The law for four sets is
\begin{equation*} \begin{split} \lvert A_1\cup A_2\cup A_3\cup A_4\rvert & =\lvert A_1\rvert +\lvert A_2\rvert +\lvert A_3\rvert +\lvert A_4\rvert\\ & \quad -\lvert A_1\cap A_2\rvert -\lvert A_1\cap A_3\rvert -\lvert A_1\cap A_4\rvert \\ & \quad \quad -\lvert A_2\cap A_3\rvert -\lvert A_2\cap A_4\rvert -\lvert A_3\cap A_4\rvert \\ & \quad +\lvert A_1\cap A_2\cap A_3\rvert +\lvert A_1\cap A_2\cap A_4\rvert \\ & \quad \quad +\lvert A_1\cap A_3\cap A_4\rvert +\lvert A_2\cap A_3\cap A_4\rvert \\ & \quad -\lvert A_1\cap A_2\cap A_3\cap A_4\rvert \end{split} \end{equation*}
Derivation:
\begin{equation*} \begin{split} \lvert A_1\cup A_2\cup A_3\cup A_4\rvert & = \lvert (A_1\cup A_2\cup A_3)\cup A_4\rvert \\ & = \lvert (A_1\cup A_2\cup A_3\rvert +\lvert A_4\rvert -\lvert (A_1\cup A_2\cup A_3)\cap A_4\rvert\\ & = \lvert (A_1\cup A_2\cup A_3\rvert +\lvert A_4\rvert \\ & \quad -\lvert (A_1\cap A_4)\cup (A_2\cap A_4)\cup (A_3\cap A_4)\rvert \\ & = \lvert A_1\rvert +\lvert A_2\rvert +\lvert A_3\rvert -\lvert A_1\cap A_2\rvert -\lvert A_1\cap A_3\rvert \\ & \quad -\lvert A_2\cap A_3\rvert +\lvert A_1\cap A_2\cap A_3\rvert +\lvert A_4\rvert -\lvert A_1\cap A_4\rvert \\ & \quad+\lvert A_2\cap A_4\rvert +\lvert A_3\cap A_4\rvert -\lvert (A_1\cap A_4)\cap (A_2\cap A_4)\rvert \\ & \quad -\lvert (A_1\cap A_4)\cap (A_3\cap A_4)\rvert -\lvert (A_2\cap A_4)\cap (A_3\cap A_4)\rvert \\ & \quad +\lvert (A_1\cap A_4)\cap (A_2\cap A_4)\cap (A_3\cap A_4)\rvert \\ & =\lvert A_1\rvert +\lvert A_2\rvert +\lvert A_3\rvert +\lvert A_4\rvert -\lvert A_1\cap A_2\rvert -\lvert A_1\cap A_3\rvert \\ & \quad -\lvert A_2\cap A_3\rvert -\lvert A_1\cap A_4\rvert -\lvert A_2\cap A_4\rvert \quad -\lvert A_3\cap A_4\rvert \\ & \quad +\lvert A_1\cap A_2\cap A_3\rvert +\lvert A_1\cap A_2\cap A_4\rvert \\ & \quad +\lvert A_1\cap A_3\cap A_4\rvert +\lvert A_2\cap A_3\cap A_4\rvert \\ & \quad -\lvert A_1\cap A_2 \cap A_3\cap A_4\rvert \end{split} \end{equation*}
###### 10
To complete your spring schedule, you must add Calculus and Physics. At 9:30, there are three Calculus sections and two Physics sections; while at 11:30, there are two Calculus sections and three Physics sections. How many ways can you complete your schedule if your only open periods are 9:30 and 11:30?
###### 11
The definition of $\mathbb{Q} = \{a/b \mid a, b \in \mathbb{Z}, b \neq 0\}$ given in Chapter 1 is awkward. If we use the definition to list elements in $\mathbb{Q}\text{,}$ we will have duplications such as $\frac{1}{2}\text{,}$ $\frac{-2}{-4}$ and $\frac{300}{600}$ Try to write a more precise definition of the rational numbers so that there is no duplication of elements. | 2018-08-14 11:21:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9948190450668335, "perplexity": 1213.4420035051069}, "config": {"markdown_headings": true, "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-2018-34/segments/1534221209021.21/warc/CC-MAIN-20180814101420-20180814121420-00492.warc.gz"} |
https://ww2.mathworks.cn/help/comm/ref/rls.html | Main Content
# rls
(To be removed) Construct recursive least squares (RLS) adaptive algorithm object
rls will be removed in a future release. Use `comm.LinearEqualizer` or `comm.DecisionFeedback` instead.
## Syntax
```alg = rls(forgetfactor) alg = rls(forgetfactor,invcorr0) ```
## Description
The `rls` function creates an adaptive algorithm object that you can use with the `lineareq` function or `dfe` function to create an equalizer object. You can then use the equalizer object with the `equalize` function to equalize a signal. To learn more about the process for equalizing a signal, see Equalization.
`alg = rls(forgetfactor)` constructs an adaptive algorithm object based on the recursive least squares (RLS) algorithm. The forgetting factor is `forgetfactor`, a real number between 0 and 1. The inverse correlation matrix is initialized to a scalar value.
`alg = rls(forgetfactor,invcorr0)` sets the initialization parameter for the inverse correlation matrix. This scalar value is used to initialize or reset the diagonal elements of the inverse correlation matrix.
### Properties
The table below describes the properties of the RLS adaptive algorithm object. To learn how to view or change the values of an adaptive algorithm object, see Equalization.
PropertyDescription
`AlgType`Fixed value, `'RLS'`
`ForgetFactor`Forgetting factor
`InvCorrInit`Scalar value used to initialize or reset the diagonal elements of the inverse correlation matrix
Also, when you use this adaptive algorithm object to create an equalizer object (via the `lineareq` function or `dfe` function), the equalizer object has an `InvCorrMatrix` property that represents the inverse correlation matrix for the RLS algorithm. The initial value of `InvCorrMatrix` is `InvCorrInit*eye(N)`, where `N` is the total number of equalizer weights.
## Examples
collapse all
This example configures the recommended `comm.LinearEqualizer` System object™ and the legacy `lineareq` feature with comparable settings.
Initialize Variables and Supporting Objects
```d = randi([0 3],1000,1); x = pskmod(d,4,pi/4); r = awgn(x,25); sps = 2; %samples per symbol for oversampled cases nTaps = 6; txFilter = comm.RaisedCosineTransmitFilter('FilterSpanInSymbols',nTaps, ... 'OutputSamplesPerSymbol',4); rxFilter = comm.RaisedCosineReceiveFilter('FilterSpanInSymbols',nTaps, ... 'InputSamplesPerSymbol',4,'DecimationFactor',2); x2 = txFilter(x); r2 = rxFilter(awgn(x2,25,0.5)); filterDelay = txFilter.FilterSpanInSymbols/2 + ... rxFilter.FilterSpanInSymbols/2; % Total filter delay in symbols```
To compare the equalized output, plot the constellations using code such as:
```% plot(yNew,'*') % hold on % plot(yOld,'o') % hold off; legend('New Eq','Old Eq'); grid on```
Use RLS Algorithm with Linear Equalizer
Configure `lineareq` and `comm.LinearEqualizer` objects with comparable settings.
`eqOld = lineareq(5,rls(0.95),pskmod(0:3,4,pi/4))`
```eqOld = EqType: 'Linear Equalizer' AlgType: 'RLS' nWeights: 5 nSampPerSym: 1 RefTap: 1 SigConst: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i] InvCorrInit: 0.1000 InvCorrMatrix: [5×5 double] Weights: [0 0 0 0 0] WeightInputs: [0 0 0 0 0] ResetBeforeFiltering: 1 NumSamplesProcessed: 0 ```
```eqNew = comm.LinearEqualizer('NumTaps',5,'Algorithm','RLS', ... 'ForgettingFactor',0.95,'Constellation',pskmod(0:3,4,pi/4),'ReferenceTap',1) ```
```eqNew = comm.LinearEqualizer with properties: Algorithm: 'RLS' NumTaps: 5 ForgettingFactor: 0.9500 InitialInverseCorrelationMatrix: 0.1000 Constellation: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i] ReferenceTap: 1 InputDelay: 0 InputSamplesPerSymbol: 1 TrainingFlagInputPort: false AdaptAfterTraining: true InitialWeightsSource: 'Auto' WeightUpdatePeriod: 1```
Call the equalizers. When `ResetBeforeFiltering` is set to `true`, each call of the `equalize` object resets the equalizer. To get the equivalent behavior call `reset` after each call of the `comm.LinearEqualizer` object.
```yOld1 = equalize(eqOld,r,x(1:100)); yOld2 = equalize(eqOld,r,x(1:100)); yNew1 = eqNew(r,x(1:100)); reset(eqNew) yNew2 = eqNew(r,x(1:100));```
Configure `lineareq` and `comm.LinearEqualizer` objects with comparable settings. For the `comm.LinearEqualizer` object, set the initial inverse correlation matrix to `eye(5)*0.2`.
`eqOld = lineareq(5,rls(0.95),pskmod(0:3,4,pi/4))`
```eqOld = EqType: 'Linear Equalizer' AlgType: 'RLS' nWeights: 5 nSampPerSym: 1 RefTap: 1 SigConst: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i] ForgetFactor: 0.9500 InvCorrInit: 0.1000 InvCorrMatrix: [5×5 double] Weights: [0 0 0 0 0] WeightInputs: [0 0 0 0 0] ResetBeforeFiltering: 1 NumSamplesProcessed: 0 ```
```eqNew = comm.LinearEqualizer('NumTaps',5,'Algorithm','RLS', ... 'ForgettingFactor',0.95,'Constellation',pskmod(0:3,4,pi/4),'ReferenceTap',1, ... 'InitialInverseCorrelationMatrix',eye(5)*0.2) ```
```eqNew = comm.LinearEqualizer with properties: Algorithm: 'RLS' NumTaps: 5 ForgettingFactor: 0.9500 InitialInverseCorrelationMatrix: [5×5 double] Constellation: [0.7071 + 0.7071i -0.7071 + 0.7071i -0.7071 - 0.7071i 0.7071 - 0.7071i] ReferenceTap: 1 InputDelay: 0 InputSamplesPerSymbol: 1 TrainingFlagInputPort: false AdaptAfterTraining: true InitialWeightsSource: 'Auto' WeightUpdatePeriod: 1```
Call the equalizers. When `ResetBeforeFiltering` is set to `true`, each call of the `equalize` object resets the equalizer. To get the equivalent behavior call `reset` after each call of the `comm.LinearEqualizer` object.
```yOld1 = equalize(eqOld,r,x(1:100)); yOld2 = equalize(eqOld,r,x(1:100)); yNew1 = eqNew(r,x(1:100)); reset(eqNew) yNew2 = eqNew(r,x(1:100));```
## Algorithms
Referring to the schematics presented in Equalization, define w as the vector of all weights wi and define u as the vector of all inputs ui. Based on the current set of inputs, u, and the current inverse correlation matrix, P, this adaptive algorithm first computes the Kalman gain vector, K
`$K=\frac{Pu}{\left(ForgettingFactor\right)+{u}^{H}Pu}.$`
where H denotes the Hermitian transpose.
Then the new inverse correlation matrix is given by
(`ForgetFactor`)-1(P – KuHP)
and the new set of weights is given by
w + K*e
where the * operator denotes the complex conjugate.
## Compatibility Considerations
expand all
Warns starting in R2020a
## References
[1] Farhang-Boroujeny, B., Adaptive Filters: Theory and Applications, Chichester, England, John Wiley & Sons, 1998.
[2] Haykin, S., Adaptive Filter Theory, Third Ed., Upper Saddle River, NJ, Prentice-Hall, 1996.
[3] Kurzweil, J., An Introduction to Digital Communications, New York, John Wiley & Sons, 2000.
[4] Proakis, John G., Digital Communications, Fourth Ed., New York, McGraw-Hill, 2001.
## See Also
### Topics
Introduced before R2006a
## Support
#### Bridging Wireless Communications Design and Testing with MATLAB
Download white paper | 2021-12-09 05:32:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7451891303062439, "perplexity": 1970.9307786946758}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "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-2021-49/segments/1637964363659.21/warc/CC-MAIN-20211209030858-20211209060858-00149.warc.gz"} |