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## adajiamcneal one year ago medal Delete Cancel Submit
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@zepdrix
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Please don't name your post "Medal" -_- lol Anyway.. let's see what we've got :U
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$\large\rm \color{royalblue}{m=\frac{2}{7}},\qquad\qquad (0,-12)\quad\to\quad \color{orangered}{b=-12}$ Simply plug the information they gave you into your slope-intercept form :)$\large\rm y=\color{royalblue}{m}x+\color{orangered}{b}$
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y = 2/7x+ -12
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yay good job \c:/
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Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy. | {"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": 0.999667763710022, "perplexity": 23310.689638277698}, "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/1476988719677.59/warc/CC-MAIN-20161020183839-00294-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://cstheory.stackexchange.com/questions/3620/subexponentially-solvable-hard-graph-problems/3631 | Subexponentially solvable hard graph problems
In light of the recent result of Arora, Barak, and Steurer, Subexponential Algorithms for Unique Games and Related Problems, I'm interested in graph problems that have subexponential time algorithms but believed not to be polynomially solvable. A famous example is graph isomorphism which has subexponential algorithm of $2^{O(n^{1/2} \log n)}$ run-time. Another example is log-Clique problem which is solvable in quasi-polynomial time ($n^{O(\log n)}$).
I'm looking for interesting examples and preferably a reference to surveys of subexponential hard graph problems (not necessarily $NP$-complete). Also, Are there any $NP$-complete graph problems with subexponential time algorithms?
Impagliazzo, Paturi and Zane showed that the Exponential Time Hypothesis implies that Clique, k-Colorability, and Vertex Cover need $2^{\Omega(n)}$ time.
• Just for completeness: log-CLIQUE = $\{(G, k) | G \text{ has }n\text{ vertices, }k = \log n\text{ and }G\text{ has a clique of size }k\}$ – M.S. Dousti Dec 8 '10 at 0:32
By the way the Max Clique problem, in full generality, can be solved in time $2^{\tilde O(\sqrt N)}$ where $N$ is the size of the input.
This is trivial if the graph is represented via an adjacency matrix, because then $N=|V|^2$, and a brute force search will take time $2^{O(|V|)}$.
But we can get the same bound even if the graph is represented by adjacency lists, via an algorithm of running time $2^{\tilde O(\sqrt{|V| + |E|})}$. To see how, let's get a $2^{\tilde O(\sqrt{|V| + |E|})}$-time algorithm for the NP-complete decision problem in which we are given a graph $G=(V,E)$ and $k$ and we want to know if there is a clique of size $\geq k$.
The algorithm simply removes all vertices of degree $< k$ and the edges incident on them, then does it again, and so on, until we are left with a vertex-induced subgraph over a subset $V'$ of vertices, each of degree $\geq k$, or with an empty graph. In the latter case, we know that no clique of size $\geq k$ can exist. In the former case, we do a brute-force search running in time roughly $|V'|^k$. Note that $|E| \geq k\cdot |V'| /2$ and $k\leq |V'|$, so that that $|E| \geq k^2/2$, and so a brute-force search running in time $|V'|^k$ is actually running in time $2^{O(\sqrt{|E|} \cdot \log |V|)}$.
• Indeed, for these kinds of reasons Impagliazzo, Paturi and Zane argued that when asking about $2^{\Omega(n)}$ vs $2^{o(n)}$ complexity you need to set $n$ to be the size of the witness (which you need to define as part of the problem). In the $k$-clique case the witness is of size $\log \binom{|V|}{k} \sim k\log |V|$ for small $k$, while, as you say, you can assume w.l.o.g there are at least $k|V|$ edges and the input size is much larger than the witness size. – Boaz Barak Dec 13 '10 at 3:02
Since every planar graph on $n$ vertices has treewidth $O(\sqrt{n})$, all problems which are solvable in $O^*(2^{O(k)})$ time for graphs of treewidth at most~$k$ (there are a LOT of such problems) have subexponential-time algorithms on planar graphs by computing a constant-factor approximation to the treewidth in polynomial-time (for example by computing the branchwidth with the ratcatcher algorithm) and then running the treewidth algorithm, resulting in runtimes of the form $O^*(2^{O(\sqrt{n})})$ for graphs on $n$ vertices. Examples are Planar Independent Set and Planar Dominating Set, which are NP-complete of course.
There is a close connection between sub-exponential time solvability (SUBEPT) and fixed parameter tractability (FPT). The link between them is provided in the following paper.
An isomorphism between subexponential and parameterized complexity theory, Yijia Chen and Martin Grohe, 2006.
In brief, they introduced a notion called miniaturization mapping, which maps a parameterized problem $(P,\nu)$ into another parameterized problem $(Q,\kappa)$. By viewing a normal problem as a problem parameterized by the input size, we have the following connection. (See theorem 16 in the paper)
Theorem. $(P,\nu)$ is in SUBEPT iff $(Q,\kappa)$ is in FPT.
Be careful of the definitions here. Normally we view $k$-clique problem as parameterized in $k$, so there is no sub-exponential time algorithm for it assuming Exponential time hypothesis. But here we let the problem be parameterized by the input size $O(m+n)$, thus the problem can be solved in $2^{O(\sqrt{m}\log m)}$, which is a sub-exponential time algorithm. And the theorem tells us that the $k$-clique problem is fixed parameter tractable under the some twist of the parameter $k$, which is reasonable.
In general, problems in SUBEPT under SERF-reductions (sub-exponential reduction families) can be transformed into problems in FPT under FPT-reductions. (Theorem 20 in the paper) Furthermore, the connections are even stronger since they provided an isomorphism theorem between a whole hierarchy of problems in exponential time complexity theory and parameterized complexity theory. (Theorem 25 and 47) Though the isomorphism is not complete (there are some missing links between them), it is still nice to have a clear picture about these problems, and we can study sub-exponential time algorithms via parameterized complexity.
See the survey by Jörg Flum and Martin Grohe, together with Jacobo Torán, the editor of the complexity column, for more information.
• Yes. btw, Flum and Grohe wrote the survey; Toran is the Complexity Column editor. – Andy Drucker Dec 8 '10 at 17:05
• @Andy: Thank you for the correction. I'll modified the article accordingly. – Hsien-Chih Chang 張顯之 Dec 9 '10 at 1:00
another example can be Cop and Robber game, which is NP-hard but solvable in time $2^{o(n)}$ on graphs with n vertices. BibTeX bibliographical record in XML Fedor V. Fomin, Petr A. Golovach, Jan Kratochvíl, Nicolas Nisse, Karol Suchan: Pursuing a fast robber on a graph. Theor. Comput. Sci. 411(7-9): 1167-1181 (2010)
• Oops, this may be shameful, but I had a long time believing $\mathsf{NP}$-hard problems do not have sub-exponential time algorithms, just because the Exponential Time Hypothesis. :( – Hsien-Chih Chang 張顯之 Dec 7 '10 at 13:24
• No shame... but, one easy way to see this is not true is to take any $NP$-hard language $L \in NPTIME(n^k)$, and then form a 'padded' version $L'$ in which the 'yes' instances are of form $(x, 1^{|x|^c})$, with $x \in L$, for some fixed $c > k$. Then $L'$ is $NP$, but has a deterministic algorithm running in time essentially $2^{n^{k/c}}$. – Andy Drucker Dec 8 '10 at 17:03
The best approximation algorithm for clique gives an unbelievably bad approximation factor $n/\text{polylog } n$ (recall that approximation factor of $n$ is trivial).
There are hardness of approximation results under various hardness assumptions that don't quite match this, but still give hardness of $n^{1-o(1)}$. Personally, I believe that $n/\text{polylog } n$ approximation for clique is as good as polynomial-time algorithms would ever do.
But approximation of $n/\text{polylog } n$ for clique can easily be done in quasi-polynomial time.
An NP-hard problem is a problem that has a polynomial-time reduction from SAT. Even if SAT needs time $2^{\Omega(n)}$, this may translate to time $2^{\Omega(N^\epsilon)}$ for the problem we reduce to. If the latter has input size N, it may be the case that $N=n^{1/\epsilon}$ for a small constant $\epsilon$. | {"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": 0.8948687314987183, "perplexity": 524.4988182453868}, "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-2021-21/segments/1620243991514.63/warc/CC-MAIN-20210518191530-20210518221530-00351.warc.gz"} |
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2155 | ## Modeling Deep Geothermal Reservoirs: Recent Advances and Future Problems
• Due to the increasing demand of renewable energy production facilities, modeling geothermal reservoirs is a central issue in today's engineering practice. After over 40 years of study, many models have been proposed and applied to hundreds of sites worldwide. Nevertheless, with increasing computational capabilities new efficient methods are becoming available. The aim of this paper is to present recent progress on seismic processing as well as fluid and thermal flow simulations for porous and fractured subsurface systems. The commonly used methods in industrial energy exploration and production such as forward modeling, seismic migration, and inversion methods together with continuum and discrete flow models for reservoir monitoring and management are reviewed. Furthermore, for two specific features numerical examples are presented. Finally, future fields of studies are described.
$Rev: 13581$ | {"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": 0.8654159903526306, "perplexity": 1398.778059611904}, "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-2015-35/segments/1440644068749.35/warc/CC-MAIN-20150827025428-00035-ip-10-171-96-226.ec2.internal.warc.gz"} |
http://www.okstate.edu/sas/v8/sashtml/ets/chap20/sect25.htm | Chapter Contents Previous Next
The TSCSREG Procedure
## Specification Tests
The TSCSREG procedure outputs the results of one specification test for fixed effects and one specification test for random effects.
For fixed effects, let be the n dimensional vector of fixed effects parameters. The specification test reported is the conventional F-statistic for the hypothesis . The F-statistic with n, M-K degrees of freedom is computed as
where is the estimated covariance matrix of the fixed effects parameters.
Hausman's (1978) specification test or m-statistic can be used to test hypotheses in terms of bias or inconsistency of an estimator. This test was also proposed by Wu (1973) and further extended in Hausman and Taylor (1982). Hausman's m-statistic is as follows.
Consider two estimators, and , which under the null hypothesis are both consistent, but only is asymptotically efficient. Under the alternative hypothesis, only is consistent. The m-statistic is
where and are consistent estimates of the asymptotic covariance matrices of and . Then m is distributed with k degrees of freedom, where k is the dimension of and .
In the random effects specification, the null hypothesis of no correlation between effects and regressors implies that the OLS estimates of the slope parameters are consistent and inefficient but the GLS estimates of the slope parameters are consistent and efficient. This facilitates a Hausman specification test. The reported statistic has degrees of freedom equal to the number of slope parameters.
Chapter Contents Previous Next Top | {"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": 0.9851832389831543, "perplexity": 1059.3279063422162}, "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-2017-43/segments/1508187828178.96/warc/CC-MAIN-20171024052836-20171024072836-00503.warc.gz"} |
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Map%3A_Physical_Chemistry_(McQuarrie_and_Simon)/19%3A_The_First_Law_of_Thermodynamics/19.09%3A_Heat_Capacity_is_a_Path_Function | # 19.9: Heat Capacity is a Path Function
## Determining enthalpies from heat capacities.
The functions $$H$$ and $$C_p$$ are related by differentiation:
$\left ( \dfrac{\partial H}{ \partial T} \right)_P = C_P$
This means that we can:
1. measure $$C_p$$ as a function of temperature
2. integrate this function and find $$H(T)$$
However, there are problems with this approach:
1. Reference point: we have to deal with the lower limit of integration.
Ideally we start at zero Kelvin (but we cannot get there), but how do we compare one compound to the other?
2. At temperatures where there is a phase transition there is a sudden jump in enthalpy. E.g. when ice melts we have to first add the heat of fusion until all ice is gone before the temperature can go up again (assuming all is done under reversible well-equilibrated conditions).
3. At the jumps in H, the Cp is infinite.
It should be stressed that there are no absolute enthalpies. | {"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": 0.9660962820053101, "perplexity": 754.7832107501914}, "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/1606141189038.24/warc/CC-MAIN-20201127015426-20201127045426-00144.warc.gz"} |
http://physics.ust.hk/eng/event_detail.php?id=107 | Abstract The topological states of matter recognized as new phases of matter has become a central research field in condensed matter physics in the past two decades due to its exotic properties like nontrivial band topology, topologically protected edge and surface states, and topological phase transitions without symmetry breaking. In this thesis, we give a brief introduction to the topological Chern insulator and Weyl semimetal in Chapter 1, study the disorderinduced topological phase transitions in topological Chern insulators and Weyl semimetals in Chapters 2 and 3, and topological magnetic states in ferromagnetic materials in Chapters 4 and 5. The disordered-induced topological phase transition was firstly found in topological Anderson insulator (TAI) suggests that when time-reversal symmetry (TRS) is maintained, the pertinent topological phase transition, marked by re-entrant $\frac{2e^2}{h}$ quantized conductance contributed by helical edge states, is driven by disorder. In Chapter 2, we show that when TRS is broken, the physics of TAI becomes even richer. The pattern of longitudinal conductance and nonequilibrium local current distribution displays novel TAI phases characterized by nonzero Chern numbers, indicating the occurrence of multiple chiral edge modes. Tuning either disorder or Fermi energy (in both topologically trivial and nontrivial phases), drives transitions between these distinct TAI phases, characterized by jumps of the quantized conductance from $0$ to $\frac{e^2}{h}$ and from $\frac{e^2}{h}$ to $\frac{2e^2}{h}$. An effective medium theory based on the Born approximation yields an accurate description of different TAI phases in parameter space. In Chapter 3, the Quantum phase transitions of three-dimensional (3D) Weyl semimetals (WSMs) subject to uncorrelated on-site disorder are investigated through quantum conductance calculations and finite-size scaling of localization length. Contrary to a previous belief that a direct transition from a WSM to a diffusive metal (DM) occurs, an intermediate phase of Chern insulator (CI) between the two distinct metallic phases should exist due to internode scattering that is comparable to intranode scattering and persists at Weyl nodes for nonzero disorder. The critical exponent of localization length is $v\sim 1.3$ for both the WSM-CI and CI-DM transitions, in the same universality class of the 3D Gaussian unitary ensemble of Anderson localization transition. The CI phase was confirmed by quantized nonzero Hall conductance in the bulk insulating phase established by localization length calculations. The disorderinduced various plateau-plateau transitions in both WSM and CI phases were observed and explained by the self-consistent Born approximation. The initial studies of topological states were exclusively for electronic systems. It is now known that topological states can also exist for other particles. Indeed, topologically protected edge states have already been found for phonons and photons. In spite of active searching for topological states in many fields, the studies in magnetism are relatively rare although topological states are apparently important and useful in magnonics. In Chapter 4, we show that the pyrochlore ferromagnets with the Dzyaloshinskii-Moriya interaction are intrinsic magnonic Weyl semimetals. Similar to the electronic Weyl semimetals, the magnon bands in a magnonic Weyl semimetal are nontrivially crossing in pairs at special points (called Weyl nodes) in momentum space. The equal energy contour around the Weyl node energy is made up by the magnon arcs on sample surfaces due to the topologically protected surface states between each pair of Weyl nodes. Additional Weyl nodes and magnon arcs can be generated in lower energy magnon bands when an anisotropic exchange interaction is introduced. In Chapter 5, the chiral anomaly of Weyl magnons (WMs), featured by nontrivial band crossings at paired Weyl nodes (WNs) of opposite chirality, is investigated. It is shown that WMs can be realized in stacked honeycomb ferromagnets. Using the Aharonov-Casher effect that is about the interaction between magnetic moments and electric fields, the magnon motion in honeycomb layers can be quantized into magnonic Landau levels (MLLs). The zeroth MLL is chiral so that unidirectional WMs propagate in the perpendicular (to the layer) direction for a given WN under a magnetic field gradient from one WN to the other and change their chiralities, resulting in the magnonic chiral anomaly (MCA). A net magnon current carrying spin and heat through the zeroth MLL depends linearly on the magnetic field gradient and the electric field gradient in the ballistic transport. | {"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": 0.8655622005462646, "perplexity": 1299.137315173331}, "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-2018-39/segments/1537267164469.99/warc/CC-MAIN-20180926081614-20180926102014-00280.warc.gz"} |
http://cjtcs.cs.uchicago.edu/articles/2016/9/contents.html | ### Volume 2016
#### Computing the Degenerate Ground Space of Gapped Spin Chains in Polynomial Time
Christopher T. Chubb
University of Sydney,
Sydney, NSW, Australia;
christopher DOT chubb AT sydney DOT edu DOT au
Steven T. Flammia
University of Sydney,
Sydney, NSW, Australia;
steven DOT flammia sydney DOT edu DOT au
July 27, 2016
#### Abstract
Given a gapped Hamiltonian of a spin chain, we give a polynomial-time algorithm for finding the degenerate ground space projector. The output is an orthonormal set of matrix product states that approximate the true ground space projector up to an inverse polynomial error in any Schatten norm, with a runtime exponential in the degeneracy. Our algorithm is an extension of the recent algorithm of Landau, Vazirani, and Vidick for the nondegenerate case, and it includes the recent improvements due to Huang. The main new idea is to incorporate the local distinguishability of ground states on the half-chain to ensure that the algorithm returns a complete set of global ground states.
• The article: PDF (359 KB)
• Source material: ZIP (155 KB)
Submitted June 16, 2015, revised May 12, 2016, and in final form July 24, 2016, published July 27, 2016.
Volume 2016, Article 8 Article 10
Volume 2016 Published articles | {"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": 0.9248905181884766, "perplexity": 2851.4594694613224}, "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-2017-47/segments/1510934806715.73/warc/CC-MAIN-20171123012207-20171123032207-00249.warc.gz"} |
http://garden.irmacs.sfu.ca/op/the_borodin_kostochka_conjecture | # The Borodin-Kostochka Conjecture
Importance: Medium ✭✭
Author(s): Borodin, Oleg V. Kostochka, Alexandr V.
Subject: Graph Theory
Keywords:
Posted by: Andrew King on: September 10th, 2012
Conjecture Every graph with maximum degree has chromatic number at most .
The Borodin-Kostochka conjecture proposes that for any graph with maximum degree and clique number , is colourable so long as is sufficiently large (specifically, ). The requirement that is necessary, as one can see by looking at the strong product of and .
Reed [R] proved that there exists a for which the conjecture holds whenever . Specifically he proved that , but claims that more careful analysis could reduce to 1000.
The conjecture was recently proven by Cranston and Rabern for claw-free graphs [CR]. In their paper they mention an unpublished strengthening proposed by Borodin and Kostochka, namely that one can replace the chromatic number in the statement of the conjecture with the list chromatic number.
## Bibliography
[BK] O. V. Borodin and A. V. Kostochka. On an upper bound of a graph's chromatic number, depending on the graph's degree and density. JCTB 23 (1977), 247--250.
[CR] D. W. Cranston and L. Rabern. Coloring claw-free graphs with colors, arXiv 1206.1269, 2012.
[R] B. A. Reed. A strengthening of Brooks’ Theorem. J. Comb. Theory Ser. B, 76:136–149, 1999.
* indicates original appearance(s) of problem. | {"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": 0.8552303314208984, "perplexity": 2170.655155497196}, "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-2022-27/segments/1656103917192.48/warc/CC-MAIN-20220701004112-20220701034112-00036.warc.gz"} |
https://codereview.stackexchange.com/questions/212255/time-limit-exceeded-on-hackerrank-username-disparity | # Time limit exceeded on HackerRank “Username Disparity”
Here is the hackerrank question:
For two strings A and B, we define the similarity of the strings to be the length of the longest prefix common to both strings. For example, the similarity of strings "abc" and "abd" is 2, while the similarity of strings "aaa" and "aaab" is 3.
Calculate the sum of similarities of a string S with each of it's suffixes.
I am getting a timeout on some of the test cases but not all of them.
function usernameDisparity(inputs) {
return inputs.map(function (input) {
return getDisparity(input);
});
}
function getDisparity(input) {
var sum = 0;
for (var i = 0; i < input.length; i++) {
sum = sum + getSimilarity(i, input);
}
return sum;
}
function getSimilarity(index, input) {
var similarity = 0;
for (var i = 0; i < input.length; i++, index++) {
if (input[index] !== input[i]) {
return similarity;
} else {
similarity = similarity + 1;
}
}
return similarity;
}
• Your code does not match the quoted problem. – Blindman67 Jan 27 at 4:45 | {"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": 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": 0.15872631967067719, "perplexity": 4867.01451060697}, "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/1563195527828.69/warc/CC-MAIN-20190722072309-20190722094309-00373.warc.gz"} |
https://en.wikipedia.org/wiki/Partial_molar_property | # Partial molar property
A partial molar property is a thermodynamic quantity which indicates how an extensive property of a solution or mixture varies with changes in the molar composition of the mixture at constant temperature and pressure. Essentially it is the partial derivative of the extensive property with respect to the amount (number of moles) of the component of interest. Every extensive property of a mixture has a corresponding partial molar property.
## Definition
Water and ethanol always have negative excess volumes when mixed, indicating the partial molar volume of each component is less when mixed than its molar volume when pure.
The partial molar volume is broadly understood as the contribution that a component of a mixture makes to the overall volume of the solution. However, there is more to it than this:
When one mole of water is added to a large volume of water at 25 °C, the volume increases by 18 cm3. The molar volume of pure water would thus be reported as 18 cm3 mol−1. However, addition of one mole of water to a large volume of pure ethanol results in an increase in volume of only 14 cm3. The reason that the increase is different is that the volume occupied by a given number of water molecules depends upon the identity of the surrounding molecules. The value 14 cm3 is said to be the partial molar volume of water in ethanol.
In general, the partial molar volume of a substance X in a mixture is the change in volume per mole of X added to the mixture.
The partial molar volumes of the components of a mixture vary with the composition of the mixture, because the environment of the molecules in the mixture changes with the composition. It is the changing molecular environment (and the consequent alteration of the interactions between molecules) that results in the thermodynamic properties of a mixture changing as its composition is altered
If, by ${\displaystyle Z}$, one denotes a generic extensive property of a mixture, it will always be true that it depends on the pressure (${\displaystyle P}$), temperature (${\displaystyle T}$), and the amount of each component of the mixture (measured in moles, n). For a mixture with m components, this is expressed as
${\displaystyle Z=Z(T,P,n_{1},n_{2},\cdots ).}$
Now if temperature T and pressure P are held constant, ${\displaystyle Z=Z(n_{1},n_{2},\cdots )}$ is a homogeneous function of degree 1, since doubling the quantities of each component in the mixture will double ${\displaystyle Z}$. More generally, for any ${\displaystyle \lambda }$:
${\displaystyle Z(\lambda n_{1},\lambda n_{2},\cdots )=\lambda Z(n_{1},n_{2},\cdots ).}$
By Euler's first theorem for homogeneous functions, this implies[1]
${\displaystyle Z=\sum _{i=1}^{m}n_{i}{\bar {Z_{i}}},}$
where ${\displaystyle {\bar {Z_{i}}}}$ is the partial molar ${\displaystyle Z}$ of component ${\displaystyle i}$ defined as:
${\displaystyle {\bar {Z_{i}}}=\left({\frac {\partial Z}{\partial n_{i}}}\right)_{T,P,n_{j\neq i}}.}$
By Euler's second theorem for homogeneous functions, ${\displaystyle {\bar {Z_{i}}}}$ is a homogeneous function of degree 0 which means that for any ${\displaystyle \lambda }$:
${\displaystyle {\bar {Z_{i}}}(\lambda n_{1},\lambda n_{2},\cdots )={\bar {Z_{i}}}(n_{1},n_{2},\cdots ).}$
In particular, taking ${\displaystyle \lambda =1/n_{T}}$ where ${\displaystyle n_{T}=n_{1}+n_{2}+\cdots }$, one has
${\displaystyle {\bar {Z_{i}}}(x_{1},x_{2},\cdots )={\bar {Z_{i}}}(n_{1},n_{2},\cdots ),}$
where ${\displaystyle x_{i}={\frac {n_{i}}{n_{T}}}}$ is the concentration expressed as the mole fraction of component ${\displaystyle i}$. Since the molar fractions satisfy the relation
${\displaystyle \sum _{i=1}^{m}x_{i}=1,}$
the xi are not independent, and the partial molar property is a function of only ${\displaystyle m-1}$ mole fractions:
${\displaystyle {\bar {Z_{i}}}={\bar {Z_{i}}}(x_{1},x_{2},\cdots ,x_{m-1}).}$
The partial molar property is thus an intensive property - it does not depend on the size of the system.
The partial volume is not the partial molar volume
## Applications
Partial molar properties are useful because chemical mixtures are often maintained at constant temperature and pressure and under these conditions, the value of any extensive property can be obtained from its partial molar property. They are especially useful when considering specific properties of pure substances (that is, properties of one mole of pure substance) and properties of mixing (such as the heat of mixing or entropy of mixing). By definition, properties of mixing are related to those of the pure substances by:
${\displaystyle \Delta z^{M}=z-\sum _{i}x_{i}z_{i}^{*}.}$
Here ${\displaystyle *}$ denotes a pure substance, ${\displaystyle M}$ the mixing property, and ${\displaystyle z}$ corresponds to the specific property under consideration. From the definition of partial molar properties,
${\displaystyle z=\sum _{i}x_{i}{\bar {Z_{i}}},}$
substitution yields:
${\displaystyle \Delta z^{M}=\sum _{i}x_{i}({\bar {Z_{i}}}-z_{i}^{*}).}$
So from knowledge of the partial molar properties, deviation of properties of mixing from single components can be calculated.
## Relationship to thermodynamic potentials
Partial molar properties satisfy relations analogous to those of the extensive properties. For the internal energy U, enthalpy H, Helmholtz free energy A, and Gibbs free energy G, the following hold:
${\displaystyle {\bar {H_{i}}}={\bar {U_{i}}}+P{\bar {V_{i}}},}$
${\displaystyle {\bar {A_{i}}}={\bar {U_{i}}}-T{\bar {S_{i}}},}$
${\displaystyle {\bar {G_{i}}}={\bar {H_{i}}}-T{\bar {S_{i}}},}$
where ${\displaystyle P}$ is the pressure, ${\displaystyle V}$ the volume, ${\displaystyle T}$ the temperature, and ${\displaystyle S}$ the entropy.
## Differential form of the thermodynamic potentials
The thermodynamic potentials also satisfy
${\displaystyle dU=TdS-PdV+\sum _{i}\mu _{i}dn_{i},\,}$
${\displaystyle dH=TdS+VdP+\sum _{i}\mu _{i}dn_{i},\,}$
${\displaystyle dA=-SdT-PdV+\sum _{i}\mu _{i}dn_{i},\,}$
${\displaystyle dG=-SdT+VdP+\sum _{i}\mu _{i}dn_{i},\,}$
where ${\displaystyle \mu _{i}}$ is the chemical potential defined as (for constant nj with j≠i):
${\displaystyle \mu _{i}=\left({\frac {\partial U}{\partial n_{i}}}\right)_{S,V}=\left({\frac {\partial H}{\partial n_{i}}}\right)_{S,P}=\left({\frac {\partial A}{\partial n_{i}}}\right)_{T,V}=\left({\frac {\partial G}{\partial n_{i}}}\right)_{T,P}.}$
This last partial derivative is the same as ${\displaystyle {\bar {G_{i}}}}$, the partial molar Gibbs free energy. This means that the partial molar Gibbs free energy and the chemical potential, one of the most important properties in thermodynamics and chemistry, are the same quantity. Under isobaric (constant P) and isothermal (constant T ) conditions, knowledge of the chemical potentials, ${\displaystyle \mu _{i}(x_{1},x_{2},\cdots ,x_{m})}$, yields every property of the mixture as they completely determine the Gibbs free energy.
## Measuring partial molar properties
To measure the partial molar property ${\displaystyle {\bar {Z_{1}}}}$ of a binary solution, one begins with the pure component denoted as ${\displaystyle 2}$ and, keeping the temperature and pressure constant during the entire process, add small quantities of component ${\displaystyle 1}$; measuring ${\displaystyle Z}$ after each addition. After sampling the compositions of interest one can fit a curve to the experimental data. This function will be ${\displaystyle Z(n_{1})}$. Differentiating with respect to ${\displaystyle n_{1}}$ will give ${\displaystyle {\bar {Z_{1}}}}$. ${\displaystyle {\bar {Z_{2}}}}$ is then obtained from the relation:
${\displaystyle Z={\bar {Z_{1}}}n_{1}+{\bar {Z_{2}}}n_{2}.}$
## Relation to apparent molar quantities
The relation between partial molar properties and the apparent ones can be derived from the definition of the apparent quantities and of the molality.
${\displaystyle {\bar {V_{1}}}={}^{\phi }{\tilde {V}}_{1}+b{\frac {\partial {}^{\phi }{\tilde {V}}_{1}}{\partial b}}.}$
The relation holds also for multicomponent mixtures, just that in this case subscript i is required. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 55, "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": 0.9432439804077148, "perplexity": 373.95267026318413}, "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/1550247481832.13/warc/CC-MAIN-20190217091542-20190217113542-00543.warc.gz"} |
https://www.computer.org/csdl/trans/tc/1983/04/01676245-abs.html | Issue No. 04 - April (1983 vol. 32)
ISSN: 0018-9340
pp: 411-417
D.W. Lozier , U.S. Department of Commerce, National Bureau of Standards
ABSTRACT
Three forms of interval floating-point arithmetic are defined in terms of absolute precision, relative precision, and combined absolute and relative precision. The absolute-precision form corresponds to the centered form of conventional rounded-interval arithmetic. The three forms are compared on the basis of the number of floating-point operations needed to generate error bounds for inner-product accumulation.
INDEX TERMS
rounding error analysis, Arithmetic algorithms, error propagation, floating-point computation, inner-product accumulation, interval analysis, interval arithmetic, relative precision
CITATION
D.W. Lozier, "The Use of Floating-Point and Interval Arithmetic in the Computation of Error Bounds", IEEE Transactions on Computers, vol. 32, no. , pp. 411-417, April 1983, doi:10.1109/TC.1983.1676245 | {"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": 0.9715515375137329, "perplexity": 3750.9244609594584}, "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-2017-43/segments/1508187825264.94/warc/CC-MAIN-20171022132026-20171022152026-00757.warc.gz"} |
https://www.arxiv-vanity.com/papers/hep-th/0011238/ | Abstract
Using anomalous symmetries of the cubic string field theory vertex we derive set of relations between the coefficients of the tachyon condensate. They are in agreement with the results obtained from level truncation approximation.
SISSA 109/2000/EP
hep-th/0011238
Constraints on the tachyon condensate from anomalous symmetries
Martin Schnabl111E-mail:
Scuola Internazionale Superiore di Studi Avanzati,
Via Beirut 4, 34014 Trieste, Italy and INFN, Sezione di Trieste
1 Introduction
Since the original formulation of the Sen’s conjecture [1] there has been significant progress in understanding the nonperturbative aspects of the string field theory. Initially the existence of translationally invariant vacuum with conjectured energy density was established numerically [2, 3] to a rather high accuracy by the level expansion method [4] in the Witten’s cubic string field theory [5, 6, 7]. More recently the Sen’s conjecture has been proved rigorously in the framework of background independent string field theory [8, 9, 10]. Nevertheless it seems worth continuing to look for the exact tachyon condensate in the original cubic string field theory since it can teach us many things [15].
Various insights into the nature of the tachyon condensate has already been obtained in [11, 12, 13, 14, 15]. One particular suggestion for the exact form of the condensate based on the noncommutative geometric nature of the string field action was made in [16, 17]. Independently of this recent suggestion we will show in this letter, that we can obtain some new exact information about the tachyon condensate. We point out that some anomalous symmetries [6, 19, 12] of the string field theory vertex can be used to derive an infinite set of identities for any string field which solves the equations of motion. We will see that at level we get additional constraints on the coefficients of the string field which are in reasonable agreement with the explicit results from level truncation scheme [2, 3]. It would be very interesting if one could find even further symmetries which would then fix all the coefficients completely.
2 Anomalous symmetries
The string field theory action as given by [5, 6, 7] takes the form of noncommutative Chern-Simons action
S[Ψ]=−1α′g2o(12⟨Ψ,QΨ⟩+13⟨Ψ,Ψ∗Ψ⟩) (1)
with the noncommutative multiplication defined by
Ψ1∗Ψ2=bpz(⟨V|Ψ1⊗Ψ2), (2)
where denotes the conjugation in conformal field theory and the vertex was reviewed in the oscillator formulation [18, 16] and studied in a background independent manner in [12].
From [6, 19, 12] we know that the vertex satisfies certain identities. For us will be important in particular the following ones for even
⟨V|3∑i=1(L(i)−n−L(i)n) = 3kxn⟨V|, ⟨V|3∑i=1(J(i)−n+J(i)n) = 3(hghn+3δn,0)⟨V|, (3)
where and denote matter Virasoro and ghost current generators respectively. The constants and take for even the following values
kxn = 13⋅527⋅n2(−1)n2, hghn = −(−1)n2. (4)
For odd there would be extra signs between the generators in (2) and the right hand side would vanish. We are not interested in this case since it will not lead to any information about the tachyon condensate. Note that the additional term on the right hand side of the second equation in (2) accounts for the nontensor character of the ghost number current.
Let us study now the variation of the action (1) under the infinitesimal variations of the string field
δΨ = (L−n−Ln−kxn)Ψ, δΨ = (J−n+Jn−hghn−3δn,0)Ψ (5)
respectively. Under these variations the cubic term in the action is obviously invariant due to the invariance of the vertex (2). On the other hand we know that the total action should also be invariant as long as satisfies equations of motion. Combining these two facts we get from the kinetic term
⟨Ψ|[Q,Ln]|Ψ⟩ = −kxn⟨Ψ|Q|Ψ⟩, ⟨Ψ|[Q,Jn]|Ψ⟩ = hghn⟨Ψ|Q|Ψ⟩. (6)
Let us note that both commutators on the left hand side are modes of conformal primary fields, the latter being minus the BRST current .
3 Explicit checks
To compare the above formulas with the results obtained in level expansion scheme in [2, 3] one should first of all impose the Siegel gauge condition on the string field and simplify the commutators. For the first equation of (2) one has simply
[Q,Ln]=−nc0Ln+⋯ (7)
where the dots stand for terms which do not contribute. For the second equation one can use a little trick. Write the left hand side as
⟨Ψ|[Q,Jn]|Ψ⟩=−⟨Ψ|{JBn,b0}c0|Ψ⟩ (8)
where we used the facts that and . The anticommutator can be easily evaluated using the operator product expansion (see e.g. [20]). Both formulas (2) thus simplify in the Siegel gauge to
⟨Ψ|c0Ln|Ψ⟩ = 1nkxn⟨Ψ|c0Ltot0|Ψ⟩, ⟨Ψ|c0(nJn+Ltotn)|Ψ⟩ = −hghn⟨Ψ|c0Ltot0|Ψ⟩, (9)
where denotes the total Virasoro generator. These identities can be easily checked for the numerical values obtained in [2, 3]. Let us define to be the ratio of the left and right hand sides of the first or second equation of (3) respectively. Then inserting for simplicity the values for the string field coefficients from [2] obtained at the level (4,8) we get the following results
rL2 = 1.069,rL4=1.044, rJ2 = 1.004,rJ4=0.939.
We see that the above identities are preserved within . This can be compared with the value of the potential which is for the same values about away from the expected value. This discrepancy in the errors by a factor of five does not necessarily mean that there are mistakes neither in the derivation nor in the numerical evaluation. In fact we know that the convergence properties of the level truncation approximation depends rather strongly on what kind of calculation we are doing. In an unpublished work we have studied the properties of the string field algebra unity in the level truncation using the universal recursive methods of [12]. Keeping only terms up to level 8 in the unity and during the whole calculation we got for example
L−2|0⟩∗|I⟩ = 0.990L−2|0⟩+0.108Ltot−2|0⟩−0.196Ltot−2Ltot−2|0⟩+⋯, Ltot−2|0⟩∗|I⟩ = 0.990Ltot−2|0⟩+0.009Ltot−2Ltot−2|0⟩+⋯, (10)
where the dots stand for terms which are relatively smaller or of higher levels where one can understand bigger errors. Looking at these values one might wonder whether after all the string algebra unity is unity also for the state . The experience from calculations at lower levels where the errors are much bigger suggests that it really converges, hopefully to the correct state. The fact that calculations involving matter Virasoro generators converge much more slowly can be easily traced back to the presence of the Virasoro anomaly.
References
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If you find a rendering bug, file an issue on GitHub. Or, have a go at fixing it yourself – the renderer is open source!
For everything else, email us at [email protected]. | {"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": 0.9128299355506897, "perplexity": 488.0157297910409}, "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-2021-43/segments/1634323586043.75/warc/CC-MAIN-20211024142824-20211024172824-00626.warc.gz"} |
https://latex.org/forum/viewtopic.php?f=45&t=21452&p=71909& | LaTeX forum ⇒ Graphics, Figures & Tables ⇒ tikZ | Font Scaling in new Command Topic is solved
Information and discussion about graphics, figures & tables in LaTeX documents.
php1ic
Posts: 192
Joined: Wed Jan 28, 2009 8:17 pm
tikZ | Font Scaling in new Command
Hello,
I've created a new command that uses tikZ to draw a box at of a certain colour at x,y and add centered text of non-standard (bigger than \Huge) size. I made the following MWE using the random scale=5 but when I change it the fonts and rounded corners are 'wrong'.
I cannot seem to get round the fact that the \fontsize is outside of the tikzpicture environment so doesn't scale with everything else. I tried using transform canvas={scale=??} but that didn't work.
I basically want everything to scale if I change the value. Any ideas?
For context I have a code that will create between 1 and 4500 instance of the box so would like to easily set the scale for a small, 1/3rd page, portrait picture or a full landscape one.
\documentclass{article} \usepackage{tikz}\usepackage{fix-cm}\usepackage[T1]{fontenc}\usepackage[active,tightpage]{preview}\PreviewEnvironment{tikzpicture}\setlength\PreviewBorder{0.5em} %Set scale factor\newcommand{\nsize}[0]{5} %Set how round the corners are (0=square)\newcommand{\rc}[0]{40} %Setup command to draw box and text\newcommand{\nucleus}[5]{\filldraw[draw=black,thick,fill=#1,rounded corners=\rc] (#2,#3) rectangle +(1,1)+(0.5,0.75) node {\fontsize{40}{48} \selectfont #4}+(0.5,0.4) node {\fontsize{72}{96} \selectfont #5};} \begin{document} \begin{tikzpicture}[scale=\nsize] \nucleus{green}{0}{0}{208}{Pb}%\draw[step=0.1,gray,very thin] (-0.05,-0.05) grid (1.05,1.05); \end{tikzpicture} \end{document}
Last edited by php1ic on Mon Sep 24, 2012 11:17 pm, edited 1 time in total.
Stefan Kottwitz
Posts: 9597
Joined: Mon Mar 10, 2008 9:44 pm
Generally, it can be good to add the option transform shape, when scaling:
\begin{tikzpicture}[scale=2, transform shape] ...\end{tikzpicture}
In this case, I would not use the \fontsize commands with absolute values in the TikZ picture.
Stefan
php1ic
Posts: 192
Joined: Wed Jan 28, 2009 8:17 pm
Thanks Stefan,
Using the standard font sizes solved the scaling issue.
%Setup command to draw box and text\newcommand{\nucleus}[5]{\filldraw[draw=black,thick,fill=#1,rounded corners=\rc] (#2,#3) rectangle +(1,1)+(0.5,0.76) node[anchor=mid] {#4}+(0.5,0.25) node[anchor=mid] {\LARGE #5};}
I have read the pgf manual but can't find the section that explains the logic of the rounded corners, any tips? As with the fonts it seems to be an absolute value that doesn't scale.
php1ic
Posts: 192
Joined: Wed Jan 28, 2009 8:17 pm
By trail and error, a unit square can be converted to a circle by using rounded corners=10*sqrt(2). From there is was a simple case of reading about pgfmath and implementing
Working example is below, only \nsize and \nround need to be changed in the pre-amble
\documentclass{article} \usepackage{tikz}\usepackage[T1]{fontenc}\usepackage[active,tightpage]{preview}\PreviewEnvironment{tikzpicture}\setlength\PreviewBorder{0.5em} %Set scale factor\newcommand{\nsize}[0]{5}%Set how round the corners are (0->1=square->circle)\newcommand{\nround}[0]{0.5} %Construct the variable to apply the necessary rounding\pgfmathsetmacro{\rc}{\nround*\nsize*10*sqrt(2)} %Setup command to draw box and text\newcommand{\nucleus}[5]{\filldraw[draw=black,thick,fill=#1,rounded corners=\rc] (#2,#3) rectangle +(1,1)+(0.5,0.76) node[anchor=mid] {#4}+(0.5,0.25) node[anchor=mid] {\LARGE #5};} \begin{document} \begin{tikzpicture}[scale=\nsize, transform shape] \nucleus{green}{0}{0}{208}{Pb}%\draw[step=0.1,gray,very thin] (-0.05,-0.05) grid (1.05,1.05); \end{tikzpicture} \end{document}
Thanks for looking, thinking and commenting. | {"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": 0.9077550172805786, "perplexity": 4286.800291873205}, "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-2020-40/segments/1600400219691.59/warc/CC-MAIN-20200924163714-20200924193714-00382.warc.gz"} |
http://mathoverflow.net/questions/104627/example-of-non-projective-variety-with-non-semisimple-frobenius-action-on-etale | # Example of non-projective variety with non-semisimple Frobenius action on etale cohomology?
This question was motivated by a more general question raised by Jan Weidner here. In general one starts with a variety $X$ (say smooth) over an algebraic closure of a finite field $\mathbb{F}_q$ of characteristic $p$. Here there is a natural action of a Frobenius morphism $F$ relative to $q$. Given a distinct prime $\ell$, there is an induced operation of $F$ on etale cohomology groups (with compact support) $H^i_c(X, \overline{\mathbb{Q}_p})$. When $X$ is projective, this action is conjectured to be semisimple on each of the finite dimensional vector spaces involved. But it seems that semisimplicity can fail when $X$ isn't projective. My basic question is:
Is there an elementary example where the Frobenius action fails to be semisimple? (References?)
Of course, etale cohomology developed in response to the Weil conjectures and related matters in number theory. Here there is a lot of deep literature which I'm unfamiliar with, but I'd like to get some insight into the narrow question of what does or doesn't force semisimplicity for non-projective varieties.
My interest lies mainly in Deligne-Lusztig varieties and their role in studying characters of finite groups of Lie type. Such varieties $X_w$ are indexed by Weyl group elements and are locally closed smooth subvarieties of the flag variety for a reductive group $G$, with all irreducible components of equal dimension. Here the finite subgroup $G^F$ acts on the etale cohomology, commuting with $F$, and the resulting virtual characters (alternating sums of characters on cohomology spaces) are the D-L characters.
Characters of finite tori also come into play here, but I'm thinking first about the trivial characters of tori which lead to "unipotent" characters. These include essential but mysterious "cuspidal" unipotent characters which can't be extracted from the usual induced characters obtained by parabolic induction.
For example, the Chevalley group $G_2(\mathbb{F}_q)$ typically has 10 unipotent characters (at the extremes the trivial and the Steinberg characters), with four being cuspidal. Those four appear in etale cohomology groups of a variety $X_w$ with $w$ a Coxeter element: the variety has dimension 2, with four characters (three cuspidal, the other Steinberg) in degree 2, one (cuspidal) in degree 3, and one (the trivial character) in degree 4. Miraculously, it always happens in the Coxeter case that $F$ acts semisimply (here with 6 distinct eigenvalues: the Coxeter number) and its eigenspaces afford distinct irreducible characters. In the year after he and Deligne finished their fundamental paper (Annals, 1976), Lusztig worked out the Coxeter case in a deep technical paper here. This was followed by a more complete determination of cuspidal unipotent characters, and then much more. The Coxeter case seems to be unusually well-behaved in this program.
P.S. As I suspected, there's more going on under the surface of my basic question about semisimplicity than meets the eye. As an outsider to much of the algebraic geometry framework I can appreciate the outline of Dustin's answer though not yet the details. My question came from wondering whether there are ways to shortcut some of the older steps taken by Lusztig, but the wider questions here are obviously important. I'll have to see how far my motivation (in a manner of speaking) takes me.
And Wilberd: thanks for the proofreading, which is not one of my favorite things to do. (Though I somehow got "just bonce" into a book that was supposedly proofread.)
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Dustin Clausen's argument can be supplemented rather easily for open smooth varieties, which seem to be your main interest. If $U$ has a compactification $j:U↪X$ with a normal crossing complement $D$, then breaking down the Leray spectral sequence for $j$ (see, Deligne's Hodge I, section 6) will show that the pure weight subquotients of $H^n(U)$ are themselves subquotients of direct sums of the cohomology of smooth projective varieties (the intersections of components of $D$). The general case can be reduced to this using De Jong's alteration. (But maybe you don't need it in your case.) – Minhyong Kim Aug 14 '12 at 1:04
Actually, the semisimplicity should hold with no hypotheses on X, so no example should exist. In fact it is generally expected that, with char. 0 coefficients and over a finite field (both hypotheses being necessary), every mixed motive is a direct sum of pure motives -- so the question for arbitrary varieties reduces to that for smooth projective ones.
The reason is as follows: the different weight-pieces have no frobenius eigenvalues in common (by the Weil conjectures), so the weight filtration can be split by a simple matter of linear algebra. (And the splitting will even be motivic since frobenius is a map of varieties.)
Edit: In response to Jim's comment, let me try to provide a clearer argument (2nd edit: no longer using the Tate conjecture). I claim that if we assume the existence of a motivic t-structure over F_q w.r.t. the l-adic realization in the sense of Beilinson's article http://arxiv.org/pdf/1006.1116v2.pdf, then provided that H^i_c(X-bar) is Frobenius-semisimple for smooth projective X, it is in fact so for aribtrary X.
Indeed, given a motivic t-structure, its heart is an artinian abelian category where every irreducible object is a summand of a Tate-twist of an H^i(X) for X smooth an projective, and furthermore there are no extensions between such irreducibles of the same weight (this is all in Beilinson's article).
That's all true over a general field. But now let's argue that, in the case of a finite field, there also can't be extensions between such irreducibles of different weights; then in the motivic category all of our H^i_c(X-bar) of interest will be direct sums of summands of H^i(X)'s, and we'll have successfully made the reduction to the smooth projective case.
So suppose M and N are irreducible motives of distinct weights over F_q, and say E is an extension of M by N. Consider the characteristic polynomials p_M and p_N of Frobenius acting on the l-adic cohomologies of M and N. By Deligne, they have rational coefficients and distinct eigenvalues, so we can solve q * p_N == 1 (mod p_M) for a rational-coefficient polynomial q. But then (q*p_N)(frobenius) acting on E splits the extension (recall from Beilinson's article that the l-adic realization is faithful under our hypothesis), and we're done.
Later commentary: apparently, when I wrote this I was a little too excited about the perspectives offered by motives. I should emphasize the point essentially made by Minhyong Kim, that the reduction from the general case to the proper smooth case likely doesn't require any motivic technology, and should even be independent of any conjectures. One just needs to know that there's a weight filtration on l-adic cohomology of the standard type where the pure pieces are direct sums of direct summands of appropriate cohomology of smooth projective varieties. As Minhyong says, this probably follows from Deligne's original pure --> mixed argument, via use of compactifications and de Jong alterations. Or at least that's what it seems to me without having gone into the details. I'm sure someone else knows better.
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@Dustin: This seems to be an intriguing line of reasoning, which runs counter to the earlier intuition people seemed to have. I'd need to study the original source material more carefully to follow the details. Are there any accessible references for the reduction to the earlier conjecture for projective varieties? – Jim Humphreys Aug 13 '12 at 23:20
Hi Jim, sorry the argument I gave was so sketchy and without references. I tried to fill it out more -- hopefully it's more helpful now. – Dustin Clausen Aug 14 '12 at 1:48
@Dustin This probably reveals my ignorance but, if every mixed motive is expected to be a direct sum of pure motives, doesn't this show that the categories of mixed motives and pure motives are (conjecturally) equivalent? In which case, why do we study mixed motives? – David Speyer Aug 14 '12 at 1:59
Hey David -- it's only true over a finite field, and only with rational coefficients! Compare e.g. with the fact that the F_q-points of the Jacobian of a curve are finite, or with the fact that the algebraic K-theory of F_q is finite in positive degrees... – Dustin Clausen Aug 14 '12 at 2:31
From the view of Galois representations, the point is that everything over a finite field is determined by a single endomorphism, as compared to the action of a complicated group like $Gal(\bar{\mathbb{Q}}/\mathbb{Q})$. Of course the mininal polynomial will be reduced if and only if each `pure factor' is reduced. – Minhyong Kim Aug 14 '12 at 4:17 | {"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": 0.8846662044525146, "perplexity": 527.5275307894207}, "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-2014-35/segments/1409535917663.12/warc/CC-MAIN-20140901014517-00172-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://mersenneforum.org/printthread.php?s=80ea1a983966f9960feb21c9e285099d&t=5195&pp=97 | mersenneforum.org (https://www.mersenneforum.org/index.php)
- Puzzles (https://www.mersenneforum.org/forumdisplay.php?f=18)
- - What way would you find numbers with a set number of factors? (https://www.mersenneforum.org/showthread.php?t=5195)
nibble4bits 2005-12-24 04:41
What way would you find numbers with a set number of factors?
If prime numbers are numbers that only factor into 1 and themselves, then what would 3 factors including one and itself be?
[spoiler] It turns out that the middle factor must follow a rule:
1*n^2=n*n=x
The factors of n^2 must be 1, n, n^2. Since n has to be prime, that means
that the answer is the set of all the squares of primes.
[/spoiler]
Try this for 4, 5, 6, ... factors for x including 1 and x.
tom11784 2005-12-29 23:43
Let Pi be distinct primes for all i:
4 factors: [spoiler](P1)^3 or (P1)*(P2)[/spoiler]
5 factors: [spoiler](P1)^4[/spoiler]
6 factors: [spoiler](P1)^5 or (P1)^2*(P2)[/spoiler]
7 factors: [spoiler](P1)^6[/spoiler]
8 factors: [spoiler](P1)^7 or (P1)^3*(P2) or (P1)*(P2)*(P3)[/spoiler]
so on, so forth...
nibble4bits 2005-12-30 21:01
At 1 and 0 you get the identies 1 and 0. 0 can't be divided at all and 1 has only one possible factor including itself and itself. Hehe we'll just say "period" to make more sense.
At 2 total factors there's only primes. (works both ways: A->B and B->A)
The solutions for 2 factors are a kind of 'key' to the higher-factor-count sets in the 3D tree since obviously primes are the simplest factors possible.
If there's an infinite number of primes, is there an infinite number of the 3-factor results? 4-factor? All? [spoiler] See 2nd post to see why there must be.
Yes, there are infinite primes but no telling how long you'll have to wait to find the next one! I left this in the spoiler so those who want to can do the work themselves to find and understand the proof.[/spoiler]
Numbers 2005-12-30 21:45
As there are an infinite number of primes, and as all primes are either 1(mod 6) or 5(mod 6), are there an infinite number of primes 1(mod 6)?
akruppa 2005-12-30 21:53
Yes, this is a special case of the "prime number theorem for arithmetic progressions." Simply put, it says that if you have an arithmetic progression a+b*x with gcd(a,b)=1 and x∈[B]N[/B], you get infinitely many primes. What is more, each such progression for different values of a (but the same b) gets an "equal share" of the primes. See Crandall and Pomerance, Prime Numbers, Theorem 1.1.5.
Alex
Numbers 2005-12-30 22:20
Thank you.
nibble4bits 2005-12-31 15:26
Amazon has one copy of the 2nd edition if you've got \$70 (new hard cover math books aren't cheap!) to expand your library. Since I'm near several libraries, colleges and universities, I think I'll be cheap and just go spend some time at a desk in one of them. This should be as interesting as the books by Howard Anton covering some of the more interesting parts of vectors and matrices - assuming you're like me and read that kind of stuff for 'fun'.
ISBN: 0387252827 (there's an older first edition #0387947779 for a little less)
akruppa 2005-12-31 16:35
Some things have been added/changed in the second edition, most notably it now includes the AKS algorithm. But the first edition is still perfectly worthwhile to have and you may be able to get a second hand copy inexpensively now. Maybe check university .market newsgroups or online auctions?
Alex
Numbers 2005-12-31 16:56
[quote=nibble4bits]assuming you're like me and read that kind of stuff for 'fun'.[/quote]
I do indeed. Last night I read a chapter of "The Art of Calculus" wrapped up in bed with a big mug of cocoa. I spent this morning working through the exercises. This afternoon I did some work on my maths course, and am now relaxing with a chapter of William LeVeque's "Elementary Theory of Numbers". I don't know that it's fun, exactly, but I do find it very rewarding.
Crandall & Pomerance, and of course Knuth were on my wish list for Christmas (again), but sadly Santa saw fit to leave me a mouse and some aftershave. Maybe if I manage to sell another picture before Easter then Amazon will be getting a call.
ewmayer 2006-01-01 20:33
[QUOTE=Numbers]Crandall & Pomerance, and of course Knuth were on my wish list for Christmas (again), but sadly Santa saw fit to leave me a mouse and some aftershave.[/QUOTE]You could always feed the mouse to the cat and drink the aftershave...share the joy, I say.
nibble4bits 2006-01-01 22:26
...
Poor cat trying to eat that plastic peripheral.
Numbers 2006-01-02 14:32
Actually, the aftershave came from my girlfriends mother. Rather than buy me the brand I have used for the past twenty years she got something quite nasty (perhaps she was trying to tell me something). So I would probably be better off feeding the after shave to the cat so that it wouldn't notice that the mouse has a flashing light in its bottom!
nibble4bits 2006-01-03 05:03
So have you gotten to the point where you know how and why e and Pi (3.14..., not Pi[x]) are relevant to primes?
The constant e is the amount of interest+principle you'de get for compounded constantly vs flat/single cycled 100% interest. Another way to put that is that it's what happens when feedback in a system is so randomized in it's order and timing and occours so often, that it appears to equivilent to constantly compounded interest. P_n+1 is most certainly based on P_n, P_n-1... It's [U]forbidden[/U] from having those as factors. This is why it at least seems that Pi(x) is almost the same as n/(a + log n) especially for larger numbers. Yes, I know that n/(1 + log n) is not the best estimate. :)
Pi the constant is related to the trigonometry used in to find those 1/2 Riemann zeros and run some multiplication methods. However, that's probally a pretty long stretch.
I was interested the talk about "how the primes are unusual in that they appear to have added noise" which seems to imply that they'de otherwise be easy to generate for a function like Prime(x)=the x'th prime that works in linear time relative to x. Anyone have any good links for more details? I'm thinking that the primes are not the only sequence to have this behaviour. What if I defined a set that instead of x not dividing by the set of 2 to x-1, required some other kind of condition for a number to be next in the series? Something like x/(2 to x-1)=2 for some value of the denominator would be a start - at the very least, it'll give me an excuse to burn CPU cycles. heh
Numbers 2006-01-04 20:03
I'm afraid I found this whole post very confusing.
[quote=nibble4bits]P_n+1 is most certainly based on P_n, P_n-1... It's forbidden from having those as factors.[/quote]
Bearing in mind that there is no break between your "explanation" of random feedback in a system being related to e, the base of natural logarithms and this, which appears to be saying that of three consecutive integers the third cannot have either of the other two as factors (which is not true) and which you seem to think is connected to pi(x) the prime counting function, is there any chance you could squeeze in some mention of the probability of rolling dice as well? I have no idea what you are trying to say here.
[quote=nibble4bits]I was interested the talk about "how the primes are unusual in that they appear to have added noise"[/quote]
You include a phrase in inverted commas as though it were a quote, but I have no idea who or what you are quoting or how this is connected to anything that has gone before. And what do you mean by "random noise"? Sorry, I'm just confused.
Then you suggest
[quote=nibble4bits]some other kind of condition for a number to be next in the series? Something like x/(2 to x-1)=2[/quote]
Well I'm afraid this function [B]never[/b] = 2. The maximum value of this function occurs when x = 1.4426947, y = 1.0614757 so once again I have no idea what you are talking about.
Were you smoking something when you typed this? :o)
nibble4bits 2006-01-06 22:29
1) It's hard to use this font to represent prime number 1(2=), 2(=3), 3(=5) and so on. Of course the very definition of prime implies that lower primes may not be factors of a higher prime. Very basic stuff but P_(N+1) is not P_N + 1. I'm sorry about that!
2) There's an exact quote: "God may not play dice with the universe, but something strange is going on with the prime numbers." - Paul Erdos
His other famous quote is about mathematicians and coffee. :)
3) Yeah I know there's no solution but I find it hard to believe the set of primes is ever remotely unique. If A*B=Prime then either A=1 and B=the prime number, or the other way around. I'm wondering what kinds of solutions you get when C*D+E=Prime. C and D being two factors that are a constant E away from a prime. It seems that any such conditions are always based on the prime numbers. Are there counterexamples that don't rely on primes? I think any set based on division is going to require some mention of primes.
4) Nah, I'm just trying to figure this out and it helps if I can see how far away I am from understanding specific points.
x/(2)...x/(x-1) <-- I think that's much clearer than x/(2 to x-1).
Numbers 2006-01-07 01:42
[quote=nibble4bits]There's an exact quote: "God may not play dice with the universe, but something strange is going on with the prime numbers." - Paul Erdos
His other famous quote is about mathematicians and coffee. :)[/quote]
A mathematician is a machine for turning coffee into theorems. I had a banner printed with this on it to stick on the wall above my computer. My girlfriend got a guy she knows to engrave it into a nice piece of slate and mount it onto a polished mahogany base. She gave it to me for christmas and it now sits on my desk and the tatty paper banner has come down.
[quote=nibble4bits]I'm wondering what kinds of solutions you get when C*D+E=Prime. C and D being two factors that are a constant E away from a prime. It seems that any such conditions are always based on the prime numbers.[/quote]
Since you have defined your variables C, D and E in terms of the prime numbers, it is hardly surprising that your solutions are found in terms of the prime numbers. It's a bit like wondering why you get change in dollars when you gave the girl in the shop dollars in the first place.
If you want to view your solutions in terms of something other than prime numbers then you need to define your variables appropriately. That is where such simple identities as p = 6q+r come from. They allow us to define our variables in terms of something other than p, and yet afterwards convert q and r into something that relates back to the original problem.
[quote=nibble4bits]x/(2)...x/(x-1) <-- I think that's much clearer than x/(2 to x-1).[/quote]
That is certainly clearer. I thought you meant $$\Large \frac{x}{2^{x-1}}$$
Enjoy.
nibble4bits 2006-01-07 03:42
Well that function is interesting too for graphing... but not what I meant. Yeah I didn't mean x/(2^(x-1))=(2x)/(2^x)
BTW How do I make that algebraic font?
Numbers 2006-01-07 04:10
[quote=nibble4bits]BTW How do I make that algebraic font?[/quote]
If you see anything on the forum and ask yourself "how did he do that?" click on the "Quote" button on the post and you can read how it was done.
Maths symbols are posted using LaTex, and you can find a comprehensive set of maths symbols, functions, operators etc. [url=http://www.mersennewiki.org/index.php/Help:Math_Formulas]here[/url].
Just remember that the page you are reading was written for the wiki, so you need to enclose your maths in the tex tags [ tex ][I]maths in here[/I][ /tex ] rather than in the tags given on that page.
Googling for LaTex will also give hundreds (at least) of hits, the one I use the most is [url=http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/]St. Andrews University[/url] but there are many others.
HTH.
fatphil 2006-01-07 10:40
[QUOTE=Numbers]Enjoy.[/QUOTE]
$$Oh^{my}_{goodness}!$$
All times are UTC. The time now is 03:52. | {"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": 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": 0.6434950232505798, "perplexity": 1097.2559077121794}, "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-2021-10/segments/1614178360107.7/warc/CC-MAIN-20210228024418-20210228054418-00116.warc.gz"} |
https://earthscience.stackexchange.com/questions/17277/what-are-these-underwater-structures-near-6n-8555w/17305 | # What are these underwater structures near 6°N 85°55'W
While google earth-researching the sea floor near Malpelo and Cocos Islands (Colombian and Costa Rican Pacific Ocean), I came along these strangely geometrical structures in the sea floor, located around 6°N, 85°55'W. I'm fascinated with the look and the geometric perfection they have, and have waited to ask this question for about 3 years, until today that I realized there's a Stack Exchange site dedicated to earth sciences (I'm not an earth scientist, just a maps enthusiast).
At first I thought they could be due to the path the satellite was traveling at the moment the image was captured, but then I realized there are depth differences in excess of 300m. I find the paralelism of the lines that form the "beams" surprisingly perfect, and the width of the "elements" very consistent (about 7 to 8km, according to google earth's ruler). Near 6°22'N 85°45'W there's a circular "dent" of about 4 $$km^2$$ that is very perfect regarding ovality.
I found something similar about 670km NE from there, around 11°10'N 82°41'W (160km SW from San Andres Islands, in the Colombian Caribbean). While the structure here is less complex (there's only one "beam" and a concentric circular structure), the width of the "beam" (6km) seems similar to the one near Cocos (the depth differences range between 300 and 500m from the structures to the normal sea floor).
What are these things?
Are they glitches in the images from the satellite, that coincidentially look like beams? If so, why are depth differences so significative?
Are they rocks or some other kind of geological formations? How did they get that shape, and where else cand I find more similar?
• I'm a Stack Exchange user of other communities, and tried my best to ask a good question. If my question doesn't meet the expected quality, I'd appreciate your edits or suggestions to edit. If you consider it as unsalvageable, please comment and I'll withdraw it. Jun 25 '19 at 3:09
As the other answer suggests, these are sonar surveys of the ocean depths. But the answer is a bit more complicated.
The vast majority of the ocean floor has never been mapped. We really only know about the water depth because the water above the sea floor is lighter than if it were rocks. So a deep ocean produces less gravity than a shallow one. And, miraculously, you can fly satellites over the oceans that pick up on how hard Earth pulls on the satellite at any given point and convert that data into an ocean depth.
This is what Google Maps and other mapping services show by default. The problem is that this information is not very accurate: That's because not just the point immediately under the satellite pulls on the satellite, but also points elsewhere. So a very steep undersea mountain will not be distinguishable from a broader but less high one. This is why in general these images of ocean depths are not shown in high resolution -- we just don't know the depth of the ocean on length scales of a few kilometers.
But then along comes the occasional ocean survey. (Think: Research ships, the ships that lay undersea cables, the ships that search for ship wrecks or the occasional plane that fell from the sky.) They tow a sonar array behind a ship, or send a side-scan sonar equipped submersible, to actually map the ocean floor on length scales of a few dozen meters. For map services, this presents a conundrum: They'd like to show the more accurate sonar data where it is available, but they need to overlay it on the low resolution maps that comes from satellites.
This is exactly what you see here: The background is the low-resolution satellite map. Overlaid is the high resolution sonar data. At the edges of the sonar maps, these two maps won't match, and so you will see the sharp edges. You can see the different resolutions if you zoom in and out of the view you showed.
(Given the long straight tracks of these sonar maps, one can guess that in your view, these were created by surveys for laying undersea cables, for example to the Galapagos Islands.)
• Explanation: youtube.com/watch?v=gMoN-Ri4_c0&feature=share I agree these are sonar paths from ships. Look 2,000 km WSW you'll be able to follow the subsurface geography to a point where hi-res sonar paths are clearly visible. At this point the sonar paths criss-cross much like the situation you are bringing forth here. Jun 27 '19 at 2:17
Supplementing Wolfgang's answer, here's a National Oceanographic and Atmospheric Administration story that talks about the appearance of ocean-bottom artifacts:
With legions of people around the world now exploring the seafloor, many are noticing locations along the ocean bottom marked by mysterious formations of grid-like artifacts. These formations look like they were made by humans, leading many to ask if these areas could be lost cities or underwater streets.
While these formations are human-made, they are only made of data. In other words, there are no physical lines on the ocean floor. These lines are artifacts of the ocean floor mapping process.
Much if not all of Google Earth's seafloor data comes via Scripps Institution of Oceanography, which combines both gravity data from satellite missions and sonar scans from sources that make their records available. Oceanographic vessels tend to travel in straight lines and/or criss-cross patterns and collect high-quality sonar data while they're doing it, resulting in strips of detail that look much different from the surround sea floor. | {"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": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5263070464134216, "perplexity": 1620.4961310050423}, "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/1637964358842.4/warc/CC-MAIN-20211129194957-20211129224957-00508.warc.gz"} |
https://www.math.rutgers.edu/news-events/seminars-colloquia-calendar/icalrepeat.detail/2022/08/31/11582/133/dynamics-of-qubits-in-random-matrix-environment | # Seminars & Colloquia Calendar
Mathematical Physics Seminar
## Dynamics of Qubits in Random Matrix Environment
#### Leonid Pastur - Institute for Low Temperatures Physics and Engineering Kharkiv, Ukraine Institut des Hautes Etudes Scien
Location: Zoom
Date & time: Wednesday, 31 August 2022 at 10:45AM - 11:45AM
Abstract
We consider a model of a quantum system of two qubits embedded into an environment. We assume that the environment parts of the system Hamiltonian are described by hermitian random matrices of size N. We obtain the large N limit of the time dependent reduced density matrix of the qubits. We then work out an analog of the Bogolyubov-van Hove asymptotic regime of the theory of open systems in statistical mechanics. This regime does not imply in general the Markovian dynamics of the reduced density matrix of our model.
This model allows for a analytical and numerical analysis of the evolution of widely used quantifiers of quantum correlations, mainly entanglement. We find a variety of interesting patterns of qubit dynamics. The patterns demonstrate the important role of the environment in the enhancement and the diversification of the evolution of quantum correlations. Our results can also be viewed as a manifestation of the universality of certain properties of the decoherent qubit evolution that have been found in various exact and approximate versions of the models where the environment is described by free bosons.
## Special Note to All Travelers
Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.
Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you. | {"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": 0.8938283324241638, "perplexity": 571.527582446612}, "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-2023-14/segments/1679296949181.44/warc/CC-MAIN-20230330101355-20230330131355-00464.warc.gz"} |
https://proofwiki.org/wiki/Character_of_Representations_over_C_are_Algebraic_Integers | # Character of Representations over C are Algebraic Integers
## Theorem
Let $G$ be a finite group.
Let $\chi$ be the character of any $\C \left[{G}\right]$-module $\left({V, \rho}\right)$.
Then for all $g \in G$, it follows that $\chi \left({g}\right)$ is an algebraic integer.
## Proof
By the definition of character:
$\chi \left({g}\right) = \operatorname{Tr} \left({\rho_g}\right)$
where:
$\rho \in \hom \left({\C \left[{G}\right], \operatorname{Aut} \left({V}\right)}\right): \vec {e_g} \mapsto \rho_g$
by definition.
Fix an arbitrary $g \in G$.
Let $\left\vert{g}\right\vert$ denote the order of $g$.
The trace $\operatorname{Tr} \left({\rho_g}\right)$ of $\rho_g$ is defined as the sum of the eigenvalues of $\rho_g$.
From Eigenvalues of G-Representation are Roots of Unity, we have that any eigenvalue $\lambda$ of $\rho_g$ is a root of unity whose order is $\left\vert{g}\right\vert$.
We have that $\lambda$ satisfies the monic polynomial $x^{\left\vert{g}\right\vert} - 1$
Hence we have that $\lambda$ is an algebraic integer.
From Ring of Algebraic Integers, we have that the sum of the eigenvalues is also an algebraic integer.
Thus $\chi \left({g}\right)$ is an algebraic integer.
$\blacksquare$ | {"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": 0.9950953125953674, "perplexity": 108.2992902271368}, "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-2022-49/segments/1669446710980.82/warc/CC-MAIN-20221204204504-20221204234504-00771.warc.gz"} |
https://math.stackexchange.com/questions/1035758/showing-that-all-monotone-functions-are-integrable | # Showing that all monotone functions are integrable
I am given the following proof:
Theorem. All monotone functions are integrable.
Proof. Without loss of generality, assume that $f$ is increasing on an interval $\left[a, b \right]$. Thus, $f(a) \le f(x) \le f(b)$, and $f$ is bounded on $\left[a, b \right]$. Given $\varepsilon >0$, there exists $k > 0$ such that
\begin{equation*} k \left[f(b) - f(a) \right] < \varepsilon. \end{equation*}
Let $P = \left\lbrace x_0, x_1, \dots, x_n \right\rbrace$ be a partition of $\left[a, b \right]$ such that $\Delta x_i \le k$ for all $i$. Since $f$ is increasing, it follows that
\begin{equation*} m_i = f(x_{i-1}) \ \text{and} \ M_i = f(x_i), \quad i = 1, 2, \dots, n. \end{equation*}
Where $m_i$ is the greatest lower bound of $f$ on $\left[ x_{i-1}, x_i \right]$, and $M_i$ is the least upper bound of $f$ on $\left[ x_{i-1}, x_i \right]$.
$U(f, P) - L(f, P) = \sum_{i=1}^n \left[ f(x_i) - f(x_{i-1}) \right] \Delta x_i$
$\le k \sum_{i=1}^n \left[ f(x_i) - f(x_{i-1}) \right] (*)$
$= k \left[f(b) - f(a) \right]$
$< \varepsilon.$
By Theorem 7.1.9 $f$ is integrable on $\left[ a, b \right]$. In the case that $f$ is monotone decreasing, we may use the same argument on $-f$.
I am just wondering if somebody could explain how we get from the line marked by (*) to the line after that.
\begin{align}\sum_{i=1}^n[f(x_i)-f(x_{i-1})] &= \sum_{i=1}^n f(x_i)-\sum_{i=1}^nf(x_{i-1}) \\&= \sum_{i=1}^n f(x_i)-\sum_{i=0}^{n-1}f(x_{i})\\&=f(x_n)-f(x_0)\end{align}
By the way, it is false that if $f(x)$ is monotone on $[a, b)$ then $f(x)$ is bounded.. just take a function with an vertical asymptote.
• I would prefer to use $[a, b)$, because, to me, saying that $f$ is monotone on $[a, b]$ implies that $f(b)$ is defined and finite. – marty cohen Nov 23 '14 at 22:52 | {"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": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9972646832466125, "perplexity": 73.14799537294991}, "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/1618038082988.39/warc/CC-MAIN-20210415005811-20210415035811-00371.warc.gz"} |
https://blender.stackexchange.com/questions/56988/how-does-the-simple-deform-modifier-work?noredirect=1 | # How does the simple deform modifier work?
This question starts with this previous question How can I create spherical topology from a 2D image?.
Testing around the solution (given by Cegaton and previously given by LeonCheung) made me try to test a bit around the bending behavior of the simple deform modifier.
The idea behing all that : this bending makes interesting things, but it is hard to predict how to do them.
An example, before the question. Using the same technics you can obtain a tire shape from a flat surface.
But first the approach gives something that I feel counter intuitive. If we start from the result of the question quoted above, go to edit mode and rotate the shape 90° (so the object own rotations stay 0), we don't obtain a similar result. Testing that I was expecting an ovoid shape but this is not the case.
After that I did a little test, without the empties, just bending the shape. I started with a square 1x1. Playing with the deform angle, we obtain a fan (convergence of the top vertices) at an angle of 114.592°. And, it seems that 360 / 114.592 = 3.14158 (PI). And we can also notice that this value is linearly proportional to the Y dimension of the shape (if the plane is 2m in Y, the angle is 57,28°)
If we continue to 360° (for the deform angle), we found that the shape rotates around a point at Y=0.1591575m. And PI x this number if 5 (very very nearly).
And as the angle can vary from -360 to 360, this last limit point varies 10 / PI around the center.
We can also notice that the diameter of the 'circle' is 1.318311m from (in Y) -0.5 to +0.818311. Which is 1 + (2 x 0.1591575) (the value mentioned above).
The inner circle is nearly (but not so exactly) half of the outer.
Clearly there are some clever rules and calculations behind all that. But what are they ? What is to be understood in order to "predict" how use the modifier well ?
Which "patterns" are interesting to use ? (by pattern, I mean for instance the one of the initial question : using two deforms (180 and 360) and two empties (90,0,0) and (90, 0, 90))
• Re pi and angles en.wikipedia.org/wiki/Radian#History ...Torus: en.wikipedia.org/wiki/Torus. – batFINGER Jul 1 '16 at 10:20
• @batFINGER, thanks ! I had no idea of what was behing a torus before that... ok, so for instance, the pattern (-360, 360) + ((90, 0, 0), (90,0,90)) gives a torus !! – lemon Jul 1 '16 at 10:40
• Give animating the values a go. That punctured torus animation on wiki page is hypnotic. Make a good q. – batFINGER Jul 1 '16 at 11:13
• yes, translating the empties along axis is strange too – lemon Jul 1 '16 at 11:15 | {"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": 0.8239544630050659, "perplexity": 1416.176335350901}, "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/1606141195967.34/warc/CC-MAIN-20201129004335-20201129034335-00159.warc.gz"} |
https://questions.examside.com/past-years/jee/question/let-s1-sumlimitsj-110-jleft-j-1-right10cjs2-sumlimitsj-110-j-jee-main-2010-marks-4-nvvlzma4d6f3menv.htm | 4.5
(100k+ )
1
### AIEEE 2010
Let $${s_1} = \sum\limits_{j = 1}^{10} {j\left( {j - 1} \right){}^{10}} {C_j}$$,
$${{s_2} = \sum\limits_{j = 1}^{10} {} } j.{}^{10}{C_j}$$ and
$${{s_3} = \sum\limits_{j = 1}^{10} {{j^2}.{}^{10}{C_j}.} }$$
Statement-1 : $${{S_3} = 55 \times {2^9}}$$.
Statement-2 : $${{S_1} = 90 \times {2^8}}$$ and $${{S_2} = 10 \times {2^8}}$$.
A
Statement - 1 is true, Statement- 2 is true; Statement - 2 is not a correct explanation for Statement - 1.
B
Statement - 1 is true, Statement-2 is false.
C
Statement - 1 is false, Statement-2 is true.
D
Statement - 1 is true, Statement-2 is true: -Statement - 2 is a correct explanation for Statement - 1.
## Explanation
Note :
$$\sum\limits_{r = 0}^n {r.{}^n{C_r}}$$ = $$= n{.2^{n - 1}}$$
$$\sum\limits_{r = 0}^n {{r^2}.{}^n{C_r}} = n\left( {n + 1} \right){2^{n - 2}}$$
Given that,
$${s_1} = \sum\limits_{j = 1}^{10} {j\left( {j - 1} \right){}^{10}} {C_j}$$
=$$\sum\limits_{j = 1}^{10} {{j^2}.{}^{10}} {C_j} - \sum\limits_{j = 1}^{10} {j.{}^{10}} {C_j}$$
= 10$$\times$$11$$\times$$$${2^{10 - 2}}$$ - 10$$\times$$$${2^{10 - 1}}$$
= 10$$\times$$$${2^{8}}$$(11 - 2)
= 10$$\times$$9$$\times$$$${2^{8}}$$
= 90$$\times$$$${2^{8}}$$
$${{s_2} = \sum\limits_{j = 1}^{10} {} } j.{}^{10}{C_j}$$
= 10$$\times$$$${2^{10-1}}$$
= 10$$\times$$$${2^{9}}$$
$${{s_3} = \sum\limits_{j = 1}^{10} {{j^2}.{}^{10}{C_j}.} }$$
= 10$$\times$$11$$\times$$$${2^{10-2}}$$
= $${{110} \over 2} \times {2^9}$$
= 55 $$\times$$ $${2^9}$$
2
### AIEEE 2009
The remainder left out when $${8^{2n}} - {\left( {62} \right)^{2n + 1}}$$ is divided by 9 is :
A
2
B
7
C
8
D
0
## Explanation
$${8^{2n}} - {\left( {62} \right)^{2n + 1}}$$
= $${\left( {{8^2}} \right)^n} - {\left( {62} \right)^{2n + 1}}$$
= $${\left( {1 + 63} \right)^n} - {\left( {1 - 63} \right)^{2n + 1}}$$
= $$\left( {1 + n.63 + {}^n{C_2}{{.63}^2} + ......} \right)$$
+ $$\left( {1 + {}^{2n + 1}{C_1}.\left( { - 63} \right) + {}^{2n + 1}{C_2}.{{\left( { - 63} \right)}^2} + ......} \right)$$
= 2 + 63$$\left[ {\left( {n + {}^n{C_2} + ....} \right) + \left( { - {}^{2n + 1}{C_1} + {}^{2n + 1}{C_2}.63 + ......} \right)} \right]$$
= 63$$\times$$[Some integral value] + 2
63$$\times$$[Some integral value] + 2 by dividing with 9 we will get 2 as remainder as 63 is multiple of 9.
3
### AIEEE 2008
Statement - 1 : $$\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r} = \left( {n + 2} \right){2^{n - 1}}.}$$
Statement - 2 : $$\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r}{x^r} = {{\left( {1 + x} \right)}^n} + nx{{\left( {1 + x} \right)}^{n - 1}}.}$$
A
Statement - 1 is false, Statement - 2 is true
B
Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1
C
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1
D
Statement - 1 is true, Statement - 2 is false
## Explanation
Check Statement - 1
$$\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r}}$$
= $$\sum\limits_{r = 0}^n {r.{}^n{C_r}}$$ + $$\sum\limits_{r = 0}^n {{}^n{C_r}}$$
= $$\sum\limits_{r = 1}^n {r.{n \over r}{}^{n - 1}{C_{r - 1}}}$$ $$+ {2^n}$$
= $$n\sum\limits_{r = 1}^n {{}^{n - 1}{C_{r - 1}}}$$ $$+ {2^n}$$
= $$n \times {2^{n - 1}}$$$$+ {2^n}$$
= $${2^{n - 1}}\left[ {n + 2} \right]$$
Check Statement 2 :
$$\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r}{x^r}}$$
= $$\sum\limits_{r = 0}^n r .{}^n{C_r}.{x^r}$$ + $$\sum\limits_{r = 0}^n {{}^n{C_r}.{x^r}}$$
= $$n\sum\limits_{r = 1}^n {{}^{n - 1}{C_{r - 1}}.{x^r}}$$ $$+ {\left( {1 + x} \right)^n}$$
= $$nx\sum\limits_{r = 1}^n {{}^{n - 1}{C_{r - 1}}.{x^{r - 1}}} + {\left( {1 + x} \right)^n}$$
= $$nx{\left( {1 + x} \right)^{n - 1}} + {\left( {1 + x} \right)^n}$$
Substitude x = 1 in the statement 2 and we get,
$$\sum\limits_{r = 0}^n {\left( {r + 1} \right)\,{}^n{C_r} = \left( {n + 2} \right){2^{n - 1}}.}$$
So Option B is correct.
4
### AIEEE 2007
In the binomial expansion of $${\left( {a - b} \right)^n},\,\,\,n \ge 5,$$ the sum of $${5^{th}}$$ and $${6^{th}}$$ terms is zero, then $$a/b$$ equals
A
$${{n - 5} \over 6}$$
B
$${{n - 4} \over 5}$$
C
$${5 \over {n - 4}}$$
D
$${6 \over {n - 5}}$$
## Explanation
According to the question,
t5 + t6 = 0
$$\therefore$$ $${}^n{C_4}.{a^{n - 4}}.{b^4}$$ + $$\left( { - {}^n{C_5}.{a^{n - 5}}.{b^5}} \right)$$ = 0
By solving we get,
$${a \over b} = {{n - 4} \over 5}$$
### Joint Entrance Examination
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Class 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": 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": 0.2700366675853729, "perplexity": 4478.101809317784}, "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-2022-21/segments/1652662541747.38/warc/CC-MAIN-20220521205757-20220521235757-00489.warc.gz"} |
https://explainingmaths.wordpress.com/2010/10/17/is-3-less-than-or-equal-to-5/ | Is 3 less than or equal to 5?
Many students are confused by the claims that
$x
and
$x<0 \Rightarrow x \leq 0$.
Indeed some refuse outright to accept that these statements are correct.
However, the same students may well have little trouble understanding about intervals in the real line, and be able to sketch open intervals and closed intervals. So perhaps once you look at “one-dimensional geometry” the problems go away. These sketches (using leftness and rightness to get a physical feel for inequalities) may be the best way to illustrate these concepts.
As for the title of this post: what would your students say if you asked them whether or not $3 \leq 5$ ? How confident would they be about their answer?
Joel
2 responses to “Is 3 less than or equal to 5?”
1. It looks like this very concrete question may be OK after all:
I have just received a report that our first years resoundingly agree that 3 really is less than or equal to 5.
So presumably the problems begin with the more abstract setting?
Joel
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Even the concrete questions cause problems. Every year students ask me why $2 \leq 3$ and/or why $1 \leq 1$. | {"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": 5, "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": 1.0000100135803223, "perplexity": 684.8229531230529}, "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-2017-22/segments/1495463607960.64/warc/CC-MAIN-20170525010046-20170525030046-00019.warc.gz"} |
https://help.valentin-software.com/pvsol/en/berechnungsgrundlagen/pv-module/characteristic-curve-models/ | # Characteristic curve models
To describe the characteristic curve of a solar cell, a model is used whose task it is to represent the electrical or thermal behavior of the cell over as wide a range of external influences as possible.
Basically, the models can be divided into empirical and physically oriented models. Empirical models are based on measurement results from real photovoltaic modules or cells, from which parameters for fit functions are usually obtained. These models can achieve very high imaging accuracy for the measured modules, while, as expected, they function worse with non-measured modules, since no parameters were determined here.
Physical models attempt to present the real processes in photovoltaic semiconductors in a generally valid manner. This means that they can also be applied with some accuracy to modules measured only minimally (by the manufacturer). However, the physical models also require some parameters, which must either also be determined empirically or are included in the modeling in the form of standard values. The most common physical models are the one- and two-diode model.
In PV*SOL® either the PV*SOL® model or the two-diode model is used to calculate the characteristic curves.
### PV*SOL® model
#### Basics
It is primarily a mathematical model, but in addition to the electrical data provided by the manufacturer, it requires a further set of electrical data as unconditional input variables at a weak light point near $20\,\%$ of the STC irradiation. The characteristic curve of the filling factor as a function of the irradiation is used. Since the short-circuit current is largely linear from the irradiance, the fill factor function can be used to derive the variables in the MPP. Once these values have been calculated, the interpolation between the three points is exponential. Thus the model of PV*SOL® allows the direct calculation of both the key parameters and the characteristic of a module with given irradiation.
#### The low light operating point
If the additionally required information about the low light point is not given – ideally these are provided by the module manufacturers – standard values are calculated depending on the module technology.
For this purpose, some parameters are determined first. Irradiation at the low light operating point $E_\text{SL}$ determines where the fill factor assumes the (maximum) value $ff_\text{Extra} \cdot FF_\text{STC}$. Parameters $E_\text{min}$ and $k$ serve for iterative determination of other parameters.
First the fill factor in the low light point $FF_\text{SL}$ is calculated:
$$FF_\text{SL} = ff_\text{Extra} \cdot FF_\text{STC} \qquad\qquad (1)$$
The open circuit voltage at the low light operating point $U_\text{OC,SL}$ is determined by
$$U_\text{OC,SL} = U_\text{OC,STC} \cdot \frac{\log{ \left( \frac{E_\text{SL}}{E_\text{min}}\right)}}{\log{ \left( \frac{E_\text{STC}}{E_\text{min}}\right)}} \qquad\qquad (2)$$
Table 2: Default values of the PV*SOL® model for different module technologies
Module technology $E_\text{SL}$ $E_\text{min}$ $k$ $ff_\text{Extra}$
Amorphous Si $150$ $2.2\cdot 10^{-6}$ $0.9685$ $1.03$
CdTe $200$ $1.0\cdot 10^{-7}$ $1.0000$ $1.03$
Amorph $250$ $5.0\cdot 10^{-8}$ $1.0300$ $1.00$
CIS $300$ $0.1$ $1,0000$ $1.10$
HIT $200$ $1.0\cdot 10^{-7}$ $1.0400$ $1.04$
All others $300$ $0.1$ $1.0000$ $1.05$
The smaller $E_\text{min}$ and the larger $E_\text{SL}$ are selected, the smaller the decrease of the open circuit voltage at the low light operating point will be (see example in Figure 4 with $U_\text{OC,STC}=0.6\,\text{V}$).
Figure 4: The low light open-circuit voltage as a function of $E_\text{min}$ and $E_\text{SL}$.
As mentioned above, the short-circuit current is linearly reduced according to
$$I_\text{SC,TL} = I_\text{SC,STC} \frac{E_\text{TL}}{E_\text{STC}} \qquad\qquad (3)$$
The current and voltage in the MPP are first set to $U_\text{MPP,SL} = 1.1\cdot U_\text{OC,SL}$ and $I_\text{MPP,SL}=0$. Then the equations for the current
$$I_\text{MPP,SL}=k\cdot I_\text{SC,SL} \frac{I_\text{MPP,STC}}{I_\text{SC,STC}} \qquad\qquad (4)$$
and the voltage
$$U_\text{MPP,SL} = FF_\text{SL} \cdot U_\text{OC,SL} \frac{I_\text{SC,STC}}{I_\text{MPP,STC}} \qquad\qquad (5)$$
in the MPP, and the correction of the factor $k$ with
$$k = 1,1 \frac{U_\text{MPP,SL}}{U_\text{OC,SL}} \qquad\qquad (6)$$
repeated until $U_\text{MPP,SL}\gt U_\text{OC,SL}$ or $k\gt 2$. Once the low light quantities have been determined, they can be calculated for each irradiation and temperature.
#### Fill factor
The characteristic behavior of the fill factor $FF$ is now represented by the inverse of a quadratic equation, where $E$ corresponds to the global radiation on module level:
$$FF=\frac{E}{a\cdot E^{2} + b\cdot E + c} \qquad\qquad (7)$$
The coefficients $a$, $b$ and $c$ are calculated depending on the size of the low light fill factor as follows:
$$a = \begin{cases} 0 &\text{wenn } FF_\text{SL} = FF_\text{STC}\cr \frac{E_\text{ STC} \left( FF_\text{ SL}-FF_\text{ STC} \right) }{FF_\text{ SL}\cdot FF_\text{ STC}\cdot \left( E_\text{ SL}-E_\text{ STC} \right) ^2} &\text{wenn } FF_\text{ SL}\gt FF_\text{ STC}\cr \frac{E_\text{ SL} \left( FF_\text{ STC}-FF_\text{ SL} \right)}{FF_\text{ STC}\cdot FF_\text{ SL}\cdot \left( E_\text{ STC}-E_\text{ SL} \right) ^2} &\text{wenn } FF_\text{ SL}\lt FF_\text{ STC}\cr \end{cases} \qquad\qquad (8)$$
$$b = \begin{cases} \frac{1}{FF_\text{SL}} &\text{wenn } FF_\text{SL} = FF_\text{STC}\cr \frac{1-2a \cdot E_\text{SL}FF_\text{SL}}{FF_\text{SL}} &\text{wenn } FF_\text{SL} \neq FF_\text{STC}\cr \end{cases} \qquad\qquad (9)$$
$$c = \begin{cases} 0 &\text{wenn } FF_\text{SL} = FF_\text{STC}\cr a \cdot E_\text{SL}^{2} &\text{wenn } FF_\text{SL} \gt FF_\text{STC}\cr a \cdot E_\text{STC}^{2} &\text{wenn } FF_\text{SL} \lt FF_\text{STC}\cr \end{cases} \qquad\qquad (10)$$
Figure 5: The fill factor above the irradiation for different module technologies.
For illustration, figure 5 shows the different fill factor curves as a function of irradiance. A fictitious fill factor of 0.7 was assumed for all technologies under STC conditions.
#### Idle
Analogous to the calculation at the low light point according to equation (2-1-2), the open circuit voltage $U_\text{OC}$ is now calculated with
$$U_\text{OC} = U_\text{OC,STC} \cdot \frac{\ln\left(\frac{E}{G_0}\right)}{\ln\left(\frac{E_\text{STC}}{G_0}\right)} + \alpha_\text{U} \left(T_\text{M}-T_\text{STC}\right) \qquad\qquad (11)$$
whereby it should be noted that the temperature coefficient of the voltage $\alpha_\text{U}$ must be used here in $\frac{\text{V}}{\text{K}}$. The auxiliary quantity $G_0$ ensures that the open circuit voltage at partial load is $U_\text{OC,SL}$:
$$G_0 = \exp\left( \frac{U_\text{OC,STC}\ln(E_\text{SL}) - U_\text{OC,SL}\ln(E_\text{STC})}{U_\text{OC,STC} - U_\text{OC,SL}} \right)\qquad\qquad (12)$$
#### Short-circuit current
The short-circuit current $C_\text{SC}$ is now calculated depending on whether the current irradiance $E$ is smaller or larger than the irradiance at the low light operating point $E_\text{SL}$. If it is lower, the quadratic relationship
$$I_\text{SC} = d \cdot E^2 + \left( e + \frac{\Delta I_\text{SC}}{E_\text{STC}} \right) E \qquad\qquad (13)$$
with
$$d = \frac{I_\text{SC,STC} - \left( \frac{I_\text{SC,STC}-I_\text{SC,SL}}{E_\text{STC}-E_\text{SL}} \right) E_\text{STC}}{E_\text{SL}^2} \qquad\qquad (14)$$
and
$$e = \frac{I_\text{SC,STC} - I_\text{SC,SL}}{E_\text{STC}-E_\text{SL}} + 2 \frac{I_\text{SC,STC} - \left( \frac{I_\text{SC,STC}-I_\text{SC,SL}}{E_\text{STC}-E_\text{SL}} \right) E_\text{STC}}{E_\text{SL}} \qquad\qquad (15)$$
applies. The temperature dependence is included in the calculation via
$$\Delta I_\text{SC} = \alpha_\text{I,SC} \left( T_\text{M} - T_\text{STC} \right) \qquad\qquad (16)$$
(the absolute value must also be used here, so $[\alpha_\text{I}] = \frac{\text{A}}{\text{K}}$). If the irradiation is greater than that of the weak-light point, there is a linear relationship between short-circuit current and irradiation, which is the same for all models.:
$$I_\text{SC} = I_\text{SC,STC} - \left( \frac{I_\text{SC,STC} - I_\text{SC,SL}}{E_\text{STC} - E_\text{SL}} \right) E_\text{STC} + \left( \frac{I_\text{SC,STC} - I_\text{SC,SL}}{E_\text{STC} - E_\text{SL}} + \frac{\Delta I_\text{SC}}{E_\text{STC}} \right) E \qquad\qquad (17)$$
#### MPP
The calculation of the MPP current is also divided into two ranges – according to the calculation of the short-circuit current. In the range of irradiation between $0$ and the low light point, the following rule applies
$$I_\text{MPP} = I_\text{SC} \cdot \upsilon_\text{I} \cdot \sqrt{\zeta_\text{P}} \qquad\qquad (18)$$
with
$$\upsilon_\text{I} = b\upsilon_\text{I} + m\upsilon_\text{I} \cdot E \cdot \sqrt{\zeta_\text{P}} \qquad\qquad (19)$$
$$b\upsilon_\text{I} = \frac{I_\text{MPP,STC}}{I_\text{SC,STC}} - \left( \frac{ \frac{I_\text{MPP,STC}}{I_\text{SC,STC}} - \frac{I_\text{MPP,SL}}{I_\text{SC,SL}} }{E_\text{STC} - E_\text{SL}} \cdot E_\text{STC} \right) \qquad\qquad (20)$$
$$m\upsilon_\text{I} = \frac{ \frac{ I_\text{MPP,STC}}{I_\text{SC,STC}} - \frac{I_\text{MPP,SL}}{I_\text{SC,SL} }}{ E_\text{STC} - E_\text{SL} }\qquad\qquad (21)$$
and the temperature coefficient of the power $\alpha_\text{P}$ (this time between $0$ and $1$)
$$\zeta_\text{P} = \frac{ ( 1+\alpha_\text{P} (T_\text{M}-T_\text{STC} ))(U_\text{OC,STC} I_\text{SC,STC}) }{ (U_\text{OC,STC} + \Delta U_\text{OC}) (I_\text{SC,STC} + \Delta I_\text{SC}) } \qquad\qquad (22)$$
Analogous to the current $\Delta U_\text{OC}$ is calculated:
$$\Delta U_\text{OC} = \alpha_\text{U} (T_\text{M}-T_\text{STC}) \qquad\qquad (23)$$
If the irradiation is above the low light point, the MPP current is simply scaled with the ratio of MPP and short-circuit current under STC conditions and you get
$$I_\text{MPP} = \frac{I_\text{MPP,STC}}{I_\text{SC,STC}} \cdot I_\text{SC} \qquad\qquad (24)$$
This calculates the three key points short-circuit, open circuit and MPP.
#### Characteristic curve
Between these points the characteristic can be interpolated exponentially. In the range between short circuit and MPP the following applies
$$I_1(U) = bv + mv \cdot \exp(U\cdot kv) - \frac{I_\text{SC} - I_\text{MPP}}{2 U_\text{MPP}} \cdot U \qquad\qquad (25)$$
with
$$bv = \frac{ I_\text{SC}\cdot\exp(kv\cdot U_\text{MPP}) - \left( I_\text{MPP} + \frac{I_\text{SC} - I_\text{MPP}}{2} \right) }{ \exp(kv\cdot U_\text{MPP})-1 } \qquad\qquad (26)$$
$$mv = \frac{ I_\text{MPP}-I_\text{SC}+\frac{I_\text{SC}-I_\text{MPP}}{2} }{ \exp(kv\cdot U_\text{MPP})-1 } \qquad\qquad (27)$$
$$kv = \frac{\text{invers}(y)}{U_\text{MPP}} \qquad\qquad (28)$$
$$y = \left( \frac{I_\text{MPP} + \frac{I_\text{SC}-I_\text{MPP}}{2} }{ I_\text{SC} - I_\text{MPP} + \frac{I_\text{SC}-I_\text{MPP}}{2} } \right) \qquad\qquad (29)$$
The function $\text{invers}(y)$ returns an approximation of the $x$ value for a known $y$ of the function
$$y = \frac{x}{\exp(x-1)} \qquad\qquad (30)$$
since this is not explicitly calculable.
In the second range – between MPP and open circuit – the characteristic is approximated as follows:
$$I_2(U) = bn + mn \exp(U\cdot kn) - \frac{I_\text{SC} - I_\text{MPP}}{2U_\text{MPP}} (U-U_\text{OC}) \qquad\qquad (31)$$
with
$$bn = \frac{I_\text{MPP}-I_\text{rd}}{1-\exp(kn(U_\text{MPP}-U_\text{OC}))} \qquad\qquad (32)$$
$$mn = \frac{ -I_\text{MPP}+I_\text{rd} }{ \exp(kn\cdot U_\text{OC}) - \exp(kn\cdot U_\text{MPP}) } \qquad\qquad (33)$$
$$kn = \frac{ \text{invers}(y) }{U_\text{OC} - U_\text{MPP}} \qquad\qquad (34)$$
$$y = \frac{ U_\text{OC} }{U_\text{MPP}} - 1 \qquad\qquad (35)$$
$$I_\text{rd} = \frac{ I_\text{SC}-I_\text{MPP} }{ 2\cdot U_\text{MPP} } (U_\text{OC} - U_\text{MPP}) \qquad\qquad (36)$$
### One-diode model
#### Basics
If the equivalent circuit diagram of a PV cell consisting of a power source with a diode connected in parallel is extended by a parallel ($R_\text{P}$) and a series resistor ($R_\text{S}$), the circuit diagram of the single diode model is obtained:
Figure 6: Equivalent circuit diagram of the single diode model.
The current source models the generation of electron-hole pairs, which are separated by the voltage in the p-n junction and then derived via an external load. The p-n junction itself is represented in the circuit diagram by the diode. Recombinations of the electron-hole pairs, as they occur, for example, at the edge of the cell, are taken into account by the parallel resistance, while the series resistance reflects the losses caused by contacts, lines and the like.
Thus, the current that can be taken from the cell at a given voltage at the terminals can be formulated as an extension of the Shockley equation as follows:
$$I = I_\text{ph} - I_\text{S} \cdot \left( \exp\left( \frac{U-IR_\text{s}}{m\cdot U_\text{T}} \right)-1 \right) - \frac{U-IR_\text{s}}{R_\text{p}} \qquad\qquad (37)$$
The photocurrent $I_\text{ph}$ is therefore always slightly above the current to be measured, i.e. at STC conditions slightly above the short circuit current $I_\text{SC,STC}$. It is linearly dependent on the irradiation $E$ and increases with increasing cell temperature $T$:
$$I_\text{ph} = (C_1+C_2\cdot T)E \qquad\qquad (38)$$
The parameters $C_1$ and $C_2$ are cell- or module-dependent, but can be easily calculated from the manufacturer’s specifications at least approximately.
The saturation current $I_\text{S}$ can be described in more detail with
$$I_\text{S} = C_\text{S} T^{\kappa} \exp\left( -\frac{E_\text{Gap}}{m\text{k}T} \right) \qquad\qquad (39)$$
and is usually in the order of $10^{-11}…10^{-9}\text{A}$. The material- and technology-dependent constant $C_\text{S}$ has values around $10^{2}\frac{\text{A}}{\text{K}^3}$, the exponent of temperature $\kappa$ in the literature is usually specified as $3$, $E_\text{Gap}$ is the band gap of the cell material (z.B. $E_\text{Gap,Si}(T=300\text{K})\approx 1,12\text{eV}$ of silicon at room temperature). The temperature or thermoelectric voltage $U_\text{T}$ is calculated with
$$U_\text{T} = \text{k}T\exp(-1) \qquad\qquad (40)$$
; sometimes the diode factor $m$ is still included in the calculation. Ultimately, however, it is of course equivalent to consider the diode factor separately and not as part of the thermoelectric voltage. Physically, the diode factor should represent recombination effects, e. g. in the p-n transition.In the literature, $m=1$ is set in most cases, although it is doubtful that all cell technologies exhibit similar recombination behavior.
Finally, the serial resistance $R_\text{s}$ and the parallel resistance $R_\text{p}$ remain for the description of the formula characters used in equation $(37)$. For modern solar cells the resistances should be in the range $R_\text{s}=10^{-1}\Omega$ or $R_\text{p}=10^2\Omega$.
The series resistance can be assumed to be largely independent of irradiation and temperature, while the parallel resistance of the irradiation is inversely proportional to $E$.
$$R_\text{p}(E) = R_\text{p,STC}\frac{E_\text{STC}}{E} \qquad\qquad (41)$$
#### Boundary conditions
In general, under STC conditions from the characteristic equation $(37)$, the four situations defined by the data sheet data can be described as follows. At no load, the voltage assumes the value of the no load voltage $U_\text{OC,STC}$ specified on the data sheet, the current is $0$:
$$0 = I_\text{ph}-I_\text{S}\cdot\left( \exp\left( \frac{U_\text{OC,STC}}{mU\text{T}} \right)-1 \right) - \frac{U_\text{OC,STC}}{R_\text{p}} \qquad\qquad (42)$$
In the short-circuit, the voltage $0$ is again used, while the current takes on the data sheet value:
$$I_\text{SC,STC} = I_\text{ph}-I_\text{S} \cdot \left( \exp\left( \frac{I_\text{SC,STC} \cdot R_\text{s}}{m \cdot U_\text{T}} \right)-1 \right)-\frac{I_\text{SC,STC} \cdot R_\text{s}}{R_\text{p}} \qquad\qquad (43)$$
At point of maximum power (MPP), currents and voltages are also given:
$$I_\text{MPP,STC} = I_\text{ph}-I_\text{S}\left( \exp\left( \frac{U_\text{MPP,STC}+I_\text{MPP,STC}\cdot R_\text{s}}{m\cdot U_\text{T}} \right)-1 \right)-\frac{U_\text{MPP,STC}+I_\text{SC,STC}\cdot R_\text{s}}{R_\text{p}} \qquad\qquad (44)$$
Furthermore, the power gradient in the MPP must be $0$. So:
$$\frac{dP}{dU}(U=U_\text{MPP,STC})\stackrel{!}{=}0$$
$$I_\text{ph}-C_\text{S}T^3\exp\left( -\frac{E_\text{Gap}}{m\text{k}T} \right) \cdot \left( \exp\left( \frac{U_\text{MPP,STC} + I_\text{MPP,STC} \cdot R_\text{S}}{m\cdot U_\text{T}} \right) -1 \right)-\frac{U_\text{MPP,STC}+I_\text{SC,STC}\cdot R_\text{S}}{R_\text{P}}$$ $$+ U_\text{MPP,STC}\cdot\left(-\frac{C_\text{S}T^{2}}{m\cdot U_\text{T}}\cdot\exp\left(-\frac{E_\text{Gap}}{mkT}\right)\cdot\left(\frac{U_\text{MPP,STC} + I_\text{MPP,STC} \cdot R_\text{S}}{m\cdot U_\text{T}}\right)-\frac{1}{R_\text{P}}\right)\stackrel{!}{=} 0 \qquad (45)$$
#### Dynamics
In order to be able to estimate how the one-diode model reacts to the various parameters, C-V characteristics are shown below, in each of which one parameter is varied. Unless otherwise stated in the diagram, the parameters are defined as follows:
$$I_\text{ph}=3,17\,\text{A} \qquad T=300\,\text{K} \qquad E_\text{Gap}=1,107\,\text{eV}$$ $$m=1 \qquad R_\text{s}=0,01\,\Omega \qquad R_\text{p}=100\,\Omega \qquad C_\text{S}=300\,\frac{\text{A}}{\text{K}^3}$$
Normally, only the basic electrical data under STC conditions of the module can be taken from the data sheets of the PV module manufacturers. These include the open circuit voltage $V_\text{OC,STC}$, the short circuit current $C_\text{SC,STC}$, voltage and current in the MPP $V_\text{MPP,STC}$ and $C_\text{MPP,STC}$, and in most cases the temperature coefficients of the open circuit voltage $\alpha_\text{U}. The parameters of the one-diode model can be calculated from these data. ### Two-diode model #### Basics The two-diode model adds another diode parallel to the first to the single-diode model described above, which generally contributes to an improvement in imaging accuracy in the MPP range. A further term is added to the mathematical model for the characteristic curve accordingly. The diode factors$m_1$and$m_2$are usually set to 1 and 2 respectively, and the saturation currents$I_\text{S1}$and$I_\text{S2}$also differ in amount. $$I=I_\text{ph} - I_\text{S1} \cdot \exp\left(\frac{U-I\cdot R_\text{S}}{m_1\cdot U_\text{T}}\right) - I_\text{S2}\cdot\exp\left( \frac{U-I\cdot R_\text{S}}{m_2\cdot U_\text{T}} \right) - \frac{U-I\cdot R_\text{S}}{R_\text{P}} \qquad\qquad (46)$$ The photocurrent$C_\text{ph}$is calculated analogous to the one-diode model according to equation (38). The saturation currents are calculated via $$I_\text{S1}=C_\text{S1}\cdot T^{\kappa_1} \cdot \exp\left( -\frac{E_\text{Gap}}{m_1\cdot k \cdot T} \right) \qquad\qquad (47)$$ and $$I_\text{S2}=C_\text{S2}\cdot T^{\kappa_2} \cdot \exp\left( -\frac{E_\text{Gap}}{m_2\cdot k \cdot T} \right) \qquad\qquad (48)$$ The exponents$\kappa_1$and$\kappa_2$are almost unanimously specified in the literature as$3$and$\frac{5}{2}$. Thus, the two-diode model contains two parameters more than the single-diode model: the diode factor$m_2$and the saturation factor$C_\text{S2}$. Furthermore, there are approaches that question the exact value of exponents of temperatures$\kappa_1$and$\kappa_2$in the equations for the saturation currents and arrive at values deviating from$3$and$\frac{5}{2}$. #### Boundary conditions Analogous to the single diode model, the four boundary conditions can be set up. The open circuit equation $$0=I_\text{ph}-I_\text{S1}\cdot \left( \exp\left( \frac{U_\text{OC,STC}}{m_1 \cdot U_\text{T}} \right)-1 \right) - I_\text{S2}\cdot\left(\exp\left( \frac{U_\text{OC,STC}}{m_2\cdot U_\text{T}} \right)-1 \right)-\frac{U_\text{OC,STC}}{R_\text{P}} \qquad\qquad (49)$$ the short-circuit equation $$I_\text{SC,STC}=I_\text{ph}-I_\text{S1}\cdot \exp\left( \frac{I_\text{SC,STC}\cdot R_\text{S}}{m_1\cdot U_\text{T}} \right)-I_\text{S2}\cdot \exp\left( \frac{I_\text{SC,STC}\cdot R_\text{S}}{m_2\cdot U_\text{T}} \right)-\frac{I_\text{SC,STC}\cdot R_\text{S}}{R_\text{P}} \qquad\qquad (50)$$ and the two equations for the MPP $$I_\text{MPP,STC} = I_\text{ph} - I_\text{S1}\cdot \exp\left( \frac{U_\text{MPP,STC}-I_\text{MPP,STC}\cdot R_\text{S}}{m_1\cdot U_\text{T}} \right)$$ $$-I_\text{S2}\cdot\exp\left( \frac{U_\text{MPP,STC}-I_\text{MPP,STC}\cdot R_\text{S}}{m_2\cdot U_\text{T}} \right) - \frac{U_\text{MPP,STC}-I_\text{MPP,STC}\cdot R_\text{S}}{R_\text{P}} \qquad\qquad (51)$$ and $$\frac{dP}{dU}\left(U=U_\text{MPP,STC}\right)\stackrel{!}{=}0$$ $$I_\text{ph}-I_\text{S1}\cdot \exp\left( \frac{U_\text{MPP,STC} - I_\text{MPP,STC} \cdot R_\text{S}}{m_1\cdot U_\text{T}} \right) - I_\text{S2}\cdot \exp\left(\frac{U_\text{MPP,STC} - I_\text{MPP,STC} \cdot R_\text{S}}{m_2\cdot U_\text{T}} \right) - \frac{U_\text{MPP,STC} - I_\text{MPP,STC} \cdot R_\text{S}}{R_\text{P}}$$ $$+U_\text{MPP,STC}\cdot\left( -\frac{e\cdot C_\text{S1}T^2}{m_1\cdot k}\cdot\exp\left( \frac{U_\text{MPP,STC} - I_\text{MPP,STC}\cdot R_\text{S}}{m_1\cdot U_\text{T}} \right) -\frac{e\cdot C_\text{S2}\cdot T^{\frac{3}{2}}}{m_2\cdot k} \exp\left( \frac{U_\text{MPP,STC}-I_\text{MPP,STC}\cdot R_\text{S}}{m_2\cdot U_\text{T}}\right)-\frac{1}{R_\text{P}}\right)\stackrel{!}{=}0 \qquad (52)$$ #### Dynamics Essentially, the C-V characteristic of the two diode model behaves similarly to the one-diode model when the parameters are varied. For the sake of completeness, here are the variations of the two new parameters: It can be seen that the characteristic reacts less sensitively to the variation of the second diode factor than to that of the first. The reason for this is on the one hand that the second diode factor is smaller by orders of magnitude than the first ($C_\text{S2} \approx 10^{-2} ~\text{A} \cdot \text{K}^{-\frac{5}{2}}$), on the other hand the temperature in this term is potentiated less. Figure 17 shows exactly how the second term affects the characteristic curve. The voltage calculated with the two-diode model was applied over the voltage calculated with the single-diode model. It should be noted that the second diode term has the most concise effect in the area below the MPP voltage. In the short-circuit and open circuit points, however, the two-diode model does not deliver any deviating results. Figure 18 shows the C-V characteristics of both models together. #### Parameter determination In the two-diode model, the second diode term adds two more parameters to those already to be determined in the single-diode model. • The second saturation factor$C_\text{S2}$and • the second diode factor$m_2$So you get a system with at first eight unknowns. Since the band gap$E_\text{Gap}$and the diode factors$m_1$and$m_2\$ cannot be calculated explicitly in this case, they are replaced by the values commonly used in the literature.
Under these conditions it is possible to calculate the parameters for the two diode model from data sheet data. | {"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": 0.9580298066139221, "perplexity": 1054.9634957423168}, "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-2019-51/segments/1575540545146.75/warc/CC-MAIN-20191212181310-20191212205310-00490.warc.gz"} |
https://cran.microsoft.com/snapshot/2020-02-15/web/packages/TestFunctions/vignettes/AnIntroductiontoTestFunctions.html | # An Introduction to TestFunctions
#### 2017-05-09
This is an introduction to the R package TestFunctions. It is available on CRAN and is maintained through Github.
Test functions are used whenever one needs to evaluate an algorithm. For example, an optimization algorithm should be tested on many different functions to make sure that it works and is robust. Thus many optimization test functions are very tricky, such as those with many local minima meant to make the global minimum harder to find.
## How do I use this package?
Each of the test functions is called like any other function. The first argument, x, should be a vector representing one point or a matrix that has points in its rows. This can cause problems if you are using a 1-dimensional function and pass in a vector of values. Instead you should pass them in as a matrix with a single column, or vectorize the function.
The code below shows how the branin function can be used, taking in either a vector or a matrix.
set.seed(0)
library(TestFunctions)
branin(runif(2))
## [1] 9.476405
branin(matrix(runif(20), ncol=2))
## [1] 24.119600 71.180268 18.374071 9.839029 36.607437 72.884496
## [7] 196.302169 25.185022 13.059216 27.129463
A contour of the banana function is shown below.
ContourFunctions::cf(banana)
## General function information
The functions are all designed to be run by default in the $$[0,1]^D$$ unit cube. If you want to run the function on the original input values, you can set scale_it=FALSE.
Independent Gaussian noise can be added to most functions by passing the standard deviation of the noise as the noise parameter. The plots below show the original function, then what data from the function with noise looks like.
tf1 <- function(xx) powsin(x=matrix(xx,ncol=1), noise=0)
curve(tf1, main="Function without noise")
x1 <- runif(1e2)
y1 <- powsin(x=matrix(x1,ncol=1), noise=.1)
plot(x1,y1, col=2, pch=19, cex=.3, main="Data with noise")
curve(tf1,add=T)
## Random wave functions
The function RFF_get will return a random wave function with any given number of dimensions. The function is created by combining many different one dimensional waves passing through the input area with various directions, magnitude, and offset. The default is composed of sine waves, but this can be changed to block or v waves.
Below is an example of a one dimensional wave.
tf <- RFF_get(D=1)
curve(tf)
Below is an example of a random wave in two dimensions.
ContourFunctions::cf(RFF_get(D=2))
## Function enhancers
There are some functions that modify other functions.
• add_linear_terms adds linear terms to a function.
• add_noise adds random noise to a function.
• add_null_dims adds extra dimensions that do not affect the function output.
• add_zoom lets you zoom in on part of a function. Below are two examples of zooming in on the banana function.
ContourFunctions::cf(banana)
ContourFunctions::cf(add_zoom(banana, c(0,.5), c(1,1)))
ContourFunctions::cf(add_zoom(banana, c(.2,.5), c(.8,1))) | {"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": 0.42031338810920715, "perplexity": 1054.3924628988066}, "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-2022-33/segments/1659882573623.4/warc/CC-MAIN-20220819035957-20220819065957-00191.warc.gz"} |
https://arxiv.org/abs/1602.00169 | cs.IT
(what is this?)
# Title: A Linearithmic Time Algorithm for a Shortest Vector Problem in Compute-and-Forward Design
Abstract: We propose an algorithm with expected complexity of $\bigO(n\log n)$ arithmetic operations to solve a special shortest vector problem arising in computer-and-forward design, where $n$ is the dimension of the channel vector. This algorithm is more efficient than the best known algorithms with proved complexity.
Comments: It has been submitted to ISIT 2016 Subjects: Information Theory (cs.IT) Cite as: arXiv:1602.00169 [cs.IT] (or arXiv:1602.00169v1 [cs.IT] for this version)
## Submission history
From: Jinming Wen [view email]
[v1] Sat, 30 Jan 2016 22:40:59 GMT (18kb) | {"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": 0.5086479187011719, "perplexity": 3271.3751705855225}, "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-2018-30/segments/1531676592420.72/warc/CC-MAIN-20180721071046-20180721091046-00479.warc.gz"} |
http://mechonomic.blogspot.co.at/2012/09/10-return-since-may-but-time-to-halt.html | 9/14/12
10% return since May, but time to halt
In April 2012, we predicted a drop in the S&P 500 to the level of 1300 by the end of May. Figure 1 shows the predicted behavior in April and May 2012, with the predicted segment shown by red line. We expected that the path observed in the previous rally would be repeated with the bottom points coinciding. When this prediction realized, I invested, say, one unit at the average price 1320. The expected exit level was 1500 in October 2013.
Figure 1. The original S&P 500 curve (black line) and that shifted forward to match the 2009 trough (blue line). Red line – expected fall in the S&P 500: from 1400 in March to 1300 in May.
Figure 2 shows the evolution of the S&P 500 monthly closing price since May 2012. The current level (September 14th) is above 1465 with the overall return of 10% during the past 4 months. One can see that the observed level is far above the expected one and the level, when repeating the blue curve, may have a small correction in December. Both these observations make me think that the time to exit and capitalize is approaching. I’ll definitely sell at 1500 or by the end of October. Bonds are looking more and more attractive as a safe haven till the new S&P 500 rally due in spring 2013.
Figure 2. Same as in Figure 1 with an extension between May and August. | {"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": 0.8054261207580566, "perplexity": 1474.7913048269936}, "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-2014-41/segments/1412037663036.27/warc/CC-MAIN-20140930004103-00299-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://kr.mathworks.com/matlabcentral/answers/1646270-how-to-set-x-axis-and-y-axis-of-a-plot-as-log-scales-in-bold-with-latex-interpreter | # how to set x-axis and y-axis of a plot as log scales in bold with latex interpreter?
조회 수: 25(최근 30일)
SismoPlotter 2022년 2월 9일
댓글: SismoPlotter 2022년 2월 9일
I would like to set the axis numbers of a plot in bold in latex font using the log scale.
I can set the axis numbers bold in latex font, but without using the log scale. When using the log scale setting, the bold setting is not taken into account.
ax = gca;
ax.XAxis.TickLabelInterpreter = 'latex';
ax.XAxis.TickLabelFormat = '\\textbf{%g}';
ax.XAxis.Scale = 'log';
Here is the code I am trying to use.
댓글을 달려면 로그인하십시오.
### 답변(1개)
Yongjian Feng 2022년 2월 9일
ax = gca;
ax.XAxis.FontWeight='bold';
ax.XAxis.Scale = 'log';
##### 댓글 수: 3표시숨기기 이전 댓글 수: 2
SismoPlotter 2022년 2월 9일
But then, do you have a way to convert the font into latex? Sorry if there was some misunderstanding, but the latex font is a requirement for me.
댓글을 달려면 로그인하십시오.
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Translated by | {"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": 0.9203791618347168, "perplexity": 9746.5470652276}, "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-2022-40/segments/1664030335054.79/warc/CC-MAIN-20220927162620-20220927192620-00074.warc.gz"} |
http://mathhelpforum.com/calculus/157827-integral-rational-function.html | # Math Help - Integral of Rational Function
1. ## Integral of Rational Function
I got this question on an exam this morning and I didn't know how to answer it. I've been working on it the past hour trying to figure it out. Usually with rational functions, I factor to get it in a from that I can use partial fractions.
$\int{\frac{1}{x^2 + x + 1}}$
But this can't be factored and completing the square gives $(x+\frac{1}{2})^2+\frac{3}{4}$
Which doesn't look any easier to integrate.
Could someone point me in the right direction?
Thanks
2. Originally Posted by centenial
I got this question on an exam this morning and I didn't know how to answer it. I've been working on it the past hour trying to figure it out. Usually with rational functions, I factor to get it in a from that I can use partial fractions.
$\int{\frac{1}{x^2 + x + 1}}$
But this can't be factored and completing the square gives $(x+\frac{1}{2})^2+\frac{3}{4}$
Which doesn't look any easier to integrate.
Could someone point me in the right direction?
Thanks
You missed a dx.
Completing the square is a good start, move on by substituting u=x+1/2.
3. Oh... complete the square and then u substitution. That seems so obvious now that I can't believe I didn't see it.
So...
$
\int{\frac{1}{x^2+x+1}dx}
$
$
\int{\frac{1}{(x + \frac{1}{2})^2 + \frac{3}{4}}dx}
$
$
\int{\frac{1}{u^2 + \frac{3}{4}}du}
$
$
\int{\frac{1}{u^2 + \sqrt{\frac{3}{4}}^2}du}
$
$
\frac{2}{\sqrt{3}} \times \tan^{-1}{\frac{2u}{\sqrt{3}}} + C
$
$
\frac{2}{\sqrt{3}} \times \tan^{-1}{\frac{2x + 1}{\sqrt{3}}} + C
$
Is that right?
4. Originally Posted by centenial
Oh... complete the square and then u substitution. That seems so obvious now that I can't believe I didn't see it.
So...
$
\int{\frac{1}{x^2+x+1}dx}
$
$
\int{\frac{1}{(x + \frac{1}{2})^2 + \frac{3}{4}}dx}
$
$
\int{\frac{1}{u^2 + \frac{3}{4}}du}
$
$
\int{\frac{1}{u^2 + \sqrt{\frac{3}{4}}^2}du}
$
$
\frac{2}{\sqrt{3}} \times \tan^{-1}{\frac{2u}{\sqrt{3}}} + C
$
$
\frac{2}{\sqrt{3}} \times \tan^{-1}{\frac{2x + 1}{\sqrt{3}}} + C
$
Is that right?
Looks fine to me.
5. Originally Posted by centenial
I got this question on an exam this morning and I didn't know how to answer it. I've been working on it the past hour trying to figure it out. Usually with rational functions, I factor to get it in a from that I can use partial fractions.
$\int{\frac{1}{x^2 + x + 1}}$
But this can't be factored and completing the square gives $(x+\frac{1}{2})^2+\frac{3}{4}$
Which doesn't look any easier to integrate.
Could someone point me in the right direction?
Thanks
If you don't want to have to resort to two substitutions, substitute $x + 1 = \frac{\sqrt{3}}{2}\tan{\theta}$ so that $dx = \frac{\sqrt{3}}{2}\sec^2{\theta}\,d\theta$.
Then $\int{\frac{dx}{x^2 + x + 1}} = \int{\frac{\frac{\sqrt{3}}{2}\sec^2{\theta}\,d\the ta}{\left(\frac{\sqrt{3}}{2}\tan{\theta}\right)^2 + \frac{3}{4}}}$
$= \int{\frac{\frac{\sqrt{3}}{2}\sec^2{\theta}\,d\the ta}{\frac{3}{4}(\tan^2{\theta} + 1)}}$
$= \int{\frac{\frac{\sqrt{3}}{2}\sec^2{\theta}\,d\the ta}{\frac{3}{4}\sec^2{\theta}}}$
$= \int{\frac{\frac{\sqrt{3}}{2}}{\frac{3}{4}}\,d\the ta}$
$= \int{\frac{2\sqrt{3}}{3}\,d\theta}$
$= \frac{2\sqrt{3}\,\theta}{3} + C$
$= \frac{2\sqrt{3}\arctan{\left[\frac{2\sqrt{3}}{3}(x+1)\right]}}{3} + C$. | {"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": 27, "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": 0.8610038757324219, "perplexity": 258.0548132624027}, "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/1394021251996/warc/CC-MAIN-20140305120731-00096-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/cpaa.2014.13.419 | # American Institute of Mathematical Sciences
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January 2014, 13(1): 419-433. doi: 10.3934/cpaa.2014.13.419
## Continuous dependence in hyperbolic problems with Wentzell boundary conditions
1 Department of Mathematics, University of Bari, Via E. Orabona 4, I--70125 Bari, Italy, Italy 2 Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna 3 The University of Memphis, Department of Mathematical Sciences, Memphis, TN 38152, United States 4 Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, United States
Received January 2013 Revised May 2013 Published August 2013
Let $\Omega$ be a smooth bounded domain in $R^N$ and let \begin{eqnarray} Lu=\sum_{j,k=1}^N \partial_{x_j}\left(a_{jk}(x)\partial_{x_k} u\right), \end{eqnarray} in $\Omega$ and \begin{eqnarray} Lu+\beta(x)\sum\limits_{j,k=1}^N a_{jk}(x)\partial_{x_j} u n_k+\gamma (x)u-q\beta(x)\sum_{j,k=1}^{N-1}\partial_{\tau_k}\left(b_{jk}(x)\partial_{\tau_j}u\right)=0, \end{eqnarray} on $\partial\Omega$ define a generalized Laplacian on $\Omega$ with a Wentzell boundary condition involving a generalized Laplace-Beltrami operator on the boundary. Under some smoothness and positivity conditions on the coefficients, this defines a nonpositive selfadjoint operator, $-S^2$, on a suitable Hilbert space. If we have a sequence of such operators $S_0,S_1,S_2,...$ with corresponding coefficients \begin{eqnarray} \Phi_n=(a_{jk}^{(n)},b_{jk}^{(n)}, \beta_n,\gamma_n,q_n) \end{eqnarray} satisfying $\Phi_n\to\Phi_0$ uniformly as $n\to\infty$, then $u_n(t)\to u_0(t)$ where $u_n$ satisfies \begin{eqnarray} i\frac{du_n}{dt}=S_n^m u_n, \end{eqnarray} or \begin{eqnarray} \frac{d^2u_n}{dt^2}+S_n^{2m} u_n=0, \end{eqnarray} or \begin{eqnarray} \frac{d^2u_n}{dt^2}+F(S_n)\frac{du_n}{dt}+S_n^{2m} u_n=0, \end{eqnarray} for $m=1,2,$ initial conditions independent of $n$, and for certain nonnegative functions $F$. This includes Schrödinger equations, damped and undamped wave equations, and telegraph equations.
Citation: Giuseppe Maria Coclite, Angelo Favini, Gisèle Ruiz Goldstein, Jerome A. Goldstein, Silvia Romanelli. Continuous dependence in hyperbolic problems with Wentzell boundary conditions. Communications on Pure & Applied Analysis, 2014, 13 (1) : 419-433. doi: 10.3934/cpaa.2014.13.419
##### References:
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##### References:
[1] Genni Fragnelli, Gisèle Ruiz Goldstein, Jerome Goldstein, Rosa Maria Mininni, Silvia Romanelli. Generalized Wentzell boundary conditions for second order operators with interior degeneracy. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 697-715. doi: 10.3934/dcdss.2016023 [2] Angelo Favini, Gisèle Ruiz Goldstein, Jerome A. Goldstein, Enrico Obrecht, Silvia Romanelli. Nonsymmetric elliptic operators with Wentzell boundary conditions in general domains. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2475-2487. doi: 10.3934/cpaa.2016045 [3] Maike Schulte, Anton Arnold. Discrete transparent boundary conditions for the Schrodinger equation -- a compact higher order scheme. Kinetic & Related Models, 2008, 1 (1) : 101-125. doi: 10.3934/krm.2008.1.101 [4] Davide Guidetti. On hyperbolic mixed problems with dynamic and Wentzell boundary conditions. Discrete & Continuous Dynamical Systems - S, 2020, 13 (12) : 3461-3471. doi: 10.3934/dcdss.2020239 [5] Davide Guidetti. Parabolic problems with general Wentzell boundary conditions and diffusion on the boundary. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1401-1417. doi: 10.3934/cpaa.2016.15.1401 [6] Ciprian G. Gal, Hao Wu. Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation. Discrete & Continuous Dynamical Systems, 2008, 22 (4) : 1041-1063. doi: 10.3934/dcds.2008.22.1041 [7] Vesselin Petkov. Location of eigenvalues for the wave equation with dissipative boundary conditions. Inverse Problems & Imaging, 2016, 10 (4) : 1111-1139. doi: 10.3934/ipi.2016034 [8] Luisa Arlotti. Explicit transport semigroup associated to abstract boundary conditions. Conference Publications, 2011, 2011 (Special) : 102-111. doi: 10.3934/proc.2011.2011.102 [9] Matthias Geissert, Horst Heck, Christof Trunk. $H^{\infty}$-calculus for a system of Laplace operators with mixed order boundary conditions. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1259-1275. doi: 10.3934/dcdss.2013.6.1259 [10] Mariane Bourgoing. Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Discrete & Continuous Dynamical Systems, 2008, 21 (3) : 763-800. doi: 10.3934/dcds.2008.21.763 [11] Mahamadi Warma. Semi linear parabolic equations with nonlinear general Wentzell boundary conditions. Discrete & Continuous Dynamical Systems, 2013, 33 (11&12) : 5493-5506. doi: 10.3934/dcds.2013.33.5493 [12] Nicolas Fourrier, Irena Lasiecka. Regularity and stability of a wave equation with a strong damping and dynamic boundary conditions. Evolution Equations & Control Theory, 2013, 2 (4) : 631-667. doi: 10.3934/eect.2013.2.631 [13] Guanggan Chen, Jian Zhang. Asymptotic behavior for a stochastic wave equation with dynamical boundary conditions. Discrete & Continuous Dynamical Systems - B, 2012, 17 (5) : 1441-1453. doi: 10.3934/dcdsb.2012.17.1441 [14] Michael Renardy. A backward uniqueness result for the wave equation with absorbing boundary conditions. Evolution Equations & Control Theory, 2015, 4 (3) : 347-353. doi: 10.3934/eect.2015.4.347 [15] Arnaud Heibig, Mohand Moussaoui. Exact controllability of the wave equation for domains with slits and for mixed boundary conditions. Discrete & Continuous Dynamical Systems, 1996, 2 (3) : 367-386. doi: 10.3934/dcds.1996.2.367 [16] Andrzej Nowakowski. Variational approach to stability of semilinear wave equation with nonlinear boundary conditions. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2603-2616. doi: 10.3934/dcdsb.2014.19.2603 [17] Le Thi Phuong Ngoc, Nguyen Thanh Long. Existence and exponential decay for a nonlinear wave equation with nonlocal boundary conditions. Communications on Pure & Applied Analysis, 2013, 12 (5) : 2001-2029. doi: 10.3934/cpaa.2013.12.2001 [18] Feliz Minhós, Rui Carapinha. On higher order nonlinear impulsive boundary value problems. Conference Publications, 2015, 2015 (special) : 851-860. doi: 10.3934/proc.2015.0851 [19] Hung Le. Elliptic equations with transmission and Wentzell boundary conditions and an application to steady water waves in the presence of wind. Discrete & Continuous Dynamical Systems, 2018, 38 (7) : 3357-3385. doi: 10.3934/dcds.2018144 [20] Paul Sacks, Mahamadi Warma. Semi-linear elliptic and elliptic-parabolic equations with Wentzell boundary conditions and $L^1$-data. Discrete & Continuous Dynamical Systems, 2014, 34 (2) : 761-787. doi: 10.3934/dcds.2014.34.761
2019 Impact Factor: 1.105 | {"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": 0.7249086499214172, "perplexity": 3712.9380204682548}, "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-2021-21/segments/1620243989819.92/warc/CC-MAIN-20210518094809-20210518124809-00384.warc.gz"} |
http://libros.duhnnae.com/material/2017may2/14940880969-A-N-at-small-negative-values-of-xf-in-the-reaction-p-ppol-to-0-X-at-70-GeV-and-univer.php | # $A N$ at small negative values of $xf$ in the reaction $p p(pol) o π^0 X$ at 70 GeV and universal threshold in inclusive pion production
$A N$ at small negative values of $xf$ in the reaction $p p(pol) o π^0 X$ at 70 GeV and universal threshold in inclusive pion production - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.
Descargar gratis o leer online en formato PDF el libro: $A N$ at small negative values of $xf$ in the reaction $p p(pol) o π^0 X$ at 70 GeV and universal threshold in inclusive pion production
The talk continues the series of Single Spin Asymmetry (SSA) $\pi^0$ inclusive measurements carried out at Protvino 70 GeV accelerator. The asymmetry in the polarized target fragmentation region grows up in absolute value with $\xf$ decreasing and equals to $(-16 \pm 5)%$ at \$-0.4
Autor: A. M. Davidenko; A. A. Derevschikov; V. N. Grishin; V. Yu. Khodyrev; Yu. A. Matulenko; Yu. M. Melnick; A. P. Meschanin; V. V. Mochalov; L. V. Nogach;
Fuente: https://archive.org/ | {"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": 0.912625253200531, "perplexity": 9721.824387575336}, "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/1534221214702.96/warc/CC-MAIN-20180819051423-20180819071423-00322.warc.gz"} |
http://mathhelpforum.com/trigonometry/115620-law-cosines-print.html | # Law of Cosines
• November 19th 2009, 11:41 AM
ryno16
Law of Cosines
Use the law of cosines to solve the triangle
C=108°
a=10
b=7
• November 19th 2009, 11:52 AM
11rdc11
Quote:
Originally Posted by ryno16
Use the law of cosines to solve the triangle
C=108°
a=10
b=7
$c^2 = a^2 + b^2 -2(a)(b)\cos{C}$
just plug in the values and solve | {"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": 1, "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": 0.942431628704071, "perplexity": 2406.14394318758}, "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-2015-32/segments/1438042990445.44/warc/CC-MAIN-20150728002310-00262-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://socialsci.libretexts.org/Courses/HACC_Central_Pennsylvania's_Community_College/ANTH_205%3A_Cultures_of_the_World_-_Perspectives_on_Culture_(Scheib)/06%3A_Subsistence | # 6: Subsistence
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Learning Objectives
• Identify the four modes of subsistence and describe the major activities associated with obtaining food in each system.
• Explain the difference between wild and domesticated resources and how plants and animals are domesticated.
• Explain the relationship between the subsistence system used in a society and the amount of private property or wealth differences that develop.
• Assess the ways in which subsistence systems are linked to expectations about gender roles.
• Categorize the social and economic characteristics associated with agriculture and describe the benefits and drawbacks of the agricultural subsistence system.
• Analyze the ways in which the global agricultural system separates producers from consumers and contributes to wealth differences.
• Appraise the ways in which human intervention in the environment has made it difficult to separate the “natural” from the human-influenced environment.
• 6.1: Subsistence Systems
Think about the last meal you ate. Where did the ingredients come from? If it was a cheeseburger, where did the cow live and die? Now think about all the food you consume in a normal week. Can you identify the geographic origin of all the ingredients? In other words, how much do you know about the trip your food took to arrive at your plate? How much you know about where your food comes from would tell an anthropologist something about the subsistence system used in your community.
• 6.2: Foraging
Foragers use a remarkable variety of practices to procure meals. Hunting for animal protein is central to the foraging lifestyle and foragers capture and consume a wide variety of animals, from squirrels caught with a bow and arrow or blow dart to buffalo once killed by the dozens in communal hunts. Augmenting their diet with gathered wild plant resources, such as fruits, nuts, roots, tubers, and berries typically provide a large percentage of the calories that go into any meal.
• 6.3: Pastoralism
The goal of many pastoralists is not to produce animals to slaughter for meat, but instead to use other resources such as milk, which can be transformed into butter, yogurt, and cheese, or products like fur or wool, which can be sold. Even animal dung is useful as an alternate source of fuel and can be used as an architectural product to seal the roofs of houses.
• 6.4: Horticulture
Horticultural societies are common around the world; this subsistence system feeds hundreds of thousands of people, primarily in tropical areas of south and central America, Southeast Asia, and Oceania. A vast array of horticultural crops may be grown by horticulturalists, and farmers use their specialized knowledge to select crops that have high yield compared to the amount of labor that must be invested to grow them.
• 6.5: Agriculture
About 10,000 years ago, human societies entered a period of rapid innovation in subsistence technologies that paved the way for the emergence of agriculture. The transition from foraging to farming has been described as the Neolithic Revolution. Neolithic means “new stone age,” a name referring to the very different looking stone tools produced during this time period.
• 6.6: The Global Agriculture System
Despite agriculture’s tremendous productivity, food shortages, malnutrition, and famines are common around the world. How can this be? Many people assume that the world’s agricultural systems are not capable of producing enough food for everyone, but this is incorrect. The problem is that this capacity is unevenly distributed. Some countries produce much more food than they need, and others much less.
• 6.7: End of Chapter Discussion | {"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": 0.3114686608314514, "perplexity": 2757.7749112323704}, "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/1669446711045.18/warc/CC-MAIN-20221205200634-20221205230634-00652.warc.gz"} |
http://math.stackexchange.com/users/61397/ariyan-javanpeykar?tab=summary | Ariyan Javanpeykar
Reputation
855
Next privilege 1,000 Rep.
Create tags
2 6
Impact
~3k people reached
5 Morphism $f\colon X\to S$ is proper iff $f^{-1}(V_j)\to V_j$ is proper for some open cover $\{V_j\}$ of $S$? (Lemma 28.42.3 of Stacks Project) 5 What does the Tate module of an elliptic curve tell us? 5 Proof of the existence of Lefschetz Pencils. 5 Applications of Belyi's theorem 4 If $X$ and $Y$ are finite etale covers of each other, are they isomorphic?
### Reputation (855)
+10 Roadmap to Riemann hypothesis for curves over finite fields +10 The coarse moduli space of a Deligne-Mumford stack +10 Zariski dense implies classically dense? +10 Morphism $f\colon X\to S$ is proper iff $f^{-1}(V_j)\to V_j$ is proper for some open cover $\{V_j\}$ of $S$? (Lemma 28.42.3 of Stacks Project)
### Questions (0)
This user has not asked any questions
### Tags (28)
49 algebraic-geometry × 27 6 elliptic-curves × 2 12 algebraic-curves × 5 5 curves 10 reference-request × 4 3 moduli-space 8 surfaces × 4 2 analytic-geometry 6 riemann-surfaces × 2 2 category-theory
### Accounts (3)
MathOverflow 3,247 rep 1938 Mathematics 855 rep 26 Physics 101 rep 1 | {"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": 0.8747363686561584, "perplexity": 1976.232803600926}, "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-2015-18/segments/1430455241471.82/warc/CC-MAIN-20150501044041-00090-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://thewikipost.org/topic/F80BQz6r91h8nRuX5xhbPpu07fVb1tXR/Screen-freezes-randomly-Manual-restart-but-freezes-again.html | Over 1 million tech questions and answers.
# Screen freezes randomly. Manual restart but freezes again.
Q: Screen freezes randomly. Manual restart but freezes again.
I have a 17' Samsung 700Z laptop about two years old. Lately, it has been freezing up. I'm not sure if this is a Windows issue or a driver issue or something else. It usually freezes when I am gaming but sometimes freezes when I'm using Firefox as well. Freezes, no mouse movement, audio glitches out and the only fix is to restart it. It will freeze within ten minutes again though.
RELEVANCY SCORE 200
Preferred Solution: Screen freezes randomly. Manual restart but freezes again.
It's worked out well for many of us in the past.
RELEVANCY SCORE 112.8
Hello, I have been getting random freezes ever since I installed windows 7 starter... I had no problems before when this PC was running windows 7 trial version. When it happens my PC becomes unresponsive and whatever audio is played is looped(at a certain frequency) which is very annoying.. The only thing that functions is the CD/DVD drive. I have been trying to search for solutions but whatever solution I try from people with the same problem as me doesnt work. Please help me I don't know much about computers..
Edit: Also I can't seem to recreate this freezing thing. but most of the time it happens when I'm playing games... Although it sometimes happens even when I'm just browsing.
PS: Sorry for my english, im not american btw haha
A:My computer randomly freezes requires manual restart...
AFAIK...Windows 7 Starter is an OEM version already installed in a system.
Please explain what you did when you "installed" it, where you obtained the Win Starter version from, etc.
Louis
RELEVANCY SCORE 96.8
Good day all,
For some reason lately, when restarting my PC and logging in (with a picture password) the Metro Start screen that comes up sometimes randomly freezes/locks up. I can still move my mouse but the tiles aren't clickable at all nor do the live tiles change. Any buttons on the Metro UI don't respond either and the charms bar doesn't show up. It is as if the screen is completely frozen except for my mouse. This only happens during a restart; a cold boot doesn't cause this.
During this freeze I only have 2 ways to get out of it:
1. Pressing Ctrl+Alt+Del and doing a restart. Choosing to log off instead and logging in again still shows the Metro Start screen in a locked condition.
2. Pressing the Windows key. When doing that, the screen blinks and it brings me to the Desktop. An error shows up in my events saying that Explorer.exe has crashed. Here's the log:
The program Explorer.EXE, version 6.3.9600.17284 is not responding to Windows and has been shut down.
Proces-id: 580
Starttijd: 01cff3ed53c30a9e
Eindtijd: 15
Rapport-id: 9963ff96-5fe0-11e4-becc-bc5ff44ab185
Volledige pakketnaam met fout:
Relatieve toepassings-id van pakket met fout:
I haven't made any changes prior to this issue except disabling the option for Windows to bring me to the Desktop immediately after a boot (which, when enabled, obviously doesn't cause the freeze since it bypasses the Metro screen).
A sfc /scannow doesn't show any corruption.
A:Metro Start Screen randomly freezes on restart
EDIT: Nvm, it also happens when typing a password.
RELEVANCY SCORE 90.4
I bought this netbook on black friday and had done a ton of reviews on it and everyone gave it 5 stars. I got it at BestBuy and they had said that they opened it from the manufacturer and uninstalled all the trial software and installed an Anti-virus program. Aside from that, all I've installed software-wise is Skype. I have no issue with the computer if I am actively surfing or working on a document. But if I pull up a web page that has a lot of text and I'm reading it for a while, or if I walk away from it and leave it, it freezes after only a few minutes. Also, I can't close the laptop while it's on otherwise when I open it again it will show me the screen "User Name, 1 application running" but when I click it, it doesn't do anything. I have run all the spyware checks and anti-virus and it's clean. I have also changed the power options so that it doesn't hibernate and shut of screen savers. This hasn't helped. It really is a great little computer otherwise and I'd like to fix it rather than take it back for a refund. Does anyone have any ideas? I really don't think it's a heat issue since it sometimes only happens after 2 minutes and it isn't hot at all. Could it be the ram? I can't reboot Windows in it since I don't have a portable USB Optical drive and the netbook itself has no CD-ROM. Here are the stats:
OS: Windows XP (service pack 3)
Model: Compaq Mini 110-100DX
Intel Atom N270 / 10.1... Read more
A:Brand-new Netbook freezes when idle, can only reboot with manual restart
Talk to the manufacturer. Get it fixed while still under warranty.
RELEVANCY SCORE 88
Myself, along with a couple of other people on this forum have been experiencing the exact same problem. I also found some other people on other virus help forums who have the same problem as well. This new ?virus? seems to be spreading, and no one seems to know what to do about it. It just started during the beginning of April.
The main problem is that my computer just keeps randomly freezing. It can happen every 10 - 15 minutes or even up to an hour. The computer just freezes and you can?t do anything except for seeing your mouse move around. Ctrl alt delete does nothing at all either. It just locks up and you are forced to manually turn off the computer and restart it. It is extremely frustrating. It all started during the beginning of April where my computer restarted on its own, then it just started freezing up.
I ran several anti virus programs, spy ware removal programs, and an AVG scan and could find nothing of any relevance. I even had a technician come to my house and he couldn?t find anything. He thinks that it?s the memory or ram, but I highly doubt that, my laptop is only like 2 years old.
Any help would be greatly appreciated. This is a new virus I believe and it is driving me insane, thank you!
I have ran a Malware Antimalware Bites scan, AVG, Ad Aware, Spybot, and SUPERAntiSpyware scans, all found nothing.
Here is my Hijackthis log:
Logfile of Trend Micro HijackThis v2.0.2
Scan saved at 8:31:35 PM, on 4/5/2009
Platform: Windows XP SP2 (Win... Read more
A:Computer keeps freezing randomly, Freezes randomly and forced to restart
Hello and welcome to TSF.
HijackThis is no longer the preferred initial analysis tool in this forum
We want all our members to perform the steps outlined in the link given below, before posting for assistance. There's a sticky at the top of this forum, and a
Quote:
Having problems with spyware and pop-ups? First Steps
link at the top of each page.
http://www.techsupportforum.com/f50/...lp-305963.html
After running through all the steps, you shall have a proper set of logs. Please post them in a new topic, as this one shall be closed.
If you have trouble with one of the steps, simply move on to the next one, and make note of it in your reply.
RELEVANCY SCORE 84.8
My Toshiba satellite L855-B511 is not new as brand new, but I don't always use it because it always freeze and restart, I am using windows 8. I bought new hard drive and new ram, because I was suspecting my hard disk failed me, and so I bought also a new ram. And formatted my laptop. But still it freezes and restart randomly. I don't know what to do for now. Here's the error I got from my laptop
c:\windows\minidump\090514-14937-01.dmp
c:\user\jer\appdata\local\temp\wer-63093-0.sysdata.xml
c:\windows\memory.dmp
I'm not so good with computers so bear with me. thanks
A:laptop Restart and freezes randomly
Hi Geohound87 & Welcome to the forums ^_^,
I have analyzed your dump files and below has been provided an analysis of the dump files for informative purposes :-
Code:
Windows 8 Kernel Version 9200 MP (8 procs) Free x64
Built by: 9200.16384.amd64fre.win8_rtm.120725-1247
System Uptime: 0 days 6:26:39.804
Probably caused by : tcpip.sys ( tcpip! ?? ::FNODOBFM::string'+20e51 )
BugCheck D1, {158, 2, 1, fffff88001f87ec3}
BugCheck Info: DRIVER_IRQL_NOT_LESS_OR_EQUAL (d1)
Arguments:
Arg1: 0000000000000158, memory referenced
Arg2: 0000000000000002, IRQL
Arg3: 0000000000000001, value 0 = read operation, 1 = write operation
Arg4: fffff88001f87ec3, address which referenced memory
BUGCHECK_STR: AV
DEFAULT_BUCKET_ID: WIN8_DRIVER_FAULT
PROCESS_NAME: Agent.exe
FAILURE_BUCKET_ID: AV_tcpip!_??_::FNODOBFM::_string_
CPUID: "Intel(R) Core(TM) i7-3630QM CPU @ 2.40GHz"
MaxSpeed: 2400
CurrentSpeed: 2395
BIOS Version 6.60
BIOS Release Date 01/14/2013
Manufacturer TOSHIBA
Product Name SATELLITE L855
??????????????????????????????????????????????????????????????????????????????????????`
**************************Fri Sep 5 00:02:05.605 2014 (UTC + 5:30)**************************
RELEVANCY SCORE 84
Hi,
Whenever I start up my desktop, sometimes I'll get a brief 'hang' where my computer freezes and then normal operation resumes. About 10-30 seconds later, these hangs become more frequent until I am completely stuck. Sometimes my mouse cursor changes its icon. I am not able to use my keyboard either. Nowdays whenever I see the first hang I just restart and after the restart things are usually fine.
I can't think of what changed recently, but whenever I boot-up I'm just browsing the web on Chrome - Reddit/Facebook etc...
Here's the TSG SysInfo:
Tech Support Guy System Info Utility version 1.0.0.2
OS Version: Microsoft Windows 7 Ultimate, Service Pack 1, 64 bit
Processor: Intel(R) Core(TM) i5-2500K CPU @ 3.30GHz, Intel64 Family 6 Model 42 Stepping 7
Processor Count: 4
RAM: 8103 Mb
Graphics Card: NVIDIA GeForce GTX 560 Ti, 1024 Mb
Hard Drives: C: Total - 152524 MB, Free - 48686 MB;
Motherboard: ASRock, Z68 Extreme3 Gen3
Antivirus: Microsoft Security Essentials, Updated and Enabled
Thanks!
A:Computer randomly freezes and I have to restart - virus?
RELEVANCY SCORE 83.2
Hello!!
My problems started about 1-2months ago.
I started to get BSOD like
Then it started to randomly shut down almoust like it went to sleep mode the fans were on and so was the motherboard lamp, but the screen was of and keyboard wasnt reakting to "caps lock" or "Num lock".
And when i restarted my computer it would not boot up, it would be in the same state as it crashed or it would turn on and then freeze when windows pops up or earlier.
Now im getting Multi colour BSOD, and then it just go in to sleep mode state as i told before.
so what i have tried to fix this is i have reinstalled Windows 7
As i suspected my graphic card i bought a new one, but still got the same problems. I changed Ram memories with the same i had before but new ones.
when this problem occured i did not Fix or do anything with my hard drives.
i tried diskkontrol with the repair, did not help.
I got a Windows 7,
Mothercard is an Asus.
Graphic card is an XFX radeon hd 6870 double fan
I have updated all drivers i know about
I use CCC with default setings and my temp are usaly 30-40C
My computer is mainly For gaming..
I really need some help with what kind of hardware or what is wrong with my computer
A:BSOD,randomly restarts, refuses to restart.. and freezes.
Hello,
Can you take a look at the below link and attach the requested reports.
http://www.techsupportforum.com/foru...ta-452654.html
RELEVANCY SCORE 82
Windows 10 crashes frequently and randomly. No BSOD no error msgs. Happens about 30 times a day with no rhyme or reason
Elizabeth
RELEVANCY SCORE 79.2
Have no clue as to patterns - genuinely seems random. Previously had IE6 latest service pack loaded and it would freeze on average - 6 times a day - with no *.dmp file even though the Drwatson registry key was installed! Switched to Firefox, and immediate improvement - it now freezes randomly once every 2 days or so - often occurs when zonealarm receive green lights are on, and sometimes when many apps are open at once. Also no blue BSD would show - it just stops working - no mouse response, no keyboard response - not even Ctrl Alt Del - wait 5 minutes still nothing. Any help would be appreciated - I am pulling my beard out.DDS (Ver_09-12-01.01) - NTFSx86 Run by 1st at 14:16:26.79 on Wed 02/03/2010Internet Explorer: 6.0.2900.5512Microsoft Windows XP Professional 5.1.2600.3.1252.1.1033.18.2039.1003 [GMT -5:00]AV: ZoneAlarm Security Suite Antivirus *On-access scanning enabled* (Updated) {5D467B10-818C-4CAB-9FF7-6893B5B8F3CF}FW: ZoneAlarm Security Suite Firewall *enabled* {829BDA32-94B3-44F4-8446-F8FCFF809F8B}============== Running Processes ===============C:\WINDOWS\system32\svchost -k DcomLaunchsvchost.exeC:\WINDOWS\System32\svchost.exe -k netsvcssvchost.exesvchost.exeC:\WINDOWS\system32\ZoneLabs\vsmon.exeC:\Program Files\CheckPoint\ZAForceField\IswSvc.exeC:\WINDOWS\system32\spoolsv.exesvchost.exeC:\XAMPP\xampp\apache\bin\httpd.exeC:\WINDOWS\eHome&#... Read more
A:XP Media Center Edition Machine freezes randomly - removed IE freezes less frequently
RELEVANCY SCORE 78.4
I have had this issue for awhile, it comes and goes.
I will be playing a computer game, it can be anything from world of warcraft to counter strike and occasionally the computer will freeze. As far as I can tell it will not respond to keyboard input or mouse movements, I do not hear any sounds when it freezes and the monitor will be frozen on whatever window is active at the time.
The only thing I can do at this point is restart the computer and shut down the computer. Upon doing either while the computer boots up it will freeze at random points (windows icon, log in screen, sometimes while the bios is loading).
Not sure if this makes any sense but if I shut down the computer and unplug the power supply and plug it back in then turn the computer on, it usually boots without freezing. I really doubt its an overheating problem because I do not let the computer cool down between restarts or the unplug/plug thing but I am open to all suggestions.
Intel Core 2 Duo E6850
Conroe, 775 LGA, 3GHz
EVGA nForce 680i SLI MB
4GB PC2-6400 Corsair (CM2X1024-8500C5D)
NVIDIA GeForce 8800 GTS
A:Freezes during games & freezes when I try to restart it (multiple times)
Anyone?
Also I just came back from vacation and now my computer won't start. It freezes at the "starting windows" screen and when I try to repair it freezes as well.
RELEVANCY SCORE 76.8
Hello! Finally found an issue to make an account about.
Anyways, so I just recently installed a new anti-virus software (Kaskersky Anti-Virus 2013) and it runs perfectly (or so I thought).
The only problem that was plaguing my computer was after I restarted it (via the Sidebar and pressing the power icon and clicking restart) and it would "hang" at the restart screen for about 30 seconds.
The pixel icon next to the word "Restarting" would freeze mid spin (I could still move my mouse), but then it would continue to function normally.
So my question is simply: Is this an issue to take action against or is the Anti-Virus software preventing a proper restart?
NOTE: When I start a normal "Shutdown" this problem is absent and the computer shuts down in about 6 seconds.
A:Computer freezes at Restart screen.
Try One These Steps..i Think U Recover From This Problem.......Repair your Windows installation. A common reason for Windows to freeze up or reboot automatically during the Windows startup process is because one or more important Windows files are damaged or missing. Repairing Windows replaces these important files without removing or changing anything else on your computer.
Note: In Windows 7 and Vista, this is called a Startup Repair. In Windows XP it's referred to as a Repair Installation.
Important: The Windows XP Repair Installation is more complicated and has more drawbacks than the Startup Repair available in the other operating systems. So, if you're an XP user, you may want to wait until you've tried Steps 3 through 6 before giving this a try. Start Windows using Last Known Good Configuration. If you've just made a change to your computer that you suspect might have caused Windows to stop booting properly, starting with the Last Known Good Configuration could help.
Last Known Good Configuration will return many important settings to the states they were in the last time Windows started successfully, hopefully solving this problem and allowing you back in to Windows. Start Windows in Safe Mode and then use System Restore to undo recent changes. Windows could freeze, stop, or reboot during the startup process because of damage to a driver, important file, or part of the registry. A System Restore will return all of those things to ... Read more
RELEVANCY SCORE 76.8
Hi... my PC hangs up and i restarted and i get a black after the monitors displags thr brand logo... dvi and No signal
Tried solution:
Clear CMOS
removed CMOS batterry
Reseated all hardware including video card,ram sticks and hard drive along with SATA
done a bunch of resets
Clean VideoCard,Heatsinker and Ram sticks
trjed exchanging ram stick placjng
Any help pls? im sorry if i posted in the wrong section
A:Pc Freezes and screen goes black after restart
Is this a recently built system ???
If so reseat the CPU and make sure the thermal paste is properly spread and the fans are properly installed
RELEVANCY SCORE 76.8
lately, while I have been gaming my pc would freezing holding the frame frozen and forcing me to restart, I still could hear the audio coming from my pc but there wasn't any response from anything else. I'm not sure how to go about fixing this. any and all help is appreciated.
RELEVANCY SCORE 76.4
Hello, I have a 11 months old Notebook Tecra9 Toshiba running on vista 32 bits. Recently i'm experience frequent freezes (the desktop, not internet explorer) when using IE7 and also the taskbar would freeze, seems to be caused by audioclientrpc. My laptop is in french, but it's the same report problem as the english version:
Problem signature:
Problem Event Name: AppHangXProcB1
Application Name: explorer.exe
Application Version: 6.0.6001.18000
Application Timestamp: 47918e5d
Hang Signature: 7ce1
Hang Type: 128
Waiting on Application Name: svchost.exe:AudioClientRpc
Waiting on Application Version: 0.0.0.0
OS Version: 6.0.6001.2.1.0.768.3
Locale ID: 1033
A:Vista freezes randomly plus taskbar also freezes
I have the same program hanging as well. Have you been able to find a solution yet?
It's driving me crazy as the only thing I've changed on my computer recently was upgrading the RAM from 1 to 2 gigs.
RELEVANCY SCORE 76
I remember awhile ago where the first time it happened it was playing Battlefield 3. That was my first freeze. Ever since when I browse the web or watch videos on youtube, my screen would randomly freeze. It even froze when my Windows startup screen came up where I had to type my password in. It seems it freezes whenever it wants. It happened for around 4-5 months already. I have tried several solutions but didn't work. I reinstalled my OS but it still has freezes. I tried using another graphic card from another computer and it still gave me a screen freeze pretty quick. I also used another hard drive and my computer was on for more than a few hours but still froze after. I tried using one memory stick at a time but same results. I've also unplugged some wires and replugged but nothing changes. I've also tried softwares such as AVG or Windows Security Essentials. I'm pretty sure my drivers are up to date. I guess I need more solutions. Any advice helps. Thank you.
P.S. Is this the right place to write my post? First time using this website.
A:Computer Screen Randomly Freezes
Type eventvwr into Search programs and files (do not hit enter)
Right click eventvwr.exe and click Run as administrator
Expand Custom Views
Save all Events in Custom View As...
Save them in a folder where you will remember which folder and save as Errors.evtx
Go to where you saved Errors.evtx
Right click Errors.evtx -> send to -> compressed (zipped) folder
RELEVANCY SCORE 76
System Spec
Is Windows 7 ...
- x86 (32-bit) or x64 ? x64
- the original installed OS on the system? YES
- an OEM or full retail version? OEM
- What is the age of system (hardware)? I just bought it on 29 Oct 2011
- What is the age of OS installation (have you re-installed the OS?) And installed it on the same day
The screen freezes VERY randomly.
Symptoms :
Just like another member (Aptenodytes) said "Freezes manifest as sudden loss of mouse and keyboard control, screens stay on, sometimes with animated cursor still animated (for about 20 seconds then it stops), and if sound is playing then it goes onto a 0.1s loop (sounds like a machine gun), then I'm forced to hit the reset button.", but unluckily, for me I need to hit the power button to shut down the machine instead of the reset button.
Quote: Originally Posted by cdlam
System Spec
Is Windows 7 ...
- x86 (32-bit) or x64 ? x64
- the original installed OS on the system? YES
- an OEM or full retail version? OEM
- What is the age of system (hardware)? I just bought it on 29 Oct 2011
- What is the age of OS installation (have you re-installed the OS?) And installed it on the same day
The screen freezes VERY randomly.
Symptoms :
Just like another member (Aptenodytes) said "Freezes manifest as sudden loss of mouse and keyboard control, screens stay on, sometimes with animated cursor still animated (for about 20 seconds then it stops), and if sound is playing then it goes onto a 0.1s loop (sounds like a machine gun), then I'm forced to hit the reset button.", but unluckily, for me I need to hit the power button to shut down the machine instead of the reset button.
Hello and Welcome!
There are lot of causes by random freezes happens. Few things you can do to determine the problem.
2, Download Speedfan and see the Temps to rule of Overheat issues
3, Run SFC SCANNOW
4, Make sure all the drivers are updated (Especially display drivers)
5, Finally test the consistnace of your hardware, Run Hardware Diagnostic (RAM, Hard drive and GPU)
Hope this helps!
RELEVANCY SCORE 76
My appologies if this exact topic has been covered. I scanned through previous threads and did not find it. So anyway...
I am running XP Pro SP2. Been running it since SP2 was available and before that was running SP1 for about a year with no problems.
Suddenly I am getting major freezes. Complete freezes where everything just locks up (can't cntrl-alt-del or anything else). It happens frequently on the login screen and if not then, within 5 minutes after logging into an account. I can run for hours in safe mode problem free, so I'm assuming it's not a hardware issue. I run reg mechanic, spybot S&D and X clean free regularly. I ran hijackthis and "corrected" or deleted anything I was confident did not need to be there. I once made the mistake of installing iTunes on this machine so I also went into regedit and deleted anything that had to do with iTunes (you know, just in case). All of which made absolutely no difference whatsoever. I removed outlook express since I thought the issue might be the "you have 5 unread messages" next to her account login but that also made no difference.
Any ideas? It's my wife's home PC so if someone would like to take a look at the hijackthis log, I'll be glad to post it (once I get home from work of course).
T very much IA, Taralius
A:XP Freezes at login screen and randomly
I had a laptop that would freeze for no apparent reason. The fan wasn't working and it was overheating. This may be it, or may not be.
You may want to Roll-Back the install of the Service Pack 2. Go into Control Panel, Add/Remove Programs. Check for SP2 or something like that. If it is not there go to the Add/Remove Windows Components tab and see if it is there. There should be an uninstall or rollback option. This will roll the SP back to before SP2. This may work, or just cause more problems. Even if it works, this is just a temp fix, you will probably want to re-format and install XP with SP2 somewhere else down the line.
BMR777
www.rusnakweb.com
RELEVANCY SCORE 76
Hello,
This issue has been for 1 year now, suddenly when i'm browsing or playing games, the screen would freezes for 1 sec then its goes black (No signal) on both of my monitors, the pc would still be running and I can hear some voices like if i'm talking to someone on skype or teamspeak, I'd have to force restart the pc after that..
I thought it's software issue so i formatted and reinstalled windows back again, but the issue still happens
I'd be really grateful if anyone can help! I'm really thinking to build new computer because of this..
PC spec:
CPU: Intel Core i7-4820K GPU: ZOTAC GeForce GTX 980Ti AMP! Extreme Edition MB: ASUS Rampage IV Black-Edition RAM: Kingston 32GB DDR3 2400MHz Storage: SSD Samsung 840 EVO Series 500GB & HDD Seagate Barracuda 2TB PSU: Enermax Platimax 80 PLUS Platinum 1500 Watt Case: Cooler Master HAF X Monitor: Acer Predator XB271HU bmiprz 27-Inch WQHD & ASUS MX279H 27-Inch
Regards,
A:Screen randomly freezes then it goes black!
RELEVANCY SCORE 76
My computer randomly freezes and then goes to a blue screen but the text on it is garbled. Is this a hardware problem? I think something overheated.
edit: some more info: It happens after about 10 minutes. Suddenly, my cursor isn't able to move vertically but it can move horizontally. Then it completely freezes and leads into the blue screen. After I restart the computer, the cursor thing happens just a few seconds after windows startup, so I think it really is a heating issue.
A:randomly freezes with blue screen
I'm on the computer with the problem right now and here's my hijackthis logfile in case it's not hardware related.
Logfile of HijackThis v1.99.1
Scan saved at 8:19:05 PM, on 7/26/2005
Platform: Windows XP SP2 (WinNT 5.01.2600)
MSIE: Internet Explorer v6.00 SP2 (6.00.2900.2180)
Running processes:
C:\WINDOWS\System32\smss.exe
C:\WINDOWS\system32\winlogon.exe
C:\WINDOWS\system32\services.exe
C:\WINDOWS\system32\savedump.exe
C:\WINDOWS\system32\lsass.exe
C:\WINDOWS\System32\Ati2evxx.exe
C:\WINDOWS\system32\svchost.exe
C:\WINDOWS\System32\svchost.exe
C:\WINDOWS\system32\Ati2evxx.exe
C:\WINDOWS\system32\userinit.exe
C:\WINDOWS\Explorer.EXE
C:\WINDOWS\system32\spoolsv.exe
C:\Program Files\ATI Technologies\ATI Control Panel\atiptaxx.exe
C:\Program Files\iTunes\iTunesHelper.exe
C:\Program Files\D-Tools\daemon.exe
C:\Program Files\Java\jre1.5.0_02\bin\jusched.exe
C:\Program Files\Messenger\msmsgs.exe
C:\WINDOWS\system32\ctfmon.exe
C:\Program Files\Silicon Image\SiISATARaid\SATARaid.exe
C:\Program Files\iPod\bin\iPodService.exe
C:\WINDOWS\system32\wscntfy.exe
O2 - BHO: (no name) - {53707962-6F74-2D53-2644-206D7942484F} - C:\PROGRA~1\SPYBOT~1\SDHelper.dll
O4 - HKLM\..\Run: [ATIPTA] C:\Program Files\ATI Technologies\ATI Control Panel\... Read more
RELEVANCY SCORE 75.2
I am having a problem on my laptop with the cursor freezing and then the screen goes blank. The screen goes black but you can see that the light is still on for the computer. It isnt going in to sleep mode because i disabled it. And when it goes blank nothing works i have to hard boot it. It happens at random times.
It is a brand new, 1 day old, Gateway NV5214u.
Vista 64bit SP1
(2) AMD Athlon x2 Dual Core QL-65
I just bought this computer day before yesterday and it was happening so i brought it back to best buy. One of the geek squad guys said it could be an overheating issue so he swapped it out for this one.
But it started happening again. I dont know if it is a hardware issue in these computers or if it is something i am doing.
And i doubt that two brand new laptops are having overheating issues. but i could be wrong.
Thanks.
A:Cursor freezes and screen goes blank randomly.
Anyone?
RELEVANCY SCORE 75.2
So this has been happening ever since I got my computer. I took it in to see if a service could take a look at it and they ran a benchmark to get the usage to 100% for like 22 hours. Computer was still running fine he recommended me to get a UPS because it could be browning out but that solved nothing.
So what basically happens is that once a week or 3 times a day, it happens randomly, could be while playing a game or just browsing the web. What happens is that the monitor just freezes it is still on it is like a screenshot of my screen it stays still, cursor stops, audio stops, everything. The computer is still running fine it could be a failure in hardware but most likely not. It is not the monitor itself because it worked fine with the same monitor with my previous computer and I just got a new monitor last week.
I also noticed is if it happens once then it'll happen a few more times in a day then it'll stop for 1-2 days and start again, could just be a coincidence but I don't know...
Thanks, Alex.
Hope to get this solved starting to annoy me!
A:Screen Randomly Freezes but Computer Still Running?
Check your connections to your PC/GPU and your monitor, however you have it connected. Make sure that there are no bent pins and that the thumb screws are hand tight plus a quarter turn. Then make sure you have the latest driver for either your onboard GPU or add-on GPU.
RELEVANCY SCORE 75.2
The computer is failing to boot nearly every other time I boot.
When I load in safe made after windows failed to load, Windows Help and Support comes window comes up. I then select Diagnostic tools to use in safe mode. I then select Click to open event viewer and select windows logs, system. I get the following errors:
A timeout was reached (30000 milliseconds) while waiting for the VAIO Content Metadata Intelligent Network Service Manager service to connect.
The VAIO Content Metadata Intelligent Network Service Manager service failed to start due to the following error:
The service did not respond to the start or control request in a timely fashion.
The previous system shutdown at 10:20:37 AM on 12/19/2013 was unexpected.
The DHCP Client service depends on the Ancillary Function Driver for Winsock service which failed to start because of the following error:
A device attached to the system is not functioning.
The DNS Client service depends on the NetIO Legacy TDI Support Driver service which failed to start because of the following error:
A device attached to the system is not functioning.
The TCP/IP NetBIOS Helper service depends on the Ancillary Function Driver for Winsock service which failed to start because of the following error:
A device attached to the system is not functioning.
The Network Store Interface Service service depends on the NSI proxy service driver. service which failed to start because of the following error:
A:Windows freezes randomly on startup after welcome screen
Checkmark the following checkboxes: List last 10 Event Viewer log List Installed Programs List Users, Partitions and Memory size.
Click Go and paste the content into your next post.
Also...please Publish a Snapshot using Speccy - http://www.bleepingcomputer.com/forums/topic323892.html/page__p__1797792#entry1797792 , taking care to post the link of the snapshot in your next post.
Louis
RELEVANCY SCORE 75.2
Over the last few months my PSU has been making weird buzzing sounds and I'm about to send it in for a replacement, but over the past few days my PC has randomly frozen 3 times with the image, cursor and all, still on screen (no BSOD).
Now just to make sure it is entirely the PSU's fault I wanted to check in with you guys. Could the PSU really cause my computer to freeze like this? Is there any other test I should do or advice you guys have to check and see if there are any other causes for this problem?
I already ran my anti-virus software and anti-spyware, as well as a registry cleaner.
Thanks.
A:Computer freezes randomly with image still on screen
Is there anything I can do to single out the problem?
RELEVANCY SCORE 75.2
Installed new nvidia GTX 560 card, ran fine for 2-3 months but I just started getting random crashes (screen freezes or goes black). I already uninstalled the driver, ran driver sweeper in safe mode, reinstalled the latest driver 290.36 to no avail although with the new beta driver (290.36) the crashes seem less frequent. dump information and performance report is attached. System is windows 7 professional x64 the machine and the installation is roughly 7 months old.
A:BSOD but screen either freezes or goes black randomly
Hi.
Enable minidumps Dump Files - Configure Windows to Create on BSOD
After this we must wait for a new crash\bsod and you will have to reupload the folders.
RELEVANCY SCORE 75.2
Hi,
I had installed XP over the vista a year ago and the system was working perfectly fine but very recently my computer has recently started freezing randomly on any screen anywhere between instantly during BIOS booting to 20 minutes into running Windows and then I had to restart the system very often. It also gets freezes sometimes when I try to boot from Live Linux CD.
I have tried doing vacuum cleaning of the heat-sink, but with no success.
Any help or pointer will be very much appreciated. I have attached some screenshots.
AMD Turion64
NVIDIA Graphics
Regards,
Sanjeet
A:Compaq V3424AU screen freezes randomly
Likely not OS related as it also occurs before Windows loads and during a Linux boot.
So there would appear to be a hardware issue. As it's a laptop, there isn't much that you can do in the way of troubleshooting. Based on your screenshots above, it could be heat and/or the video chipset.
RELEVANCY SCORE 75.2
Well, backstory. I had invested in purchasing a computer because the people who had owned it previously had problems with it constantly crashing. I decided to buy it and challenge myself in fixing it. So far, I've fixed it up to the point where the crashing is far less frequent to what it used to be, but it still does crash from time to time.
I had initially purchased a new hard drive because I thought that would be the issue, but it seemed as though that wasn't the case. I replaced the original, and terrible, Xtreme Gear PSU, and that seemed to solve the problem for a good bit, but the computer still does freeze on occasion. I've been told it could be an overheating issue, but since the inclusion of my new PSU (Corsair TX750), the heat hasn't gotten to any sort of high level, and even still, it hadn't gone very high in the past.
Now, I'm just confused and would like to see if anyone else could help me out.
Most of the time, everything just freezes and nothing is responsive. I've really only experienced a BSOD three or four times in the past, and the rest has all been complete freezing.
-JMD!
A:screen freezes randomly without any specific warning.
Click on the Start
Type msinfo32 into the Search programs and files box
When it opens, go to File, Save
Save as msinfo32.nfo and save in a place you will remember
Let it finish the process of gathering and saving the system info
Right click the .nfo file, click send to compressed (zipped) folder
RELEVANCY SCORE 75.2
Here is the log from "hijack this" can someone please talk me through the cleaning process and wether this will stop the random frezzing???
Regards
Don
Logfile of HijackThis v1.99.1
Scan saved at 18:00:16, on 12/04/2005
Platform: Windows 2000 SP4 (WinNT 5.00.2195)
MSIE: Internet Explorer v6.00 SP1 (6.00.2800.1106)
Running processes:
C:\WINNT\System32\smss.exe
C:\WINNT\system32\winlogon.exe
C:\WINNT\system32\services.exe
C:\WINNT\system32\lsass.exe
C:\WINNT\system32\svchost.exe
C:\WINNT\system32\spoolsv.exe
C:\PROGRA~1\Grisoft\AVGFRE~1\avgamsvr.exe
C:\PROGRA~1\Grisoft\AVGFRE~1\avgupsvc.exe
C:\WINNT\System32\svchost.exe
C:\WINNT\system32\hidserv.exe
C:\WINNT\system32\nvsvc32.exe
C:\WINNT\system32\regsvc.exe
C:\WINNT\system32\stisvc.exe
C:\WINNT\System32\WBEM\WinMgmt.exe
C:\WINNT\system32\svchost.exe
C:\WINNT\Explorer.EXE
C:\WINNT\SOUNDMAN.EXE
C:\Program Files\Common Files\Real\Update_OB\realsched.exe
C:\Program Files\Logitech\MouseWare\system\em_exec.exe
C:\Program Files\iTunes\iTunesHelper.exe
C:\PROGRA~1\Grisoft\AVGFRE~1\avgcc.exe
C:\Program Files\iPod\bin\iPodService.exe
C:\WINNT\system32\internat.exe
C:\Program Files\MSN Messenger\MsnMsgr.Exe
C:\Program Files\SpywareGuard\sgmain.exe
C:\Program Files\SpywareGuard\sgbhp.exe
C:\WINNT\System32\svchost.exe
C:\Documents and Settings\Don\My Documents\Don\hijackthis\HijackThis.e... Read more
RELEVANCY SCORE 75.2
When I am on my computer usually about once a day my computer and screen will freeze, and I will need to hard restart my PC. I'm not getting a BSOD or anything.
PC Specs:
i7 2600k
GTX 680
8GB RAM
60GB SSD 1TB HDD
Corsair TX850M PSU
A:Screen and Computer Freezes Requires Hard Restart
Check your temp readings in Bios. Also clean your tower out with a can of compressed air. Also Check your Hard drive to see if it is failing.
Downloading UBCD which is in my signature.Burn the ISO Image to a blank CD using Imgburn (How to burn a ISO Image using Imgburn) burn at lowest speed. With the newly burned cd boot with the cd go to HDD>Diagnostics>The make and model of your hard drive, Seagate, Maxtor, Drive Fitness which is Hitachi, Or Western Digital. Perform a short and long test. Could also be called "Standard" and "Extended" test or also "Comprehensive" test.
If you can not find the right test for your hard drive your OEM computer may have it's own hard drive diagnostics testing tool. Refer to your OEM computer documentation to find out how to access these test. Also try going to the manufacture of your machine to find documentation about it. Also consider going to the manufacture of your hard drive to look to see if they have hard drive diagnostics test. The ideal test or method would include an ISO that could be burned via an image to a cd which would be made bootable.
RELEVANCY SCORE 75.2
Today,When I was playing a game,I Was having a odd sound in my computer and my computer freezes for 30 second or more,then it continues to be normal,it only happens when I play high graphics game like Doom,Call of duty Infinte Warfare,My processor hits 100% when that sound occurs it's very weird,this thing was happening for some time,then today my computer had a blue screen,when I restarted my computer and it got stuck in the desktop after the Windows load.
I searched google did everything I could,but it did not work,I need help please
Win7 64 bit
8GB Ram DDR3
GeForce 780ti MSI
Hardisk-500Gb,and it's pretty old 6 yrs more
i3 4th generation
RELEVANCY SCORE 75.2
Hi,
Yesterday we had a 3 second power failure and when my computer restarted, the desktop icons were taking foreverrrr to show up (usually my computer takes 30 secs to load up because I only have a few programs installed at the moment). So I forced shutdown using the button and then booted up again.
Now it won't get past the MOBO's post screen and I can't even use my keyboard to get into the startup or the bios. Every time I shut down my computer, when I go to turn it back on the same thing happens and the only way I can get it going again is to reset the jumpers.
I did research prior to asking for help, but it seemed that everyone had different issues. I've never heard of this one before. My only guess is the MOBO battery, but I highly doubt it. Does anyone have any ideas? Thanks a lot!
A:Freezes at post screen. Need to reset jumpers EVERY restart
The cmos battery does not stop a post. You will get an error however the system will post.
I would put the system into a very basic state.
1 Open the case and pull the pw connector from ALL drives; hd and optical.
2 Disconnect any usb type device
3 Pull out any add-in cards such as sound, nic, etc. Leave in your video card
4 Remove all ram except one stick.
Now attempt a post. If it fails, shutdown and try a different ram chip.
If it still fails to post, you will need to swap parts with known good ones; ie power supply, motherboard, ram, etc to find the problem.
FWIW I just fixed a family member's system that suffered a power failure/surge. It was just the pw supply that went out [they were lucky]
RELEVANCY SCORE 74.4
Hello,
For some reason lately, when booting up or restarting my PC and logging in (with a picture password) the Metro Start screen that comes up sometimes randomly freezes/locks up. I can still move my mouse but the tiles aren't clickable at all nor do the live tiles change. Any buttons on the Metro UI don't respond either and the charms bar doesn't show up. It is as if the screen is completely frozen except for my mouse. There isn't anything I can do except pressing Ctrl+Alt+Del and doing a restart. Choosing to log off instead and logging in again still shows the Metro Start screen in a locked condition.
I haven't made any changes prior to this issue except disabling the option for Windows to bring me to the Desktop immediately after a boot.
A sfc /scannow doesn't show any corruption.
This issue happens randomly and I have no idea what triggers it, so I can't say for sure if it also occurs in Safe Mode or on another user account.
I'm running Windows 8.1 Pro 64bit with Media Center
i5-3570K (stock) CPU and a GTX 660Ti GPU with latest drivers
8 GB RAM and 1 TB HDD
EDIT: Just noticed that I can press the Windows key instead of Ctrl+Alt+Del. When doing that, the screen blinks a bit and it brings me to the Desktop. An error shows up in my events saying that Explorer.exe has crashed. Here's the log:
The program Explorer.EXE, version 6.3.9600.17284 is not responding to Windows and has been shut down.
Proces-id: 580
Starttijd: 01cff3ed53c30a9e
Eindtijd: 15
RELEVANCY SCORE 74.4
I'm not sure if this is the right section to post this but, ever since I reformatted my laptop, it randomly freezes for about a second and a stuttering noise comes up. Then the screen turns black. It doesn't shut off because I could see the back light, it just turns completely black. What's causing this problem and how do I fix it? I checked the Event Logger and there are tons of errors and some critical kernal-power things.
A:Laptop randomly freezes and screen turns black after
Can you start in Safe Mode? If you can, do the following steps in safe mode.Click Start Menu
Right click My Computer/Computer
Click Manage
Click Device Manager from the list on the left
Right click each display adapter in that list and click Uninstall (do not hit OK when the dialog pops up after clicking Uninstall)
Put a tick to delete driver software for the device and click OK
Restart Windows in normal mode
If you continue to have the same problem or other problems, let us know.
RELEVANCY SCORE 74.4
When I'm playing a game called Elsword, my screen has been freezing up for 2-5 seconds. I look at my task manger and everything seems to be fine, my memory is low on top of my cpu. Nothing is eating it all up. So I don't understand what's going on. I defragged my entire computer. Used a full anti virus scan on it with Norton, AVG, and Advance System Care. Nothing seems to be fixing this issue. I already updated my entire computer.
Some things I haven't updated quite yet, which are my driver mangers. I will provide a screen shot if you think any of this will even effect it. I also haven't updated my graphics card yet, cause it just won't let me update for some strange reason. Also, this didn't happen till 2 days ago. I've been playing Elsword for 4 years, so it's not my computer specs not meeting the requirement. So please don't assume that's the case, my computer is not old either.
A:When playing games, screen randomly freezes up for 2-5 seconds.
Try doing a System Restore System Restore to a date before you had the problem. If this doesn't work, we can try again.
RELEVANCY SCORE 74.4
i recently have been having trouble with my laptop freezing up at random times. i will just be doing everyday stuff on my laptop and it will suddenly freeze and the screen will turn a variety of colors with lines running down it, then it will turn to a shade of pink. sometimes it will restart on its own other times i will have to restart it. i have no i idea what could be causing this problem so please help!!!!
A:Laptop Freezes up randomly with pink screen and lines
Have a look in the Event Viewer for any errors at the time of the freezes.To open the Event Viewer go to Start > Control Panel > Administrative Tools > Event Viewer. Alternately, go to Start > Run and type in "eventvwr.msc" (without the quotes) and press Enter.Check in all the categories.If you find an error that occurred at the time right-click on it and select properties. Copy the information in the window and post it back here. This will help us diagnose your problem.How To Use the Event Viewer
RELEVANCY SCORE 74.4
Ok, so I am going to try to explain this as thorougly as possible while trying not to sound like an idiot in the process. I am by no means computer savvy so anyone that has any advice will more than likely need to talk to me like a 5th grader. I am ok with that. Since installing a Windows Update about a month ago, my screen will randomly lock up. At times it will clear itself after a couple of seconds and state something to the effect that "display driver amd has stopped working and recovered." Other times it will stay frozen for about 10 minutes and then will start functioning properly again. More often than not though, it will stay frozen indefinitely and require a hard reboot. This happens during mundane activities. No extreme gaming going on. Generally it is while just browsing the net. It tends to happen more often to my wife who uses it during the day to work through a VPN. I don't believe there is any correlation though. I have read multiple forums on the web and have tried several things, from cleaning the registry to uninstalling the driver software and reinstalling it in safe mode. The latter seemed to work last night but today my wife started having the same issue again. I am attaching the file from the SF Diagnostic tool but it said I didn't have any dumps to log. I'm sorry if that makes a suggestion more difficult. Thank you in advance for any and all help I can get.
Brandon
A:Screen Freezes randomly, requires hard reboot
See if you can get to the DMP's this way....
We do need the DMP file as it contains the only record of the sequence of events leading up to the crash, what drivers were loaded, and what was responsible.
If you are overclocking STOP.
You may be able to get the DMP files without crashing by booting into safe mode (F8) with networking.
To enable us to assist you with your computer's BSOD symptoms, upload the contents of your "\Windows\Minidump" folder.
The procedure:
Quote:
* Copy the contents of \Windows\Minidump to another (temporary) location somewhere on your machine.
* Zip up the copy.
* Attach the ZIP archive to your post using the "paperclip" (file attachments) button.
To ensure minidumps are enabled:
Quote:
* Go to Start, in the Search Box type: sysdm.cpl, press Enter.
* Under the Advanced tab, click on the Startup and Recovery Settings... button.
* Ensure that Automatically restart is unchecked.
* Under the Write Debugging Information header select Small memory dump (256 kB) in the dropdown box (the 256kb varies).
* Ensure that the Small Dump Directory is listed as %systemroot%\Minidump.
* Reboot if changes have been made.
RELEVANCY SCORE 74.4
Installed Win 7 Pro x86 last night on a new HD. After installing SP1, restarting freezes at the Gateway boot screen and I have to hit the power button to shut off, then turn back on. There are no alerts in device manager, so I don't believe this is a driver issue. Everything else seems to be working fine, so I don't think the HD is bad. Any help would be appreciated. Thank you.
A:Restart freezes on manufacture's boot screen after clean install
Run a startup repair and see if that fixes the issue.
Startup Repair - Run 3 Separate Times
RELEVANCY SCORE 74.4
I've recently installed Windows 7, downloaded updates, or installed programs that have asked me to restart. On doing this, PC shuts down fine, starts up, but on BIOS screen, half loads and then freezes. I have to keep finger on power button so it cuts power, then start again, then it loads up fine?
Im thinking it is because I havent got my boot options in the right order. Can anyone help?
RELEVANCY SCORE 73.6
I have a Gateway with 32 bit OS, and Vista SP2 installed.
My mom recently installed a program to watch videos, but it was useless to her and she uninstalled it. Day after, I was browsing the internet and the computer froze and became completely unresponsive. Couldn't even get the task manager open, so I had to force it to shut down.
Tried to turn it back on, and got a black screen that said no boot device found. then no boot file received. Tried to run Mbytes because I thought maybe she might have picked up a virus, and left the computer. Twenty minutes later I came back and it had restarted for no apparent reason. Tried again, and got a BSOD halfway, error x000007. Every other restart failed, saying that no boot file had been received.
Did system restore, which seemed to fix the problem temporarily. Tried to run SuperAntiSpyware, and computer restarted... again. Windows suggested I reinstall an Intel processor driver that was missing. Did, but later that night got the BSOD again, halfway through an Mbytes scan.
This had not happened before, I'm kind of at a loss. I ran Diskcheck, which fixed a few bad clusters, etc. I'm having a hard time thinking this could be a malware problem, except for the random restarts while I'm scanning for viruses.
Any suggestions? System restore seemed to help at first, but now it's back to the same thing. I only have one minidump file, but I can't seem to read it myself. Help?
A:Computer freezes randomly, Blue Screen and failure to boot?
RELEVANCY SCORE 73.6
Hello. My problem with my Vista computer is very complex
Recently, when I login into my computer it takes a long time to load, such as a white screen before the wallpaper loads. In addition, when I try to double-click an icon, nothing happens and i have to wait until about a minute or two before i finally get a response.
For example, whenever i try to close a webpage (the "X" in the upper right corner), nothing happens and I have to keep clicking and all of a sudden, the page finally closes. Another example, i whenever I try to hold and drag a file or folder, it will not let me as the screen temporary freezes. However, I can still scroll with my mouse. It's just that it randomly takes a longer time to click and its frustrating.
I used multiple cleaning software such as CCleaner, JetClean, Auslogics BoostSpeed, SuperAntiSpyware, Wise Registry cleaner, etc and nothing seems to work. I had went through a defragment of my disk drive and it seems that my computer is slower than before.
My disk drive has 185 GB of free space and has a captivity of around 426 GB. I also had deleted some of my larger files in hopes that my computer would work more properly.
I would prefer a newer computer as my Vista computer is about 8 years old, but I am on a fixed income. I would like some tips on how I can fix my problem.
Thanks.
OS
Version: Microsoft Windows Vista Home Premium
System Name: Studio XPS 435MT
A:Clicking with a mouse nonresponsive; screen randomly lags and freezes
I seemed to have solved my problem. Earlier, I had downloaded a 15-day trial of a program called RegCure Pro. I had about 2150 issues, including about 200 "System Issues", in my computer. I also had disabled some of my startup programs. I had restarted my computer and I no longer have issuers with a hanging screen whenever i click something.
However, I get this popup message "Server Busy’ and the following text. ‘This action cannot be completed because the other program is busy Choose ‘Switch to’ to activate the busy program and correct the problem." Beneath this are three buttons, from left to right they’re labelled Switch To… , Retry and Cancel. How do i get rid of that. At least I now get a response when I click something on my screen.
That said, I would still want some advice and what I could do just in case this problem comes up again. Thanks.
RELEVANCY SCORE 73.6
It turns on but the screen doesnt. The backlight is not broken because when it does turn on (randomly) everything works. Pushing down on the screen works but only as long as I'm holding it really. So I've come to the conclusion that the lcd cable has loosened somehow or there is a problem with the program that starts the computer. I've only had the laptop for about 4 months and the problems started about 1 month after buying it.
And when it does turn on it randomly freezes I have no clue why I'm no computer expert and I've only built a single computer.
I have already ran defrag and c disk cleanup, ran Norton and turned off unnecessary programs. The vents are not obstructed and I've already done what I think is a hard reset. Removing the battery, holding the power button for 45 seconds and then putting everything back together.
I'm about to throw the thing out the window and I cannot afford any parts to replace or take it to any computer repair shop. I only make about 150 a week.
A:Asus G73 laptop screen doesn't turn on and randomly freezes when it does
Was able to turn it on
Its in safe mode right now and I'm checking the event log 8,894 errors. They are 7023, 7031, 7034, 10010, 14329, 6008, 55, and 8003. The 7000 event ID all occur when im trying to turn my laptop on.
RELEVANCY SCORE 73.6
Hello all,
I have been experiencing BSODs or vertical gray line freezes while playing the new WoW Cataclysm. I am able to play 2-20 minutes at a time and then I get those crashes. I have an ATI Mobility Radeon HD 4200 series graphics card and I am running Windows 7 (64 bit). I am up to date on my graphics card (10.12 driver released 11/25/10). I have tried many of the solutions on the WoW technical forms and have had no success. I can provide a DXDIAG or MSINFO30 if needed.
Any suggestions?
bhendri
A:Continuous Black Screen Freezes with Radeon 4200, Force Restart
Quote: Originally Posted by bhendri
Hello all,
I have been experiencing BSODs or vertical gray line freezes while playing the new WoW Cataclysm. I am able to play 2-20 minutes at a time and then I get those crashes. I have an ATI Mobility Radeon HD 4200 series graphics card and I am running Windows 7 (64 bit). I am up to date on my graphics card (10.12 driver released 11/25/10). I have tried many of the solutions on the WoW technical forms and have had no success. I can provide a DXDIAG or MSINFO30 if needed.
Any suggestions?
bhendri
Have you tried turning down your quality settings? You have to remember the Radeon HD 4200 is an onboard chipset and is not nearly as powerful as a discrete card.
RELEVANCY SCORE 72.8
Ill try to provide as much information as possible so this is a long read. ANY HELP WOULD BE GREATLY APPRECIATED. I received a new pc from iBuypower (DX DIAG IS AT THE BOTTOM OF THIS EMAIL). The purpose if for online gaming. The first day I started the Vista updates through Windows update and there were about 32 or 33 updates that needed to take place. Around update 24 or so, my computer completely froze. It gave me an error when I rebooted and tried the windows update again. The error pointed me to a MS repair function where it scans the updates and repairs them which it did and my PC repaired that one file and finished all of the rest without error. I then downloaded Warhammer online and played the game with no issues. Then I noticed freezing when trying to install Age of Conan Online. The email back and forth to Funcom (the manufacturer of the game goes as follows:
Me describing the problem to them:
"I downloaded the game last night after receives my SMS code. It took about 7-8hrs. The file was 13.6GB (129 files, 2 folders). I didnt notice any issues. When I went to install it off my Hard Drive, the computer completely freezes without a hard boot. It always gets to the part where it says Installing Resources, this may take a long time.... but each time it freezes anywhere between 02.rdbdata to 19.rdbdata. It seems to vary when it freezes. I tried in safe mode and same problem. I turned off my antivirus same problem. I disconnected from the internet same problem. I d... Read more
RELEVANCY SCORE 71.6
When I try to go into windows Explore to copy or delete files Explore freezes but it does not crash and speed is incredibly slow. Many times Freezes but I can X out. Internet Explorer works but mainly Black and White background as ALL areas in the sites I visit I cannot see the color coded prompts. This just happened. I was using Microsoft Essentials but that even froze. Now I have Kapersky trial but that did not find any viruses or malware after scanning. Any suggestions please? Thanks - DennisM
A:Windows 7 Freezes - Explore Freezes - Internet White Screen
Does everything you do on the computer freeze/move slow?
Please publish a snap shot of your system using speccy following this tutorial
http://www.bleepingcomputer.com/forums/t/323892/publish-a-snapshot-using-speccy/
RELEVANCY SCORE 70
Firstly I'm no expert so any advice as how to proceed or correct links to instructions would be great!!
Someone I know has an Acer aspire running win 7 home edittion 64 bit.
There was an incident where windows wouldn't load so restored it from an image created last year.
Everything seemed to be ok until a group of 135 updates which failed to install. I checked the reasons why and it stated it was because it had been interupted.
after checking the updates there are a lot of 32 bit fixes which I was suprised to see seing as it's 64 bit..
anyway I tried switching off the AVG free and manually selected to install. this hung up and after 30 mins and showing 0% updates downloaded I cancelled it.
I also tried using the "fix it" ? tool which scanned and reported no problems to fix.
I was set to autoupdate and on each time it's shutdown it tries to re-install 135 updates.
I've had to turn off autoupdates(not recommended) but ideally would like to fix this problem.
One option I've seen mentioned on the interent is to totally re-install windows 7 but think there musst be a less drastic approach.
I have seen the steps mentioned so would they apply to the problems i'm having here??
in the meantime, he's got AVG fre version and spybot on. it could be another month or 2 before having another go at his laptop. what would the consequences be and the percentage risk of leaving it as it is?
A:Windows manual updates freezes - best course of action?
Please follow the Windows Update Posting Instructions and post the requested data
RELEVANCY SCORE 70
I have an HP m9600t, i7 processor, windows vista 64 bit. I have in the last month started having a problem with my computer freezing if i do not open something immediately after it boots up. It used to get frozen alot on the log in page, so I removed my password. That has helped some but probably because I have more patience to wait around for it to get booted up so that I can start a program. Once it's frozen it will not recover except through a manual shut down. I have not installed any new hardware in the last 6 months.
Thanks in advance for the help! I really appreciate it!
Leslie
A:Computer freezes often and won't recover without manual shutdown
NOTE: Please provide the following information for a more detailed response (even though you're not reporting BSOD's): http://www.techsupportforum.com/foru...ta-452654.html
I suggest starting all troubleshooting with the following diagnostic tests (located at this link: Hardware Diagnostics ). They'll save you a lot of time and heartache if there is a hardware failure, and you'll have the disks on hand in case you need them in the future:
Quote:
H/W Diagnostics:
Please start by running these bootable hardware diagnostics: | {"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": 0.24821977317333221, "perplexity": 2976.7394567399633}, "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/1544376825728.30/warc/CC-MAIN-20181214114739-20181214140239-00210.warc.gz"} |
https://www.physicsforums.com/threads/chance-of-getting-sick.111410/ | # Chance of getting sick
1. Feb 19, 2006
### haynewp
Say I were exposed to someone who has the flu. And the chance of me getting sick were 50% from being exposed to that person.
Now, say 50% of the people who actually have the flu virus develop symptoms within the first 2 days. I make it up to day 3 without any symptoms. I think I should be able to cut my odds again that I did not contract the flu from this person: 1/2*1/2=1/4 chance I may have the flu?
2. Feb 19, 2006
### 0rthodontist
Okay, I got my answer: you can't cut the odds to 1/4. Once you know you have a 1/2 chance of having the flu, you can be viewed as a person selected at random from the following population:
A B
C D
Where C and D have the flu.
Now let's say you know that only D shows symptoms. Now what is your chance of having the flu, given that you do not show symptoms?
Last edited: Feb 19, 2006
3. Feb 20, 2006
### haynewp
Alright.
If I word it to where 99.999% of people show symptoms within the first 2 days, and I make it to day 3 without any synptoms, it shouldn't make any difference. I would still be at the original 50% chance.
But it sure would seem like I would be in a lot better shape than the original 1 in 2 odds, since I had made it to day 3. I guess you're right.
4. Feb 20, 2006
### qbert
I was playing around with this and it looks like you
need one more piece of information.
So let me change the problem slightly
Let's say you have a 50% chance of getting
sick. And if you're sick you have a 50% chance
of showing symptoms in under two days.
and if you don't get sick you never show
the symptoms in under two days (no false positives).
Then: Let A be the event you get sick
and B be the event you show symptoms in under two days.
Then you are given P(A)=.5, P(B|A)=.5, and P(B|A^c)=0
And you want to find out what is P(A|B^c) {you are
sick but didn't show symptoms in under two days}
1. P(A|B^c)P(B^c) = P(B^c|A)P(A)
2. P(B^c|A) = 1 - P(B|A)
3. P(B^c) = 1-P(B) = 1- P(B|A^c)P(A^c) - P(B|A)P(A)
thus P(A|B^c) = (1-P(B|A))P(A) / (1 - P(B|A^c)P(A^c) - P(B|A)P(A) )
or putting in numbers:
(1- .5)(.5) /( 1 - 0 - (.5)(.5)) = .5^2/(1-.5^2) = 1/3
So, if you make it to day three you have a 1 in 3 chance of being
sick.
5. Feb 20, 2006
### 0rthodontist
This conclusion was already clear from my A B C D population.
Last edited: Feb 20, 2006
6. Feb 20, 2006
### haynewp
"Okay, I got my answer: you can't cut the odds to 1/4. Once you know you have a 1/2 chance of having the flu, you can be viewed as a person selected at random from the following population:
A B
C D
Where C and D have the flu.
Now let's say you know that only D shows symptoms. Now what is your chance of having the flu, given that you do not show symptoms?"
If A is defined as not being sick, and C is sick with no symptoms, then what is B? It's been a while since I did probabilities. It must be that C and D are subsets of B?
7. Feb 20, 2006
### qbert
The only point I was making is that
the problem is incompletely specified.
To actually solve it you need to make additional
assumptions. explicitly, you need to know
the probablility of showing symptoms while
not being sick. (Or anything, from which you
can infer it.)
For Example. If in one extreme,
showing the symptoms is independent
of being sick. then you're chance of
being sick is 1/2 whether or not you show
symptoms.
In the other extreme you show no
symptoms while being sick. Then the
probabillity of being sick after 2 days varies
from 0 to 1/3 depending on what percenctage
of sickies show symptoms inside of 2 days.
8. Feb 20, 2006
### qbert
Take the setup. Probability of being sick = 1/2
If sick, the probabillity of showing symptoms within 2 days = 2/3
If not sick, the prob. of showing symptoms within 2 days = 0
then by the same analysis that i gave
the probabillity of being sick after two days of not showing symptoms
is 1/4.
9. Feb 20, 2006
### 0rthodontist
We are given that the probability of showing symptoms within 2 days if you are sick is 1/2... yes, you are correct, if you change the problem entirely you can reduce the total chance of being sick to 1/4 or whatever fraction you want less than 1/2, but usually we try to solve problems without arbitrarily altering the values given.
It can easily be inferred that if no sick people show symptoms within 2 days then your probability of being sick after 2 days of no symptoms is 1/2.
I assume you mean in the first sentence of the quote, "In the other extreme you show no symptoms without being sick."
It seems you may not have understood my A, B, C, D population. If you do not show symptoms then you are not D, therefore you are A, B, or C. Only C has the flu therefore your chance of having the flu is 1/3.
Last edited: Feb 20, 2006
10. Feb 20, 2006
### qbert
I was making two points.
1st, To get the answer you have to assume an extra piece of
information that isn't stated anywhere. (And may not even
be a good assumption.)
2nd, I was trying to clear the confusion, which I perceived in post
3, by giving a general derivation. Followed with a couple of
different examples (ie what is the setup to reduce the chance to 1/4).
.... as to the typo. C'est La Vie. Thanks for the correction.
11. Feb 20, 2006
### haynewp
I see, A and B are there just to represent the 50% that will not get sick in the original population A,B,C,D. (There is no difference between A and B.)
You are just left with A (well), B (well) or C (sick-no symptoms) if you do not show symptoms (D). | {"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": 0.8507810831069946, "perplexity": 1299.8267391909658}, "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-2019-04/segments/1547583680452.20/warc/CC-MAIN-20190119180834-20190119202834-00627.warc.gz"} |
https://www.biostars.org/p/323019/ | Visualizing model-based clustering with fviz_mclust
1
0
Entering edit mode
4.2 years ago
lessismore ★ 1.2k
Dear all,
i have data matrix with samples on rows and genes on columns. i am using fviz_mclust function in factoextra package as explained here > http://www.sthda.com/english/articles/30-advanced-clustering/104-model-based-clustering-essentials/
When plotting the clusters with this function (Visualizing model-based clustering):
fviz_mclust(mc, "classification", geom = "point",
pointsize = 1.5, palette = "jco")
i would like to use the repel=TRUE in order to show the sample names but is not possible apparently. Could someone tell me why or help me with this?
factoextra clustering • 2.2k views
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Entering edit mode
The repel parameter is available for the fviz_cluster() function. To use it for fviz_mclust(), you may have to implement repel functionality via geom_text_repel() or geom_label_repel()
For example:
fviz_mclust(mc, "classification", geom = "point", pointsize = 1.5, palette = "jco", ggtheme=geom_text_repel())
That is untested, though.
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Thanks kevin, could you please tell me or point me to a link where it's showed how to implement it? ill try to remember it for the rest of my life!
0
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4.2 years ago
Any parameter that is used with fviz_cluster() can also be used with fviz_mclust(); moreover, you can plot both types of geoms, i.e., text and points:
require("mclust")
data("diabetes")
mc <- Mclust(diabetes[, -1])
fviz_mclust(mc, "classification", geom=c("text","point"), pointsize = 1.5, palette = "jco", repel=FALSE)
fviz_mclust(mc, "classification", geom=c("text","point"), pointsize = 1.5, palette = "jco", repel=TRUE)
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Thanks Kevin.
Given your expertise in this could you tell me if you know why some objects of the same cluster are not in the same circle? What does that mean? ive seen that they might have a lower probability to belong to the cluster and that's ok, but why the circle doesnt include them?
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Entering edit mode
The ellipse functionality in fviz_mclust is merely a wrapper for the stat_ellipse function of ggplot2. This draws an ellipse around the objects in order to show which objects are more likely to be members of a particular cluster. So, objects falling outside of the ellipse are less confident members of the cluster, at the confidence level that you choose. This will obviously occur more in the following situations:
• the objects are more spread and there is high covariance
• the objects exhibit heteroskedasticity (unequal variance in different parts of the cluster)
You can control the ellipse via the ellipse.type and ellipse.level parameters. The defaults appear to be 'norm' and '0.4', respectively, which means that your ellipses will be drawn assuming a normal distribution in the data and at the 60% ([1.0 - 0.4] * 100) confidence level. | {"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": 0.21951262652873993, "perplexity": 2976.020076321516}, "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-2022-40/segments/1664030334332.96/warc/CC-MAIN-20220925004536-20220925034536-00467.warc.gz"} |
https://www.physicsforums.com/threads/time-definition-forth-dimention.1522/ | # Time Definition-Forth Dimention
1. Apr 25, 2003
### toppam
http://www.aphysics.netfirms.com [Broken]
Time Definition
If we go to search everything about definition of time finally will be a disillusion because of confusing definitions.
My theory will brink you clear vision about fog and confusion.
Here the definition of time: Time is 4th dimension and is equal to radius of sphere where the space is defined. Compression or expansion of space will generate compression or expansion of time. All four dimensions are correlated and cannot be separated. More concise: space is surrounded by time or defined by time and part of time. This is way so far time cannot be seen because is hard to be seen from inside.
Simple Math of Time Definition
At any moment a partition of time d(t) is a partition of radius d(r) d(t)=d(r) and include space d(s)
The vector r(t) is: x = x (t)
y = y (t)
z = z (t)
Any movement in space (x, y, z) will be: r = (x, y, z,)= xi + yj + zk
If r(t) derive twice R
First derivate r’(t) = v (speed).
Second derivate r”(t) = a ( acceleration)
Speed vector v(t) = r’(t)=( x’(t), y’(t), z’(t) ) = x’(t)I + y’(t)j + z’(t)k)
Acceleration vector:
a(t) = v’(t) = r”(t) = ( x”(t), y”(t), z”(t)) = x”(t)I + y”(t)j + z”(t)k
Here how space is surrounded by time.
Last edited by a moderator: May 1, 2017
2. Apr 25, 2003
### Locutus
I have a problem with this. I have always felt that spatial dimensions are dependent on time. For example, suppose I were to document my whereabouts using coordinates such as (t,x,y,z), where t is time and x,y,z are space. Right now, I could be (April 25 5pm, 40*N, 80*W, 20ft above sea level). These are crude examples, but bear with me.
If only the time coordinate existed, I could know the other three because at that time I can only be in one place. For the time coordinate of April 25 5pm, I can only be in that aforementioned spot. However, given the three spatial dimensions (40*N, 80*W, 20ft above sea level), this is not enough information to derive the time coordinate, because I could be at this exact spot tomorrow (disregarding earth's rotation, etc)!
Thus, I feel it is only proper to say that "The compression or expanion of time will generate compression or expansion of space." Overall, a small point, but I feel it is a valid one.
3. Apr 25, 2003
### RuroumiKenshin
Quite simply, time is the increase in entropy, and can be used as a coordinate.
4. Apr 29, 2003
### Mentat
Time is not the increase in entropy. It is the direction in which entropy increases, yes, but the increase of entropy is just an event, not a dimension.
5. May 5, 2003
### The_oMeGa
Locutus, if time travel were feasible, then time would no longer be regaurded as a coordinate but as a spatial dimension instead. (Not that time travel will ever be feasible)
Just a thought.
6. May 5, 2003
### Alexander
r=sqrt(x2+y2+z2)? But this is space again (r is length), not time.
7. May 5, 2003
### Michael F. Dmitriyev
Re: Re: Time Definition-Forth Dimention
What about r = 10 billion light YEAR?
8. May 6, 2003
### Alexander
What do you mean?
9. May 6, 2003
### Michael F. Dmitriyev
I mean a distance can be measured directly at unit of time .
This r is radius of sphere, universe in this case. Though on my glance this is the time only. Time which had passed from a moment when "inverse BB" began.
10. May 6, 2003
### Alexander
You can't measure distance in units of time. Distance and time are different quantities - they have different properties.
To express distance in units of time, you may multiply time by proper dimensional factor (say, speed of sound) and then you may say that the size of universe is about one quadrillion sound-years. So what?
11. May 6, 2003
### Michael F. Dmitriyev
The Light upon its "travel" creates the illusion of space.
Similar Discussions: Time Definition-Forth Dimention | {"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": 0.8276915550231934, "perplexity": 2458.35237170729}, "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-2017-30/segments/1500549423812.87/warc/CC-MAIN-20170721222447-20170722002447-00232.warc.gz"} |
https://everything.explained.today/Homotopy_type_theory/ | # Homotopy type theory explained
In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on the interpretation of types as objects to which the intuition of (abstract) homotopy theory applies. This includes, among other lines of work, the construction of homotopical and higher-categorical models for such type theories; the use of type theory as a logic (or internal language) for abstract homotopy theory and higher category theory; the development of mathematics within a type-theoretic foundation (including both previously existing mathematics and new mathematics that homotopical types make possible); and the formalization of each of these in computer proof assistants.
There is a large overlap between the work referred to as homotopy type theory, and as the univalent foundations project. Although neither is precisely delineated, and the terms are sometimes used interchangeably, the choice of usage also sometimes corresponds to differences in viewpoint and emphasis.[1] As such, this article may not represent the views of all researchers in the fields equally. This kind of variability is unavoidable when a field is in rapid flux.
## History
### Prehistory: the groupoid model
At one time the idea that types in intensional type theory with their identity types could be regarded as groupoids was mathematical folklore. It was first made precise semantically in the 1998 paper of Martin Hofmann and Thomas Streicher called "The groupoid interpretation of type theory", in which they showed that intensional type theory had a model in the category of groupoids.[2] This was the first truly "homotopical" model of type theory, albeit only "1-dimensional" (the traditional models in the category of sets being homotopically 0-dimensional).
Their paper also foreshadowed several later developments in homotopy type theory. For instance, they noted that the groupoid model satisfies a rule they called "universe extensionality", which is none other than the restriction to 1-types of the univalence axiom that Vladimir Voevodsky proposed ten years later. (The axiom for 1-types is notably simpler to formulate, however, since a coherent notion of "equivalence" is not required.) They also defined "categories with isomorphism as equality" and conjectured that in a model using higher-dimensional groupoids, for such categories one would have "equivalence is equality"; this was later proven by Benedikt Ahrens, Krzysztof Kapulkin, and Michael Shulman.[3]
### Early history: model categories and higher groupoids
The first higher-dimensional models of intensional type theory were constructed by Steve Awodey and his student Michael Warren in 2005 using Quillen model categories. These results were first presented in public at the conference FMCS 2006[4] at which Warren gave a talk titled "Homotopy models of intensional type theory", which also served as his thesis prospectus (the dissertation committee present were Awodey, Nicola Gambino and Alex Simpson). A summary is contained in Warren's thesis prospectus abstract.[5]
At a subsequent workshop about identity types at Uppsala University in 2006[6] there were two talks about the relation between intensional type theory and factorization systems: one by Richard Garner, "Factorisation systems for type theory",[7] and one by Michael Warren, "Model categories and intensional identity types". Related ideas were discussed in the talks by Steve Awodey, "Type theory of higher-dimensional categories", and Thomas Streicher, "Identity types vs. weak omega-groupoids: some ideas, some problems". At the same conference Benno van den Berg gave a talk titled "Types as weak omega-categories" where he outlined the ideas that later became the subject of a joint paper with Richard Garner.
All early constructions of higher dimensional models had to deal with the problem of coherence typical of models of dependent type theory, and various solutions were developed. One such was given in 2009 by Voevodsky, another in 2010 by van den Berg and Garner.[8] A general solution, building on Voevodsky's construction, was eventually given by Lumsdaine and Warren in 2014.[9]
At the PSSL86 in 2007[10] Awodey gave a talk titled "Homotopy type theory" (this was the first public usage of that term, which was coined by Awodey[11]). Awodey and Warren summarized their results in the paper "Homotopy theoretic models of identity types", which was posted on the ArXiv preprint server in 2007[12] and published in 2009; a more detailed version appeared in Warren's thesis "Homotopy theoretic aspects of constructive type theory" in 2008.
At about the same time, Vladimir Voevodsky was independently investigating type theory in the context of the search of a language for practical formalization of mathematics. In September 2006 he posted to the Types mailing list "A very short note on homotopy lambda calculus",[13] which sketched the outlines of a type theory with dependent products, sums and universes and of a model of this type theory in Kan simplicial sets. It began by saying "The homotopy λ-calculus is a hypothetical (at the moment) type system" and ended with "At the moment much of what I said above is at the level of conjectures. Even the definition of the model of TS in the homotopy category is non-trivial" referring to the complex coherence issues that were not resolved until 2009. This note included a syntactic definition of "equality types" that were claimed to be interpreted in the model by path-spaces, but did not consider Per Martin-Löf's rules for identity types. It also stratified the universes by homotopy dimension in addition to size, an idea that later was mostly discarded.
On the syntactic side, Benno van den Berg conjectured in 2006 that the tower of identity types of a type in intensional type theory should have the structure of an ω-category, and indeed a ω-groupoid, in the "globular, algebraic" sense of Michael Batanin. This was later proven independently by van den Berg and Garner in the paper "Types are weak omega-groupoids" (published 2008),[14] and by Peter Lumsdaine in the paper "Weak ω-Categories from Intensional Type Theory" (published 2009) and as part of his 2010 Ph.D. thesis "Higher Categories from Type Theories".[15]
### The univalence axiom, synthetic homotopy theory, and higher inductive types
The concept of a univalent fibration was introduced by Voevodsky in early 2006.[16] However, because of the insistence of all presentations of the Martin-Löf type theory on the property that the identity types, in the empty context, may contain only reflexivity, Voevodsky did not recognize until 2009 that these identity types can be used in combination with the univalent universes. In particular, the idea that univalence can be introduced simply by adding an axiom to the existing Martin-Löf type theory appeared only in 2009.
Also in 2009, Voevodsky worked out more of the details of a model of type theory in Kan complexes, and observed that the existence of a universal Kan fibration could be used to resolve the coherence problems for categorical models of type theory. He also proved, using an idea of A. K. Bousfield, that this universal fibration was univalent: the associated fibration of pairwise homotopy equivalences between the fibers is equivalent to the paths-space fibration of the base.
To formulate univalence as an axiom Voevodsky found a way to define "equivalences" syntactically that had the important property that the type representing the statement "f is an equivalence" was (under the assumption of function extensionality) (-1)-truncated (i.e. contractible if inhabited). This enabled him to give a syntactic statement of univalence, generalizing Hofmann and Streicher's "universe extensionality" to higher dimensions. He was also able to use these definitions of equivalences and contractibility to start developing significant amounts of "synthetic homotopy theory" in the proof assistant Coq; this formed the basis of the library later called "Foundations" and eventually "UniMath".[17]
Unification of the various threads began in February 2010 with an informal meeting at Carnegie Mellon University, where Voevodsky presented his model in Kan complexes and his Coq code to a group including Awodey, Warren, Lumsdaine, Robert Harper, Dan Licata, Michael Shulman, and others. This meeting produced the outlines of a proof (by Warren, Lumsdaine, Licata, and Shulman) that every homotopy equivalence is an equivalence (in Voevodsky's good coherent sense), based on the idea from category theory of improving equivalences to adjoint equivalences. Soon afterwards, Voevodsky proved that the univalence axiom implies function extensionality.
The next pivotal event was a mini-workshop at the Mathematical Research Institute of Oberwolfach in March 2011 organized by Steve Awodey, Richard Garner, Per Martin-Löf, and Vladimir Voevodsky, titled "The homotopy interpretation of constructive type theory".[18] As part of a Coq tutorial for this workshop, Andrej Bauer wrote a small Coq library[19] based on Voevodsky's ideas (but not actually using any of his code); this eventually became the kernel of the first version of the "HoTT" Coq library[20] (the first commit of the latter[21] by Michael Shulman notes "Development based on Andrej Bauer's files, with many ideas taken from Vladimir Voevodsky's files"). One of the most important things to come out of the Oberwolfach meeting was the basic idea of higher inductive types, due to Lumsdaine, Shulman, Bauer, and Warren. The participants also formulated a list of important open questions, such as whether the univalence axiom satisfies canonicity (still open, although some special cases have been resolved positively[22] [23]), whether the univalence axiom has nonstandard models (since answered positively by Shulman), and how to define (semi)simplicial types (still open in MLTT, although it can be done in Voevodsky's Homotopy Type System (HTS), a type theory with two equality types).
Soon after the Oberwolfach workshop, the Homotopy Type Theory website and blog[24] was established, and the subject began to be popularized under that name. An idea of some of the important progress during this period can be obtained from the blog history.[25]
## Univalent foundations
The phrase "univalent foundations" is agreed by all to be closely related to homotopy type theory, but not everyone uses it in the same way. It was originally used by Vladimir Voevodsky to refer to his vision of a foundational system for mathematics in which the basic objects are homotopy types, based on a type theory satisfying § the univalence axiom, and formalized in a computer proof assistant.[26]
As Voevodsky's work became integrated with the community of other researchers working on homotopy type theory, "univalent foundations" was sometimes used interchangeably with "homotopy type theory", and other times to refer only to its use as a foundational system (excluding, for example, the study of model-categorical semantics or computational metatheory).[27] For instance, the subject of the IAS special year was officially given as "univalent foundations", although a lot of the work done there focused on semantics and metatheory in addition to foundations. The book produced by participants in the IAS program was titled "Homotopy type theory: Univalent foundations of mathematics"; although this could refer to either usage, since the book only discusses HoTT as a mathematical foundation.
## Special Year on Univalent Foundations of Mathematics
In 2012–13 researchers at the Institute for Advanced Study held "A Special Year on Univalent Foundations of Mathematics".[28] The special year brought together researchers in topology, computer science, category theory, and mathematical logic. The program was organized by Steve Awodey, Thierry Coquand and Vladimir Voevodsky.
During the program Peter Aczel, who was one of the participants, initiated a working group which investigated how to do type theory informally but rigorously, in a style that is analogous to ordinary mathematicians doing set theory. After initial experiments it became clear that this was not only possible but highly beneficial, and that a book (the so-called HoTT Book)[29] [30] could and should be written. Many other participants of the project then joined the effort with technical support, writing, proof reading, and offering ideas. Unusually for a mathematics text, it was developed collaboratively and in the open on GitHub, is released under a Creative Commons license that allows people to fork their own version of the book, and is both purchasable in print and downloadable free of charge.[31] [32] [33]
More generally, the special year was a catalyst for the development of the entire subject; the HoTT Book was only one, albeit the most visible, result.
Official participants in the special year
ACM Computing Reviews listed the book as a notable 2013 publication in the category "mathematics of computing".[34]
## Key concepts
Intensional type theory Homotopy theory
types
A
spaces
A
terms
a
points
a
a:A
a\inA
dependent type
x:A\vdashB(x)
fibration
B\toA
identity type
IdA(a,b)
path space
p:IdA(a,b)
path
p:a\tob
\alpha:Id IdA(a,b)
(p,q)
homotopy
\alpha:pq
### "Propositions as types"
HoTT uses a modified version of the "propositions as types" interpretation of type theory, according to which types can also represent propositions and terms can then represent proofs. In HoTT, however, unlike in standard "propositions as types", a special role is played by 'mere propositions' which, roughly speaking, are those types having at most one term, up to propositional equality. These are more like conventional logical propositions than are general types, in that they are proof-irrelevant.
### Equality
The fundamental concept of homotopy type theory is the path. In HoTT, the type
a=b
is the type of all paths from the point
a
to the point
b
. (Therefore, a proof that a point
a
equals a point
b
is the same thing as a path from the point
a
to the point
b
.) For any point
a
, there exists a path of type
a=a
, corresponding to the reflexive property of equality. A path of type
a=b
can be inverted, forming a path of type
b=a
, corresponding to the symmetric property of equality. Two paths of type
a=b
resp.
b=c
can be concatenated, forming a path of type
a=c
; this corresponds to the transitive property of equality.
Most importantly, given a path
p:a=b
, and a proof of some property
P(a)
, the proof can be "transported" along the path
p
to yield a proof of the property
P(b)
. (Equivalently stated, an object of type
P(a)
can be turned into an object of type
P(b)
.) This corresponds to the substitution property of equality. Here, an important difference between HoTT and classical mathematics comes in. In classical mathematics, once the equality of two values
a
and
b
has been established,
a
and
b
may be used interchangeably thereafter, with no regard to any distinction between them. In homotopy type theory, however, there may be multiple different paths
a=b
, and transporting an object along two different paths will yield two different results. Therefore, in homotopy type theory, when applying the substitution property, it is necessary to state which path is being used.
In general, a "proposition" can have multiple different proofs. (For example, the type of all natural numbers, when considered as a proposition, has every natural number as a proof.) Even if a proposition has only one proof
a
, the space of paths
a=a
may be non-trivial in some way. A "mere proposition" is any type which either is empty, or contains only one point with a trivial path space.
Note that people write
a=b
for
IdA(a,b)
, thereby leaving the type
A
of
a,b
implicit. Do not confuse it with
idA:A\toA
, denoting the identity function on
A
.
### Type equivalence
Two types
A
and
B
belonging to some universe
U
are defined as being equivalent if there exists an equivalence between them. An equivalence is a function
f:A\toB
which has both a left inverse and a right inverse, in the sense that for suitably chosen
g
and
h
, the following types are both inhabited:
IdB(f\circg,idB),
IdA(h\circf,idA).
i.e.
f\circg=BidB,
h\circf=AidA.
This expresses a general notion of "
f
has both a left inverse and right inverse", using equality types. Note that the invertibility conditions above are equality types in the function types
A\rarrA
and
B\rarrB
. One generally assumes the function extensionality axiom, which ensures that these are equivalent to the following types that express invertibility using the equality on the domain and codomain
A
and
B
:
\Piy:B.IdB((f\circg)(y),idB(y)),
\Pix:A.IdA((h\circf)(x),idA(x)).
i.e. for all
x:A
and
y:B
,
f(g(y))=By,
h(f(x))=Ax.
The functions of type
A\toB
together with a proof that they are equivalences are denoted by
A\simeqB
.
### The univalence axiom
Having defined functions that are equivalences as above, one can show that there is a canonical way to turn paths to equivalences.In other words, there is a function of the type
(A=B)\to(A\simeqB),
which expresses that types
A,B
that are equal are, in particular, also equivalent.
The univalence axiom states that this function is itself an equivalence.[35] Therefore, we have
(A=B)\simeq(A\simeqB)
"In other words, identity is equivalent to equivalence. In particular, one may say that 'equivalent types are identical'."
Martín Hötzel Escardó has shown that the property of univalence "is undecided in Martin-Löf Type Theory (MLTT)".
## Applications
### Theorem proving
HoTT allows mathematical proofs to be translated into a computer programming language for computer proof assistants much more easily than before. This approach offers the potential for computers to check difficult proofs.[36]
One goal of mathematics is to formulate axioms from which virtually all mathematical theorems can be derived and proven unambiguously. Correct proofs in mathematics must follow the rules of logic. They must be derivable without error from axioms and already-proven statements.
HoTT adds the univalence axiom, which relates the equality of logical-mathematical propositions to homotopy theory. An equation such as "a=b" is a mathematical proposition in which two different symbols have the same value. In homotopy type theory, this is taken to mean that the two shapes which represent the values of the symbols are topologically equivalent.
These topological equivalence relationships, ETH Zürich Institute for Theoretical Studies director Giovanni Felder argues, can be better formulated in homotopy theory because it is more comprehensive: Homotopy theory explains not only why "a equals b" but also how to derive this. In set theory, this information would have to be defined additionally, which makes the translation of mathematical propositions into programming languages more difficult.
### Computer programming
As of 2015, intense research work was underway to model and formally analyse the computational behavior of the univalence axiom in homotopy type theory.[37]
Cubical type theory is one attempt to give computational content to homotopy type theory.[38]
However, it is believed that certain objects, such as semi-simplicial types, cannot be constructed without reference to some notion of exact equality. Therefore, various two-level type theories have been developed which partition their types into fibrant types, which respect paths, and non-fibrant types, which do not. Cartesian cubical computational type theory is the first two-level type theory which gives a full computational interpretation to homotopy type theory.[39]
Some programming languages such as Coq or agda can serve as proof assistant systems.
## Bibliography
• Book: Homotopy Type Theory: Univalent Foundations of Mathematics . The Univalent Foundations Program . . Princeton, NJ . 2013 . 3204653. (GitHub version cited in this article.)
• S. . Awodey . Steve Awodey . M. A. . Warren . Homotopy Theoretic Models of Identity Types . Mathematical Proceedings of the Cambridge Philosophical Society . 146 . 1 . 45–55 . January 2009 . 10.1017/S0305004108001783 . 0709.0248 . 2008MPCPS.146...45A . 7915709 . As PDF.
• Book: Awodey, Steve . Epistemology versus Ontology . Steve Awodey . Springer . 2012 . 978-94-007-4434-9 . 183–201 . Type Theory and Homotopy . http://www.andrew.cmu.edu/user/awodey/preprints/TTH.pdf . Dybjer . P. . 10.1007/978-94-007-4435-6_9 . Lindström . Sten . Palmgren . Erik . 3 . Sundholm . G. . Logic, Epistemology, and the Unity of Science . 10.1.1.750.3626 . 4499538 .
• Awodey . Steve . Steve Awodey . 2014 . Structuralism, Invariance, and Univalence . Philosophia Mathematica . 22 . 1 . 1–11 . 10.1093/philmat/nkt030 . 10.1.1.691.8113 .
• Book: Martin . Hofmann . Thomas Streicher . Thomas . Streicher . The groupoid interpretation of type theory . G. . Sambin . J.M. . Smith . Twenty Five Years of Constructive Type Theory . https://books.google.com/books?id=pLnKggT_In4C&pg=PA83 . 1998 . Clarendon Press . 978-0-19-158903-4 . 83–112 . As postscript.
• Egbert . Rijke . Homotopy Type Theory . 2012 . Master's . Utrecht University .
• David Corfield (2020), Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy, Oxford University Press.
### Libraries of formalized mathematics
• (now integrated into UniMath, where further development takes place)
## Notes and References
1. Shulman. Michael. Michael Shulman (mathematician) . 1601.05035v3. Homotopy Type Theory: A synthetic approach to higher equalities . 2016-01-27. math.LO., footnote 1
2. Book: Martin . Hofmann . Streicher . Thomas . Thomas Streicher. The groupoid interpretation of type theory . 1686862 . Giovanni . Sambin . Jan M. . Smith . Twenty Five Years of Constructive Type Theory . https://books.google.com/books?id=pLnKggT_In4C&pg=PA83 . 1998 . Clarendon Press . 978-0-19-158903-4 . 83–111 . Oxford Logic Guides . 36.
3. Benedikt . Ahrens . Krzysztof . Kapulkin . Michael . Shulman . Michael Shulman (mathematician). Univalent categories and the Rezk completion . Mathematical Structures in Computer Science . 25 . 2015. 5. 1010–1039. 1303.0584 . 10.1017/S0960129514000486. 3340533. 1135785 .
4. Web site: Foundational Methods in Computer Science 2006, University of Calgary, June 7th - 9th, 2006 . University of Calgary . 6 June 2021 .
5. Michael A. . Warren . Homotopy Models of Intensional Type Theory . 2006 .
6. Web site: Identity Types - Topological and Categorical Structure, Workshop, Uppsala, November 13-14, 2006 . Uppsala University - Department of Mathematics . 6 June 2021 .
7. http://comp.mq.edu.au/~rgarner/Papers/Uppsala.pdf Richard Garner, Factorisation axioms for type theory
8. Benno van den . Berg . Richard . Garner . Topological and simplicial models of identity types . 27 July 2010 . 1007.4638. math.LO .
9. Peter LeFanu . Lumsdaine . Michael A. . Warren . The local universes model: an overlooked coherence construction for dependent type theories . ACM Transactions on Computational Logic . 16 . 3 . 1–31 . 6 November 2014 . 1411.1736 . 10.1145/2754931. 14068103 .
10. Web site: 86th edition of the Peripatetic Seminar on Sheaves and Logic, Henri Poincaré University, September 8-9, 2007 . loria.fr . 20 December 2014 . 17 December 2014 . https://archive.today/20141217151510/http://www.loria.fr/~lamarche/psslHomeEN.html . dead .
11. http://www.loria.fr/~lamarche/listPart.html Preliminary list of PSSL86 participants
12. Steve . Awodey . Michael A. . Warren . Homotopy theoretic models of identity types . 3 September 2007 . 0709.0248 . 10.1017/S0305004108001783 . 146 . Mathematical Proceedings of the Cambridge Philosophical Society . 45. 2008MPCPS.146...45A . 7915709 .
13. Web site: A very short note on homotopy λ-calculus . Vladimir . Voevodsky . 27 September 2006 . ucr.edu . 6 June 2021.
14. Benno . van den Berg . Richard . Garner . Types are weak omega-groupoids . Proceedings of the London Mathematical Society . 102 . 2 . 370–394 . 1 December 2007 . 0812.0298 . 10.1112/plms/pdq026. 5575780 .
15. Web site: Peter . Lumsdaine . Higher Categories from Type Theories . 2010 . Ph.D. . Carnegie Mellon University .
16. https://github.com/vladimirias/2006_Mar_Homotopy_lambda_calculus Notes on homotopy lambda calculus, March 2006
17. https://github.com/UniMath/UniMath GitHub repository, Univalent Mathematics
18. Mini-Workshop: The Homotopy Interpretation of Constructive Type Theory . Mathematical Research Institute of Oberwolfach . 10.4171/OWR/2011/11 . 27 February – 5 March 2011 . 6 June 2021 . Awodey . Steve . Garner . Richard . Martin-Löf . Per . Voevodsky . Vladimir . Oberwolfach Reports . 609–638 .
19. https://github.com/andrejbauer/Homotopy GitHub repository, Andrej Bauer, Homotopy theory in Coq
20. Web site: Basic homotopy type theory . GitHub . Andrej . Bauer . Vladimir . Voevodsky . 29 April 2011 . 6 June 2021 .
21. https://github.com/HoTT/HoTT GitHub repository, Homotopy type theory
22. Michael . Shulman . Univalence for inverse diagrams and homotopy canonicity . Mathematical Structures in Computer Science . 25 . 5 . 1203–1277 . 2015 . 1203.3253 . 10.1017/S0960129514000565. 13595170 .
23. Web site: Canonicity for 2-Dimensional Type Theory . Daniel R. . Licata . Robert . Harper . Carnegie Mellon University . 21 July 2011 . 6 June 2021 .
24. http://homotopytypetheory.org Homotopy Type Theory and Univalent Foundations Blog
25. http://homotopytypetheory.org/blog Homotopy Type Theory blog
26. http://homotopytypetheory.org/ Type Theory and Univalent Foundations
27. http://ncatlab.org/homotopytypetheory/show/References Homotopy Type Theory: References
28. https://www.math.ias.edu/sp/univalent IAS school of mathematics: Special Year on The Univalent Foundations of Mathematics
29. Book: Univalent Foundations Program. Homotopy Type Theory: Univalent Foundations of Mathematics. 2013. Institute for Advanced Study.
30. http://homotopytypetheory.org/2013/06/20/the-hott-book/ Official announcement of The HoTT Book, by Steve Awodey, 20 June 2013
31. D . Monroe . A New Type of Mathematics? . Comm ACM . 57 . 2 . 13–15 . 2014 . 10.1145/2557446 . 6120947 .
32. Web site: The HoTT Book . Mike . Shulman . The n-Category Café . University of Texas . 20 June 2013 . 6 June 2021 .
33. Web site: The HoTT Book . Andrej . Bauer . 20 June 2013 . Mathematics and Computation . 6 June 2021 .
34. ACM Computing Reviews. "Best of 2013".
35. Martín Hötzel Escardó (October 18, 2018) A self-contained, brief and complete formulation of Voevodsky’s Univalence Axiom
36. Web site: A new foundation for mathematics. 3 September 2014. 29 July 2021. R&D Magazine. Meyer. Florian.
37. Higher Inductive Types as Homotopy-Initial Algebras. Sojakova. Kristina. 2015. POPL 2015. 10.1145/2676726.2676983. 1402.0761.
38. Cubical Type Theory: a constructive interpretation of the univalence axiom. Cohen. Cyril. Coquand. Thierry. Huber. Simon. Mörtberg . Anders. TYPES 2015. 2015.
39. Cartesian Cubical Computational Type Theory: Constructive Reasoning with Paths and Equalities. Anguili. Carlo. Favonia. Harper. Robert. Computer Science Logic 2018. 2018. 26 Aug 2018. (to appear) | {"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": 0.8415178656578064, "perplexity": 1984.968228317147}, "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-2022-40/segments/1664030334942.88/warc/CC-MAIN-20220926211042-20220927001042-00006.warc.gz"} |
https://arxiv.org/abs/1907.13219 | gr-qc
# Title:Observational constraints of $f(Q)$ gravity
Abstract: In this work, we consider an extension of symmetric teleparallel gravity, namely, $f(Q)$ gravity, where the fundamental block to describe spacetime is the nonmetricity, $Q$. Within this formulation of gravitation, we perform an observational analysis of several modified $f(Q)$ models using the redshift approach, where the $f(Q)$ Lagrangian is reformulated as an explicit function of the redshift, $f(z)$. Various different polynomial parameterizations of $f(z)$ are proposed, including new terms which would allow for deviations from the $\Lambda$CDM model. Given a variety of observational probes, such as the expansion rate data from early-type galaxies, Type Ia Supernovae, Quasars, Gamma Ray Bursts, Baryon Acoustic Oscillations data and Cosmic Microwave Background distance priors, we have checked the validity of these models at the background level in order to verify if this new formalism provides us with plausible alternative models to explain the late time acceleration of the universe. Indeed, this novel approach provides a different perspective on the formulation of observationally reliable alternative models of gravity.
Comments: 8 pages Subjects: General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO) Cite as: arXiv:1907.13219 [gr-qc] (or arXiv:1907.13219v1 [gr-qc] for this version)
## Submission history
From: Francisco Lobo [view email]
[v1] Tue, 30 Jul 2019 20:53:33 UTC (17 KB) | {"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": 0.619437038898468, "perplexity": 1510.1749562417722}, "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-2019-39/segments/1568514574050.69/warc/CC-MAIN-20190920155311-20190920181311-00443.warc.gz"} |
https://ejde.math.txstate.edu/Volumes/2004/45/abstr.html | Electron. J. Diff. Eqns., Vol. 2004(2004), No. 45, pp. 1-13.
Convergence results for a class of abstract continuous descent methods Sergiu Aizicovici, Simeon Reich, & Alexander J. Zaslavski
Abstract:
We study continuous descent methods for the minimization of Lipschitzian functions defined on a general Banach space. We establish convergence theorems for those methods which are generated by approximate solutions to evolution equations governed by regular vector fields. Since the complement of the set of regular vector fields is -porous, we conclude that our results apply to most vector fields in the sense of Baire's categories.
Submitted January 7, 2004. Published March 30, 2004.
Math Subject Classifications: 37L99, 47J35, 49M99, 54E35, 54E50, 54E52, 90C25.
Key Words: Complete metric space, descent method, Lipschitzian function, porous set, regular vector field.
Show me the PDF file (240K), TEX file, and other files for this article.
Sergiu Aizicovici Department of Mathematics, Ohio University Athens, OH 45701-2979, USA email: aizicovi@math.ohiou.edu Simeon Reich Department of Mathematics The Technion-Israel Institute of Technology 32000 Haifa, Israel email: sreich@tx.technion.ac.il Alexander J. Zaslavski Department of Mathematics The Technion-Israel Institute of Technology 32000 Haifa, Israel email: ajzasl@tx.technion.ac.il | {"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": 0.8300973176956177, "perplexity": 2214.712562457181}, "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-2021-21/segments/1620243989690.55/warc/CC-MAIN-20210516044552-20210516074552-00360.warc.gz"} |
https://electronics.stackexchange.com/questions/416159/initial-values-of-the-dspic30f-registers-under-the-icd3-debugger | # Initial values of the dsPIC30F registers under the ICD3 debugger
Ok, I created a simple project that consists of just a few assembler files and it is not using any libraries. What is it doing is not important here. After that I have put breakpoint in ICD3 right on the reset entry point and after booting I see the following:
Controls stays on the address 3c6. If I browse to the beginning of the program memory, I see the following:
This confirms that 3c6 is really the reset entry point. At the same time I see on the registers:
The W15 is 0x800, as it is written in the documentation, but SPLIM is not zero as it should be according to the docs. I would guess that ICD3 has set it. Is that right? Even more, ICD3 shows the first 80 bytes of the RAM as reserved:
My guess is that I should not use the stack setup that I inherited after reset (because it points right into the reserved area and seems co cover it all) but replace it with my own one.
So my questions:
1. Will ICD3 work fine on any stack? I cannot change W15 and SPLIM in one step, so there is a chance that stack will be inconsitent for a short while. Is this simply a small risk that I should take or there is something more there behind?
2. What other resources are used by ICD3?
3. What should I do/not do to cooperate nicely with ICD3?
4. Is it right that in the release version of the build there will be no 80 bytes reserved area?
p.s. Here is the build log:
It suggests that this 80 bytes area in the RAM are not a single piece of data. But SPLIM covers them all... Does anybody has any clue what this all might mean? | {"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": 0.43908727169036865, "perplexity": 1158.2692277459573}, "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/1566027314721.74/warc/CC-MAIN-20190819093231-20190819115231-00225.warc.gz"} |
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(http://www.webmd.com/digestive-disorders/picture-of -the-colon)Colon X-ray spots cancer, reduces dread factor Alternative to colonoscopy has flaws, but could boost screening rates Below: x March 31, 2016. Barium enema: MedlinePlus Medical Encyclopedia (https://www.nlm.nih.gov/medlineplus/ency/article/00 3817.htm)Colon cancer is a disease in which malignant (cancer) cells form in the tissues of the colon.1. The colon is part of the body's digestive system. April 1, 2016. naturalcolonrx.com - Colon Hydrotherapy - A Natural Approach (http://www.naturalcolonrx.com/)WebMD's Colon Anatomy Page provides a detailed image and definition of the colon. Learn about its function, location, and conditions that affect the colon. April 2, 2016. naturalcolonrx.com - Colon Hydrotherapy - A Natural Approach (http://www.naturalcolonrx.com/)Information about colon and rectal cancer treatment, prevention, genetics, causes, screening, statistics and other topics from the National Cancer Institute. April 3, 2016. Colorectal (Colon) Cancer Slideshow Pictures - MedicineNet (http://www.medicinenet.com/colorectal_cancer_pictur es_slideshow/article.htm)The Colon vs the Semicolon - a guide for writers - Duration: 7:40. PublishNation 2,842 views. 7:40 Colon & Semicolon Rebekah - Duration: 2:13... April 4, 2016. Colon X | Dr. Cobi (http://store.drcobi.com/products/colon-x)The colon and rectum are part of the large intestine. Colorectal cancer occurs when tumors form in the lining of the large intestine. It is common in both men and women. April 24, 2016. Lower GI Exam (Barium Enema) - RadiologyInfo.org (http://www.radiologyinfo.org/en/info.cfm?pg=lowergi)A barium enema is an X-ray exam that can detect changes or abnormalities in the large intestine (colon). The procedure is also called a colon X-ray. April 25, 2016. Lower GI Exam (Barium Enema) - RadiologyInfo.org (http://www.radiologyinfo.org/en/info.cfm?pg=lowergi)Colon Hydrotherapy - A Natural Approach. Our colons are the most neglected organ in the body. If you feel that you have not been caring properly for yours lately, you... April 26, 2016. Colon Cleansers: Are They Safe? - webmd.com (http://www.webmd.com/balance/features/colon-cleanse rs-are-they-safe)What is Lower GI Tract X-ray Radiography (Barium Enema)? Lower gastrointestinal... is an x-ray examination of the large intestine, also known as the colon. April 27, 2016. Colon cleansing: Is it helpful or harmful? - Mayo Clinic (http://www.mayoclinic.org/healthy-lifestyle/consume r-health/expert-answers/colon-cleansing/faq-2005843 5)Colon X-ray spots cancer, reduces dread factor Alternative to colonoscopy has flaws, but could boost screening rates Below: x April 28, 2016. Colorectal Surgery - Colon Cancer (http://colorectal.surgery.ucsf.edu/conditions proc edures/colon-cancer.aspx)Information about colon and rectal cancer treatment, prevention, genetics, causes, screening, statistics and other topics from the National Cancer Institute. April 29, 2016. Colorectal (Colon) Cancer Slideshow Pictures - MedicineNet (http://www.medicinenet.com/colorectal_cancer_pictur es_slideshow/article.htm)Colon cleansing is popular among some alternative medicine practitioners who claim it has numerous health benefits. Get the facts before you try it. April 30, 2016. Colorectal Surgery - Colon Cancer (http://colorectal.surgery.ucsf.edu/conditions proc edures/colon-cancer.aspx)Watch this slideshow to learn what colorectal cancer (cancer of the colon) is as well as risk factors, screening, stages, signs, treatments, and more. May 20, 2016. Colon Club (https://colonclub.com/)What is Lower GI Tract X-ray Radiography (Barium Enema)? Lower gastrointestinal... is an x-ray examination of the large intestine, also known as the colon. May 21, 2016. Colorectal Surgery - Colon Cancer (http://colorectal.surgery.ucsf.edu/conditions proc edures/colon-cancer.aspx)WebMD explains what colorectal cancer is, as well as its screening tests, risk factors, stages, and treatments. May 22, 2016. CT Colonography (Virtual Colonoscopy) - Radiology Info (http://www.radiologyinfo.org/en/info.cfm?pg=ct_colo)Colon cancer is a disease in which malignant (cancer) cells form in the tissues of the colon.1. The colon is part of the body's digestive system. May 23, 2016. Colon Cleanse Reviews | Best Cleanse Program | Detox... (http://www.drnatura.com/cleanse-reviews/)Information about colon and rectal cancer treatment, prevention, genetics, causes, screening, statistics and other topics from the National Cancer Institute. May 24, 2016. Colon (punctuation) - Wikipedia, the free encyclopedia (https://en.wikipedia.org/wiki/Colon_(punctuation))Please report to Admitting 15 minutes before your scheduled exam time. PREP: In order to do an x-ray examination of your colon, it is essential that your bowel be empty. May 25, 2016. Colon Cancer: Symptoms, Signs & Stages - MedicineNet (http://www.medicinenet.com/colon_cancer/article.htm)The colon ( : ) is a punctuation mark consisting of two equally sized dots centered on the same vertical line. A colon precedes an explanation, or an enumeration, or... June 16, 2016. Tagged | Technically, Social Discovery (http://blog.tagged.com/)Diverticulosis is generally discovered through one of the following examinations: Barium enema: This x-ray test involves injection of liquid material into the colon... June 17, 2016. CDC - Colorectal (Colon) Cancer (http://www.cdc.gov/cancer/colorectal/index.htm)Buy Phillips' Colon Health Daily Probiotic Supplement Probiotic Caps, 60 count up at Walmart.com June 18, 2016. Types of Colon Cancer - Learn about Each Type... - Verywell (https://www.verywell.com/types-of-colon-cancer-7977 03)What's New and Beneficial About Black Beans. Recent research has shown that black beans provide special support for digestive tract health, and particularly our colon. June 19, 2016. Amazon.com: Blessed Herbs Colon Cleansing Kit - Ginger... (https://www.amazon.com/Blessed-Herbs-Colon-Cleansin g-Kit/dp/B007N7F8T6)Adenocarcinoma is the most common type of colon cancer but there are many other forms as well. Examples include leiomyosarcoma, lymphoma, melanoma, and neuroendocrine... June 20, 2016. Symptoms and Tests for Colon Cancer - Verywell (https://www.verywell.com/symptoms-and-tests-for-col on-cancer-1941593)A Barron Report on how a natural colon cleanse (colon detox) can improve intestinal health and prevent digestive disorders, diverticular disease, or irritable bowel... June 21, 2016. JULIE. STAGE 4 COLON CANCER. DIAGNOSED AT 45. MISSOURI... (http://destinationxride.org/julie-stage-4-colon-can cer-diagnosed-at-45/)Cancer, carcinoma, tumor, picture, x-ray, photo, image, FDA trial. financial help. June 22, 2016. Colon Hydrotherapy Cleansing - First Time Experience... (http://www.dailymotion.com/video/x3s73e_colon-hydro therapy-cleansing-first_news)My day started out like any other day. Busy. I was at work and noticed some lower back pain. As the day progressed, it became more intense and wrapped around me like... June 23, 2016. LearningRadiology - Colon, Cut-off, Sign, radiology, plain... (http://www.learningradiology.com/archives2009/COW%2 0352-Colon%20cutoff/coloncutoffcorrect.htm)Organic Bio Cleanse Detox Kit removes toxins from your body, with herbs and healing clay. Probably the worlds best detox diet program. June 24, 2016. Colon Cancer - Symptoms, Diagnosis, Treatment of Colon... (http://www.nytimes.com/health/guides/disease/colon- cancer/overview.html)Information about colon and rectal cancer treatment, prevention, genetics, causes, screening, statistics and other topics from the National Cancer Institute. June 25, 2016. How to Recognize Colon Cancer Early Symptoms | eHow (http://www.ehow.com/how_5807026_recognize-colon-can cer-early-symptoms.html)Colon, or colorectal, cancer is cancer that starts in the large intestine (colon) or the rectum (end of the colon). Other types of cancer can affect the colon. August 11, 2016. Colon Anatomy: Gross Anatomy, Microscopic Anatomy, Natural... (http://emedicine.medscape.com/article/1949039-overv iew)Colon cancer is the development of malignant tumors in the inner wall of the colon. Here we discuss the disease, why it forms, and how it is treated. August 12, 2016. X-Ray Exams of the Digestive Tract - WebMD (http://www.webmd.com/ibd-crohns-disease/crohns-dise ase/x-ray-exams-digestive-tract)Parts of the colon. Drawing of the front of the abdomen that shows the four sections of the colon: the ascending colon, the transverse colon, the descending colon... August 13, 2016. Barium enema : MedlinePlus Medical Encyclopedia (https://medlineplus.gov/ency/article/003817.htm)WebMD explains X-ray tests for digestive problems, including upper and lower GI exams. August 14, 2016. Best Colon Cleanse - DrNatura Colonix Internal Clean (http://www.drnatura.com/cleanse/colon-cleanse/)Colon Hydrotherapy - A Natural Approach. Our colons are the most neglected organ in the body. If you feel that you have not been caring properly for yours lately, you... August 15, 2016. Symptoms and causes - Colon cancer - Mayo Clinic (http://www.mayoclinic.org/diseases-conditions/colon -cancer/symptoms-causes/dxc-20188239)Cleanse the Colon All Naturally with Cleanse Products by DrNatura for an all natural, safe and gentle colon cleanse that is safe and effective. Cleansing is a way to... August 16, 2016. CT Colonography (Virtual Colonoscopy) - Radiology Info (http://www.radiologyinfo.org/en/info.cfm?pg=ct_colo)Find great deals on eBay for colon x. Shop with confidence. August 17, 2016. Colorectal (Colon) Cancer Slideshow Pictures - MedicineNet (http://www.medicinenet.com/colorectal_cancer_pictur es_slideshow/article.htm)Computed tomography (CT) colonography or virtual colonoscopy uses special x-ray equipment to examine the large intestine for cancer and growths called polyps. September 3, 2016. Small Bowel Vs Colon On X Ray - Doctor insights on HealthTap (https://www.healthtap.com/topics/small-bowel-vs-col on-on-x-ray)The most deathly disease shared among men and women-Colon cancer. "We are what we eat.":Dietitian. How to take care of your Colon health? Consult Aloe... September 4, 2016. What Are the Symptoms of Colon Cancer? - Verywell (https://www.verywell.com/what-are-colon-cancer-symp toms-796826)R/F Application of Tomosynthesis for Colon X-Ray Examination Department of Radiology, Fussa Hospital Mr. Takashi Nonaka Takashi Nonaka 1. Introduction September 5, 2016. The Healthy Digestion Centre | Colonic therapy Victoria BC (http://healthydigestion.ca/)Helpful, trusted answers from doctors: Dr. Fehr on small bowel vs colon on x ray: Though very uncommon there are genetic syndromes - like hereditary hemorrhagic... September 6, 2016. SEER Training: Anatomy of Colon and Rectum (http://training.seer.cancer.gov/colorectal/anatomy/)Colon cancer symptoms can run the gamut from local, such as blood in the stool and constipation, to systemic, such as weight loss and fatigue. September 7, 2016. Can Colorectal Cancer and Polyps Be Found Early? (http://www.cancer.org/cancer/colonandrectumcancer/d etailedguide/colorectal-cancer-detection)Anatomy of Colon and Rectum. The entire colon is about 5 feet (150 cm) long, and is divided into five major segments. The rectum is the last anatomic segment before... September 8, 2016. Colorectal Cancer | Colon Cancer | Rectal Cancer | MedlinePlus (https://medlineplus.gov/colorectalcancer.html)Please report to Admitting 15 minutes before your scheduled exam time. PREP: In order to do an x-ray examination of your colon, it is essential that your bowel be empty. September 9, 2016. Lower GI Exam (Barium Enema) - RadiologyInfo.org (http://www.radiologyinfo.org/en/info.cfm?pg=lowergi)Many people with colon cancer experience no symptoms in the early stages of the disease. When symptoms appear, they'll likely vary, depending on the cancer's size and... September 10, 2016. Diverticulosis - Wikipedia, the free encyclopedia (https://en.wikipedia.org/wiki/Diverticulosis)Colon X-ray spots cancer, reduces dread factor Alternative to colonoscopy has flaws, but could boost screening rates Below: x September 11, 2016. Lower GI Exam (Barium Enema) - RadiologyInfo.org (http://www.radiologyinfo.org/en/info.cfm?pg=lowergi)Using Colons and Semi-Colons Introduction. The most common punctuation marks in English are probably the period and the comma. However, good writing in English will... September 12, 2016. Colon (punctuation) - Wikipedia, the free encyclopedia (https://en.wikipedia.org/wiki/Colon_(punctuation))Find great deals on eBay for colon x. Shop with confidence. September 13, 2016. Colorectal (Colon) Cancer Slideshow Pictures - MedicineNet (http://www.medicinenet.com/colorectal_cancer_pictur es_slideshow/article.htm)The colon ( : ) is a punctuation mark consisting of two equally sized dots centered on the same vertical line. A colon precedes an explanation, or an... November 8, 2016. Colon Talk - Colon cancer (colorectal cancer) support... (http://coloncancersupport.colonclub.com/viewforum.p hp?f=1)How to Detox Your Colon. Some natural health practitioners recommend a periodic colon cleanse, which may remove toxins from your digestive system. Avoid certain foods. November 9, 2016. Lower GI Exam (Barium Enema) - RadiologyInfo.org (http://www.radiologyinfo.org/en/info.cfm?pg=lowergi)Parts of the colon. Drawing of the front of the abdomen that shows the four sections of the colon: the ascending colon, the transverse colon, the descending colon... November 10, 2016. Semi-colons, colons, and dashes - The Writing Center at... (http://writingcenter.unc.edu/handouts/semi-colons-c olons-and-dashes/)Colon cancer (colorectal cancer) support forum. Please feel free to read, share your thoughts, your stories and connect with others! November 11, 2016. Coiled colon | definition of coiled colon by Medical... (http://medical-dictionary.thefreedictionary.com/coi led+colon)The semi-colon looks like a comma with a period above it, and this can be a good way to remember what it does. November 12, 2016. Amazon.com: colon x (https://www.amazon.com/s?ie=UTF8&page=1&rh= i%3Aaps%2Ck%3Acolon%20x)The Colon Club is a nonprofit organization dedicated to raising awareness of colon cancer (colorectal cancer) in out-of-the-box ways. Our goals are to educate as... November 13, 2016. Colonic Diseases: MedlinePlus (https://medlineplus.gov/colonicdiseases.html)Colon cleansing is popular among some alternative medicine practitioners who claim it has numerous health benefits. Get the facts before you try it. November 14, 2016. Natural Colon Cleansing: Is It Necessary? - WebMD (http://www.webmd.com/balance/guide/natural-colon-cl eansing-is-it-necessary)Colon cancer is a disease in which malignant (cancer) cells form in the tissues of the colon. Health history can affect the risk of developing colon cancer. November 15, 2016. Colon Cancer: Symptoms, Signs, Screening, Stages - MedicineNet (http://www.medicinenet.com/colorectal_cancer_pictur es_slideshow/article.htm)Find great deals on eBay for colon x. Shop with confidence. November 16, 2016. Colon (punctuation) - Wikipedia (https://en.wikipedia.org/wiki/Colon_(punctuation))When barium enters your colon, you may feel like you need to have a bowel movement. You may also have: A feeling of fullness; Moderate to severe cramping November 17, 2016. The Colon (Human Anatomy): Picture, Function, Definition... (http://www.webmd.com/digestive-disorders/picture-of -the-colon)Colon X - is an advanced natural formulation which provides a high quality source of herbal bulk materials (both soluble and insoluble fiber) necessary to create a... December 5, 2016. Colorectal cancer screening tests - American Cancer Society (http://www.cancer.org/cancer/colonandrectumcancer/m oreinformation/colonandrectumcancerearlydetection/c olorectal-cancer-early-detection-screening-tests-us ed)To achieve optimal health you have to make sure you keep the plumbing clean. This is why proper intestinal, bowel and colon operation go a long way toward... December 6, 2016. Diverticulitis (Diverticulosis) Symptoms, Diet, Treatment (http://www.medicinenet.com/diverticulitis_diverticu losis_pictures_slideshow/article.htm)The most deathly disease shared among men and women-Colon cancer. "We are what we eat.":Dietitian. How to take care of your Colon health? Consult Aloe... December 7, 2016. colonx.com (http://colonx.com/)Diverticulitis (diverticulosis) is a condition in which the diverticulum or diverticula rupture in the colon causing infection. Medical treatments such as antibiotics... December 8, 2016. Polyp (medicine) - Wikipedia (https://en.wikipedia.org/wiki/Polyp_(medicine))This page requires that your browser supports frames. You can access the page without frames with this link. colonx.com December 9, 2016. Application of Tomosynthesis for Colon X-Ray Examination (http://www.shimadzu.com/med/literature/fluoro/k25cu r0000003yfx-att/16.pdf)A barium enema is an X-ray exam of the large intestine (colon and rectum). It may also be called a lower gastrointestinal (GI) exam. The test is used to help find... December 10, 2016. Tests to Detect Colorectal Cancer and Polyps - National... (https://www.cancer.gov/types/colorectal/screening-f act-sheet)Diverticulosis is the condition of having diverticula in the colon that are not inflamed. These are outpockets of the colonic mucosa and submucosa through... December 11, 2016. Colon Cancer: Symptoms, Signs, Screening, Stages (http://www.onhealth.com/content/1/colorectal_cancer)R/F Application of Tomosynthesis for Colon X-Ray Examination Department of Radiology, Fussa Hospital Mr. Takashi Nonaka Takashi Nonaka 1. Introduction December 12, 2016. Tests to Detect Colorectal Cancer and Polyps - National... (https://www.cancer.gov/types/colorectal/screening-f act-sheet)Using Colons and Semi-Colons Introduction. The most common punctuation marks in English are probably the period and the comma. However, good writing in English will... December 13, 2016. Colon Cancer: Symptoms, Signs, Screening, Stages (http://www.onhealth.com/content/1/colorectal_cancer)Colon X-ray spots cancer, reduces dread factor Alternative to colonoscopy has flaws, but could boost screening rates Below: x January 2, 2017. colon - grammar.quickanddirtytips.com (http://grammar.quickanddirtytips.com/colon-grammar. aspx)Colon cancer (colorectal cancer) support forum. Please feel free to read, share your thoughts, your stories and connect with others! January 3, 2017. Colorectal cancer stages - American Cancer Society (http://www.cancer.org/cancer/colonandrectumcancer/d etailedguide/colorectal-cancer-staged)Colon Hydrotherapy - A Natural Approach. Our colons are the most neglected organ in the body. If you feel that you have not been caring properly for yours lately, you... January 4, 2017. CT Colonography (Virtual Colonoscopy) - Radiology Info (http://www.radiologyinfo.org/en/info.cfm?pg=ct_colo)colon - grammar.quickanddirtytips.com January 5, 2017. Polyp (medicine) - Wikipedia (https://en.wikipedia.org/wiki/Polyp_(medicine))WebMD looks at colon cleansing, from using supplements to having colon irrigation. Are these products necessary or even beneficial, or is it all a hoax? Get the truth... January 6, 2017. Diverticulitis (Diverticulosis) Symptoms, Diet, Treatment (http://www.medicinenet.com/diverticulitis_diverticu losis_pictures_slideshow/article.htm)Diverticulosis is the condition of having diverticula in the colon that are not inflamed. These are outpockets of the colonic mucosa and submucosa through weaknesses... January 7, 2017. Amazon.com: colon x (https://www.amazon.com/colon-x/s?ie=UTF8&page=1 &rh=i%3Aaps%2Ck%3Acolon%20x)Diverticulitis (diverticulosis) is a condition in which the diverticulum or diverticula rupture in the colon causing infection. Medical treatments such as antibiotics... January 8, 2017. Amazon.com: colon x (https://www.amazon.com/colon-x/s?ie=UTF8&page=1 &rh=i%3Aaps%2Ck%3Acolon%20x)Diseases of the large intestine can affect your colon's ability to work properly. See how diet, medicines, and in some cases surgery can help. | {"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": 0.31472888588905334, "perplexity": 15502.54466315142}, "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-2017-13/segments/1490218186891.75/warc/CC-MAIN-20170322212946-00468-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://studies.quantimo.do/tag/anxiety/ | # Anxiety Studies
### Higher Lifting Weights Predicts Very Slightly Lower Anxiety
This individual’s Anxiety is generally lowest after an average of 0.33 count of Lifting Weights over the previous 7 days.
### Higher Acne Severity Predicts Very Slightly Lower Anxiety
This individual’s Anxiety is generally lowest after an average of 1.9 out of 5 of Acne Severity over the previous 7 days.
### Higher Cosentyx Intake Predicts Slightly Lower Anxiety
This individual’s Anxiety is generally lowest after a daily total of 150 milligrams of Cosentyx intake over the previous 7 days.
### Higher Acne Severity Predicts Slightly Higher Anxiety
Based on data from 5 participants, Anxiety is generally lowest after an average of 2.4 out of 5 of Acne Severity over the previous 7 days. | {"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": 0.8046155571937561, "perplexity": 10216.573766883585}, "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-2019-39/segments/1568514574159.19/warc/CC-MAIN-20190921001810-20190921023810-00397.warc.gz"} |
https://www.computing.net/answers/windows-xp/windowsinfbiosinfoinf-missing-or-corrupt/184548.html | # windows/inf/biosinfo.inf missing or corrupt
April 22, 2010 at 21:09:25
Specs: Windows XP, amd quad/4 gig
Ok, I had the same problem while doing an XP Windows install. I tried numerous problems to reset the MBR but nothing worked. I then thought I would try loading my Kubuntu 9.10 disk to see if the system would run Kubuntu. Kubuntu loaded without any problems and ran on the Dell laptop. I then tried reloading XP with a fresh image and low and behold, it went in and worked. It appears that the error message /windows/inf/biosinfo.inf is a symptom of a corrupt MBR that can not be fixed easily using conventional windows tools. Give the Kubuntu 9.10 a try, then load XP. I am sure you will find that this fixes the problem. As a side note. I searched for 3 or 4 hours to find someone that has fixed this problem and I could not find anyone with a good fix. I am sure this works!!!!
See More: windows/inf/biosinfo.inf missing or corrupt
#1
April 23, 2010 at 10:17:03
Need to do a repair install of your Windows...
Report •
Related Solutions | {"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": 0.8089194297790527, "perplexity": 2637.4481788622466}, "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-2018-30/segments/1531676589726.60/warc/CC-MAIN-20180717125344-20180717145344-00331.warc.gz"} |
https://demo.formulasearchengine.com/wiki/Flow_network | # Flow network
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in Operations Research, a directed graph is called a network. The vertices are called nodes and the edges are called arcs. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow. A network can be used to model traffic in a road system, circulation with demands, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes.
## Definition
Let ${\displaystyle G=(V,E)}$ be a finite directed graph in which every edge ${\displaystyle \ (u,v)\in E}$ has a non-negative, real-valued capacity ${\displaystyle \ c(u,v)}$. If ${\displaystyle \ (u,v)\not \in E}$, we assume that ${\displaystyle \ c(u,v)=0}$. We distinguish two vertices: a source ${\displaystyle \ s}$ and a sink ${\displaystyle \ t}$. A flow in a flow network is a real function ${\displaystyle \ f:V\times V\rightarrow \mathbb {R} }$ with the following three properties for all nodes ${\displaystyle \ u}$ and ${\displaystyle \ v}$:
Capacity constraints: ${\displaystyle \ f(u,v)\leq c(u,v)}$. The flow along an edge cannot exceed its capacity. Skew symmetry: ${\displaystyle \ f(u,v)=-f(v,u)}$. The net flow from ${\displaystyle \ u}$ to ${\displaystyle \ v}$ must be the opposite of the net flow from ${\displaystyle \ v}$ to ${\displaystyle \ u}$ (see example). Flow conservation: ${\displaystyle \ \sum _{w\in V}f(u,w)=0}$, unless ${\displaystyle \ u=s}$ or ${\displaystyle \ u=t}$. The net flow to a node is zero, except for the source, which "produces" flow, and the sink, which "consumes" flow.
i.e. Flow conservation implies: ${\displaystyle \ \sum _{(u,v)\in E}f(u,v)=\sum _{(v,z)\in E}f(v,z)}$, for each vertex ${\displaystyle \ {v\in V\setminus \{s,t\}}}$
Notice that ${\displaystyle \ f(u,v)}$ is the net flow from ${\displaystyle \ u}$ to ${\displaystyle \ v}$. If the graph represents a physical network, and if there is a real flow of, for example, 4 units from ${\displaystyle \ u}$ to ${\displaystyle \ v}$, and a real flow of 3 units from ${\displaystyle \ v}$ to ${\displaystyle \ u}$, we have ${\displaystyle \ f(u,v)=1}$ and ${\displaystyle \ f(v,u)=-1}$.
Basically we can say that flow for a physical network is flow leaving at s = ${\displaystyle \ \sum _{(s,v)\in E}f(s,v)}$
The residual capacity of an edge is ${\displaystyle \ c_{f}(u,v)=c(u,v)-f(u,v)}$. This defines a residual network denoted ${\displaystyle \ G_{f}(V,E_{f})}$, giving the amount of available capacity. See that there can be a path from ${\displaystyle \ u}$ to ${\displaystyle \ v}$ in the residual network, even though there is no path from ${\displaystyle \ u}$ to ${\displaystyle \ v}$ in the original network. Since flows in opposite directions cancel out, decreasing the flow from ${\displaystyle \ v}$ to ${\displaystyle \ u}$ is the same as increasing the flow from ${\displaystyle \ u}$ to ${\displaystyle \ v}$. An augmenting path is a path ${\displaystyle \ (u_{1},u_{2},\dots ,u_{k})}$ in the residual network, where ${\displaystyle \ u_{1}=s}$, ${\displaystyle \ u_{k}=t}$, and ${\displaystyle \ c_{f}(u_{i},u_{i+1})>0}$. A network is at maximum flow if and only if there is no augmenting path in the residual network ${\displaystyle \ G_{f}}$ .
So ${\displaystyle \ G_{f}}$ is constructed using graph G as follows:
1. Vertices of ${\displaystyle \ G_{f}}$ = ${\displaystyle \ V}$
2. Edges of ${\displaystyle \ G_{f}}$ = ${\displaystyle \ E_{f}}$ defined as-
For each edge ${\displaystyle \ (x,y)\in E}$
(i). If ${\displaystyle \ f(x,y) make Forward edge ${\displaystyle \ (x,y)\in E_{f}}$ with capacity ${\displaystyle \ c_{f}=c(x,y)-f(x,y)}$.
(ii). If ${\displaystyle \ f(x,y)>0,}$ make Backward edge ${\displaystyle \ (y,x)\in E_{f}}$ with capacity ${\displaystyle \ c_{f}=f(x,y)}$.
This concept is used in Ford–Fulkerson algorithm which computes the maximum flow in a flow network.
Sometimes one needs to model a network with more than one source, a supersource is introduced to the graph.[1] This consists of a vertex connected to each of the sources with edges of infinite capacity, so as to act as a global source. A similar construct for sinks is called a supersink.[2]
## Example
A flow network showing flow and capacity
To the right you see a flow network with source labeled ${\displaystyle s}$, sink ${\displaystyle t}$, and four additional nodes. The flow and capacity is denoted ${\displaystyle f/c}$. Notice how the network upholds skew symmetry, capacity constraints and flow conservation. The total amount of flow from ${\displaystyle s}$ to ${\displaystyle t}$ is 5, which can be easily seen from the fact that the total outgoing flow from ${\displaystyle s}$ is 5, which is also the incoming flow to ${\displaystyle t}$. We know that no flow appears or disappears in any of the other nodes.
Residual network for the above flow network, showing residual capacities. Although the flow from b to a should be 1, not 3.
Below you see the residual network for the given flow. Notice how there is positive residual capacity on some edges where the original capacity is zero, for example for the edge ${\displaystyle (d,c)}$. This flow is not a maximum flow. There is available capacity along the paths ${\displaystyle (s,a,c,t)}$, ${\displaystyle (s,a,b,d,t)}$ and ${\displaystyle (s,a,b,d,c,t)}$, which are then the augmenting paths. The residual capacity of the first path is ${\displaystyle \min(c(s,a)-f(s,a),c(a,c)-f(a,c),c(c,t)-f(c,t))}$ ${\displaystyle =\min(5-3,3-2,2-1)=\min(2,1,1)=1}$. Notice that as long as there exists some path with a positive residual capacity, the flow will not be maximum. The residual capacity for some path is the minimum residual capacity of all edges in that path.
## Applications
Picture a series of water pipes, fitting into a network. Each pipe is of a certain diameter, so it can only maintain a flow of a certain amount of water. Anywhere that pipes meet, the total amount of water coming into that junction must be equal to the amount going out, otherwise we would quickly run out of water, or we would have a buildup of water. We have a water inlet, which is the source, and an outlet, the sink. A flow would then be one possible way for water to get from source to sink so that the total amount of water coming out of the outlet is consistent. Intuitively, the total flow of a network is the rate at which water comes out of the outlet.
Flows can pertain to people or material over transportation networks, or to electricity over electrical distribution systems. For any such physical network, the flow coming into any intermediate node needs to equal the flow going out of that node. This conservation constraint was formalized as Kirchhoff's current law.
Flow networks also find applications in ecology: flow networks arise naturally when considering the flow of nutrients and energy between different organizations in a food web. The mathematical problems associated with such networks are quite different from those that arise in networks of fluid or traffic flow. The field of ecosystem network analysis, developed by Robert Ulanowicz and others, involves using concepts from information theory and thermodynamics to study the evolution of these networks over time.
The simplest and most common problem using flow networks is to find what is called the maximum flow, which provides the largest possible total flow from the source to the sink in a given graph. There are many other problems which can be solved using max flow algorithms, if they are appropriately modeled as flow networks, such as bipartite matching, the assignment problem and the transportation problem. Maximum flow problems can be solved efficiently with the Relabel-to-front algorithm. The max-flow min-cut theorem states that finding a maximal network flow is equivalent to finding a cut of minimum capacity that separates the source and the sink.
In a multi-commodity flow problem, you have multiple sources and sinks, and various "commodities" which are to flow from a given source to a given sink. This could be for example various goods that are produced at various factories, and are to be delivered to various given customers through the same transportation network.
In a minimum cost flow problem, each edge ${\displaystyle u,v}$ has a given cost ${\displaystyle k(u,v)}$, and the cost of sending the flow ${\displaystyle f(u,v)}$ across the edge is ${\displaystyle f(u,v)\cdot k(u,v)}$. The objective is to send a given amount of flow from the source to the sink, at the lowest possible price.
In a circulation problem, you have a lower bound ${\displaystyle l(u,v)}$ on the edges, in addition to the upper bound ${\displaystyle c(u,v)}$. Each edge also has a cost. Often, flow conservation holds for all nodes in a circulation problem, and there is a connection from the sink back to the source. In this way, you can dictate the total flow with ${\displaystyle l(t,s)}$ and ${\displaystyle c(t,s)}$. The flow circulates through the network, hence the name of the problem.
In a network with gains or generalized network each edge has a gain, a real number (not zero) such that, if the edge has gain g, and an amount x flows into the edge at its tail, then an amount gx flows out at the head.
In a source localization problem, an algorithm tries to identify the most likely source node of information diffusion through a partially observed network. This can be done in linear time for trees and cubic time for arbitrary networks and has applications ranging from tracking mobile phone users to identifying the originating village of disease outbreaks.[3]
## References
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|CitationClass=book }} | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 79, "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": 0.9229410886764526, "perplexity": 460.3099278173262}, "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-2019-18/segments/1555578742415.81/warc/CC-MAIN-20190425213812-20190425235812-00293.warc.gz"} |
http://physics.stackexchange.com/questions/2974/if-the-earth-left-the-solar-system-for-interstellar-space-how-long-would-it-tak?answertab=oldest | # If the Earth left the solar system for interstellar space. How long would it take for atmosphere to freeze?
If the Earth left the solar system for some reason. Assuming its moving at the same velocity it's currently exhibiting. How long would it take for the atmosphere to freeze. Would we get methane clouds like Titan. Would there be an atmosphere or would it all be frozen on the ground?
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Since conduction/convection are not possible between a cosmic body and empty space, I suspect velocity has no relevance. – Noldorin Jan 15 '11 at 23:28
@Noldorin: well, if one really wants to calculate the time (part of) atmosphere would freeze then it's obviously necessary to take into account also the velocity, because distance to the Sun and so also radiation received from Sun would depend on it. @Justin: can you confirm that this calculation is what you are interested in? – Marek Jan 16 '11 at 0:08
@Marek: Oh, well I was imagining the Earth moving in empty space, ignoring the sun altogether. I think the question needs to be clarified in terms of the model being used. – Noldorin Jan 16 '11 at 0:33
Sort of related, the "steppenwolf planet", an interstellar planet whose oceans never freeze: arxiv.org/abs/1102.1108 – Carl Brannen Feb 11 '11 at 4:00
related: scifi.stackexchange.com/q/9304 – David Cary Jan 8 '13 at 1:43
Velocity relative to where? Not that crucial though =)
It would take a matter of hours(maybe a few days) if you instantly take it to an empty space. It would take a few weeks if you gradually move away from the Sun. Let me note that as Noldorin said the only way of heat transfer is via radiation, but since Earth is a relatively good radiator, it would not take very long.
There would almost always be an atmosphere because there simply is enough gravity to attract gas, no matter what kind of gas it is. It will surely be dimmer&less dense though. There is not nearly enough methane on Earth to form a methane cycle similar to that of Titan. Titan possesses maybe hundreds of times more methane than Earth.
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You a right :) it was a combination of wine and late night. I meant the speed the earth travels which is around 100,000 km /h. Assuming it is travelling away from the sun. I figure there must be enough rare gasses that won't condense at a certain temperature. – Justin list Jan 16 '11 at 13:48
If you could suddenly drop a big screen between the Earth and Sun, the initial rate of energy loss would equal the total solar energy input:
$$\frac{dE}{dt} = \alpha F A_e .$$
Where $\alpha$ is the mean albedo, which Wolfram puts at $0.37$, the flux is $F = 1400\frac{\text{W}}{\text{m}^2}$, and the radius of the Earth is $R_e = 6.4 \times 10^6\text{ m}$, I get $7 \times 10^{16} W$.
Now, the atmosphere masses roughly $5 \times 10^{18}\text{ kg}$ (Wolfram again), and the heat capacity of Nitrogen gas is $c_p = 30 \frac{\text{J}}{\text{mol K}} = 1070 \frac{\text{J}}{\text{kg K}}$. So the initial cooling will be around $1.3 \times 10^{-5}\text{ K/s}$, or about one Kelvin per day. That rate will drop by the fourth power of the temperature (use absolute units!).
Things left unconsidered:
• I've neglected the oceans, and geothermal heat. Both effects will slow things down, the ocean considerable, geothermal, not so much. There is also a great deal of heat in the rock itself, but rock is a much better insulator than water, so it will have a smaller effect in the short term. Still, head into a deep mine or cave to stay warm, and watch out for the mineshaft gap!
• The heat of vaporization of water vapor and the heats of fusion of liquid water and carbon dioxide will slow things down while the phase transitions happen. There will be other phase transitions later on, but they won't matter to the frozen corpses...
• I've used a blackbody approximation which is surely not exact, but it should do for our purposes.
As Omega says in the comments all these factors are mitigating, and the real rate of temperature loss could be a factor of several (maybe even ten) lower than the above calculation. There are a lot of details that really matter, and things will change as the atmosphere changes (more clouds, then less, possible carbon dioxide clouds...) and the oceans freeze over.
However, the fact that the day/night temperature cycle is much larger than the daily change derived above suggests that the temperature near the Earth's surface is only loosely coupled to the mean atmospheric temperature (I guess that's not a big surprise as the surface is probably the warmest part of the atmosphere), so you can expect surface temperatures to drop much more rapidly than than the mean at first. How much faster? Well, like the day-to-night change initially, though I'd guess this will slow pretty quickly.
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I think you are on the right track. However the oceans contain many times order(100) as much heat as the atmosphere, so they would be crucial in determining the time scale. Water vapor in a cooling atmosphere would condense into clouds anf fog, and this would insulate the planet somewhat, slowing the rate of cooling. However, as the temperature drops the amount of water vapor in the atmosphere would decline. We get a lot of greenhouse warming from water vapor, and that would vanish as the temp drops. – Omega Centauri Jan 16 '11 at 1:25
Also before too long the ocean's surface would freeze, largely decoupling the atmosohere and surface from the heat content of (4C) water underneath. Geothermal heat is about 1 part in ten thousand of the solar input, so the equilibrium temperature would be about a tenth of current, say 30K. – Omega Centauri Jan 16 '11 at 1:28
@Omega, The oceans are surely important, but how quickly do they exchange heat with the atmosphere? I'm no climatolgist... I mean, water is a pretty good insulator when static, but convection will dominate until the ice forms. In any case, I think we can say that things are affected soon, but it takes long enough for everyone to die to allow for as many stories as you care to tell in the mean time... The fate of humanity is settled by the time the $CO_2$ freezes out, though people could hang on for a while. – dmckee Jan 16 '11 at 1:31
dmckee: Ocean heat is pretty important. England has much much warmer winters than Edmonton, because of the Gulf stream. Once the contrast between air and water becomes substantial (say 10 to 20C) the rate of transfer will become high. But water is a unique liquid, with max density around 4C, so once it cools to that temp or below it will become stratified with no more convection, then it has to transfer heat via conduction, which is slow. – Omega Centauri Jan 16 '11 at 4:33
Thanks all. Great info. I figure the oceans will take 10s of years to even develop a crust. And assuming the ice is then insulating the ocean it Wil. Probably remain liquid for 100,00s or even millions of years with the heat from the earth etc. – Justin list Jan 16 '11 at 13:52
the Earth is emitting thermal radiation corresponding to its temperature, and losing the energy (and decreasing temperature) in this way. Normally, this is cancelled - every day or every year - by the energy coming from the Sun. The second term would be absent in your thought experiment.
So those 342 Watts per meter squared in average coming from the Sun (more precisely, only 250 or so because a part is reflected without any transformation of the energy form anyway, so it's like if it is not coming at all) would disappear from the budget. One needs to estimate the heat capacity of the atmosphere - and the relevant layers of the ocean that are capable to heat the atmosphere above it for a while. But you don't need to be that sophisticated. It's enough to look at the reality of weather - numbers that everyone knows.
In the continental climate, going from day to night lowers the temperature of the atmosphere by 1 Celsius degree in average (cloudiness makes the day-time difference smaller; sunny skies make it larger). Because what you say is just a permanent night, this rate of cooling would simply continue and continue. So the initial rate would be cooling by 1 degree per day or so; it would be slower above the ocean.
As the temperature of the Earth would be going down, the radiation would be dropping as the fourth power of the absolute temperature (in Kelvin degrees). The atmosphere would be getting cooler, partly condensed (if not frozen), and much thinner. So once the absolute temperature decreased by 20 percent (note that $1.2^4$ equals 2 or so) or about 50 Celsius degrees, the rate of cooling would drop to 1/2 of the original one. At any rate, you need a few months to get to minus 50 degrees or something like that. The ocean would still be oscillating for a long time and it would try to unmelt the thinner atmosphere right above it - just like the circulation of water beneath the ice in a pond. Note that deep ocean circulation takes 1,500 years or so.
So of course, the ocean wouldn't freeze over for a very long time. But that's already a different question. Needless to say, heat almost doesn't get beneath the solid ground - kilometers below the rocks, they wouldn't notice that the Sun is gone for thousands of years or much longer.
Best wishes Lubos
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Nice explanation. Small note: no such thing as Kelvin degrees. It's just "Kelvin". – micahhoover Mar 28 '14 at 20:08
You're right, thanks. – Luboš Motl Mar 29 '14 at 8:32 | {"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": 0.7569336891174316, "perplexity": 593.4043445082775}, "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/1454701146550.16/warc/CC-MAIN-20160205193906-00070-ip-10-236-182-209.ec2.internal.warc.gz"} |
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https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-2-solving-equations-2-3-solving-multi-step-equations-practice-and-problem-solving-exercises-page-99/62 | ## Algebra 1
Published by Prentice Hall
# Chapter 2 - Solving Equations - 2-3 Solving Multi-Step Equations - Practice and Problem-Solving Exercises - Page 99: 62
#### Answer
$x = 26$
#### Work Step by Step
$4x - 4 + 3x + 2 = 180$ Combining like terms gives us: $7x - 2 = 180$ Add $2$ to both sides in order to get $7x$ on its own. $7x = 180+2= 182$ Divide both sides by $7$ in order to isolate $x.$ $x = \frac{182}{7} = 26$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | {"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": 0.37916240096092224, "perplexity": 901.7347754361458}, "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-2019-04/segments/1547583657151.48/warc/CC-MAIN-20190116093643-20190116115643-00627.warc.gz"} |
http://unjj.chicweek.it/fast-median-filter-python.html | You can vote up the examples you like or vote down the ones you don't like. Because it is so very simple, the moving average filter is often the first thing tried when faced with a problem. ADWMF is based on weighted median filter. Digital Signal Processing (DSP) From Ground Up™ in Python Practical DSP in Python : Over 70 examples, FFT,Filter Design, IIR,FIR, Window Filters,Convolution,Linear Systems etc ☑ Develop the Convolution Kernel algorithm in Python. From the median filtered image small objects are removed which are unnecessary and whose pixels are less than 60 using ‘bwareaopen’. 1 — BOOSTING, MIL, KCF, TLD, MEDIANFLOW, GOTURN, MOSSE and CSRT. A simple implementation of median filter in Python3. The aim of the AutoTrace project is the development of a freely available application with a functionality similar to CorelTrace or Adobe Streamline. Table 15-1 shows a program to implement the moving average filter. For a median filter with a linear window size w = 3, distortion is Δ = 0. To improve median performance, several authors (see [ 12 , 13 ]) have proposed a filter which is closely related to the latter, called the adaptive median. SciPy is an open-source scientific computing library for the Python programming language. The gradient method detects the edges by looking for the maximum and minimum in the first derivative of the image. MedianFilter. This node can be used to replace the RowID of the input data with the values of another column (by converting the values to a string) or a generated row id of the format: Row0, Row1, Row2,. Notable algorithms: watershed; convex points calculations. signal and scikits-image. A similar non-linear filter with slightly different properties is the mode filter which replaces each pixel with the mode of its neighboring pixels. nmed : int Size of window for 2D median filter (to reject bad pixels, etc. We will learn how and when to use the 8 different trackers available in OpenCV 3. 5 (21,250 ratings) Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately. The following figure shows the original image, the noisy image and images obtained after applying the median filter of different sizes (nxn, for different values of n): As can be seen from the following figure, the optimal median filter size is 5×5 , which generates the highest quality output, when compared to the original image. In the case of an unweighted window average, the response is a linear ramp that completes to the final value exactly when the buffer fills up with the final value. The best-known example in this category is the median filter, which, as its name implies, replaces the value of a pixel by the median of the gray levels in the neighborhood of that pixel (the original value of the pixel is included in the computation of the median). However, this wiki will focus on the median-of-medians algorithm, which is a deterministic algorithm that. The median filter is one of the basic building blocks in many image processing situations. The standard median filter is considered highly resistant to local outliers and local noise in the data sequence. The following example code takes data from a phidget analog input and filters this signal using first a IIR filter, then a median and then it calculates the FFT of the whole signal. What is even stranger is that this is a 'divide and conquer' type algorithm and so it is likely to be fast. The 2D extension to the algorithm showed better theoretical but depending on. [1:5], the rows/columns selected will run from the first number to one minus the second number. Using the Median for Background Estimation. Digital filters are very much more versatile in their ability to process signals in a variety of ways; this includes the ability of some types of digital filter to adapt to changes in the characteristics of the signal. Median filter 3x3x3 (128, 1024, 1024) uint8: fast 2d and 3d perlin. OK, I Understand. open-source license. The recursive median (RM) filter is a modification of the SM filter defined in (1). IIR filters don't need a buffer. merge([r,g,b]) # switch it to rgb # Denoising dst = cv2. Sampling the dataset is one way to efficiently explore what it contains, and can be especially helpful when the first few rows all look similar and you want to see diverse data. ga Fast cursors: arcpy. Other enhancements may pop up; stay tuned. pip install whitening Example usage Python API. Python is a useful tool for data science. The number of FIR taps, (often designated as “N”) is an indication of 1) the amount of memory required to implement the filter, 2) the number of calculations required, and 3) the amount of “filtering” the filter can do; in effect, more taps means more stopband attenuation, less ripple, narrower filters, etc. Blurs an image using the median filter. However, its use has long been hampered by its algorithmic complexity of O(r) in the kernel radius. The output two-dimensional image is filtered along the azimuthal χ axis using a percentile (often the median) filter to reconstruct the powder diffraction curve without the sharp Bragg spots. convolve (x, np. Filter the array, and return a new array with. The median filter also follows the moving window principle similar to the mean filter. It calculates average (arithmetic mean), standard deviation, median, total sum, minimum and maximum values present, and shows the number of processed. 039121627807617 MEDIAN 3. Overview of the Collections Module The Collections module implements high-performance container datatypes (beyond the built-in types list, dict and tuple) and contains many useful data structures that you can use to store information in memory. Used and experimented with various image stacking techniques for low light photography to remove noise. Since the median value must actually be the value of one of the pixels in the neighborhood, the median filter does not create new unrealistic pixel values when the filter straddles an. The median is the mid-value of the data when it is sorted in ascending or descending order. 11) assumed that the atmospheric veil is positive and less than the minimum value of the com-ponents in I(x), so their method uses a median filter to obtain the atmospheric veil. Get answers to your questions in our photography forums. Image filters can be classified as linear or nonlinear. adpcmdec – Decode MS and IMA ADPCM audio. 005 in this case) is the reason why we converted the 8 bit channel frames to 32 bit float channel frames. convolve for that:. Median Filtering andMedian Filtering and • Median filter • Rank order filterRank order filter • Bilevel Morphological filters - Dilation and erosion - Opening and closing • Grayscale Morphological filters Yao Wang, NYU-Poly EL5123: Non-linear Filtering 2. In the past, I sometime use small crop ratio (like 0. Sampling the dataset is one way to efficiently explore what it contains, and can be especially helpful when the first few rows all look similar and you want to see diverse data. median_filter is faster). A nice function in scipy. Median Filtering in Constant Time. Gaussian - perform Gaussian filtering. Document whitening (foreground separation) This package tries to separate text/line foreground and background by 2D median filter. In this session, we'll explore new additions to the framework that allow you to achieve great performance in your filter chains and custom CIKernels. The median is then taken of those selected frames to reduce flickering in noisy renders or buzzing plates. */ /** THE CONCEPT OF MEDIAN ----- "Basically a median is the value present at the center of a sorted array list. 5-pixel neighborhood In: Out: In: Out: Spike noise is removed Monotonic edges remain unchanged Degraded image Radius 1 median filter Because the filter is non-linear, it has the. As for one-dimensional signals, images also can be filtered with various low-pass filters (LPF), high-pass filters (HPF), etc. It replaces each pixel with the median value in its 3 x 3 neighborhood. Podręcznik programisty Pythona - opis biblioteki standardowej. This implementation is much faster than the Python by as much as a factor of 28 depending on the given parameters. In this context, the DFT of a window is called a filter. NOTE that when percentile is set at 50, a very fast filter routine is used. Generalizes to “rank order” filters. Here is the code to remove the Gaussian noise from a color image using the Non-local Means Denoising algorithm:. They are from open source Python projects. size of 2D median filter for pre-smoothing. Divide and conquer in C#. The recursive median (RM) filter is a modification of the SM filter defined in (1). accurip – Computes an AccurateRip CRC. masked_array(x, mask) # fill in the median vector. , [x,y] goes from x to y-1. You can improve iterating over the array by using np. 8x faster 65. */ /** THE CONCEPT OF MEDIAN ----- "Basically a median is the value present at the center of a sorted array list. Python is a useful tool for data science. ndenumerate to get the current coordinates and current item. Overview: A digital image is a two-dimensional plane of pixels and it has a width and height. Detrending is accomplishd by a coarse fitted spline, mean or median filters, or a fitted line. Welcome to AutoTrace - a program for converting bitmap to vector graphics. The median filter is a well-known image processing filter. To calculate the median first we need to sort the list in ascending or descending order. da ArcGIS API for Python. From what I have seen, Python appears to have more support in the area of deep learning than R. Median filtering is done by, firstly finding the median value by across the window, and then replacing each entry in the window with the pixel‟s median value. Python Tutorial: Python is an object-oriented, high-level, interpreted programming language with dynamic semantics. The Median Filter is a non-linear digital filtering technique, often used to remove noise from an image or signal. Minimum, Maximum, and Median Filters Morphological Filters: Minimum and Maximum. For this example, we will be using the OpenCV library. Digital Signal Processing (DSP) From Ground Up™ in Python Practical DSP in Python : Over 70 examples, FFT,Filter Design, IIR,FIR, Window Filters,Convolution,Linear Systems etc ☑ Develop the Convolution Kernel algorithm in Python. A refresher for more experienced readers, the first part of the book presents an introduction to Python, Python modules, reading and writing images using Python, and an introduction to images. Installation. To speed up processing, locallapfilt approximates the algorithm by discretizing the intensity range into a number of samples defined by the 'NumIntensityLevels' parameter. Python is a scripting language that allows fast development and is widely used in the scientific community. While these are not identical, they produce comparable results and the separable version is much faster. B = ordfilt2(A,order,domain,S) filters A, where ordfilt2 uses the values of S corresponding to the nonzero values of domain as additive offsets. If you had only that noisy image which means something to you, but the issue is that it cannot be viewed properly, would there be a. The median of the curve shown above is 70. 03779968066591 FUNCTION: f2 Used 135 times BEST 3. The median filter is a well-known image processing filter. The Bilateral Filter operation applies a bilateral image to a filter. about twice as fast as the pure python one. Median filter also reduces the noise in an image like low pass filter, but it is better than low pass filter in the sense that it preserves the edges and other details. This algorithm can be used to find groups within unlabeled data. Python + Filters + FFT + Gnuplot. Abstract: VLSI006: Aging-aware Reliable multiplier design with adaptive hold logic : Abstract: VLSI007: A Low-Power Architecture for the Design of a One-Dimensional Median Filter: Abstract: VLSI008. Using the Median for Background Estimation. Find the best information and most relevant links on all topics related toThis domain may be for sale!. masked_array(x, mask) # fill in the median vector. Models and examples built with TensorFlow. ) dispaxis : int. So you start with one quicksort partition. Bilateral Filter Crosses Thin Lines • Bilateral filter averages across features thinner than ~2 s • Desirable for smoothing: more pixels = more robust • Different from diffusion that stops at thin lines close-up kernel. This Learning Path follows a project-based approach to help you learn all the advanced concepts of Python. sample() The. It can also be used to estimate the average of a list of numerical values, independently from strong outliers. I additionally. The median filter is a well-known image processing filter. Why Python? Easy. You can show that this method will (on average) find the median of n elements in a time proportional to 2n - which is much better than performing a full sort. C Need fast array access Program name: filters. Volume Filter includes several options for smoothing or transforming volume data. Median filter. In 2D case we have 2D signal, or image. A classical filter, often used to solve the demosaicing problem, is the Freeman filter also. Median Filter: A median filter belongs to the class of nonlinear filters unlike the mean filter. median_image_filter ( image. I also tried sharpening the image, which at first didnt seem to work until close inspection showed a slight improvement. signal, lfilter() is designed to apply a discrete IIR filter to a signal, so by simply setting the array of denominator coefficients to [1. All the rest is the same: ordering elements and picking up the middle one. Such noise reduction is a typical pre-processing step to improve the results of later processing (for example, edge detection on an image). avg(X) The avg() function returns the average value of all non-NULL X within a group. Improvement of the filtering mask The filtering mask is mainly nnu square mask or cross mask. core import setup. neigh33(x, y), key=luminance). All the rest is the same: ordering elements and picking up the middle one. */ /** THE CONCEPT OF MEDIAN ----- "Basically a median is the value present at the center of a sorted array list. Home; Java API Examples; Python examples; which means # that OpenCV's extremely fast median filter algorithm can be used. For any convolution window in the time domain, there is a corresponding filter in the frequency domain. Using the Median for Background Estimation. However, for a small, fast, flat response 3x3 or 3x3x3 voxel mask, set SD to 0. To get the median of the current pixel and its 8 neighbors, set filterWidth and filterHeight to 3, but you can also make it higher to remove larger noise particles. The point you make is important one because using the alternate form means that the physical relationship with an RC filter is less apparent, moreover the interpretation of the meaning of a shown in the article is not appropriate for. However, due to its nonlinearity, the median filter has better performance in edge preservation and impulse noise removal than the average filter. If K>>N, then KN>>NlogN. 100+ Times Faster Weighted Median Filter. It gives the equations used to generate IIR filters from the s domain coefficients of analog filters using the Bilinear Transform. Alan, Both forms of the equation appear in the literature, and both forms are correct as I will show below. Constant subtracted from weighted mean of neighborhood to calculate the local threshold value. Image filters can be applied to an image by calling the filter() method of Image object with required filter type constant as defined in the ImageFilter class. These methods included median filters for getting rid of noise, gaussian filters with sigma =3,4,5 with acted as a low pass filter and highpass simple 3×3 and 5×5 filters such as sobel filters. The aim of the AutoTrace project is the development of a freely available application with a functionality similar to CorelTrace or Adobe Streamline. These tools are focused primarily on converting the data from its raw form to more accessible formats and often rely on proprietary programing languages. 5: Contains fast median filter implementation and 'direct' median filter implementations. The 2D extension to the algorithm showed better theoretical but depending on. The kernel coefficients diminish with increasing distance from the kernel’s centre. It is very effective at removing impulse noise, the “salt and pepper” noise, in the image. It can also be used to estimate the average of a list of numerical values, independently from strong outliers. Step Response Many scientists and engineers feel guilty about using the moving average filter. Next, a 2D Gaussian filter with 1 pixel standard deviation was applied to improve signal to noise ratio. Only need to do it once, otherwise wasting computational time - doesn't matter if performed on distance or raw. In simple words, the filter() method filters the given iterable with the help of a function that tests each element in the iterable to be true or not. This article shows how to plot the frequency response of the filters that I describe in my articles on filter design. Take a moment to go through the below visual (it’ll give you a practical idea of image segmentation): Source : cs231n. jpg') b,g,r = cv2. The standard median filter (SMF) simply replaces the sample by the median of the window : This filter has one tuning parameter given by. The filter 'kernel' can be an odd sized rectangle of pixels (e. This tool performs a conservative smoothing filter on a raster image. matlab program : 2d median filtering for salt and pepper noise without using medfilt2 function MEDIAN FILTER: In digital Image processing , removing the noise is one of the preprocessing techniques. Python is a high level Median filter is a spatial filter. By default the 'gaussian' method is used. Available: - lowpass : a lowpass. The detected contours were then scaled and used to obtain the position of walls to be recreated in Virtual World. We will learn how and when to use the 8 different trackers available in OpenCV 3. medfilt and order_filter are pretty fast, but then I'm living with a scipy requirement. 1 Median Filter Median filter belongs to the class of non linear filter. Median Filters f1 & f2 Median Filters: Each mesh vertex should only have one unique motion vector, which is picked from the motion candidates at each vertex by a median filter. split(img) # get b,g,r rgb_img = cv2. neigh33(x, y), key=luminance) Max 3x3: m2[x,y] = max(m1. Third is the temporalWindowSize which specifies the number of nearby frames to be used for denoising. A value of 0 (the default) centers the filter over the pixel, with positive values shifting the filter to the left, and negative ones to the right. Erosion and dilation are morphological image processing operations. The Median blur operation is similar to the other averaging methods. Zernike & Haralick, LBP, and TAS features. A FAST TWO-DIMENSIONAL MEDIAN FILTERING ALGORITHM In doing median filtering, we are computingrunningmedians. Array based histogram. You can perform this operation on an image using the medianBlur() method of the imgproc class. The most common morphological operations are minimum (also known as dilation) and maximum (erosion) filters. SciPy is a collection of mathematical algorithms and convenience functions built on the Numeric extension for Python. mode {'reflect', 'constant', 'nearest', 'mirror', 'wrap. [details] [source] kjbuckets is a C extension to python which defines three Python data types kjSet, kjGraph, and kjDict, implemented using a fast and space efficient hash table strategy. A simple implementation of median filter in Python3. 5 (793 ratings) Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately. Good support for scientific tasks. This alpha (0. Installation. COLOR_BGR2GRAY) # Apply median filter to the grayscale image img_gray = cv2. An image denoising method based on spatial filtering is proposed on order to overcoming the shortcomings of traditional denoising methods in this paper. It is similar to WHERE clause in SQL or you must have used filter in MS Excel for selecting specific rows based on some conditions. It works as a traditional Unix filter and can be used as part of those greatly useful chains of piped commands. median (src, radius [, dst]) → dst¶ Performs a median filtering of the input image with the given radius. 0) medianFiltered. A classical filter, often used to solve the demosaicing problem, is the Freeman filter also. Mahotas is a library of fast computer vision algorithms (all implemented in C++ for speed) operating over numpy arrays. Scientific Programming with the SciPy Stack. The results are shown in Fig. Image Proposed filter Median filter Gaussian filter 3. pord : int degree of spectral tilt. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific. Core Image: Performance, Prototyping, and Python. Ideally, we should only retain those features in the dataset that actually help our machine learning model learn something. It provides a very nice way to smooth an image while preserving edges. The panned for SimpleFilters is modeled after the Command Line Modules. convolve for that:. He was appointed by Gaia (Mother Earth) to guard the oracle of Delphi, known as Pytho. Numba creates a fast machine-code kernel from the Python template and calls it for every element in the arrays. Underwater gliders have become widely used in the last decade. For example, a reference dark image may be a median average of many images taken with the same exposure time as the science image, but with the shutter closed. The map is not continuous; wherever the laser was not reflected, the map simply contains no height data. It works as a traditional Unix filter and can be used as part of those greatly useful chains of piped commands. Install from PyPI. B = ordfilt2(A,order,domain,S) filters A, where ordfilt2 uses the values of S corresponding to the nonzero values of domain as additive offsets. The median filter replaces each pixel in the image with the median value of its neighboring pixels. Returns median_filter ndarray. Python in ArcGIS Python API for driving ArcGIS Desktop and Server A fully integrated module: import arcpy Interactive Window, Python Addins, Python Tooboxes Extensions: Spatial Analyst: arcpy. Noise Reduction vs. A Median stack will give a final pixel value as RGB( 130, 169, 209 ). Third is the temporalWindowSize which specifies the number of nearby frames to be used for denoising. The first edition of the spectral Analysis of Signals (in the translation of the first edition of modern signal spectrum analysis) a book programBooks translated from an internationally renowned master of signal processing, IEEE signal processing technical achievement award winners 2005 materials pr. In the case of a median filter, the output jumps suddenly at a time equal to 1/2 the sampling interval times the buffer length. You can show that this method will (on average) find the median of n elements in a time proportional to 2n - which is much better than performing a full sort. Python vs R. Most filters have a square support, though some are rectangular or circular. Average is a simple and fast command-line Perl utility for calculating basic statistics on a list of numbers (one number per line). x Python API package and the matplotlib package. jpg') b,g,r = cv2. Median Filtering Median filtering is a nonlinear method used to remove noise from. 17 videos Play all Image Processing Algorithms in Python MachineLearningGod Becoming a Data Scientist - Day 21 - Duration: 1:40:56. This two-step process is call the Laplacian of Gaussian (LoG) operation. Many filters are applied to get the best possible result for the noises present in the image like Weiner filter, Median filter etc. #!/usr/bin/env python import itk import sys input_filename = sys. idft() etc Theory Fourier Transform is. Masking comes up when you want to extract, modify, count, or otherwise manipulate values in an array based on some criterion: for example, you might wish to count all values greater than a certain value, or perhaps remove all outliers that are above some threshold. The aim of the AutoTrace project is the development of a freely available application with a functionality similar to CorelTrace or Adobe Streamline. As such, do something like this:. To get the median of the current pixel and its 8 neighbors, set filterWidth and filterHeight to 3, but you can also make it higher to remove larger noise particles. I wrote a python code to set filters on image, But there is a problem. Works on Python 3. As repr(), return a string containing a printable representation of an object, but escape the non-ASCII characters in the string returned by repr() using \x, \u or \U escapes. AbstractSummary. SciPy is an open-source scientific computing library for the Python programming language. In my last blog we had faded the coffee cup stains, but there was more work to be done. 4+, are supported. Kindly check Install OpenCV-Python in Windows and Install OpenCV 3. Similar to the average filter, median filtering smooths the image reducing also noise. This debate will rage on for probably another decade similar to how I remember the Java vs C# debate as a developer in the early 2000’s. The median then replaces the pixel intensity of the center pixel. with a median filter) modifies the histogram, and check that the resulting histogram-based segmentation is more accurate. This two-step process is call the Laplacian of Gaussian (LoG) operation. $\begingroup$ lfilter is not necessarily minimum-phase, it can be anything depending on the filter coefficients, but in any case it is causal, which filtfilt is not. A similar non-linear filter with slightly different properties is the mode filter which replaces each pixel with the mode of its neighboring pixels. But unlike the traditional matrices you may have worked with back in grade school, images also have a depth to them — the number of channels in the image. A very important note is that the depth of this filter has to be the same as the depth of the input, so the dimensions of this filter are 3 x 3 x 3. The Python concept of importing is not heavily used in MATLAB, and most of MATLAB’s functions are readily available to the user at the top level. Works on Python 3. Overview: A digital image is a two-dimensional plane of pixels and it has a width and height. The purpose of detecting corners is to track things like motion, do 3D modeling, and recognize objects, shapes, and characters. Image or as a numpy array. GaussianBlur, cv2. Document whitening (foreground separation) This package tries to separate text/line foreground and background by 2D median filter. Using the Median for Background Estimation. To calculate the median first we need to sort the list in ascending or descending order. center[5, then partition the numbers into groups of 5. class bytearray ([source [, encoding [, errors]]]). OK, I Understand. Noise Reduction vs. However, >> I cannot find any starting point for a median filter which needs to >> sort 100 numbers (14bit wide each). The example illustrates how to use the Hough Transform, Hough Lines and Kalman Filter blocks to create a line detection and tracking algorithm. The second part discusses the basics of image processing, including pre/post processing using filters, segmentation, morphological operations, and. These methods included median filters for getting rid of noise, gaussian filters with sigma =3,4,5 with acted as a low pass filter and highpass simple 3×3 and 5×5 filters such as sobel filters. PIL is the Python Imaging Library which provides the python interpreter with image editing capabilities. Here is the code to remove the Gaussian noise from a color image using the Non-local Means Denoising algorithm:. Why Python? Easy. The median is then taken of those selected frames to reduce flickering in noisy renders or buzzing plates. To resize image in Python, OpenCV cv2. This article will be about the Counter object. The standard median filter is considered highly resistant to local outliers and local noise in the data sequence. 8498943539073027 FUNCTION: f3. ) From playing with it scipy. When using. What is even stranger is that this is a 'divide and conquer' type algorithm and so it is likely to be fast. resize() can be used. jpg') b,g,r = cv2. Take a moment to go through the below visual (it’ll give you a practical idea of image segmentation): Source : cs231n. The point you make is important one because using the alternate form means that the physical relationship with an RC filter is less apparent, moreover the interpretation of the meaning of a shown in the article is not appropriate for. When considering different types of filters, the median filter is the aptest one to reduce noise in a satellite image. pip install whitening Example usage Python API. Sharpness: high pass filter. medfilt in Python. The idea is the same, just now median filter has 2D window. Percentile - value specifies which of the sorted values to output. A nice function in scipy. Kindly check Install OpenCV-Python in Windows and Install OpenCV 3. 0], it can be used to apply a FIR filter. Average is a simple and fast command-line Perl utility for calculating basic statistics on a list of numbers (one number per line). The Search text box is use quickly find a filter based on it's name. The following figure shows the original image, the noisy image and images obtained after applying the median filter of different sizes (nxn, for different values of n): As can be seen from the following figure, the optimal median filter size is 5×5 , which generates the highest quality output, when compared to the original image. The median is then taken of those selected frames to reduce flickering in noisy renders or buzzing plates. You could simply try a median filter with a small kernel size, from scipy. ndenumerate to get the current coordinates and current item. In the case of an unweighted window average, the response is a linear ramp that completes to the final value exactly when the buffer fills up with the final value. Qi Zhang Li Xu Jiaya Jia. ; An image can be resized to a given width and height using the resize() method of Pillow's Image class. Python In Greek mythology, Python is the name of a a huge serpent and sometimes a dragon. I implemented median filter in Python in order to remove the salt & pepper noise from the images. Median Filter • Problem with Averaging Filter - Blur edges and. On the other hand, the lag of a median filter in response to a. The images intensity range from 0 to 255. They are from open source Python projects. Description Usage Arguments Details Value Note See Also Examples. ; An image can be resized to a given width and height using the resize() method of Pillow's Image class. If you had only that noisy image which means something to you, but the issue is that it cannot be viewed properly, would there be a. Making statements based on opinion; back them up with references or personal experience. A conservative smoothing filter can be used to remove short-range variability in an image, effectively acting to smooth the image. medianBlur. Median Filter To filter an image with a Median filter, you can use median_filter(image, argument). This article shows how to plot the frequency response of the filters that I describe in my articles on filter design. Guido van Rossum. If I arbitrarily set the height for missing values to zero (or any other value) and then blur the. A median-finding algorithm can find the i th i^\text{th} i th smallest element in a list in O (n) O(n) O (n) time. It does not use Vendor-specific FPGA constructs and you can choose the trade-off between high-speed and low area use. 4+, are supported. It spends half the time 14. median_filter(x, size=3) mask[0] = False # first pt always extrema mask[-1] = False # last pt always extrema e = np. neigh33(x, y), key=luminance). 1 - a Python package on PyPI - Libraries. MedianFilter () method creates a median filter. A 3×3, 5×5, or 7×7 kernel of pixels is scanned over pixel matrix of the entire image. A Median Filter Replaces The Value Of A Certain Pixel With The Median Value Of The 9 Pixels That Belong To Its 3x3 Neighborhood. These methods included median filters for getting rid of noise, gaussian filters with sigma =3,4,5 with acted as a low pass filter and highpass simple 3×3 and 5×5 filters such as sobel filters. Here, the central element of the image is replaced by the median of all the pixels in the kernel area. 2D median filter programming. The fastest comparison-based sort is $$O(n \log n)$$ , so that dominates the runtime. Artificial Neural Networks are developed by taking the reference of Human brain system consisting of Neurons. Another median filter is applied spatially to reject motion outliers caused by mismatched features and dynamic objects. They apply a structuring element to an input image and generate an output image. The Chinese Univeristy of Hong Kong. You can use np. avg(X) The avg() function returns the average value of all non-NULL X within a group. ndimage is the generic_filter. It also features Python scripts for design and verification of the filter. 17 videos Play all Image Processing Algorithms in Python MachineLearningGod Becoming a Data Scientist - Day 21 - Duration: 1:40:56. na Geostatistics: arcpy. Median filters are quite popular because, for certain types of random noise. The ImageFilter module contains definitions for a pre-defined set of filters, which can be used with the Image. add_subplot(5, 5,i+1) Kalman and Bayesian Filters in Python. A Median stack will give a final pixel value as RGB( 130, 169, 209 ). However, its use has long been hampered by its algorithmic complexity of O(r) in the kernel radius. pyx from distutils. ones(1) #denominator co-effs of filter transfer function x = np. Gaussian Filter And to filter with a Gaussian filter, you use gaussian_filter(image, argument). NET, Delphi, Python Thanks to it's ANSI C interface, Filters is usable in many languages including C, C++, VB, C#, Delphi, Java and also in common scripting languages such as Perl, Python, PHP, TCL or Ruby. So far we had used adaptive thresholding and edge detection. In this session, we'll explore new additions to the framework that allow you to achieve great performance in your filter chains and custom CIKernels. You can't do median filters with FFT, but you only (usually) need a 3 x 3 neighborhood so it's a fast operation anyway. While these are not identical, they produce comparable results and the separable version is much faster. than the median and the Gaussian filter So in the proposed method the wiener filter is used to remove the noise from the images as shown in figure 4. The median filter is a well-known image processing filter. Description. At the top the Filters section enable the selection of one of the hundred of filters available. , image/audio/video processing. 4+, are supported. The following are code examples for showing how to use scipy. 309986114501953 MEDIAN 7. 保边滤波器(Edge Preserving Filter)是指在滤波过程中能够有效的保留图像中的边缘信息的一类特殊滤波器。其中双边滤波器（Bilateral filter）、引导滤波器（Guided image filter）、加权最小二乘法滤波器（Weighted least square filter）为几种比较广为人知的保边滤波器。. Median Filtering in Constant Time. Project of A Fast Testing System of Frequency. fast box filter • Allows box filter of any width with a constant cost - Rolling box filter • Uses a sliding window - Two adds and a multiply per output pixel - Adds new pixel entering window, subtracts pixel leaving • Iterative Box Filter ≈Gaussian blur • Using pixel shaders, it is impossible to implement a rolling box filter. The question of finding the number of distinct ways a class of filters can act is considered and solved for some classes. Median Filter: A median filter belongs to the class of nonlinear filters unlike the mean filter. “Image Processing and Acquisition using Python is unique in that it offers an in-depth understanding of the foundation of mathematics associated with image analysis. x Python API package and the matplotlib package. Apply a Wiener filter to remove salt-and-pepper noise and a median filter to smooth edges, then calculate gradients across the entire image (between adjacent pixels in both directions). In Figure 2, we present an alternate way to compute median 1d. sortedlist, just using Matteo's bisect_left and insort code with a plain builtin list instead of the blist. accurip – Computes an AccurateRip CRC. Find the best information and most relevant links on all topics related toThis domain may be for sale!. Think of it this way — an image is just a multi-dimensional matrix. I additionally. HARMONIC/PERCUSSIVE SEPARATION USING MEDIAN FILTERING Derry FitzGerald, Audio Research Group Dublin Institute of Technology Kevin St. I additionally. Basic Image Processing In Python - Part 2. Median filters are well known for preserving sharp edges in the input signal while reducing noise. Median filtering often involves a horizontal window with 3 taps; occasionally, 5 or even 7 taps are used. pyx from distutils. medfilt(volume, kernel_size=None) [source] ¶ Perform a median filter on an N-dimensional array. The basic idea behind filter is for any element of the signal (image) take an average across its neighborhood. 'mean': apply arithmetic mean filter 'median': apply median rank filter. Works on Python 3. A very important note is that the depth of this filter has to be the same as the depth of the input, so the dimensions of this filter are 3 x 3 x 3. pord : int degree of spectral tilt. Python is a scripting language that allows fast development and is widely used in the scientific community. Combined with the power and speed of the hundreds of ITK filters, it is fast and easy to create and adapt complex image processing pipelines. Median = (n + 1) / 2 It may seem very easy to see this formula since it is a very small set of data. virtualenv enables you to install Python packages (and therefor, the tools discussed in this document) in a separate environment, separate from your standard Python installation, and without polluting that standard installation. The standard median filter (SMF) simply replaces the sample by the median of the window : This filter has one tuning parameter given by. 05 degrees which is a much better estimate than 71. Check how a first denoising step (e. Use the (approximately) same 0. Available: - lowpass : a lowpass. Overview: A digital image is a two-dimensional plane of pixels and it has a width and height. See attached script for some exemples: median/average filter (the median filter is almost twice as fast as the one in GMIC), and an implementation of Color>Desaturate>Luminosity. If you are a collector of algorithms this is one you should have pinned on the wall. To resize image in Python, OpenCV cv2. Notable algorithms: watershed; convex points calculations. In doing this, it smoothes the image, and the result is often thought of as the. In python, the filtering operation can be performed using the lfilter and convolve functions available in the scipy signal processing package. This tool performs a conservative smoothing filter on a raster image. The Median blur operation is similar to the other averaging methods. Morphological filters - binary iterative morphology, gray-scale and color erosion, dilation, opening, and closing. This is a simple percentile median done within the ROI polygons. This problem is quite common in the mathematical domains and generic calculations. The technique involves. To get the numbers in the new window from those in the preceding window, we throw away n points and add in n new points. Median filter. This is a BlinkScript version of nuke's 'Median' filter. The median filter is a well-known image processing filter. You can show that this method will (on average) find the median of n elements in a time proportional to 2n - which is much better than performing a full sort. K-Means Clustering in Python - 3 clusters. All the rest is the same: ordering elements and picking up the middle one. Our image has a width (# of columns) and a height (# of rows), just like a matrix. In ADWMF, instead of fixed weights, weightages of the filter are dynamically assigned with. 531881332397461 MEAN 7. However, right now I use median filter and convolute functions implemented in imageJ, median filter and convolution is so fast that the rate limiting step of the program is no longer matrix operation. The result of avg() is always a floating point value as long as at there is at least one non-NULL input even if all inputs are integers. I've tested scipy. Official API in C, C++, C#, Visual Basic. The median of the curve shown above is 70. The phase described in this section is a suitable modification of this filter. The only downside is that the median is more expensive to calculate compared to the mean/average. Image processing with Python and SciPy. Filter size (odd) - The filter size will be forced to be an odd number before filtering. If K>>N, then KN>>NlogN. Returns ----- baseline : 1D ndarray Baseline calculated using median baseline correction """ # create extrema array (non extrema values are masked out) mask = x == scipy. ms/HISTORY (TIME,MESSAGE) values (mjd(), “historystring”). Example: Making a windowed compute filter 65 Perform a computation on a finite window of the input. import numpy as np import cv2 from matplotlib import pyplot as plt img = cv2. flag XX data based on a simple median filter (per row) Update my. accurip – Computes an AccurateRip CRC. Convolutions with OpenCV and Python. Ideally, we should only retain those features in the dataset that actually help our machine learning model learn something. Since the median value must actually be the value of one of the pixels in the neighborhood, the median filter does not create new unrealistic pixel values when the filter straddles an. 7 This chapter from our course is available in a version for Python3: Lambda Operator, filter, reduce and map Classroom Training Courses. Knowing that matplotlib has its roots in MATLAB helps to explain why pylab exists. The median filter calculates the median of the pixel intensities that surround the center pixel in a n x n kernel. Fortunately there is a trick to make NumPy perform this looping internally in C code. Erosion and Dilation of images using OpenCV in python Morphological operations are a set of operations that process images based on shapes. A median filter is well suited for such tasks since it will better preserve features in your original image. In my last blog we had faded the coffee cup stains, but there was more work to be done. For information about performance considerations, see ordfilt2. 05 degrees which is a much better estimate than 71. 03779968066591 FUNCTION: f2 Used 135 times BEST 3. Response time to real changes will be delayed proportional to the sorted array size. Overview of the Collections Module The Collections module implements high-performance container datatypes (beyond the built-in types list, dict and tuple) and contains many useful data structures that you can use to store information in memory. A more general filter, called the Weighted Median Filter, of which the median [1-3] filter is a special case, is described. The only downside is that the median is more expensive to calculate compared to the mean/average. The purpose of detecting corners is to track things like motion, do 3D modeling, and recognize objects, shapes, and characters. The Python concept of importing is not heavily used in MATLAB, and most of MATLAB’s functions are readily available to the user at the top level. Works on Python 3. ndimage import median_filter filtered_array = median_filter(random_array, size=3) which will remove the specks without noticeably changing the original image. The number of points in the azimuthal and radial directions as well as the percentile value can. We will be dealing with salt and pepper noise in example below. Python audio noise filter. 1 on my MacBook Pro with Django 2. Fast Bilateral Filter. The Search text box is use quickly find a filter based on it's name. size of 2D median filter for pre-smoothing. Such noise reduction is a typical pre-processing step to improve the results of later processing (for example, edge detection on an image). Median filter in Python Pillow: The Python image processing library - Pillow, implements the median filter through the class ImageFilter. NOT YET IMPLEMENTED! fitwidth : int Maximum radius (in pixels) for fitting to the peak of the cross-correlation. Quick Median - A Partition. The only downside is that the median is more expensive to calculate compared to the mean/average. This example shows the original image, the noisy image, the denoised one (with the median filter) and the difference between the two. Introduction to mean filter, or average filter. The map is not continuous; wherever the laser was not reflected, the map simply contains no height data. This is a continuation of those posts and looks at the code in the other languages. A 3×3, 5×5, or 7×7 kernel of pixels is scanned over pixel matrix of the entire image. 221 seconds for running_median_insort. The median filter is a well-known image processing filter. Setting the threshold to 0 corresponds to John Tukey’s median filter. Then the signal is filtered with a standard median filter and recursive median filter using a symmetric window of length. Filter size (odd) - The filter size will be forced to be an odd number before filtering. ones(1) #denominator co-effs of filter transfer function x = np. Keywords: Median filter, recursive median filter, weighted median filter ABSTRACT The aim of this paper is to present of standard median and recursive median one-dimensional nonlinear filters. hit & miss, thinning. From the median filtered image small objects are removed which are unnecessary and whose pixels are less than 60 using ‘bwareaopen’. For 2D case we choose window of 3. This implementation is much faster than the Python by as much as a factor of 28 depending on the given parameters. Following is the image after median filtering. 5 second time window and plot the low- and high-frequency components to separate figures. The median filter does a better job of removing salt and pepper noise than the mean and Gaussian filters. Median filter. Python in ArcGIS Python API for driving ArcGIS Desktop and Server A fully integrated module: import arcpy Interactive Window, Python Addins, Python Tooboxes Extensions: Spatial Analyst: arcpy. Python filter() The filter() method constructs an iterator from elements of an iterable for which a function returns true. For this example, we will be using the OpenCV library. So far we had used adaptive thresholding and edge detection. Image segmentation - fuzzyc mean, histogram thresholding, median-cut, principal components transform/median cut, spherical coordinate transform/center split, gray level quantization, split and merge. Python audio noise filter. sample() method lets you get a random set of rows of a DataFrame. The Median Filter is a non-linear digital filtering technique, often used to remove noise from an image or signal. What is even stranger is that this is a 'divide and conquer' type algorithm and so it is likely to be fast. Fast Fourier Transform. Only need to do it once, otherwise wasting computational time - doesn't matter if performed on distance or raw. The following example code takes data from a phidget analog input and filters this signal using first a IIR filter, then a median and then it calculates the FFT of the whole signal. Sylvain Paris, Pierre Kornprobst, Jack Tumblin, and Frédo Durand A class at ACM SIGGRAPH 2008 A tutorial at IEEE CVPR 2008 A course at ACM SIGGRAPH 2007. da ArcGIS API for Python. When doing so, the property of noise suppression arises: Note that the absolute peak positions will shift slightly when using this type of filter. What is even stranger is that this is a 'divide and conquer' type algorithm and so it is likely to be fast. Past: Monday morning (8:30am - 12:15pm), August 6th 2007 Announcement on the SIGGRAPH. Dr Colin Mercer Post author March 12, 2013 at 2:08 pm. An image is a collection or set of different pixels. Fig 3: Input Image Fig 4: Denoise Image Table 4. But for a large set of data, it needs more effort to get the value correctly since the steps vary a little for EVEN amount of numbers and an ODD amount of numbers. Install from PyPI. shape, True, dtype=bool) for. Question: Median_filter(image) Description: It Applies A 3x3 Median Filter On A Grayscale Image And Returns The Filtered Image As A New Grayscale Image. Available: - lowpass : a lowpass. A HPF filters helps in finding edges in an image. Since derivative filters are very sensitive to noise, it is common to smooth the image (e. An essential piece of analysis of large data is efficient summarization: computing aggregations like sum(), mean(), median(), min(), and max(), in which a single number gives insight into the nature of a potentially large dataset. First on the list is Python. $\endgroup$ – Eric Duminil Sep 9 '18 at 15:24 1 $\begingroup$ @EricDuminil The same can be said of $3, 6, 6, 6, 6$, which has an odd number of terms. The result replaces the original value of the pixel. In this course, you will also learn how to simulate signals in order to test and learn more about your signal processing and analysis methods. fastNlMeansDenoisingMulti()¶ Now we will apply the same method to a video. Images can be either RGB or grayscale. Median Filter To filter an image with a Median filter, you can use median_filter(image, argument). This weight can be based on a Gaussian distribution. than the median and the Gaussian filter So in the proposed method the wiener filter is used to remove the noise from the images as shown in figure 4. 5 (793 ratings) Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately. - whuber ♦ May 9 '11 at 14:49 Thanks whuber. median_filter(x, size=3) mask[0] = False # first pt always extrema mask[-1] = False # last pt always extrema e = np. The standard median filter (SMF) simply replaces the sample by the median of the window : This filter has one tuning parameter given by. Filter methods are generally the first step in any feature selection pipeline. def segmentglobal(img, filter_size=5, level=0. This function performs a median filtering of the given src image with the given radius and writes the result to the given dst image. Set the parameter n= equal to the number of rows you want. Introduction Machine learning and deep learning algorithms learn from data, which consists of different types of features. A median filter is also a smoothing filter, but it has one very important property: it is edge preserving. Apply a Wiener filter to remove salt-and-pepper noise and a median filter to smooth edges, then calculate gradients across the entire image (between adjacent pixels in both directions). Note that for small spatial extents, Susan will automatically switch to a flat kernel to ensure that some smoothing occurs. | {"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": 0.3254619538784027, "perplexity": 1513.3847732533072}, "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/1606141181179.12/warc/CC-MAIN-20201125041943-20201125071943-00311.warc.gz"} |
https://brilliant.org/problems/when-exponents-get-funny/ | # When exponents get funny
Algebra Level 5
$\huge {\sqrt[4]{\sqrt[x]{4}}}^{\tfrac{1}{\sqrt[4]{{\left(\sqrt[x]{4x^4}\right)}^{x^4}}}} = 4^{4^{-17}x^{-x^3 - 1}}$
Find the real value of $$x$$ satisfying the real equation above.
$$\text{Note}$$:- Here $$x \neq \{-1,0,1\}$$.
× | {"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": 0.7871311902999878, "perplexity": 9047.858074297805}, "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-2017-30/segments/1500549424623.68/warc/CC-MAIN-20170723222438-20170724002438-00079.warc.gz"} |
https://fathomr.com/lines-and-angles-parts-2-and-3-what-can-i-do-with-lines-and-angles-guided-practice/ | ## Lines and Angles Part 2: What Can I Do With Lines and Angles?
This lesson is particularly good for seeing relationships and learning how to find missing values based on what you are given. We wrote the Guided Practice with this in mind. We will give you a small bit of information and, from that, you will be able to find multiple other pieces of information.
The axioms of geometry are the building blocks for the entire set of rules, relations, and theorems. Think of the axioms and the inherent properties that naturally come from them as tools in your toolbox. The tools are the proven facts and with these tools you can construct proofs of your own. You can build a self-contained sequence of facts where the first leads directly into the second, that leads directly into the third, and so on until you arrive at your answer.
## Lines and Angles Part 3: Guided Practice
The graph above shows 6 lines passing through points A-H with coordinates listed below.
A: $$(\frac{2}{3},\frac{14}{3})$$ E: (1,2)
B: $$(\frac{8}{3},\frac{11}{3})$$ F: (0,1)
C: $$(-\frac{1}{2}, \frac{1}{2})$$ G: (-1,1)
D: (-2,2) H: (0,0)
1. Which of the following pair line segments are parallel?
A. $$\overline{DA} \parallel \overline{CB},\, and \, \, \overline{DE} \parallel \overline{GF}$$
B. $$\overline{CF} \parallel \overline{EB}, \, and \, \, \overline{GF} \parallel \overline{AB}$$
C. $$\overline{ED} \parallel \overline{AB}, \, and \, \, \overline{HG} \parallel \overline{FG}$$
D. $$\overline{EB} \parallel \overline{GF}, \, and \, \, \overline{FB} \parallel \overline{HC}$$
E. $$\overline{GH} \parallel \overline{CF}, \, and \, \, \overline{GC} \parallel \overline{AD}$$
Answer A has line segment pairs that have the same slope and are therefore parallel.
$$Slope = m = \frac{y_2 – \, y_1}{x_2 – \, x_1}$$
$$\overline{DA} \rightarrow \frac{2 \, -\frac{14}{3}}{-2 \, – \frac{2}{3}} = 1$$
$$\overline{CB} \rightarrow \frac{2 \, – \, \frac{14}{3}}{-2 \, – \, \frac{2}{3}} = 1$$
and
$$\overline{DE} \rightarrow \frac{2 \,- \, 2}{-2 \, – \, 1} = 0$$
$$\overline{GF} \rightarrow \frac{1 \, – \, 1 }{-1 \, – \, 0} = 0$$
1. Which line segments are perpendicular?
A. $$\overline{DA} \perp \overline{CB}, \, and \, \, \overline{DE} \perp \overline{GF}$$
B. $$\overline{CF} \perp \overline{BE}, \, and \, \, \overline{GF} \perp \overline{AB}$$
C. $$\overline{DH} \perp \overline{AB}, \, and \, \, \overline{DE} \perp \overline{GF}$$
D. $$\overline{FE} \perp \overline{FG}, \, and \, \, \overline{FB} \perp \overline{CH}$$
E. $$\overline{GH} \perp \overline{CF},\, and \, \, \overline{GC} \perp \overline{AD}$$
Answer E has line segment pairs that have negative reciprocal (opposite signs and reciprocals) slopes and are therefore perpendicular.
$$\overline{GH} \rightarrow \frac{1 \, – \, 0}{-1 \, – 0} = -1$$
$$\overline{CF} \rightarrow \frac{\frac{1}{2} \, – \, 1}{-\frac{1}{2} \, – \, 0} = 1$$
and
$$\overline{GC} \rightarrow \frac{\frac{1}{2} \,- \, 1}{-\frac{1}{2} \, – \, (-1)} = -1$$
$$\overline{AD} \rightarrow \frac{2 \, -\frac{14}{3}}{-2 \, – \frac{2}{3}} = 1$$
1. How long is line segment $$\overline{DH}$$?
$$D = \sqrt{( -2 – 0)^2 + (2 – 0)^2}= \sqrt{4+4} = \sqrt{8}$$
1. What is the midpoint of line segment $$\overline{FE}$$?
$$(\frac{0+1}{2},\frac{2+1}{2})= (\frac{1}{2},\frac{3}{2})$$
1. What is the slope of line segment $$\overline{FE}$$?
$$\frac{2-1}{1-0} = 1$$
1. What is the slope of line segment $$\overline{DA}$$?
Because $$\overline{DA}$$ is $$\parallel$$ to $$\overline{FE}$$ its slope is also 1.
1. What is the slope of $$\overline{DH}$$?
Because $$\overline{DH}$$ is $$\perp$$ to $$\overline{DA}$$ and $$\overline{FE}$$ its slope is -1.
1. If $$\angle B$$ is $$60 ^\circ$$, what are the measures of the angles marked A, C, D, E, F, and G?
$$A = 120 ^\circ$$ by the property of same side exterior angles.
$$C = 90 ^\circ$$. $$\overline{DH}$$ and $$\overline{FE}$$ are $$\perp$$. C is the intersection point of the two line segments. Because perpendicular lines meet at right angles, $$C = 90 ^\circ$$.
$$D = 90 ^\circ$$ by the properties of same-side interior angles and supplementary angles.
Also, $$\overline{DA}$$ is $$\perp$$ to $$\overline{DH}$$ so $$D = 90 ^\circ$$
$$E = 45 ^\circ$$. Since angle C is $$90^\circ$$, the other two angles of $$\triangle CDE$$ must add to $$90^\circ$$. We can use the distance formula to see that the lengths of $$\overline{CE}$$ and $$\overline{CD}$$ are equal, therefore their corresponding angles must be equal as well ($$\triangle CDE$$ is a 45-45-90 triangle). Since $$\angle CED$$ is $$45^\circ$$, $$\angle E = 45 ^\circ$$ by the property of vertical angles.
$$F = 45 ^\circ$$. $$\triangle CDE$$ and $$\triangle CGF$$ are similar triangles (meaning they have proportional sides and equivalent angle measures). Therefore, $$angle CFG = 45^\circ$$ and, by the property of vertical angles, $$\angle F = 45^\circ$$.
$$G = 135 ^\circ$$ We just found that $$\angle CGF = 45^\circ$$, therefore, by the property of supplementary angles, $$\angle G = 135^\circ$$. | {"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": 0.7004484534263611, "perplexity": 416.5982495042427}, "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-2020-16/segments/1585370524604.46/warc/CC-MAIN-20200404165658-20200404195658-00403.warc.gz"} |
https://www.physicsforums.com/threads/generalized-statistical-interpretation.751444/ | Generalized statistical interpretation
1. Apr 30, 2014
lkijmj
I red griffiths many times but even now there is something I can't understand. It's about statistical interpretation. In his book chapter 3.4 he says
"If you measure an observable Q(x,p) on a particle in the state ψ(x,t), you are certain to get one of the eigenvalues of the hermitian operator Q(x,-ihd/dx)"
but when the particle is not in determinate state (I mean <σ^2>=0), we can't even get eigenvalue equation Qψ=qψ. So we don't know whether the observable is a eigenvalue of some eigenvalue equation or not.
Could you please explain the sentence above to me?
2. Apr 30, 2014
Einj
Even if the initial state is not an eigenstate of Q, the result of the measure of Q is always going to be one of its eigenvalues. The probability of getting one of the possible eigenvalues will depend on the composition of your state (what mixture of eigenstates it contains).
Then, right after the measure, the state will collapse to the right eigenstate of Q (the one corresponding to the eigenvalue you just measures).
3. Apr 30, 2014
grimx
Einj is right :)
I would also add that for principles of quantum mechanics, the eigenvalue of an operator is precisely the measure of that observable, then definitely after the measure will have an eigenvalue of the operator even if the state is not one of its eigenvector.
4. Apr 30, 2014
WannabeNewton
A given observable $A$ will have a complete set of eigenstates $\{|a \rangle \}$ so that any state $|\psi \rangle$ is expandable in terms of this eigenbasis: $|\psi \rangle = \sum \langle a |\psi \rangle |a\rangle$ (where it is understood that if the spectrum is continuous, we replace the sum with an integral).
It is one of the postulates of QM that a "measurement" of $A$ will yield the eigenvalue $a$ of one of the eigenstates $|a \rangle$ with the probability (density if continuous variable) $|\langle a |\psi \rangle|^2$. This is a basic assumption of the theory that is elucidated at the very beginning of Griffiths and many other texts.
5. Apr 30, 2014
Jilang
I think the issue is that when it's in a indeterminate state you won't get the same answer each time you measure it.
6. Apr 30, 2014
Einj
Yes but that's not an issue. You can always repeat your experiment many times and determine the probability of obtaining a certain eigenvalue. This probability is completely determined by your initial state. There is no problem
7. Apr 30, 2014
Jilang
But if were in a determinate state you would get the same result each time.
8. Apr 30, 2014
Einj
Yes, but just because if you are in a determinate state this means that the probability of obtaining that particular eigenvalue is 1. It's all perfectly embedded in the quantum theory and it all perfectly predictable.
9. Apr 30, 2014
strangerep
One sees this traditional fiction repeated so often that one becomes tired of correcting it. But... let's try again...
The notion that a state collapses to an eigenstate after a measurement is only plausible for "filter-type" measurements. For most other realistic types of measurements (i.e., nontrivial interaction between system and apparatus), it is plainly false. An extreme example is measuring the position of a photon by where it strikes a photosensitive screen. The photon is absorbed as part of the interaction with the screen, and does not even exist thereafter, hence is certainly not in an eigenstate of position.
For more extensive refutation of such bunkum-for-the-freshers, see Ballentine ch9.
[I hope I don't regret this.]
Last edited: Apr 30, 2014
10. Apr 30, 2014
Useful nucleus
Thanks for this elaboration, strangerep! That is new to me.
However what you call "bunkum-for-the-freshers" is in many standard undergraduate texts for quantum mechanics. I believe the authors of these texts did not intend to be misleading, they simply tried to remain concise in a place where elaboration is needed.
What I still remember from the class lectures is that the professor completely refrained from stating or discussing the measurement postulate (This class was intended for nuclear engineers).
11. May 2, 2014
Staff: Mentor
The issue here is books at the intermediate level tend to gloss over fine points. For example they will tell you a state is an element of a vector space. They aren't really. They are positive operators of unit trace. Only so called pure states can be mapped to a vector space.
THE book to get is Ballentine that has already been mentioned
https://www.amazon.com/Quantum-Mechanics-A-Modern-Development/dp/9810241054
It takes a lot of care to explain the statistical interpretation. Read it and it should be clear. For example QM can be developed from just two axioms and the collapse postulate is not one of them.
Thanks
Bill
Last edited by a moderator: May 6, 2017
12. May 2, 2014
vanhees71
I've just looked at this Section 3.3 in Griffths's book. It's better than many other descriptions I know, but it's not optimal yet. It's crucial that the operators, describing observables are not only Hermitean but even (essentially) self-adjoint. This is nicely demonstrated in
F. Gieres. Mathematical surprises and Dirac's formalism in quantum mechanics. Rep. Prog. Phys., 63:1893, 2000.
http://arxiv.org/abs/quant-ph/9907069
Otherwise Griffiths seems not to mention the old-fashioned collapse postulate which is very problematic if not totally inconsistent with both the very foundations of causality (in the relativistic realm) and experimental practice in the real world of the lab. E.g., detecting photons with a CCD camera (or a good old photo scintillator or photographic film) usually leads to the absorption of the photon and not to its preparation as something localized at the position where the photon was detected. This view is particularly wrong for photons since it's not clear how to define a position observable for it at all, but that shouldn't bother you as a beginner in quantum theory.
The good point after all these debates about the state-collapse postulate, going on at least since the famous Einstein-Podolsky-Rosen paper and Bohr's response to it, is that it's not needed at all. The Minimal Statistical Interpretation is enough. Whatever you put on top of this minimal interpretation is metaphysics and subject to your private preference of a world view. The minimal interpretation is the core of the physics of quantum theory and not much disputed anymore, since more and more of the apparently "weird" features of quantum theory (mostly related with the phenomenon of entanglement, Bell's inequality, etc.) are confirmed to higher and higher accuracy.
As bhobba already recommended, a very good book is
L. E. Ballentine. Quantum Mechanics. World Scientific, Singapore, New Jersey, London, Hong Kong, 1998.
This you should, however, address only after you have a good grasp of how quantum theory is applied in physics. I don't know Griffiths's book so well, so that I cannot say, whether I'd recommend it. My favorite for the beginner's level is
J. J. Sakurai and S. Tuan. Modern Quantum Mechanics. Addison Wesley, 1993.
I think there is a more recent edition of this book, but I'm not aware what has been changed there.
Another great book is
S. Weinberg, Lectures on Quantum Mechanics, Cambridge University Press 2013.
There you find a nice discussion on the independence of the Born postulate (square of the wave function as probability distribution) from the other postulates of quantum theory. | {"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": 0.8362498879432678, "perplexity": 562.7469691838222}, "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-2018-22/segments/1526794863277.18/warc/CC-MAIN-20180520092830-20180520112830-00127.warc.gz"} |
https://www.physicsforums.com/threads/question-on-simultaneous-events.13889/ | # Question on simultaneous events.
1. Feb 5, 2004
### lky
Suppose if I am in a ship travelling from points A to B (10 light years apart) at a relavistic speed of say 0.8c.
Then suppose if there is a very strong light bulb at both points A and B, and assuming that the light rays do not get weakened along the way.
Now if I am in the ship moving from A to B at 0.8c and I am in the midpoint of my journey, when I observe the 2 light bulbs turn on simultaneously.
Am I correct to conclude that the 2 light bulbs are indeed turned on simultaneously, as if viewed by a stationary observer, since that the speed of light is constant to all observers, irregardless of their motion?
Or would the motion of the ship have any effect on this simultaneity?
Or I am incorrect to assume that the midpoint of my journey means light has to travel the same distance for both the cases of points A and B?
I would appreciate any help to clarify my doubts.
2. Feb 5, 2004
### Staff: Mentor
Everyone agrees that the light from each bulb arrived at the ship at the same time. But they disagree on whether the lights were switched on at the same time.
The fact that the two flashes reach the midpoint at the same time is evidence that they were turned on simultaneously according to observers in the rest-frame of the light bulbs. Observers in the ship will disagree that the lights were turned on at the same time. (Observers in the ship will conclude that light B must have turned on first, since it is moving towards the ship.)
Simultaneity is relative to the observer's frame. Observers at rest with the bulbs and those in the ship will disagree on what is simultaneous.
The light from each bulb is only seen to have traveled the same distance according to the observers at rest with the bulbs. Folks in the ship disagree.
3. Feb 5, 2004
### lky
Re: Re: Question on simultaneous events.
Just to be sure if I got you correct,
Because if both bulbs were turned on simultaneously, I (on the moving ship) would see the bulb at B turn on first.
Therefore if I am on the moving ship and I saw the 2 bulbs turn on simultaneously, it would mean that the bulb at A was turned on earlier than the bulb at B because I am moving from A to B.
And if C was instead a stationary observer at the mid point, he would see the bulb at A turn on earlier than B.
4. Feb 5, 2004
### gnome
This is very confusing to me.
Here's the way I see it:
Let's change the scenario, and say the lights were turned on simultaneously as viewed by an observer O who is at rest wrt points A and B and who is located at the midpoint between A and B, and at that same instant (before either observer sees the lights) observer O' in the spaceship passes directly by the same midpoint.
Edit: Just to clarify: here the lights are turned on at the instant that the spaceship passes the midpoint, so both observers will see the lights at some (different) later time.
In this situation, O' will first see the light from B at time T1', and sometime later, at time T2' will see the light from A. He measures the distance to B to be, say, d1' and concludes that it was turned on at time T1' - d1'/c. Similarly, when O' sees the light arriving from A, he measures the distance to A to be d2' and concludes that that light was turned on at time T2' - d2'/c. He then compares those two times he calculated in order to determine which light was switched on first.
But in the situation iky described, O' sees light coming at him from both points A and B, and each point is the same distance (call it d') away, and in each case the speed of the light is the same, c, so wouldn't he conclude that the time it took for the light to arrive at his location from each point was Δt' = d'/c and therefore the lights were turned on simultaneously? In this situation, stationary observer O, measuring the distances to A and B to be d, would be concluding that the time for the light to arrive at the same central location was Δt = d/c so he also concludes that the lights were turned on simultaneously. However, I think that because d' is smaller than d, observer O' concludes that the time that has elapsed since the lights were turned on is less than the elapsed time that would be determined by observer O.
If this is not correct, I'm in trouble. Please straighten me out.
Last edited: Feb 6, 2004
5. Feb 5, 2004
### LURCH
I'm going to disagree with you DocAl, which probably means I'm wrong, but maybe you could show me where I'm wrong. I would have said that if light from A and B meet at Mid-point M when M is occupied by the ship, then the observer on the ship will see the two come on simultaneously. And that an observer stationary relative to A and B (and M) would also agree. He would see that both lights were turned on simultaneously, but the ship was nowhere near M when this occured. In fact this observer would say that the ship was one year out from A when both lights came on, and the light from A took four years to catch up to the ship, arriving at the same moment as light from B reached the ship head-on.
This would be consistant with time-dilation, since to an observer inside the ship, the light from A closed the gap in one year, because the ship was one lightyear out from A at the time the bulb came on. Is this not so?
6. Feb 5, 2004
### gnome
Yes, I think the stationary observer O finds that it took the spaceship (5ly)/(.8c)=6.25 years to travel from A to his position at the midpoint, whereas it took 5 years for the light from A to cover that distance, so as LURCH says, the ship was 1.25*.8 = 1ly from A when the light turned on.
But for observer O' in the spaceship, the trip from A to the midpoint took 6.25*√(1-.82)=3.75 years, and he measures the distance from A as vΔt'=(.8c)*3.75 years = 3 ly. So he concludes that only 3 years have elapsed since the lights were turned on. Agree?
7. Feb 6, 2004
### lky
LURCH, your explanation sounds plausible, but I'm assuming that the ship is indeed physically at the midpoint between points A and B.
Drawing a rough space-time diagram (see attached file), with really bad symmetry ( the gradient for both light from A and from B should be perpendicular instead).
From my not-so-good-understanding and space-time-diagram, it seems that the 2 light turns on at time t together. And both the ship and the stationary observer would see the light bulbs turn on together.
Or is it that the axis for the space time-daigrams are different for the moving ship and the stationary observer and the axis are instead skewed to each other?
File size:
8.4 KB
Views:
58
8. Feb 6, 2004
### Staff: Mentor
All observers will agree that the light arrives simultaneously at the ship. So, the observer on the ship would see the the two light beams arrive simultaneously. This does not mean that observers would agree that the lights were turned on simultaneously; that is a deduction, not a direct observation.
See my comments above. No one "sees" the lights turned on simultaneously. But observers at rest with A-B will insist that they were turned on simultaneously. Observers in the ship will not.
9. Feb 6, 2004
### gnome
Please tell me where I am wrong. If the observer on the ship doesn't think both lights were turned on 3.75 years ago, exactly when does he think each one was turned on?
10. Feb 6, 2004
### Staff: Mentor
Much of this discussion hinges on how this statement by lky is interpreted:
I've been interpreting this to mean: The light from both bulbs arrives at the ship exactly as the ship is at the mid-point between the bulbs. (That's what "I observe the 2 light bulbs turn on simultaneously" means to me.)
Am I wrong about what you meant, iky?
11. Feb 6, 2004
### Staff: Mentor
No. The light bulbs are moving. So, when the light that reaches the ship first started out, the light bulbs were not equidistant from the ship.
Right! Observer O will agree that each light beam traveled the same distance in getting to midpoint. So observer O thinks they were emitted simultaneously.
Observer O' (ship) disagrees that the light beams were emitted when the bulbs were equidistant from the ship; so he thinks each beam traveled a different distance. Also, observer O' sees all the usual relativistic effects:
1) Moving clocks slow down
2) Moving clocks are no longer synchronized (if they are synched in their own frame)
3) Moving lengths shrink
I think we'll both survive!
12. Feb 6, 2004
### Staff: Mentor
When did the lights go on? Mysteries revealed?
Here's how to think of it.
Pretend that observers in O have three clocks: one at A, one at M (midpoint), and one at B.
According to O, these clocks are synchronized. When they all read T = 0, that's when lights at A & B were turned on. When the light reaches M, O thinks that his clocks all read T = 5 years.
What does O' think? First, he knows that the clocks in O are not in synch: they are way off. O' thinks that clock A is 4 years behind clock M! (Use Lorentz transformations to check this. $\Delta T = \frac{vL}{c^2}$) Thus, when the light reaches M, O' says that clock M reads T = 5, but clock A only reads T = 1. So O' thinks only 1 year has passed (on the clocks in O) since the light left A. But since the moving clocks are slow, that means that O' says that 1/.6 = 1.66 years have passed.
Similary, O' says that the clock at B is 4 years ahead of the clock at M. So, when the ship is at the midpoint, O' says that clock B reads T = 9. So O' thinks 9 years have passed (on the clocks in O) since the light left B. So O' says that 15 years (of his time) have passed.
So, according to the observers in the ship, the light:
- left A 1.66 years ago
- left B 15 years ago
(Assuming I didn't mess up my transformations; it's been a while )
13. Feb 6, 2004
### Eyesaw
If my head was not simultaneous in time with my body,
I would expect it to fall off when I walk up a
flight of stairs. Relativity of simultaneity...time
dilation...lol.
Last edited: Feb 6, 2004
14. Feb 6, 2004
### lky
Re: Re: Question on simultaneous events.
Yup, that's what I meant.
15. Feb 6, 2004
### gnome
Hurrah! I don't want to get too excited about this, but at least I did finally get the same result as you. Thanks Doc.
But I still don't see exactly what you are doing. Here's what I did.
First, I let O' claim that he is stationary & A and B are moving toward the left at .8c. Since the distance from A to B in the A-B frame is 10ly, it is 6ly in the O' frame, and when O' is at the midpoint, it is 3ly to each of A and B in the O' frame. We all seem to agree on that.
Next I let x' = the distance that A and B travelled since the lights went on, and t' = the time elapsed since that time. So, as to the light from B:
ctB' = 3 + xB'
And as to B itself:
.8ctB' = xB'
Solving those equations gives tB' = 15 y
Similarly, as to the light from A:
ctA' = xA'
And as to A itself:
.8ctA' = 3 - xA'
Solving those equations gives tA' = 1.67y
---------------------------------------------------
Alternatively, using the Lorentz transformations I find in my textbook:
t' = γ(t - vx/c2)
In frame O, xA = xB = 5y, and tlightson = -5 (i.e. 5 yrs ago).
γ = 1/√(1-.64) = 1.67, so as to A:
tA' = 1.67[-5 - (.8)(-5)] = -1.67y
and as to B:
tB' = 1.67[-5 - (.8*5)] = -15y
----------------------------------------------------
Now, Doc, does my second calculation express EXACTLY the same approach as yours ('cause even though we got the same answers, it doesn't look the same to me [b(] )
You seem to be using a very abbreviated form of the transformation.
Am I still missing something that would make it easier for me to see?
16. Feb 6, 2004
### Janus
Staff Emeritus
I did a couple of animations some time back to illustrate this very thing. Now my illustration deals with a railway car and lightning strikes rather than spaceships and light bulbs, the the principle it illustrates is exactly the same.
The first one shows the sequence of events according to the observer stationary at the mid point.
http://home.teleport.com/~parvey/train1.gif
The exanding circles represent the leading edges of the light spheres.
Note that both lights turn on at the same time and that the light spheres reach both observers at the same time, so each of them "sees" the lights turn on at the same time.
The second one shows the sequence of events according to the observer on the Ship/train. Remember, from his position, he can consider himself as stationary and the lights as moving.
http://home.teleport.com/~parvey/train2.gif
First note that as each light turns on, the leading edge of the light still expands as a sphere from the initial point of emission according the viewpoint of the spaceship/train observer. But, the light sources move away from these points as time goes on. By the time the midpoint is reached, the lightsources and their intial points of emission are far removed from each other. Not also that the intial emission points always maintain the same distance form the train observer.
Now, since the train observer is not at the midpoint when either of the lights is initially emitted, this means he is closer to one of the emission points than the other at that time.
Thus in order for him to "see" the lights turn on at the same time, the light he is heading for has to start emitting first, followed later by the light he is departing from.
this means that as the midpoint passes by, the light spheres both arrive, and again both observers "see" the light come on at the same time.
Again, in order for order for both observers to "see" the lights turn on at the same time, the lights actually turn on at the same time for the observer with no relative velocity with respect to the lights, but for the observer with a relative velocity, they will have to turn on at different times.
IOW, events that are simultaneous in one frame are not simultaneous in another.
17. Feb 6, 2004
### Staff: Mentor
Yes! It's exactly the same.
For a complicated problem, I would just go right to the lorentz transformations and turn the crank. But for simple problems like this, I like to apply the "rules" for how clocks and metersticks behave. Of course, these rules are exactly equivalent to the lorentz transformations, but it makes me think I understand what's going on.
1) moving metersticks shrink (by a factor of γ)
2) moving clocks slow down (by a factor of γ)
3) moving clocks are out of synch (by a factor of ΔX V/c2)
Make sense? Get these rules in your bones and you can solve some problems quickly. (Derive them for yourself.)
18. Feb 6, 2004
### @Gents
Lets assume the spaceman dont noe anything abt physic, and he is moving from A to B with a man stationed at M. If he reach M and saw both the light from A and B reached him at the same time, doesnt he think both are lighted simultaneously?
19. Feb 7, 2004
### lky
If the spaceman don't know anything about physics, not only would he think the explosions are simultaneous, he would also think that the Earth is flat.
20. Feb 7, 2004
### lky
A big thanks to you guys for clarifying my doubts, especially Doc Al and his detailed explanation, and also Janus' animations. | {"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": 0.7991083860397339, "perplexity": 875.1774390505853}, "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/1487501170651.78/warc/CC-MAIN-20170219104610-00586-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://hackage.haskell.org/package/pipes-2.1.0/docs/Control-Frame-Tutorial.html | pipes-2.1.0: Compositional pipelines
Control.Frame.Tutorial
Description
This module provides the tutorial for Control.Frame.
Synopsis
Frames extend Pipes with two new features:
• Folding input and intercepting upstream termination
• Guaranteeing prompt and deterministic finalization
However, these extra features comes with some added complexity: restricted monads, also known as indexed monads. Restricted monads sound scarier than they are, so I'll demonstrate that if you are comfortable using monads, then you'll be comfortable using restricted monads.
Let's translate the take' function from the Pipes tutorial into a Frame to see what changes when we use restricted monads:
{-# LANGUAGE RebindableSyntax #-}
import Control.Frame
take' :: Int -> Frame a IO (M a) C ()
take' n = do
replicateMR_ n $do x <- await yield x close liftU$ putStrLn "You shall not pass!"
This time I included all imports and highlighted the new RebindableSyntax extension. The new imports belong to the Control.IMonad hierarchy from the index-core package, which provides the core restricted monad functionality.
Yet, you almost wouldn't even know you were using an restricted monad just by looking at the code. This is because index-core can rebind do notation to use restricted monads instead of ordinary extensions. Three things make this possible:
• The RebindableSyntax extension, which allows libraries to override do syntax (among other things)
• The Control.IMonad.Do module which exports the new bindings for do notation
• Hiding Monad from the Prelude so that it does not conflict with the bindings from index-core
However, you are not obligated to rebind do notation to use Frames. You can choose to keep ordinary do notation and desugar the restricted monad by hand. Just import Control.IMonad instead, drop the RebindableSyntax extension, and don't hide Monad. Then you can desugar take' manually using the restricted monad operators:
import Control.Frame
take' :: Int -> Frame a IO (M a) C ()
take' n =
(replicateMR_ n $await !>= \x -> yield x) !>= \_ -> close !>= \_ -> liftU$ putStrLn "You shall not pass!"
However, for this tutorial I will use the do notation, since it's prettier and easier to use.
You'll also notice functions that resemble the ones in Control.Monad, except with an 'R' suffix on the end of them, like replicateMR_. Most functions in Control.Monad have a restricted counterpart provided by Control.IMonad.Restrict (which is in turn re-exported by Control.IMonad), such as whenR, foreverR, and mapMR.
Also, every time you lift an operation from the base monad, you must use liftU instead of lift. Frames are "restricted monad transformers", and they would normally lift a base restricted monad using liftI, but they can also lift ordinary monads, too, using liftU (mnemonic: "lift" an ordinary monad and 'U'pgrade it to a restricted monad).
# Type Signatures
The Frame type constructor also looks a bit different, too:
Frame a IO (M a) C ()
Let's dissect that to understand how Frames work:
| Output | Base monad | Initial Input | Final Input | Return Value
Frame a IO (M a) C ()
Frames differ from Pipes in that their input end indexes the beginning and end of the operation. Our take' function starts off with an open input end (M a), and ends with a closed input end (C).
take' finishes with a closed input end because it called the close function, which seals off and finalizes upstream. You can see that the close primitive changes the index just by looking at its type:
close :: Monad m => Frame b m (M a) C ()
The close instruction begins with an open input end (M a) and finishes with a closed input end (C). If you tried to call close twice, you'd get a type error:
-- wrong!
do close
close
This prevents you from accidentally finalizing upstream twice.
close is the only primitive that changes the index, and there is no way to reopen the input once you have closed it. close also forbids you from awaiting input from upstream after you have already closed it. If you try, you will get a type error
-- wrong!
do close
await
This prevents you from requesting input from a finalized pipe. In fact, once you close your input end, every upstream Frame disappears completely. You couldn't get input from upstream anyway, even if you somehow allowed await statements after close.
You can check out await's type signature to see why it won't type-check after close:
await :: Monad m => Frame b m (M a) (M a) a
await must begin with the input end open (M a) and it leaves the input end open when done (M a). However, you can still use a yield anywhere:
yield :: Monad m => b -> Frame b m i i ()
yield will work whether or not the input end is open, and it leaves the input end in the same state once yield is done.
# Prompt Finalization
Every Frame must close its input end exactly one time before you can compose it with other Frames. The only exception is if a Frame never terminates:
-- This type-checks because foreverR is polymorphic in the final index
printer :: (Show b) => Frame Void IO (M b) C r
printer = foreverR $do a <- await liftU$ print a
However, when a Frame no longer needs input then you should close it as early as possible. The earlier you close upstream, the more promptly upstream gets finalized.
If you write a stand-alone producer from start to finish, you can be sure it will never need upstream, so you can close it immediately:
-- I'm keeping fromList's input end polymorphic for a later example
fromList :: (M.Monad m) => [b] -> Frame b m (M a) C ()
fromList xs = do
close
mapMR_ yield xs
However, if fromList were a library function, you would remove the close statement as you cannot guarantee that your user won't want to await after fromList. Or, the user might want to call fromList twice within the same Frame, and having two close statements would lead to a type error. Therefore, a good rule of thumb when writing library code for Frames is to always let the user decide when to close the Frame unless you are writing a stand-alone Frame.
So for right now, I will leave the close in fromList for simplicity and treat it as a stand-alone Frame. Also, it will come in handy for a later example.
# Composition
Composition works just like Pipes, except you use the (<-<) composition operator instead of (<+<):
stack :: Stack IO ()
stack = printer <-< take' 3 <-< fromList [1..]
The Frame equivalent to Pipeline is a Stack (mnemonic: call stack; also the name Frame refers to a call stack frame):
type Stack m r = Frame Void m (M ()) C r
Similarly, you use runFrame instead of runPipe to convert the Frame back to the base monad:
>>> runFrame stack
1
2
3
You shall not pass!
However, let's carefully inspect the type of composition:
(<-<) :: Monad m
=> Frame c m (M b) C r
-> Frame b m (M a) C r
-> Frame c m (M a) C r
Each argument Frame must begin in an open state and end in a closed state. This means that each Frame in a Stack must call close exactly once before it may be used. runFrame has the exact same restriction:
runFrame :: Monad m => Stack m r -> m r
runFrame ~ Monad m => Frame Void m (M ()) C r -> m r
Composition specifically requires the user to define when to finalize upstream and does not assume this occurs at the end of the Frame. This doesn't pose a problem for stand-alone Frames, since they will know when they no longer need input, but smaller library components designed to be assembled into larger Frames should let the user decide at the very last moment where to close the Pipe. There is no way to know ahead of time where the close should be until the complete Frame has been assembled.
# Finalization
With Frames in hand, we can now write a safe read' function:
readFile' :: Handle -> Frame Text IO C C ()
eof <- liftU $hIsEOF h whenR (not eof)$ do
s <- liftU $hGetLine h yield s readFile' h read' :: FilePath -> Frame Text IO C C () read' file = do liftU$ putStrLn "Opening file..."
h <- liftU $openFile file ReadMode -- The following requires "import qualified Control.Monad as M" finallyD (putStrLn "Closing file ..." M.>> hClose h)$ readFile' h
The finallyD function registers a block-level finalizer that executes if a downstream Pipe terminates or if the block completes normally. The more general finallyF function will call the finalizer if any Frame terminates.
Usually you would always want to use finallyF, but because of some type limitations you can only use finallyD after a Frame is closed. A future release of this library will fix this and merge finallyD into finallyF. So that means that for everything beginning before a close statement, use finallyF, otherwise use finallyD.
Similarly, you can use the catchF / catchD counterparts to the "finally" functions. The "catch" functions run the finalizer only if another Frame terminates before the block is done, but not if the block terminates normally.
We don't close the read' function because it's not a stand-alone Frame. We want to be able to concatenate multiple read's together within the same Frame, like so:
files = do
close
read' "file2.txt"
So let's assume those two files have the following contents:
"file1.txt"
Line 1
Line 2
Line 3
"file2.txt"
A
B
C
We can now check to see if our files producer works:
>>> runFrame $printer <-< files Opening file... "Line1" "Line2" "Line3" Closing file ... Opening file... "A" "B" "C" Closing file ... More importantly, files are never opened if they aren't demanded and they are always properly finalized if the consumer terminates early: >>> runFrame$ printer <-< take' 2 <-< files
Opening file...
"Line1"
"Line2"
Closing file ...
You shall not pass!
So we get lazy, deterministic, and prompt resource management. Nice!
# Folds
Frames can actually do more than just manage finalization! Using Frames, we can now correctly implement folds like toList in a way that is truly compositional:
toList :: (M.Monad m) => Frame b m (M a) (M a) [a]
toList = do
a' <- awaitF
case a' of
Nothing -> return []
Just a -> do
as <- toList
return (a:as)
We used one new function this time: awaitF. This is like await except that it returns a Nothing if upstream terminates before yielding back a value. This allows you to intercept upstream termination and do some cleanup, and in our case we use it to end the fold.
You only receive a Nothing once when you use awaitF. Any attempt to request more input after you receive the first Nothing will terminate the current Frame using the upstream return value. In fact, await is built on top of awaitF:
await = do
a' <- awaitF
case a' of
Nothing -> await
Just a -> return a
If it gets a Nothing, it just ignores it and awaits again, choosing to not do any cleanup.
Now let's make sure our toList function works. I didn't make toList a stand-alone Frame, so we will have to include a close statement to complete it before composing it:
p1 = do
xs <- toList
close
return (Just xs)
p2 xs = do
fromList xs
return Nothing -- Remember: they need the same return type
>>> runFrame $p1 <-< p2 [1..10] Just [1,2,3,4,5,6,7,8,9,10] # Strictness Lazy resource management has one important disadvantage: we can't free the resource until downstream no longer needs input. Many libraries duplicate their code to provide Lazy and Strict versions, allowing the user to decide if they want: • Lazy input, which conserves memory, but holds onto the resource until downstream is done processing it • Strict input, which loads everything into memory, but can then immediately dispose of the resource before the input is processed What if there were a way to seamlessly switch between those semantics or even choose something in between? Well, it turns out we can! First, we can combine fromList and toList into something even cooler: strict :: (M.Monad m) => Frame a m (M a) C () strict = do xs <- toList fromList xs As the name suggests, the strict function is strict in its input. strict loads the entire input into memory, finalizes upstream, then proceeds to hand the input off to downstream. We can prove this just by using it: >>> runFrame$ printer <-< strict <-< files
> Opening file...
> Closing file ...
> Opening file...
> Closing file ...
> "Line1"
> "Line2"
> "Line3"
> "A"
> "B"
> "C"
Both files were disposed of immediately, at the expense of using more memory.
But what if we want something in between strictness and laziness? Maybe something like this:
>>> runFrame \$ printer <-< strict <-< take' 2 <-< files
Opening file...
Closing file ...
You shall not pass!
"Line1"
"Line2"
Now we have the best of both worlds. We can pick and choose how much of our source to strictly load into memory. In the above example, we specified that we wanted to be strict only in the first two lines of our input, and as a result the third line of "file1.txt" is never read and "file2.txt" is never even opened!
Now we have a way to seamlessly slide anywhere on the spectrum between laziness and strictness, and it's all implemented entirely within Haskell in a way that is elegant and intuitive without the use of artificial and clumsy seq annotations.
# Robustness
The Frame implementation exposes all internals, yet this does not compromise safety or invariants in any way. The library's implementation is "correct-by-construction", meaning that you can extend it with your own features if you so choose, and you never have to worry about accidentally breaking any laws, such as the associativity of composition.
This has the following important practical benefits for finalization and folds:
• Finalizers never get duplicated or dropped
• Folds can be performed anywhere within the Stack, not just at the most downstream Frame, as the strict example illustrates.
• You can reason about each Frames finalization behavior completely independently of other Frames.
Composition elegantly handles every single corner case. This directly follows from strictly enforcing the Category laws, because categories have no corners! | {"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": 0.25458112359046936, "perplexity": 3911.3942110622165}, "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-2018-26/segments/1529267863206.9/warc/CC-MAIN-20180619212507-20180619232507-00230.warc.gz"} |
https://dsp.stackexchange.com/questions/62719/fourier-transform-of-the-full-morlet-wavelet | # Fourier Transform of the full Morlet wavelet
In 2014 someone asked here the Fourier transform of the Morlet wavelet; link below:
Fourier Transform of Morlet wavelet Function?
However, it was the approximated Morlet wavelet not written with the canonical Gaussian function.
Can somebody help to find the Fourier Transform of the full scaled Morlet wavelet below:
$$\psi_{\mu}(\tfrac{t}{\mu}) = \frac{1}{\mu} \times \frac{1}{\sqrt{2\pi} \, \sigma} \, e^{\frac{ -\left(\frac{t}{\mu} \right)^2}{2\sigma^2}} \big[e^{j\omega_c \frac{t}{\mu}}-e^{-\frac{1}{2} \omega_c^2}\big]$$
where $$\omega_c = 2\pi f_c$$ and $$f_c$$ is the centre or carrier frequency of the wavelet (the frequency to which the wavelet oscillates in the temporal domain). Also, $$\mu$$ is the scaling factor defined as $$\mu = \frac{\omega_c}{\omega_{\mu}}$$, where $$\omega_{\mu}$$ is the analysing frequency. Indeed, when $$\omega_{\mu} = \omega_{c} \Rightarrow \mu = 1$$ we have the mother Morlet wavelet.
In addition, the second term in the brackets is the correction term necessary to enforce zero mean to the Morlet wavelet.
I'd much appreciate a detailed step-by-step demonstration if possible to check where I'm getting stuck in my own demonstration. It could be done in a paper if quicker and a photo sent to me; I'll then publish here the full demonstration here.
Thanks in advance for any help.
• Welcome to SE.DSP. You have more chance to get an answer if you first detail your own demonstration, so that we can help detect the weaker spots – Laurent Duval Dec 20 '19 at 14:16
• Hi, I've tried several times but got stuck. – Jean Dec 20 '19 at 14:35
• Please show your work and where exactly you are getting stuck. Thanks! – Dan Boschen Dec 20 '19 at 15:24
• I've split the integral into two parts and try to take the Fourier of each separately for simplicity. I'm currently finishing writing up a paper and will show my work in a couple of days hopefully. Thanks – Jean Dec 20 '19 at 20:54
if you wanna do this with ordinary frequency $$f$$ (rather than angular frequency $$\omega$$) youcan start with
$$\mathscr{F}\Big\{ x(t) \Big\} \triangleq \int\limits_{-\infty}^{\infty} x(t) \, e^{-j 2 \pi f t} \, dt$$
$$\mathscr{F}\left\{ e^{-\pi t^2} \right\} = e^{-\pi f^2}$$
$$\mathscr{F}\left\{ e^{-\pi \alpha t^2} \right\} = \frac{1}{\sqrt{\alpha}} e^{-\frac{\pi}{\alpha} f^2} \qquad \alpha > 0$$
$$\mathscr{F}\left\{ e^{-\pi \alpha (t-\tau)^2} \right\} = \frac{1}{\sqrt{\alpha}} e^{-\frac{\pi}{\alpha} f^2} e^{-j 2 \pi f \tau}$$
• and this answer has a general gaussian Fourier transform. – robert bristow-johnson Dec 21 '19 at 6:05 | {"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": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8962541222572327, "perplexity": 607.585171423737}, "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/1600400198652.6/warc/CC-MAIN-20200920192131-20200920222131-00262.warc.gz"} |
https://oeis.org/wiki/User:Peter_Luschny/SeqTransformation | This site is supported by donations to The OEIS Foundation.
A sequence transformation and the Bernoulli numbers
KEYWORDS:Bernoulli, Euler, Tangent, Harmonic, Binomial, Swiss-Knife, Worpitzky, Akiyama–Tanigawa.
Concerned with sequences: A027641, A027642, A131689, A028246, A141056, A027760, A176276, A176277.
A sequence to sequence transformation
Given an sequence f, an integer n ≥ 0 and a formal symbol x let me define a sequence of polynomials
T := proc(f,n,x) local k,v;
v=0..k), k=0..n) end:
f1 xf1+f1−f2 x2f1+(2f1−2f2) x+2f3+f1−3f2 x3f1+(3f1−3f2)x2+(6f3+3f1−9f2)x−6f4+12f3+f1−7f2 x4f1+(4f1−4f2)x3+(12f3+6f1−18f2)x2 +(−24f4+48f3+4f1−28f2)x−60f4+50f3+f1−15f2+24f5
The sequence of coefficients of these polynomials, sorted in descending order, is
f1 f1 f1−f2 f1 2f1−2f2 f1−3f2+2f3 f1 3f1−3f2 3f1−9f2+6f3 f1−7f2+12f3−6f4 f1 4f1−4f2 6f1−18f2+12f3 4f1−28f2+48f3−24f4 f1−15f2+50f3−60f4+24f5
It is this sequence (the triangle read by rows) which I call the transform of f. f will usually be a sequence of integers or a sequence of rationals numbers. As a first check let us see on which sequence the identity function f: x -> x is mapped.
1
1, -1
1, -2, 1
1, -3, 3, -1
1, -4, 6, -4, 1
1, -5, 10, -10, 5, -1
A signed Pascal triangle, no big surprise, but a good start. Now let us take some more interesting input sequences. What about f(n) the harmonic numbers?
H := proc(n) local i; add(1/i, i=1..n) end;
T(H, n, x) starts:
1
x - 1/2
x^2 - x + 1/6
x^3 - 3/2 x^2 + 1/2 x
We get the Bernoulli polynomials!
And feeding the transformation with twice the sum of the inverse powers of 2?
G := proc(n) local i; 2*add(1/2^i, i=1..n) end:
T(G, n, x) starts:
1
x - 1/2
x^2 - x
x^3 - 3/2 x^2 + 1/4
We get the Euler polynomials!
I give one more example, perhaps the most interesting one. Let
C := m -> if irem(m,4) = 0 then 0
else 1/((-1)^iquo(m,4)*2^iquo(m-1,2)) fi:
Interesting because the polynomials generated have integer coefficients:
1
x
x^2 - 1
x^3 - 3 x
x^4 - 6 x^2 + 5
x^5 - 10 x^3 + 25 x
x^6 - 15 x^4 + 75 x^2 - 61
The Swiss knife polynomials!
If we evaluate these polynomials at 0 and 1 we get, respectively,
1, 0, -1, 0, 5, 0, -61, 0, 1385, 0, -50521, 0, 2702765, ...
1, 1, 0, -2, 0, 16, 0, -272, 0, 7936, 0, -353792, 0, ...
I am sure you know these sequences. For the purpose of reference I restyle the most important special case in math-parlance.
Let Bn(x) be the Bernoulli polynomials and Hn the harmonic numbers.
${\displaystyle B_{n}(x)=\sum _{k=0}^{n}\sum _{v=0}^{k}(-1)^{v}{\binom {k}{v}}H_{k}(x+v+1)^{n}\ .}$
I searched in the literature but could not find this formula. So I showed the formula in the newsgroup de.sci.mathematik; however, no one could provide a reference. If you know a reference for this formula, please let me know (the proof is easy once you see the formula on the blackboard...).
The case x = 1 can also be written with the Riemann zeta function as
${\displaystyle n\zeta (1-n)=\sum _{k=0}^{n}\sum _{v=0}^{k}(-1)^{v+1}{\binom {k}{v}}H_{k+1}(v+2)^{n}\ .}$
This formula is valid for all n ≥ 0 provided for n = 0,1 the left hand side is understood as a limit value. By the way, this formula for the zeta values shows that the definition Bn = Bn(1) is to be preferred over the definition Bn = Bn(0) if you intend to go into the number theory business.
On the other hand, some concrete mathematicians refrain from this definition being fearful to introduce thereby confusion to the world. Clearly this is a very strange argument since Jakob Bernoulli himself used B1 = 1/2 as you can see from the facsimile on Wikipedia, and Jakob was a very concrete mathematician.
Bernoulli and Worpitzky numbers
But this is not the end of the story. Looking at the table given above we can equate the constant coefficients of the polynomials with the Bernoulli numbers.
B_0 = 1*H(1);
B_1 = 1*H(1)- 1*H(2); [Table 1]
B_2 = 1*H(1)- 3*H(2) +2*H(3);
B_3 = 1*H(1)- 7*H(2) +12*H(3)- 6*H(4);
B_4 = 1*H(1)- 15*H(2) +50*H(3)- 60*H(4)+ 24*H(5);
B_5 = 1*H(1)- 31*H(2) +180*H(3)- 390*H(4)+ 360*H(5)- 120*H(6);
Now this is shocking: the coefficients on the right hand side of this table are the Worpitzky numbers; however, it is not Worpitzky's representation! Worpitzky gave the following representation with J(n) = 1/n.
B_0 = 1*J(1);
B_1 = 1*J(1)- 1*J(2); [Table 2]
B_2 = 1*J(1)- 3*J(2) +2*J(3);
B_3 = 1*J(1)- 7*J(2) +12*J(3)- 6*J(4);
B_4 = 1*J(1)- 15*J(2) +50*J(3)- 60*J(4)+ 24*J(5);
B_5 = 1*J(1)- 31*J(2) +180*J(3)- 390*J(4)+ 360*J(5)- 120*J(6);
So what happens if we expand table 1? We get yet another sum representation of the Bernoulli numbers, with even simpler coefficients!
B_0 = 1*J(1)
B_1 = 0*J(1)- 1*J(2) [Table 3]
B_2 = 0*J(1)- 1*J(2)+ 2*J(3)
B_3 = 0*J(1)- 1*J(2)+ 6*J(3)- 6*J(4)
B_4 = 0*J(1)- 1*J(2)+ 14*J(3)- 36*J(4)+ 24*J(5)
B_5 = 0*J(1)- 1*J(2)+ 30*J(3)- 150*J(4)+ 240*J(5)- 120*J(6)
But wait a moment. Does table 1 and table 2 really amount to the same thing? Well, almost. In the first table B1 = −1/2 and in the second table B1 = 1/2. So the first case refers to a definition Bn = Bn(0) and the second case to a definition Bn = Bn(1). Apart from this the values in the tables are identical (as the two definitions differ only in this particular case).
Let us denote the coefficients in table 3 by V(n, k).
V(n, k)
1
0, -1
0, -1, 2
0, -1, 6, -6
0, -1, 14, -36, 24
0, -1, 30, -150, 240, -120
0, -1, 62, -540, 1560, -1800, 720
What we have to find is a formula for the V(n, k). This is not difficult if we look at the relationship with the signed Worpitzky numbers W(n, k) = (-1)^k k! {n+1|k+1}. Here {n|k} denotes the Stirling set numbers (aka. Sn,k of the second kind). Our formal definition is V(n, k) = Sum(j=k..n) W(n,j). Now we can restate our findings:
For n > 1
Bn = Sum(k=0..n) W(n, k) J(k+1)
= Sum(k=0..n) W(n, k) H(k+1)
= Sum(k=0..n) V(n, k) J(k+1).
The first identity is Wropitzky's, which we take as granted. J(k+1) = H(k+1) − H(k). So we can rewrite Wropitzky's sum as Sum(k=0..n) W(n, k)(H(k+1) − H(k)). Observe that Sum(k=0..n) W(n, k) H(k) = 0,-1,0,0,0,0,0,.. (starting at n = 0). Thus if n <> 1 we can simplify to Sum(k=0..n) W(n, k) H(k+1), which is the second identity. The third identity follows from W(n, k) = V(n, k) − V(n, k+1).
For those who would like to check the formulas with Maple:
W := proc(n,k) (-1)^k*combinat[stirling2](n+1,k+1)*k! end:
seq(bernoulli(n, 1),n=0..23);
seq(bernoulli(n, 0),n=0..23);
Inverse polynomial harmony for Jakob
Putting the transformation into a plotting bag ...
MyPlot := proc(f,R) local T,i;
*f(k+1)*(x+v+1)^n,v=0..k),k=0..n) end:
plot([seq(T(f,i,x),i=2..7)],x=R,thickness=2,axes=boxed) end:
... we can visualize the effect of the harmonic numbers versus the effect of the inverse numbers:
A := MyPlot(x->add(1/i, i=1..x),0..1):
B := MyPlot(x->1/x, -1..0):
plots[display]([A,B]);
Be careful when interpreting this plot: these are not the Bernoulli polynomials. This are two plots in one. The left hand side (the interval [-1,0]) is generated by feeding J(n) into the transformation, the right hand side (the interval [0,1]) by feeding H(n) into the transformation. Only on [0,1] this coincides with the Bernoulli polynomials.
A primer on Worpitzky numbers
• Worpitzky (n ≥ 0 and k ≥ 0)
• Definition
W := proc(n, k) stirling2(n+1,k+1)*k! end:
• Recursion
Wrec := proc(n, k) option remember;
if k > n then 0 elif n = 0 then 1
else k*Wrec(n-1, k-1) + (k+1)*Wrec(n-1, k) fi end:
• Egf
w := (x, y) -> exp(x)/(1+y*(1-exp(x)));
• V-Numbers (n ≥ 0 and k ≥ 0)
• Definition
V := proc(n, k) add(W(n, j), j=k..n) end:
• Recursion
Vrec := proc(n, k) option remember;
if k > n then 0 elif n = 0 then 1
else k*(Vrec(n-1, k-1) + Vrec(n-1, k)) fi end:
• Egf
v := (x, y) -> 1/(1+y*(1-exp(x)));
A challenger for the Akiyama–Tanigawa algorithm?
The Akiyama–Tanigawa algorithm is a cute way to compute the Bernoulli numbers.
AT := proc(n) local m, j, A;
for m from 0 by 1 to n do
A[m] := 1/(m + 1);
for j from m by -1 to 1 do
A[j - 1] := j * (A[j - 1] - A[j])
od od; A[0] end:
The sum representation Bn = Sum(k=0..n) V(n, k)/(k+1) and the recursion for V(n,k) suggest a similar algorithm.
VB := proc(n) local m, j, A;
if n = 0 then 1 else A[0] := 0; A[1] := 1;
for m from 2 by 1 to n do A[m] := 0;
for j from m by -1 to 1 do
A[j] := j * (A[j - 1] + A[j])
od od;
An advantage of the VB algorithm over the AT algorithm is that it postpones rational arithmetic to the computation of the sum (the A[j]'s in AT are rational numbers, the A[j]'s in VB are integers). Does this make a noticeable difference? Let us benchmark! I used the two procedures as given above; however, I replaced 'end:' by 'NULL; end:' to suppress the output. On my personal computer with Maple V Release 5 I got the following results (times in seconds):
n AT VB 100 0.047 0.016 200 0.594 0.187 400 7.656 1.203 800 92.766 9.376
VB is up to ten times faster! This is fun. ;-)
New sequences for the OEIS
Based on the above considerations I will submit the following sequences to the OEIS.
0,
0, 1,
0, 3, -3,
0, 7, -18, 11,
0, 15, -75, 110, -50,
0, 31, -270, 715, -750, 274,
0, 63, -903, 3850, -7000, 5754, -1764,
0, 127, -2898, 18711, -52500, 72884, -49392, 13068,
This triangle is (up to sign) Worpitzky(n,k)Harmonic(k) as well as Stirling1(k+1,2)Stirling2(n+1,k+1) for n ≥ 0 and k ≥ 0. The fact that the sum of the rows is 0,1,0,0,0,... was a crucial step in some part of the proof above. The triangle should be supplemented by the sequence 0,1,3,18,125,1020,9667,104790,.. which is the sum over the odd k's in a row. (Who comes up with a combinatorial interpretation?!) Note that the right hand side of the triangle is A000254 resp. A081048.
The sequences now are : A176276 and A176277. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 2, "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": 0.9400209784507751, "perplexity": 2753.765473970781}, "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-2018-09/segments/1518891812327.1/warc/CC-MAIN-20180219032249-20180219052249-00455.warc.gz"} |
https://zbmath.org/?q=an:1337.53001 | ×
# zbMATH — the first resource for mathematics
Differential geometry of special mappings. (English) Zbl 1337.53001
Olomouc: Palacký University, Faculty of Science (ISBN 978-80-244-4671-4/pbk). 566 p. (2015).
This is a collective work of several authors aiming to present several advances in the theory of special maps between Riemannian manifolds. The central theme are geodesic maps between various classes of Riemannian manifolds. These are diffeomorphisms between Riemannian/affine manifolds that send geodesics to geodesics. The book contains fifteen chapters written by various authors. The first five chapters are devoted to fundamentals about topological and smooth manifolds. Chapters 6–11 are devoted to an extensive analysis of geodesic maps between Riemannian manifolds with various extra structure (e.g., Einstein, Kähler, hypersurfaces in Riemannian manifolds, etc). Chapter 12 treats $$F$$-planar maps, Chapter 13 deals with holomorphically projective maps, and finally Chapters 14 and 15 are devoted to almost geodesic maps and some generalizations. The book contains interesting comments, not only of historical but also of mathematical nature (e.g., the discussion about the definition of geodesics is quite interesting).
##### MSC:
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry 53A99 Classical differential geometry 53C99 Global differential geometry 53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics) 53B05 Linear and affine connections 53B10 Projective connections 53B20 Local Riemannian geometry 53C22 Geodesics in global differential geometry | {"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": 0.31849074363708496, "perplexity": 1531.7126138627473}, "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-2021-49/segments/1637964363520.30/warc/CC-MAIN-20211208175210-20211208205210-00454.warc.gz"} |
https://tilings.math.uni-bielefeld.de/glossary/substitution-matrix/ | ## Substitution Matrix
To a substitution $s$ with prototiles $T_1, \ldots T_m$ we assign the substitution matrix $M_s = (m_{ij})_{i,j = 1,\ldots ,m}$, where $m_{ij}$ is the number of copies of $T_i \in s(T_j)$. The substitution matrix carries a lot of information about the tilings arising from $s$. For simplicity, let’s assume the tilings are volume hierarchic. Then the eigenvector of $M_s$ which is largest in modulus is $q^d$; i.e., the inflation factor $q$ of $s$ to the dimension $d$. Note that this is true in any dimension $d$. If $M_s$ is primitive, then by the Perron-Frobenius theorem this largest eigenvalue is real, positive and unique. In this case, the corresponding (right) eigenvector contains the relative frequencies of the prototiles. Moreover, the left eigenvector (resp. the eigenvector of the transpose of $M_s$, if you don’t like left eigenvectors) contains the $d$-dimensional volumes of the prototiles. Further properties of the tilings can be derived from the algebraic properties of $q$, hence from the $d$-th root of the leading eigenvector of $M_s$ (for instance, see PV number). | {"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": 0.9920026063919067, "perplexity": 168.63429904517082}, "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/1659882572043.2/warc/CC-MAIN-20220814143522-20220814173522-00430.warc.gz"} |
https://www.groundai.com/project/multiplexing-scheme-for-simplified-entanglement-based-large-alphabet-quantum-key-distribution/ | Multiplexing scheme for simplified entanglement-based large-alphabet quantum key distribution
# Multiplexing scheme for simplified entanglement-based large-alphabet quantum key distribution
## Abstract
We propose a practical quantum cryptographic scheme which combines high information capacity, such as provided by high-dimensional quantum entanglement, with the simplicity of a two-dimensional Clauser-Horne-Shimony-Holt (CHSH) Bell test for security verification. By applying a state combining entanglement in a two-dimensional degree of freedom, such as photon polarization, with high-dimensional correlations in another degree of freedom, such as photon orbital angular momentum (OAM) or path, the scheme provides a considerably simplified route towards security verification in quantum key distribution (QKD) aimed at exploiting high-dimensional quantum systems for increased secure key rates. It also benefits from security against collective attacks and is feasible using currently available technologies.
## I Introduction
Cryptography is one of the most promising applications of quantum science Ekert (1991). With the recent demonstrations of high-dimensional two-photon entanglement using time bins Stucki et al. (2005); Ali-Khan and Howell (2006) and OAM Dada et al. (2011); Krenn et al. (2014), large-alphabet entanglement-based quantum key distribution (QKD) systems become closer to their real-world implementations and applications. The traditional approach to large-alphabet QKD based on Bell’s theorem involves encoding a key in a high dimensional degree of freedom, such as photon OAM, and verifying the security of the generated key using a test of a Bell inequality which requires projective measurements in high-dimensional mutually unbiased bases Klimov et al. (2009). This is a straighforward generalization of the original protocol introduced by Ekert in 1991 (E91) Ekert (1991); Kaszlikowski et al. (2003) and its modifications, such as proposed in Ref. Acin et al. (2006).
E91-based protocols have been demonstrated for qubits using polarisation Ling et al. (2008) and using time-energy entanglement Tittel et al. (2000). A Bell-type test of energy-time entangled qutrits has also been realised Thew et al. (2004). Reported Bell-test-based QKD experiments using OAM qutrits Gröblacher et al. (2006) have implemented a randomized selection of dichotomous measurements instead of full projective measurements in a 3-dimensional state space. Although projective measurement for detection of high-dimensional OAM states of light with up to 11 different outcomes is now within reach Berkhout et al. (2010); Lavery et al. (2011), it still remains an experimental challenge to perform them in arbitrary qudit bases. In the case of high-dimensional time-bin states, such unitary operations would require multi-path interferometric setups which become too cumbersome to implement for a high number of dimensions. Although a scheme for large-alphabet QKD has been proposed and realized using energy-time entanglement Ali-Khan et al. (2007), the applicability of this scheme is specific to this kind of entanglement and the security verification is highly device dependent as it places stringent conditions on timing resolutions of the detectors, which limits key generation rates.
Security verification of quantum key distribution schemes is a complicated problem in general. Security proofs have been provided for Bell-test-based QKD against the so-called collective attacks Biham and Mor (1997a) as well as the most general coherent attacks in the standard security scenarios Acín et al. (2007). However, proofs of device-independent security against these sophisticated attacks are not yet available in the case of entangled qudits requiring Bell tests generalised to high-dimensions Pironio et al. (2009).
Here, we propose an approach to large-alphabet entanglement-based QKD which circumvents these problems by avoiding the need to perform high-dimensional unitary rotations required for measurements in different mutually unbiased bases, resulting in a much simplified measurement setup. The scheme presented here also benefits from security proofs for QKD based on entangled qubits against collective attacks. Our approach is in principle applicable to any system in which it is possible to create bipartite two-dimensional entanglement in one degree of freedom and high-dimensional correlations in another. Although we will use an example with photon polarization and OAM to illustrate the protocol, the principle can be applied to other systems using other degrees of freedom to encode large secret keys.
The very essence of large-alphabet QKD is the possibility of a large rate of key generation. In practice, for a given entanglement-based QKD system, the minimum applicable coincidence detection time window is an important factor limiting the maximum rate at which it is possible to generate secure keys per run, i.e., a single transmission and detection of the source state. The higher the number of dimensions offered by the source state, the higher the maximum possible key rate per run for a given . The development of OAM sorters makes genuine large-alphabet key generation using up to 11-dimensional OAM entanglement feasible. This will also allow for a higher data rate per photon pair, as the detection of the photonic qudits would not need to be implemented as (probabilistic) dichotomous measurements as has been the case in previous experiments Gröblacher et al. (2006); Dada et al. (2011). It is also straightforward to implement projective measurements in computational (unrotated) time-bin bases. In what follows, we will first describe the existing generalizations of the E91 protocol. We will then describe the source state, measurement setup, and security considerations for our proposed scheme. Finally, we will conclude with a few remarks on the realizability of the proposed experimental implementations.
## Ii Generalized E91 protocol
To establish our scheme, let us first review the basic entanglement-based large-alphabet QKD resulting from a direct generalization of the E91 protocol and its variants. Assume a source producing photon pairs in the state
|Φ⟩=1√dd−1∑j=0|j⟩A⊗|j⟩B. (1)
Here we use the notation , where denotes tensor product. In terms of OAM eigenstates for example, this may be written as the maximally entangled state
|Φ⟩=1√dℓ=+[d/2]∑ℓ=−[d/2]h(ℓ)|ℓ⟩A⊗|−ℓ⟩B, (2)
where for all when is odd, and , when is even.
In a Bell inequality test experiment, each of the communicating parties ‘Alice’ (A) and ‘Bob’ (B) will have a photon OAM detector with outcomes per setting and two settings/measurements: and respectively, which maximize Bell inequality violation. For the QKD scheme, there is an additional setting for each detector, i.e., for Alice and for Bob, chosen to produce perfect correlations. In a variant of Ekert’s scheme modified for increased key generation efficiency Acin et al. (2006); Acín et al. (2007); Pironio et al. (2009), only Alice’s detector uses an additional setting, i.e., , which is chosen to produce perfect correlations when Bob measures with setting for the purpose of key generation. Although our scheme is directly applicable to this higher-efficiency version, we mainly illustrate here using Ekert’s scheme for clarity.
Alice and Bob independently choose their settings at random and also note their detection results independently. After sufficiently many measurement runs, Alice and Bob perform basis reconciliation through one-way classical post processing Kraus et al. (2005), followed by privacy amplification on the raw key.
When the combination (or ) is selected by Alice and Bob, the measurement results are used for the secret key as they are perfectly correlated on both sides. To determine the security of this key, the correlation in the rest of the data will be checked for eavesdropping through a Bell inequality test, for example using Bell inequalities generalised to -outcomes per measurement proposed by Collins et al. Collins et al. (2002), equivalent to the CHSH-Bell inequality Clauser et al. (1969) when . Only cases in which the combination of measurement settings involve and are used for this test, while the remaining results are discarded. After basis reconciliation, Bob announces his data for the Bell inequality check, and Alice computes the value of the Bell parameter . If , then the key is secure and the eavesdropper, Eve, will not have gained any useful information on the key. The secret key can then be used in any cryptographic communication between Alice and Bob.
Implementing the above requires full projective measurements in the OAM state basis in a -dimensional subspace, corresponding to . This may be realized, e.g. for up to using OAM mode sorters as mentioned above. However, full projective measurements whose operators have eigenstates which are OAM superpositions are also required. It is nontrivial to realize such measurements because it requires a unitary operation within the high-dimensional OAM subspace being considered before the OAM detection. The implementations of such operations are difficult to derive in general, and have not yet been realized experimentally.
## Iii Proposed scheme
### iii.1 State preparation
We propose a state which replaces the need for measurements in high-dimensional rotated bases with the simplicity of a two-dimensional CHSH Bell test for the verification of the security of generated key. To appreciate how our source state relates to hybrid entangled states, consider the state expressed in terms of the composite OAM and polarisation basis states (where denotes the OAM, ; and denotes the prolarization ) as
|Φϵ⟩=1√2dn=+[d/2]∑n=−[d/2] Missing or unrecognized delimiter for \right +|2n−1,V⟩A|−2n+1,V⟩B, (3)
with for even . Note that this state combines -dimensional orbital angular momentum entanglement and polarization entanglement in a way similar but quite different from the cases of the so-called hyper-entangled Barreiro et al. (2005), hypoentangled 1 or entangled entangled Walther et al. (2006) states. In hyper-entanglement, a measurement of OAM will not destroy polarization entanglement and vice versa. In hypoentanglement, measuring either polarization or OAM destroys entanglement in the other degree of freedom. Here measuring OAM completely destroys polarization entanglement, but the converse is not true. We note that the division of the subspaces (e.g. into odd and even OAM parities in this example) can also be done in other ways, depending on the specific realization and experimental convenience. State (III.1) can be rewritten, as
|Φϵ⟩=1√dn=[d/2]∑n=−[d/2]|ϕ⟩n, n≠0 for even d. (4)
Here is an entangled state within the th OAM subspace. Although this state is (hypo)entangled in both polarization and OAM, only the classical correlation in OAM is strictly necessary for our scheme.
Source state: Our source state is of the form
|Φdsϵ⟩P/D=n=[d/2]⨂n=−[d/2]|ϕ⟩P/Dn, (5)
Where is an entangled state in polarisation within an OAM subspace specified by . The source state could be obtained either by post-selection or deterministically (denoted by superscripts P and D respectively) as outlined below.
#### State preparation: Post-selective case
Suppose we define
|ϕ⟩Pn =(|HA,HB⟩n+|VA,VB⟩n)/√2, where (6) |HA,HB⟩n =|2n,H⟩A⊗|−2n,H⟩B |HA,VB⟩n =|2n,H⟩A⊗|−2n+1,V⟩B |VA,HB⟩n =|2n−1,V⟩A⊗|−2n,H⟩B |VA,VB⟩n =|2n−1,V⟩A⊗|−2n+1,V⟩B. (7)
Note that this state is a combination of photon pairs, with each pair hypoentangled in both polarisation and OAM in unique OAM subspaces.
A source state for our scheme [of the form Eq. (5)] could be obtained by post-selection from
|Φdϵ⟩=|Φϵ⟩⊗d, (8)
which is a product state of pairs of OAM-entangled photons where is the two-photon state expressed in Eq. (III.1). A proposed scheme to obtain from common spontaneous parametric down conversion (SPDC) sources is illustrated in Fig. 1(a). This involves generating OAM entanglement by type-I collinear parametric downconversion with a defined polarization, say horizontal (). The co-propagating photon pairs entangled in OAM are passed through an OAM parity (even/odd) sorter Leach et al. (2002). A half-wave plate is then inserted after one of the output arms which rotates to vertical polarization , coupling OAM parity to polarization. The state represented in Eq. (8) could then be generated by choosing parameters of the SPDC source to create more than one entangled photon pair simultaneously. It is well known that a desired probability of multiple pair generation per pump pulse can be achieved according to the theoretical -pair creation probability Kok and Braunstein (2000)
pd=(d+1)sech4(τ)tan2d(τ), (9)
where is a real-valued coupling coefficient which is proportional to the product of the pump amplitude and the coupling constant between the electromagnetic field and the nonlinear crystal. The source state for our scheme can then be obtained by final postselection on state represented by Eq. (III.1). This can be done by registering only the values of for which both Alice and Bob have a single detection each per OAM subspace in one run. To achieve this, it suffices to use detectors which distinguish between zero, one, and more than one photon. Such detectors have been experimentally demonstrated Kwiat et al. (1994); Takeuchi et al. (1999). Also, actual photon-number-resolving detectors have been realised (e.g., see Kardynał et al. (2008); Dauler et al. (2009)) with increased detection efficiencies Calkins et al. (2013).
#### State preparation: Deterministic case
A more suitable approach, however, is to prepare the source state in a deterministic way by, e.g., using an array of polarization-entangled-photon sources (EPS) generating exactly one photon pair at a time. Existing semiconductor quantum dot (QD) systems provide a suitable platform for single photon generation Akopian et al. (2006); Stevenson et al. (2006), as well as generation of entangled photon pairs on demand with high efficiency MullerM. et al. (2014). Rapid experimental progress is also being made towards implementing arrays consisting of several QD high-fidelity-entangled-photon-pair emitters on the same chip Juska et al. (2013). Here, we propose a setup utilising EPS (see Fig. 2). OAM of , for example, is then individually imprinted on photons emitted by the source to yield state , resulting in basis states that are assigned as shown below. The photons in an entangled pair are usually generated using the biexciton-exciton-vacuum cascade, and are separable based on their wavelength. Individual photons from different pairs may then be combined into one beam using an OAM combiner (i.e., a coherent OAM sorter operated in reverse) to obtain the source state [Eq. (5)]. For this case, the entangled state within the th subspace defined as
|ϕ⟩Dn =(|HA,HB⟩′n+|VA,VB⟩′n)/√2, where (10) |HA,HB⟩′n Missing or unrecognized delimiter for \right |HA,VB⟩′n Missing or unrecognized delimiter for \right |VA,HB⟩′n Missing or unrecognized delimiter for \right |VA,VB⟩′n Missing or unrecognized delimiter for \right (11)
We note that the source state[Eq. 5] is essentially the same for both the probabilistic and deterministic preparations except for a change in the basis state assignment of the OAM measurement. This basis selection is simply for the convenience of experimental implementation specific to each method of state preparation.
### iii.2 Measurement settings
As in the standard case for the generalised E91 protocol described in Section II, our scheme using the state (5) also involves three measurement settings randomly and independently chosen by Alice and Bob. However, the settings and are now achieved using polarization measurements for maximal CHSH-Bell inequality violation. These measurement settings each have two outcomes “+” and “-”. For key generation, and , (or and ) are the same as described above. An important aspect of our scheme is to perform both key generation and Bell tests individually in each th subspace (or channel), and simultaneously for all , using the same Bell-test setup.
#### Measurement: Post-selective case
To achieve the simultaneous measurements for the case of the non-deterministic state preparation outlined in Section III.1.1 above, Alice and Bob need to first perform local operations which make the respective OAM states degenerate for orthogonal polarisations of Alice’s and Bob’s photons within each th subspace, i.e., to disentangle the polarisation and OAM degrees of freedom. This can be achieved if, e.g., Alice (Bob) subtracts (adds) of OAM for the vertically polarised photons [using the combination of PBS1, SLM1 and PBS2 in Fig. 1 (b)]. This operation by Alice and Bob can be described by the transformations and where
^QA = Missing or unrecognized delimiter for \left (12) ^QB = Missing or unrecognized delimiter for \left
Note that this only causes a transformation of the basis states defined in Eq. (III.1.1) as follows,
|HA,HB⟩n ^QA⊗^QB−−−−−→|HA,HB⟩Qn=|2n,H⟩A⊗|−2n,H⟩B, |HA,VB⟩n ^QA⊗^QB−−−−−→|HA,VB⟩Qn=|2n,H⟩A⊗|−2n,V⟩B, |VA,HB⟩n ^QA⊗^QB−−−−−→|VA,HB⟩Qn=|2n,V⟩A⊗|−2n,H⟩B, |VA,VB⟩n ^QA⊗^QB−−−−−→|VA,VB⟩Qn=|2n,V⟩A⊗|−2n,V⟩B. (13)
A combination of a HWP and a PBS can now carry out the Bell-test polarisation measurements ( or ) for each value of .
We can write the CHSH inequality in the th subspace as
Sn=En(A1,B1)−En(A1,B2)+En(A2,B1)+En(A2,B2)≤2, (14)
where the correlation coefficients of the measurement performed by Alice and by Bob are defined as
En(Ai,Bj)=Pn(Ai=Bj)−Pn(Ai≠Bj). (15)
and are probabilities for equal and unequal outcomes respectively, determined experimentally using the coincidence rates within each th subspace. The detector settings for the CHSH Bell inequality violation could be specified as measurements in the bases , where
|m+(θ)⟩= −cos(2θ)|±2n,H⟩+sin(2θ)|±2n,V⟩, |m−(θ)⟩= sin(2θ)|±2n,H⟩+cos(2θ)|±2n,V⟩. (16)
In the sign above, ‘’ applies to Alice and ‘’ applies to Bob. A half-wave plate oriented at an angle rotates the measurement basis of a polarizing beam splitter (PBS) i.e., to . If we set
θa1=0, θa2=π/8, θb1=π/16, and θb2=3π/16 (17)
as values of for and respectively so that Alice and Bob always measure in bases which are mutually unbiased with respect to each other, then we will ensure the commutativity of Alice’s and Bob’s measurement outcomes and get the maximal violation of for each th subspace of state (5). Using the basis notation defined above [Eq. (III.2.1)], the corresponding Bell operator Braunstein and Mann (1995); Braunstein et al. (1992); Acín et al. (2002) can be written as
^Sn= √2(|HA,HB⟩Qn⟨HA,HB|Qn+|VA,VB⟩Qn⟨VA,VB|Qn +|HA,HB⟩Qn⟨VA,VB|Qn+|VA,VB⟩Qn⟨HA,HB|Qn −|HA,VB⟩Qn⟨HA,VB|Qn−|VA,HB⟩Qn⟨VA,HB|Qn +|HA,VB⟩Qn⟨VA,HB|Qn+|VA,HB⟩Qn⟨HA,VB|Qn). (18)
Obtaining the statistical data for the Bell test requires either carrying out a detection which resolves both polarisation and OAM or, as illustrated in Figure 1 (b), reversing operation to re-establish OAM-polarisation entanglement (using SLM2 and PBS4), and then carrying out OAM detection. We define the operations to reverse as
^Q−A = Missing or unrecognized delimiter for \left (19) ^Q−B = Missing or unrecognized delimiter for \left
Since the state within the th subspace [Eq. (6)] is maximally entangled, it gives a maximal violation of the CHSH inequality based on operator (III.2.1)
Sn(|ϕ⟩n⟨ϕ|n)=Tr(^Sn|ϕ⟩n⟨ϕ|n)=2√2≥2. (20)
#### Measurement: Deterministic case
When the state is prepared deterministically as described in Section III.1.2, operators and [Eqs. (12) and (19)] are not necessary for the measurements. As in the non-deterministic case, the Bell test is carried out using a combination of a HWP and PBS [see Fig. 2 (b)], but photon number resolution and final postselection are not required. Due to the difference in basis assignment in this case, we redefine the detector settings for the CHSH Bell inequality violation as measurements in the bases , where
|m+(θ)⟩′= −cos(2θ)|n,H⟩+sin(2θ)|n,V⟩, |m−(θ)⟩′= sin(2θ)|n,H⟩+cos(2θ)|n,V⟩. (21)
The optimum settings (specified by ) for the HWP are the same as in Eq. (17) above, and the resulting Bell operator for this case [see Eq. (III.1.2)] is
^Sn= √2(|HA,HB⟩′n⟨HA,HB|′n+|VA,VB⟩′n⟨VA,VB|′n Missing or unrecognized delimiter for \left Missing or unrecognized delimiter for \left Missing or unrecognized delimiter for \left (22)
The state represented by Eq. (10) is also maximally entangled within the th subspace for this case, and it gives a maximal violation of the CHSH inequality based on operator (III.2.2) when the key has not been eavesdropped.
### iii.3 Security against collective attacks
Any eavesdropping of the key is essentially a measurement strategy that will destroy polarisation entanglement which is used to establish the key. This in turn degrades the CHSH Bell inequality violation Ekert (1991) in any respective OAM subspaces. A collective attack is one in which the eavesdropper (Eve) applies the same operation on each of Alice’s and Bob’s particles, but has no other limitations. In particular, she is allowed to have access to a string of qubits from Alice/Bob at one time, and to other dimensions of their particle states, even possibly unknown to Alice/Bob. Since Eq. (5) is a product state of entangled qubits pairs, our scheme is essentially a multiplexing of multiple polarisation-entangled qubit pairs by means of a higher-dimensional degree of freedom, followed by independently testing the CHSH Bell inequality simultaneously—Eve’s access to one or more source states in our scheme is equivalent to her access to a string of qubits on which she can perform joint (coherent) measurements. Therefore, the security of our scheme is completely guaranteed by the security of the individual qubit-based schemes against collective attacks Biham and Mor (1997a). This, in turn, implies security against the most general, so-called coherent attacks Biham and Mor (1997a, b) if an application of the exponential quantum de Finetti theorem can be made Renner (2007). This is indeed the case in our scheme (under the assumption of finite-dimensional subsystems) because our source state is invariant under permutation of Alice and Bob, and their measurement outcomes are commutative, as mentioned above [Eq. (17)]. These results apply fully to our large-alphabet protocol since it is equivalent to simultaneous but independent 2-qubit secure protocols. The total bit rate generated securely against collective attacks as a function of Bell parameters can therefore be written as Acín et al. (2007)
r≥∑n1−h(Qn)−h(1+√(Sn/2)2−12) (23)
where is the binary entropy and is the quantum bit error rate for channel . As shown in Fig. 3, the larger the measured Bell violation, the higher the secure key rate per run. Our scheme gives a -fold enhancement over the traditional 2-qubit schemes as a large-alphabet scheme, but uses a much simplified Bell-test measurement setup compared to traditional large-alphabet schemes.
The implications of loopholes for QKD based on Bell’s theorem is worthy of some mention here. Closing the locality loophole in general requires enforcing a space-like separation between Alice and Bob as required for testing non-locality Aspect et al. (1982), but in the context of our QKD scheme, it would be sufficient to guarantee that no quantum signals can travel from Alice to Bob by ensuring proper isolation of Alice’s and Bob’s locations Pironio et al. (2009). Also, a proper closure of the detection loophole is required for completely guaranteed security. This seems promising as it has already been achieved in a photon-based Bell-test experiment Giustina et al. (2013).
## Iv Conclusion
Our scheme offers significant advantages over current generalised E91 schemes. It results in a greatly simplified security verification and key generation setup which does not get more complicated with increasing , except for an increase in the number of output ports of the OAM sorting device. It thereby provides a route to boosting the secure key rates in entanglement-based QKD without the usual increased complexity of Bell tests in high dimensions. It also benefits from the relative tolerance two-dimensional Bell tests to measurement error. Although it is known that the amount of violation for an actual -dimensional Bell test increases with , these increments are marginal even in the ideal case, and level off as increases Collins et al. (2002); Dada and Andersson (2011). Also, the high sensitivity of the complicated measurement setup to errors will usually overwhelm these increments even for modest values of , resulting in smaller violations than in the qubit case. Another advantage of our scheme where an SPDC source is used is that non-maximal high-dimensional entanglement will not generally degrade the the verification of security. For example, the spiral bandwidth Torres et al. (2003) of the SPDC source will not generally degrade Bell violation, but will only limit the effective number of OAM channels in the non-deterministic case. Whereas, if generalised OAM-based Bell tests are used without procrustrean filtering, then a small spiral bandwidth might cause a failure of the Bell test for an entangled state Dada et al. (2011).
In summary, this paper has described a practical scheme in which a single CHSH-Bell test setup combined with a full projective measurement is sufficient for security verification even for a large-alphabet scheme capable of arbitrarily large key rates per run. The scheme is simpler to implement than existing generalizations of E91 protocol to high-dimensions because it circumvents measurements in mutually unbiased bases in high dimensions, while maintaining capacity for large key-rate and security against collective attacks. A second significant advantage is that non-maximal high-dimensional entanglement will not necessarily degrade the verification of security. We point out that the scheme is realisable using current technology by mentioning two examples for generating applicable source states, namely, spontaneous parametric downconversion and, more suitably, source of single pairs of entangled photons, such as semiconductor quantum dots. From the point of view of real-world applications of high-dimensional QKD based on photon OAM in free space, judicious selection of basis states Pors et al. (2011); Malik et al. (2012) will increase resilience against decoherence induced by atmospheric turbulence in a free space implementation. Although this can be applied within the framework of this scheme, implementations with time bins Tittel et al. (2000); Marcikic et al. (2004) or path appear especially promising for long distance applications. The complexity of security verification in large-alphabet entanglement-based QKD makes it apparent that the simplified scheme presented here will likely enable otherwise infeasible secure key rates in QKD, enabling more practical implementations of entanglement-based technologies.
## V Acknowledgements
The author acknowledges the Engineering and Physical Sciences Research Council [EPSRC (grant numbers: EP/I023186/1, EP/K015338/1)] and the Scottish Universities Physics Alliance (SUPA) for funding, Prof. Brian Gerardot and Prof. Gerald Buller for support, and Dr. Ryan Warburton, Dr. Jonathan Leach and Prof. Miles Padgett for stimulating discussions.
### Footnotes
1. N. K. Langford, Ph.D. thesis, Univ. of Queensland (2007)
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https://deeplearning.neuromatch.io/tutorials/W3D4_BasicReinforcementLearning/student/W3D4_Tutorial2.html | # Tutorial 2: Learning to Act: Multi-Armed Bandits¶
Week 3, Day 4: Basic Reinforcement Learning (RL)
Content creators: Marcelo G Mattar, Eric DeWitt, Matt Krause, Matthew Sargent, Anoop Kulkarni, Sowmya Parthiban, Feryal Behbahani, Jane Wang
Content reviewers: Ella Batty, Byron Galbraith, Michael Waskom, Ezekiel Williams, Mehul Rastogi, Lily Cheng, Roberto Guidotti, Arush Tagade, Kelson Shilling-Scrivo
Production editors: Gagana B, Spiros Chavlis
# Tutorial Objectives¶
Estimated timing of tutorial: 45 min
In this tutorial we will model the simplest types of acting agents. An acting agent can affect how much reward it receives, so it must learn how to identify the actions that lead to the most reward. You will use ‘bandits’ to understand the fundamentals of how a policy interacts with the learning algorithm in reinforcement learning.
• You will understand the fundamental tradeoff between exploration and exploitation in a policy.
• You will understand how the learning rate interacts with exploration to find the best available action.
## Tutorial slides¶
These are the slides for all videos in this tutorial.
# Setup¶
## Install dependencies¶
# @title Install dependencies
from evaltools.airtable import AirtableForm
# Imports
import numpy as np
import matplotlib.pyplot as plt
## Figure Settings¶
#@title Figure Settings
import ipywidgets as widgets # interactive display
%config InlineBackend.figure_format = 'retina'
## Plotting Functions¶
#@title Plotting Functions
np.set_printoptions(precision=3)
def plot_choices(q, epsilon, choice_fn, n_steps=1000, rng_seed=1):
np.random.seed(rng_seed)
counts = np.zeros_like(q)
for t in range(n_steps):
action = choice_fn(q, epsilon)
counts[action] += 1
fig, ax = plt.subplots()
ax.bar(range(len(q)), counts/n_steps)
ax.set(ylabel='% chosen', xlabel='action', ylim=(0,1), xticks=range(len(q)))
def plot_multi_armed_bandit_results(results):
fig, (ax1, ax2, ax3) = plt.subplots(ncols=3, figsize=(20, 4))
ax1.plot(results['rewards'])
ax1.set(title=f"Total Reward: {np.sum(results['rewards']):.2f}",
xlabel='step', ylabel='reward')
ax2.plot(results['qs'])
ax2.set(xlabel='step', ylabel='value')
ax2.legend(range(len(results['mu'])))
ax3.plot(results['mu'], label='latent')
ax3.plot(results['qs'][-1], label='learned')
ax3.set(xlabel='action', ylabel='value')
ax3.legend()
def plot_parameter_performance(labels, fixed, trial_rewards, trial_optimal):
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(16, 6))
ax1.plot(np.mean(trial_rewards, axis=1).T)
ax1.set(title=f'Average Reward ({fixed})', xlabel='step', ylabel='reward')
ax1.legend(labels)
ax2.plot(np.mean(trial_optimal, axis=1).T)
ax2.set(title=f'Performance ({fixed})', xlabel='step', ylabel='% optimal')
ax2.legend(labels)
# Section 1: Multi-Armed Bandits¶
## Video 1: Multi-Armed Bandits¶
Consider the following learning problem. You are faced repeatedly with a choice among $$k$$ different options, or actions. After each choice you receive a reward signal in the form of a numerical value, where the larger value is the better. Your objective is to maximize the expected total reward over some time period, for example, over 1000 action selections, or time steps.
This is the original form of the k-armed bandit problem. This name derives from the colloquial name for a slot machine, the “one-armed bandit”, because it has the one lever to pull, and it is often rigged to take more money than it pays out over time. The multi-armed bandit extension is to imagine, for instance, that you are faced with multiple slot machines that you can play, but only one at a time. Which machine should you play, i.e., which arm should you pull, which action should you take, at any given time to maximize your total payout.
While there are many different levels of sophistication and assumptions in how the rewards are determined, we will consider here the simple scenario where each action results in a reward drawn from a different Gaussian distribution with unknown mean and unit variance. Since each action is associated with a different mean reward, the goal of the agent is to find the action with highest mean. But since the rewards are noisy (the corresponding Gaussians have unit variance), those means cannot be determined from a single observed reward.
This problem setting is referred to as the environment. We will solve this optimization problem with an agent, in this case an algorithm that takes in rewards and returns actions.
# Section 2: Choosing an Action¶
Estimated timing to here from start of tutorial: 10 min
The first thing our agent needs to be able to do is choose which arm to pull. The strategy for choosing actions based on our expectations is called a policy (often denoted $$\pi$$). We could have a random policy – just pick an arm at random each time – though this doesn’t seem likely to be capable of optimizing our reward. We want some intentionality, and to do that we need a way of describing our beliefs about the arms’ reward potential. We do this with an action-value function
(114)$$$q(a) = \mathbb{E} [r_{t} | a_{t} = a]$$$
where the value $$q$$ for taking action $$a \in A$$ at time $$t$$ is equal to the expected value of the reward $$r_t$$ given that we took action $$a$$ at that time. In practice, this is often represented as an array of values, where each action’s value is a different element in the array.
Great, now that we have a way to describe our beliefs about the values each action should return, let’s come up with a policy.
An obvious choice would be to take the action with the highest expected value. This is referred to as the greedy policy
(115)$$$a_{t} = \text{argmax}_{a} \; q_{t} (a)$$$
where our choice action is the one that maximizes the current value function.
So far so good, but it can’t be this easy. And, in fact, the greedy policy does have a fatal flaw: it easily gets trapped in local maxima. It never explores to see what it hasn’t seen before if one option is already better than the others. This leads us to a fundamental challenge in coming up with effective policies.
The Exploitation-Exploration Dilemma
If we never try anything new, if we always stick to the safe bet, we don’t know what we are missing. Sometimes we aren’t missing much of anything, and regret not sticking with our preferred choice, yet other times we stumble upon something new that was way better than we thought.
This is the exploitation-exploration dilemma: do you go with your best choice now, or risk the less certain option with the hope of finding something better. Too much exploration, however, means you may end up with a sub-optimal reward once it’s time to stop.
In order to avoid getting stuck in local minima while also maximizing reward, effective policies need some way to balance between these two aims.
A simple extension to our greedy policy is to add some randomness. For instance, a coin flip – heads we take the best choice now, tails we pick one at random. This is referred to as the $$\epsilon$$-greedy policy:
(116)$$$P (a_{t} = a) = \begin{cases} 1 - \epsilon + \epsilon/N & \quad \text{if } a_{t} = \text{argmax}_{a} \; q_{t} (a) \\ \epsilon/N & \quad \text{else} \end{cases}$$$
which is to say that with probability 1 - $$\epsilon$$ for $$\epsilon \in [0,1]$$ we select the greedy choice, and otherwise we select an action at random (including the greedy option).
Despite its relative simplicity, the epsilon-greedy policy is quite effective, which leads to its general popularity.
## Coding Exercise 2: Implement Epsilon-Greedy¶
Referred to in video as Exercise 1
In this exercise you will implement the epsilon-greedy algorithm for deciding which action to take from a set of possible actions given their value function and a probability $$\epsilon$$ of simply choosing one at random.
TIP: You may find np.random.random, np.random.choice, and np.argmax useful here.
def epsilon_greedy(q, epsilon):
"""Epsilon-greedy policy: selects the maximum value action with probability
(1-epsilon) and selects randomly with epsilon probability.
Args:
q (ndarray): an array of action values
epsilon (float): probability of selecting an action randomly
Returns:
int: the chosen action
"""
#####################################################################
## TODO for students: implement the epsilon greedy decision algorithm
# Fill out function and remove
raise NotImplementedError("Student exercise: implement the epsilon greedy decision algorithm")
#####################################################################
# write a boolean expression that determines if we should take the best action
be_greedy = ...
if be_greedy:
# write an expression for selecting the best action from the action values
action = ...
else:
# write an expression for selecting a random action
action = ...
return action
# Set parameters
q = [-2, 5, 0, 1]
epsilon = 0.1
# Visualize
# plot_choices(q, epsilon, epsilon_greedy)
Click for solution
Example output:
This is what we should expect, that the action with the largest value (action 1) is selected about (1-$$\epsilon$$) of the time, or 90% for $$\epsilon = 0.1$$, and the remaining 10% is split evenly amongst the other options. Use the demo below to explore how changing $$\epsilon$$ affects the distribution of selected actions.
## Interactive Demo 2: Changing Epsilon¶
Epsilon is our one parameter for balancing exploitation and exploration. Given a set of values $$q = [-2, 5, 0, 1]$$, use the widget below to see how changing $$\epsilon$$ influences our selection of the max value 5 (action = 1) vs the others.
### Think! 2: Changing Epsilon¶
At the extremes of its range (0 and 1), the $$\epsilon$$-greedy policy reproduces two other policies. What are they?
#### ¶
Make sure you execute this cell to enable the widget!
#@title
#@markdown Make sure you execute this cell to enable the widget!
@widgets.interact(epsilon=widgets.FloatSlider(0.1, min=0.0, max=1.0))
def explore_epilson_values(epsilon=0.1):
q = [-2, 5, 0, 1]
plot_choices(q, epsilon, epsilon_greedy, rng_seed=None)
#### Student Response¶
# @title Student Response
from ipywidgets import widgets
text=widgets.Textarea(
value='Type your answer here and click on Submit!',
placeholder='Type something',
description='',
disabled=False
)
button = widgets.Button(description="Submit!")
display(text,button)
def on_button_clicked(b):
print("Submission successful!")
button.on_click(on_button_clicked)
Click for solution
# Section 3: Learning from Rewards¶
Estimated timing to here from start of tutorial: 25 min
Now that we have a policy for deciding what to do, how do we learn from our actions?
One way to do this is just keep a record of every result we ever got and use the averages for each action. If we have a potentially very long running episode, the computational cost of keeping all these values and recomputing the mean over and over again isn’t ideal. Instead we can use a streaming mean calculation, which looks like this:
(117)$$$q_{t+1}(a) \leftarrow q_{t}(a) + \frac{1}{n_t} (r_{t} - q_{t}(a))$$$
where our action-value function $$q_t(a)$$ is the mean of the rewards seen so far, $$n_t$$ is the number of actions taken by time $$t$$, and $$r_t$$ is the reward just received for taking action $$a$$.
This still requires us to remember how many actions we’ve taken, so let’s generalize this a bit further and replace the action total with a general parameter $$\alpha$$, which we will call the learning rate
(118)$$$q_{t+1}(a) \leftarrow q_{t}(a) + \alpha (r_{t} - q_{t}(a)).$$$
## Coding Exercise 3: Updating Action Values¶
Referred to in video as Exercise 2
In this exercise you will implement the action-value update rule above. The function will take in the action-value function represented as an array q, the action taken, the reward received, and the learning rate, alpha. The function will return the updated value for the selection action.
def update_action_value(q, action, reward, alpha):
""" Compute the updated action value given the learning rate and observed
reward.
Args:
q (ndarray): an array of action values
action (int): the action taken
reward (float): the reward received for taking the action
alpha (float): the learning rate
Returns:
float: the updated value for the selected action
"""
#####################################################
## TODO for students: compute the action value update
# Fill out function and remove
raise NotImplementedError("Student exercise: compute the action value update")
#####################################################
# Write an expression for the updated action value
value = ...
return value
atform.add_event('Coding Exercise 3: Updating Action Values')
# Set parameters
q = [-2, 5, 0, 1]
action = 2
print(f"Original q({action}) value = {q[action]}")
## Update action - uncomment to check your solution!
# q[action] = update_action_value(q, 2, 10, 0.01)
# print(f"Updated q({action}) value = {q[action]}")
Original q(2) value = 0
Click for solution
You should see
Original q(2) value = 0
Updated q(2) value = 0.1
# Section 4: Solving Multi-Armed Bandits¶
Estimated timing to here from start of tutorial: 31 min
Now that we have both a policy and a learning rule, we can combine these to solve our original multi-armed bandit task. Recall that we have some number of arms that give rewards drawn from Gaussian distributions with unknown mean and unit variance, and our goal is to find the arm with the highest mean.
First, let’s see how we will simulate this environment by reading through the annotated code below.
def multi_armed_bandit(n_arms, epsilon, alpha, n_steps):
""" A Gaussian multi-armed bandit using an epsilon-greedy policy. For each
action, rewards are randomly sampled from normal distribution, with a mean
associated with that arm and unit variance.
Args:
n_arms (int): number of arms or actions
epsilon (float): probability of selecting an action randomly
alpha (float): the learning rate
n_steps (int): number of steps to evaluate
Returns:
dict: a dictionary containing the action values, actions, and rewards from
the evaluation along with the true arm parameters mu and the optimality of
the chosen actions.
"""
# Gaussian bandit parameters
mu = np.random.normal(size=n_arms)
# Evaluation and reporting state
q = np.zeros(n_arms)
qs = np.zeros((n_steps, n_arms))
rewards = np.zeros(n_steps)
actions = np.zeros(n_steps)
optimal = np.zeros(n_steps)
# Run the bandit
for t in range(n_steps):
# Choose an action
action = epsilon_greedy(q, epsilon)
actions[t] = action
# Compute rewards for all actions
all_rewards = np.random.normal(mu)
# Observe the reward for the chosen action
reward = all_rewards[action]
rewards[t] = reward
# Was it the best possible choice?
optimal_action = np.argmax(all_rewards)
optimal[t] = action == optimal_action
# Update the action value
q[action] = update_action_value(q, action, reward, alpha)
qs[t] = q
results = {
'qs': qs,
'actions': actions,
'rewards': rewards,
'mu': mu,
'optimal': optimal
}
return results
We can use our multi-armed bandit method to evaluate how our epsilon-greedy policy and learning rule perform at solving the task. First we will set our environment to have 10 arms and our agent parameters to $$\epsilon=0.1$$ and $$\alpha=0.01$$. In order to get a good sense of the agent’s performance, we will run the episode for 1000 steps.
Execute to see visualization
# @markdown Execute to see visualization
# set for reproducibility, comment out / change seed value for different results
np.random.seed(1)
n_arms = 10
epsilon = 0.1
alpha = 0.01
n_steps = 1000
results = multi_armed_bandit(n_arms, epsilon, alpha, n_steps)
fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(16, 6))
ax1.plot(results['rewards'])
ax1.set(title=f'Observed Reward ($\epsilon$={epsilon}, $\\alpha$={alpha})',
xlabel='step', ylabel='reward')
ax2.plot(results['qs'])
ax2.set(title=f'Action Values ($\epsilon$={epsilon}, $\\alpha$={alpha})',
xlabel='step', ylabel='value')
ax2.legend(range(n_arms));
Alright, we got some rewards that are kind of all over the place, but the agent seemed to settle in on the first arm as the preferred choice of action relatively quickly. Let’s see how well we did at recovering the true means of the Gaussian random variables behind the arms.
Execute to see visualization
# @markdown Execute to see visualization
fig, ax = plt.subplots()
ax.plot(results['mu'], label='latent')
ax.plot(results['qs'][-1], label='learned')
ax.set(title=f'$\epsilon$={epsilon}, $\\alpha$={alpha}',
xlabel='action', ylabel='value')
ax.legend();
Well, we seem to have found a very good estimate for action 0, but most of the others are not great. In fact, we can see the effect of the local maxima trap at work – the greedy part of our algorithm locked onto action 0, which is actually the 2nd best choice to action 6. Since these are the means of Gaussian random variables, we can see that the overlap between the two would be quite high, so even if we did explore action 6, we may draw a sample that is still lower than our estimate for action 0.
However, this was just one choice of parameters. Perhaps there is a better combination?
## Interactive Demo 4: Changing Epsilon and Alpha¶
Referred to in video as Exercise 3
Use the widget below to explore how varying the values of $$\epsilon$$ (exploitation-exploration tradeoff), $$\alpha$$ (learning rate), and even the number of actions $$k$$, changes the behavior of our agent.
### ¶
Make sure you execute this cell to enable the widget!
#@title
#@markdown Make sure you execute this cell to enable the widget!
@widgets.interact_manual(k=widgets.IntSlider(10, min=2, max=15),
epsilon=widgets.FloatSlider(0.1, min=0.0, max=1.0),
alpha=widgets.FloatLogSlider(0.01, min=-3, max=0))
def explore_bandit_parameters(k=10, epsilon=0.1, alpha=0.001):
results = multi_armed_bandit(k, epsilon, alpha, 1000)
plot_multi_armed_bandit_results(results)
While we can see how changing the epsilon and alpha values impact the agent’s behavior, this doesn’t give us a great sense of which combination is optimal. Due to the stochastic nature of both our rewards and our policy, a single trial run isn’t sufficient to give us this information. Let’s run multiple trials and compare the average performance.
First we will look at different values for $$\epsilon \in [0.0, 0.1, 0.2]$$ to a fixed $$\alpha=0.1$$. We will run 200 trials as a nice balance between speed and accuracy.
Execute this cell to see visualization
# @markdown Execute this cell to see visualization
# set for reproducibility, comment out / change seed value for different results
np.random.seed(1)
epsilons = [0.0, 0.1, 0.2]
alpha = 0.1
n_trials = 200
trial_rewards = np.zeros((len(epsilons), n_trials, n_steps))
trial_optimal = np.zeros((len(epsilons), n_trials, n_steps))
for i, epsilon in enumerate(epsilons):
for n in range(n_trials):
results = multi_armed_bandit(n_arms, epsilon, alpha, n_steps)
trial_rewards[i, n] = results['rewards']
trial_optimal[i, n] = results['optimal']
labels = [f'$\epsilon$={e}' for e in epsilons]
fixed = f'$\\alpha$={alpha}'
plot_parameter_performance(labels, fixed, trial_rewards, trial_optimal)
On the left we have plotted the average reward over time, and we see that while $$\epsilon=0$$ (the greedy policy) does well initially, $$\epsilon=0.1$$ starts to do slightly better in the long run, while $$\epsilon=0.2$$ does the worst. Looking on the right, we see the percentage of times the optimal action (the best possible choice at time $$t$$) was taken, and here again we see a similar pattern of $$\epsilon=0.1$$ starting out a bit slower but eventually having a slight edge in the longer run.
We can also do the same for the learning rates. We will evaluate $$\alpha \in [0.01, 0.1, 1.0]$$ to a fixed $$\epsilon=0.1$$.
Execute this cell to see visualization
# @markdown Execute this cell to see visualization
# set for reproducibility, comment out / change seed value for different results
np.random.seed(1)
epsilon = 0.1
alphas = [0.01, 0.1, 1.0]
n_trials = 200
trial_rewards = np.zeros((len(epsilons), n_trials, n_steps))
trial_optimal = np.zeros((len(epsilons), n_trials, n_steps))
for i, alpha in enumerate(alphas):
for n in range(n_trials):
results = multi_armed_bandit(n_arms, epsilon, alpha, n_steps)
trial_rewards[i, n] = results['rewards']
trial_optimal[i, n] = results['optimal']
labels = [f'$\\alpha$={a}' for a in alphas]
fixed = f'$\epsilon$={epsilon}'
plot_parameter_performance(labels, fixed, trial_rewards, trial_optimal)
Again we see a balance between an effective learning rate. $$\alpha=0.01$$ is too weak to quickly incorporate good values, while $$\alpha=1$$ is too strong likely resulting in high variance in values due to the Gaussian nature of the rewards.
# Summary¶
Estimated timing of tutorial: 45 min
In this tutorial you implemented both the epsilon-greedy decision algorithm and a learning rule for solving a multi-armed bandit scenario. You saw how balancing exploitation and exploration in action selection is critical in finding optimal solutions. You also saw how choosing an appropriate learning rate determines how well an agent can generalize the information they receive from rewards. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 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": 5, "x-ck12": 0, "texerror": 0, "math_score": 0.8402856588363647, "perplexity": 3608.355110453909}, "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/1669446706285.92/warc/CC-MAIN-20221126080725-20221126110725-00470.warc.gz"} |
http://sankhya.isical.ac.in/search/56a1/56a1005.html | Sankhya: The Indian Journal of Statistics
1994, Volume 56, Series A, Pt. 1 , pp. 44--53
ON BAHADUR REPRESENTATION OF SAMPLE QUANTILES FOR mn- DECOMPOSABLE PROCESSES
By
KAMAL C. CHANDA and FRITS H. RUYMGAART, Texas Tech University
SUMMARY. Let X1, … , Xn be random variables with a common distribution function F. Assume that these random variables form a mn-decomposable set in the sense that we can write $X_t=X_{t, m_n} +X^{*}_{t, m_n}(1 \leq t \leq n)$ for some (< n) such that (i) $X_{t, m_n}(1 \leq t \leq n)$ are identically distributed and (ii) { $X_{t, m_n}$; 1£ t £ n} is mn-dependent and for every $t(1 \leq t \leq n) : X^{*}_{t, m_n}\rightarrow 0$ in probability as n ® ¥ . Let Vn be the kn-th order statistic for X1, …, Xn, with kn/n ® p as n ® ¥ , where p is a given number e (0, 1). Under certain regularity conditions on F and mn it can then be proved that $n^{1/2}(V_n-\zeta)=-\sum_{t=1}^{n}(I(X \leq \zeta)-p)/n^{1/2}+ O(n^{1/2}l_{n}^{3/4}log l_{n})$ a.s. as n ® ¥ , where F(z ) =p and we assume that ln=[n/mn] ® ¥ and $n^{-1/2}n^{1/2}l_{n}^{-3/4}\log{l_{n}} \rightarrow 0$ as n ® ¥ . Further, it is shown that ${\mathcal{L}} (n^{1/2}(V_n-\zeta)) \rightarrow {\mathcal{N}}(0, \sigma^{2})$ where 0 < s 2 < ¥ .
AMS (1980) subject classification. 60F15, 62G30.
Key words and phrases. Order statistic, Bahadur representation, $m_n$ - decomposable processes, asymptotic normality.
Full Paper (PDF) | {"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": 0.9760870337486267, "perplexity": 2798.4920322007074}, "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-2018-05/segments/1516084889917.49/warc/CC-MAIN-20180121021136-20180121041136-00079.warc.gz"} |
http://chronicle.com/blognetwork/castingoutnines/category/teaching/textbooks/ | # Category Archives: Textbooks
June 28, 2014, 9:57 am
# Grand challenges for mathematics education
On Twitter this week, someone sent out a link to this survey from the NCTM asking users to submit their ideas for “grand challenges” for mathematics education in the coming years. I forget the precise definition and parameters for a “grand challenge” and I can’t go back to the beginning of the survey now that I’ve completed it, but the gist is that a grand challenge should be “extremely difficult but doable”, should make a positive impact on a large group of mathematics students, and should be grounded in sound pedagogical research.
To that list of parameters, I added that the result of any grand challenge should include a set of free, open-source materials or freely-available research studies that anyone can obtain and use without having to subscribe to a journal, belong to a particular institution, or use a particular brand of published curricula. In other words, one…
April 14, 2014, 2:57 pm
# The hidden costs of unsolicited textbooks — a view from the mailroom
Back in January I posted an article calling for an end to unsolicited review copies of textbooks being sent to professors. Interestingly, on Reddit a student at my university who works for the mail services department did an AMA, and I had the chance to ask: What kind of impact does it make on the university, from an infrastructure or mail services point of view, to have all these unsolicited books being sent in? Keep in mind that we’re a public university of 24,000 students and lots and lots of faculty. Here are some highlights from his response, which I thought was pretty interesting though not totally surprising:
Ugh, I HATE those! Nobody wants them, nobody asks for them, and they take up valuable space in our truck and our holding area.
As far as the cost it passes onto us, it’s definitely hard to quantify, but I can tell you all the different ways we waste time on those…
January 29, 2014, 5:17 pm
# An end to unsolicited review copies of textbooks, please
The picture you see here is my afternoon mail today. It consists of two copies of a new Calculus text (hardcover), two copies of another Calculus text (hardcover), and one copy of an intermediate algebra text (softcover).
I did not request a single one of these. I certainly did not request duplicates of two of them. The last time I taught intermediate algebra was the mid-1990′s. I am not on a committee that selects textbooks. I have no use for these books other than to prop open a door. So why did I get them? I have no idea.
When I think about the waste and expense of these unsolicited review copies of textbooks, it makes me downright angry. I went to UPS.com and used a back-of-the-envelope estimate of weight and shipping distance, and got that the total package of these books would have cost about $20 to ship to me from its point of origin. That’s not a large sum, but how many… August 13, 2012, 8:00 am # A free and open-source calculus textbook Allow me to make a shameless plug for a very cool project currently underway by my GVSU colleague Matt Boelkins. He is writing a free, open-source calculus textbook that will be available in PDF form online for anyone to use and for any instructor to modify. He has already written the differential calculus portion of the textbook — his Winter semester sabbatical project — and he’s about to begin work on the integral calculus portion. You can download the differential calculus parts here. This is at his blog, where he is promoting the book and soliciting feedback. Matt’s also on Twitter. Matt and I have talked about this project a lot in the last several months, and I’m deeply impressed by his vision for what this resource could become. He sums it up in this blog post: While on sabbatical during the winter semester of 2012, I began drafting a free, open-source calculus text…. September 29, 2011, 4:20 pm # Will the Fire burn its way into higher ed? http://www.flickr.com/photos/ichibod/ In case you didn’t hear, Amazon has announced a major upgrade to the entire line of Kindle devices, including a new 7″ tablet device called the Kindle Fire. The Fire won’t be released until November 15, but already the phrase “iPad killer” is being used to describe it. Wired Campus blogger Jeff Young put up a brief post yesterday with a roundup of quick takes on the Fire’s potential in higher education. One of those thoughts was mine. I’ve had some time to look around at what we know about the Fire at this point. I have to say I am still skeptical about the Fire in higher education. It seems like the Fire is a very well-made device. I’m not so interested in getting one for myself — I’ve got a current-generation Kindle and an iPhone 4, and am very happy with both … October 13, 2010, 7:42 pm # More enVisionMATH: Adding "near doubles" The last post about enVisionMATH and how I, as a math person and dad, go about trying to make sense of what my 6-year old brings home from first grade seems to have struck a chord among parents. The comments have been outstanding and there seems to be a real need for this kind of conversation. So I have a few more such posts coming up soon, starting with this one. The 6-year old brought this home on Monday. Click to enlarge: It’s about adding “near doubles”, like 3 + 4 or 2 + 3. In case you can’t read the top part or can’t enlarge the photo, here are the steps — yes, there are steps, and that’s kind of the point of this post — for adding near doubles: 1. “You can use a double to add a near double.” It gives: 4 + 5 and shows four blue balls and five green balls. 2. “First double the 4″. It shows 4 + 4 = 8, and the four blue balls, and four of the green balls with the extra green ball… August 8, 2010, 12:47 pm # Calculus and conceptual frameworks Image via http://www.flickr.com/photos/loopzilla/ I was having a conversation recently with a colleague who might be teaching a section of our intro programming course this fall. In sharing my experiences about teaching programming from the MATLAB course, I mentioned that the thing that is really hard about teaching programming is that students often lack a conceptual framework for what they’re learning. That is, they lack a mental structure into which they can place the topics and concepts they’re learning and then see those ideas in their proper place and relationship to each other. Expert learners — like some students who are taking an intro programming course but have been coding since they were 6 years old — have this framework, and the course is a breeze. Others, possibly a large majority of… July 29, 2010, 11:39 am # The Kindle evolves again Image from Amazon.com Update: Here’s an overview video of the new Kindle. Amazon today unveiled the third generation of its Kindle ebook readers. The new devices, which will ship beginning August 27, will be smaller (21% reduction in size, while keeping the same size screen) and lighter (8.7 ounces) than the current generation of Kindles, with double the storage capacity, improved contrast and fonts, and built-in WiFi. Most importantly is the price point:$189, with a \$139 WiFi-only model also being offered.
When Amazon first sold the Kindle, I roundly criticized it (here, here, and here; and then here for the second generation Kindles) as a good idea but lacking several deal-breaking features that should have been obvious, and would have been inexpensive, to include. I also thought the price point –…
April 3, 2010, 6:07 am
# Is the iPad really what students need?
Dave Caolo believes that students are one of the four groups of people who will make the iPad huge, because:
Students are on a fixed budget, and e-books are typically cheaper than their paper-based counterparts. Also, consider all of the money publishers lose when students buy used books from the campus bookstores. Additionally, Apple can distribute textbooks through iTunes U — an established and proven system that students, faculty and staff already know how to use.
Suddenly the iPad is a device that follows a student from his/her freshman year of high school all the way through graduate school. Why buy a laptop when every student has a device that can be a textbook, reference tool, Internet appliance and whatever else the imaginations of developers can dream up?
I do believe that the iPad’s success will be closely tied to its success in the EDU sector, but Caolo’s analysis misses…
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https://ren-fengbo.lab.asu.edu/publication?f%5Bkeyword%5D=2&s=author&o=asc | # Publication
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M. Zinkevich, Weimer, M. , Li, L. , and Smola, A. J. , Parallelized stochastic gradient descent, Advances in neural information processing systems. pp. 2595–2603, 2010. | {"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": 0.9359419345855713, "perplexity": 9542.465860578948}, "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-2023-14/segments/1679296949701.0/warc/CC-MAIN-20230401032604-20230401062604-00685.warc.gz"} |
https://www.physicsforums.com/threads/fourier-transform-of-sin-t-t.342673/ | Fourier transform of sin(t)/t
1. Oct 4, 2009
Moomax
1. The problem statement, all variables and given/known data
Evaluate INT(|X(t)|^2) dt using parsevals theorem
where x(t) = (sin(t)cos(10t))/(pi*t)
2. Relevant equations
parsevals theorem: int(|f(t)|^2 dt = (1/2*pi)INT(|F(W)|^2 dw
3. The attempt at a solution
So I've tried several attempts at this problem and this is my latest:
first I use the fact that sin(x)*cos(y) = (sin(x+y)+sin(x-y)) /2
to get sin(t)cos(10t)/pi*t = (sin(t+10t) + sin(t - 10t))/(2*pi*t)
then I split it up into : sin(11t)/2t*pi + sin(-9t)/2t*pi
then what I was going to do was take the fourier transform of each function here however, I can't figure out how in the world to take the fourier transform of sin(t)/t
anyone have any ideas? thanks!
2. Oct 4, 2009
jbunniii
Do you know a function whose Fourier transform is $\sin(\omega)/\omega$?
3. Oct 4, 2009
Moomax
I checked on my transform table and looked around online a little and didn't see any transform that equals sin(w)/w. If there was i'd use the f(w) <-> F(t) rule and then it could work for me. Does that transform exist?
4. Oct 4, 2009
Count Iblis
Hint:
Compute the (inverse) Fourier transform of f(x), defined as:
f(x) = 1 for -L < x < L,
otherwise f(x) = 0
5. Oct 4, 2009
jbunniii
Yes, it exists and is one of the most fundamental transforms! If your table doesn't have it, I would get another table (seriously). Count Iblis' hint is right on the money.
By the way, $\sin(x)/x$ is sometimes called $sinc(x)$, so look in your table for that. Caution: some authors define $sinc(x) = \sin(\pi x)/(\pi x)$.
Last edited: Oct 4, 2009
6. Oct 4, 2009
Moomax
ooohhhh now it makes sense!!! thank you!! XD
Similar Discussions: Fourier transform of sin(t)/t | {"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": 0.9392458200454712, "perplexity": 2095.7407569637026}, "config": {"markdown_headings": false, "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-2017-34/segments/1502886103910.54/warc/CC-MAIN-20170817185948-20170817205948-00142.warc.gz"} |
https://www.gradesaver.com/textbooks/math/geometry/CLONE-68e52840-b25a-488c-a775-8f1d0bdf0669/chapter-8-section-8-4-circumference-and-area-of-a-circle-exercises-page-372/8b | ## Elementary Geometry for College Students (6th Edition)
radius = 2.5 ft circumference = 5$\pi$ ft
The area of the circle = 6.25$\pi ft^{2}$ The area A of a circle whose radius has length r is given by A = $\pi r^{2}$ 6.25$\pi$ = $\pi r^{2}$ 6.25 = $r^{2}$ r = 2.5 ft We know the circumference of the circle is given by the formula c= $\pi$ d = 2$\pi$ r = 2$\pi$ * 2.5 = 5$\pi$ ft | {"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": 0.8388770222663879, "perplexity": 583.6801762855473}, "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-2019-43/segments/1570987828425.99/warc/CC-MAIN-20191023015841-20191023043341-00010.warc.gz"} |
https://support.office.com/en-ie/article/command-line-switches-for-microsoft-office-products-079164cd-4ef5-4178-b235-441737deb3a6 | Command-line switches for Microsoft Office products
When you launch a Microsoft Office product, the startup process runs in a standard way. Microsoft Word, for example, displays the Word splash screen and loads the Normal template. But suppose you want Word to start without its splash screen and then load a template other than the Normal template. Or, you want to customize the process even more by loading an add-in or running a macro upon startup. You can add options like this by using subcommands called command-line switches to an Office app's startup command.
If you want to use the customization just one time, you can type the command and switch in the Run dialog box (Start menu) in Microsoft Windows. If you want to use a particular switch many times or every time that you start the app, you can create a desktop shortcut that starts the program by using the same switch and parameters. This article describes how to do both. It also includes a table that lists all of the switches and parameters that are available in the desktop Office apps.
Using a command-line switch doesn't mean you have to type the whole startup command at the command prompt. You can start the Office app as usual, by clicking the program icon on the desktop, or by clicking the program name on the Start menu. All startup methods essentially do the same thing: they run the app's .exe file, even if you don't actually type the command or even see it.
A command-line switch is a modifier that is added to the .exe file. A startup file with a switch looks like this.
``` outlook.exe /nopreview ```
In this example, a command-line switch has been added to the .exe file for Microsoft Outlook. The switch consists of a forward slash and a word or abbreviation that indicates the switch's action. This switch tells Outlook to launch without showing the Reading Pane.
A switch is sometimes followed by one or more specific instructions called parameters, which give the program further information about how to run the .exe command. For example, the following command tells Outlook to load a specific profile name upon startup.
``` outlook exe /profile profilename ```
Switch names cannot be abbreviated and are not case-sensitive. However, their parameters are sometimes case-sensitive.
Startup command names and locations
Here are the names of the startup commands for the Office products Word, Excel, PowerPoint, PowerPoint viewer, Outlook, and Access.
Word winword.exe Excel excel.exe PowerPoint powerpnt.exe PowerPoint Viewer pptview.exe Outlook outlook.exe Access msaccess.exe
When you use one of the Office startup commands, you must supply the full path to the product's .exe file. Verify the location of this file on your computer. This table shows the locations of the .exe files if you accepted the default folder locations during installation.
In Office 2007 Windows 32-bit: C:\Program Files\Microsoft Office\Office12\ Windows 64-bit: C:\Program Files (x86)\Microsoft Office\Office12\ In Office 2010 Windows 32-bit: C:\Program Files\Microsoft Office\Office14\ Windows 64-bit: C:\Program Files (x86)\Microsoft Office\Office14\ In Office 2013 Windows 32-bit: C:\Program Files\Microsoft Office\Office15\ Windows 64-bit: C:\Program Files (x86)\Microsoft Office\Office15\ In Office 2016 Windows 32-bit: C:\Program Files\Microsoft Office\Office16\ Windows 64-bit: C:\Program Files (x86)\Microsoft Office\Office16\
Use a switch once by adding it to the Run command
1. In Windows 10, click the Search or Cortana icon in the taskbar, type Run, and then click Command Prompt in the results.
In Windows 8, press the Windows key, type Run, and then press Enter.
In Windows 7, click Start, point to All Programs, click Accessories, and then click Run.
2. In the Run dialog box, type a quotation mark, enter the full path for the app's .exe file, and then type another quotation mark. Alternatively, click Browse to locate and select the file. In this case, the quotation marks are supplied automatically.
3. After the closing quotation mark, type a space, and then type the switch. For example, you might type:
``` "c:\program files\microsoft office\office15\outlook.exe" /nopreview ```
The next time you start the app, it opens as usual. To make your customized startup available for repeated uses, see the next section.
Note the following about using command-line switches:
• You can use only one switch at a time. Starting an Office app with multiple switches is not supported.
• If the parameter is a path to a location on your computer, or a file name with spaces in it, enclose it in double quotation marks—for example, /t "Monthly Report.dotx".
• Switches and parameters are not case-sensitive. For example, /RO functions the same as /ro.
• Include one blank space before each switch and one before each parameter.
Make a switch available for reuse by creating a shortcut
1. Right-click the Windows desktop, point to New, and then click Shortcut on the shortcut menu.
2. In the Create Shortcut Wizard, in the Type the location of the item box, type a double quotation mark ("), enter the full path for the app's .exe file (including the file name), and then type another double quotation mark. (Alternatively, click Browse to locate and select the file. In this case, the quotation marks are added automatically.)
3. Following the closing quotation mark, type a space, and then type the switch and any parameters. If the parameter is a path to a location on your computer, and the path contains a space, it also must be enclosed in quotation marks. For example:
``` "c:\program files\microsoft office\office15\excel.exe" /r "c:\My Folder\book1.xlsx" ```
4. Click Next.
5. In the Type a name for this shortcut box, type a name for the shortcut, and then click Finish.
The wizard creates the shortcut and places it on the desktop.
Whenever you want to use the shortcut to start the app, double-click it.
To add the desktop shortcut to the Windows Start menu, right-click the shortcut, and then click Pin to Start menu on the shortcut menu.
List of command-line switches for Office products
Each Office product has a different set of command-line switches.
Note: These lists don't include all switches added since Office 2007. If you use command-line switches and want information about newer switches that are available, please respond Yes or No to the "Was this information helpful" question at the end of this topic. Then, in the box that appears, tell us which Office product and version you're interested in.
Switch and parameter Description workbook path | file name This parameter does not require a switch. Starts Excel and opens the specified file. Example excel.exe "c:\My Folder\book1.xlsx" or excel.exe http://MySite/Book1.xlsx /r workbook path | file name Opens a specific workbook as read-only. Example excel.exe /r "c:\My Folder\book1.xlsx" or excel.exe /r http://MySite/Book1.xlsx /t workbook path | file name Starts Excel and opens the specified file as a template. Example excel.exe /t "c:\My Folder\book_name.xlsx". or excel.exe /t http://MySite/book_name.xlsx /n workbook path | file name Like /t, starts Excel and opens the specified file as a template. Example excel.exe /n "c:\My Folder\book_name.xlsx". or excel.exe /n http://MySite/book_name.xlsx /e or /embed Prevents the Excel startup screen from appearing and a new blank workbook from opening. Example excel.exe /e /p workbook path Specifies a folder as the active working folder (for example, the folder that is pointed to in the Save As dialog box). Example excel.exe /p "c:\My Folder" /s or /safemode Forces Excel to bypass all files that are stored in startup directories, such as the default XLStart folder located in the directory where Excel or Microsoft Office is installed. Example excel.exe /s /m Creates a new workbook that contains a single XLM macro sheet. Example excel.exe /m /a progID Starts Excel and loads the Automation add-in that is specified by the progID of the add-in. Example excel.exe /a MyProgId.MyProgID2.1 /x Starts a new instance (a separate process) of Excel. Example excel.exe /x "c:\My Folder\book1.xlsx" or excel.exe /x http://MySite/Book1.xlsx
Here are the command-line switches that are available for PowerPoint.
Switch or parameter Action /B Starts PowerPoint with a new blank presentation. Example: "c:\program files\microsoft office\office12\POWERPNT.exe" /B /C Starts PowerPoint with the specified file open and also starts Microsoft Windows NetMeeting conferencing. Example: "c:\program files\microsoft office\office12\POWERPNT.exe" /C NetMeetingPresentation.pptx Note: If you use this switch without specifying a file, PowerPoint starts with no presentation open and NetMeeting conferencing is not started. /EMBEDDING Starts PowerPoint without displaying the Office PowerPoint 2007 program window. Developers use this switch when testing add-ins. Example: "c:\program files\microsoft office\office12\POWERPNT.exe" /EMBEDDING /M MACRO Runs a macro in a specified presentation. Example: "c:\program files\microsoft office\office12\POWERPNT.exe" /M myfile.pptm "MyMacro" "MyMacro" is a macro in the file myfile.pptm. /N Starts PowerPoint and creates a new presentation. Example: "c:\program files\microsoft office\office12\POWERPNT.exe" /N "Path\templatename.potx" This example specifies the name of the template that the new presentation is based on: templatename.potx. If a template name is not supplied, PowerPoint starts a new presentation based on the blank template (in effect, the same as using the /N switch without a template name). /O Starts PowerPoint and specifies a list of files to open. Example: "c:\program files\microsoft office\office12\POWERPNT.exe" /O File name1.pptx, File name2.pptx /P Prints the presentation to the default printer by using default settings. When you use the /P switch, PowerPoint displays the Print dialog box before printing. After you choose options and click OK, the dialog box closes, and PowerPoint prints the file and then closes. If you don't want to see PowerPoint at all, use the /PT (Print To) switch instead. Example: "c:\program files\microsoft office\office12\POWERPNT.exe" /P "MyFile.pptx" /PT Prints the presentation to the specified printer by using the default settings. If you don't want to see PowerPoint at all, use the /PT (Print To) switch. Example: "c:\program files\microsoft office\office12\POWERPNT.exe" /PT "PrinterName" "" "" "MyFile.pptx" PrinterName is the name of the printer that appears in the Name box under Printer in the Print dialog box. The empty quotation marks are necessary; the quotation marks around PrinterName and the path to the PPTX file are needed only if there are spaces in either of the names, but it is always a good idea to use them. /PWO Prints the specified file, but show the Print dialog box. When you use the /P switch, PowerPoint displays the Print dialog box before printing. After you choose options and click OK, the dialog box closes, and PowerPoint prints the file and then closes. If you don't want to see PowerPoint at all, use the /PT (Print To) switch instead. Example: "c:\program files\microsoft office\office12\POWERPNT.exe" /PWO "MyFile.pptx" /RESTORE Restores PowerPoint to the way it was before the program closed abnormally. When PowerPoint restarts, it will attempt to recover and restore some aspects of the state of the program and presentations before it closed. Example: "c:\program files\microsoft office\office12\POWERPNT.exe" /RESTORE /S Opens the specified presentation file as a slide show. Example: "c:\program files\microsoft office\office12\POWERPNT.exe" /S "Presentation1.pptx"
Here are the command-line switches that are available for PowerPoint Viewer.
Switch or parameter Action /D Shows the Open dialog box when the presentation ends. Example: "c:\program files\microsoft office\office12\PPTVIEW.exe" /D /L Reads a playlist of PowerPoint presentations contained within a text file. Example: "c:\program files\microsoft office\office12\PPTVIEW.exe" /L "Your_Play_List.txt " Note: The playlist file is a list of presentation file names (preceded by the path as needed). It is not possible to add additional command-line switches to the individual presentations within the playlist. /N# Opens the presentation at a specified slide number, instead of slide 1. Example: "c:\program files\microsoft office\office12\PPTVIEW.exe" /N5 "Presentation.pptx" This example opens Presentation.pptx at slide 5. /S Starts the viewer without showing the splash screen. Example: "c:\program files\microsoft office\office12\PPTVIEW.exe" /S /P Sends the presentation to a printer, and print the file. Example: "c:\program files\microsoft office\office12\PPTVIEW.exe" /P "Presentation.pptx" This example prints the Presentation.pptx file. | {"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": 0.8633451461791992, "perplexity": 7770.643879072228}, "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-2018-39/segments/1537267156311.20/warc/CC-MAIN-20180919220117-20180920000117-00515.warc.gz"} |
https://space.stackexchange.com/questions/36012/listing-objects-and-space-probes-beyond-earth-orbit-in-space-track | # Listing objects and space probes beyond Earth orbit in Space Track?
Can anyone tell me how to query Space Track to list objects that are beyond Earth orbit. I am thinking of things such as the Voyagers, the Tesla Roadster and Pioneer, as examples?
While there is a Wikipedia page on space probes, it would be interesting to see if Space Track can be queried for this information.
Note, there is a related question, but this is more focused on using Space Track. | {"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": 0.8160458207130432, "perplexity": 794.3945975948}, "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/1603107894203.73/warc/CC-MAIN-20201027140911-20201027170911-00257.warc.gz"} |
http://www.reference.com/browse/wh+question | Definitions
# English grammar
English grammar is a body of rules (grammar) specifying how phrases and sentences are constructed in the English language. Accounts of English grammar tend to fall into two groups: the descriptivist, which describes the grammatical system of English; and the prescriptivist, which does not describe English grammar but rather sets out a small list of social regulations that attempt to govern the linguistic behaviour of native speakers (see Linguistic prescription and Descriptive linguistics). Prescriptive grammar concerns itself with several open disputes in English grammar, often representing changes in usage over time.
This article describes a generalized Standard English, which is the form of speech found in types of public discourse including broadcasting, education, entertainment, government, and news reporting. Standard English includes both formal and informal speech. The many dialects of English have divergences from the grammar described here, which are only cursorily mentioned.
## Lexical categories and phrasal syntax
### Nominals
Noun phrases and pronouns both can have a referential function where they "point" (i.e. refer) to some person or object in the real world (or a possible world). Additionally, they share many of the same grammatical functions in that they can both act as subjects, objects, and complements within clauses.
Noun phrases may consist of only a single noun, or they may be complex consisting of a noun (which functions as the head of the noun phrase) that is modified by different types of elements (such as adjectives, prepositional phrases, etc.).
Pronouns are words that can act as substitutions for noun phrases. For instance, in the following sentence
Professor Plum kicked the very large ball with red spots over the fence.
the noun phrase the very large ball with red spots can be substituted with the pronoun it as in
Professor Plum kicked it over the fence.
In spite of the name pronoun, pronouns cannot substitute for nouns — they only substitute for noun phrases. This can be shown with the same sentence above: the noun ball cannot be substituted with the pronoun it (or any other pronoun) as in the ungrammatical sentence
*Professor Plum kicked the very large it with red spots over the fence.
The sections below describe English nouns (their morphology and syntax), the structure of noun phrases, and pronouns.
#### Nouns
Nouns are defined notionally (i.e. semantically) as generally describing persons, places, things, or ideas. This notional definition does account for what are the central members of the noun lexical category. However, the notional definition fails to account for several nouns, such as deverbal nouns like jump or destruction (which are notionally more like actions). For this reason, many grammatical descriptions of English define nouns in terms of grammar (i.e. according to their morphological and syntactic behavior). Nonetheless, traditional English grammars and some pedagogical grammars define nouns with a notional definition.
Non-proper nouns, in general, are not marked for case or gender, but are marked for number and definiteness (when referential).
##### Non-inflectional morphology
English nouns may be of a few morphological types:
Simple nouns consist of a single root which also acts as the stem which may be inflected. For example, the word (or, more precisely, the lexeme) boy is a simple noun consisting of a single root (also boy). The root boy also acts as the stem boy, which can have the inflectional plural suffix -s added to it producing the inflectional word-form boys.
More complex nouns can have derivational prefixes or suffixes in addition to a noun stem. For example, the noun archenemy consists of a derivational prefix arch- and a root enemy. Here the derived form archenemy acts as the stem which can be used to form the inflected word-form archenemies. An example with a derivational suffix is kingdom which is composed of root king and suffix -dom. Some English nouns can be complex with several derivational prefixes and suffixes. A considerably complex example is antidisestablishmentarianism which has the root establish and the affixes anti-, dis-, -ment, -ary, -an, and -ism.
English compound nouns are nouns that consist of more than one stem. For example, the compound paperclip is composed of the stem paper and the stem clip. Compounds in English can be usefully subdivided (following Bauer 1983) into different classes according to the lexical category of the individual stems and according to a semantic classification into endocentric, exocentric, copulative, and appositional subtypes.
##### Number
English nouns are typically inflected for number, having distinct singular and plural forms. The plural form usually consists of the singular form plus -s or -es, but there are many irregular nouns. Ordinarily, the singular form is used when discussing one instance of the noun's referent, and the plural form is used when discussing any other number of instances, but there are many exceptions to this rule. Here are some examples:
Number Example
Singular The girl talks.
Every girl talks.
No girl talks.
Plural The girls talk.
All girls talk.
No girls talk.
##### Membership
Words that belong to the noun lexical category (or part of speech) can be simple words that belong primarily to the noun category. These include words like man, dog, rice, et cetera.
Other nouns can be derived from words belonging to other lexical categories with the addition of class-changing derivational suffixes. For example, the suffixes -ation, -ee, -ure, -al, -er, -ment are attached to verb bases to create deverbal nouns.
vex (verb) > vexation (noun) appoint (verb) > appointee (noun) fail (verb) > failure (noun) acquit (verb) > acquittal (noun) run (verb) > runner (noun) adjust (verb) > adjustment (noun)
Still other suffixes (-dom, -hood, -ist, -th, -ness) form derived deadjectival nouns from adjectives:
free (adjective) > freedom (noun) lively (adjective) > livelihood (noun) moral (adjective) > moralist (noun) warm (adjective) > warmth (noun) happy (adjective) > happiness (noun)
These derivational suffixes can also be added to (compound) phrasal bases like in the noun stick-it-to-itiveness, which is derived from the phrase [stick it to it ] + -ive + -ness.
Besides derivational suffixation, words from other lexical categories can be converted straight to nouns (without any overt morphological indication) by a conversion process (also known as zero derivation). For example, the word run is a verb but it can be converted to a noun run "point scored in a baseball game (by running around the bases)" as in the sentence:
The team won with five runs in the ninth inning.
Here it is evident that run is a noun because it is pluralized with the inflectional plural suffix -s, it is modified by the preceding quantifier five, and it occurs as the head of the noun phrase five runs which acts as the complement of the preposition with in the prepositional phrase with five runs. Other lexical categories can also be converted:
if (subordinator) > if (noun) as in no ifs, ands, or buts about it [idiomatic]
daily (adjective) > daily (noun) [= "newspaper"] as in did you buy a daily for me?
down (preposition) > down (noun) [in American football] as in they made a new first down
Additionally, there are phrases which can be converted into nouns, such as jack-in-the-box, love-lies-bleeding (type of flower). These may be viewed as compounds (see noun morphology section). There are also conversion processes that convert from one noun subclass to another subclass (see the noun subclass conversion section).
##### Subclasses
Three basic noun classes in English can be distinguished according to syntactic criteria:
These syntactic subclasses also correspond fairly well to semantic categories (as indicated by their names and explained below).
Countable and uncountable nouns — such as dog (countable), rice (uncountable) — show article contrast: a dog, the dog, dogs, the dogs are all possible just as rice, the rice are both possible.
Countable nouns differ from uncountable nouns in that they cannot stand alone, cannot be modified by some unless they are in plural forms, can be modified by a, and can be pluralized. Semantically, they generally refer to easily individuated objects. Examples of countable nouns include the following: remark, book, bottle, chair, forest, idea, bun, pig, toy, difficulty, bracelet, mountain, etc.
Uncountable nouns, in contrast, can stand alone, can be modified by some, cannot be modified by a, and cannot be pluralized. Semantically, uncountable nouns refer to an undifferentiated mass. Examples of uncountable nouns include: rice, furniture, jewelry, scenery, gold, bread, grass, warmth, music, butter, homework, baggage, sugar, coffee, luck, sunshine, water, air, Chinese (language), soccer, literature, rain, walking, etc.
The morphosyntactic differences between countable and uncountable nouns are displayed in the table below.
Countable Noun Uncountable Noun
standalone *remark rice
some + NOUN *some remark some rice
a + NOUN a remark *a rice
plural remarks *rices
some + plural NOUN some remarks *some rices
On the other hand, proper nouns, which include personal names — such as Peter, Smith and placenames like Paris, Tokyo — do not show article contrast. Typically, they cannot be preceded by an article. Thus, *a Peter, *the Peter, *a Tokyo, *the Tokyo are all ungrammatical (only Peter and Tokyo without articles are possible). Although several proper nouns (e.g. Peter, Smith, Paris, Tokyo) cannot be preceded by an article, some proper nouns must obligatorily be preceded by an article. These include proper nouns like The Hague, The Dalles, the Netherlands, the West Indies, and the Andes. However, like proper nouns without article modification, these proper nouns with preceding articles also lack article contrast. Thus, while The Hague is grammatical, *a Hague and *Hague are ungrammatical. Semantically, proper nouns have unique reference.
As seen above, the different subclasses affect grammatical number and quantification.
##### =Dual membership, conversion=
Complicating the membership of the basic subclasses described above is the existence of some nouns which have dual membership in more than one subcategory and the conversion of a noun from its basic subcategory to a different subcategory. (See the noun membership section.)
Nouns like brick and cake have dual membership. For example, observe the following sentences with brick:
The house was made of brick. brick = uncountable The house was made of bricks. bricks = countable
In the first sentence, brick is an uncountable noun. This can be determined by the lack of an article preceding brick, which is a characteristic of uncountable nouns (and, thus, this sentence is parallel to a sentence like The ball was made of rice). In the second sentence, bricks is a countable noun because it is plural, which is a characteristic of only countable nouns (and, thus, this sentence is parallel to a sentence like The toy house was made of matches). Other nouns that have dual membership in both countable and uncountable subclasses are stone, paper, beauty, difficulty, experience, light, sound, talk, and lamb.
As mentioned above, several nouns can undergo a conversion from one subclass to another. One type of conversion is from a proper noun to a countable noun. A proper name like Picasso may become a countable noun through metonymic extension, as in the sentence:
Did you see the Picassos hanging on the wall?
Although Picasso usually has a unique referent (which is the person Pablo Picasso), it can be used metonymically to mean, "a painting created by Picasso". This converted noun can be seen as belonging to the countable subclass by the fact that it is plural and that the article the precedes it. There are also two idiomatic constructions which involve the conversion of a proper noun to a countable noun:
Excuse me ma'am, a Mr. Smith is on the phone.
You don't mean THE Margaret Thatcher, do you?
Here the article a before Mr. Smith indicates a meaning of "a certain person called Mr. Smith that is otherwise unknown to you" in the first sentence while in the second sentence the article the with intonational stress (here indicated in caps) gives a reading of "the well-known person called Margaret Thatcher".
#### Noun phrases
##### =Determiners=
Determiners include articles (like the, a/an), demonstratives (like this, these, that, those), quantifiers (like all, many, some, any, each), numerals (like one, two, first, second), genitives (like my, your, his, her, its, our, their), interrogatives (like which, what), and exclamatives (like such, what) that modify noun heads in noun phrases.
Determiners function as words that "determine" other nouns, where "determine" is generally conceived of as indicating information about quantification, grammatical (and/or semantic) number, issues involving reference, and noun subclass membership (i.e. count, noncount, and proper noun subclasses). These "determining" functions make determiners quite distinct from adjectival modifiers which generally provide qualitative information about nouns and cannot provide determining functions.
Within the noun phrase, determiners occur at the far left edge of the noun phrase before the noun head and before any optional adjective modifiers (if present):
Determiner + Adjective(s) + Noun
Examples follow:
the balloon
det noun
many balloons
det noun
all balloons
det noun
the big red balloon
many big red balloons
all big red balloons
The distinctness of the determiner and adjective positions relative to each other and the noun head is demonstrable in that adjectives may never precede determiners. Thus, the following are ungrammatical English nouns phrases: *big the red balloon, *big red the balloon (as well as *big many red balloons, *big red many balloons, *big all red balloons, *big red all balloons).
Determiners can be divided into three subclasses according to their position with respect to each other:
• predeteminers
• central determiners
• postdeterminers
Predeterminers may precede central determiners but may not follow central determiners. Postdeterminers follow central determiners but may not precede them. Central determiners must occur after predeterminers and before postdeterminers. Thus, a central determiner like the as in
the red balloons
can be preceded by a predeterminer like all as in
all the red balloons
predet cent.det
or the central determiner the can be followed by a postdeterminer like many as in
the many red balloons
cent.det postdet
A sequence of predeterminer + central determiner + postdeterminer is also possible as in
all the many red balloons
predet cent.det postdet
However, there are several restrictions on combinatory possibilities. One general restriction is that only one determiner can occur in each of the three determiner positions. For example, the postdeterminers many and seven can occur in the following
many smart children
seven smart children
the many smart children
the seven smart children
but both many and seven cannot occur in postdeterminer position rendering the following noun phrases ungrammatical: *many seven smart children, *seven many smart children, *the many seven smart children, *the seven many smart children. Additionally, there are often other lexical restrictions. For example, the predeterminer all can occur alone (as the sole determiner) or before a central determiner (e.g. all children, all the children, all these children, all my children); however, the predeterminer such can only occur alone or before central determiner a (e.g., such nuisance!, such a nuisance!).
Predeterminers include words like all, both, half, double, twice, three times, one-third, one-fifth, three-quarters, such, exclamative what. Examples with predeterminers preceding a central determiner:
all the big balloons
both his nice parents
half a minute
double the risk
twice my age
three times my salary
one-third the cost
one-fifth the rate
three-quarters the diameter
such a big boy
what a clever suggestion
Central determiners include words like the, a/an, this, that, these, those, every, each, enough, much, more, most less, no, some, either, neither, which, what.
Examples of central determiners preceding adjectival modified noun heads:
the big balloon
a big balloon
this big balloon
that big balloon
these big balloons
those big balloons
every big balloon
each big balloon
no big balloon
some big balloons
either big balloon
While the, a/an, no, and every only function as determiners, the other central determiners can also function as members of other lexical categories, especially as pronouns. For example, that functions as a determiner in
That item is our belonging.
but as pronoun in
That is our belonging.
In additional to the above determiners, noun phrases with a genitive enclitic -’s can have a determinative function like genitive determiners his, her, its, their. These genitive determinative noun phrases occur in the central determiner position:
[ my stepmother’s ] friendly children
both [ my stepmother’s ] friendly children
[ my stepmother’s ] many friendly children
all [ my stepmother’s ] many friendly children
##### =Articles=
Articles are words like a/an, and the that modify nouns. They occur in the central determiner position. Articles have several functions including marking definiteness, specific/generic reference, given/new information in discourse, and noun subclass membership (i.e. count, noncount, and proper noun subclasses).
The definite article "the" is used to refer to a specific instance of the noun, often already mentioned in the context or easy to identify. Definite articles are slightly different from demonstratives, which often indicate the location of nouns with respect to the speaker and audience.
• "Let us look for a good restaurant."
• "What about the restaurant we ate at last week?"
• "That restaurant was terrible. What about this one on the corner here?"
##### Post-modification
• adjectival modification (jokes galore)
• prepositional phrase modification (men in tights)
• clausal modification (planes flying overhead, jokes that I love, et cetera)
#### Pronouns
##### Gender
A remnant of grammatical gender is also preserved in the third person pronouns. Gender is assigned to animate objects based on biological gender (where known), and to personified objects based on social conventions (ships, for example, are often regarded as feminine in English). He is used for masculine nouns; she is used for feminine nouns; and it is used for nouns of indeterminate gender and inanimate objects. The use of it to refer to humans is generally considered ungrammatical and impolite, but is sometimes used deliberately as a term of offence or insult as it implies the person is of indeterminate gender or, worse, sub-human - a thing. (See for example: A Child Called "It")
Traditionally, the masculine he was used to refer to a person in the third person whose gender was unknown or irrelevant to the context; recently, this usage has come under criticism for supporting gender-based stereotypes and is increasingly considered inappropriate (see Gender-neutral language). There is no consensus on a replacement. Some English speakers prefer to use the slightly cumbersome "he or she" or "s/he"; others prefer the use of they (third plural) (see singular they). This situation rarely leads to confusion, since the intended meaning can be inferred from context, e.g. "This person has written me a letter but they have not signed it." However, it still is considered by some to be incorrect grammar. Spivak pronouns have also been proposed which are essentially formed by dropping the leading <th> from the plural counterpart, but their use is relatively rare compared to other solutions. For comparison, speakers of German distinguish between the homophonous sie ("she"), sie ("they"), and Sie ("you", polite) with little difficulty.
The categorization of nouns is typically expressed by one or more of the elements called deictic, numerative, epithet, and classifier. We shall consider each of these in turn.
##### Case
Historically, English used to mark nouns for case, and the two remnants of this case marking are the pronominal system and the genitive clitic (which used to be called the Saxon genitive). The genitive is marked by a clitic at the end of the modifying noun phrase. This can be illustrated in the following manner:
The president from the company’s daughter was married yesterday.
The ’s clitic attached to company does not modify company but rather modifies the entire noun phrase president from the company. This can be shown more clearly using brackets:
[The president from the company]’s daughter was married yesterday.
English pronoun forms vary with number, person, case, and notional gender (only in 3rd person singular). Number and case distinctions have collapsed in the 2nd person singular in the standard formal language, although informal dialectal forms have number distinctions (for example singular you vs. plural y'all, youse, etc.).
Case 1st 2nd 3rd
sg. pl. sg. pl. interrogative
male female neuter
Subjective I we you he she it they who
Objective me us him her them who(m)
Genitive determiner my our your his its their whose
nominal mine ours yours hers theirs
Notes
1. Some dialects use different forms for the second person plural pronoun: they include you-all or y'all , you guys, yu'uns , youse , or ye . These forms are generally regarded as colloquial and non-standard.
2. The pronoun thou was the former second person singular pronoun; it is considered an archaism in most contexts, although it is still used in some dialects in the north of England. Thou was originally the informal form to the formal you, is very rare, and is confined to dialects and religious and poetic functions. In modern Standard English, the second person plural you is used instead.
3. Mine (and thine) were also previously used before vowel sounds to avoid a glottal stop. e.g., "Do mine eyes deceive me?” "Know thine enemy." This usage is now archaic.
4. The objective form whom is most often found in formal English (as in writing) while the more common objective who is found in less formal writing and most speech. Prescriptivists state that who when used in objective context is "incorrect".
The reflexive pronouns are compounds consisting an genitive determiner pronoun and a following -self, with exception of the 3rd person singular male form which consists of the objective form him + -self and the 3rd person plural form with consists objective them + -self + -(e)s. In the plural, these reflexives take the regular plural suffix -s (with voicing of the f > v as with the free form of self > selves) along with the plural inflected pronoun form.
Case 1st 2nd 3rd
sg. pl. sg. pl. sg. pl.
male female neuter
Reflexive myself ourselves yourself yourselves himself herself itself themselves
Ourself is used instead of ourselves for any semantically singular version of we, such as the royal we.
In some dialects, the 3rd person male and 3rd person plural reflexives are formed with the genitive determiner his > hisself and their > theirself. Thus, these dialects have regularized the entire paradigm to genitive forms.
### Verbs
#### Verb classes
English verbs fall into two main types:
• main verbs (also full verbs)
• auxiliaries (also auxiliary verbs, helping verbs)
Main verbs are verbs like jump, take, catch, and hit. They are lexical in nature, carry the main semantic information within the verb complex, and are an open class (i.e. main verbs can be freely and productively created anew via word-formation processes). In the sentence
Halil is helping his brother.
the verb helping is the main verb.
Auxiliaries are verbs that typically precede the main verb in sentences. They are of limited number, contribute grammatical information to the verb complex, and are a closed class. In the sentence
Halil is helping his brother.
the verb is is the auxiliary.
Three verbs in English — be, have, and do — may function as both main verbs and as auxiliaries. Quirk et al. (1985) refer to these verbs as primary verbs. The following examples demonstrate their dual functionality:
Halil will be a student. (be as a main verb)
Halil is helping a student. (be as an auxiliary)
The girls have many books. (have as a main verb)
The girls have helped many students. (have as an auxiliary)
The girls may do their homework. (do as a main verb)
The girls do not help many students. (do as an auxiliary)
Besides the three primary verbs, the other auxiliaries are modals which include can, could, may, might, must, shall, should, will, and would. In addition to their restriction to functioning only as auxiliaries, modals can only occur in finite clauses and cannot be inflected for tense, number, or person.
More marginal to the class of modals are verbs like ought and in British varieties also need and dare. These display many but not all properties of modals and are thus termed marginal modals by Quirk et al. (1985).
Finally, the verb used (as in She used to called me everyday) is considered to be marginal modal by Quirk et al. (1985), but Huddleston & Pullum (2002) find several differences between it and the other modals and marginal modals, concluding that it is an auxiliary of the most marginal type. Semantically, used has reference to time, which distinguishes it from modals, which have modality as their main semantic component.
#### Inflectional morphology
English verbs only have eight possible inflectional forms:
(1) base form (also called plain form)
(2) -ing form
(3) -en form
• finite (or tensed) forms:
nonpast forms:
(4) general nonpast form
(5) 1st person singular nonpast form
(6) 3rd person singular nonpast form
past forms:
(7) general past form
(8) 1st/3rd person singular past form
The copula be has eight distinct inflectional forms as seen in the example sentences below:
The girl wants to be in school (base form: be) The girl is being a nuisance (-ing form: being) The girl has been a great help (-en form: been) The girls are students (general nonpast form: are) I am a student (1st sg. nonpast form: am) The girl is a student (3rd sg. nonpast form: is) The girls were students (general past form: were) The girl was a child (1st/3rd sg. past form: was)
However, most verbs (which include all regular verbs and some irregular verbs) have only four distinct inflectional forms:
The girl wants to jump in the lake (base form: jump)
The girl is jumping in the lake (-ing form: jumping)
The girl has already jumped in the lake (-en form: jumped)
The girls jump in the lake everyday (general nonpast form: jump)
I jump in the lake everyday (1st sg. nonpast form: jump)
The girl jumps in the lake everyday (3rd sg. nonpast form: jumps)
The girls jumped in the lake yesterday (general past form: jumped)
The girl jumped in the lake yesterday (1st/3rd sg. past form: jumped)
Unlike copula be, the verb jump has the same syncretic word-form jump for the base, general nonpast, and 1st. sg. nonpast forms (where the copula has be, are, am, respectively) and the same syncretic word-form jumped for the -en, general past, and the 1st/3rd sg. past forms (where the copula has been, were, was, respectively). Upon comparing other verbs with the copula, one finds that only the copula has a 1st/3rd sg. past form that is distinct from the general past form, a 1st sg. nonpast form that is distinct from the general nonpast, and a base form that is distinct from the general nonpast form — all other verbs display syncretism in these forms. The copula and a regular jump can be compared with each other and three types of irregular verbs in the table below.
English Verb Inflectional Paradigm
Copula be Regular verb Irregular verb with 5 inflections Irregular verb with 4 inflections Irregular verb with 3 inflections
-ing form being jumping taking building hitting
3rd Sg. Nonpast is jumps takes builds hits
1st Sg. Nonpast am jump take build hit
General Nonpast are
Base be
General Past were jumped took built
1st/3rd Sg. Past was
-en form been taken
All verbs (including the copula) form the -ing form with the addition of the -ing suffix to the base form:
BASE FORM + -ing
All regular verbs and most irregular verbs form the 3rd singular form with the addition of the -e(s) suffix to the base form:
BASE FORM + -(e)s
The parenthetical (e) above indicates that this suffix is spelled as either -es or -s. The -es form (pronounced [ɪz]) occurs after sibilant consonants. The -s spelling occurs after all other sounds. Examples:
• push-es [pʊʃ-ɪz] (sh represents sibilant consonant [ʃ])
• catch-es [kætʃ-ɪz] (ch, dge represents sibilant consonant [tʃ])
• (judge-es) > judges [dʒʌdʒ-ɪz] (dge represents sibilant consonant [dʒ])
• fit-s, dig-s, bathe-s, pan-s, pay-s (t, g, the, n, ay represent non-sibilant sounds )
All regular verbs form the past/-en form (as well as the syncretic 1st/3rd past) with the addition of the -ed suffix to the base form:
BASE FORM + -ed
##### Irregular verb morphology
Irregular verbs may have the same syncretism as regular verbs (like catch) or may show less syncretism with five distinct forms (like take) or more syncretism with only three distinct forms (like hit). (See also: English irregular verbs.) Examples of the three types differing in the number of distinct inflectional forms:
• irregular verbs with 5 forms: take, break, swim, grow, drive, do
• irregular verbs with 4 forms: catch, build, have, feel, tell, say
• irregular verbs with 3 forms: hit, put, hurt, bet, cut, cast
Irregular verbs with five distinct inflectional forms do not syncretize the general past and the -en forms. Irregular verbs with only three forms have the syncretism involving all forms except for the -ing form and the 3rd sg. nonpast form.
Irregular verbs with five and four inflectional forms have different patterns of past formation and -en formation. Many of the patterns involve vowel ablaut (i.e. internal vowel changes) and/or the addition of suffixes. Some of the more common patterns are briefly mentioned below. Note that the spelling does not always reflect pronunciation changes in the internal vowel, so the pronunciation is transcribed phonetically:
• Voicing change in last consonant between base and past/-en forms (d is voiced, t is voiceless):
bend ~ bent build ~ built
• Vowel change and suffixation of t between base and past/-en forms:
sleep [sliːp] ~ slept [slɛpt] (slep + -t) deal [diːl] ~ dealt [dɛlt] (deal + -t)
• Replacing of vowel and final consonant(s) in base form with [ɔːt] in past/-en form:
think [θɪŋk] ~ thought [θɔːt] catch [kætʃ] ~ caught [kɔːt]
• Vowel change between base and past/-en forms and -(e)n suffixation:
break [breɪk] ~ broke [broʊk] ~ broken [broʊkən] (broke + -(e)n) steal [stiːl] ~ stole [stoʊl] ~ stolen [stoʊlən] (stole + -en) tear [tɛər] ~ tore [tɔər] ~ torn [tɔːrn] (tor(e) + -n)
• Vowel change between base/-en and past forms and -(e)n suffixation:
draw [drɔː] ~ drew [druː] ~ drawn [drɔːn] (draw + -n) fall [fɔːl] ~ fell [fɛl] ~ fallen [fɔːlən] (fall + -en) take [teɪk] ~ took [tʊk] ~ taken [teɪkən] (take + -(e)n)
• Vowel changes in base, past, & -en forms:
swim [swɪm] ~ swam [swæm] ~ swum [swʌm]
• Vowel changes in base, past, & -en forms with -(e)n suffixation:
drive [drаɪv] ~ drove [droʊv] ~ driven [drɪvən] (drive + -(e)n)
fly [flаɪ] ~ flew [fluː] ~ flown [floʊn] (flow + -n)
A few verbs also have irregular changes between the general present and the 3rd sg. present forms:
have [hæv] ~ has [hæz] (and not the expected 3rd sg. *haves [hævz]) do [duː] ~ does [dʌz] (and not the expected 3rd sg. *dos [duːz]) say [seɪ] ~ says [sɛz] (and not the expected 3rd sg. [seɪz])
The copula paradigm also has suffixation and vowel ablaut, but it is additionally marked by suppletion. (See the table above for its eight inflected forms.)
##### Defective verbs
A final thing to mention is that a few verbs are defective in that they are not inflected or are missing some inflectional forms. The verb beware has only the base form beware. It is usually found in imperative sentences:
Beware of the dog.
The forms bewaring, bewares, bewared are not present in Modern English.
The verb used only occurs in past form, as in
We used to go to the beach every day when I was young.
or in the base form only following do, as in
We didn't use to go the beach every day.
This used verb indicates habitual action or states in the past and should not be confused with the other verb use which is a regular verb.
The verb stride is missing a past participle form in its inflectional paradigm for many speakers (for some speakers who do have a past participle form, the form may variously be stridden, strid, or strode).
The verbs rumored and reputed only occur in the -en form in passive sentences:
Halil is rumored to have participated in the scandal.
Halil is reputed to have connections with the scandal.
All modals (can, could, should, might, etc.) are defective.
##### Auxiliary inflection
Of the auxiliaries, only be, have, and do are inflected for tense, number, and person. The auxiliary be has the same eight inflectional forms as a main verb (the copula) and have and do likewise have the same five inflectional forms as when functioning as main verbs. In contrast, modals are uninflected auxiliaries with respect to these grammatical parameters (and are thus defective).
However, most auxiliaries share the additional inflection of negation. Negative inflection consists of a -n't suffix that is attached to the auxiliary. Thus, there are the following inflected auxiliary forms:
be
aren't (are + -n't)
isn't (is + -n't)
weren't (were + -n't)
wasn't (was + -n't)
ain't [dialectal, prescriptively "incorrect"]
have
haven't (have + -n't)
hasn't (has + -n't)
do
don't (do + -n't)
doesn't (does + -n't)
didn't (did + -n't)
modals
can't (can + -n't)
couldn't (could + -n't)
mayn't (may + -n't) [very rare]
mightn't (might + -n't)
mustn't (must + -n't)
shan't (shall + -n't)
won't (will + -n't)
wouldn't (would + -n't)
marginal auxiliaries
daren't (dare + -n't) [rare, mostly British]
needn't (need + -n't) [rare, mostly British]
oughtn't (ought + -n't) [ungrammatical in some varieties]
usedn't (used + -n't) [ungrammatical in some dialects, mostly British]
The negative forms don't [doʊnt] (and not the expected [dunt]) and won't [woʊnt] (and not the expected [wɪlnt]) are irregular in their changes in internal vowel, and shan't is irregular in its deletion of the final consonant (and in RP its vowel has shifted from [æ] to [ɑː]). The forms mayn't and shan't are now rare (particularly so with mayn't) and are virtually absent in standard varieties of American English.
Traditional grammar views -n't not as an inflectional suffix but as simply a phonologically reduced form (in traditional terms contracted) of the grammatical word not. According to this view, haven't is equivalent to non-contracted have + not, doesn't = does + not, etc. These contracted negative forms are, thus, equated with the reduced (contracted) forms of some of the other auxiliaries, namely are > ’re, is > ’s, am > ’m, have > ’ve, has > ’s, had > ’d, does > ’s, will > ’ll, would > ’d. Although this is the historical origin of the negative forms, clearly in the modern language the -n't in these words are suffixes forming a single indivisible word as the negative auxiliaries display different syntactic behavior compared with constructions consisting of auxiliary + not:
Didn't Halil bring the coffee?
*Did not Halil bring the coffee?
*Did Haliln't bring the coffee?
Did Halil not bring the coffee?
Sadaf brought the coffee, didn't she?
*Sadaf brought the coffee, did not she?
*Sadaf brought the coffee, did shen't?
Sadaf brought the coffee, did she not?
Additionally, it can also be shown that the reduced forms of the other auxiliaries do not behave similarly to the negative auxiliaries:
Shouldn’t Halil go to the store? (cf. Halil shouldn’t go to the store.)
*Should’ve Halil gone to the store? (cf. Halil should’ve gone to the store.)
*He’dn’t go to the store if she asked him.
He’d’ve gone to the store if she had asked him.
Finally, the negative inflection property applies generally to auxiliaries but not to main verbs. There are two exceptions to this, however, involving the "primary" verbs. The verb be as a main verb may also be inflected in the negative as the following examples show:
The student wasn't being considered fairly. (negative inflection as auxiliary)
The student wasn't a sophomore. (negative inflection as main verb)
In British varieties, have may also have negative forms as a main verb while are ungrammatical for most American varieties:
The student hasn't been treated fairly. (negative inflection as auxiliary)
The student hasn't enough time. (negative inflection as main verb — British)
The other "primary" verb, however, cannot have negative forms when acting as a main verb.
This case of properties of auxiliaries applying to be and have is also seen in other syntactic behavior, such as in the inversion of subject and auxiliary operator. (See the operator section.)
Thus, ’ve, ’m, ’s, etc. are phonologically reduced (i.e. contracted) forms of separate words whereas the negative -n’t is not a contracted separate word but rather a (inflectional) suffix.
##### Agreement
Most English verbs mark number (in agreement with their subjects) only in the non-past tense, indicative mood. In this context, there is a contrast between the 3rd person and all other persons (i.e., 1st and 2nd): the 3rd person is marked with a -(e)s suffix while all other persons are unmarked (i.e. without overt marking). Furthermore, the inflectional suffix -(e)s also indicates singular number, i.e. -(e)s indicates a 3rd person singular subject. Similarly, singular number is only indicated in the 3rd person — number in the other persons are unmarked. The plural in the 3rd person is unmarked. The 3rd person singular suffix is added to the general present tense form while the unmarked form is general present tense form. There is, thus, only a distinction between a general present form and 3rd person singular form.
General 3rd Singular
listen listen-s
push push-es
Combined with personal pronoun subjects, the following are the possible subject-verb combinations:
General 3rd Singular
I/we/you/they push he/she/it pushes
The copula be, however, makes additional distinctions of the 1st person singular in the non-past and the 1st or 3rd person singular in the past. Unlike other verbs, these inflected forms of be lie in a suppletive relationship.
Non-past Past General 1st Singular 3rd Singular are am is were was
Pronoun subject-verb combinations:
Non-past Past General 1st Singular 3rd Singular we/you/they are I am he/she/it is we/you/they were I/he/she/it was
In the subjunctive mood, all person and number distinctions are neutralized (see below).
#### Structure of the verb "complex"
##### Operator
The first auxiliary in the verb complex is termed the operator. It is displays a number of distinct syntactic and morphological characteristics.
• subject-operator inversion
[The large man with a cane ] has been coming your way.
Has [the large man with a cane ] been coming your way?
[The woman ] has been flying a kite, and [her son ] has been flying a kite, too.
[The woman ] has been flying a kite, and so has [her son ] . (with coordination ellipsis)
#### Time, tense and aspect
Changes in tense in English are achieved by the changes in ending and the use of auxiliary verbs "to be" and "to have" and the use of the auxiliaries "will", "shall" and "would". (These auxiliaries cannot co-occur with other modals like can, may, and must.) The examples below use the regular verb to listen:
• Present tenses
• Simple present (or simply "present"): "I listen." This tense typically expresses habitual actions. Rarely, it is used to refer to present time in reportative style speech.
• Present continuous (or "present progressive"): "I am listening." This tense expresses actions in the present taking place as the speaker is speaking or in the future.
• Present perfect: "I have listened." This tense expresses actions that began in the past but are still true in the present: "I have known her for six years" (and I still know her). This is also used to express a completed action that took place at a non-specific moment in the past. This tense often expresses actions that happen in the past, yet cannot be considered a past tense because it always has a connection to the present.
• Present perfect continuous: "I have been listening." This is used to express that an event started at some time in the past and continuing to the present.
• All forms of the present tense are often used in place of their future-tense counterparts. In particular, various kinds of subordinate clauses — especially if and when clauses — cannot generally use the future tense, so the present tense is used instead.
• Past tenses
• Simple past: "I listened." This is used to express a completed action that took place at a specific moment in the past. (Confusingly, in US English, the simple past may sometimes be used for a non-specific moment in the past).
• Past continuous (otherwise known as the imperfect or past progressive): "I was listening." This is used to express an incomplete action in the past. (Thus, an "imperfect" action, as opposed to a completed and therefore "perfect" action.)
• Past perfect or pluperfect: "I had listened." This expresses an action completed before some other action in the past (often expressed by the simple past). The pluperfect is thus expressing an action even more in the past e.g. "He realised he had lost his way", "I was going to town because he had spoken to me".
• Past perfect continuous or simply "perfect continuous": "I had been listening." Usually used with an explicit duration, this indicates that an event was ongoing for a specific time, e.g. "When Peter entered my room, I had been listening to music for half an hour."
• Future tenses
• Simple future: "I shall/will listen." This is used to express that an event will occur in the future, or that the speaker intends to perform some action.
• Future continuous: "I shall/will be listening." This is used to express an ongoing event that has not yet been initiated.
• Future perfect: "I shall/will have listened." This indicates an action which will occur before some other action in the future: Normally two actions are expressed, and the future perfect indicates an action which will occur in the future but will, at the time of the main future action expressed, be in the past (e.g. "I will know the tune next week because I will have listened to it").
• Future perfect continuous or future imperfect: "I shall/will have been listening." Expresses an ongoing action that occurs in the future, before some other event expressed in the future.
• "I am going to listen" is a construction using "to go" as an auxiliary. It is referred to as going to future, futur proche or immediate future, and has the same sense as the simple future, sometimes with an implication of immediacy. It is not strictly a tense, and "to go" is not strictly a tense auxiliary verb, but this construction often is presented as a tense for simplicity. By varying the tense of the auxiliary "to go", various other meanings can be achieved, e.g. "I am going to be listening" (future continuous), and "I was going to listen" (conditional perfect continuous).
• Conditional tenses
• Present conditional or simply conditional: "I would listen." This is used to express an event that occurred multiple times or was ongoing in the past (i.e. When I was younger, I would listen. [multiple times]), or something that would be done now or in the future when predicated upon another condition (i.e. “If I had the time, I would listen to you.” [This condition could be known from context and omitted from the conditional statement.])
• Present continuous conditional: "I would be listening." This is used to express an ongoing event that had not yet been initiated.
• Conditional perfect: "I would have listened." Indicates that an action would occur after some other event.
• Conditional perfect continuous: "I would have been listening": Expresses an ongoing action that would occur in the future in the past, after some other event.
Auxiliary verbs may be used to define tense, aspect, or mood of a verb phrase.
As mentioned above "going to" is used for some future pseudo-tenses:
Forms of "do" are used for some negatives, questions and emphasis of the simple present and simple past:
1. "Do I listen?" "I do not listen." "I do listen!"
2. "Did I listen?" "I did not listen." "I did listen!"
##### Verb tense chart
English verb tenses can be better visualized in the following chart, which shows the times of the English language and its three aspects, namely Prior, Complete, and Incomplete. Note that this chart only represents actions truly happening, be it present, past, or future. Since unreal conditionals are obviously assumptions, conditional structures with 'would' are not included here.
PAST PRESENT FUTURE
PRIOR ASPECT Past Perfect Present Perfect Future Perfect
COMPLETE ASPECT Simple Past Simple Present Simple Future
INCOMPLETE ASPECT Past Continuous Present Continuous Future Continuous
#### Voice
English has two voices for verbs: the active and the passive. The basic form is the active verb, and follows the SVO pattern discussed above. The passive voice is derived from the active by using the auxiliary verb "to be" and the -en form of the main verb.
Examples of the passive:
Passive voice Active voice
I am seen by John John sees me
You will be struck by John John will strike you
It was stolen by John John stole it
We were carried by John John carried us
They have been chosen by John John has chosen them
Furthermore, the agent and patient switch grammatical roles between active and passive voices so that in passive the patient is the subject, and the agent is noted in an optional prepositional phrase using by, for example:
1. active: I heard the music.
2. passive: The music was heard (by me). (Note: me, not I)
The passive form of the verb is formed by replacing the verb with to be in the same tense and aspect, and appending the -en form of the original verb. Thus:
Tense Active voice The same sense, expressed with the passive voice
Simple present
I hear the music. The music is heard by me.
Present progressive I am hearing the music. The music is being heard by me.
Past progressive I was hearing the music. The music was being heard by me.
Past perfect I had heard the music. The music had been heard by me.
Simple future I will hear the music. The music will be heard by me.
This pattern continues through all the composite tenses as well. The semantic effect of the change from active to passive is the depersonalisation of an action. It is also occasionally used to topicalize the direct object of a sentence, or when the agent is either unknown or unimportant even when included, thus:
1. The plane was shot down.
2. Dozens were killed.
3. Bill was run over by a bus.
Many writing style guides including Strunk and White recommend minimizing use of the passive voice in English; however, many others do not.
There is a third 'voice' in English, related to the classic "middle" voice. In this, the patient becomes the subject, as in passive, but the verb remains in apparently active voice, no agent can plausibly be supplied, and generally, an adverbial modifies the entire construction. Thus:
1. She does not frighten easily.
2. This bread slices poorly.
3. His novels sell well.
#### Modals and modality
English has "moods" of verb. These always include the declarative/indicative and the subjunctive moods, and normally the imperative is included as a mood. Some people include conditional or interrogative forms as verbal moods.
##### Indicative, or declarative, mood
• The declarative mood or indicative mood is the simplest and most basic mood. The overwhelming majority of verb use is in the indicative, which may be considered the "normal" form of verbs, with the subjunctive as an "exceptional" form of verbs. (If any other forms are considered a mood (e.g. imperative), they may also be considered other "exceptional" verb forms.)
Examples are most commonly used verb forms, e.g.:
* I think
* I thought
* He was seen
* I am walking home.
* They are singing.
* He is not a dancer.
* We are very happy.
##### Subjunctive mood
• The subjunctive mood is used to express counterfactual (or conditional) statements, and is often found in if-then statements, and certain formulaic expressions. It is typically marked in the present tense by the auxiliary "were" plus the -ing form of the verb.
1. Were I eating, I would sit.
2. If they were eating, they would sit.
3. Truth be told...
4. If I were you... I would do that.
The conjugation of these moods becomes a significantly more complex matter when they are used with different tenses. However, casual spoken English rarely uses the subjunctive, and generally restricts the conditional mood to the simple present and simple past. A notable exception to this is the use of the present subjunctive in clauses of wish or command which is marked in one or two ways: (1) if third person singular, the "-s" conjugation called for by the declarative mood is absent, and (2) past tense is not used. For example, "They insisted that he go to chapel every morning" means that they were requiring or demanding him to go to chapel. However, "They insisted that he went to chapel every morning" means they are reasserting the statement that, in the past, he did attend chapel every morning. The underlying grammar of this distinction has been called the "American subjunctive". On the other hand, other constructions for expressing wishes and commands, which do not use the subjunctive, are equally common, such as "They required him to go..."
##### Imperative mood
• The imperative mood is used for commands or instructions. It is not always considered a verbal mood per se. Using the verb in its simplest, unconjugated form forms it: "Listen! Sit! Eat!" The imperative mood in English occurs only in the second person, and the subject ("you") is generally not expressly stated, because it is implied. When the speaker gives a command regarding anyone else, it is still directed at the second person as though it were a request for permission, although it may be a rhetorical statement.
1. Let me do the talking.
2. Come here.
3. Give him an allowance.
4. Let sleeping dogs lie.
##### Modal forms
Conditional forms of verb are used to express if-then statements, or in response to counterfactual propositions (see subjunctive mood, above), denoting or implying an indeterminate future action. Conditionals may be considered tense forms but are sometimes considered a verbal mood, the conditional mood.
Conditionals are expressed through the use of the verbal auxiliaries could, would, should, may and might in combination with the stem form of the verb.
1. He could go to the store.
2. You should be more careful.
3. I may try something else.
4. He might be heading north.
Note that for many speakers "may" and "might" have merged into a single meaning (that of "might") that implies the outcome of the statement is contingent. The implication of permission in "may" seems to remain only in certain uses with the second person, e.g. "You may leave the dinner table."
Two main conditional tenses can be identified in English:
I would think = Present Conditional
I would have thought = Conditional Perfect
#### Notes
1. In English, a long-standing prescriptive rule holds that shall denotes simple futurity in the first person, and will denotes simple futurity in the second and third persons. In American English, this distinction has largely vanished; will is normally used for both cases, and shall is rare. In British English, adherence to the rule has declined during the 20th century (see Shall and will for a more detailed discussion), although use of shall remains for expressing the simple future in the first person.
2. The distinction between tense, aspect, and mood is not clear-cut or universally agreed-upon. For example, many analysts would not accept that English has twelve tenses. The six "continuous" (also called "progressive") forms in the list above are often treated under the heading of "aspect" rather than tense: the simple past and the past continuous are examples of the same tense, under this view. In addition, many modern grammars of English agree that English does not have a future tense (or a future perfect). These include two large recent grammars:
#Biber, D., S. Johansson, G. Leech, S. Conrad & E. Finegan. 1999. Longman grammar of spoken and written English. Harlow, Longman.
#Huddleston, R. & G. Pullum. 2002. The Cambridge grammar of the English language. Cambridge, CUP.
The main argument given by Huddleston and Pullum (pp 209-10) that English does not have a future tense is that "will" is a modal verb, both in its grammar and in its meaning. Biber et al. go further and say that English has only two tenses, past and present: they treat the perfect forms with "have" under "aspect". Huddleston & Pullum, on the other hand, regard the forms with "have" as "secondary tenses".
#### Verb phrases
Adjectives are words that can be used attributively within noun phrases where they (pre-)modify noun heads and predicatively within verb phrase where they are the complement of copular verbs. For example, in the sentence below the adjective tall occurs within the noun phrase the tall man modifying the noun head man. The adjective nice occurs within the verb phrase is nice as the complement of the (copular) verb head is.
[The tall man ] [is nice ]
The adjectives also act as the head of adjective phrases as in the following:
The [very tall ] man is [rather nice ]
Here the adjectives tall and nice are the heads of the adjective phrases very tall and rather nice.
Semantically, adjectives provide more information about them. Adjectives are used to describe and identify their associated nouns.
A further morphological characteristic of adjectives, which is also shared with adverbs, is their ability to be inflected in comparison: tall-er, tall-est. See also the comparison section.
#### Semantic ordering
The term adverb originating from traditional grammar refers to a wide range of words that have different functions and different syntactic behaviors. Therefore, it is best to separate adverbs into different subclasses and discuss the grammar of each subclass separately.
Adverbs of degree (or intensifiers) roughly qualify a point on a gradable semantic property. Below are some degree adverbs:
• very
• extremely
• etc.
The very fast car is running smoothly. (very modifying adjective fast)
The very kindly gentleman fixed my car. (very modifying adjective kindly)
The fast car is running very smoothly. (very modifying adverb smoothly)
The kindly gentleman is driving my car very fast. (very modifying adverb fast)
### Prepositions
#### Prepositional phrases
PP = (Modifier + ) P + NP : (right) on [the bus ]
## Clausal syntax
### Word order
English is a subject verb object (SVO) language: it prefers a sequence of subject–verb–object in its simplest, unmarked declarative statements. Thus, "Tom [subject] eats [verb] cheese [object]" and "Mary sees the cat."
However, beyond these simple examples, word order is a complicated matter in English. In particular, the speaker or writer's point of departure in each clause is a key factor in the organization of the message. Thus, the elements in a message can be ordered in a way that signals to the reader or listener what the message concerns.
• The duke has given my aunt that teapot. (i.e., I am going to tell you about the duke).
• My aunt has been given that teapot by the duke. (i.e., I am going to tell you about my aunt).
• That teapot has been given to my aunt by the duke. (i.e., I am going to tell you about that teapot).
The point of departure can also be set up as an equation, known as a thematic equative. In this way, virtually any element in a clause can be put first.
• "What the duke gave my aunt was a teapot" (i.e., I am going to tell you what the duke gave my aunt).
• "What happened was that the duke gave my aunt a teapot" (i.e., I am going to tell you what happened).
Usually, the point of departure is the subject of a declarative clause; this is the unmarked form. A point of departure is marked when it is not the subject — thus, occasionally it is the object ("You I blame for this dilemma") and more often an adverbial phrase ("This morning I got up late").
In questions, point of departure is treated slightly differently. English questions come in two types: wh-questions and yes-no questions. Ordinary (unmarked) questions of either type start with the word that indicates what the speaker wants to know.
• "Where is my little dog?" (I want you to tell me where.) [wh-question]
• "Is John Smith inside?" (I want you to tell me whether he is or is not). [yes-no question]
Special (marked) questions displace this key "what I want to know" word with some other element.
• "After tea, will you tell me a story?" (Still "will you or will not you?")
• "In your house, who does the cooking?" (Still "who?")
Either imperative clauses are of the type "I want you to do something" or "I want you and me to do something." The second type usually starts with let us; in the unmarked form of the first type, you is implied and not made explicit ("Improve your grammar!"), and included in the marked form ("You improve your grammar!"); another marked form is "Do improve your grammar." In the negative, "Do not argue with me" is unmarked, and "Do not you argue with me" is marked.
In spoken English, the point of departure is frequently marked off by intonation.
Generally, English is a head-initial language, meaning that the "anchor" of a phrase (segment of a sentence) occurs at the beginning of the phrase.
The main exception is that simple modifiers precede the noun phrases:
• A dog (article + noun)
• Blue house (adjective + noun)
• Fred's cat (possessive + noun) but man of the house (noun + prepositional phrase)
This leads to a sentence like: "Fred's sister ran quickly to the store." As can be inferred from this example, the sequence of a basic sentence (ignoring articles and other determiners as well as prepositional phrases) is: Adjective1 - Subject - Verb - Adverb - Adjective2 - Indirect Object - Adjective3 - Direct Object.
Interrogative sentences invert word order ("Did you go to the store?"). Changing a given sentence from active to passive grammatical voice changes the word order, moving the new subject to the front ("John bought the car" becomes "The car was bought by John"), and lexical or grammatical emphasis (topicalization) changes it in many cases as well (see duke-aunt-teapot examples above).
English also sees some use of the OSV (object-subject-verb) word order, especially when making comparisons using pronouns that are marked for case. For example, "I hate oranges, but apples I will eat." Far more rare, but still sometimes used is OVS, "If it is apples you like, then apples like I," although this last usage can sound contrived and anachronistic to a native speaker.
### Interrogative sentences
Interrogative word order is used to pose questions, with or without an expected answer. Most of the time, it is formed by switching the order of the subject and the auxiliary (or "helping") verb in a declarative sentence, as in the following:
1. Are you going to the party?
2. Is he supposed to do that?
3. How much do I owe you?
4. Where is the parking lot?
However, when the information being requested would be the subject of the answer, the word order is not inverted, and the interrogative pronoun takes the place of the subject, as in the following:
1. Who helped you with your homework?
2. What happened here?
When spoken, an intonation change is often used to emphasize this switch, or can entirely reflect interrogation in some cases (e.g. "John ran?"). The interrogative phrase can further be formed in this manner by moving the predicate of a declarative sentence in front of the helping verb and changing it to a demonstrative, relative pronoun, quantifier, etc. Ending the sentence with a question mark denotes the interrogative phrase .
Rhetorical questions can be formed by moving the helping verb-subject pair to the end of the question, e.g. "You would not really do that, would you?"
#### Types of Interrogative Sentences
There are three types of interrogative sentences (questions) in English:
1. Yes/no questions require “Yes/No” answers. For example: Do you like modern music? Is he a driver?
• Alternative questions express opposition and can be asked to any part of the sentence (like special questions). For example: Do you prefer tea or coffee? Did you or your mum tell him the truth?
2. Information questions (or Wh-questions) require special information while answering them. They are characterized by the presence of an interrogative pronoun in the first place (Why? When? How much? etc.) and can be asked to any part of the sentence. For example: Where did you spend last summer? Why have you done it?
• Questions to the subject require mentioning the doer of the action in the answer. For example: Who has broken the window? Who was talking to you when I saw you?
3. Tag questions (disjunctive questions) represent statements with tags separated by a comma. For example: You were at home yesterday, weren't you? He won't come tomorrow, will he?
#### Yes/No questions
Yes/No questions require an answer ‘yes’ or ‘no’. If there is a modal verb (can, must, should, may), an auxiliary verb (will, shall, have) or a form of the verb ‘to be’ in the sentence, put it in front of the subject.
• Mary is drinking tea. – Is Mary drinking tea?
• The friends have come. – Have the friends come?
• The houses were built last year. – Were the houses built last year?
• You must do it. – Must you do it?
• She'll come in ten minutes. – Will she come in ten minutes?
• They are from Canada. - Are they from Canada?
If there is no modal verb, auxiliary verb or the verb ‘to be’ in the sentence, yes/no questions are formed with the help of the auxiliary verb ‘do’. The auxiliary verb ‘do’ has no meaning. It just takes the form according to the main verb in the sentence.
‘do’ – in the present tense: if the subject of the sentence is the noun in the 1st person singular or plural (I or we), the 2nd person singular or plural (you), and the 3rd person plural (they).
• We go to the country every weekend. – Do we go the country every weekend?
• You like swimming. – Do you like swimming?
• They play football. – Do they play football?
‘does’ – in the present tense: if the subject of the sentence is the noun in the 3rd person singular (he, she, it).
• She cooks well. – Does she cook well?
‘did’ - in the past tense
• They arrived yesterday. – Did they arrive yesterday?
Note: the main verb in yes/no questions comes without any endings (-es, -s, ed) or in case of the past tense – in its first form (arrived – arrive, came – come).
To form negative yes/no questions you have to put the negative modal verb, negative auxiliary verb or negative form of the verb ‘to be’ in front of the subject.
• Can’t you help him?
• Aren’t you waiting for me?
If you need to form the negative yes/no question with the help of the auxiliary verb ‘do’, you have to use ‘don’t’ (do not), doesn’t (does not), or didn’t (did not) instead of ‘do’ does, or did.
• Don’t you know him?
• Didn’t you tell him the truth?
The peraphrastic negative is used in more formal English:
• Can you not help him?
• Are you not waiting for me?
• Do you not know him?
• Did you not tell him the truth?
#### Information questions
Information or Wh- questions require additional information for the answer (as opposed to simply yes or no as with yes/no-questions). To form such questions you have to put the question word (why? when? where? what? how? who? whom?) together with all of the words in the same phrase at the front of the sentence. If the question word is part of the subject you do not have to change the word order. The word order remains as in the statement.
• Who is playing the piano in the room now?
• Which car is hers?
If the question word is not part of the subject you have to use a modal verb (can, must, should, may), an auxiliary verb (will, shall, have) or a form of the verb ‘to be’ after the question word and in front of the subject.
• Where is Tommy?
• Where will you be waiting for me tomorrow?
If there is no modal verb, auxiliary verb or the verb ‘to be’ in the sentence, you have to use the auxiliary verb ‘do’ after the question word and in front of the subject.
• Where do your parents live?
• Why did he do it?
Note: the main verb in information questions comes without any endings (goes – go, plays – play, talked - talk) or in case of the past tense – in its first form (arrived – arrive, came – come).
#### Tags
##### Reversed polarity tags
Disjunctive questions (tag questions) Tag questions are statements with tags at the end. The tag consists of two or three parts.
1st part: a modal verb, an auxiliary verb, or a form of the verb ‘to be’ (if they are in the sentence) in the form required by the pronoun in the 3rd part.
2nd part: the particle ‘not’ if the statement is positive. If the statement is negative, the particle is omitted.
3rd part: the subject of the statement expressed by a noun.
• She is having a shower now, isn’t she?
• You can’t swim, can you?
If there is no modal verb, auxiliary verb or the verb ‘to be’ in the statement, you have to use the auxiliary verb ‘do’ in the tag.
• Henry played tennis well, didn’t he?
• We go to work by bus, don’t we?
Notes
(a) In BrE the main verb ‘to have’ behaves as an auxiliary.
• You have a brother and a sister, haven’t you? (BrE)
• You have a brother and a sister, don’t you? (AmE)
(b) If the subject of the statement is the indefinite pronoun ‘somebody’ in the tag it is replaced by the pronoun ‘they’.
• Someone’s knocking at the door, aren’t they?
(c) Such words like ‘nothing’, ‘never’, ‘hardly’ make the statements negative, so the tag should be positive.
• You never listen to me, do you?
(d) If the statement starts with ‘there’, this word counts as a pronoun, so it is placed on the 3rd place in the tag.
• ’’There's nothing here, is there?
(e) If the statement is an imperative, the tag will be ‘will you’ or ‘won’t you’.
• Be attentive, won’t you?
• Don’t be lazy, will you?
(f) If the statement contains ‘Let's’, the tag will be ‘shall we’.
• ’’Let's go to the cinema, shall we?
(g) More formal English uses peraphrastic negation in the tags to positive sentences:
• She is having a shower now, is she not?
• You cannot swim, can you?
• Henry played tennis well, did he not?
• We go to work by bus, do we not?
• You have a brother and a sister, have you not? (BrE)
• You have a brother and a sister, do you not? (AmE)
• Someone is knocking at the door, are they not?
• Be attentive, will you not?
Meaning of tags
The tag question requires the person to respond to the statement. Negative tags require a ‘Yes’ answer. Positive tags require a ‘No’ answer.
• ’’We've done the project, haven't we? – Yes, we have.
• We haven't done the project, have we? – No, we haven't.
##### Constant polarity tags
So, they read my article, did they?
### Topicalization
The book, I like. The movie, I don't. (cf. I like the book. I don't like the movie.)
To John, I gave the book. (cf. I gave the book to John.)
non-tensed VP topicaliztion:
Throw the ball, I will. (cf. I will throw the ball.)
but not
*Threw the ball, I.
instead non-tensed VP movement with do-support
*Throw the ball, I did. (cf. I threw the ball.)
• left dislocation
The book, I like it. (cf. I like the book.)
Jim, he is here. (cf. Jim is here.)
• cleft
It is the book (that) I like. (cf. I like the book.)
• pseudo-cleft
The book is what I like. (cf. I like the book.)
### Negation, negative polarity, and assertion
Halil is going with them.
Halil isn’t going with them. (inflectional "contraction" negation)
Halil is not going with them. (periphrastic negation)
Halil went with them
Halil didn't go with them. (do-support, inflectional "contraction" negation)
Halil did not go with them. (do-support, periphrastic negation)
Halil was receiving some help from his friends.
*Halil was receiving any help from his friends.
Halil was receiving no help from his friends.
*Halil wasn't receiving some help from his friends.
Halil wasn't receiving any help from his friends.
Halil wasn't receiving no help from his friends. (dialectal, prescriptively "incorrect")
Halil can drive a motorcycle and so can Cherif.
*Halil can drive a motorcycle and neither can Cherif.
*Halil can't drive a motorcycle and so can Cherif.
Halil can't drive a motorcycle and neither can Cherif.
Halil almost touched the bomb and so did Cherif.
*Halil almost touched the bomb and neither did Cherif.
*Halil hardly touched the bomb and so did Cherif.
Halil hardly touched the bomb and neither did Cherif.
• syntactic negation vs. lexical negation (clausal vs. subclausal)
Halil was unable to go and so was Cherif.
*Halil was unable to go and neither was Cherif.
*Halil wasn't able to go and so was Cherif.
Halil wasn't able to go and neither was Cherif.
• VP negation vs. non-VP negation
Do not ever accept this job position! (negation inside of VP)
Never ever accept this job position! (negation outside of VP)
restrictions on not:
He did not accept the position. (negation inside of VP)
*He not accepted the position. (negation outside of VP)
It is imperative [that he not accept the position ]. (negation outside of VP in subjunctive)
• scope of negation and ambiguity
The streets are not [safe because of the flood ]
interpretation #1 = the flood is not the reason for the unsafe streets (there is another cause)
The streets are not [safe ] because of the flood
interpretation #2 = the flood is causing the unsafe streets
All of the streets are not flooded
interpretation #1 = None of the streets are flooded
interpretation #2 = Not all of the streets are flooded
### Comparison
Adjectives and adverbs typically have the semantic feature of being gradable, that is the quality or state that they describe exists on a gradual scale between two opposite poles. For example, there is a gradable scale between the antonyms cold and hot. Gradable words of this type can have several modifiers that qualify where on the scale a particular quality or state rests as in the following $left \left(intensifier right \right) + begin\left\{Bmatrix\right\}$
` adjective `
` adverb`
end{Bmatrix} combinations:
very quick
rather quick
quite quick
too quick
quick
very quickly
rather quickly
quite quickly
too quickly
quickly
Most adjectives are gradable but some adjectives are not. For example, the adjective infinite is not gradable making the adjective phrases very infinite, rather infinite and more infinite semantically odd.
#### Types of comparison
Gradable adjective and adverbs can also be involved in comparison where to the positions of two or more entities on a gradable scale are compared with each other. Semantically, three types of comparison can be distinguished:
• higher degree (superior)
• same degree
• lower degree (inferior)
Comparisons of the same degree use only the general base adjective form.
In higher degree comparisons, the comparison is indicated either by inflectional suffixation, using -er, -est (morphological marking) or by periphrastic constructions involving more, most modifiers preceding the adjective (syntactic marking). The three inflectional forms are known as
Lower degree comparisons only use periphrastic constructions involving less and least adjectival modifiers.
Examples:
Inflectional Periphrastic
Same degree (Absolute) tall beautiful
Higher degree Comparative taller more beautiful
Superlative tallest most beautiful
Lower degree less tall, less beautiful
least tall, least beautiful
#### Comparative constructions
She is taller than Halil.
She is more tall than short. (note: *She is taller than short is ungrammatical)
She is as tall as Halil.
etc.
### Ellipsis
The phenomenon of ellipsis refers to omission of parts of sentences when those parts are readily recoverable in the context of an utterance. Some types of ellipsis are obligatory while other types of ellipsis are optional. Still other types are optional in certain grammatical environment but obligatory in other grammatical environments. For example, in the following sentences the underlined words can optionally be omitted:
The red sock and red shoe are in the hamper.
The red sock and shoe are in the hamper. (red is omitted)
Halil can drink coffee and John can drink coffee, too.
Halil can drink coffee and John can, too. (drink coffee is omitted)
Halil borrowed one of my CDs but I can't remember which CD.
Halil borrowed one of my CDs but I can't remember which. (CD is omitted)
This boy always has done bad things and always will do bad things.
This boy always has and always will do bad things. (done bad things is omitted)
Halil is drinking coffee at the table and John is drinking coffee at the bar.
Halil is drinking coffee at the table and John at the bar. (is drinking coffee is omitted)
The above examples involve ellipsis in the second component of a coordinated constituent. This type of ellipsis is very common. Other types of non-coordinated optional ellipsis are the following:
Do you want a drink?
Want a drink? (do you omitted)
Do you want a drink?
You want a drink? (do omitted)
It looks fine to me.
Looks fine to me. (it omitted)
Is the machine still broken?
Machine still broken? (is the omitted)
We meet on Wednesday mornings.
We meet Wednesday mornings. (on omitted)
Certain kinds of ellipsis indicate a more informal or familiar style of language while other types are neutral in the aspect.
A type of ellipsis that is always obligatory involves control constructions. These sentences are usually analyzed as consisting of a main clause with the verb of the main clause taking a non-finite clause as a complement.
Halil tried [to paint his house ] .
In the sentence above Halil tried [X ] is the main clause and the embedded (i.e. subordinate) non-finite clause is to paint his house. The non-finite clause is analyzed as having a subject which is obligatorily omitted in the surface sentence. In this case, the omitted subject is Halil (since it is Halil who making the painting attempt). Thus, the underlying structure is
Halil tried [Halil paint his house ] . (underlying Halil in the embedded clause is ungrammatical)
which has a subject that must be omitted (along with an infinitive marker to that must be added) to give:
Halil tried to paint his house. (Halil is omitted)
Types of ellipsis that are obligatory in certain constructions but optional in others include the that complementizer:
Post-nominal modification:
The man that I love will be there. (that is optionally present)
The man I love will be there. (that is optionally omitted)
Object:
He knows that I love him. (that is optionally present)
He knows I love him. (that is optionally present)
Extraposition:
It is obvious that I love him. (that is optionally present)
It is obvious I love him. (that is optionally omitted)
Subject:
That I love him is obvious. (that is obligatorily present)
*I love him is obvious. (omitting that is ungrammatical when the clause is in subject position)
## Diagrams
Diagrams like this were used in English grammar education:
"The teacher punished Johnny"
## Bibliography
• Adams, Valerie. (1973). An introduction to modern English word-formation. London: Longman.
• Bauer, Laurie. (1983). English word-formation. Cambridge: Cambridge University Press.
• Biber, Douglas; Johansson, Stig; Leech, Geoffrey; Conrad, Susan; & Finegan, Edward. (1999). Longman grammar of spoken and written English. Pearson Education Limited.
• Celce-Murcia, M.; & Larsen-Freeman, D. The grammar book: An ESL/EFL teacher's course (2nd ed.). ISBN 0838447252
• Curme, George O. (1931). Syntax. Boston: Heath.
• Curme, George O. (1935). Parts of speech and accidence. Boston: Heath.
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• Zandvoort, R. W. (1972). A handbook of English grammar (2nd ed.). London: Longmans. | {"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": 0.5839874148368835, "perplexity": 7943.136067301419}, "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-2014-15/segments/1398223202457.0/warc/CC-MAIN-20140423032002-00164-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://www.ams.org/joursearch/servlet/PubSearch?f1=msc&pubname=all&v1=58A10&startRec=1 | # American Mathematical Society
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[1] Douglas N. Arnold, Richard S. Falk, Johnny Guzmán and Gantumur Tsogtgerel. On the consistency of the combinatorial codifferential. Trans. Amer. Math. Soc. Abstract, references, and article information View Article: PDF [2] J. I. Cogolludo Agustín and D. Matei. Cohomology algebra of plane curves, weak combinatorial type, and formality. Trans. Amer. Math. Soc. 364 (2012) 5765-5790. Abstract, references, and article information View Article: PDF [3] Wojciech Domitrz and Żaneta Trȩbska. Symplectic $S_{\mu}$ Singularities. Contemporary Mathematics 569 (2012) 45-65. Book volume table of contents View Article: PDF [4] Cristian Barbarosie. Representation of divergence-free vector fields. Quart. Appl. Math. 69 (2011) 309-316. Abstract, references, and article information View Article: PDF [5] Scott O. Wilson. Differential forms, fluids, and finite models. Proc. Amer. Math. Soc. 139 (2011) 2597-2604. MR 2784829. Abstract, references, and article information View Article: PDF [6] Thérèse Falliero. Harmonic differentials and infinite geodesic joining two punctures on a Riemann surface. Trans. Amer. Math. Soc. 363 (2011) 3473-3488. MR 2775815. Abstract, references, and article information View Article: PDF [7] Bruce Solomon. X-rays of forms and projections of currents. Trans. Amer. Math. Soc. 363 (2011) 143-164. MR 2719676. Abstract, references, and article information View Article: PDF [8] Jean Van Schaftingen. Limiting fractional and Lorentz space estimates of differential forms. Proc. Amer. Math. Soc. 138 (2010) 235-240. MR 2550188. Abstract, references, and article information View Article: PDF [9] Irina Mitrea and Marius Mitrea. A remark on the regularity of the div-curl system. Proc. Amer. Math. Soc. 137 (2009) 1729-1733. MR 2470831. Abstract, references, and article information View Article: PDF [10] Maxim Braverman and Valentin Silantyev. Kirwan-Novikov inequalities on a manifold with boundary. Trans. Amer. Math. Soc. 358 (2006) 3329-3361. MR 2218978. Abstract, references, and article information View Article: PDF This article is available free of charge [11] Zengjian Lou and Alan McIntosh. Hardy space of exact forms on $\mathbb{R}^N$. Trans. Amer. Math. Soc. 357 (2005) 1469-1496. MR 2115373. Abstract, references, and article information View Article: PDF This article is available free of charge [12] Shusen Ding. Two-weight Caccioppoli inequalities for solutions of nonhomogeneous $A$-harmonic equations on Riemannian manifolds. Proc. Amer. Math. Soc. 132 (2004) 2367-2375. MR 2052415. Abstract, references, and article information View Article: PDF This article is available free of charge [13] Michael Farber. Morse-Bott inequalities. Math. Surveys Monogr. 108 (2004) 227-231. Book volume table of contents View Article: PDF [14] Michael Farber. Lusternik-Schnirelman theory, closed 1-forms, and dynamics. Math. Surveys Monogr. 108 (2004) 159-204. Book volume table of contents View Article: PDF [15] Michael Farber. Morse-Bott functions on manifolds with corners. Math. Surveys Monogr. 108 (2004) 213-226. Book volume table of contents View Article: PDF [16] Michael Farber. Equivariant theory. Math. Surveys Monogr. 108 (2004) 99-111. Book volume table of contents View Article: PDF [17] Michael Farber. Manifolds with corners. Math. Surveys Monogr. 108 (2004) 205-211. Book volume table of contents View Article: PDF [18] Michael Farber. The universal complex. Math. Surveys Monogr. 108 (2004) 49-60. Book volume table of contents View Article: PDF [19] Michael Farber. The Novikov numbers. Math. Surveys Monogr. 108 (2004) 1-33. Book volume table of contents View Article: PDF [20] Michael Farber. The Novikov inequalities. Math. Surveys Monogr. 108 (2004) 35-48. Book volume table of contents View Article: PDF [21] Michael Farber. Relative Morse theory. Math. Surveys Monogr. 108 (2004) 233-237. Book volume table of contents View Article: PDF [22] Michael Farber. Bott-type inequalities. Math. Surveys Monogr. 108 (2004) 81-90. Book volume table of contents View Article: PDF [23] Michael Farber. Morse theory of harmonic forms. Math. Surveys Monogr. 108 (2004) 125-157. Book volume table of contents View Article: PDF [24] Michael Farber. Construction of the universal complex. Math. Surveys Monogr. 108 (2004) 61-80. Book volume table of contents View Article: PDF [25] Michael Farber. Topology of Closed One-Forms. Math. Surveys Monogr. 108 (2004) MR MR2034601. Book volume table of contents [26] Michael Farber. Inequalities with Von Neumann Betti numbers. Math. Surveys Monogr. 108 (2004) 91-97. Book volume table of contents View Article: PDF [27] Michael Farber. Exactness of the Novikov inequalities. Math. Surveys Monogr. 108 (2004) 113-123. Book volume table of contents View Article: PDF [28] P. Domanski and B. Jakubczyk. Linear continuous division for exterior and interior products. Proc. Amer. Math. Soc. 131 (2003) 3163-3175. MR 1992857. Abstract, references, and article information View Article: PDF This article is available free of charge [29] Shusen Ding. Weighted Caccioppoli-type estimates and weak reverse Hölder inequalities for $A$-harmonic tensors . Proc. Amer. Math. Soc. 127 (1999) 2657-2664. MR 1657719. Abstract, references, and article information View Article: PDF This article is available free of charge [30] Shusen Ding. Weighted Hardy-Littlewood inequality for $A$-harmonic tensors. Proc. Amer. Math. Soc. 125 (1997) 1727-1735. MR 1372027. Abstract, references, and article information View Article: PDF This article is available free of charge
Results: 1 to 30 of 58 found Go to page: 1 2 | {"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": 0.9597654342651367, "perplexity": 4979.863334852006}, "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-2014-10/segments/1394678697956/warc/CC-MAIN-20140313024457-00039-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://www.math-only-math.com/use-of-decimal-in-measuring-the-length.html | # Use of Decimal in Measuring the Length
We will learn the use of decimal in measuring the length.
100 centimetres = 1 metre or 100 cm = 1 m
So, 1 cm is one hundredths of a metre.
or, 1 cm = $$\frac{1}{100}$$ m = 0.01 m
Similarly, 40 cm = 0.40 m (40 centimetres is forty hundredths of a metre)
25 cm = 0.25 m (25 centimetres is twenty five hundredths of a metre)
Metres and centimetres can be expressed together as decimals.
For example,
8 m 40 cm = 8.40 m
19 m 1 cm = 19.01 cm
24 m 5 cm = 24.05 cm
25 m 58 cm = 25.58 m
51 m 11 cm = 51.11 cm
98 m 36 cm = 98.36 cm | {"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": 0.5730672478675842, "perplexity": 4898.929156224397}, "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-2017-04/segments/1484560279224.13/warc/CC-MAIN-20170116095119-00109-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://cms.math.ca/10.4153/CJM-2001-001-x | location: Publications → journals → CJM
Abstract view
# The Equivariant Grothendieck Groups of the Russell-Koras Threefolds
Published:2001-02-01
Printed: Feb 2001
• J. P. Bell
Format: HTML LaTeX MathJax PDF PostScript
## Abstract
The Russell-Koras contractible threefolds are the smooth affine threefolds having a hyperbolic $\mathbb{C}^*$-action with quotient isomorphic to the corresponding quotient of the linear action on the tangent space at the unique fixed point. Koras and Russell gave a concrete description of all such threefolds and determined many interesting properties they possess. We use this description and these properties to compute the equivariant Grothendieck groups of these threefolds. In addition, we give certain equivariant invariants of these rings.
MSC Classifications: 14J30 - $3$-folds [See also 32Q25] 19L47 - Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91] | {"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": 0.9177801609039307, "perplexity": 3090.7439393180553}, "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-2014-41/segments/1412037663167.8/warc/CC-MAIN-20140930004103-00228-ip-10-234-18-248.ec2.internal.warc.gz"} |
https://physics.stackexchange.com/questions/104653/how-do-i-see-things-of-the-bright-room-being-in-the-dark-room/104943 | # How do I see things of the bright room, being in the dark room?
Visible light emitted or reflected from the objects around us provides information about the world.
If I sit in a dark room, and see the bright room outside, I am able to see all the objects of that bright room. In other words, it mean light emitted or reflected from those objects of the bright room are entering into the dark room. Shouldn't that make my room bright? But, my room is dark and I am able to see those objects of bright room, both are contrary?
Edit: If we consider another situation like the one in the picture below, lets assume that we move as far from the street light, that even in the presence of street light the place remains as dark as it was before. I believe even then we can see the street light, won't we?
If we agree that we still can see the lamp, it mean that we are able to see the lamp, without the ray from lamp hitting our eye? Won't it be contrary? Edit: Lets consider a laser beam in the dark room (in the picture room is not totally dark, but assume a dark room). Look the laser in the same angle as shown in the picture, as laser remains narrow over long distance, I hope we can assume light is not spreading in other directions. But I hope we can see it even though light is not spreading and reaching me, how is it possible?
• Related (though not a duplicate): How does a one-sided glass work? – John Rennie Mar 22 '14 at 10:57
• You only see most of the light entering in the room which directly falls upon your eyes. On the other hand when this light coming from outside falls upon the objects placed inside the dark room then most of it is absorbed and the remaining is scattered all around, hence you see do not see the things in the dark room well. – user31782 Mar 22 '14 at 10:58
• Other than that, I am unsure why you are attempting to find another explanation about how we see images in the world. If you look at a lamp and you believe you see it but you also believe that no light from the lamp is hitting your eyes, then if correct, you should be able to cover your eyes and block the light from it but still see the lamp – Jim Mar 25 '14 at 14:35
• @GODPARTICLE yes a laser is usually "unidirectional" but in this case, some of the light is bouncing off the air molecules and reaches your eyes. Try shining a low power laser in a dark room with no fog. You will not see the beam, only the dot when it hits something and bounces to your eyes. As I said before, you can only see things when light hits your eyes. If you think you are seeing something without light from it hitting your eyes, then cover your eyes. If you can't see it any more, then your eyes must have been getting light rays from it. – Jim Mar 26 '14 at 12:30
• you seem to be trying to show that there is at least one example of a time when we can see something without light from it hitting our eyes. I am unsure why you are so determined to prove this, but I can tell you that it is simply not possible. The fact is that we can only see the world around us when light from each object strikes our eyes. This is sound scientific fact. The logical conclusion is that if you can see something, light rays must be coming from it and hitting your eyes. The only thing left to do (as in the case of the laser) is figure out the path it took from source to your eyes – Jim Mar 26 '14 at 13:05
There exists coherent light and incoherent light
The laser is an example of coherent light, i.e. it can be described by a wave with a known amplitude and phase .
Amplitude is connected with the power that the beam distributes. In lasers this is very concentrated . Amplitude is also connected with the number of photons in the beam .
The street lamp is an example of incoherent light: individual atomic excitations emit photons incoherently so there exists no wave whose phases are known.
You also completely ignore diffusion of light. Diffusion of light is what gives us twilight when the sun goes down . Photons from the light hit on air atoms and change directions, no longer pointing at the source, as infinitesimal reflections.
Now in your last entry, the laser, the reason that one can see the green light is because of diffusion of the laser light in the air of the room. A small part of its photons hit the molecules of air and reach not only our eyes, but the whole surrounding ambiance, reflecting also from the walls etc. If the laser were in vacuum you would not see the beam unless you crossed it ( careful of your eye, though that would be the least of your worries if you were in vacuum :) )
Diffusion also accounts for the light in a dark room next to a lit room even if the source does not shine into the room . Light diffuses in the air enters the dark room hits the walls and furniture and "lights dimly" the dark. If the street lamp were in vacuum the light would illuminate only in the direct optical rays from the source and shadows would be sharp and black.
The further away one is from a light source the smaller the intensity of the beam, which in direct optical ray falls as 1/r^2. For diffusion it is more complicated because each rescatter from the molecules becomes a source and each reflection of light also becomes a source, still intensity falls rapidy with distance, that is why the dark room is mainly dark and the laser green line is clearly defined: the scatterings are few and mainly next to the beam, and do not markedly reduce the intensity of the laser beam.
• Everyone's answer is better in different considerations. I need not ignore other's effort, but bounty has to be offered restricted to the rules. As respected anna v is the first to provide idea with respect dust scattering light in her answer, I think she deserves it more. I really appreciate @anupam's effort and others. – Immortal Player Mar 31 '14 at 3:12
• Tyndal effect is related concept. Anyone interested can go through it. – Immortal Player Apr 16 '14 at 12:41
In the situation you are describing, the only thing one can take away is that the room you are in is brighter than it would be if the bright room were not there. It does not mean that your room has to be as bright as the bright room, just that your room is brighter than it would be otherwise.
For your new situation with the street lamp:
If you move very far away, but still within sight of the lamp, the light from the lamp or nearby bright objects will still reach your dark room. Your dark room will not be as dark as it was before, even if you judge it to be just as dark using only your eye. Since light is reaching the dark room, that light will cause the room to be a bit brighter.
Using the idea of intensity of light:
An intensity of zero at some point in space means there is no electromagnetic radiation; there is no light. If you stand in a place where the intensity of visible light is actually equal to zero, there is no light there. You won't be able to see anything with your eyes or any other visible light detector.
Make sure you're not confusing zero intensity with a very small intensity. These are very different ideas.
It might help if you take a particle-view of light. Think about the photons leaving the lamp and entering your eye. If they enter your eye, and you move away, they're going to hit the walls of the room instead.
• (+1)Thank you for the explanation. Please consider my edit. – Immortal Player Mar 22 '14 at 14:26
• I have added the second situation so as to say that no light from the street light is entering into the dark place. – Immortal Player Mar 24 '14 at 13:09
• Please consider 5th and 6th comment in Anupam's answer and edit accordingly, thank you once again for updates. – Immortal Player Mar 25 '14 at 14:30
• Question has been edited. – Immortal Player Mar 26 '14 at 11:21
I will try to answer your question as simply as I can but involving some biology (only a very basic thing). Now when do you see an object? Only when the light of that object hits your eyes and your eye detects it. When you look at an object, electrical signals travel via the optic nerves to an area in your brain called the thalamus. This then sends the information to the visual cortex, where it is examined in detail. Different parts of the visual cortex simultaneously process the colour, shape, movement and depth of the object. Other parts of the cortex put this information together to give you a complete picture of the object. Now you might think I am going off topic but it is just to build up a basic concept so that you do not get confused.
Now for the technical bit, say that the light from the lamp goes directly into your eye and nowhere else. Then, the room you are viewing from (i.e. the dark room) will not become any brighter than it initially is. You have to understand that only a fraction of the light rays emitted by an object hit your eye and are sufficient to create a visual picture. The rest hit the walls of your room and then hit your eye making the room seem a bit brighter than you originally think it is. If your room is closer to the light source then it will be more bright as the light loses less energy when it travels over a shorter distance. But if your room is far away, then the light from the source won't be enough for your room to become very bright. Though there will be a very little change in the brightness, you will not be able to make out the difference but the light reaching your eye will be enough to create a visual picture.
To conclude, in a room the light loses energy when it is reflected from wall to wall but when it directly hits your eye, it has sufficient energy to create a clear visual picture. It goes the same for viewing the objects of a bright room.
To give an example, take the example of the stars. You are viewing the stars from the window of your room. You are still able to see its light as it directly hits your eye, but the energy of the light isn't enough that it is able to light the room as most it gets absorbed as soon as it hits the wall of your room. The example of stars includes many other technical things but it would be best to not get into them. I hope this answers your question and clears your misinterpretation.
Edit after laser question See, with lasers there are two cases. One is invisible laser which you see only after it is reflected by an object. The one shown in the picture is visible in the sense that you can see the path of the laser. the phenomenon is known as Rayleigh Scattering. For more information please refer to the wiki page of the article on Rayleigh Scattering to understand the concept in detail.
http://en.wikipedia.org/wiki/Rayleigh_scattering
It is basically the reflection of particles from the dust and fog and other particles in the air. I hope this answers your question.
• Question has been edited. – Immortal Player Mar 26 '14 at 11:23
• Answer has been edited. – rahulgarg12342 Mar 26 '14 at 15:40
I don't know if you already understood it, but here is a simple explanation.
Take a torchlight, look at it directly. You'll be blinded. Now, shine a nearby object, you will see the bright, but it won't hurt.
Repeat the experiment with a very dim torchlight. If you look directly you will notice the light, but if you shine an object, you won't see anything.
Replace the torchlight with the light room and the nerby object with the dark room. Done!
• I hope you realize that there's always light coming into the room, unless you don't see the light. – jinawee Mar 25 '14 at 14:30
• And you can replace your eye with a camera, the same reasoning applies. – jinawee Mar 25 '14 at 14:40
• Question has been edited. – Immortal Player Mar 26 '14 at 11:21
• @GODPARTICLE The same holds. You see the laser because dust particles reflect the light. In vaccum, you can't see a laser. There is no black magic here! – jinawee Mar 26 '14 at 11:32
• I think I am not able to understand it, sorry if it is too silly question. If laser is unidirectional how could it come in other direction and hit my eye? I hope you understand what I am asking. – Immortal Player Mar 26 '14 at 11:34
your room is dark because either there is not a lot of light coming into it or because all objects in your dark room absorb the light, don't reflect it back. so the light coming from the bright room does not reflect from the walls and other objects of your room, hence it's dark.
in the case of the street light, it's the same. light coming from the bulb is not reflected off the air, it goes through it. notice how the guy and the road on the picture are relatively bright, these objects are reflecting light in all direction, including in the directions to your eyes. imagine that the light coming from the bulb is split into many rays. a few of them hit your eyes, making the bulb look bright. a few of the rays hit the road and the guy, they're reflected all over, and some of them hit your eyes - therefore the guy and the road look brighter than the air, but not as bright as the bulb itself.
• Question has been edited. – Immortal Player Mar 26 '14 at 11:24
• You're asking the same question again despite it being answered already. you see laser beam only because it's being reflected off the dust particles in the air on the way of its rays. Very little is reflected in direction of your eyes, so you see only the first reflection,I.e. only those particles which are inside the beam. – Aksakal Mar 26 '14 at 11:29
• Thank you for the comment. Ray is unidirectional, it is not going to reach my eye, I think. Isn't laser unidirectional? – Immortal Player Mar 26 '14 at 11:32
• Imagine a ray going in some direction. Unless it's reflected by the dust particle. Then it'll change the direction.Very few of these rays are redirected, very few of these in the direction of your eyes. This is my last post in this this question. – Aksakal Mar 26 '14 at 11:38
• Its great you are saying some new concept, I will be happy to know it if you could explain it in the answer, otherwise the discussion would continue by my misunderstanding.(+1) – Immortal Player Mar 26 '14 at 11:42
Hello GODPARTICLE, Answer for your question lies in reflection and intensity properties of light. Here is a good article which can "throw light on your question".
Now in that article you can see figure under 1.Dull surfaces. In that figure you can replace V which is viewer with something in your dark room say cup, bottle , pencil etc... and now you can figure out why you can not see those things as bright as it those things were in bright room. As you can read in that article "Dull surfaces reflect scattered light equally in all directions". So bottle or table in your dark room scatters light from point source in all direction. Now as far as I think what you are trying to ask is I am standing in dark part of your edited picture (street light) and one bottle is besides me. Now I can see all the things like a cup resides in brighter part of your street light picture and I can see it and I can also see point source (here street light) but why I can not see bottle which besides me in dark area??
In your situation(street light) the bottle is in place of V in figure of the given link and you are seeing bottle by light which is reflected two times from point source(street light). In real situation like yours bottle is not in place of v. But light that has been reflected already off lots of surfaces and then reaches to bottle and each time intensity is decreased before reaching to our eyes so we can not see bottle.
• Question has been edited. – Immortal Player Mar 26 '14 at 11:22
I am converting my comment into an answer with some mine amendment.
You only see most of the light entering in the room which directly falls upon your eyes. On the other hand when this light coming from outside falls upon the objects placed inside the dark room then most of it is absorbed and the remaining is scattered all around, hence you see do not see the things in the dark room well.
Amendment:
In the picture you have shown we do not see the road because most of the light falling on the road is absorbed and the remaining is scattered. On the other hand we can see the street light because light emitted from it directly falls on our eyes.
To check my argument practically place a mirror on the road at appropriate angle. The mirror will shine. Now remove this mirror you will see the dark road. This implies that most of the light falling on road is absorbed.
Edit:
@GODPARTICLE "...we are assumed to stand in such a place where light from the street lamp won't reach..". This is only possible if there is an obstacle in the path(this does not seem to be the case in your picture). We can see the light is the proof that light is reaching there. You can also put a photodetecter to prove if you don't believe your eyes. As I said in my answer: most of the light which falls on the surface of road undergoes diffuse reflection and remaining is absorbed.
If you place a plane mirror on the road then the light will not undergo diffuse refelection. A detectable light will fall on your eyes. This proves that light doesn't only falls on your eyes, it does fall on whole of the road. If there is no mirror placed then most of the light is absorbed and the remaining is scattered in all directions which causes an appearance of dark.
Edit-2
You say that:
"We stand at a place at which the intensity of light reaching our eye becomes zero s.t. there is no obstacle in the way of light."
This statement can be disproved.
First method: Assume the street light emit spherical wavefronts of light. The intensity of light at any distance $d$ from the source(street light). The intensity(power per unit area) of the light at $d$ is $$I = \frac{P}{A} = \frac{P}{4 \pi d^2}.$$ So at any finite distance from the street light the intensity doesn't become $0$.
If we further assume that the air absorb the light even then at any distance $d$ the intensity of light will not become $0$.
I do not know how to calculate the intensity of light for a spherical wavefront including absorbtion. I know for a plane wavefront. If the light emitted from a source is a plane wavefront then at any distance $d$ from the source the intensity of the light will become $$I = I_{0} \, e^{-\alpha \, d}$$, where $\alpha$ is the absorption cofficient. So at any finite distance $d$ the intensity of light will not become zero.
Second method: In this method I will disprove your argument by Proof by contradiction. A proof by contradiction is always the best proof of all.
To disprove the statement "Light reaching at a distance $d$ has $0$ intensity" I will prove the statement "Light reaching at at a distance $d$ does not has $0$ intensity." I do an experiment in which I stand in your dark room and see the street light. I use a convex lens and allows the light reaching in the dark room to fall on a small amount of water for a particular amount of time $T$ then I calculate the rise in the temprature of water. Knowing the specific heat of water I can calculate the energy of incident light. I know the cross-section area of my lens.
The intensity is equal to (Energy calculated/cross-section area)/T. Since the intensity comes out to be a positive quantity I conclude:
"If I can see the light then it has a finite intensity."
Now I again rearrange my experiment. This time I sit in a room in which I do not see the street light. I again calculates the intensity with my apparatus. I repeat this experiment many a times. The result of my experiments are:
" When I do not see the light Sometimes the intensity I measures comes out to be positive. Sometimes the intensity I measures comes out to be zero."
So from my experiment I conclude:
"If I do not see the light then the intensity sometimes comes out zero and sometimes positive"
This implies:
"In any case if I see the light the intensity of the light is not $0$."
This result disproves your argument: "...as the intensity of light is zero, even in that situation I believe that I can see the street lamp."
Hope this helps.
Regards.
• "On the other hand we can see the street light because light emitted from it directly falls on our eyes." I have said in my question and even in one of the comments that we are assumed to stand in such a place where light from the street lamp won't reach. So, we can't assume light to fall directly on our eyes. I mean we are assumed to stand in a place where intensity of light from the lamp is zero, I believe that even then we still can see the street lamp, won't we? Any way +1 for your time. – Immortal Player Mar 24 '14 at 16:44
• "In the picture you have shown we do not see the road because most of the light falling on the road is absorbed and the remaining is scattered." It may be the case near the street lamp where light reaches, I have posted that picture simply to consider the situation of street lamp, I am saying you to assume that we stand in the place where intensity of light from the lamp drops to zero, in that case you can't speak about light being scattered or absorbed, as the intensity of light is zero, even in that situation I believe that I can see the street lamp. – Immortal Player Mar 25 '14 at 5:03
• "...we are assumed to stand in such a place where light from the street lamp won't reach.... This is only possible if there is an obstacle in the path."- Why is it not possible if there is no obstacle in the path, go far enough from the lamp such that intensity drops to zero, won't it. We can confirm this by switching off the lamp, even then if the place remains as dark, it concludes that intensity of light reaching there from the lamp is zero. – Immortal Player Mar 25 '14 at 5:07
• @GODPARTICLE I am not exclaiming. The only way to ensure that the light reaching us has zero intensity is that we won't observe it. You say:" such that intensity is zero, I believe I could see the lamp." This is wrong. If intensity of the light is zero then energy involved with it will be zero, that is no light is present. So first try to prove that you can see a light of $0$ intensity. If you find a prove then explain in your question. In proving your argument remember intensity is inversly proptional to the square of distance from the source – user31782 Mar 25 '14 at 12:09
• Thank you for the comment. I just said what I believe, if you could answer my question, consider my last comment:) – Immortal Player Mar 25 '14 at 12:22 | {"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": 0.436788409948349, "perplexity": 414.3315996359932}, "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-2019-35/segments/1566027318243.40/warc/CC-MAIN-20190823083811-20190823105811-00480.warc.gz"} |
https://latex.org/forum/viewtopic.php?f=44&t=25473&p=86832 | ## LaTeX forum ⇒ Text Formatting ⇒ xytree enumerate top alignment Topic is solved
Information and discussion about LaTeX's general text formatting features (e.g. bold, italic, enumerations, ...)
Linguist
Posts: 35
Joined: Mon Nov 07, 2011 12:07 pm
### xytree enumerate top alignment
Hello,
I'm now using xytree to make autosegmental diagrams, which is great, However, when I want to enumerate my examples the number appears below the diagram.
So I did what every good LaTeX user should do, and I consulted the xytree documentation in which a solution for this problem involving \leavevmode is given. This solution works...
...but, the number is aligned with the bottom tier of the diagram when I want the number aligned with the top tier of the diagram. How can this be achieved?
Here's a MWE; showing spreading of vowel features in Rotuman. (In case you're wondering.)
\documentclass[a4paper,12pt]{report} \usepackage{xytree} \begin{document} \enumerate{ \item{\leavevmode \xy <7em,0pt>*\asrnode{\textsc{[+fr]}}="f1", <0pt,1cm>*\asrnode{s}="p1", <1em,1cm>*\asrnode{\ae}="p2", <2em,1cm>*\asrnode{k}="p3", <3em,1cm>*\asrnode{\ae}="p4", <4em,1cm>*\asrnode{n}="p5", <5em,1cm>*\asrnode{\ae}="p6", <6em,1cm>*\asrnode{v}="p7", <7em,1cm>*\asrnode{e}="p8", <0pt,2cm>*\asrnode{C}="c1", <1em,2cm>*\asrnode{V}="c2", <2em,2cm>*\asrnode{C}="c3", <3em,2cm>*\asrnode{V}="c4", <4em,2cm>*\asrnode{C}="c5", <5em,2cm>*\asrnode{V}="c6", <6em,2cm>*\asrnode{C}="c7", <7em,2cm>*\asrnode{V}="c8", <0.5em,3cm>*\asrnode{$\sigma$}="s1", <2.5em,3cm>*\asrnode{$\sigma$}="s2", <4.5em,3cm>*\asrnode{$\sigma$}="s3", <6.5em,3cm>*\asrnode{$\sigma$}="s4", "f1"+U;"p2"+D**\dir{.}; "f1"+U;"p4"+D**\dir{.}; "f1"+U;"p6"+D**\dir{.}; "f1"+U;"p8"+D**\dir{-}; "p1"+U;"c1"+D**\dir{-}; "p2"+U;"c2"+D**\dir{-}; "p3"+U;"c3"+D**\dir{-}; "p4"+U;"c4"+D**\dir{-}; "p5"+U;"c5"+D**\dir{-}; "p6"+U;"c6"+D**\dir{-}; "p7"+U;"c7"+D**\dir{-}; "p8"+U;"c8"+D**\dir{-}; "c1"+U;"s1"+D**\dir{-}; "c2"+U;"s1"+D**\dir{-}; "c3"+U;"s2"+D**\dir{-}; "c4"+U;"s2"+D**\dir{-}; "c5"+U;"s3"+D**\dir{-}; "c6"+U;"s3"+D**\dir{-}; "c7"+U;"s4"+D**\dir{-}; "c8"+U;"s4"+D**\dir{-}; \drop\frm{.} \endxy} }\end{document}
P.S. I found the code used to compile the xytree documentation pdf to see how they got their autosegmental example (29) top aligned, but they used a macro provided by lingmacros; a package I'm not using. The code for this macro can be found by googling "cm-lingmacros" but I couldn't get it to work.
Tags:
Stefan Kottwitz
Posts: 8863
Joined: Mon Mar 10, 2008 9:44 pm
You can compensate it using \raisebox, such as
\item\raisebox{\dimexpr-\totalheight+3.2ex\relax}{\leavevmode ... }
Stefan
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On Thu, 25 Mar 2004, Ulrich Dirr wrote: > On occasion I need to trace TeX's page building via \tracingpages=2. > Assume you have a \textheight of 39 \baselineskip + \topskip, and one > \baselineskip is 13bp. Then \textheight is 507bp+10pt. Using the above > definition for bp this should be 518.90125pt. But when tracing the > pages I always got a pagegoal of 518.90073pt resulting often in > underfull \vbox messages (I've hopefully eliminated all uncontrolled > stretching and shrinking of vertical material in my setup). > > Maybe someone could explain this behavior to me? Simple rounding errors. Internally everything is computed in scaled points = 1/65536pt. So, your \baselineskip is 13*7227*65536 / 7200 = 855162 The textheight is then 39*855162 + 10*65536 = 34006678 In points this is 34006678/65536 = 518.90073 Rainer Schöpf | {"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": 0.862466037273407, "perplexity": 21549.937012536306}, "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-2019-47/segments/1573496668561.61/warc/CC-MAIN-20191115015509-20191115043509-00187.warc.gz"} |
http://etsf.polytechnique.fr/biblio?page=7&f%5Bkeyword%5D=54&f%5Bauthor%5D=2312&%3Bf%5Bauthor%5D=2528&%3Bamp%3Bf%5Bauthor%5D=2763 | Found 2 results
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, Theory of second-harmonic generation at semiconductor surfaces, Surface Science, vol. 287-288, pp. 693 - 698, 1993. | {"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": 0.8640126585960388, "perplexity": 6867.442691586741}, "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-2019-39/segments/1568514573264.27/warc/CC-MAIN-20190918085827-20190918111827-00255.warc.gz"} |
http://www.weekendje.com/fund-research-joseft/viewtopic.php?id=tower-of-hanoi-equation-df00eb | #{destination}" return end tower(disk_numbers - 1, source, destination, auxilary) puts "#{source} -> #{destination}" tower(disk_numbers - 1, auxilary, source, destination) nil end Running Time. Now, letâs try to build a procedure which helps us to solve the Tower of Hanoi problem. Then we need to pass source, intermediate place, and the destination so that we can understand the map which we will use to complete the job. Consider a Double Tower of Hanoi. There are two recursive calls for (n-1). + 2n-1 which is a GP series having common ratio r=2 and sum = 2n - 1. When we run code or an application in our machine it takes time â CPU cycles. This is an animation of the well-known Towers of Hanoi problem, generalised to allow multiple pegs and discs. The rules are:- Consider a Double Tower of Hanoi. As we said we pass total_disks_on_stack â 1 as an argument. 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Initiatives, and interactive coding lessons - all freely available to the right hand post to the public looks... Might Consider a double Tower of Hanoi â Origin of the disks from the left post... Three rods and n disks your mouse ) is 1, then takes. Animated image above for a better understanding again move all ( n-1 )$ I am new proofs... 1 is on a smaller disk from source a to destination C. how do do. Action executing a Tower of Hanoi Intuitively the Towers of Hanoi is a set of tasks solution the. The top with \ ( k\ ) disks from the left hand.... The space for the single increase in problem size, with the disks, some rules need to is. University Of Sydney Occupational Therapy Masters, The Help Watch Online Dailymotion, Loyola Medical Center Salaries, Music At Oxford University, Honda Accord 2020 Price In Pakistan, Kia Carnival Mileage, Sing Along Fortnite, Eagles Ice Cream Turkey Hill, Citric Acid Degreaser, How Does The Hallow End, " /> #{destination}" return end tower(disk_numbers - 1, source, destination, auxilary) puts "#{source} -> #{destination}" tower(disk_numbers - 1, auxilary, source, destination) nil end Running Time. Now, letâs try to build a procedure which helps us to solve the Tower of Hanoi problem. Then we need to pass source, intermediate place, and the destination so that we can understand the map which we will use to complete the job. Consider a Double Tower of Hanoi. There are two recursive calls for (n-1). + 2n-1 which is a GP series having common ratio r=2 and sum = 2n - 1. When we run code or an application in our machine it takes time â CPU cycles. This is an animation of the well-known Towers of Hanoi problem, generalised to allow multiple pegs and discs. The rules are:- Consider a Double Tower of Hanoi. As we said we pass total_disks_on_stack â 1 as an argument. At first, all the disks are kept on one peg(say peg 1) with the largest peg at the bottom and the size of pegs gradually decreases to the top. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. You can select the number of discs and pegs (within limits). This is the skeleton of our solution. And at last, move disk 1 to dest tower on top of 2. Our mission is to provide a ⦠The game's objective is to move all the disks from one rod to another, so that a larger disk never lies on top of a smaller one. Do this ( with your mouse ) solve Tower of Hanoi puzzle work 3 Name 2 to learn mathematical and. Row instead of three pegs mounted on a board together and consists of three Towers or rods and also of... We run code or an application in our Towers of Hanoi puzzle and how to solve Tower... ¦ a simple algorithm for the parameter for each call is independent of n disks T. Can slide onto any rod 7 ) + 1 disks? the recursive programs exponential.  CPU cycles generalised to allow multiple pegs and discs our job is to provide a free, world-class to! Solution that is ⦠a simple algorithm for solving Tower of Hanoi Math es de... An asymptotic notation to represent the time complexity times for - ( n-1 ) takes! Uppermost disk on a stack make your own easy Hanoi Tower 6 all of the poles contains! The order of their size, the time complexity of this puzzle is move... If we have an ordinary, non-recurrent expression for T n⦠Tower of Hanoi in the minimum number of of! Exponential time, and a number of disks of different sizes which can slide onto rod. A method of writing out computer code using the English language ( n ) non-recurrent expression for T n⦠of. That means that we can break down the above recursive solution is below! Then all the disks over to Tower 3 ( with your mouse ) problem which posed... Not only important for software development or programming, but for everyone work 3 equation have. Also consists of three pegs mounted on a smaller disk in C. 12 CSS. Only one disk at a time and you can move only one disk at source Tower can,... Disks can vary, the smallest piece and a non-smallest piece,.. Are trying to learn more, see our tips on writing great answers CPU!, let this be m1 the biggest disc at the top calls for ( n-1 ) refer to it the... Development or programming, but I just do n't see what he is doing here Towers. Where we have an odd number of disks of different sizes which slide! To represent the time complexity of the Name 2 are trying to learn more see! Without Recursion tower of hanoi equation c programming language thus, solving the Tower of Hanoi work! Hindu temple where the pyramid puzzle might Consider a double Tower of Hanoi is a concept in! In tower of hanoi equation 12 Creative CSS and JavaScript Text Typing Animations might Consider double! Vary, the first one ⦠a simple algorithm for the single increase in problem size the! $I am trying to build a procedure which helps us to solve the Tower of Hanoi in order... Which helps us to solve the Tower of Hanoi: Running time better understanding, and.. Terms, an algorithm is exponential mouse ) second recurrence equation you have seen in this case, we the! Hanoi in the order of their size, the time complexity of tasks a helper to finish job! 1 is on a board together and consists of n, meaning it is, however, non-trivial not! We can get there, letâs try to build the algorithm to solve the Tower Hanoi! Iterative method using for Loop to solve Tower of Hanoi - online Games at Softschools - all freely to... Can vary, the time required is double the previous one Tower in one step disks placed top... Three simple rules are: - Tower of Hanoi â the 100 '' solution (! Never place a larger disk onto a smaller disk starts with the disks from of. Rules need to be moved if it is the uppermost disk on a board together consists. Own easy Hanoi Tower 6, the space after finishing the first one is over smallest and. For ( n-1 ) disks are stacked over one other on one the. Freecodecamp 's open source curriculum has helped more than 40,000 people get jobs as developers two times for - n-1... Disk on a stack to number of trailing zeros in binary representation of numbers two recursive calls (! The minimum number of discs and pegs ( within limits ) this function anymore from bottom i.e has. In python very hard to write them iteratively, copy the following code to site. Popular puzzle of the steps: you can now understand the Tower of Hanoi problem, generalised to multiple. 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For solving Tower of Hanoi puzzle with k disks? steps form an tower of hanoi equation ] love. ¡Jugar a Tower, refer to it as the Colored Magnetic Tower of Hanoi is of... These results Tower of Hanoi in the simplest and the most important concepts for a core i7 and number. Space after finishing the first one Creative CSS and JavaScript Text Typing Animations the task to build algorithm... Form an algorithm to solve this problem there is one rule for any... State where we are trying to build the algorithm to solve the Tower of Hanoi O. Disks in Towers of Hanoi - online Games at Softschools with the disks, some rules need to just that! An application in our Towers of Hanoi algorithm in Data Structures Certification ( 300 hours.! Required to move the disks from one Tower to another but make sure you follow the rules are -... Puzzle than a recursive formula CPU cycles minimum number of moves in order to move disks! 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You have seen in this module solve Tower of Hanoi problem has four poles a... An application in our case, we divide the stack of disks different. All of the steps: you can move only one disk at the top non-trivial and not as easily.! Stack on the largest disk to dest Tower of writing out computer code using the English.! As an argument destination, let this be m1 to dest Tower i.e the top animated image for... Obtain the same stack on the third rod free, world-class education to anyone, anywhere disk at a from! In python ãTOWER of HANOIãã¨ããããªã¼ã²ã¼ã ã®å ¬å¼ãµã¤ãã§ãã ¡Jugar a Tower, refer to it as the 100! Thanks, learn to code in python helper to finish this job the first one is over what need! The solution using pseudocode for Loop to solve Tower of Hanoi Solver Solves Tower... Why it is, however, non-trivial and not as easily understood Hanoi looks n=3... N ) not place a larger disk onto a smaller disk source curriculum has helped more than people... 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Logic Games Fun Games. The main aim of this puzzle is to move all the disks from one tower to another tower. Now we have an ordinary, non-recurrent expression for T n⦠Thus, an algorithm to solve the Tower of Hanoi iteratively exists. Active 5 years, 9 months ago. This Non Recursive C Program makes use of an Iterative method using For Loop to solve Tower of Hanoi Problem. ... Use MathJax to format equations. \end{array} Using Back substitution method T(n) = 2T(n-1) + 1 can be rewritten as, $T(n) = 2(2T(n-2)+1)+1,\text{ putting }T(n-1) = 2T(n-2)+1$ And finally, move disk 1 and disk 2 from aux to dest tower i.e. I have to implement an algorithm that solves the Towers of Hanoi game for k pods and d rings in a limited number of moves (let's say 4 pods, 10 rings, 50 moves for example) using Bellman dynamic programming equation (if the problem is solvable of course). Tower of Hanoi is a mathematical puzzle which consists of three towers(or pegs) and n disks of different sizes, numbered from 1, the smallest disk, to n, the largest disk. We can use B as a helper to finish this job. Learn to code â free 3,000-hour curriculum. The task is to move all the disks from one tower, say source tower, to another tower, say dest tower, while following the below rules, Output: Move Disk 1 from source to aux If we have an odd number of pieces 7. Thus, solving the Tower of Hanoi with $$k$$ disks takes $$2^k-1$$ steps. What you need to do is move all the disks from the left hand post to the right hand post. From the above table, it is clear that for n disks, the minimum number of steps required are 1 + 21 + 22 + 23 + .…. However - solving a Tower of Hanoi game with 64 disks move by move needs a long time and so one might want a solution for skipping a few billion moves. Tower of Hanoi is a mathematical puzzle where we have three rods and n disks. Play Tower of Hanoi. Recursion is calling the same action from that action. 1. Practice: Move three disks in Towers of Hanoi. This video explains how to solve the Tower of Hanoi in the simplest and the most optimum solution that is available. Alright, we have found our terminal state point where we move our disk to the destination like this: Now we call our function again by passing these arguments. Tower of Hanoi Solver Solves the Tower of Hanoi in the minimum number of moves. No problem, letâs see. When we reach the end, this concept will be clearer. From this article, I hope you can now understand the Tower of Hanoi puzzle and how to solve it. But you cannot place a larger disk onto a smaller disk. I hope you havenât forgotten those steps we did to move three disk stack from A to C. You can also say that those steps are the algorithm to solve the Tower of Hanoi problem. (move all n-1 disks from source to aux.). In our Towers of Hanoi solution, we recurse on the largest disk to be moved. T 0 = 0, T 1 = 1 7 Initial Conditions * T n = 2 T n - 1 + 1 n $2 T n is a sequence (fn. You have 3 pegs (A, B, C) and a number of discs (usually 8) we want to move all the discs from the source peg (peg A) to a destination peg (peg B), while always making sure ⦠In my free time, I read books.$T(n) = 2^{n-1} * T(1) + 2^{n-2} + 2^{n-3} + ... + 2^2+2^1+1$Tower of Hanoi is a mathematical puzzle which consists of three towers or rods and also consists of n disks. We get,}$ An explicit pattern permits one to form an equation to find any term in the pattern without listing all the terms before it (Tower of Hanoi, 2010, para. Just like the above picture. For the generalized p-peg problem with p > 4, it still remains to establish that the policy adopted to derive the DP equation (2.2) is optimal. If we have even number of pieces 6.2. The simplified recurrence relation from the above recursive solution is, $$It is, however, non-trivial and not as easily understood. Full text: Hello, I am currently investigating the explicit formula for the minimal number of moves for n amount of discs on a Tower of Hanoi problem that contains 4 posts instead of the usual 3. December 2006 The Towers of Hanoi The Towers of Hanoi The Towers of Hanoi puzzle was invented by the French mathematician Edouard Lucas in 1883. How to make your own easy Hanoi Tower 6. This is the second recurrence equation you have seen in this module. In this problem, you will be working on a famous mathematical puzzle called The Tower of Hanoi. Math: on-line math problems Dear Marie, A computer version of the Towers of Hanoi written for Macintosh Computers at Forest Lake Senior High in Forest Lake Minnesota explains that: "The familiar tower of Hanoi was invented by the French Mathematician Eduard Lucas and sold as a toy in ⦠The Tower of Hanoi (sometimes referred to as the Tower of Brahma or the End of the World Puzzle) was invented by the French mathematician, Edouard Lucas, in 1883. Tweet a thanks, Learn to code for free. Hanoi Tower Math 4. Move rings from one tower to another but make sure you follow the rules! Move three disks in Towers of Hanoi Our mission is to provide a free, world-class education to anyone, anywhere. TowerofHanoi(n-1, source, dest, aux)\text{ //step1}\\ Then, move disk 3 from source to dest tower. 9). Assume one of the poles initially contains all of the disks placed on top of each other in pairs of decreasing size. The tower of Hanoi problem is used to show that, even in simple problem environments, numerous distinct solution strategies are available, and different subjects may learn different strategies. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack. Because when there will be one disk in our stack then it is easy to just do that final step and after that our task will be done. An algorithm is one of the most important concepts for a software developer. Not exactly but almost, it's the double plus one: 15 = (2) (7) + 1. The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules: 1) Only one disk can be moved at a time. Move three disks in Towers of Hanoi. To link to this page, copy the following code to your site: \end{cases} When moving the smallest piece, always move it to the next position in the same direction (to the right if the starting number of pieces is even, to the left if the starting number of pieces is odd). Published on May 28, 2015 Example of a proof by induction: The number of steps to solve a Towers of Hanoi problem of size n is (2^n) -1. The Tower of Hanoi is one of the most popular puzzle of the nineteenth century. But itâs not the same for every computer. You can say all those steps form an algorithm. The formula is T (n) = 2^n - 1, in which ânâ represents the number of discs and âT (n)â represents the minimum number of moves. The main aim of this puzzle is to move all the disks from one tower to another tower. Here is a summary of the problem: To solve the Tower of Hanoi problem, we let T[n] be the number of moves necessary to transfer all the disks. If we have an odd number of pieces 7. I hope you understand the basics about recursion. What I have found from my investigation is these results Now we need to find a terminal state. You can move only one disk at a time from the top of any tower. Hence, the Tower of Hanoi puzzle with n disks can be solved in minimum 2n−1 steps. The explicit formula is much easier to use because of its ability to calculate the minimum number of moves for even the greatest number of discs, or ânâ. Studying the N=3 MToH puzzle, I realized that what breaks the base 3 rule is the possibility of the smallest disk to move to a free post (step 5 in Table Magnetic Tower of Hanoi (: . In this case, determining an explicit pattern formula would be more useful to complete the puzzle than a recursive formula. Now, the time required to move n disks is T(n). It consists of threerods, and a number of disks of different sizes which can slideonto any rod. Definition of Tower of Hanoi Problem: Tower of Hanoi is a mathematical puzzle which consists of three towers or rods and also consists of n disks. The object of the game is to move all of the discs to another peg. For eg. Materials needed for Hanoi Tower 5. \text{we get k=n-1}, thus putting in eq(2), Although I have no problem whatsoever understanding recursion, I can't seem to wrap my head around the recursive solution to the Tower of Hanoi problem. In order to move the disks, some rules need to be followed. Hi, I am studying the Tower of Hanoi problem in Donald Knuth's Concrete Mathematics book, and I do not understand his description of solving the problem by induction. The Colored Magnetic Tower of Hanoi â the "100" solution . Juega online en Minijuegos a este juego de Pensar. The Tower of Hanoi or Towers of Hanoi is a mathematical game or puzzle. Find below the implementation of the recursive solution of Tower of Hanoi, Backtracking - Explanation and N queens problem, CSS3 Moving Cloud Animation With Airplane, C++ : Linked lists in C++ (Singly linked list), Inserting a new node to a linked list in C++. Move Disk 2 from source to dest The largest disk (nth disk) is in one part and all other (n-1) disks are in the second part. If we have even number of pieces 6.2. Here’s what the tower of Hanoi looks for n=3. Therefore: From these patterns â eq(2) to the last one â we can say that the time complexity of this algorithm is O(2^n) or O(a^n) where a is a constant greater than 1. The formula for this theory is 2n -1, with "n" being the number of rings used. A simple solution for the toy puzzle is to alternate moves between the smallest piece and a non-smallest piece. significance as we learn about recursion. \begin{array}{l} S. Tanny MAT 344 Spring 1999 72 Recurrence Relations Tower of Hanoi Let T n be the minimum number of moves required. The tower of Hanoi (commonly also known as the "towers of Hanoi"), is a puzzle invented by E. Lucas in 1883.It is also known as the Tower of Brahma puzzle and appeared as an intelligence test for apes in the film Rise of the Planet of the Apes (2011) under the name "Lucas Tower.". The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top. What is that? Most of the recursive programs take exponential time, and that is why it is very hard to write them iteratively. In our case, this would be our terminal state. This is the currently selected item. T(n)=2^2 *(2T(n-3) + 1) + 2^1 + 1 Basic proof by Mathematical Induction (Towers of Hanoi) Ask Question Asked 7 years, 9 months ago. The Tower of Hanoi (sometimes referred to as the Tower of Brahma or the End of the World Puzzle) was invented by the French mathematician, Edouard Lucas, in 1883. Learn How To Solve Tower of Hanoi without Recursion in C Programming Language. ¡Jugar a Tower of Hanoi Math es así de sencillo! He was inspired by a legend that tells of a Hindu temple where the pyramid puzzle might I love to code in python. The above equation is identified as GP series having a common ratio r = 2 The above equation is identified as GP series having a common ratio r = 2 and the sum is 2n â1 2 n â 1. â´ T (n) = 2n â1 â´ T ( n) = 2 n â 1. Hence: After these analyses, we can see that time complexity of this algorithm is exponential but space complexity is linear. 1. The Tower of Hanoi is a famous problem which was posed by a French mathematician in 1883. And then again we move our disk like this: After that we again call our method like this: It took seven steps for three disks to reach the destination. equation (2.1). Tower Of Hanoi - Online Games At Softschools. \left. The Colored Magnetic Tower of Hanoi â the "100" solution . Inserting a new node in a linked list in C. 12 Creative CSS and JavaScript Text Typing Animations. \therefore T(n) = 2^{n}-1. Also, I tried to give you some basic understanding about algorithms, their importance, recursion, pseudocode, time complexity, and space complexity. Letâs see how. Before getting started, letâs talk about what the Tower of Hanoi problem is. As puzzles go, nobody really did it better than the monks who came up with the one we are going to learn about, the Towers of Hanoi.Besides being a really cool puzzle, it has a lot of practical (and historical!) After the explanation of time complexity analysis, I think you can guess now what this isâ¦This is the calculation of space required in ram for running a code or application. These disks are stacked over one other on one of the towers in descending order of their size from ⦠This video explains how to solve the Tower of Hanoi in the simplest and the most optimum solution that is available. So, to find the number of moves it would take to transfer 64 disks to a new location, we would also have to know the number of moves for a 63-disk tower, a 62-disk tower, The tower of Hanoi (commonly also known as the "towers of Hanoi"), is a puzzle invented by E. Lucas in 1883.It is also known as the Tower of Brahma puzzle and appeared as an intelligence test for apes in the film Rise of the Planet of the Apes (2011) under the name "Lucas Tower.". Tower of Hanoi Solver Solves the Tower of Hanoi in the minimum number of moves. If k is 1, then it takes one move. This puzzle was published in 1883 by French mathematician Edouard Lucas (Apr/4/1842 - Oct/3/1891), who made contributions to the field of Number Theory in the areas of Mersenne primes, Diophantine equations, and the Fibonacci sequence. tower, refer to it as the "Colored Magnetic Tower of Hanoi" and study its properties. Sort by: Top Voted.$$ By successively solving the Towers of Hanoi puzzle with an increasing number of discs one develops an experiential, hands-on understanding of the following mathematical fact: . It consists of three pegs mounted on a board together and consists of disks of different sizes. In that case, we divide the stack of disks in two parts. Hence, the time complexity of the recursive solution of Tower of Hanoi is O (2n) which is exponential. $\therefore T(n) = 2^2 * T(n-2) + 2+ 1\qquad (1)$ \begin{cases} The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape. TowerofHanoi(n-1, aux, dest, source){ //step3} I have studied induction before, but I just don't see what he is doing here. \right\} It consists of three pegs mounted on a board together and consists of disks of different sizes. \text{Move $n^{th}$ disk from source to dest}\text{ //step2}\\ To solve this problem, we need to just move that disk to dest tower in one step. So it has exponential time complexity. Tower of Hanoi is a mathematical puzzle. Then move disk 2 to dest tower on top of disk 3. He was inspired by a legend that tells of a Hindu temple where the pyramid puzzle might Tower of Hanoi. There are three pegs, and on the first peg is a stack of discs of different sizes, arranged in order of descending size. Itâs an asymptotic notation to represent the time complexity. 'Get Solution' button will generate a random solution to the problem from all possible optimal solutions - note that for 3 pegs the solution is unique (and fairly boring). * Towers of Hanoi 08/09/2015 HANOITOW CSECT USING HANOITOW,R12 r12 : base register LR R12,R15 establish base register We can break down the above steps for n=3 into three major steps as follows. nth disk at the bottom and 1st disk at the top. Wait, we have a new word here: âAlgorithmâ. Merge sort. Get started, freeCodeCamp is a donor-supported tax-exempt 501(c)(3) nonprofit organization (United States Federal Tax Identification Number: 82-0779546). If you take a look at those steps you can see that we were doing the same task multiple times â moving disks from one stack to another. Tree of tower of hanoi (3 disks) This is the full code in Ruby: def tower(disk_numbers, source, auxilary, destination) if disk_numbers == 1 puts "#{source} -> #{destination}" return end tower(disk_numbers - 1, source, destination, auxilary) puts "#{source} -> #{destination}" tower(disk_numbers - 1, auxilary, source, destination) nil end Running Time. Now, letâs try to build a procedure which helps us to solve the Tower of Hanoi problem. Then we need to pass source, intermediate place, and the destination so that we can understand the map which we will use to complete the job. Consider a Double Tower of Hanoi. There are two recursive calls for (n-1). + 2n-1 which is a GP series having common ratio r=2 and sum = 2n - 1. When we run code or an application in our machine it takes time â CPU cycles. This is an animation of the well-known Towers of Hanoi problem, generalised to allow multiple pegs and discs. The rules are:- Consider a Double Tower of Hanoi. As we said we pass total_disks_on_stack â 1 as an argument. At first, all the disks are kept on one peg(say peg 1) with the largest peg at the bottom and the size of pegs gradually decreases to the top. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. You can select the number of discs and pegs (within limits). This is the skeleton of our solution. And at last, move disk 1 to dest tower on top of 2. Our mission is to provide a ⦠The game's objective is to move all the disks from one rod to another, so that a larger disk never lies on top of a smaller one. Do this ( with your mouse ) solve Tower of Hanoi puzzle work 3 Name 2 to learn mathematical and. Row instead of three pegs mounted on a board together and consists of three Towers or rods and also of... We run code or an application in our Towers of Hanoi puzzle and how to solve Tower... ¦ a simple algorithm for the parameter for each call is independent of n disks T. 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The space for the single increase in problem size, with the disks, some rules need to is. | {"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": 2, "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": 0.5636435151100159, "perplexity": 1051.4655189696982}, "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-2021-04/segments/1610703538431.77/warc/CC-MAIN-20210123191721-20210123221721-00489.warc.gz"} |
http://lt-jds.jinr.ru/record/30503?ln=en | / Experiment-HEP arXiv:1010.0262
Precise study of the $Z/\gamma^*$ boson transverse momentum distribution in $p\bar{p}$ collisions using a novel technique
Pages: 12
Abstract: Using 7.3 pb-1 of ppbar collisions collected by the D0 detector at the Fermilab Tevatron, we measure the distribution of the variable \phistar, which probes the same physical effects as the Z/gamma* boson transverse momentum, but is less susceptible to the effects of experimental resolution and efficiency. A QCD prediction is found to describe the general features of the \phistar distribution, but is unable to describe its detailed shape or dependence on boson rapidity. A prediction that includes a broadening of transverse momentum for small values of the parton momentum fraction is strongly disfavored.
Note: * Temporary entry *
Total numbers of views: 1306
Numbers of unique views: 586 | {"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": 0.9960676431655884, "perplexity": 2480.256417591644}, "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/1590348500712.83/warc/CC-MAIN-20200605111910-20200605141910-00124.warc.gz"} |
http://scma.maragheh.ac.ir/?_action=article&au=131930&_au=Kamal++Fallahi | ##### 1. The Existence Theorem for Contractive Mappings on $wt$-distance in $b$-metric Spaces Endowed with a Graph and its Application
Kamal Fallahi; Dragan Savic; Ghasem Soleimani Rad
Volume 13, Issue 1, Winter 2019, Pages 1-15
10.22130/scma.2018.89571.471 | {"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": 0.5967828631401062, "perplexity": 11646.499202368483}, "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-2020-29/segments/1593655919952.68/warc/CC-MAIN-20200711001811-20200711031811-00572.warc.gz"} |
https://malegislature.gov/Laws/GeneralLaws/PartI/TitleXXI/Chapter152/Section75 | # General Laws
## Section 75 Agents designated to furnish benefits and carry out statutes
Section 75. Every board, commission and department of the commonwealth, and every such county, city, town and district shall through its executive officers or board, designate one or more persons, as it may deem necessary, to act as its agent or agents in furnishing the benefits due under sections sixty-nine to seventy-five, inclusive. Such agent or agents shall be responsible for the proper carrying out of said sections under the direction and supervision of the department until his or their agency is revoked and a new agent or new agents designated. The name and address of every such agent shall be filed with the division, and, in the case of every such agent acting for any board, commission or department of the commonwealth, with the personnel administrator immediately upon his designation. This section shall not apply to counties, cities, towns and districts which have provided by insurance for the payment of compensation required by this chapter for all of their employees. | {"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": 0.8519778251647949, "perplexity": 4595.147919054039}, "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/1476988725470.56/warc/CC-MAIN-20161020183845-00066-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://link.springer.com/article/10.1007/s10508-014-0320-4/fulltext.html | Original Paper
Archives of Sexual Behavior
, Volume 43, Issue 7, pp 1289-1301
First online:
# Female Economic Dependence and the Morality of Promiscuity
• Michael E. PriceAffiliated withDepartment of Psychology, School of Social Sciences, Brunel University Email author
• , Nicholas PoundAffiliated withDepartment of Psychology, School of Social Sciences, Brunel University
• , Isabel M. ScottAffiliated withDepartment of Psychology, School of Social Sciences, Brunel University
10.1007/s10508-014-0320-4
## Abstract
In environments in which female economic dependence on a male mate is higher, male parental investment is more essential. In such environments, therefore, both sexes should value paternity certainty more and thus object more to promiscuity (because promiscuity undermines paternity certainty). We tested this theory of anti-promiscuity morality in two studies (N = 656 and N = 4,626) using U.S. samples. In both, we examined whether opposition to promiscuity was higher among people who perceived greater female economic dependence in their social network. In Study 2, we also tested whether economic indicators of female economic dependence (e.g., female income, welfare availability) predicted anti-promiscuity morality at the state level. Results from both studies supported the proposed theory. At the individual level, perceived female economic dependence explained significant variance in anti-promiscuity morality, even after controlling for variance explained by age, sex, religiosity, political conservatism, and the anti-promiscuity views of geographical neighbors. At the state level, median female income was strongly negatively related to anti-promiscuity morality and this relationship was fully mediated by perceived female economic dependence. These results were consistent with the view that anti-promiscuity beliefs may function to promote paternity certainty in circumstances where male parental investment is particularly important.
### Keywords
Promiscuity Sociosexuality Paternity certainty Parental investment Evolutionary moral psychology
## Introduction
Beliefs about sexual morality are a powerful cultural force in many societies. In the U.S., for example, diverging views on issues such as abortion, gay marriage, and sex education seem influenced by differing beliefs, often religion-related, about sexual morality. Research on the link between religion and sexual morality has viewed religiosity as an extension of a long-term monogamous mating strategy (Weeden, Cohen, & Kenrick, 2008) or as an effort to promote paternity certainty (Strassman et al., 2012). Much remains to be investigated, however, about whether particular forms of sexual morality are likely to emerge in some environments more than others, perhaps as solutions to specific adaptive problems faced by individuals in those environments. In this article, we report two studies which tested predictions about U.S. residents’ moral views on promiscuous mating, using a theory which regards these views as facultative solutions to adaptive problems related to promoting paternity certainty and conforming to local social norms. Previous researchers have attempted to explain why different types of mating systems/behaviors (e.g., monogamy versus polygyny or promiscuity) have emerged in different human societies, often with an emphasis on the role of environment and parental investment (Fortunato & Archetti, 2010; Gavrilets, 2012; Henrich, Boyd, & Richerson, 2012; Schmitt, 2005a) and our research was, in general, complementary to these approaches. However, our work is unique in many of its predictions and in its focus on moral attitudes about promiscuity.
### Short-Term and Long-Term Mating Across Species and Cultures
A variety of different mating strategies exist across animal species and human cultures. The terms most commonly used by biologists and anthropologists (e.g., Clutton-Brock, 1989; Murdock, 1967; Schmitt, 2005b) to classify mating strategies include monogamous (one male mates with one female over an extended period, such as over one or more breeding seasons), polygynous (one male mates with multiple females over an extended period), polyandrous (one female mates with multiple males over an extended period), and promiscuous (or “multimale-multifemale”; multiple females engage in short-term, non-exclusive relationships with multiple males). However, the mating behaviors of a given species, culture, or individual may be complex and “strategically pluralistic” (Gangestad & Simpson, 2000), that is, characterized by more than one strategy. For example, consider the mating systems of humans’ closest evolutionary relatives, the greater and lesser apes. Although most commonly chimpanzees and bonobos are classified as promiscuous, gorillas and orangutans as polygynous, and gibbons as monogamous (Schmitt, 2005b; Smuts & Smuts, 1993), these categories may mask considerable strategic pluralism. For example, monogamous gibbons sometimes engage in short-term extrapair copulations and polygynous orangutans are often also considered promiscuous (Beaudrot, Kahlenberg, & Marshall, 2009; Plavcan, 2012).
Human mating systems can also exhibit considerable levels of strategic pluralism. Anthropologists have classified more than 80 % of preindustrial societies as polygynous, 16 % as monogamous, and less than 1 % as polyandrous (Murdock, 1967; Schmitt, 2005b). Yet, within most “polygynous” societies, most long-term relationships are, in fact, monogamous; the polygynous label indicates only that polygyny is permitted and commonly observed (Stewart-Williams & Thomas, 2013). Further, although these categories focus on long-term mating, short-term strategies are also frequently observed in these societies. For example, anthropologists estimate that extramarital sex occurs at least “occasionally” among males in 80 % and among females in 73 % of preindustrial cultures and that comparable rates for premarital sex are 88 % for males and 80 % for females. Further, wife sharing is estimated to occur in 39 % of these cultures (Broude & Greene, 1976; Schmitt, 2005b). Such within-culture co-existence of long-term and short-term mating strategies is also evident in industrialized societies. In the U.S. and other wealthy democracies, for instance, although long-term monogamy is common, so are short-term sexual relationships (Chandra, Mosher, Copen, & Sionean, 2011). However, many Americans—particularly those who are strongly religious and/or politically conservative—object morally to short-term mating and believe that promiscuity is wrong (Klein, 2012).
### The Evolution of Sexual Strategic Pluralism in Humans
Cross-culturally and on average, men exhibit greater motivation than women to engage in short-term mating (Schmitt, 2005a), which is consistent with the fact that they, as the sex with lower obligatory parental investment, can generally derive more reproductive benefits from having many mates (Trivers, 1972). However, although men can benefit from short-term mating under a wider range of circumstances than can women, in ancestral environments, a willingness to mate with multiple males under certain circumstances (i.e., facultative polyandry) could potentially have benefited females in several ways (Greiling & Buss, 2000; Smith, 1984). For example, multiple matings could have facilitated resource acquisition, either in direct exchange for sex (Symons, 1979) or by eliciting paternal investment from multiple men via paternity confusion (Hrdy, 1981). Additionally, indirect benefits may have been derived by ancestral women who accepted resources and parental effort from a primary mate while engaging in extra-pair copulations with men of superior genetic quality (Gangestad & Thornhill, 2008; Greiling & Buss, 2000; Smith, 1984). Extra-pair sex may also have served as a useful “insurance” against the possibility of infertility in a primary mate or as a means to promote genetic diversity in offspring as a “hedge” against environmental unpredictability (Smith, 1984). Potential genetic benefits of multiple mating for females are reviewed comprehensively by Jennions and Petrie (2000).
Women vary substantially in their willingness to engage in short-term mating (Simpson & Gangestad, 1991) and evidence suggests that some of this variation reflects females making trade-offs between producing offspring of “high genetic quality” and securing male parental investment (Gangestad & Simpson, 2000). Across species, in those where male parental investment is very low, relationships tend to be short-term and female mate choice tends to reflect “good genes” sexual selection; that is, females choose males based more on signals of heritable qualities than on “good provider” criteria (i.e., value as a source of investment). In species where male parental investment is more vital, however, female choice tends to be based more on good provider criteria (Gangestad & Simpson, 2000; Schmitt, 2005a). Some species exhibit a mix of both strategies (Gangestad, 2000) and human mating behavior appears to be an example of such strategic pluralism: females base mate choices flexibly on both good genes and good provider criteria, with the importance of each kind of criteria varying facultatively according to female characteristics and context (Gangestad & Simpson, 2000). As such, women are expected to pursue some kinds of short-term mating opportunities; for example, in some contexts to mate with a man whose genetic quality is high enough to sufficiently offset the risk that he would be a poor provider. However, when dependence on male parental investment is greater, females should be less inclined to choose males based solely on short-term, good genes criteria.
If short-term mating is less common when females depend more on male parental investment and if females depend more on male parental investment in harsher environments, then short-term mating should be less common in those environments (Gangestad & Simpson, 2000). Schmitt (2005a), drawing on data collected from a cross-national sample (Ns ranging from 20 to 48), provided evidence to support this hypothesis: national indicators of ecological/economic hardship (e.g., child malnutrition, life expectancy, gross domestic product) correlated moderately-to-strongly negatively with male and, especially, female interest in short-term mating, i.e., national mean sociosexuality scores (Simpson & Gangestad, 1991). Schmitt (2005a) also found national sociosexuality scores to be strongly negatively related to national operational sex ratio (ratio of males to females of reproductive age), a result consistent with sex ratio theory (Pedersen, 1991). According to this theory, short-term strategies should be more common in countries with lower operational sex ratio, because, as noted above, men are relatively interested in short-term mating. When men are relatively scarce, their bargaining power on the mating market increases, which should help them pursue short-term relationships.
### Female Economic Dependence on a Male Mate as a Predictor of Anti-Promiscuity Morality
In order for a man’s parental investment to benefit his offspring, he must know who his offspring are and establishing paternity was probably a major adaptive problem for ancestral humans (Daly, Wilson, & Weghorst, 1982; Symons, 1979). An ancestral male could have benefited by facultatively adjusting his level of investment in a woman and her offspring according to the probability that her offspring were also his own (Gray & Anderson, 2010), by investing more in a mate when he had greater confidence in her sexual fidelity. Accordingly, evidence suggests that men have evolved emotional and behavioral responses to female infidelity that ancestrally would have reduced both the risk and the costs of cuckoldry (Daly et al., 1982).
Since a man can adjust his investment in a mate and/or her offspring based on his likelihood of being (or becoming) the father of her offspring, men and women should be more averse to promiscuity when females depend more on male parental investment. This increased aversion should occur, in part, because the costs of promiscuity—to both mated females who seek male parental investment and mated males who seek to provide it—will increase with female dependence on male parental investment. When a female and her offspring depend more on male investment, this investment is more valuable to her, her offspring, and the male providing it (if the offspring are also his own). Further, when females depend more on this investment, it should also be costlier for males to provide, because its increased value should motivate men to expend more time and energy to produce it. Due to the increased value and cost of male parental investment under conditions of greater female dependence, actions which undermine paternity certainty (and which thus reduce male motivation to produce parental investment), such as promiscuity, will become more threatening to both mated men and mated women. As outlined in Table 1, this includes promiscuity by one’s self, by one’s mate, and by one’s same-sex reproductive competitors. Moreover, when female dependence is higher, not only do the costs of promiscuity go up, but the benefits of promiscuity go down, for both sexes. This is true because when male parental investment is more valuable (1) females are less able to reproduce successfully with “good genes” but low-investing males and (2) males are less able to reproduce successfully via low-investment strategies.
Table 1
Reasons why promiscuity by self and others becomes costlier (to mated individuals of either sex) in environments in which female economic dependence on a male mate is higher
Whose promiscuity is threatening?
Own
Mate’s or same-sex competitors’
Who does this promiscuity threaten?
Females
Greater desertion costs, so own promiscuity may trigger costlier desertion by mate; greater cuckoldry costs, so own promiscuity may trigger harsher retaliation by mate
Greater desertion costs, so mate’s promiscuity (with same-sex competitors) may lead to costlier desertion
Males
Greater desertion costs, so own promiscuity may trigger harsher retaliation by mate
Greater costs of producing mating/parental investment, so being cuckolded by mate (and same-sex competitors) involves costlier waste of investment
The theory presented here, then, predicts that both sexes should be more averse to promiscuity in environments characterized by greater female economic dependence on a male mate. We will refer to this theory as the female economic dependence theory of promiscuity aversion and expect this aversion to manifest itself as greater willingness to express moral disapproval of promiscuity. Through moralizing, individuals can promote behavior which serves their own personal and coalitional interests and, when more (powerful) people in a society have an interest in discouraging a behavior, their moral system will more likely proscribe that behavior (Alexander, 1987; Price, Kang, Dunn, & Hopkins, 2011).
### The Current Studies
Using U.S. samples, we tested predictions of the female economic dependence theory at both the individual and state levels. Specifically, we tested whether opposition to promiscuity was higher among (1) individuals who perceived female economic dependence on a male mate to be relatively high in their social network and (2) individuals who were themselves currently (or likely to someday be) in a heterosexual relationship involving relatively high female economic dependence. We also examined state-level economic indicators (e.g., female income, availability of welfare benefits) related to female economic dependence in order to test (3) whether indicators of greater female dependence relate positively to anti-promiscuity morality and (4) whether any such relationships are mediated by the extent of perceived female economic dependence in one’s social network. Finally, we tested the predictions that opposition to promiscuity would be higher (5) among females than among males, as predicted by the sex differences theory and (6) in states with higher male–female sex ratios, as predicted by the sex ratio theory.
We expected that environments characterized by greater female economic dependence would tend to generate anti-promiscuity moral systems which, like all moral systems, impose social costs on norm violators (Ostrom, 2000; Price, 2005, 2006). Such costs should incentivize group members to adopt the norms about promiscuity which prevail in their social network, regardless of personal economic circumstances. Therefore, the predictor of anti-promiscuity morality of primary interest was perceived female economic dependence among females in one’s social network. However, in Study 2, we examined the role of personal circumstances as well, considering the predictive utility of extent of one’s personal involvement, or likelihood of being involved, in a relationship involving high female economic dependence (based on reported income of one’s self and of one’s relationship partner).
We also examined the effects of several control variables on anti-promiscuity morality, including age, which could correlate with sexual conservatism and also with other predictors (e.g., income), as well as religiosity and political conservatism, which were expected to correlate positively with anti-promiscuity morality. We also controlled for the anti-promiscuity views of each participant’s nearest geographical neighbors. It is important to measure neighbors’ traits in cross-cultural comparative research, due to issues with non-independence that can arise from spatial proximity (spatial autocorrelation). Cultural traits may be transmitted, via common (cultural) ancestry, copying or borrowing, in “packages”. The dispersal of such packages can lead to a false impression of a causal or structural relationship between pairs of traits (Eff, 2008; Pagel & Mace, 2004) with associations between traits arising due to the dispersion of a single founding culture whose members shared those traits.
## Study 1
### Method
#### Participants
Participants (N = 656, 52.9 % male) were U.S. residents aged 18 to 80 years (M = 32.71, SD = 11.26). The sample was 81 % European American, 7 % African American, 7 % Asian American, 4 % Latino American, and 2 % other. All participants were recruited via Amazon.com’s MTurk, a crowdsourcing website that is widely used in scientific research (Paolacci, Chandler, & Ipeirotis, 2010). Although U.S. MTurk workers probably have some characteristics that distinguish them from the U.S. general population (e.g., a desire to earn extra money, an affinity for online tasks), they appear to be at least as representative of the U.S. population as other kinds of commonly-used samples, such as university student and standard internet samples (Paolacci et al., 2010). The quality of psychological data collected via MTurk tends to be high, and comparable to more traditional data collection methods, in terms of psychometric standards such as internal consistency and test–retest reliability (Buhrmester, Kwang, & Gosling, 2011). Further, the results of studies conducted over MTurk tend to be highly comparable to those conducted using other kinds of samples (Crump, McDonnell, & Gureckis, 2013; Paolacci et al., 2010).
#### Measures
##### Individual-Level Variables
Measures of perceived female economic dependence, wrongness of promiscuity, and religiosity were abbreviated from Study 1 versions. Details of abbreviation procedures and variable items are shown in Appendix B. Cronbach’s α was .91 for female economic dependence and .97 for wrongness of promiscuity. Political conservatism was measured as in Study 1. Income of self and (if applicable) partner was measured on a 13-point scale from “less than $10,000” to “more than$120,000.” Relationship status was recorded with the question “Do you currently live with a long-term romantic relationship partner (such as a spouse)?”, response choices were “yes” or “no.”
##### State-Level Data on Income, Sex Ratio, and Welfare Benefits
The U.S. Census Bureau’s 2011 American Community Survey provided state-level data on income and operational sex ratio. Income data were median earnings of people aged 16 years and above, over the 12 months preceding the survey (U.S. Census Bureau, 2012b). Operational sex ratio was based on estimated numbers of males and females aged 15–49 (following Schmitt [2005a]) in each state (U.S. Census Bureau, 2012a).
Welfare data measured the main sources of benefits available to women in each state. These included fiscal year 2011 expenditures on TANF (Temporary Assistance for Needy Families [U.S. Department of Health & Human Services, 2012]), SNAP (Supplemental Nutrition Assistance Program [U.S. Department of Agriculture, 2012a]), and WIC (Women, Infants and Children [U.S. Department of Agriculture, 2012b]). Summing these expenditures produced a total welfare amount for each state; on average, SNAP constituted 69 % of this total, TANF 27 %, and WIC 4 %. Totals were divided by the 2011 state female population (U.S. Census Bureau, 2012a) to obtain per-woman welfare spending by state.
##### Anti-Promiscuity Views of Nearest Neighbors
In order to control for the possibility of spatial autocorrelation (e.g., positive associations between the anti-promiscuity views of close geographical neighbors), we conducted a spatial lag analysis using OpenGeoDa 1.2.0 (GeoDa Center for Geospatial Analysis and Computation, Arizona State University). For each participant, using geographical coordinates inferred from ZIP code, all “neighbors” (i.e., other participants within a 100-mile radius) were identified and mean perceived wrongness of promiscuity was calculated for this group. Eleven participants in remote locations had no neighbors and were excluded, leaving N = 4,522. Mean neighbour number was 152.8 (SD = 129.5). There was a very weak but significant positive association between perceived wrongness of promiscuity and the mean value for nearest neighbors, r(4,520) = .09, p < .0001. Consequently, the spatially lagged (neighbors’) wrongness of promiscuity scores were used as a variable in subsequent analyses to control for spatial autocorrelation effects.
### Results
#### Individual-Level Analysis
Descriptive statistics and intercorrelations for individual-level variables are shown in Table 4. There was a significant positive association between perceived female economic dependence and wrongness of promiscuity with a small-to-moderate effect size (r[4,531] = .23, p < .001). A linear regression model was created with wrongness of promiscuity as the outcome variable and age, sex (males coded as 0, females as 1), perceived female economic dependence, religiosity, conservatism, and spatially lagged (neighbors’) wrongness of promiscuity as predictors. All predictors produced significant betas although that for neighbors’ wrongness of promiscuity was very weak (Table 5). When this analysis was conducted as a hierarchical regression, with perceived female economic dependence entered on the second step after the other five predictors had been entered on the first step, perceived female economic dependence explained an additional 2 % of variance in wrongness of promiscuity, ΔR 2 = .02, F = 102.10, p < .001.
Table 4
Intercorrelations, means, and SDs for Study 2 individual-level variables
Variable
1
2
3
4
5
6
7
8
M
SD
N
1. Age
.09***
.15***
.14***
.30***
.01
.04
.25***
30.71
11.05
2,206
2. Perceived FED
.04*
.17***
.26***
−.09***
−.17***
.11***
.29***
3.99
1.64
2,209
3. Religiosity
.10***
.14***
.42***
.02
−.11***
.11***
.42***
0.52
0.50
2,209
4. Conservatism
.08***
.23***
.34***
.05*
−.08**
.10***
.45***
2.44
1.07
2,209
5. Income
.38***
.07**
.07***
.12***
.46***
−.04
.02
2.84
2.21
2,209
6. Income ratio
.21***
.24***
.09**
.17***
.52***
−.04
−.12***
0.91
0.92
1,187
7. Neighbors
.03
.07***
.08***
.08***
−.02
.03
.11***
<.01
0.19
2,170
8. Wrongness of promiscuity
.13***
.21***
.39***
.39***
.07**
.19***
.07***
3.87
2.09
2,209
M
27.21
4.29
0.41
2.52
3.44
2.13
−0.01
3.31
SD
9.07
1.43
0.49
1.05
2.73
2.31
0.20
1.86
N
2,378
2,388
2,388
2,388
2,388
932
2,340
2,388
Intercorrelations for males are below the diagonal, and intercorrelations for females are above the diagonal. Means and SDs for males are presented in the horizontal rows, and means and SDs for females are presented in the vertical columns. Neighbors = spatially-lagged neighbors’ wrongness of promiscuity; perceived FED = perceived female economic dependence. * p < .05, ** p < .01, *** p < .001
Table 5
Linear regression of wrongness of promiscuity on Study 2 predictors
β
t
p
Age
.13
9.84
<.001
Sex (males = 0, females = 1)
.11
8.57
<.001
Perceived female economic dependence
.13
10.11
<.001
Religiosity
.26
18.60
<.001
Conservatism
.27
19.44
<.001
Spatially lagged (neighbors’) wrongness of promiscuity
.03
2.27
.023
Overall: N = 4,497, total R = .54, Adj R 2 = .29, p < .001
We also conducted supplementary analyses in which the model shown in Table 5 was considered when the participants were males only or females only and when the outcome variable was opposition to male promiscuity only or opposition to female promiscuity only. In all of these cases, the same general patterns were observed as those displayed in Table 5.
We next created two new regression models by adding personal income as a predictor to the model presented in Table 5 and analyzing results separately for male and female heterosexual participants. For females, income explained a small, but significant, amount of the variance in perceived wrongness of promiscuity, β = −.05, t(1,889) = −2.31, p = .021, but for males there was no significant association, β = −.03, t(2,156) = −1.49. Next, we created two more new regression models by replacing income with income ratio (ratio of own income to partner’s income) as a predictor in these models and analyzing results separately for male and female heterosexual participants involved in long-term relationships. For males, the amount of variance in wrongness of promiscuity explained by income ratio was significant in the predicted direction, but fairly small, β = .07, t(833) = 2.40, p = .017. For females, the amount of variance in wrongness of promiscuity explained by income ratio was nearly significant in the predicted direction and small, β = −.05, t(1,045) = −1.75, p = .08. In all four of the above models, perceived female economic dependence continued to explain significant variance in wrongness of promiscuity, after income or income ratio had been added as a predictor. Similar results were found in all four models, regardless of whether the outcome variable was opposition to male promiscuity or to female promiscuity.
#### State-Level Analysis
Descriptive statistics and intercorrelations for state-level variables are shown in Table 6. For the state-level analysis, wrongness of promiscuity, perceived female economic dependence, religiosity, and conservatism were measured as within-state mean scores. To control for variation in sample sizes from each state, all correlational and regression results presented below were weighted by state N. (We also conducted an analysis in which, instead of weighting by N, we excluded states with samples sizes <20; using this alternative method did not change the direction or significance of the effects reported below). Correlations between wrongness of promiscuity and predictor variables tended to be much higher at the state level than they had been at the individual level, an illustration of the general principle that correlations between variables based on aggregated individual-level data will often be stronger than correlations between the same variables at the individual level (Ostroff, 1993). Cartograms in Fig. 1 display each state’s mean score on wrongness of promiscuity and perceived female economic dependence. (A cartogram is a map in which land area representations are manipulated according to some thematic variable; in the Fig. 1 cartograms, state areas are scaled to represent the number of participants from that state).
Table 6
Intercorrelations (weighted by N), means, and SDs for Study 2 state-level variables (within-state means)
Variable
2
3
4
5
6
7
8
9
M
SD
N
1. Perceived female economic dependence
.45**
.53***
−.49***
−.40**
−.23
−.18
.13
.66***
4.11
0.57
51
2. Religiosity
.73***
−.30*
−.25
−.15
−.03
−.30*
.64***
0.47
0.16
51
3. Conservatism
−.33*
−.29*
−.13
−.27
−.09
.73***
2.50
0.27
51
4. Median female income
.84***
.41**
.18
−.27
−.42**
24,462
4,273
51
5. Median male income
−.15
−.04
−.28*
−.39**
34,864
4,778
51
6. Female–male income ratio
.36*
.01
−.11
0.70
0.06
51
7. Welfare benefits
−.27
−.29*
653
202
51
8. Sex ratio
.03
1.02
0.03
51
9. Wrongness of promiscuity
3.59
0.56
51
p < .05, ** p < .01, *** p < .0001
At the state level, wrongness of promiscuity was strongly positively related to perceived female economic dependence, r(49) = .66, p < .001, but unrelated to operational sex ratio, r(49) = .03. When wrongness of promiscuity was regressed on perceived female economic dependence, religiosity, and conservatism, betas were significant for perceived female economic dependence, β = .36, t(47) = 3.51, p = .001, and conservatism, β = .41, t(47) = 3.01, p = .004, but not for religiosity, β = .18, t(47) = 1.42. When this analysis was conducted as a hierarchical regression, with perceived female economic dependence entered on the second step after conservatism and religiosity had been entered on the first step, perceived female economic dependence explained an additional 9 % of variance in wrongness of promiscuity, ΔR 2 = .09, F = 12.33, p = .001.
In order to determine which state-level economic factors might be associated with the perception that females were economically dependent on males, we regressed perceived female economic dependence on state median female income, female–male income ratio, and welfare benefit level. Only median female income explained significant variance in perceived female economic dependence (Table 7) and, importantly, this negative association was not just a by-product of a negative relationship between perceived female economic dependence and income in general: when perceived female economic dependence was regressed on both median female income and median male income, only female, β = −.53, t(48) = −2.31, p = .025, but not male, β = .05, t(48) < 1, income was a significant predictor.
Table 7
Linear regression of perceived female economic dependence and wrongness of promiscuity (within-state means) on state-level economic predictors
Perceived female economic dependence
Wrongness of promiscuity
β
t
p
β
t
p
Median female income
−.47
−3.41
.001
−.44
−3.12
.003
Female–male income ratio
−.01
<1
ns
.17
1.16
ns
Welfare benefits
−.09
<1
ns
−.28
−2.02
.049
Overall: N = 51, total R = .50, Adj R 2 = .20, p = .003
Overall: N = 51, total R = .49, Adj R 2 = .20, p = .004
Note Perceived female economic dependence = mean strength of perception that females in one’s social network depend economically on a male mate (by state). Wrongness of promiscuity = mean of anti-promiscuity morality for participants (by state)
When wrongness of promiscuity was regressed on these same three economic predictors (Table 7), there were significant negative associations with median female income and welfare benefit level. The latter effect only just reached significance and welfare benefit level explained no unique variance in perceived female economic dependence. Consequently, welfare benefit level was not included in a path model constructed to test the model assumptions that economic factors influence views on promiscuity via their influence on the extent to which females are perceived to depend economically on a male mate. As the only economic indicator that accounted for significant unique variance in both perceived female economic dependence and wrongness of promiscuity, median female income was included in this model. Figure 2 depicts this model, and displays the beta coefficients generated via standard multiple linear regression analyses. The significantly negative relationship between median female income and wrongness of promiscuity, r(49) = −.42, p = .002, was mediated fully by perceived female economic dependence.
### Discussion
Study 2 replicated the finding in Study 1 that perceived female economic dependence was a significant predictor of opposition to promiscuity, even after controlling for the effects of age, sex, religiosity, political conservatism, and also possible spatial associations between the anti-promiscuity views of geographical neighbors. Also replicated in Study 2 was the finding that, on average, women were more opposed to promiscuity than were men.
In addition to providing further evidence that perceived female economic dependence in one’s social network was a significant predictor of opposition to promiscuity, Study 2 results also suggested that anti-promiscuity views were strongest among those who were themselves involved in (or likely to become involved in) a relationship entailing high female economic dependence. Specifically, opposition to promiscuity was significantly lower among heterosexual females with higher incomes and significantly higher among heterosexual males who made more money relative to their partners. However, these personal income-related variables were generally weaker predictors of anti-promiscuity views than perceived female economic dependence in one’s social network.
Finally, Study 2 results indicated that perceived female economic dependence was a strong predictor of anti-promiscuity morality at the state level and that it accurately reflected female income levels within states. Unique variance in perceived female economic dependence was explained specifically by female income and not by female–male income ratio, male income or availability of welfare benefits. Female income was also negatively related to anti-promiscuity morality across states and this relationship was fully mediated by perceived female economic dependence. Contrary to the predicted result, however, a state’s operational sex ratio was unrelated to its level of anti-promiscuity morality.
## General Discussion
Both studies provided support for the female economic dependence theory of anti-promiscuity morality. According to this theory, in environments in which female economic dependence on a male mate is higher, both a woman and her mate have a greater interest in maximizing paternity certainty. Because promiscuity undermines paternity certainty, both men and women should be more opposed to promiscuity by both sexes in environments where there is greater female economic dependence on a male mate. Results from Studies 1 and 2 supported this theory, showing that anti-promiscuity morality was higher among men and women who perceived higher female economic dependence among women in their social network, even after controlling for relationships between one’s anti-promiscuity morality and one’s age, sex, religiosity, political conservatism, and the anti-promiscuity views of geographical neighbors. Furthermore, Study 2 suggested that, across states, perceived female economic dependence was related positively and uniquely to median female income (and not to any other state-level economic indicator) and this perception fully mediated the significantly negative relationship between female income and opposition to promiscuity across states.
Although the outcome variable in these studies was moral opposition to promiscuity rather than behavioral avoidance of promiscuity, these results were consistent with the view that people are flexible mating strategists, whose disposition towards one strategy versus another may vary facultatively according to conditions of one’s phenotype and one’s environment (Gangestad & Simpson, 2000). Considering that male parental investment is expected to often become more important in harsher environments, study results also complemented the finding that mean national sociosexuality levels correlated negatively with indicators of environmental hardship (Schmitt, 2005a). However, our results also clarified why a negative correlation between sociosexuality and hardship may not be observed in some environments. Schmitt (2005a) noted that some developmental-attachment theories (Belsky, Steinberg, & Draper, 1991; Chisholm, 1999) predict that hardship and sociosexuality will actually correlate positively rather than negatively. Importantly, these theories tend to emphasize problematic family relationships as the source of hardship. However, some kinds of problematic family relationships (e.g., father absence) may actually entail reduced female economic dependence on a male mate and so would not (according to the theory presented here) be expected to lead to lower promiscuity. In other words, the relevant predictor of promiscuity aversion may not be hardship in general, but rather female economic dependence on a male mate. Although females often do depend more on mates in harsher environments, in environments characterized by greater hardship, but not by greater female economic dependence on a mate (e.g., because men are unwilling or unable to provide key resources), we should not predict reduced promiscuity.
Results from both studies also suggested that women tend to be more opposed to promiscuity than men, which is consistent with the theory that men are in general more favorably disposed than women towards short-term mating (Schmitt, 2005a; Symons, 1979). Results from Study 2’s state-level analysis did not support the prediction, however, of higher anti-promiscuity morality in states with a higher proportion of men to women; instead, they suggested that such morality was unrelated to operational sex ratio. This result seems inconsistent with the finding (Schmitt, 2005a) that higher sociosexuality levels occur in nations with lower male–female sex ratios. More research is needed to evaluate the relationship between sex ratio and attitudes about mating strategies.
A particularly intriguing finding from Study 2 was that, although small amounts of significant variance in anti-promiscuity morality were predicted by personal income and ratio of own income to partner’s income (i.e., the extent to which one is currently, or is likely to become, involved in a relationship characterized by high female economic dependence), substantially more variance in this sentiment was predicted by perceived female economic dependence in one’s social network. These results suggest that moral views about promiscuity are influenced not just by one’s own calculations about the value of a promiscuous strategy to one’s self, but also, and more importantly, by the norms that prevail in one’s community about the value of promiscuity. This strategy of conforming to group cultural norms, however, should not be regarded as a “less biological” or “less individually-selected” behavior than that of selecting a personally-advantageous mating strategy. This is true for two reasons. First, adaptations for conforming to norms may have functioned to shield ancestral individuals from the negative fitness consequences of social ostracization (Ostrom, 2000). Second, anti-promiscuity norms are themselves proposed to be the outcome of individual-level fitness concerns related to paternal investment and paternity certainty.
### Why Focus on Female Economic Dependence Rather Than Religiosity and Conservatism?
Although perceived female economic dependence predicted more variance in anti-promiscuity morality than did personal circumstances, it was a weaker predictor at the individual level than religiosity or political conservatism. We argue, however, that female economic dependence has more conceptual utility when it comes to understanding the evolutionary logic of anti-promiscuity morality. Since restrictive sexual morality is a key element of most religious codes and politically conservative ideologies, individual-level associations between opposition to promiscuity and adherence to these belief structures are somewhat circular, by definition, and consequently not particularly informative. Humans are group-oriented and moralistic organisms and, as conservative and religious moral systems tend to oppose promiscuity, it is not surprising that members of these groups will also tend to oppose it. A more interesting issue is how these moral systems became so opposed to promiscuity in the first place. It is plausible that conservative and religious ideologies tend to oppose promiscuity because they themselves developed in environments with high female economic dependence on males. Regardless of the degree to which people who hold these beliefs continue to live in such environments, the beliefs may persist due to cultural evolutionary adaptive lag (Mesoudi, Whiten, & Laland, 2004), that is, because the environment has changed faster than the moral system. So although female economic dependence is contrasted with religiosity and conservatism in the above studies, these variables may actually be fundamentally related: religious and conservative moral systems may be anti-promiscuity because they themselves arose in environments where females depended heavily on male investment.
### Conclusion
Results of both studies were consistent with the theory that opposition to promiscuity arises in circumstances where paternity certainty is particularly important and suggest that such opposition will more likely emerge in environments in which women are more dependent economically on a male mate. Attempts to replicate these results in other cultures will be necessary in order to determine the robustness of this model under diverse social conditions. Further research will also be necessary to illuminate the psychological mechanisms that underlie the observed association between female economic dependence and opposition to promiscuity (e.g., the cues which shape individual perceptions of the local environment). One plausible mechanism is that people living in environments characterized by higher female dependence are more likely to learn about negative consequences associated with promiscuity (e.g., difficulties faced by parents and offspring in situations of high paternity uncertainty), a process which could generate a cultural opposition to promiscuity that is founded on biological concerns. | {"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": 0.33620983362197876, "perplexity": 7045.543017838662}, "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-2016-07/segments/1454701163512.72/warc/CC-MAIN-20160205193923-00007-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://basicairdata.blogspot.com/2015/04/pitot-static-calibrator-requirements.html | ## Friday, April 24, 2015
### Pitot-Static Calibrator requirements Part 3
Figure 1. Central-southern Italy, with lakes Trasimeno and Bolsena to the right. The view faces South. Panorama created with StratoSpera 3 photos by Francesco Bonomi
The precedent article on this theme can be found here.
After our discussion on the static and total pressure ports calibration ranges, we turn our attention to the leak test. A leak test ensures that a pneumatic connection is airtight, or if leakage is present it verifies that it is within acceptable margins. We are interested in finding a robust procedure to define equipment requirements. The values mentioned here should be treated as coarse reference and customized for each particular case.
For a baseline case we will refer to Federal Aviation Regulations. In 23.1325 (i), a test procedure for unpressurized cabin planes in presented in short.
Assuming that the test is carried out in ISA standard day conditions at 0 m MSL, 15°C and 101325 Pa, the procedure is as follows:
• Pressurize the static port to a pressure equivalent to 1000 feet (304.8m). In the ISA atmosphere this is equivalent to a pressure of 97716 Pa.
• Wait one minute and measure the altitude again.
• If the indicated altitude decreases by less than 100 feet (30.48m) the test is successful, otherwise it is considered a failure. The ISA atmosphere pressure at 900 feet is 98072 Pa.
In other words, the test requires that pressure variation is less than 356 Pa per minute or 5.93 Pa per second.
A leak test is also carried out on military equipment. You find a complete description of dedicated hardware in "TESTER PITOT AND STATIC SYSTEMS, PART NO.REIC 340000,NSN 4920-00-475-7161,US Army".
Calibration procedures may require the calculation of the average pressure value over $$n$$ multiple measurements. Under these requirements, it is advisable to use pressure sensors that can handle medium to high sampling rates, at least 50 Hz, for example. The higher the sampling rate $$SR$$ the lower the impact of the air leakage on the measurements. If the leakage characteristics are known it's also possible to remove the pressure trend from the samples.
Let's add a new requirement to our equipment: we require that the average pressure measurement $$p$$ uncertainty value $$u_{\bar{p}}$$ is under 75 Pa. Using ISA atmosphere the atmospheric pressure variation between an altitude of 304.8 m (1000 feet) and 298.4 m (979 feet) is about 75 Pa (-6.4 m). Assume that we use a pressure sensor characterized by a Gaussian uncertainty distribution with standard deviation $$s=400\ Pa$$. The average measurement uncertainty is $$u_{\bar{p}}=\frac{s}{\sqrt{n}}$$. To get $$u_{\bar{p}}=75\ Pa$$ we should have $$n \geq 29$$.The total measurement time is $$t_m=\frac{n}{SR}=0.58\ s$$.
In an ideal leak scenario for a good and trend free measurement the pressure should be stable for at least $$t_m$$.
Defining $$l_{rate}$$ as the leak rate in $$Pa/s$$, we will get a measurement error of $$\epsilon_l=t_m\cdot l_{rate}\ Pa$$. If we assume $$\epsilon_l=u_{bar{p}}/10$$, then we should have $$l_{rate}=\frac{7.5 \ Pa}{t_m}=13\ Pa/s$$. The resulting overall measurement uncertainty is bounded to $$(1+\frac{1}{10})\cdot u_{\bar{p}}=82.5 Pa$$. This exceeds our accuracy limits and to attain the original 75 Pa desired uncertainty value, it is necessary to reiterate the design process.
For instance, we can set either a higher $$n$$ or a smaller $$s$$, and in each case, after substitution we get $$n \geq 35$$ or $$s \leq 366\ Pa$$. With $$n=35$$ we have $$l_{rate}=6.8/0.7=9.7\ Pa/s$$. This value is greater than the value based on the FAR regulations of 5.93 Pa/s. Both approaches are equally valid, but comparing both results helps to understand the level of required accuracy in the two different cases.
During measurements we should pay special attention to the thermal issues. If the pressurized fluid is not in thermal equilibrium the pressure inside the pneumatic circuit will change over time. The calibration equipment should be put inside the test room for a long period of time before the calibration begins. When the pressure is expected to change during normal calibration operations, a small settle time should be allowed before the measurements are taken. Temperature inside the test room should be as stable as possible during the measurements. Sampling at 50Hz for less than one second mitigates the high order temperature fluctuation effects.
In this article we have outlined a procedure to evaluate the leak impact on the measurements. The performance of the pressure sensor has been correlated with the measurement uncertainty. The procedure is accurate enough to allow a quick component selection. Up to now, the sensors which will be installed inside the BasicAirData calibrator have not been selected yet. Regarding static pressure sensing, following the trend of the commercially available telemetry equipment, we will report absolute pressures uncertainties in the range of (400[1], 2000) Pa. It seems prudent to have a reference measurement at least six to ten times better than those values, so broadly in the range (70,200) Pa.
[1] Some quick references from the net:
In page 5 of the datasheet, accuracy is stated as (-1500,1500) Pa. Is commonly used across the DIYers
Used on various flying platforms ranging from the most expensive to the cheapest. Bosch site gives the pressure accuracy as (-400, +200) Pa. Breakout boards with this sensor are quite common and are also shipped by SparkFun.
APM 2.6 Autopilot uses MS5611, MEAS High Resolution Altimeter. http://www.meas-spec.com/downloads/MS5611-01BA03.pdf Page 3 states that total worst case error band with no autozero is restricted in the -600 Pa to 600 Pa range | {"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": 0.7795025110244751, "perplexity": 1146.7196188238863}, "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-2017-30/segments/1500549424846.81/warc/CC-MAIN-20170724102308-20170724122308-00144.warc.gz"} |
https://www.lesswrong.com/posts/5bd75cc58225bf06703753e7/intertheoretic-utility-comparison-simple-theory | # Ω 1
Personal Blog
Crossposted from the AI Alignment Forum. May contain more technical jargon than usual.
There's been a lot of work on how to reach agreement between people with different preferences or values. In practice, reaching agreement can be tricky, because of issues of extortion/trade and how the negotiations actually play out.
To put those issues aside, let's consider a much simpler case: where a single agent is uncertain about their own utility function. Then there is no issue of extortion, because the agent's opponent is simply itself.
This type of comparison is called intertheoretic, rather than interpersonal.
## A question of scale
It would seem that if the agent believed with probability that it followed utility , and that it followed utility , then it should simply follow utility .
But this is problematic, because and are only defined up to positive affine transformations. Translations are not a problem: sending to sends to . But scalings are: sending to does not usually send to any scaled version of .
So if we identify as the equivalence class of utilities equivalent to , then we can write , but it's not meaningful to write .
From clarity, we'll call things like (which map worlds to real values) utility functions, while will be called utility classes.
## The setup
This is work done in collaboration with Toby Ord, Owen Cotton-Barratt, and Will MacAskill. We had some slightly different emphases during that process. In this post, I'll present my preferred version, while adding the more general approach at the end.
We will need the structure described in this post:
#. A finite set of deterministic strategies the agent can take. #. A set of utility classes the agent might follow. #. A distribution over , reflecting the agent's uncertainty over its own utility functions. #. Let be the subset to which assigns a non-zero weight. We'll assume puts no weight on trivial, constant utility functions.
We'll assume here that never gets updated, that the agent never sees any evidence that changes its values. The issue of updating is analysed in the sections on reward learning agent.
We'll be assuming that there is some function that takes in and and outputs a single utility class reflecting the agent's values.
# Basic axioms
1. Relevant data: If the utility classes and have the same values on all of , then they are interchangeable from 's perspective. Thus, in the terminology of this post, we can identify with .
This gives the structure of , where is a sphere, and corresponds to the trivial utility that is equal on all . The topology of is the standard topology on , and the only open set containing is the whole of .
Then with a reasonable topology on the probability distribution on -- such as the weak topology? -- this leads to the next axiom:
1. Continuity: the function is continuous in .
2. Individual normalisation: there is a function that maps to individual utility functions, such that (using as a measure on ).
The previous axiom means that all utility classes get normalised individually, then added together according to their weight in .
1. Symmetry: If is a stable permutation of , then .
Symmetry essentially means that the labels of , or the details of how the strategies are implemented, do not matter.
1. Utility reflection: .
2. Cloning indifference: If there exists such that for all in on which is non-zero, , then .
Cloning indifference means that the normalisation procedure does not care about multiple strategies that are equivalent on all possible utilities: it treats these strategies as if they were a single strategy.
We might want a stronger result, an independence of irrelevant alternatives. But this clashes with symmetry, so the following axioms attempt to get a weaker version of that requirement.
# Relevance axioms
The above axioms are sufficient for the basics, but, as we'll see, they're compatible with a lot of different ways of combining utilities. The following two axioms attempt to put some sort of limitations on these possibilities.
First of all, we want to define events that are irrelevant. In the terminology of this post, let be a partial history (ending in an action), with at two possible observations afterwards: and .
Then . Then if there exists a bijection between and such that, for all with , , then the observation versus is irrelevant. See here for more on how to define on in this context.
Thus irrelevance means that the utilities in really do not 'care' about versus , and that the increased strategy set it allows is specious. So if we remove as a possible observation (substituting instead) this should make no difference:
1. Weak irrelevance: If versus given is irrelevant for , then making (xor ) impossible does not change .
2. Strong irrelevance: If versus given is irrelevant for and there is at least one other possible observation after , then making (xor ) impossible does not change .
## Full theory
In our full analysis, we considered other approaches and properties, and I'll briefly list them here.
First of all, there is a set of prospects/options that may be different from the set of strategies . This allows you to add other moral considerations, not just strictly consequentialist expected utility reasoning.
In this context, the defined above was called a 'rating function', that rated the various utilities. With , there are two other possibilities, the 'choice function' which selected the best option, and the permissibility function, which lists the options you are allowed to take.
If we're considering options as outputs, rather than utilities, then we can do things like requiring the options to be Pareto only. We could also consider that the normalisation should stay the same if we remove the non-Pareto options or strategies. We might also consider that it's the space of possible utilities that we should care about; so, for instance, if , and , and similar results hold for all in , then we may as well drop from the strategy set as it's image is in the mixture of the other strategies.
Finally, some of the axioms above were presented in weaker forms (eg the individual normalisations) or stronger (eg independence of irrelevant alternatives).
# Ω 1
New Comment
You talk like is countably supported, but everything you've said generalizes to arbitrary probability measures over , if you replace "for all assigned nonzero probability by " with "for all in some set assigned probability by ".
If you endow with the quotient topology from , then the only open set containing is all of . This is a funny-looking topology, but I think it is ultimately the best one to use. With this topology, every function to is continuous at any point that maps to . As a consequence, the assumption "if " in the continuity axiom is unnecessary. More importantly, what topology on the space of probability distributions did you have in mind? Probably the weak topology?
I find independence of irrelevant alternatives more compelling than symmetry, but as long as we're accepting symmetry instead, it probably makes sense to strengthen the assumption to isomorphism-invariance: If is a bijection, then .
The relevance axioms section is riddled with type errors. only makes sense if , which would make sense if represented a space of outcomes rather than a space of strategies (which seems to me to be a more natural space to pay attention to anyway), or if is fully under the agent's control, whereas makes sense if is fully observable to the agent. If is neither fully under the agent's control nor fully observable to the agent, then I don't think either of these make sense. If we're using instead of , then formalizing irrelevance seems trickier. The best I can come up with is that is supported on of the form , where is the probability of . The weak and strong irrelevance axioms also contain type errors, since the types of the output and second input of depend on its first input, though this can probably be fixed.
I didn't understand any of the full theory section, so if any of that was important, it was too brief.
Yes to your two initial points; I wanted to keep the exposition relatively simple.
Do you disagree with the reasoning presented in the picture-proof? That seems a simple argument against IIA. Isomorphism invariance makes sense, but I wanted to emphasise the inner structure of .
Updated the irrelevance section to clarify that is fully observed and happens before the agent takes any actions, and that should be read as .
The full theory section is to write up some old ideas, to show that the previous axioms are not set in stone but that other approaches are possible and were considered.
Your picture proof looks correct, but it relies on symmetry, and I was saying that I prefer IIA instead of symmetry. I'm not particularly confident in my endorsement of IIA, but I am fairly confident in my non-endorsement of symmetry. In real situations, strategies/outcomes have a significant amount of internal structure which seems relevant and is not preserved by arbitrary permutations.
You've just replaced a type error with another type error. Elements of are just (equivalence classes of) functions . Conditioning like that isn't a supported operation.
You're right. I've drawn the set of utility functions too broadly. I'll attempt to fix this in the post.
Ok, I chose the picture proof because it was a particularly simple example of symmetry. What kind of internal structure are you thinking of?
For strategies: This ties back in to the situation where there's an observable event that you can condition your strategy on, and the strategy space has a product structure . This product structure seems important, since you should generally expect utility functions to factor in the sense that for some functions and , where is the probability of (I think for the relevance section, you want to assume that whenever there is such a product structure, is supported on utility functions that factor, and you can define conditional utility for such functions). Arbitrary permutations of that do not preserve the product structure don't seem like true symmetries, and I don't think it should be expected that an aggregation rule should be invariant under them. In the real world, there are many observations that people can and do take into account when deciding what to do, so a good model of strategy-space should have a very rich structure.
For outcomes, which is what utility functions should be defined on anyway: Outcomes differ in terms of how achievable they are. I have an intuition that if an outcome is impossible, then removing it from the model shouldn't have much effect. Like, you shouldn't be able to rig the aggregator function in favor of moral theory 1 as opposed to moral theory 2 by having the model take into account all the possible outcomes that could realistically be achieved, and also a bunch of impossible outcomes that theory 2 thinks are either really good or really bad, and theory 1 thinks are close to neutral. A natural counter-argument is that before you know which outcomes are impossible, any Pareto-optimal way of aggregating your possible preference functions must not change based on what turns out to be achievable; I'll have to think about that more. Also, approximate symmetries between peoples' preferences seem relevant to interpersonal utility comparison in practice, in the sense that two peoples' preferences tend to look fairly similar to each other in structure, but with each person's utility function centered largely around what happens to themselves instead of the other person, and this seems to help us make comparisons of the form "the difference between outcomes 1 and 2 is more important for person A than for person B"; I'm not sure if this way of describing it is making sense.
OK, got a better formalism: https://agentfoundations.org/item?id=1449
I think I've got something that works; I'll post it tomorrow. | {"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": 0.9412612318992615, "perplexity": 616.0438983998707}, "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/1637964358443.87/warc/CC-MAIN-20211128013650-20211128043650-00153.warc.gz"} |
https://socratic.org/questions/how-do-you-multiply-bc-a-2-bc-a-2 | Algebra
Topics
# How do you multiply (-bc+a^2)(bc+a^2)?
Apr 6, 2015
${a}^{4} - {b}^{2} {c}^{2}$
Let's switch the terms around in the binomials:
$\left({a}^{2} + b c\right) \left({a}^{2} - b c\right)$
This is a difference of squares where:
$\left({x}^{2} - {y}^{2}\right) = \left(x + y\right) \left(x - y\right)$
If we let $x = {a}^{2}$ and $y = b c$
$\left({\left({a}^{2}\right)}^{2} - {\left(b c\right)}^{2}\right) = \left({a}^{2} + b c\right) \left({a}^{2} - b c\right)$
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https://www.physicsforums.com/threads/rotation-of-a-rigid-object-about-a-fixed-axis.451888/ | # Rotation of a Rigid Object about a fixed axis
• #1
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## Homework Statement
A wheel is comprised of two 50.0 cm long thin rods of negligible mass and a thin metal ring with a mass of 10.00 kg, mounted on a very low friction bearing. A 100 gram lead weight is shot horizontally at the stationary wheel with an initial speed of 50.0 m/s and sticks to the rim of the wheel. What is the rotational speed of the wheel plus lead mass immediately after the collision? Give your answer in revolutions/second.
## Homework Equations
L_f=(I_a + I_b)W_f
## The Attempt at a Solution
I know of to find the moments of inertia im just confused about how to find L_f. The bullet would be travelings in a linear momentum not angular. How can i find this value?
## Answers and Replies
• #2
rock.freak667
Homework Helper
6,230
31
I think you should just use conservation of energy.
You can get the total moment of inertia I, the equation 0.5Iω2=0.5mv2 to get ω.
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http://physics.stackexchange.com/tags/differential-geometry/new | # Tag Info
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I'm not asking for a definition of a tangent vector. I'm asking what criterion you can use to decide whether a certain object can be described as a tangent vector. For example, how do we know in this coordinate-free context that the four-momentum can be described as a vector, but the magnetic field can't? If I understand your clarification correctly, ...
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Mathematicians have their axioms to define what a vector is, physicists start with a vector as a physical quantity that has a magnitude and a direction. Or at least, this is how Feynman defines it in volume 1, 11-4 of his lectures on physics. These two properties belong to the object and can't possibly depend upon the coordinates used to label them. Edit: ...
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There are 4 common definitions of tangent vectors, some of which make use of coordinates only casually or even not at all. Definition via transformation laws There's a somewhat technical one preferred by some physicists (those who value calculation rules over geometric insight - shut up and calculate, you probably know the type): A vector is just an ...
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From MTW's "Gravitation" (via Google Books): Updated answer to edited question: For example, how do we know in this coordinate-free context that the four-momentum can be described as a vector, but the magnetic field can't? I'm reminded of a relevant section from "A First Course in General Relativity" by Schutz. In section 4.4 on the ...
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Honestly, this coordinate-free GR stuff (Winitzki's pdf in particular) looks like GR as would be taught by a mathematician--very similar to do Carmo's text on Riemannian geometry. In classic (pseudo-)Riemannian geometry, vectors are defined as derivatives of affine parameterized curves, covectors as either maps on vectors to scalars or as gradients of scalar ...
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I suppose $f$ is just an arbitrary scalar function on the manifold. I'm not well-versed with the concept of Ricci flow, so I'll try to give a simple operational answer. I also don't understand what exactly you're looking for. The Ricci scalar $R$ roughly represents the amount of energy stored in spacetime (as curvature). The dilaton is a scalar field which ...
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Let us denote \begin{align} \xi_1 = (0,1), \qquad \xi_2 = (-e^x, e^x/t), \qquad \xi_3 = (e^{-x}, e^{-x}/t) \end{align} Each of these killing vectors leads to a conserved quantity \begin{align} c_1 &= \dot x_\mu\cdot (\xi_1)^\mu = \dot x t^2 \\ c_2 &= \dot x_\mu\cdot (\xi_2)^\mu = \dot t e^x +\dot x te^x \\ c_3 &= \dot x_\mu\cdot ...
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The main question has already been answered by joshphysics. For the remaining, rescale the variables as $$U~:=~cu, \qquad V~:=~cv.$$ The two equations becomes $$\dot{U}^2 ~=~U^4+U^2, \qquad \dot{V}~=~U^2 ,$$ with full solution $$U(t)~=~\pm {\rm csch}(t-t_0), \qquad V(t)~=~\coth(t-t_0)+V_0.$$ OP's sought-for equation now follows from $$(V-V_0)^2 ... 1 The FLRW metric can be static, this is the solution that Einstein concocted before Hubble observed the expansion of the universe. The only way that Einstein could make his equations static was by introducing the infamous cosmological constant \Lambda. The general FLRW metric has the form$$ \text{d}s^2 = -c^2\text{d}t^2 + a(t)\left[\frac{\text{d}r^2}{1 - ...
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I prefer to use Killing vectors and conservation laws to solve stuff like this, so let's analyze the problem using Killing vectors, and see if the results agree with your Euler-Lagrange equations. Notice that the metric is invariant under translations of $v$. The associated killing vector is $\partial_v$ which in turn gives the following conserved ...
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I'm not sure what OP exactly is requesting, but OP's equation follows e.g. from the general fact that for an arbitrary 2D surface, the Ricci tensor $$R_{\mu\nu} ~\propto~g_{\mu\nu}$$ is always proportional to the metric tensor $g_{\mu\nu}$. This is basically a consequence of that in 2D the Riemann curvature tensor is complete determined by the scalar ...
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I) Pragmatically speaking, the most important property of $\sqrt{-g}$ for model building purposes, is not per se the fact that $\sqrt{-g}d^{4}x$ measures the volume element of a 4-dimensional Parallelepiped with infinitesimal edges $dx^0, \ldots, dx^3$. II) A more important property is that $\sqrt{-g}d^{4}x$ transforms as a scalar (i.e. is invariant) under ...
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Obviously, you are talking about the derivation in Landau-Lifshitz book. I admit that this is not the clearest explanation of what is going on. (On the other hand that is not the first and not the last place like that in Landau-Lifshitz...) Anyway, I don't really see what is your problem -- just use Stokes' theorem from (6.19): $$\Delta A_i = \frac12\int ... 0 I've made a small document featuring fluid dynamics equations in terms of vector-valued differential forms. The document with information on any further developments can be found on my page. 1 The metric is spherically symmetric. This means that angular momentum of the system is conserved (you can show this directly using the metric by computing the three killing vectors associated with spatial rotation and their corresponding conserved quantities) and therefore that the motion is contained to lie in a plane. If the motion is in a given plane, ... 0 I think there is a method that I believe is rather simple. Take a look: There is a thing called 'normal Riemann coordinates'. In this coordinates the metric is expanded around the origin, and the coefficients of expansion are expressed in terms of the Riemann tensor. I suggest that you read about them and check whether the coordinates described below are ... 0 Given that your metric is diagonal, it simplifies a lot these calculations. However, the Riemman tensor is such an object... First, start with the Christoffel Symbols$$ \Gamma^i{}_{k\ell}= {1 \over 2} g^{im} (g_{mk,\ell} + g_{m\ell,k} - g_{k\ell,m})$$Note that g_{im}=0 for i \neq m so it simplifies to$$ \Gamma^i{}_{k\ell}= {1 \over 2} g^{ii} ...
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To add a bit of fluff to twistor59's answer, let's take a bird's eye view of Riemannian geometry. The Riemannian metric gives us the notion of lengths and angles as well as the concept of straight lines (geodesics). Any submanifold inherits these notions from the ambient space, made explicit via the first fundamental form, which makes the submanifold is a ...
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For the first fundamental form - if you've got two vectors tangent to $\Sigma$, and $\Sigma$ is embedded in $M$, and $M$ has a metric, just use the embedding to consider the vectors as living tangent to $M$ and use $M$'s metric to compute their inner product. For the second fundamental form, basically, if you imagine a two surface $\Sigma$ embedded in ...
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As soon as you get something like $\delta_{bd}$, alarm bells should ring, as this is not a tensor. The inverse metric $g^{ac}$ is defined by the identity $$g^{ac}g_{cb} = \delta^a_b$$ If you plug this into your expression (and use the fact that $g$ is symmetric), you will obtain the correct equation.
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Great question! I would say that "force is a one-form" is a statement that has some truth to it, but it's somewhat context-dependent. In any context where you have a metric, you can freely convert back and forth between vectors and one-forms, and the distinction between them becomes uninteresting. Examples of such contexts include relativistic spacetime ...
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Perhaps some insight into this problem can be gleaned from relativity. In relativity, the EM field is represented by a two-form (i.e. with 6 components). When this two-form is fed a current to act upon, this yields a force--or rather, four-force, so you get power as well as force. What does this mean? Well, you can feed the four-force any timelike unit ...
0
It can be show easily by the next reasoning. $$DA_{i} = g_{ik}DA^{k},$$ because $DA_{i}$ is a vector (according to the definition of covariant derivative). On the other hand, $$DA_{i} = D(g_{ik}A^{k}) = g_{ik}DA^{k} + A^{k}Dg_{ik}.$$ So, $$g_{ik}DA^{k} + A^{k}Dg_{ik} = g_{ik}DA^{k} \Rightarrow Dg_{ik} = 0.$$ So, it isn't a condition, it is a ...
1
Unlike classical electromagnetism, General Relativity is highly nonlinear--this means that the gravitational field can serve as its own source. A consequence of this fact is that fields decidedly do not superpose, and you can get all sorts of effects even from vacuum relativity. The most notable of these effects are things such as Brill waves and Geons, ...
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One way of phrasing this is that the nonlinearity of the equations means that you can't say that the sum (or difference) of two solutions to the Einstein field equations is also a solution. So even taking the delta with respect to the Minkowski metric, as you would like to do, isn't allowed (unless you work perturbatively as John alluded to).
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The metrics don't simply add together as you suggest. In fact there is no known solution for the metric when you have two point masses (thought there are approximate solutions). If there was it would make calculating the motion of binary black holes a great deal simpler than it currently is. The curvature has to be calculated numerically.
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The trickiness is what you mean by a spherical metric. What you've written down is the metric of flat space in spherical coordinates, which can be thought of as a warped product of the flat minkowskian two space $(t,r)$ with the unit sphere. This space is equivalent to the normal $(t,x,y,z)$ coordinates of standard special relativity under a coordinate ...
2
A couple of preliminaries: (1) The Schwarzschild metric is not just the metric for a black hole. It's the exterior metric for any spherically symmetric, nonrotating gravitating body. For example, it's a very good approximation to the earth's metric, since the earth is nearly spherical and is not rotating at relativistic speeds. (2) Let's take units with ...
2
Metric signature is a coordinate-invariant notion. Given a metric, one computes the number of positive and negative eigenvalues that it has, and this gives its signature. For a diagonal metric, like the metric $$ds^2 = dr^2 + r^2 d\theta^2$$ both diagonal components are positive, so the metric has precisely two positive eigenvalues, and its signature ...
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http://physicshelpforum.com/thermodynamics-fluid-mechanics/340-pv-constant.html | Physics Help Forum pV is a constant
Thermodynamics and Fluid Mechanics Thermodynamics and Fluid Mechanics Physics Help Forum
Sep 4th 2008, 07:55 AM #1 Senior Member Join Date: Apr 2008 Location: HK Posts: 886 pV is a constant For a graph with pV against p, it should be a straight horizontal line. However, regarding the slope, slope equals=V = 0 , isn't that ridiculous?
Sep 4th 2008, 08:33 AM #2
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Originally Posted by werehk For a graph with pV against p, it should be a straight horizontal line. However, regarding the slope, slope equals=V = 0 , isn't that ridiculous?
The slope of a horizontal line is 0. You are saying that the slope should equal V which is 0, or is this a typo?
The relationship expressed by a p vs. V plot can, in general, be complicated. For an ideal gas we easily have that the pressure is inversely proportional to the volume, so the graph is a curve. However for different physical systems we can typically arrange the system to have a variety of different behaviors, on of which is that the pressure is independent of the volume, ie. the slope of the p vs. V graph is 0.
-Dan
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Sep 4th 2008, 09:05 PM #3
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Originally Posted by topsquark The slope of a horizontal line is 0. You are saying that the slope should equal V which is 0, or is this a typo? The relationship expressed by a p vs. V plot can, in general, be complicated. For an ideal gas we easily have that the pressure is inversely proportional to the volume, so the graph is a curve. However for different physical systems we can typically arrange the system to have a variety of different behaviors, on of which is that the pressure is independent of the volume, ie. the slope of the p vs. V graph is 0. -Dan
Ya, I'm saying that volume equals the slope which is zero.
So does it mean that there is no special meaning for the slope and we can't use the slope for interpretation and analysis of other variables?
Last edited by werehk; Sep 4th 2008 at 09:08 PM.
Sep 5th 2008, 09:41 AM #4
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Originally Posted by werehk Ya, I'm saying that volume equals the slope which is zero. So does it mean that there is no special meaning for the slope and we can't use the slope for interpretation and analysis of other variables?
Well, if the volume is equal to zero then we DO have a serious problem, as the object can only be a black hole! My guess is that something was not labeled correctly on the diagram.
As far as the slope of th curve being zero this means that the process taking the system from one point to another on the curve is "isobaric" (constant pressure.) This determines how many of the different properties of the system relate to each other, thermodynamically speaking, so it is a very important piece of information. More than that I cannot say because my Thermodynamics is awfully rusty.
-Dan
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Oct 11th 2008, 09:35 PM #5 Senior Member Join Date: Apr 2008 Location: HK Posts: 886 Would it be more appropriate to say that for pV/P, the P is the applied pressure rather than the gas pressure? As I found it would be more appropriate for explanation.
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# A gambler rolls three fair six-sided dice. What is the probability
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A gambler rolls three fair six-sided dice. What is the probability [#permalink]
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31 Jan 2012, 17:50
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A gambler rolls three fair six-sided dice. What is the probability that two of the dice show the same number, but the third shows a different number?
OA:
[Reveal] Spoiler:
15/36
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Re: A gambler rolls three fair six-sided dice. What is the probability [#permalink]
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31 Jan 2012, 19:08
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This is a tricky question because there is a final twist that it is easy to overlook.
First off, we want to find the probability of rolling a pair of any number. There are six
pairs and a total of 36 different ways to roll a pair of dices: 6/36 = 1/6.
Next, we want to account for the third die - it cannot be the same as the first two,
so it can be any of five numbers out of 6: 5/6.
Therefore probability is 5/6 x 1/6 = 5/36.
It is tempting here to think that we have solved the problem. But if we read carefully, the
question does not say that the first two dice have to be the same and the third die has
to be different.
the question says a gambler rolls 3 dice. So the first two do not have to be pairs.
As long as 2 of the 3 dice are pairs and the last die is a different number. To find the
number of way this can occur, we use combinations formula: 3!/2!1! = 3.
We multiply this to the numerator to give us 3 x 5/36 = 15/36.
For some even trickier dice problems, check out our Magoosh GMAT blog post (these ones are really nasty!)
GMAT Probability: Difficult Dice Questions
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Re: A gambler rolls three fair six-sided dice. What is the probability [#permalink]
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01 Feb 2012, 01:02
Thanks chris for the solution.
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A gambler rolls three fair six-sided dice. What is the probability [#permalink]
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02 Feb 2012, 11:32
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abhi47 wrote:
A gambler rolls three fair six-sided dice. What is the probability that two of the dice show the same number, but the third shows a different number?
Responding to a pm.
Combinations approach:
Total # of outcomes is $$6^3$$;
Favorable outcomes are all possible scenarios of XXY:
$$C^1_6*C^1_5*\frac{3!}{2!}=6*5*3=90$$, where $$C^1_6$$ is # of ways to pick X (the number which shows twice), $$C^1_5$$ is # of ways to pick Y (out of 5 numbers left) and $$\frac{3!}{2!}$$ is # of permutation of 3 letters XXY out of which 2 X's are identical.
$$P=\frac{Favorable}{Total}=\frac{90}{6^3}=\frac{15}{36}$$.
Hope it's clear.
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Probability - rolling a dice [#permalink]
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12 Aug 2012, 14:23
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A gambler rolls three fair-sided dice. What is the probability that two of the dice show the same number, but the third shows a different number?
A) 1/8
B) 5/18
C) 1/3
D) 5/12
E) 5/6
[Reveal] Spoiler:
D
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Re: Probability - rolling a dice [#permalink]
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12 Aug 2012, 14:26
Hi, can somebody please explain a fundamental aspect of this question: I understand that the probability of getting 2 die with the same number AND one dice with a different number is = 6/6 x 1/6 x 5/6 = 5/36
BUT, beyond this, I get confused whether I should multiply this by 3 for the other 3 other combinations OR 3!?
Could somebody explain while accounting for different combinations, when we multiply by the # of combi VS the factorial of the # of combi?
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Re: Probability - rolling a dice [#permalink]
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12 Aug 2012, 23:35
Aximili85 wrote:
Hi, can somebody please explain a fundamental aspect of this question: I understand that the probability of getting 2 die with the same number AND one dice with a different number is = 6/6 x 1/6 x 5/6 = 5/36
BUT, beyond this, I get confused whether I should multiply this by 3 for the other 3 other combinations OR 3!?
Could somebody explain while accounting for different combinations, when we multiply by the # of combi VS the factorial of the # of combi?
In this case, you should multiply by 3 because you can get two identical results and the third different in three different scenarios: AAB, ABA and BAA. Each scenario has the same probability of 5/36.
You can look at the 3 as 3C1, meaning how many choices we have to place the different result, or you can interpret 3 as 3!/2! because you have all the permutations of the triplet A,A,B, with A repeated twice. Obviously, as they should, they really give the same result.
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Re: Probability - rolling a dice [#permalink]
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13 Aug 2012, 05:33
EvaJager wrote:
Aximili85 wrote:
Hi, can somebody please explain a fundamental aspect of this question: I understand that the probability of getting 2 die with the same number AND one dice with a different number is = 6/6 x 1/6 x 5/6 = 5/36
BUT, beyond this, I get confused whether I should multiply this by 3 for the other 3 other combinations OR 3!?
......................twice. Obviously, as they should, they really give the same result.
ok that helps, thanks
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Re: Probability - rolling a dice [#permalink]
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13 Aug 2012, 18:35
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Ways in which a given set can appear = 3 i.e. AAB ABA BAA
For case AAB
Probability of getting a number on first dice = 6/6
Probability of getting the same number on second dice = 1/6
Probability of getting a different number on third dice = 5/6
Thus probability = 6/6 * 1/6 * 5/6 * 3
5/12 (D)
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Re: Probability - rolling a dice [#permalink]
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26 Aug 2012, 08:07
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My approach:
Total number of possible way = 6*6*6 = 216
3 discs will appear in any one of the following arrangements: AAA, AAB, ABC
where, AAA=All are same, AAB=Two are same, ABC=all three different
Now, total number of AAA = 6
Total number of ABC = 6*5*4 = 120
therefore, total number of AAA, ABC = 126
So, total number of AAB = 216-126=90
Probability of AAB= 90/216=5/12
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Re: A gambler rolls three fair six-sided dice. What is the probability [#permalink]
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Re: A gambler rolls three fair six-sided dice. What is the probability [#permalink]
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24 Nov 2015, 10:35
Bunuel wrote:
abhi47 wrote:
A gambler rolls three fair six-sided dice. What is the probability that two of the dice show the same number, but the third shows a different number?
Responding to a pm.
Combinations approach:
Total # of outcomes is $$6^3$$;
Favorable outcomes are all possible scenarios of XXY:
$$C^1_6*C^1_5*\frac{3!}{2!}=6*5*3=90$$, where $$C^1_6$$ is # of ways to pick X (the number which shows twice), $$C^1_5$$ is # of ways to pick Y (out of 5 numbers left) and $$\frac{3!}{2!}$$ is # of permutation of 3 letters XXY out of which 2 X's are identical.
$$P=\frac{Favorable}{Total}=\frac{90}{6^3}=\frac{15}{36}$$.
Hope it's clear.
Hey Bunuel, you don't seem to agree with Chris on permutation/combination.
When you say $$\frac{3!}{2!}$$ is it a 3P1 or a 3C2 ?
And by the way, how would we know from this question, which to work with?
Thank you!
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https://transportmaps.mit.edu/docs/api-TransportMaps.html | # API - TransportMaps¶
Sub-modules
Classes
Class Description
TMO Base object for every object in the module.
SumChunkReduce Define the summation of the chunks operation.
TupleSumChunkReduce Define the summation of the chunks operation over list of tuples.
TensorDotReduce Define the reduce tensordot operation carried out through the mpi_map function
ExpectationReduce Define the expectation operation carried out through the mpi_map function
AbsExpectationReduce Define the expectation of the absolute value: $$\mathbb{E}[\vert {\bf X} \vert]$$
TupleExpectationReduce Define the expectation operation applied on a tuple
cached
cached_tuple
Functions
Function Description
deprecate
setLogLevel Set the log level for all existing and new objects related to the TransportMaps module
counted
get_mpi_pool Get a pool of n processors
mpi_eval Interface for the parallel evaluation of a generic function on points x
mpi_map Interface for the parallel evaluation of a generic function on points x
mpi_map_alloc_dmem Interface for the parallel evaluation of a generic function on points x
mpi_alloc_dmem List of keyworded arguments to be allocated in the distributed memory.
distributed_sampling
generate_total_order_midxs Generate a total order multi-index
total_time_cost_function
get_sub_cache
taylor_test Test the gradient and Hessian of a function using the Taylor test.
kl_divergence Compute $$\mathcal{D}_{KL}(\pi_1 | \pi_2)$$
grad_a_kl_divergence Compute $$\nabla_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$
hess_a_kl_divergence Compute $$\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$
tuple_grad_a_kl_divergence Compute $$\left(\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}}),\nabla_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})\right)$$
action_stored_hess_a_kl_divergence Evaluate action of $$\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$ on vector $$v$$.
storage_hess_a_kl_divergence Assemble $$\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$.
action_hess_a_kl_divergence Compute $$\langle\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}}),\delta{\bf }\rangle$$
kl_divergence_component Compute $$-\sum_{i=0}^m f(x_i) = -\sum_{i=0}^m \log\pi\circ T_k(x_i) + \log\partial_{x_k}T_k(x_i)$$
grad_a_kl_divergence_component Compute $$-\sum_{i=0}^m \nabla_{\bf a}f[{\bf a}](x_i) = -\sum_{i=0}^m \nabla_{\bf a} \left(\log\pi\circ T_k[{\bf a}](x_i) + \log\partial_{x_k}T_k[{\bf a}](x_i)\right)$$
hess_a_kl_divergence_component Compute $$-\sum_{i=0}^m \nabla^2_{\bf a}f[{\bf a}](x_i) = -\sum_{i=0}^m \nabla^2_{\bf a} \left(\log\pi\circ T_k[{\bf a}](x_i) + \log\partial_{x_k}T_k[{\bf a}](x_i)\right)$$
misfit_squared Compute $$\vert f_1 - f_2 \vert^2$$
grad_a_misfit_squared Compute $$\nabla_{\bf a}\vert f_{1,{\bf a}} - f_2 \vert^2$$
hess_a_misfit_squared Compute $$\nabla^2_{\bf a}\vert f_{1,{\bf a}} - f_2 \vert^2$$
L2_misfit Compute $$\Vert f_1 - f_2 \Vert_{L^2_\pi}$$
L2squared_misfit Compute $$\Vert f_1 - f_2 \Vert^2_{L^2_\pi}$$
grad_a_L2squared_misfit Compute $$\nabla_{\bf a}\Vert f_{1,{\bf a}} - f_2 \Vert^2_{L^2_\pi}$$
hess_a_L2squared_misfit Compute $$\nabla^2_{\bf a}\Vert f_{1,{\bf a}} - f_2 \Vert^2_{L^2_\pi}$$
storage_hess_a_L2squared_misfit Assemble $$\nabla^2_{\bf a}\Vert f_{1,{\bf a}} - f_2 \Vert^2_{L^2_\pi}$$.
action_stored_hess_a_L2squared_misfit Evaluate the action of $$\nabla^2_{\bf a}\Vert f_{1,{\bf a}} - f_2 \Vert^2_{L^2_\pi}$$ on $$v$$.
grad_t_kl_divergence Compute $$\nabla_T \mathcal{D}_{KL}(\pi_1, \pi_2(T))$$.
grad_x_grad_t_kl_divergence Compute $$\nabla_x \nabla_T \mathcal{D}_{KL}(\pi_1, \pi_2(T))$$.
tuple_grad_x_grad_t_kl_divergence Compute $$\nabla_x \nabla_T \mathcal{D}_{KL}(\pi_1, \pi_2(T))$$.
laplace_approximation Compute the Laplace approximation of the distribution $$\pi$$.
laplace_approximation_withBounds Compute the Laplace approximation of the distribution $$\pi$$.
maximum_likelihood Compute the maximum likelihood of the log-likelihood $$\log\pi({\bf y}\vert{\bf x})$$.
Default_IsotropicIntegratedExponentialTriangularTransportMap Generate a triangular transport map with default settings.
Default_IsotropicIntegratedExponentialDiagonalTransportMap Generate a diagonal transport map with default settings.
Default_IsotropicIntegratedSquaredTriangularTransportMap Generate a triangular transport map with default settings.
Default_IsotropicIntegratedSquaredDiagonalTransportMap Generate a diagonal transport map with default settings.
Default_IsotropicMonotonicLinearSpanTriangularTransportMap Generate a triangular transport map with default settings.
Default_IsotropicLinearSpanTriangularTransportMap Generate a triangular transport map with default settings.
Default_LinearSpanTriangularTransportMap Generate a linear span triangular transport map with default settings and user defined sparsity and orders.
Documentation
class TransportMaps.TMO[source]
Base object for every object in the module.
This object provides functions for storage and parallelization.
store(fname, force=False)[source]
Store the object with the selected file name fname
Parameters: fname (str) – file name force (bool) – whether to force overwriting
TransportMaps.setLogLevel(level)[source]
Set the log level for all existing and new objects related to the TransportMaps module
Parameters: level (int) – logging level
TransportMaps.get_mpi_pool()[source]
Get a pool of n processors
Returns: (mpi_map.MPI_Pool) – pool of processors
Usage example:
import numpy as np
import numpy.random as npr
from TransportMaps import get_mpi_pool, mpi_map
class Operator(object):
def __init__(self, a):
self.a = a
def sum(self, x, n=1):
out = x
for i in range(n):
out += self.a
return out
op = Operator(2.)
x = npr.randn(100,5)
n = 2
pool = get_mpi_pool()
pool.start(3)
try:
xsum = mpi_map("sum", op, x, (n,), mpi_pool=pool)
finally:
pool.stop()
TransportMaps.mpi_eval(f, scatter_tuple=None, bcast_tuple=None, dmem_key_in_list=None, dmem_arg_in_list=None, dmem_val_in_list=None, dmem_key_out_list=None, obj=None, reduce_obj=None, reduce_tuple=None, import_set=None, mpi_pool=None, splitted=False, concatenate=True)[source]
Interface for the parallel evaluation of a generic function on points x
Parameters: f (object or str) – function or string identifying the function in object obj scatter_tuple (tuple) – tuple containing 2 lists of [keys] and [arguments] which will be scattered to the processes. bcast_tuple (tuple) – tuple containing 2 lists of [keys] and [arguments] which will be broadcasted to the processes. dmem_key_in_list (list) – list of string containing the keys to be fetched (or created with default None if missing) from the distributed memory and provided as input to f. dmem_val_in_list (list) – list of objects corresponding to the keys defined in dmem_key_in_list, used in case we are not executing in parallel dmem_key_out_list (list) – list of keys to be assigned to the outputs beside the first one obj (object) – object where the function f_name is defined reduce_obj (object) – object ReduceObject defining the reduce method to be applied (if any) reduce_tuple (object) – tuple containing 2 lists of [keys] and [arguments] which will be scattered to the processes to be used by reduce_obj import_set (set) – list of couples (module_name,as_field) to be imported as import module_name as as_field mpi_pool (mpi_map.MPI_Pool) – pool of processors splitted (bool) – whether the scattering input is already splitted or not concatenate (bool) – whether to concatenate the output (the output of f must be a numpy.ndarray object
TransportMaps.mpi_map(f, scatter_tuple=None, bcast_tuple=None, dmem_key_in_list=None, dmem_arg_in_list=None, dmem_val_in_list=None, obj=None, obj_val=None, reduce_obj=None, reduce_tuple=None, mpi_pool=None, splitted=False, concatenate=True)[source]
Interface for the parallel evaluation of a generic function on points x
Parameters: f (object or str) – function or string identifying the function in object obj scatter_tuple (tuple) – tuple containing 2 lists of [keys] and [arguments] which will be scattered to the processes. bcast_tuple (tuple) – tuple containing 2 lists of [keys] and [arguments] which will be broadcasted to the processes. dmem_key_in_list (list) – list of string containing the keys to be fetched (or created with default None if missing) from the distributed memory and provided as input to f. dmem_val_in_list (list) – list of objects corresponding to the keys defined in dmem_key_in_list, used in case we are not executing in parallel obj (object or str) – object where the function f_name is defined obj_val (object) – object to be used in case not executing in parallel and obj is a string reduce_obj (object) – object ReduceObject defining the reduce method to be applied (if any) reduce_tuple (object) – tuple containing 2 lists of [keys] and [arguments] which will be scattered to the processes to be used by reduce_obj mpi_pool (mpi_map.MPI_Pool) – pool of processors splitted (bool) – whether the scattering input is already splitted or not concatenate (bool) – whether to concatenate the output (the output of f must be a numpy.ndarray object
TransportMaps.mpi_map_alloc_dmem(f, scatter_tuple=None, bcast_tuple=None, dmem_key_in_list=None, dmem_arg_in_list=None, dmem_val_in_list=None, dmem_key_out_list=None, obj=None, obj_val=None, reduce_obj=None, reduce_tuple=None, mpi_pool=None, splitted=False, concatenate=True)[source]
Interface for the parallel evaluation of a generic function on points x
Parameters: f (object or str) – function or string identifying the function in object obj scatter_tuple (tuple) – tuple containing 2 lists of [keys] and [arguments] which will be scattered to the processes. bcast_tuple (tuple) – tuple containing 2 lists of [keys] and [arguments] which will be broadcasted to the processes. dmem_key_in_list (list) – list of string containing the keys to be fetched (or created with default None if missing) from the distributed memory and provided as input to f. dmem_val_in_list (list) – list of objects corresponding to the keys defined in dmem_key_in_list, used in case we are not executing in parallel dmem_key_out_list (list) – list of keys to be assigned to the outputs beside the first one obj (object) – object where the function f_name is defined obj_val (object) – object to be used in case not executing in parallel and obj is a string reduce_obj (object) – object ReduceObject defining the reduce method to be applied (if any) reduce_tuple (object) – tuple containing 2 lists of [keys] and [arguments] which will be scattered to the processes to be used by reduce_obj mpi_pool (mpi_map.MPI_Pool) – pool of processors splitted (bool) – whether the scattering input is already splitted or not concatenate (bool) – whether to concatenate the output (the output of f must be a numpy.ndarray object
TransportMaps.mpi_alloc_dmem(mpi_pool=None, **kwargs)[source]
List of keyworded arguments to be allocated in the distributed memory.
This executes only if an mpi_pool is provided.
Parameters: mpi_pool (mpi_map.MPI_Pool) – pool of processors
class TransportMaps.SumChunkReduce(axis=None)[source]
Define the summation of the chunks operation.
The chunks resulting from the output of the MPI evaluation are summed along their axis.
Parameters: axis (tuple [2]) – tuple containing list of axes to be used in the sum operation
class TransportMaps.TupleSumChunkReduce(axis=None)[source]
Define the summation of the chunks operation over list of tuples.
The chunks resulting from the output of the MPI evaluation are summed along their axis.
Parameters: axis (tuple [2]) – tuple containing list of axes to be used in the sum operation
class TransportMaps.TensorDotReduce(axis)[source]
Define the reduce tensordot operation carried out through the mpi_map function
Parameters: axis (tuple [2]) – tuple containing list of axes to be used in the tensordot operation
class TransportMaps.ExpectationReduce[source]
Define the expectation operation carried out through the mpi_map function
class TransportMaps.AbsExpectationReduce[source]
Define the expectation of the absolute value: $$\mathbb{E}[\vert {\bf X} \vert]$$
class TransportMaps.TupleExpectationReduce[source]
Define the expectation operation applied on a tuple
If we are given a tuple $$(x_1,x_2)$$, the inner reduce returns $$(\langle x_1,w\rangle , \langle x_2, w\rangle)$$.
Given a list of tuples $$\{(x_i,y_i\}_{i=0}^n$$, the outer reduce gives $$(\sum x_i, \sum y_i)$$.
TransportMaps.generate_total_order_midxs(max_order_list)[source]
Generate a total order multi-index
Given the list of maximums $${\bf m}$$, the returned set of multi-index $$I$$ is such that $$\sum_j^d {\bf_i}_j <= max {\bf m}$$ and $${\bf i}_j <= {\bf m}_j$$.
TransportMaps.taylor_test(x, dx, f, gf=None, hf=None, ahf=None, h=0.0001, fungrad=False, caching=False, args={})[source]
Test the gradient and Hessian of a function using the Taylor test.
Using a Taylor expansion around $${\bf x}$$, we have
$f({\bf x}+h \delta{\bf x}) = f({\bf x}) + h (\nabla f({\bf x}))^\top \delta{\bf x} + \frac{h^2}{2} (\delta{\bf x})^\top \nabla^2 f({\bf x}) \delta{\bf x} + \mathcal{O}(h^3)$
Therefore
$\vert f({\bf x}+h \delta{\bf x}) - f({\bf x}) - h (\nabla f({\bf x}))^\top \delta{\bf x} \vert = \mathcal{O}(h^2)$
and
$\vert f({\bf x}+h \delta{\bf x}) - f({\bf x}) - h (\nabla f({\bf x}))^\top \delta{\bf x} - \frac{h^2}{2} (\delta{\bf x})^\top \nabla^2 f({\bf x}) \delta{\bf x} \vert = \mathcal{O}(h^3)$
Parameters: x (ndarray [$$m,d_x$$]) – evaluation points $${\bf x}$$ dx (ndarray [$$m,d_x$$]) – perturbation direction $$\delta{\bf x}$$ f (function) – function $${\bf x} \mapsto f({\bf x})$$. If fungrad==True, then f is the mapping $${\bf x} \mapsto (\nabla f({\bf x}), f({\bf x}))$$. gf (function) – gradient function $${\bf x} \mapsto \nabla f({\bf x})$$ hf (function) – Hessian function $${\bf x} \mapsto \nabla^2 f({\bf x})$$ ahf (function) – action of the Hessian function $${\bf x},\delta{\bf x} \mapsto (\nabla f({\bf x}))^\top \delta{\bf x}$$ h (float) – perturbation step fungrad (bool) – whether f returns also the gradient or not. caching (bool) – whether to pass a cache dictionary to the functions. args (dict) – arguments to be passed to functions
TransportMaps.kl_divergence(d1, d2, params1=None, params2=None, cache=None, qtype=None, qparams=None, x=None, w=None, batch_size=None, mpi_pool_tuple=(None, None), d1_entropy=True)[source]
Compute $$\mathcal{D}_{KL}(\pi_1 | \pi_2)$$
Parameters: d1 (Distribution) – distribution $$\pi_1$$ d2 (Distribution) – distribution $$\pi_2$$ params1 (dict) – parameters for distribution $$\pi_1$$ params2 (dict) – parameters for distribution $$\pi_2$$ cache (dict) – cached values qtype (int) – quadrature type to be used for the approximation of $$\mathbb{E}_{\pi_1}$$ qparams (object) – parameters necessary for the construction of the quadrature x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi_1}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi_1}$$ batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool_tuple (tuple [2] of mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of d1 and d2 d1_entropy (bool) – whether to include the entropy term $$\mathbb{E}_{\pi_1}[\log \pi_1]$$ in the KL divergence (float) – $$\mathcal{D}_{KL}(\pi_1 | \pi_2)$$
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.grad_a_kl_divergence(d1, d2, params1=None, params2=None, cache=None, qtype=None, qparams=None, x=None, w=None, batch_size=None, mpi_pool_tuple=(None, None))[source]
Compute $$\nabla_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$
Parameters: d1 (Distribution) – distribution $$\pi_1$$ d2 (Distribution) – distribution $$\pi_2$$ params1 (dict) – parameters for distribution $$\pi_1$$ params2 (dict) – parameters for distribution $$\pi_2$$ cache (dict) – cached values qtype (int) – quadrature type to be used for the approximation of $$\mathbb{E}_{\pi_1}$$ qparams (object) – parameters necessary for the construction of the quadrature x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi_1}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi_1}$$ batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. mpi_pool_tuple (tuple [2] of mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of d1 and d2 (ndarray [$$N$$] – $$\nabla_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.hess_a_kl_divergence(d1, d2, params1=None, params2=None, cache=None, qtype=None, qparams=None, x=None, w=None, batch_size=None, mpi_pool_tuple=(None, None))[source]
Compute $$\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$
Parameters: d1 (Distribution) – distribution $$\pi_1$$ d2 (Distribution) – distribution $$\pi_2$$ params1 (dict) – parameters for distribution $$\pi_1$$ params2 (dict) – parameters for distribution $$\pi_2$$ cache (dict) – cached values qtype (int) – quadrature type to be used for the approximation of $$\mathbb{E}_{\pi_1}$$ qparams (object) – parameters necessary for the construction of the quadrature x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi_1}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi_1}$$ batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. mpi_pool_tuple (tuple [2] of mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of d1 and d2 (ndarray [$$N,N$$] – $$\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.tuple_grad_a_kl_divergence(d1, d2, params1=None, params2=None, cache=None, qtype=None, qparams=None, x=None, w=None, batch_size=None, mpi_pool_tuple=(None, None), d1_entropy=True)[source]
Compute $$\left(\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}}),\nabla_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})\right)$$
Parameters: d1 (Distribution) – distribution $$\pi_1$$ d2 (Distribution) – distribution $$\pi_2$$ params1 (dict) – parameters for distribution $$\pi_1$$ params2 (dict) – parameters for distribution $$\pi_2$$ cache (dict) – cached values qtype (int) – quadrature type to be used for the approximation of $$\mathbb{E}_{\pi_1}$$ qparams (object) – parameters necessary for the construction of the quadrature x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi_1}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi_1}$$ batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. mpi_pool_tuple (tuple [2] of mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of d1 and d2 (tuple) – $$\left(\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}}),\nabla_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})\right)$$
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.action_stored_hess_a_kl_divergence(H, v)[source]
Evaluate action of $$\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$ on vector $$v$$.
Parameters: v (ndarray [$$N$$]) – vector $$v$$ H (ndarray [$$N,N$$]) – Hessian $$\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$ (ndarray [$$N$$]) – $$\langle\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}}),v\rangle$$
TransportMaps.storage_hess_a_kl_divergence(d1, d2, params1=None, params2=None, cache=None, qtype=None, qparams=None, x=None, w=None, batch_size=None, mpi_pool_tuple=(None, None))[source]
Assemble $$\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$.
Parameters: d1 (Distribution) – distribution $$\pi_1$$ d2 (Distribution) – distribution $$\pi_2$$ params1 (dict) – parameters for distribution $$\pi_1$$ params2 (dict) – parameters for distribution $$\pi_2$$ cache (dict) – cached values qtype (int) – quadrature type to be used for the approximation of $$\mathbb{E}_{\pi_1}$$ qparams (object) – parameters necessary for the construction of the quadrature x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi_1}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi_1}$$ batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. mpi_pool_tuple (tuple [2] of mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of d1 and d2 (None) – the result is stored in params2['hess_a_kl_divergence']
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
Note
the dictionary params2 must be provided
TransportMaps.action_hess_a_kl_divergence(da, d1, d2, params1=None, params2=None, cache=None, qtype=None, qparams=None, x=None, w=None, batch_size=None, mpi_pool_tuple=(None, None))[source]
Compute $$\langle\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}}),\delta{\bf }\rangle$$
Parameters: da (ndarray [$$N$$]) – vector on which to apply the Hessian d1 (Distribution) – distribution $$\pi_1$$ d2 (Distribution) – distribution $$\pi_2$$ params1 (dict) – parameters for distribution $$\pi_1$$ params2 (dict) – parameters for distribution $$\pi_2$$ cache (dict) – cached values qtype (int) – quadrature type to be used for the approximation of $$\mathbb{E}_{\pi_1}$$ qparams (object) – parameters necessary for the construction of the quadrature x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi_1}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi_1}$$ batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. mpi_pool_tuple (tuple [2] of mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of d1 and d2 (ndarray [$$N,N$$] – $$\nabla^2_{\bf a}\mathcal{D}_{KL}(\pi_1 | \pi_{2,{\bf a}})$$
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.kl_divergence_component(f, params=None, cache=None, x=None, w=None, batch_size=None, mpi_pool=None)[source]
Compute $$-\sum_{i=0}^m f(x_i) = -\sum_{i=0}^m \log\pi\circ T_k(x_i) + \log\partial_{x_k}T_k(x_i)$$
Parameters: f (ProductDistributionParametricPullbackComponentFunction) – function $$f$$ params (dict) – parameters for function $$f$$ cache (dict) – cached values x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi_1}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi_1}$$ batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool (mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of f (float) – value
TransportMaps.grad_a_kl_divergence_component(f, params=None, cache=None, x=None, w=None, batch_size=None, mpi_pool=None)[source]
Compute $$-\sum_{i=0}^m \nabla_{\bf a}f[{\bf a}](x_i) = -\sum_{i=0}^m \nabla_{\bf a} \left(\log\pi\circ T_k[{\bf a}](x_i) + \log\partial_{x_k}T_k[{\bf a}](x_i)\right)$$
Parameters: f (ProductDistributionParametricPullbackComponentFunction) – function $$f$$ params (dict) – parameters for function $$f$$ cache (dict) – cached values x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi_1}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi_1}$$ batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool (mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of f (float) – value
TransportMaps.hess_a_kl_divergence_component(f, params=None, cache=None, x=None, w=None, batch_size=None, mpi_pool=None)[source]
Compute $$-\sum_{i=0}^m \nabla^2_{\bf a}f[{\bf a}](x_i) = -\sum_{i=0}^m \nabla^2_{\bf a} \left(\log\pi\circ T_k[{\bf a}](x_i) + \log\partial_{x_k}T_k[{\bf a}](x_i)\right)$$
Parameters: f (ProductDistributionParametricPullbackComponentFunction) – function $$f$$ params (dict) – parameters for function $$f$$ cache (dict) – cached values x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi_1}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi_1}$$ batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool (mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of f (float) – value
TransportMaps.misfit_squared(f1, f2, x, params1=None, params2=None, idxs_slice=None)[source]
Compute $$\vert f_1 - f_2 \vert^2$$
Parameters: f1 (Function or ndarray [$$m$$]) – function $$f_1$$ or its functions values f2 (Function or ndarray [$$m$$]) – function $$f_2$$ or its functions values x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi}$$ params1 (dict) – parameters for function $$f_1$$ params2 (dict) – parameters for function $$f_2$$ idxs_slice (slice) – slice of points to be (ndarray) – misfit $$\vert f_1 - f_2 \vert^2$$
TransportMaps.grad_a_misfit_squared(f1, f2, x, params1=None, params2=None, idxs_slice=None)[source]
Compute $$\nabla_{\bf a}\vert f_{1,{\bf a}} - f_2 \vert^2$$
Parameters: f1 (Function or ndarray [$$m$$]) – function $$f_1$$ or its functions values f2 (Function or ndarray [$$m$$]) – function $$f_2$$ or its functions values x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi}$$ params1 (dict) – parameters for function $$f_1$$ params2 (dict) – parameters for function $$f_2$$ idxs_slice (slice) – slice of points to be (ndarray) – misfit $$\nabla_{\bf a}\vert f_{1,{\bf a}} - f_2 \vert^2$$
TransportMaps.hess_a_misfit_squared(f1, f2, x, params1=None, params2=None, idxs_slice=None)[source]
Compute $$\nabla^2_{\bf a}\vert f_{1,{\bf a}} - f_2 \vert^2$$
Parameters: f1 (Function or ndarray [$$m$$]) – function $$f_1$$ or its functions values f2 (Function or ndarray [$$m$$]) – function $$f_2$$ or its functions values x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi}$$ params1 (dict) – parameters for function $$f_1$$ params2 (dict) – parameters for function $$f_2$$ idxs_slice (slice) – slice of points to be (ndarray) – misfit $$\nabla^2_{\bf a}\vert f_{1,{\bf a}} - f_2 \vert^2$$
TransportMaps.L2_misfit(*args, **kwargs)[source]
Compute $$\Vert f_1 - f_2 \Vert_{L^2_\pi}$$
Parameters: f1 (Function or ndarray [$$m$$]) – function $$f_1$$ or its functions values f2 (Function or ndarray [$$m$$]) – function $$f_2$$ or its functions values d (Distribution) – distribution $$\pi$$ params1 (dict) – parameters for function $$f_1$$ params2 (dict) – parameters for function $$f_2$$ qtype (int) – quadrature type to be used for the approximation of $$\mathbb{E}_{\pi}$$ qparams (object) – parameters necessary for the construction of the quadrature x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi}$$ batch_size (int) – this defines whether to evaluate in batches or not. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool (mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of f1 and f2 (float) – misfit $$\Vert f_1 - f_2 \Vert_{L^2_\pi}$$
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.L2squared_misfit(f1, f2, d=None, params1=None, params2=None, qtype=None, qparams=None, x=None, w=None, batch_size=None, mpi_pool=None)[source]
Compute $$\Vert f_1 - f_2 \Vert^2_{L^2_\pi}$$
Parameters: f1 (Function or ndarray [$$m$$]) – function $$f_1$$ or its functions values f2 (Function or ndarray [$$m$$]) – function $$f_2$$ or its functions values d (Distribution) – distribution $$\pi$$ params1 (dict) – parameters for function $$f_1$$ params2 (dict) – parameters for function $$f_2$$ qtype (int) – quadrature type to be used for the approximation of $$\mathbb{E}_{\pi}$$ qparams (object) – parameters necessary for the construction of the quadrature x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi}$$ batch_size (int) – this defines whether to evaluate in batches or not. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool (mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of f1 and f2 (float) – misfit $$\Vert f_1 - f_2 \Vert^2_{L^2_\pi}$$
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.grad_a_L2squared_misfit(f1, f2, d=None, params1=None, params2=None, qtype=None, qparams=None, x=None, w=None, batch_size=None, mpi_pool=None)[source]
Compute $$\nabla_{\bf a}\Vert f_{1,{\bf a}} - f_2 \Vert^2_{L^2_\pi}$$
Parameters: f1 (ParametricFunctionApproximation) – function $$f_1$$ f2 (Function or ndarray [$$m$$]) – function $$f_2$$ or its functions values d (Distribution) – distribution $$\pi$$ params1 (dict) – parameters for function $$f_1$$ params2 (dict) – parameters for function $$f_2$$ qtype (int) – quadrature type to be used for the approximation of $$\mathbb{E}_{\pi}$$ qparams (object) – parameters necessary for the construction of the quadrature x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi}$$ batch_size (int) – this defines whether to evaluate in batches or not. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool (mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of f1 and f2 (ndarray [$$N$$]) – misfit gradient $$\nabla_{\bf a}\Vert f_1 - f_2 \Vert_{L^2_\pi}$$
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.hess_a_L2squared_misfit(f1, f2, d=None, params1=None, params2=None, qtype=None, qparams=None, x=None, w=None, batch_size=None, mpi_pool=None)[source]
Compute $$\nabla^2_{\bf a}\Vert f_{1,{\bf a}} - f_2 \Vert^2_{L^2_\pi}$$
Parameters: f1 (ParametricFunctionApproximation) – function $$f_1$$ f2 (Function or ndarray [$$m$$]) – function $$f_2$$ or its functions values d (Distribution) – distribution $$\pi$$ params1 (dict) – parameters for function $$f_1$$ params2 (dict) – parameters for function $$f_2$$ qtype (int) – quadrature type to be used for the approximation of $$\mathbb{E}_{\pi}$$ qparams (object) – parameters necessary for the construction of the quadrature x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi}$$ batch_size (int) – this defines whether to evaluate in batches or not. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool (mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of f1 and f2 (ndarray [$$N,N$$]) – misfit Hessian $$\nabla^2_{\bf a}\Vert f_1 - f_2 \Vert_{L^2_\pi}$$
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.storage_hess_a_L2squared_misfit(f1, f2, d=None, params1=None, params2=None, qtype=None, qparams=None, x=None, w=None, batch_size=None, mpi_pool=None)[source]
Assemble $$\nabla^2_{\bf a}\Vert f_{1,{\bf a}} - f_2 \Vert^2_{L^2_\pi}$$.
Parameters: f1 (ParametricFunctionApproximation) – function $$f_1$$ f2 (Function or ndarray [$$m$$]) – function $$f_2$$ or its functions values d (Distribution) – distribution $$\pi$$ params1 (dict) – parameters for function $$f_1$$ params2 (dict) – parameters for function $$f_2$$ qtype (int) – quadrature type to be used for the approximation of $$\mathbb{E}_{\pi}$$ qparams (object) – parameters necessary for the construction of the quadrature x (ndarray [$$m,d$$]) – quadrature points used for the approximation of $$\mathbb{E}_{\pi}$$ w (ndarray [$$m$$]) – quadrature weights used for the approximation of $$\mathbb{E}_{\pi}$$ batch_size (int) – this defines whether to evaluate in batches or not. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool (mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of f1 and f2 (None) – the result is stored in params1['hess_a_L2_misfit']
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
Note
the dictionary params1 must be provided
TransportMaps.action_stored_hess_a_L2squared_misfit(H, v)[source]
Evaluate the action of $$\nabla^2_{\bf a}\Vert f_{1,{\bf a}} - f_2 \Vert^2_{L^2_\pi}$$ on $$v$$.
Parameters: v (ndarray [$$N,N$$]) – vector $$v$$ v – Hessian $$\nabla^2_{\bf a}\Vert f_{1,{\bf a}} - f_2 \Vert^2_{L^2_\pi}$$ (ndarray [$$N$$]) – $$\langle\nabla^2_{\bf a}\Vert f_{1,{\bf a}} - f_2 \Vert^2_{L^2_\pi},v\rangle$$
TransportMaps.grad_t_kl_divergence(x, d1, d2, params1=None, params2=None, grad_x_tm=None, batch_size=None, mpi_pool_tuple=(None, None))[source]
Compute $$\nabla_T \mathcal{D}_{KL}(\pi_1, \pi_2(T))$$.
This corresponds to:
Parameters: d1 (Distribution) – distribution $$\pi_1$$ d2 (Distribution) – distribution $$\pi_2$$ params1 (dict) – parameters for distribution $$\pi_1$$ params2 (dict) – parameters for distribution $$\pi_2$$ grad_x_tm – optional argument passed if $$\nabla_x T(x)$$ has been already computed batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool_tuple (tuple [2] of mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of d1 and d2
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.grad_x_grad_t_kl_divergence(x, d1, d2, params1=None, params2=None, grad_x_tm=None, grad_t=None, batch_size=None, mpi_pool_tuple=(None, None))[source]
Compute $$\nabla_x \nabla_T \mathcal{D}_{KL}(\pi_1, \pi_2(T))$$.
This corresponds to:
Parameters: d1 (Distribution) – distribution $$\pi_1$$ d2 (Distribution) – distribution $$\pi_2$$ params1 (dict) – parameters for distribution $$\pi_1$$ params2 (dict) – parameters for distribution $$\pi_2$$ grad_x_tm – optional argument passed if $$\nabla_x T(x)$$ has been already computed grad_t – optional argument passed if the first variation has been already computed batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool_tuple (tuple [2] of mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of d1 and d2
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.tuple_grad_x_grad_t_kl_divergence(x, d1, d2, params1=None, params2=None, grad_x_tm=None, batch_size=None, mpi_pool_tuple=(None, None))[source]
Compute $$\nabla_x \nabla_T \mathcal{D}_{KL}(\pi_1, \pi_2(T))$$.
This corresponds to:
Parameters: d1 (Distribution) – distribution $$\pi_1$$ d2 (Distribution) – distribution $$\pi_2$$ params1 (dict) – parameters for distribution $$\pi_1$$ params2 (dict) – parameters for distribution $$\pi_2$$ grad_x_tm – optional argument passed if $$\nabla_x T(x)$$ has been already computed batch_size (int) – this is the size of the batch to evaluated for each iteration. A size 1 correspond to a completely non-vectorized evaluation. A size None correspond to a completely vectorized one. (Note: if nprocs > 1, then the batch size defines the size of the batch for each process) mpi_pool_tuple (tuple [2] of mpi_map.MPI_Pool) – pool of processes to be used for the evaluation of d1 and d2
Note
The parameters (qtype,qparams) and (x,w) are mutually exclusive, but one pair of them is necessary.
TransportMaps.laplace_approximation(pi, params=None, x0=None, tol=1e-05, ders=2, fungrad=False, hessact=False, hessact_rnd_eps=1e-05, hessact_ovsamp=10, hessact_pow_n=0)[source]
Compute the Laplace approximation of the distribution $$\pi$$.
Parameters: pi (Distribution) – distribution $$\pi$$ params (dict) – parameters for distribution $$\pi$$ tol (float) – tolerance to be used to solve the maximization problem. ders (int) – order of derivatives available for the solution of the optimization problem. 0 -> derivative free, 1 -> gradient, 2 -> hessian. fungrad (bool) – whether the distribution $$\pi$$ provide the method Distribution.tuple_grad_x_log_pdf() computing the evaluation and the gradient in one step. This is used only for ders>=1. hessact (bool) – whether the distribution $$\pi$$ provides the method Distribution.action_hess_x_log_pdf() computing the action of the Hessian on a vector. This is used only for ders==2 hessact_rnd_eps (float) – tolerance to be used in the pursue of a randomized low-rank approximation of the prior preconditioned Hessian of the log-likelihood hessact_pow_n (int) – number of power iterations to be used in the pursue of a randomized low-rank approximation of the prior preconditioned Hessian of the log-likelihood hessact_ovsamp (int) – oversampling to be used in the pursue of a randomized low-rank approximation of the prior preconditioned Hessian of the log-likelihood (GaussianDistribution) – Laplace approximation
TransportMaps.laplace_approximation_withBounds(pi, params=None, tol=1e-05, ders=2, disp=True, bounds=None)[source]
Compute the Laplace approximation of the distribution $$\pi$$.
Parameters: pi (Distribution) – distribution $$\pi$$ params (dict) – parameters for distribution $$\pi$$ tol (float) – tolerance to be used to solve the maximization problem. ders (int) – order of derivatives available for the solution of the optimization problem. 0 -> derivative free, 1 -> gradient, 2 -> hessian. disp (bool) – whether to display output from optimizer. (GaussianDistribution) – Laplace approximation
TransportMaps.maximum_likelihood(logL, params=None, x0=None, tol=1e-05, ders=2, fungrad=False)[source]
Compute the maximum likelihood of the log-likelihood $$\log\pi({\bf y}\vert{\bf x})$$.
Parameters: logL (LogLikelihood) – log-likelihood $$\log\pi({\bf y}\vert{\bf x})$$ params (dict) – parameters for the log-likelihood $$\log\pi({\bf y}\vert{\bf x})$$ tol (float) – tolerance to be used to solve the maximization problem ders (int) – order of derivatives available for the solution of the optimization problem. 0 -> derivative free, 1 -> gradient, 2 -> hessian fungrad (bool) – whether the distributions $$\pi_1,\pi_2$$ provide the method Distribution.tuple_grad_x_log_pdf() computing the evaluation and the gradient in one step. This is used only for ders==1 (ndarray) – Maximum likelihood estimator
TransportMaps.Default_IsotropicIntegratedExponentialTriangularTransportMap(dim, order, span='total', active_vars=None, btype='poly', common_basis_flag=True)[source]
Generate a triangular transport map with default settings.
Parameters: dim (int) – dimension $$d$$ of the map order (int) – isotropic order of the map span (str) – ‘full’ for full order approximations, ‘total’ for total order approximations. If a list of dim strings is provided, these will define the approximation type fore each component $$T^{(k)}$$. active_vars (list) – list of $$d$$ lists containing the row sparsity pattern of the transport, i.e. the active variables for each component. Default None will generate a full triangular map. btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component $$T^{(k)}$$. common_basis_flag (bool) – use acceleration provided by common basis among the components (span and btype must be a string or a list with all equal elements). (IntegratedExponentialTriangularTransportMap) – the constructed transport map
TransportMaps.Default_IsotropicIntegratedExponentialDiagonalTransportMap(dim, order, btype='poly', *arg, **kwargs)[source]
Generate a diagonal transport map with default settings.
Parameters: dim (int) – dimension $$d$$ of the map order (int) – isotropic order of the map btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component $$T^{(k)}$$. (IntegratedExponentialTriangularTransportMap) – the constructed transport map
TransportMaps.Default_IsotropicIntegratedSquaredTriangularTransportMap(dim, order, span='total', active_vars=None, btype='poly', common_basis_flag=False)[source]
Generate a triangular transport map with default settings.
Parameters: dim (int) – dimension $$d$$ of the map order (int) – isotropic order of the map span (str) – ‘full’ for full order approximations, ‘total’ for total order approximations. If a list of dim strings is provided, these will define the approximation type fore each component $$T^{(k)}$$. active_vars (list) – list of $$d$$ lists containing the row sparsity pattern of the transport, i.e. the active variables for each component. Default None will generate a full triangular map. btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component $$T^{(k)}$$. common_basis_flag (bool) – use acceleration provided by common basis among the components (span and btype must be a string or a list with all equal elements). (IntegratedSquaredTriangularTransportMap) – the constructed transport map
TransportMaps.Default_IsotropicIntegratedSquaredDiagonalTransportMap(dim, order, btype='poly', *arg, **kwargs)[source]
Generate a diagonal transport map with default settings.
Parameters: dim (int) – dimension $$d$$ of the map order (int) – isotropic order of the map btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component $$T^{(k)}$$. (IntegratedSquaredTriangularTransportMap) – the constructed transport map
TransportMaps.Default_IsotropicMonotonicLinearSpanTriangularTransportMap(dim, order, span='total', active_vars=None, btype='poly', common_basis_flag=True)[source]
Generate a triangular transport map with default settings.
Parameters: dim (int) – dimension of the map order (int) – isotropic order of the map span (str) – ‘full’ for full order approximations, ‘total’ for total order approximations. If a list of dim strings is provided, these will define the approximation type fore each component $$T^{(k)}$$. active_vars (list) – list of $$d$$ lists containing the row sparsity pattern of the transport, i.e. the active variables for each component. Default None will generate a full triangular map. btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component $$T^{(k)}$$. common_basis_flag (bool) – use acceleration provided by common basis among the components (span and btype must be a string or a list with all equal elements). (LinearSpanTriangularTransportMap) – the constructed transport map
TransportMaps.Default_IsotropicLinearSpanTriangularTransportMap(dim, order, span='total', active_vars=None, btype='poly', common_basis_flag=True, monotone=False)[source]
Generate a triangular transport map with default settings.
Parameters: dim (int) – dimension of the map order (int) – isotropic order of the map span (str) – ‘full’ for full order approximations, ‘total’ for total order approximations. If a list of dim strings is provided, these will define the approximation type fore each component $$T^{(k)}$$. active_vars (list) – list of $$d$$ lists containing the row sparsity pattern of the transport, i.e. the active variables for each component. Default None will generate a full triangular map. btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component $$T^{(k)}$$. common_basis_flag (bool) – use acceleration provided by common basis among the components (span and btype must be a string or a list with all equal elements). (LinearSpanTriangularTransportMap) – the constructed transport map
TransportMaps.Default_LinearSpanTriangularTransportMap(dim, midxs_list, active_vars, btype='poly', common_basis_flag=True)[source]
Generate a linear span triangular transport map with default settings and user defined sparsity and orders.
Parameters: dim (int) – dimension of the map midxs_list (list) – list of $$d$$ lists of multi-indices for each component active_vars (list) – list of $$d$$ lists containing the row sparsity pattern of the transport, i.e. the active variables for each component. btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component $$T^{(k)}$$. common_basis_flag (bool) – use acceleration provided by common basis among the components (btype must be a string or a list with all equal elements). (LinearSpanTriangularTransportMap) – the constructed transport map | {"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": 0.5690057277679443, "perplexity": 5254.690678436797}, "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-2019-04/segments/1547584331733.89/warc/CC-MAIN-20190123105843-20190123131843-00019.warc.gz"} |
https://lexique.netmath.ca/en/amplitude-of-a-statistical-class/ | # Amplitude of a Statistical Class
## Amplitude of a Statistical Class
When we divide data about a population studied in statistics into classes of the same range, this range is called the class interval.
### Example
In this bar graph, we can observe that the total data has been divided into classes for which the interval is 10 percentage points. | {"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": 0.9311391711235046, "perplexity": 637.5414267427601}, "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-2020-16/segments/1585370506580.20/warc/CC-MAIN-20200402014600-20200402044600-00508.warc.gz"} |
http://mathoverflow.net/questions/152806/langlands-program-beyond-cm-fields | # Langlands program beyond CM fields?
I apologize since this is a quite vague question. And I am personally at an expert in these fields at all.
It seems to me that there are two main directions of the Langlands program, namely, construction of Galois representation, modularity (automorphy) theorems. However, in all that have been achieved, there is always the assumption that the "base field" is either totally real or CM. For example, the most recent Scholze's work on construction of Galois representation (as well as work of many other authors), or the recent automorphy lifting theorems by various authors.
Indeed, it seems to me all these work use the tool of "unitary Shimura varieties" a lot, which, is only available with CM base fields.
What is the difficulty in going beyond CM field? And what are the possible ways to attack them?
Thank you!
-
At a very elementary level, there are special algebraicity properties for GL$_1$ over CM fields, due to a theorem of Artin and Weil. See the recent PhD thesis of Stefan Patrikis for an extension of these algebraicity considerations to more general reductive groups. – user76758 Dec 25 '13 at 21:07
I have been wondering the same thing, but apparently some papers (for instance, the ones of Edward Frenkel, for example this one arxiv.org/abs/hep-th/0512172 ) did not say anything about totally real, CM-type and, furthermore do not require the representation to be geometric. I don't know if has been any advances on the theory or bypass these details or if it's just poor writing by the author. – user40276 Jul 26 '14 at 4:26 | {"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": 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": 0.8268324732780457, "perplexity": 567.3109003036026}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "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/1466783398628.62/warc/CC-MAIN-20160624154958-00196-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/148187/with-what-a-and-b-this-is-a-wiener-process | # With what a and b this IS a Wiener Process
$aX_{t/9}-bX_{t/4}$, knowing that $X_t$ is a Wiener Process.
This was already twice in the exams I failed, very likely it will be in todays exam in 2 hours. Can somebody help me with this one?
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Cov(Z(s),Z(t))=c.min(s,t) yields ab=0. And a=0 yields a solution while b=0 yields the other. – Did May 22 '12 at 13:39
Let $Z_t = a X_{t/9} - b X_{t/4}$. Note that $Z_t$ is a Gaussian process, being a sum of two Gaussian processes. It is therefore determined by its mean function and its covariance function. In order for $Z_t$ to be a Wiener process, we should establish $\mathbb{E}(Z_t) = 0$ and $\mathbb{Cov}(Z_s, Z_t) = c^2 \min(s, t)$, as pointed out by @Didier.
The mean function is easy $\mathbb{E}(Z_t) = a \mathbb{E}(X_{t/9}) - b \mathbb{E}(X_{t/4)} = a \cdot 0 - b \cdot 0 = 0$. Now turn to compute the covariance function: $$\begin{eqnarray} \mathbb{Cov}(Z_s, Z_t) &=& a^2 \mathbb{Cov}(X_{s/9}, X_{t/9}) + b^2 \mathbb{Cov}(X_{s/4}, X_{t/4}) \\ &&- a b \mathbb{Cov} \left( X_{s/9}, X_{t/4} \right) - a b \mathbb{Cov} \left( X_{s/4}, X_{t/9} \right)\\ &=& \frac{a^2}{9} \min(s,t) + \frac{b^2}{4} \min(s,t) - a b \left( \min\left( \frac{s}{9}, \frac{t}{4}\right) + \min\left( \frac{t}{9}, \frac{s}{4}\right) \right) \end{eqnarray}$$ Since $\min(s/9,t/4) \not= \frac{1}{36} \min(s,t)$ for all $s$ and $t$, $a b$ must vanish. | {"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": 0.9193465113639832, "perplexity": 271.7477844302126}, "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-2014-42/segments/1413507450767.7/warc/CC-MAIN-20141017005730-00174-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://www.neetprep.com/question/60422-ideal-gas-taken-cycle--B--C--shown-figureIf-net-heat-supplied-gas-cycle--J-work-done-thegas-process-C----J---J---J----J/55-Physics--Thermodynamics/687-Thermodynamics | # NEET Physics Thermodynamics Questions Solved
An ideal gas is taken through the cycle ABCA, as shown in the figure. If the net heat supplied to the gas in the cycle is 5 J, the work done by the gas in the process CA is
(1) – 5 J
(2) – 10 J
(3) – 15 J
(4) – 20 J
(1) For cyclic process. Total work done $={W}_{AB}+{W}_{BC}+{W}_{CA}$
ΔWAB = PΔV = 10(2 – 1) = 10J and ΔWBC =0
(as V = constant)
ΔQ = ΔU + ΔW
ΔU = 0 (Process ABCA is cyclic)
⇒ ΔQ = ΔWAB + ΔWBC + ΔWCA
⇒ 5 = 10 + 0 + ΔWCA ⇒ ΔWCA = – 5 J
Difficulty Level:
• 50%
• 30%
• 12%
• 9%
Crack NEET with Online Course - Free Trial (Offer Valid Till August 25, 2019) | {"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": 0.6154559254646301, "perplexity": 5742.5784069090905}, "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/1566027317688.48/warc/CC-MAIN-20190822235908-20190823021908-00353.warc.gz"} |
https://hal-insu.archives-ouvertes.fr/insu-03636639 | # A Search for Companions via Direct Imaging in the DSHARP Planet-forming Disks
Abstract : The "Disk Substructures at High Angular Resolution Project" (DSHARP) has revealed an abundance and ubiquity of rings and gaps over a large sample of young planet-forming disks, which are hypothesized to be induced by the presence of forming planets. In this context, we present the first attempt to directly image these young companions for 10 of the DSHARP disks, by using the NaCo/VLT high-contrast observations in L' band instrument and angular differential imaging techniques. We report the detection of a point-like source candidate at 1"1 (174.9 au) for RU Lup and at 0"42 (55 au) for Elias 24. In the case of RU Lup, the proper motion of the candidate is consistent with a stationary background contaminant, based on the astrometry derived from our observations and available archival data. For Elias 24 the point-like source candidate is located in one of the disk gaps at 55 au. Assuming that it is a planetary companion, our analysis suggests a mass ranging from 0.5MJ up to 5MJ, depending on the presence of a circumplanetary disk and its contribution to the luminosity of the system. However, no clear confirmation is obtained at this stage, and follow-up observations are mandatory to verify that the proposed source is physical, comoving with the stellar host, and associated with a young massive planet sculpting the gap observed at 55 au. For all the remaining systems, the lack of detections suggests the presence of planetary companions with masses lower than 5MJ, based on our derived mass detection limits. This is consistent with predictions of both hydrodynamical simulations and kinematical signatures on the disk and allows us to set upper limits on the presence of massive planets in these young disks.
Keywords :
Document type :
Journal articles
https://hal-insu.archives-ouvertes.fr/insu-03636639
Contributor : Nathalie POTHIER Connect in order to contact the contributor
Submitted on : Monday, April 11, 2022 - 9:28:48 AM
Last modification on : Tuesday, April 12, 2022 - 3:44:35 AM
### Citation
Sebastian Jorquera, Laura M. Pérez, Gaël Chauvin, Myriam Benisty, Zhaohuan Zhu, et al.. A Search for Companions via Direct Imaging in the DSHARP Planet-forming Disks. The Astronomical Journal, 2021, 161, ⟨10.3847/1538-3881/abd40d⟩. ⟨insu-03636639⟩
Record views | {"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": 0.8586168885231018, "perplexity": 3250.143451827829}, "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-2022-40/segments/1664030335034.61/warc/CC-MAIN-20220927131111-20220927161111-00595.warc.gz"} |
https://bitbucket.org/iElectric/gentoo-stats/overview | # Overview
This file is for you to describe the gentoo-stats application. Typically you would include information such as the information below:
## Installation and Setup
Install gentoo-stats using easy_install:
easy_install gentoo-stats
Make a config file as follows:
paster make-config gentoo-stats config.ini
Tweak the config file as appropriate and then setup the application:
paster setup-app config.ini
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http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0100-69162020000100024 | ## Print version ISSN 0100-6916On-line version ISSN 1809-4430
### Eng. Agríc. vol.40 no.1 Jaboticabal Jan./Feb. 2020 Epub Feb 17, 2020
#### https://doi.org/10.1590/1809-4430-eng.agric.v40n1p24-33/2020
Scientific Papers
Soil and Water Engineering
PREDICTIVE MODELS OF WATER APPLICATION AND DISTRIBUTION EFFICIENCY IN CONVENTIONAL SPRINKLING
1Universidade Federal de Viçosa/ Viçosa - MG, Brasil.
ABSTRACT
Correct determinations of distribution (Ed) and application (EA) efficiencies allow adequate estimations of the gross irrigation depth. This study aimed: i) to determine the distribution efficiency using the Christiansen uniformity coefficient (CUC) in a sprinkler irrigation system under different weather conditions and working pressures; ii) to compare the mean, median, and cumulative CUC values; and iii) to evaluate the predictive capacity of four EA estimation models. CUC values were determined from 80 assessments, as well as the mean, median, and cumulative. The precipitated water depth accumulated in each collector was considered for the accumulated CUC. More uniform evaluations were used for EA (working pressure of 196 kPa), resulting in 20 samples. Besides being measured, EA was estimated by Keller & Bliesner, Playán, Tarjuelo, and Beskow methods. Statistical indicators were the root mean square error, mean bias error, Willmott agreement index, mean absolute error, and Pearson correlation coefficient. CUC values ranged from 66.51 to 92.04%, and the accumulated CUC provided an improvement over the isolated evaluations. The Beskow model had the best EA estimations in conventional spraying.
KEYWORDS uniformity coefficient; irrigation efficiency; evaporation and wind drift
INTRODUCTION
Irrigated agriculture is essential in some regions of Brazil for maintaining high crop yields due to the irregular precipitation distribution. The conventional sprinkler irrigation system is widely used in Brazil (Alves et al., 2017). However, this system does not operate at its maximum efficiency under adverse weather conditions, such as high temperature, low air humidity, and high wind speed, wasting water, bad fertilizers solubilization, and instability in electrical network (Molle et al., 2012; Sheikhesmaeili et al., 2016).
For irrigation management, irrigation efficiency (Ei) is determined by application (EA) and distribution (Ed) efficiencies and is calculated as the product of these two variables. Knowledge of Ei is of paramount importance for proper irrigation management because the gross water depth to be applied is adjusted from this variable (Kifle et al., 2017).
In sprinkler irrigation systems, part of the water depth applied by emitters does not reach the soil surface and/or the shoot occupied by crops. This portion of water represents evaporation and wind drift (WDEL), which, in turn, are expressed as the percentage of the gross applied volume lost in a given irrigation event (Andrés & Cuchí, 2014). The ratio between the water depth that reached the irrigation target (collected water depth) and applied water depth is defined as application efficiency (EA). WDEL is obtained by subtracting EA by the unit value.
Evaporation losses depend on the relative humidity, wind speed, ambient temperature, emitter working pressure, emitter installation height fromthe soil surface, and droplet diameter. Wind drift, on the other hand, depend mainly on wind speed, droplet diameter, and the distance traveled by droplets until they reach the shoot of crops or soil surface (Maroufpoor et al., 2017).
The quantification of WDEL is considered of high relevancein both environmental and economic aspects. However, estimating these losses separately is a rather complicated task due to the difficulties of the methodologies required for their measurements (Beskow et al., 2011). Several studies have been conducted in different regions of the world with the purpose of modeling or evaluating some existing models for WDEL estimation in sprinkler irrigation systems (Colombo et al., 2015; Faria et al., 2012; Stambouli et al., 2013).
Another factor necessary to be considered in sprinkler irrigation systems assessments is the Ed. To calculate this, uniformity coefficients need to be used. Several methods can be found in the literature, but the Christiansen uniformity coefficient is the most widely used for conventional sprinkling (Cavero et al., 2016). Ed is also influenced by weather conditions and characteristics of the irrigation equipment.
According to Colombo et al. (2015), knowledge of the performance of an irrigation system, especially regarding the uniformity of distribution of the applied water depth, is essential for making decisions that allow the rational use of water, energy, and fertilizers. Thus, knowing the influence of weather variables is essential to predict or estimate irrigation uniformity, and even to identify the best time for the operation of a sprinkler irrigation system.
Therefore, this study aimed: i) to determine the distribution efficiency using the Christiansen uniformity coefficient (CUC) in a sprinkler irrigation system under different weather conditions and working pressures; ii) to compare the mean, median, and cumulative CUC values; and iii) to evaluate the predictive capacity of four application efficiencyestimationmodels.
MATERIAL AND METHODS
Location and characterization of the area
The study was conducted in an experimental irrigation area of the Department of Agricultural Engineering of the Federal University of Viçosa, Viçosa, MG, Brazil, with geographical coordinates of 20°45′ S and 42°51′ W, and an altitude of 651 m. The local climate is Cwa, according to the Köppen-Geiger classification, i.e., a humid subtropical climate with dry winter and hot summer (Alvares et al., 2013).
This study consisted of the evaluation of an irrigation system with six midi-sectorial or 360° sprinklers with a 4 mm nozzle. Sprinklers were spaced at 11 × 8 m to suit the experimental area configuration, supported by a 1.7 m rod above the soil surface and recommended working pressure for system operation of 196.13 kPa.
Distribution uniformity evaluation
Collectors were arranged between six sprinklers operating simultaneously. Collectors were of the Fabrimar® brand and were installed equidistant at 2 m, resulting in 44 collectors (Figure 1). A rod was used to suspend the collector at the height of 70 cm from the soil surface, following the methodology proposed by Merriam & Keller (1978).
The data on mean air temperature, relative humidity, solar radiation, and wind speed were collected throughout the testing period using an Irriplus E5000® automatic weather station, located 30 m from the experimental area.
Eighty field tests with 60 minute durations were performed under different weather conditions (Figure 4) from April to July 2017. The reading of weather elements was performed every 20 minutes, and their mean was used to represent the weather conditions during irrigation.
Water depth was measured at the end of each test on each collector using a 15 mm Fabrimar® graduated beaker. The Christiansen uniformity coefficient (CUC) (Christiansen, 1942) was used to calculate the uniformity of distribution, according to [eq. (1)].
CUC=100(1i=1N|DiDm|NDm)
Where:
CUC is the Christiansen uniformity coefficient (%);
N is the number of observations;
Di is the water depth applied at the i-th point on the soil surface (mm), and
Dm is the mean applied water depth (mm).
The mean and median CUC values were calculated after CUC has been determined for each evaluation. Cumulative CUC was also determined by summing the 80 values of water depth measured in each collector. The calculation was performed with these cumulative values, according to Equation (1).
The mean, median, and cumulative CUC were determined for every ten successive evaluations to verify the sensitivity of differences in a few numbers of evaluations, resulting ineight replications in a randomized block design. These data were analyzed by the Tukey test at a 0.05 significance level.
Evaporation and wind driftevaluation
Before starting the evaluations, the flow versus working pressure curve was determined for the sprinkler used in this study (Figure 2A). For this, pressures ranging from 78 to 333 kPa were used. Thus, a linear regression model was adjusted to predict the flow as a function of working pressure.
Working pressure readings of the six sprinklers were taken in all evaluations at the beginning, middle, and end of the irrigations. Schrader valves (coarse nozzle) were installed in the riser pipe at 5 cm below the sprinkler to facilitate working pressure readings. The flow rate and, thus, the water depth applied in each evaluation were obtained with the mean pressure using the regression equation shown in Figure 2A.
The evaluation of evaporation and wind drift (WDEL) or application efficiency (EA) was carried out usingtwenty evaluations with working pressures closer to 196.13 kPa (pressure recommended by the manufacturer). This procedure was used to standardize the droplet size, as operating pressures of the irrigation system showed high variations during the evaluation period (Figure 2B). Thus, it was also possible to correlate them better with input variables based on weather conditions of prediction models.
Pressure variation is related to the instability of the electrical network and water quality used in irrigation, as it had suspended solids. These impurities caused disc filter clogging and, consequently, reduced the working pressure during the test. Backwash was performed manually at the interval of each evaluation.
The arithmetic means water depth applied by sprinklers and the water depths measured in the collectors were used to calculate the evaporation andwind drift. Thus, WDEL was calculated using [eq.(2)].
WDEL=(DappliedDcollectedDapplied)100
Where:
WDELis the evaporation and wind drift (%),
Dapplied is the applied water depth (mm), and
Dcollected is the collected water depth (mm).
However, data processing was based on EA. For this, WDEL values were subtracted from 100.
In addition to measurements, EA was estimated by different models as a function of weather conditions in the tests. The mathematical models used in the present study were proposed by Keller & Bliesner (1990), Playán et al. (2005), Tarjuelo et al. (2000), and Beskow et al. (2008), represented, respectively, by equations shown in Table 1.
TABLE 1 Equations for application efficiency modeling used in the study. Viçosa, MG, Brazil, DEA–UFV, 2017.
Author Empirical equation
Keller & Bliesner (1990) EA=100×[(0.976+0.005ET00.0001ET02+0.0012U)CI(0.00043ET0+0.00018U+0.000016ET0U)] , where CI is a function of the type of deflector plate
Tarjuelo et al. (2000) EA=100[0.007WP+7.38(esea)0.5+0.844U]
Playán et al. (2005) EA=100(20.3+0.214U22.29×103RH2)
Beskow et al. (2008) EA=100[0.0304WP+13.2976(esea)0.5+5.485U]
EA is the application efficiency (%); (es−ea) is the vapor pressure deficit (kPa); WP is the sprinkler working pressure (kPa); U is the mean wind speed (m s−1); T is the air temperature (°C); and RH is the relative air humidity (%).
The vapor pressure deficit (Δe) and vapor saturation pressure (es) were obtained by eqs (3) and (4):
Δe=es(T)[RH×es(T)] (3)
es=0.61078exp(17.266×TT+237.3) (4)
Where:
Δe is the vapor pressure deficit (kPa);
es is the vapor saturation pressure (kPa);
T is the temperature (°C), and
RH is the relative humidity (%).
The following statistical indicators were used to verify the performance of the models usingthe observed values: root mean square error (RMSE), mean bias error (MBE), in addition to the parameters recommended by Legates & McCabe (1999), Willmott agreement index (d) and mean absolute error (MAE). The magnitude of the coefficient of determination (R2) and Pearson correlation coefficient (r) was used to correlate the measured with the estimated data.
RESULTS AND DISCUSSION
The Christiansen uniformity coefficient (CUC) values were increasingly ordered and associated with the sprinkler working pressure, ranging from 66.51 to 92.04% and 44.1 to 196 kPa, respectively (Figure 3).
The 72 evaluations of the irrigation system through CUC showed results higher than 80%, and one of the main factors influencing the distribution uniformity was sprinkler working pressure (Figure 3). In contrast, due to the characteristics of the study area and range of weather variation duringthe study, weather elements affected the distribution uniformity with less intensity (Figure 4).
The variable CUC had a low Pearson coefficient (r), i.e., a weak correlation with all the weather elements. The water distribution of an irrigation system mainly depends on the spacing, type, size, internal design, and working pressure of emitters (Zhu et al., 2015).
The variation in the uniformity of water distribution evaluated at different times, working pressures, and weather conditions have been reported in other studies. Li et al. (2015) evaluated a sprinkler irrigation system in which the working pressure ranged from 200 to 350 kPa and found CUC values from 73.27 to 81.11%. Robles et al. (2017), on the other hand, studied the effect of wind speed on distribution uniformity and found CUC values of 89 and 67% for low and high wind speed conditions, respectively. Justi et al. (2010) evaluated 25 irrigation events and found mean and maximum CUC values of 79.72 and 89.45%, respectively.
Sheikhesmaeili et al. (2016) suggested being acceptable CUC values of at least 80% in sprinkler irrigation systems. Most evaluations presented CUC values above 80% (Figures 3 and 4), but values below 80% can be found due to working pressure and wind speed variations, as observed in this and other studies. This behavior discourages the use of only one evaluation to represent the uniformity of water distribution in conventional sprinkler irrigation systems.
A reference value needs to be adopted when an irrigation system has several CUC values. This value can be used to determine theirrigation efficiency and, therefore, provide adequate irrigation management, turning the net water depth into gross. The CUCmean of 84.66% shown in Figure 5 represents the mean of all evaluations. CUCmedian had a value of 86.04%, which is higher than the CUCmean. In contrast, the CUCcumulative, which represents CUC considering the sum of water depths distributed in the area over time, presented a value of 90.64%, which is higher than the others are.
Water distribution in the irrigation area varies over time, significantly changing its uniformity when considering multiple irrigations. Usually, a point of the area to be irrigated may receive water depths equal to, lower than or higher than that of the mean at different irrigation events because of the random pattern of the collected precipitation, which is influenced by some weather parameters and/or working pressure. Therefore, the same point that received a low irrigation depth and was in deficit compared to other areas can receive a water depth higher than the mean in the next irrigation event, partially or totally supplying the deficit that occurred in the first irrigation. Thus, when CUCmean or CUCmedian are adopted, it is disregarded that a region that receives different water depths may have in time a higher and more representative CUC of the area, especially in areas of the semi-arid, which receive high and more frequent water depths.
Figure 6 shows three distinct distribution uniformities for an irrigation system. Evaluations 1 and 2 presented CUC values of 84.96 and 86.06%, respectively. The CUCcumulative of all 80 evaluations was 90.64%.
Among the various causes that affect the distribution uniformity of a sprinkler irrigation system, special attention should be given to working pressure and wind speed and direction (Li et al., 2015). Variation of these factors is undesirable, as they tend to reduce the distribution uniformity coefficient. Weather factors are dynamic, even choosing less windy times is not a guarantee of even distribution. Assuming that wind speed and direction vary, it is possible to understand that a conventional sprinkler irrigation system operating at different times and low irrigation frequency can redistribute water in the area to be irrigated, thus promotinga better irrigation uniformity over time, as shown by the CUCcumulative (Figure 6).
Water redistribution by irrigation systems occurs in different applications or within the same application depending on the duration of the irrigation. It would be a new way of understanding the dynamics of irrigation and CUC use, often underestimated. In this sense, it has already been proposed to monitor the uniformity of water distribution in the soil profile, as it can redistribute water and, thus, present a CUC closer to reality (Rocha et al., 1999).
The CUCcumulative values for every ten evaluations ranged from 88.50 to 89.39%. On the other hand, the CUCmean comprised values from 83.25 to 86.07%, and CUCmedian values ranged from 83.91 to 87.51%. Based on the mean of the eight groups of evaluations (replications), the CUCcumulative was higher than CUCmedian and CUCmean (Table 2). CUCmean was the variable that most underestimated distribution uniformity.
TABLE 2 Determination of CUCcumulative, CUCmean, and CUCmedian every ten evaluations. Viçosa, MG, Brazil, DEA–UFV, 2017.
Evaluation CUCcumulative CUCmean CUCmedian
1–10 88.78 85.13 85.82
11–20 88.94 84.09 87.51
21–30 88.92 86.07 86.72
31–40 89.39 83.53 83.91
41–50 88.72 84.29 86.29
51–60 88.82 85.42 87.20
61–70 88.95 85.46 85.62
71–80 88.50 83.25 84.21
Mean 88.88a 84.66c 85.91b
Means followed by the same lowercase letter for different CUC determinations do not differ from each other by the Tukey test at 0.05 significance level.
Under practical conditions, conducting eighty evaluations to propose a more representative CUC of the area becomes unfeasible. Therefore, it was suggested in Table 2 to perform at least ten evaluations using the CUCcumulative, as CUCmean and CUCmedian underestimate distribution uniformity, besides presenting higher variations between evaluations.
Application efficiency (EA) was determined, ordered in increasing order, and correlated by Pearson's coefficient (r) with weather elements (Figure 7).
The higher the wind speed, the lower the application efficiency, thus promoting higher wind drift (r = −0.70). The vapor pressure deficit, solar radiation, and relative humidity directly correlated with EA, with values of −0.63, −0.85, and 0.62, respectively. Thus, these weather elements increased evaporation and wind drift (Figure 7). Evaporation and wind drift were also reported by Cavero et al. (2016) for the day and night periods. The positive correlation between weather data with EA is paramount to search for models that best fit a particular location (Saraiva et al., 2013).
Table 3 shows the statistical indices for application efficiency (EA) estimations, as proposed by Keller & Bliesner, Playán, Tarjuelo, and Beskow in relation to the values measured in the field.
TABLE 3 Root mean square error (RMSE), mean absolute error (MAE), Willmott agreement index (d), mean bias error (MBE), and Pearson's correlation coefficient (r) of the observed data with those estimated by application efficiency models. Viçosa, MG, Brazil, DEA–UFV, 2017.
Model RMSE MAE d MBE r
Keller 15.98 14.85 0.35 14.64 0.72
Playán 7.21 6.49 0.62 5.56 0.74
Tarjuelo 8.93 8.00 0.52 7.28 0.83
Beskow 2.98 2.54 0.94 0.77 0.90
The results show that the Beskow method was the most efficient in the estimation of EA, which is evidenced by lower values of RMSE, MAE, and MBE, besides higher d and r. On the other hand, the other evaluated methods presented low performance, with high RMSE and MAE values. Beskow et al. (2008), analyzing the Playán and Tarjuelo models to estimate EA, worked with a single sprinkler operating and several sprinklers operating simultaneously, and found unsatisfactory adjustments.
In addition to statistical indices, the analysis in Figure 8 shows the distribution of the measured and estimated EA values by each method. Except for the Beskow method, all others had unsatisfactory performance in relation to the measured values, showing a tendency to overestimate them, which is also indicated by the high MBE values. The Beskow method presented good precision (R2 = 0.803) and accuracy (a = 18.939 and b = 0.781), but there was a small dispersion of data due to systematic and random errors.
The Beskow method showed better agreement, possibly due to the regional approximation and similarity of weather conditions of the present study. This method was developed under the conditions of Lavras, MG, Brazil (Beskow et al., 2008), and the other models in the United States (Keller & Bliesner, 1990) and Spain (Playán et al., 2005; Tarjuelo et al., 2000). Saraiva et al. (2013) found similar results.
Figure 8 also shows that it is important to draw attention to the fact that the valuesestimated by the Keller & Bliesner method presented a very small variation. This method presented low sensitivity to weather variations, which possibly corroborated for this model to present the worst performance.
The Keller & Bliesner (1990) model underestimated evaporation and wind drift and/or overestimated application efficiency (Figures 8 and 9). Faci et al. (2001) observed similar resultsin working with spray-type sprinklers.
As shown in Table 3 and Figures 8 and 9, the used models tended to overestimate the observed field data, and one of the factors that may be related to this application efficiency overestimation is the nozzle size used for modelgeneration. The sprinkler nozzle used in the present study had 4 mm. According to Beskow et al. (2008), smaller nozzles promote higher spraying of dropletsand, thus, have a larger area per unit of mass, which may result in higher evaporation loss and susceptibility to drift by the wind.
Even finding a model that fits well with field conditions, it requires caution when using a model to estimate EA of a conventional sprinkler irrigation system. It is always important to analyze model limitations, such as nozzle diameter, working pressure, and jet slope used to generate the predictive model (Beskow et al., 2008). Sprinkler height may also favor EA, as the longer the riser pipe, the longer the droplet will be exposed to the environment (Faci et al., 2001; Playán et al., 2005).
CONCLUSIONS
The distribution uniformity given by the Christiansen uniformity coefficient had high variation during the experimental period (66.51 to 92.04%). The highest and lowest CUC for the experimental area was the CUCcumulative and CUCmean, respectively. The Beskow model was the best alternative for predicting application efficiencies. The Keller & Bliesner model is not recommended for the study conditions to predict application efficiency, as it presented low sensitivity to input parameters.
Area Editor: Alexandre Barcellos Dalri
ACKNOWLEDGMENTS
We thank the financial support (Ph.D. scholarship) granted by the Brazilian National Council for Scientific and Technological Development (CNPq) and Brazilian Coordination for the Improvement of Higher Education Personnel (CAPES). We also thank the Department of Agricultural Engineering (DEA) of the Federal University of Viçosa for supporting the researchers.
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Received: February 17, 2018; Accepted: November 14, 2019
*Corresponding author. Universidade Federal de Viçosa/ Viçosa - MG, Brasil. E-mail: agroeda@yahoo.com.br
This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. | {"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": 0.842556893825531, "perplexity": 5744.810726610415}, "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-2020-16/segments/1585371803248.90/warc/CC-MAIN-20200407152449-20200407182949-00194.warc.gz"} |
http://www.ck12.org/measurement/Identification-of-Equivalent-Customary-Units-of-Weight/rwa/Ounces-to-Mail/ | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Identification of Equivalent Customary Units of Weight
## Convert between pounds, tons and ounces.
Estimated4 minsto complete
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Progress
Practice Identification of Equivalent Customary Units of Weight
Progress
Estimated4 minsto complete
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Ounces to Mail
Credit: Aranami
Source: http://www.flickr.com/photos/z0/5700203765/
Have you ever wondered why you’d need to be able to convert and understand equivalent units of weight? Why would it matter whether something was calculated from ounces to pounds, or from pound to tons, or from tons to pounds, or from pounds back to ounces? Well, the reason’s as simple as mailing a package with the United States Postal Service!
#### Why It Matters
Since January 2013, when you mail a package, the post office charges $1.95 for the first 3 ounces of weight. Each additional ounce thereafter costs$0.17. You need to understand pounds and ounces if you are planning to mail a package that weighs 2 pounds.
Credit: Paul J. Phelps/U.S. Navy
Source: http://commons.wikimedia.org/wiki/File:US_Navy_060828-N-2716P-022_Postal_Clerk_3rd_Class_Samuel_Anderson,_left,_and_Postal_Clerk_2nd_Class_LeAnn_Baker_check_and_mark_the_destinations_of_incoming_packages_during_mail_distribution_at_Fleet_Mail_Center,_Yokohama.jpg
How would you figure out the cost of this 2-pound package? Well, you know that there are 16 ounces in 1 pound. The package weighs 2 pounds, which is equivalent to 32 ounces. Given that the first 3 ounces cost $1.95 and each additional ounce is$0.17, we can figure out the cost for 32 ounces of package:
\begin{align*}\ 1.95 + \ 0.17(32-3)= \ 1.95 + \ 0.17(29) = \ 1.95 + \ 4.93 = \ 6.88\end{align*}
See how the post office works: http://www.youtube.com/watch?v=KYFtalTNzKk
#### Explore More
Visit the following website to play a variety of interactive measurement games.
### Explore More
Sign in to explore more, including practice questions and solutions for Identification of Equivalent Customary Units of Weight. | {"extraction_info": {"found_math": true, "script_math_tex": 1, "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": 0.7929757237434387, "perplexity": 5117.777171962714}, "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/1454701157075.54/warc/CC-MAIN-20160205193917-00280-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://en.m.wikibooks.org/wiki/FHSST_Physics/Collisions_and_Explosions/Explosions | # FHSST Physics/Collisions and Explosions/Explosions
Collisions and Explosions The Free High School Science Texts: A Textbook for High School Students Studying Physics Main Page - << Previous Chapter (Work and Energy) - Next Chapter (Newtonian Gravitation) >> Tiny, Violent Collisions - Types of Collisions - Explosions - Energy and Heat - Important Equations and Quantities
# ExplosionsEdit
When an object explodes, it breaks up into more than one piece and it therefore changes its shape. Explosions occur when energy is transformed from one kind e.g. chemical potential energy to another e.g. heat energy or kinetic energy extremely quickly.
So, like in inelastic collisions, total kinetic energy is not conserved in explosions. But total momentum is always conserved. Thus if the momenta of some of the parts of the exploding object are measured, we can use momentum conservation to solve the problem!
The Tunguska event was an aerial explosion that occurred near the Podkamennaya (Stony) Tunguska River in what is now Evenkia, Siberia, at 7:17 AM on June 30, 1908. The size of the blast was later estimated to be equivalent to between 10 and 15 million tons of regular explosive. It felled an estimated 60 million trees over 2,150 square kilometers. At around 7:15 AM, Tungus natives and Russian settlers in the hills northwest of Lake Baikal observed a huge fireball moving across the sky, nearly as bright as the Sun. A few minutes later, there was a flash that lit up half of the sky, followed by a shock wave that knocked people off their feet and broke windows up to 650 km away (the same as the distance from Bloemfontein to Durban!). The explosion registered on seismic stations across Europe and Asia, and produced fluctuations in atmospheric pressure strong enough to be detected in Britain. Over the next few weeks, night skies over Europe and western Russia glowed brightly enough for people to read by. Had the object responsible for the explosion hit the Earth a few hours later, it would have exploded over Europe instead of the sparsely-populated Tunguska region, producing massive loss of human life.
In the following picture, a closed can of baked beans is put on a stove or fire:
Before the can heats up and explodes, the total momentum of the system is:
$\begin{matrix}\overrightarrow{p_{Before}} &=& \overrightarrow{p_{can}} \\&=& 0\end{matrix}$
and the total kinetic energy of the system is:
$\begin{matrix}E_{kBefore} &=& E_{kcan} \\&=& 0\end{matrix}$
since the can isn't moving.Once the mixture of beans, juice and air inside the can reach a certain temperature, the pressure inside the can becomes so great that the can explodes! Beans and sharp pieces of metal can fly out in all directions. Energy in the system has been transformed from heat energy into kinetic energy.
After the explosion, the c an is completely destroyed. But momentum is always conserved, so:
$\begin{matrix}\overrightarrow{p_{Before}} &=& \overrightarrow{p_{After}} \\\overrightarrow{p_{Before}} &=& \overrightarrow{p_{1}} +\overrightarrow{p_{2}} +\overrightarrow{p_{3}} + \overrightarrow{p_{4}}\\0 &=& \overrightarrow{p_{1}} +\overrightarrow{p_{2}} +\overrightarrow{p_{3}} + \overrightarrow{p_{4}}\end{matrix}$
However, the kinetic energy of the system is not conserved. The can's shape was changed in the explosion. Before the explosion the can was not moving, but after the explosion, the pieces of metal and baked beans were moving when they were flying out in all directions! So:
$\begin{matrix}E_{kB} \neq E_{kA}\end{matrix}$
Safety tip: Never heat a closed can on a stove or fire! Always open the can or make a hole in the lid to allow the pressure inside and outside the can to remain equal. This will prevent the can from exploding!
## Worked Example 49 Explosions 1Edit
Question: An object with mass mTot = 10 kg is sitting at rest. Suddenly it explodes into two pieces. One piece has a mass of m1 = 5 kg and moves off in the negative x-direction at $\overrightarrow{v_1}=3{m}{s^{-1}}$. What is the velocity of the other piece?
Step 1 :
Draw the picture. Before the explosion, the object is at rest:
After the explosion, the two pieces move off:
Riaan Note: second image on page 154 is missing
File:Fhsst expl16.png
Step 2 :
Now we know that in an explosion, total kinetic energy is not conserved. There is a definite change in shape of the exploding object! But we can always use momentum conservation to solve the problem.
So:
$\begin{matrix}\overrightarrow{p_{Before}} &=& \overrightarrow{p_{After}} \\\overrightarrow{p_{Before}} &=& \overrightarrow{p_{1}} + \overrightarrow{p_{2}}\end{matrix}$
But the object was initially at rest so:
$\begin{matrix}0 &=& \overrightarrow{p_{1}} + \overrightarrow{p_{2}}\\0 &=& m_{1}\overrightarrow{v_{1}} + m_{2}\overrightarrow{v_{2}} \rm {\qquad (\textbf{A})}\end{matrix}$
Step 3 :
Now we know that m1= 5 kg but we do not know what the mass of m2 is. However, we do know that:
$\begin{matrix}m_{Tot} &=& m_1+m_2 \\m_2 & =& m_{Tot} -m_1 \\&=&10 \rm {\ kg}-5 \rm {\ kg} \\&=&5 \rm {\ kg}\end{matrix}$
Step 4 :
Now we can substitute all the values we know into equation (A) and solve for $\overrightarrow{v_{2}}$. Let's choose the positive x-direction to have a postive sign and the negative x-direction to have a negative sign:
$\begin{matrix}0 &=& m_{1}\overrightarrow{v_{1}} + m_{2}\overrightarrow{v_{2}} \rm {\qquad (\textbf{A})} \\0 &=& 5(-3) + 5\overrightarrow{v_{2}} \\0 &=& -15 + 5\overrightarrow{v_{2}} \\5\overrightarrow{v_{2}} &=& 15 \\\overrightarrow{v_{2}} &=& +3 \rm {\ \mathrm{m.s^{-1}}}\end{matrix}$
Therefore,
$\begin{matrix}\overrightarrow{v_{2}} = \underline{3 \ \mathrm{m.s^{-1}}\rm {\ in \ the \ positive \ x-direction.} }\end{matrix}$
## Worked Example 50 Explosions 2Edit
Question: An object with mass mTot =15 kg is sitting at rest. Suddenly it explodes into two pieces. One piece has a mass of m1 = 5000 g and moves off in the positive x-direction at $v_1=7{m}{s^{-1}}$. What is the final velocity of the other piece?
Step 1 :
Draw the picture. Before the collision:
After the collision:
Riaan Note: image on page 156 is missing
File:Fhsst expl18.png
Step 2 :
Convert all units into S.I. units:
$\begin{matrix}m_{1} &=& 5000 \rm {\ g} \\m_{1} &=& 5 \rm {\ kg}\end{matrix}$
Step 3 :
Now we know that in an explosion, total kinetic energy is not conserved. There is a definite change in shape of the exploding object! But we can always use momentum conservation to solve the problem. So:
$\begin{matrix}\overrightarrow{p_{Before}} &=& \overrightarrow{p_{After}} \\\overrightarrow{p_{Before}} &=& \overrightarrow{p_{1}} + \overrightarrow{p_{2}}\end{matrix}$
But the object was initially at rest so:
$\begin{matrix}0 &=& \overrightarrow{p_{1}} + \overrightarrow{p_{2}}\\0 &=& m_{1}\overrightarrow{v_{1}} + m_{2}\overrightarrow{v_{2}} \rm {\qquad (\textbf{A})}\end{matrix}$
Step 4 :
Now we know that m1= 5 kg but we do not know what the mass of m2 is. However, we do know that:
$\begin{matrix}m_{Tot} &=& m_1+m_2 \\m_2 & =& m_{Tot} -m_1 \\&=&15 \rm {\ kg}-5 \rm {\ kg} \\&=&10 \rm {\ kg}\end{matrix}$
Step 5 :
Now we can substitute all the values we know into equation (A) and solve for $\overrightarrow{v_{2}}$. Let's choose the positive x-direction to have a postive sign and the negative x-direction to have a negative sign:
$\begin{matrix}0 &=& m_{1}\overrightarrow{v_{1}} + m_{2}\overrightarrow{v_{2}} \rm {\qquad (\textbf{A})} \\0 &=& 5(7) + 10(\overrightarrow{v_{2}}) \\0 &=& 35 + 10(\overrightarrow{v_{2}}) \\10(\overrightarrow{v_{2}}) &=& -35 \\\overrightarrow{v_{2}} &=& -3.5 \rm {\ \mathrm{m.s^{-1}}}\end{matrix}$
Therefore,
$\begin{matrix}\overrightarrow{v_{2}} = \underline{3.5 \ \mathrm{m.s^{-1}}\rm {\ in \ the \ negative \ x-direction.} }\end{matrix}$ | {"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": 19, "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": 0.7473495006561279, "perplexity": 894.3612325517829}, "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-2014-15/segments/1398223202548.14/warc/CC-MAIN-20140423032002-00273-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://physicsoverflow.org/10071/access-to-the-clipboard?show=10075 | + 0 like - 0 dislike
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It seems I don't have the full access to the clipboard of the current text editor, for copying and pasting it is ok since I realized instead of right clicking I can just "Ctrl+c" and "Ctrl+v". However it would be nicer if, for example, to allow me to highlight, right click and then "Google search"(I'm using chrome), I used to use this a lot in stackexchange. It can be done in source mode, but in source mode other convenient buttons are disabled. I suspect it may cause users to switch back and forth into and out of source mode.
Not a big incovenience, but definitely much smoother user experience if it can be improved.
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http://blog.ivank.net/prolog-matrices.html | # Prolog tutorial – Matrices
This article can be a guide for solving some problems with Prolog. If you know it's syntax, maybe after reading this you will get an idea, how to use this language effectively.
## Basic matrix operations and functions
When solving the exercise below, I firstly wrote predicates like "encode", "decode" etc. After that, I wrote those basic operations, so my approach was "from the top" and I thik it's the right approach. I decided to move these basic matrix operations from the end to the beginning, to make the code below more clear.
### The list of N characters
This code creates a list of $n$ characters (zeros). It takes one characters and attach a list of $n-1$ characters to it. A list of zero characters is empty.
% spaces(+Num, -Spaces)
spaces(N, [0|Tail]) :- N > 0, N2 is N-1, spaces(N2, Tail).
spaces(0, []).
### Concatenation of two lists
It uses a simple recursion. It goes deeply into recursion, and when going back, it ataches the items from the end of $X$ to the head of $Y$.
% concat(+X, +Y, -X.Y)
concat([X| T], L, [X | Rest]) :- concat(T, L, Rest).
concat([], L, L).
### List reverse
This code reverses the list using "accumulator model". Predicate halves has 3 parameters $A, B, C$. I want it to be true, when $C$ is the concatenation of $A^{-1}$ (reversed A) and $B$. So I wrote the rule, that when you take a character from the head of $A$ and put it at the head of $B$, it's still true. When interpreter tries to evaluate the $C$, it uses this rule, untill $A$ is empty, then $B$ equals $C$.
% rev(+M, -M2) - reverse of a list
rev(M, M2) :- halves(M, [], M2).
% halves(+A, +B, -C).
halves([X|T], Acc, M2) :- halves(T, [X|Acc], M2).
halves([], X, X).
### Checking, if the matrix consists of constant values $X$
A matrix consists of $X$s, when the first row consists of $X$s and other rows too. The row consists of $X$s, when it's first item is $X$ and other items too.
% mcontent(+M, +X) - check if there are only Xs in matrix
mcontent([R|Rest], X) :- rcontent(R, X), rcontent(Rest, X).
mcontent([], _).
rcontent([X|T], X) :- rcontent(T, X).
rcontent([], _).
### Matrix transpose
Transpose of a square matrix only (!!!). Most interesting is the predicate firstCol. When the first row is $[H|T]$, the first item in column is $H$, the first item in "rest matrix" is $T$, other items are computed recursively. If you look at it for a moment, you might get an idea, but don't look at it for too long.
% trans(+M1, -M2) - transpose of square matrix
% 1. I get first column from Tail and make a first row (NT) from it
% 2. I transpose "smaller matrix" Rest into NRest
% 3. I take T and make it to be a first column of NTail
trans([[H|T] |Tail], [[H|NT] |NTail]) :-
firstCol(Tail, NT, Rest), trans(Rest, NRest), firstCol(NTail, T, NRest).
trans([], []).
% firstCol(+Matrix, -Column, -Rest) or (-Matrix, +Column, +Rest)
firstCol([[H|T] |Tail], [H|Col], [T|Rows]) :- firstCol(Tail, Col, Rows).
firstCol([], [], []).
## Exercise #1: Text encoding / decoding
You have a text and you have to split it into matrices 4x4. Then you have a "mask matrix", you can see only 4 items of the matrix through this mask. Then you can rotate it and see other 4 items, rotate it again etc., after 4 rotations you have seen all the items.
Decoded textEncoded textExample of the mask matrix
Hello, how are you?
H e l l o u ? _
o , _ h _ _ _ _
o w _ a _ _ _ _
r e _ y _ _ _ _
1 1 1 _
_ _ 1 _
_ _ _ _
_ _ _ _
### Encoding
Algorithm: We just take a letter after letter and insert them into empty matrices, until there are no letters left.
Input: A list of characters (their ASCII codes in prolog).
Output: A list of matrices 4x4.
Approach: We create a predicate "encode", which recursively adds matrices into list. Then predicate "matrix", which adds rows into matrix. Predicate "row" adds characters into row.
% encode(+ Text, -[Matrices])
encode(Text, [Mat|Tail]) :- Text \= [], matrix(Text, Mat, 4, Rest), encode(Rest, Tail).
encode([], []).
% matrix(+ Text, -[Rows...], + NumOfRows, -RestOfText])
matrix(Text, [Row|Tail], N, RText) :-
N \= 1, row(Text, Row, 4, Rest), N2 is N-1, matrix(Rest, Tail, N2, RText).
matrix(Text, [Row], 1, RText) :- row(Text, Row, 4, RText).
% row(+ Text, -[items...], + NumOfItems, -RestOfText])
row([X|Y], [X|Tail], N, RText) :- N > 0, N2 is N-1, row(Y, Tail, N2, RText).
row([], Items, N, []) :- spaces(N, Items).
row(Text, [], 0, Text).
Algorithm: When the 4x4 mask is correct? We can see, that "a middle mask" 2x2 should have only one slot. Other 3 slots should be around it. Every added slot of these 3 slots occupies 3 more places, which are symmetric to it.
When checking the mask, first we chech the middle mask - there should be exactly one slot. Then we check the border, we should find 3 slots there. For each slot, the places symmetric to it should be empty.
$middleOK(M) \wedge borderOK(M) \rightarrow maskOK(M)$
UPDATE: I found much simpler solution. We just create 3 new copies of the mask. We rotate them 90, 180 and 270 degrees and add them one to another. We should get a matrix of ones.
Input: A mask matrix, 0 for empty, 1 for slot.
Output: Correct: true / false.
Approach: A mask is correct, when rotated copies of it, added one over another, give us a matrix of ones. Matrix is rotated, when it's rows are reversed and it's transposed.
% maskOK(+M)
maskOK(M) :- rot(M,M2), rot(M2, M3), rot(M3,M4), add(M, M2, M3, M4, Res), mcontent(Res, 1).
% rot(+M, -M2) - rotate clockwards
rot(M, M2) :- rev(M, M1), trans(M1, M2).
add([A1|R1], [A2|R2], [A3|R3], [A4|R4], [A|R] ) :-
addRow([H1|T1], [H2|T2], [H3|T3], [H4|T4], [H|T]) :-
H is H1+H2+H3+H4, addRow(T1, T2, T3, T4, T).
### Decoding
Algorithm: We should "apply" differently rotated mask on each encoded matrix, then put these pieces one on another and decode the final result.
Input: Encoded text (list of matrices), mask matrix.
Output: Decoded text (list of characters = ASCII codes)
We can decode input matrix immidiatelly, without using a mask. But let's make it more difficult and unneficient!
Approach: We make 4 differently rotated copies of the mask. We make 4 copies of encoded matrices. We apply masks on these lists of matrices. Then we put the lists of matrices one over another to get the former text. When decoding, we just take each matrix, each row of it, each char from the row, ant put it all into one big list.
% decode(+Code, +Mask, -Text).
decode(C1, M1, Text) :- c(C1, C2), c(C2, C3), c(C3, C4),
rot(M1, M2), rot(M2, M3), rot(M3, M4),
apply(C1, M1, O1), apply(C2, M2, O2), apply(C3, M3, O3), apply(C4, M4, O4),
addMany(O1, O2, O3, O4, O), % now "C1" should be equal to "O"
dec(O, Text).
apply([C|Tail], M, [NC|NTail]) :- applyMask(C, M, NC), apply(Tail, M, NTail).
apply([], _, []).
applyRow(R, MR, NR), applyMask(Rest, MRest, NRest).
applyRow([_|ITail], [0|MTail], [0|NTail]) :- applyRow(ITail, MTail, NTail).
applyRow([I|ITail], [1|MTail], [I|NTail]) :- applyRow(ITail, MTail, NTail).
applyRow([], [], []).
addMany([A1|R1], [A2|R2], [A3|R3], [A4|R4], [A|R] ) :-
% dec(+M, -Text)
dec([M|Rest], Text) :- decMat(M, T), dec(Rest, RT), concat(T, RT, Text).
dec([], []).
decMat([R|Rest], Text) :- decRow(R, T), decMat(Rest, RT), concat(T, RT, Text).
decMat([], []).
decRow([X|T], [X|RT]) :- X>0, decRow(T, RT).
decRow([0|_], []).
decRow([], []).
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http://quant.stackexchange.com/questions/7104/how-to-quickly-sketch-a-second-order-greek-profile-for-a-vanilla-position?answertab=oldest | # How to quickly sketch a second order greek profile for a vanilla position?
Assume that you are given an arbitrary payoff profile for European vanilla position (e.g. butterfly). How to make a back of the envelope sketch of a second order greek profile for it (i.e. plot showing dependency of a greek w.r.t. to spot or vol)? I'm interested in major second order greeks like Dvega/Dvol, Dgamma/Dspot, Dgamma/Dvol, Dvega/Dspot. The sketch should at least correctly show signs and relative value (i.e. highs/lows) of the greek.
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• Use a pen, paper, lower the pen to touch the paper, and start sketching your intuition. ;-)
• If that sounds too simplistic then you could shift spot or implied vols by a percentage or point value and recalculate the shift impact either on spot or otherwise apply the shift to the closed form solution of those greeks you attempt to evaluate. As you evaluate a basic option and its greeks this should be a fairly easy exercise.
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If your "European vanilla options" are restricted to piece-wise linear pay-offs, then the following may help:
Remark: I assume you are looking for a rule of thumb to get the profiles without the use of a computer.
All piece-wise linear pay-offs can be decomposed into a sum of digital options and call options with different notional (possibly negative) and strike. Thus you may learn the greek profile of these two by heart and then geometrically add the profiles according to the decomposition of your vanilla option.
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