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# Tag Info

7

I have written a tutorial on how to write simulation-based proofs. I think that it should be helpful.

7

Sigma protocols as-is are secure only for honest verifiers. However, they can be easily compiled into full-blown zero knowledge protocols. If you don't want interaction, then the Fiat-Shamir transform suffices, with security in the random oracle model. With interaction, you can do the transform at little cost using commitments based on DDH. For more ...

6

I'm no FIPS expert but I strongly suspect the answer is no. FIPS is incredibly restrictive and laughably behind the times. To evaluate those algorithms that don't appear in FIPS, first make sure their component parts are secure (maybe even built with FIPS algorithms as subroutines). Then, if there are known answer tests anywhere, maybe from the authors of ...

6

This does seem to be zero knowledge; as you say, you don't actually commit to the adjacency list. Rather, you commit to a series of edges, in random order. Regarding the question: First, your assumption is that $n^2$ commitments, each to a single bit, is more expensive than $|E|$ commitments, each to $2\log n$ bits (to encode two numbers for the edge). This ...

6

There are certainly ZK proof systems which are not known to be POK, and for which no knowledge extractor is known. For example, take the Goldreich-Kahan 4-round ZK proof system. However, do we know of a non-trivial proof system that is provably not a proof of knowledge? Not that I know of.

5

If one-way functions exist, then there is a distribution over graphs (or SAT formulas, or ...) having the property you're asking for. In short, just put the OWF through the Cook-Levin reduction. In a little more detail, Cook-Levin transforms the NP witness-finding question "what is a preimage of $y = f(x)$?" (for random unknown $x$) into the NP witness-...

5

Even following your edits, there's still some confusion about honest verifier zero knowledge and plain-old (i.e., "possibly malicious verifier") zero knowledge, which is a much stronger property. Your description of HVZK is essentially correct, but with the following clarifications: A 3-move protocol between a prover P and a verifier V for a language $L$...

5

There are many ways of doing this. A very nice read (but with informal presentation) is this paper by Fagin, Naor and Winkler on Comparing Information without Leaking It. A very fast protocol exists which requires a single oblivious transfer for every bit. Let $n$ be a security parameter; say $n=128$, and let $\ell$ be the bit-length of the inputs. For $i=... 5 What does this mean, exactly? The purpose of the environment is to model "everything else happening in the universe" besides the protocol execution. In the UC model, the adversary is allowed to talk to the environment during the execution of the protocol. So UC security means "security no matter what else is going on in the world, even if other things are ... 5 The question mentions FIPS 140-2 Level 3 compliant. I answer this as if the question had said the intent is to validate the product as FIPS 140-2 Level 3. This may sound like hairsplitting, but there are many modules claiming to be FIPS 140-2 compliant, which factually could not be validated without large changes to functionality. FIPS 140-2 really intends ... 5 This is not zero knowledge. In particular, you give away information in the form of signatures on challenges. This is something that the verifier doesn't have and so it is something that is "learned". This can be meaningful for two reasons. Let's say that I want to prove to YOU that I wrote the book, but I don't want you to be able to convince anyone else ... 4 There is quite a bit of confusion in your question. First, differentiate between the real and ideal models. The adversary in the ideal model sends the adversary's input and gets its output (and can also sometimes determine if the honest party gets output, depending on the model). We often call the ideal adversary a "simulator" since this is how we build the ... 4 This cannot be done. It is provably impossible. In order to explain this in technical terms, what you are looking for is a FAIR protocol to compute equality of long random strings (I added the latter since it adds a constraint and so in theory could make it easier). In any case, if I had such a protocol, then I could toss a fair unbiased coin. Here is the ... 4 I guess you are talking about Figure 5.3? It is said that the Schnorr proof (sigma protocol for discrete log relation) is insecure against cheating verifiers - it is only honest-verifier zero knowledge. Sigma protocols are always only defined in the honest-verifier zero-knowledge setting. To see why a cheating verifier is a problem in Figure 5.3 think ... 3 If you use a one-time pad as your encryption function then this simplifies to a proof that Alice knows some$F$that hashes to$H$.$K$can be trivially derived from$F$and$E(K, F)$by xor-ing. An interactive zero-knowledge proof of this simpler problem - Alice proving she knows a pre-image of$H(F)$- would go something like this: You need to use a ... 3 The simplest example I know of is actually for a pathological case. Namely, it is presented in Chapter 2 of the book of Hazay and Lindell as an example of a two-party MPC protocol which is secure against a malicious adversary but not against a semi-honest one (in the classical sense, for this reason they prefer the notion of augmented semi-honest adversaries)... 3 Answering the question in your title (and not addressing your proposed alternative which I don't quite understand) there is a zero knowledge proof of password protocol "SRP" which is fast and effective. SRP does not seem to have been given as wide publicity as it should get. Having implemented it, and being an advocate of its use, I don't really understand ... 3 Yes, you are right. In a proof, the soundness holds against a computationally unbounded prover and in an argument, the soundness only holds against a polynomially bounded prover. Arguments are thus often called "computationally sound proofs". 2 Yes, it's okay. This is actually mentioned in passing in the SRP 6 design paper. Previous versions used a random$u$where an attacker who saw (or could predict) it before revealing$A$could compute$A = g^a v^{-u}$and use this to effectively cancel out the long term secret. With$u$derived from a hash, even if the attacker saw$B$, the dependence of$u$... 2 The probabilistic nature is not specific to special-honest verifier zero-knowledge but that's what zero-knowledge is about. With zero-knowledge you want to formulate that such an interactive proof does not leak any information besides the validity of the claim, as it is efficiently simulatable meaning that real and simulated transcripts are not ... 2 The simulator obtains "client$B$'s input" in the same way the simulator obtains$\:\{\hspace{-0.03 in}0,\hspace{-0.04 in}0\hspace{-0.03 in}\}\;$. Even in the real world, the server computes its response without using any secrets, that response is the only message$B$receives, and (from your description) no other party gives any output.$\:$Thus, it doesn'... 2 The objective of the simulator is to make the simulated world (often called the ideal world) indistinguishable from the real world (running the actual protocol). See my write-up on the UC framework here for more detail. In the proof setup, the entity attempting to distinguish between the two worlds is often assumed to provide the inputs to the parties. That ... 2 Do you allow Bob to ask all the users having$F$to encrypt, then to upload the file with a same secret key deriving from$F$? Here would be the principle of the tweaked protocol : all the users must encrypt the file with the same key which depends on the file (calculated via another hash). The key would be a kind of shared key, but which can only decrypt ... 2 Consider a multiplicative group of an order$q$generated by some$g$. For simplicity, let commitment be$C_1 = g^{L_1}$. Consider a proof of knowledge of$L_1$committed to at$C_1$. At the first step of an interactive proof, choose some$L_2$at random and send$C_2 = g^{L_2}$to the verifying party. Second step, receive a challenge$c$. Third step, send a ... 2 I figured it out, it's quite simple actually. The$d$values (and$r$values) are all exponents and chosen from$\mathbb{Z}_q$. Thus all calculations on them directly take place in$\mathbb{Z}_q$. Applying mod$q$(not mod$p$) to all of my calculations on$d$and$r$fixed any problems with calculations. 2 Sure they can, it's called the socialist millionaires problem. The most common solution is to use Yao's protocol: Alice sends a garbled circuit of the equality function to Bob, and then Alice use oblivious transfers to send the keys necessary for the evaluation of the circuit to Bob. Another option is to rely on additively homomorphic IND-CPA encryption: ... 1 No, but if the problem isn't known to be in promiseMA then we do "assume that the prover can always solve the problem". http://cstheory.stackexchange.com/questions/696/mip-with-efficient-provers Graph isomorphism is trivially in NP, so for graph isomorphism, we just "assume that the prover" has an isomorphism between the graphs. Graph non-isomorphism is ... 1 This may look like a homework, so I would not present any complete "Ctrl-C Ctrl-V" -style solution. A proof for equality of logarithms was introduced at Chaum, Evertse and van de Graaf paper, "An Improved Protocol for Demonstrating Possession of Discrete Logarithms and Some Generalizations", Eurocrypt 1987. At the core, Prover shows that the same single ... 1 I've found some lecture notes where, in section 2.4, they give the steps that a simulator would do in order to simulate the view of the honest prover talking to the honest verifier (HVZK). In response to the first question, in the case when the simulator initially guessed wrong the challenge coming from the verifier, the verifier is rewinded but the ... 1 Yes it proves that$y \ne 1 \pmod{n}$is not an$e$-th root. That is, no$x$exists such that$x^e = y \pmod{n}$. In particular, if$e | \phi(n)$then for any$x$it holds that$\left( x^{ \frac{\phi(n)} {e}} \right)^e = 1 \ne y$. This probably means one last final conclusion designed as a homework. Regarding GQ protocol: prover will be unable to pick an$...

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What is Problem Mining? This is a tool based on data of arXiv.org which periodically scans packets of full texts of papers hosted on arXiv and available through arXiv's bulk data access policy, with the aim to automatically detect papers containing discussions on open problems or conjectures. It then creates a list from the detected papers putting together papers' descriptive data and some short snippets extracted from the full texts displaying information on open problems or conjectures presented in the paper. The papers appearing on this list are only references to the arXiv's versions and we do NOT store the actual papers (TeX sources or PDFs) on our servers. To read any of the papers in this list one needs to follow the arXiv link displayed on the papers' blocks.

You can search within the list using keywords, author names, and subject area. By a simple click of the Interesting button, you may anonymously indicate your interest in the problem. If you think the automatic extraction resulted in incorrect data, you may click on the False positive button instead. The Stats section shows the worldwide interest by our users on a specific problem.

• Affine factorable surfaces in isotropic spaces

year of publication: 2018 arXiv

• Differential Geometry

MSC 2010: 53A35 53A40 53B25

• Entanglement Entropy for Open Bosonic Strings on $Dp$-branes

year of publication: 2018 arXiv

• Overview of Plasma Lens Experiments and Recent Results at SPARC_LAB

year of publication: 2018 arXiv

• Accelerator Physics
• The Igusa local zeta functions of superelliptic curves

year of publication: 2018 arXiv

• Number Theory
• Local strong solution to General Landau-Lifshitz-Bloch equation

year of publication: 2018 arXiv

• Differential Geometry
• Superfluidity in nuclear systems and neutron stars

year of publication: 2018 arXiv

• High Energy Astrophysical Phenomena
• Quantum Gases
• Minimally toughness in special graph classes

year of publication: 2018 arXiv

• Combinatorics

MSC 2010: 05C99

• Fujii's development on Chebyshev's conjecture

year of publication: 2018 arXiv

• Number Theory

MSC 2010: 11M06 11N13

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• Programming Languages
• On the Lichnerowicz conjecture for CR manifolds with mixed signature

year of publication: 2018 arXiv

• Complex Variables
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## Is Statistics The In Cv What

Resume English Teacher Korea This resume was created for a career Statistician hoping to receive a significant promotion, either within his current company or with a new company.As a trained Statistician with a degree in Computer Science and an advanced degree in Statistics, this client has some very specific skills that ar. Coefficient of variation is a measure of the ratio of the standard deviation to the mean. These are our current charts, based on …. There are four major types of descriptive statistics: 1. where n is the sample size When the coefficient of variation is calculated from a sample drawn from a normal population, then the. Although COV is most. Author: Math and Science Views: 157K What Does Coefficient of Variation Measure? However, this seems wrong. Coefficient of Variation (CV) and Relative Standard Deviation: No doubt, the (CV) coeffcieint of variation is very similar to the relative standard deviation (RSD), but the only prominent difference between both that the coefficient of variance can be negative, while RSD is always positive CV refers to the "coefficient of variation," which describes the standard deviation as a percentage of the mean, as shown in the following equation: CV = (s/ )100 where s is the standard deviation, is the mean, and the multiplier of 100 is used to convert the s/ ratio to a percentage A s the virus that causes Covid-19 spreads worldwide, this dashboard offers What Is The Cv In Statistics a snapshot of the crisis right now. For many people with disabilities, much of the data available regarding the COVID19 (coronavirus) outbreak is in a graphical format, which is impossible to access. There are many CV templates and guides on the internet that are handy for when you are writing, or re-drafting, your CV. 2. In statistics it is abbreviated as CV. Measures of Central Tendency * Mean, Median, and Mode.if you are using and applying What Is The Cv In Statistics a statistical method with your data collections already, the CV value is what it is and part of the study.

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Look it up now! Easy enough. The smaller the variation between a data set the greater the precision; Usually used in the What Is The Cv In Statistics laboratory to determine if the CV is within a certain standard deviation (SD) Pipette precision - taking several pipette readings and determining the variation within the values taken. In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. But if you. For example: 823.2 310.5 280.9 725.9 -203.4 273.0 470.5 210.0 448.5 371.8 352.7 -760.7 -499.7. In the field of statistics, we typically use different formulas when working with population data and sample data Coefficient of Variation (CV) The coefficient of variation is the ratio of the standard deviation to the mean. Description: The sample coefficient of variation (CV) is defined as the ratio of the standard deviation to the mean: $$\mbox{cv} = \frac{s}{\bar{x}}$$. When employers read your CV, they should get the impression that you would be competent to begin working immediately with minimal training. A tailored resume summary might look like the following: Good example: Digital Marketing Manager Resume Summary. CV refers to the "coefficient of variation," which describes the standard deviation as a percentage of the mean, as shown in the following equation: CV = (s/ )100 where s is the standard deviation, is the mean, and the What Is The Cv In Statistics multiplier of 100 is used to convert the s/ ratio to a percentage In statistics the coefficient of variation is a fairly natural parameter if variation follows either the gamma or the lognormal, as may be seen by looking at the form of the coefficient of variation for those distributions. Home > Resume > Resume Templates > Mathematics > Mathematician > Entry Level Mathematics and Statistics Resume Templates A resume is an essential document in your job search portfolio. Within the lab, it is mainly used to determine how reliable assays are by determining the ratio of the standard deviation to the mean.

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Pricewaterhousecoopers International Assignments European Policy If you decide to replicate the experiment on another area. Descriptive statistics allow you to characterize your data based on its properties. Descriptive statistics allow you to characterize your data based on its properties. The coefficient of variation is defined as the ratio of …. If you decide to replicate the experiment on another area. I What Is The Cv In Statistics don't think my undergraduate statistics course even mentioned the coefficient of variation. The coefficient of variation (CV), also known as “relative variability”, equals the standard deviation divided by the mean. Express CV as a percentage. Express CV as a percentage. For example, the expression “The standard deviation is …. Maybe it is just me, but when I compute descriptive statistics for univariate data, the coefficient of variation is not a statistic that I look at. In other words, a set of data is graphed and the CV equation is used to measure the variation in points from each other and the mean The insights contained What Is The Cv In Statistics within these statistics give you a blueprint for how to position yourself to stand out more prominently among the job-search noise and land the job of your dreams faster. The calculation of Coefficient of Variation (CV) from duplicate measurements made on a number of different subjects or materials is used to determine the reproducibility of the measurements as an alternative to making a large number of.

(CareerBuilder, 2018) The typical job seeker writes only one resume in their job search. This tool will calculate the coefficient of variation of a set of data. To calculate CV you take the standard deviation of the data and divide it …. Coefficient of variation (CV) % time-in-range, % high, and % low. Coefficient of variation. In probability theory and statistics, the coefficient of variation (CV) is a normalized measure What Is The Cv In Statistics of the dispersion of a probability distribution. Coefficient of Variation (CV) The coefficient of variation is the ratio of the standard deviation to the mean. The CV for a single variable aims to describe the dispersion of the variable in a way that does not depend on the variable's measurement unit The coefficient of variation (CV) for a sample is the standard deviation of the observations divided by the mean. For example, if the mean is 80 and standard deviation is 12, the cv = 12/80 = .15 or 15% COEFFICIENT OF VARIATION Name: COEFFICIENT OF VARIATION (LET) Type: Let Subcommand Purpose: Compute the coefficient of variation of a variable. CV refers to the "coefficient of variation," which describes the standard deviation as a percentage of the mean, as shown in the following equation: CV = (s/ )100 where s is the standard deviation, is the mean, and the multiplier of 100 is used to convert the s/ ratio to a percentage..


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# 8.2: Newton's Method

We want to look at finding the roots of a polynomial. Sometimes the polynomial cannot be easily factored, and other algebraic methods (e.g., the quadratic equation) are not applicable, or do not work. When faced with a mathematical problem that cannot be solved with simple algebraic means, calculus sometimes provides a way of finding approximate solutions.

### Newton's Method

A simple example will help introduce Newton’s Method for approximating the roots of a polynomial equation.

Let's say you want to compute $$\sqrt{5} \nonumber$$ without using a calculator or a table. Any ideas how this could be done? Try thinking about this problem in a different way, so that you make use of linearization.

Assume that we are interested in solving the quadratic equation:

$f(x)=x^2−5=0 \nonumber$

We know this equation has the roots $$x=± \sqrt{5} \nonumber$$.

The idea here is to find the linearization of f(x) at an appropriate point, and then solve the linear equation for x. This is an added twist to the linearization problem!

How to choose the linearization point? Since $$\sqrt{4}<\sqrt{5}<\sqrt{9} \nonumber$$, this mean $$2<\sqrt{5}<3 \nonumber$$.

We choose the linear approximation of f(x) to be near $$x_0=2 \nonumber$$ (but, $$x_0=3 \nonumber$$ could also could be selected).

$f(x)=x^2−5 \mbox{ and } f(2)=−1 \nonumber$

$f′(x)=2x \mbox{ and } f′(2)=4 \nonumber$

Using the linear approximation formula,

$f(x)≈f(x_0)+f′(x_0)(x−x_0) \nonumber$

$≈−1+(4)(x−2) \nonumber$

$≈−1+4x−8 \nonumber$

$≈4x−9 \nonumber$

Notice that this equation is much easier to solve than $$f(x)=x^2−5=0 \nonumber$$.

Setting f(x)=0 and solving for x, we obtain,

$4x−9=0 \nonumber$

$x=\frac{9}{4} \nonumber$

$=2.25 \nonumber$

This is a fairly good approximation, since a calculator would give x=2.23607, lower by 0.014. We can actually make this approximation to the root of f(x) even better by repeating what we have just done but using the latest estimate $$x_1=2.25= \frac{9}{4} \nonumber$$, a number that is even closer to the actual value of $$\sqrt{5} \nonumber$$.

$f(x)=x^2−5 \mbox{ and } f(2.25)=\frac{1}{16} \nonumber$

$f′(x)=2x \mbox{ and } f′(2)= \frac{9}{2} \nonumber$

Using the linear approximation again,

$f(x)≈f(x_1)+f′(x_1)(x−x_1) \nonumber$

$≈ \frac{1}{16}+\frac{9}{2}(x−\frac{9}{4}) \nonumber$

$≈\frac{9}{2}x−\frac{161}{16} \nonumber$.

Solving for x by setting f(x)=0, we obtain

$x=x_2=\frac{161}{72}=2.23611 \nonumber$

which is an even better approximation than $x_1=\frac{9}{4} \nonumber$.

We could continue this process generating a better approximation to $$\sqrt{5} \nonumber$$, as shown in the table, where the last estimate approximates the correct answer to 5 places. Thank goodness for calculators!

 n $$x_n \nonumber$$ $$f(x_n) \nonumber$$ $$f′(x-n) \nonumber$$ $$\frac{f(x_n)}{f′(x_n)} \nonumber$$ $$x_n−\frac{f(x_n)}{f′(x_n)} \nonumber$$ 1 2 -1 4 -0.25 2.25 2 2.25 0.0625 4.5 0.01389 2.23611 3 2.23611 0.00019 4.47222 0.00004 2.23607 4 2.23607 -- -- -- --

This is the basic idea of Newton’s Method. Here is a summary of the method:

1. Given the function f(x), find f′(x).
2. Estimate the first approximation, x0, to a solution of the equation f(x)=0. Use a graph to help in finding the first approximation if necessary (see Figure below).
3. Use the current approximation xn to find the next approximation, xn+1, by using the recursion relation.

$x_{n+1}=x_n−\frac{f(x_n)}{f′(x_n)} \nonumber$.

1. Repeat the previous step until the desired level of convergence occurs.

Note that in some cases, Newton’s Method does not converge.

CC BY-NC-SA

## Examples

### Example 1

Compare the solutions to f(x)=5x2+7x−52 in the interval [2, 3] from using the Quadratic formula and using Newton’s Method.

The function is shown in the figure.

For f(x)=5x2+7x−52=0, use of the quadratic formula gives the exact solution x=2.6 in the interval.

CC BY-NC-SA

Use of Newton’s Method with an initial estimate of x0=3, yields the results shown in the table.

 n $$x_n \nonumber$$ $$f(x_n) \nonumber$$ $$f′(x-n) \nonumber$$ $$\frac{f(x_n)}{f′(x_n)} \nonumber$$ $$x_n−\frac{f(x_n)}{f′(x_n)} \nonumber$$ 1 3 14 37 0.3784 2.6216 2 2.6216 0.7151 33.216 0.0215 2.6001 3 2.6001 0.0033 33.001 0.0001 2.6000 4 2.6000 -- -- -- --

The technique rapidly converges to a solution.

### Example 2

Use Newton’s method to find the roots of the polynomial $$f(x)=x^3+x−1 \nonumber$$.

The problem is to solve the equation $$f(x)=x^3+x−1=0 \nonumber$$.

The equations we need are:

$f(x)=x^3+x−1 \nonumber$

$f′(x)=3x^2+1 \nonumber$.

Using the recursion relation,

$x_{n+1}=x_n−\frac{f(x_n)}{f′(x_n)} \nonumber$

$=x_n−\frac{x^3_n+x_n−1}{3x^2_n+1} \nonumber$.

To help us find the first approximation, we make a graph of f(x). As the figure suggests, set $$x_1=0.6 \nonumber$$.

CC BY-NC-SA

Then using the recursion relation, we can generate x1:

$x_{n+1}=x_n−\frac{x^3_n+x_n−1}{3x^2_n+1} \nonumber$

$x_2=0.6−\frac{(0.6)^3+(0.6)−1}{3(0.6)^2+1} \nonumber$

$=0.6884615 \nonumber$.

By using the recursion relation several times, we can find x3 and x4 as shown in the table.

 n $$x_n \nonumber$$ $$f(x_n) \nonumber$$ $$f′(x-n) \nonumber$$ $$\frac{f(x_n)}{f′(x_n)} \nonumber$$ $$x_n−\frac{f(x_n)}{f′(x_n)} \nonumber$$ 1 0.6 -0.184 2.08 -0.0884615 0.6884615 2 0.6884615 0.01477796 2.4219377 0.0061017 0.6823598 3 0.6823598 0.00007669 2.3968445 0.0000320 0.6823278 4 0.6823278 -- -- -- --

We conclude that the solution to the equation $x^3+x−1=0 \nonumber$ is about 0.6823.

### Example 3

Use Newton’s Method to show to find the root of $$f(x)=cos(2x)−x \nonumber$$.

The equations we need are:

$$f(x)=cos(2x)−x \nonumber$$

$$f(x)=−2sin(2x)−1 \nonumber$$

Using the recursion relation,

x_{n+1}=x_n\frac{f(x_n)}{f′(x_n)} \nonumber\)

$$=x_n−\frac{cos(2x_n)−x_n}{−2sin(2x_n)−1} \nonumber$$

To help us find the first approximation, we make a graph of f(x). As the figure suggests, set the first estimate at 0.5.

CC BY-NC-SA

Using the recursion relation several times gives the table values:

 n $$x_n \nonumber$$ $$f(x_n) \nonumber$$ $$\frac{f(x_n)}{f′(xn)} \nonumber$$ 1 0.500000 0.0403023 -0.015216_8 2 0.515022 -0.0002400 0.0000884 3 0.514933 -0.0000000 0.0000000 4 0.514933 -- --

We conclude that the solution to the equation cos(2x)−x=0 is 0.514933.

## Review

For all the problems, use Newton’s Method to find the roots.

1. $$x^3+3=0 \nonumber$$.
2. $$−x+3\sqrt{−1+x}=0 \nonumber$$.
3. $$4x^2−x−2 \mbox{ in the interval } [-1, 0] \nonumber$$.
4. $$4x^3−6x^2−1 \nonumber$$.
5. $$5e^{−x}+x^3 \nonumber$$.
6. $$cosx−x \nonumber$$.
7. $$x^5−7x^2+2 \mbox{ in the interval} [-1, 0] \nonumber$$.
8. $$x^5−7x^2+2 \mbox{ in the interval } [0, 1] \nonumber$$.
9. $$x^2cosx−x \mbox{ in the interval } [4, 5] \nonumber$$.
10. $$x^2cosx−x \mbox{ in the interval } [7, 8] \nonumber$$.
11. $$f(x)=x−2sin(x) \mbox{ to five decimal places, starting with initial guess } x_0=3 \nonumber$$.
12. $$f(x)=6x^3−4x+1 \nonumber$$ to three decimal places, starting with initial guess $$x_0=1.2 \nonumber$$.
13. $$f(x)=ln(x)×(ln(x)+4)+1 \nonumber$$ to five decimal places, starting with initial guess $$x_0=1 \nonumber$$.
14. $$f(x)=tan(x)−csc(x) \nonumber$$ to six digits of accuracy, starting with initial guess $$x_0=0.7 \nonumber$$.
15. $$f(x)=tan^{−1}(x)+cos(x) \nonumber$$ to four digits of accuracy, starting with initial guess $$x_0=−2 \nonumber$$.

To see the Review answers, open this PDF file and look for section 4.11.

## Vocabulary

Term Definition
Newton's method Newton’s method is an iterative procedure for computing the root of an equation.


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Document Type : Research Articles

Authors

Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Nigeria

10.22080/cjms.2020.19945.1553

Abstract

The aim of this paper is to introduce the concepts of $\alpha$-continuity, $\eta$-admissible pair for fuzzy set-valued maps and define a notion of fuzzy $\eta-(\psi, F)$-contraction. The existence of common fuzzy fixed points for such contraction is investigated in the setting of a complete metric space. The ideas presented herein complement the results of Wardowski, Banach, Heilpern and other results on point-to-point and point-to-set-valued mappings in the comparable literature of metric and fuzzy fixed point theory. A few important of these consequences of our results are highlighted and discussed. Some nontrivial examples and an application to a system of integral inclusions of Fredholm type are considered to support our theorems and to illustrate a usability of the results obtained herein.

Keywords


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# Definition:Elementary Equivalence

Let $\mathcal{M},\mathcal{N}$ be $\mathcal{L}$-structures.
We say that $\mathcal{M}$ and $\mathcal{N}$ are elementarily equivalent if for all $\mathcal{L}$-sentences $\phi$, we have $\mathcal{M}\models \phi$ if and only if $\mathcal{N}\models \phi$.


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## How does Lipschitz Regularization Influence GAN Training?

Sep 25, 2019 Withdrawn Submission readers: everyone
• Abstract: Despite the recent success of Lipschitz regularization in stabilizing GAN training, the exact reason of its effectiveness remains poorly understood. It is commonly believed that the main function of K-Lipschitz regularization is to restrict the L2-norm of the neural network gradient to be smaller than a threshold K (e.g. K=1) such that || grad f || <= K. While in this work, we uncover a counter-intuitive fact that under typical GAN setups, the choice of K does not matter. This finding suggests that instead of keeping the neural network gradients small, an even more important function of Lipschitz regularization is its restriction on the domain and interval of attainable gradient values of the loss function. This avoids the bias of the loss function over input samples. Empirically, we verify our proposition on the MNIST, CIFAR10 and CelebA datasets.
• Original Pdf:  pdf
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How do I cross Del with (scalar*vector)?

Tags:
1. Sep 5, 2016

Fido

1. The problem statement, all variables and given/known data
Show that for any scalar field α and vector field B:

∇ x (αB) = ∇α x B + α∇ x B

2. Relevant equations

(∇ x B)i = εijk vk,j
(∇α)i = αi
(u x v)i = eijkujvk
3. The attempt at a solution
Since α is a scalar i wasn't quite sure how to cross it with ∇

So on the left side I have:
εijkBk,j αi

I'm pretty sure I'm supposed to solve out the left side to get to the right because that what I did for the previous problem.

The right side all I could get it to simplify to was:
αi x B + α∇ x B

2. Sep 5, 2016

3. Sep 5, 2016

Fido

So does that mean that my left side is just εijk Bk,j α ? I feel like it's supposed to be broken up into two parts

Last edited: Sep 5, 2016
4. Sep 5, 2016

Simon Bridge

It needs to if you are going to get RHS = LHS ... if in doubt go back to the definitions.
Maybe look at $(\alpha B)_i$ also see what the RHS looks like in components. Play around until you understand it.


text:
It is clear that to further improve the efficiency it is necessary to reduce the electrical losses at the surfaces and specifically the contact between the semiconductor and the metallisation. Current technology has pushed this to their limit and new disruptive solutions are now required. As a result carrier selective or passivating contacts have recently attracted significant interest in the photovoltaic scientific community [1]. These passivating or carrier-selective contacts by design exhibit extremely low recombination currents for minority carriers (i.e. passivation) while having a low resistivity for majority carriers (i.e., carrier selectivity). An elegant way to look at this was recently proposed by Brendel et al. [2] Based on the theoretical framework proposed by Wuerfel et al. [3] which attributes carrier selectivity to the asymmetry in the electron and hole conduction, Brendel et al. defined the electron conductance ρn and hole conductance ρp as follows (in this case for a hole-selective contact):

$\rho_n=(\frac{\partial dJ_n}{\partial dV})^{-1}=\frac{v_th}{f_c j_c }$  (1)

$\rho_p=(\frac{dJ_p}{dV})^{-1}=\frac{\rho_c}{f_c}$  (2)

Where Jn,p is the electron/hole current, V is the voltage, vth is the thermal voltage, fc is the contact fraction, and jc is the minority carrier combination current. When dividing the electron and hole conductance we can define the selectivity S10:

$S_{10}=log_{10}( \frac{\rho_n}{\rho_p})=log_{10} (\frac{v_tj}{j_c \rho_c})$  (3)

where log10 is the logarithm with base 10. This selectivity is a very useful parameter to consider as it is an excellent figure of merit to estimate the efficiency potential of a certain contact. This is shown schematically in Figure 1 where we plot the upper limit efficiency as a function of the jc and ρc of a contact. It should be noted that you can move along the iso-selectivity lines (dotted lines in Figure 1) by changing the contact fraction of the contact. This is for example already exploited in the PERC solar cell where the optimal rear contact fraction (with a selectivity of 13 [2]) is around 1% thereby limiting the solar cell efficiency to 27.2%. Unfortunately, the selectivity of the electron contact in a PERC cell is ~12 [2] and this limits the PERC solar cell to roughly 25% in very good agreement with champion results achieved by UNSW in 1999 [4].

In Figure 2 we show various ways to fabricate a carrier-selective contact. The first type shown in Fig. 2(a) is the well-known diffused electron collector (typically referred to as emitter). This system is currently dominating the photovoltaic industry and has a reasonable selectivity of 12 for electrons and 13 for holes [2]. The types shown in Figure 2(b) – (d) are typically referred to as passivating contact and these contact systems are the main focus of this project. It can be seen that these contact systems typically consist of a multilayer structure of a layer with a high level of surface passivation such as silicon oxide and amorphous silicon in combination with a material that results in the selectivity of the contact. This passivation layer is predominantly aimed at reducing jc of the contact as this is typically unacceptably high due to a high density of interface states at the c-Si surface. The second layer in the structure yields the carrier selectivity and this can be grouped in three different categories. The first category of materials as shown in Figure 2(b) has a high asymmetry in electron/hole conduction. Most notable examples are doped amorphous silicon and doped poly-silicon which are e.g. applied in heterojunction and TOPCon solar cells, respectively. The second category shown in Figure 2(c) relies on band alignment with either the valence band (for a hole contact) or with the conduction band (for an electron contact). The band-offset for the other band should be as high as possible to ensure minimal conductance for the other charge carrier. The third and last category as shown in Figure 2(d) relies on extreme work function materials which result in a band-bending in the underlying silicon. This band bending results in a shift of the quasi-Fermi levels towards the valence band (for hole contacts) or conduction band (for electron contacts) and this gives the contact a high selectivity. In Figure 3, we show the band alignment of various thin films in comparison to c-SiFigure 2 Types of carrier selective contacts. Graphs are adapted from Macco et al. [5]

As shown in Figure 1, the efficiency potential of passivating contacts have already been demonstrated at the solar cell device level and they have resulted in a string of world record silicon wafer solar cell efficiencies recently such as the 26.7% efficient all-back-contact heterojunction with intrinsic thin film solar cell from Panasonic [6] and the 25.7% efficient TOPCon (tunnel oxide passivated contact) solar cell from Fraunhofer ISE [7]. Both have now overtaken the landmark 25% efficiency result set by UNSW in 1999 [4].

[1]             Cuevas, A., T. Allen, J. Bullock, Y. Wan, D. Yan, and X. Zhang, Skin Care for Healthy Silicon Solar Cells, in 42nd IEEE PVSC. 2015. p. 10.1109/PVSC.2015.7356379.

[2]             Brendel, R. and R. Peibst, IEEE Journal of Photovoltaics 6, 1413-1420 (2016)

[3]             Wurfel, U., A. Cuevas, and P. Wurfel, IEEE Journal of Photovoltaics 5, 461-469 (2015)

[4]             Zhao, J.H., A.H. Wang, and M.A. Green, Progress in Photovoltaics 7, 471-474 (1999)

[5]             Macco, B., B.W.H. van de Loo, and W.M.M. Kessels, Atomic Layer Deposition for High Efficiency Crystalline Silicon Solar Cells, in Atomic Layer Deposition in Energy Conversion Applications, J. Bachmann, Editor. 2016, Willey.

[6]             Yoshikawa, K., H. Kawasaki, W. Yoshida, T. Irie, K. Konishi, K. Nakano, T. Uto, D. Adachi, M. Kanematsu, H. Uzu, and K. Yamamoto, Nature Energy 2, 17032 (2017)

[7]             Richter, A., J. Benick, F. Feldmann, A. Fell, M. Hermle, and S.W. Glunz, Solar Energy Materials and Solar Cells,  (2017)

[8]             Stradins, P., S. Essig, W. Nemeth, B.G. Lee, D. Young, A. Norman, Y.Y. Liu, J.W. Luo, E. Warren, A. Dameron, V. LaSalvia, M. Page, A. Rohatgi, A. Udaphyaya, B. Rounsaville, Y.W. Ok, S. Glunz, J. Benick, F. Feldman, and M. Hermle. “Passivated Tunneling Contacts to N-Type Wafer Silicon and Their Implementation into High Performance Solar Cells“, WCPEC-6 proceedings, edited by 2014), pp.


text:
Abdelhamied Mostafa
· CairoEgypt
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IDEA

i’ve a new idea to travel forward and backward in time
did you ever hear about White hole ?
- you mean black hole
no , i meant white hole , the black hole pull things down , and white hole push things up

so i think if there is no white hole so black hole will collapse on itself

even all of that , sure we can’t go inside black hole (“sure i’m not thinking in black holes at all don’t worry 😄”)

yes , worm hole
we can build one but it collapse on itself immediately when i try to open it

but i wrote the story of white and black hole to explain that we need another worm hole in the other side to push (like a white hole)

just open a worm hole in place (A) to pull and open another one in place (B) to push

what do you think guys ?
who agrees with me ??

and thank you guys !! 😄

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Bi Sh
· KathmanduNepal
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'd like to comment… but its mostly critical ones… i am not discouraging you but Time Travel doesn’t stand on Logical Ground itself. Einsteins Theroy is also not backed up by evidence or proven. Possibility of Curvature itself is on question. No evidence or proof still.
We have no clue about simple curvature in Space…
Worm Holes are very Special and Extreme cases of such Space-Time distortions… exotic results of Amazing Mathematics. Like 4 dimension, 11 Dimension, 21 Dimension, 27 dimensions put forward by M-Theroy and String-Theroy. These are outcome of Exotic Abstract Mathematics. Might not be right answer or solution… If it corresponds with Reality it is right otherwise we need to reject it as absurd.
Personally im more than convinced that Time Travel is Impossibility. Can only be imagined… but can never happen in real time.
We can explain it better in terms of ever increasing #Entropy.

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Gokul Nair
Mechanical Engineer
· MysuruIndia
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If we wish to influence space and matter, we need to influence gravity, in order to do that we need to increase density of objects so that other objects are drawn towards it at high velocity,a portal to other world is possible only if the space is bent and different co ordinates are co-incided, so material research, including that of plasma, understanding of the four fundamental force field need to be also be clear from an independent outlook or perspective,when that doesn’t work out we need to consider existing theories.

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Gokul Nair
Mechanical Engineer
· MysuruIndia
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I believe physical phenomeon like piezo electric effect,the concept of natural frequency,resonance effect etc could be put to good use,but again manned missions for time travel may prove to be dangerous to people inside the mission shuttle

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Gokul Nair
Mechanical Engineer
· MysuruIndia
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Navigation may be the biggest challenge, sensors, smart materials ,good use of electronic cooling methods,for eg peltier effect,AI programs, well built circuits, cryogenics ,these may prove to be useful. Check out wolframalpha language,its a knowledge based programming language. Many built in Algorithms, time saving platform to build and deploy programs

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Gokul Nair
Mechanical Engineer
· MysuruIndia
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https://youtu.be/7SYSxJsdfM0
Check out the above link.I am working on it actually,just found out that many others also doing the same, but since its a radical or different take on our understanding of this world,I was refused a platform to pursue doctoral studies at a premier Institute where I appeared for the interview,I really appreciate the initiative by Mr Steven for building a platform to bring ideas and people together

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DISCOVER
CHAT


text:
# Rotation Matrices

A rotation matrix rotates a point (or vector) by a given angle around the origin. For a 3D rotation, there are three degrees of freedom, so a different matrix is needed for a rotation around each axis. But, for a 2D rotation, the only rotation which leaves the points in the original plane is a rotation about the (imagined) Z axis.

### 2D Rotation

$$R{\bf v} = \begin{bmatrix} \cos\theta & -\sin\theta\\ \sin\theta & \cos\theta\\ \end{bmatrix} \begin{bmatrix} x\\ y\\ \end{bmatrix} = \begin{bmatrix} x\cos\theta - y\sin\theta\\ x\sin\theta + y\cos\theta\\ \end{bmatrix}$$

### 3D Rotation

$${\bf v} = \begin{bmatrix} x\\ y\\ z \end{bmatrix}$$ $$R_x(\theta)= \begin{bmatrix} 1 & 0 & 0\\ 0 & \cos\theta & -\sin\theta\\ 0 & \sin\theta & \cos\theta\\ \end{bmatrix}$$ $$R_y(\theta)= \begin{bmatrix} \cos\theta & 0 & \sin\theta\\ 0 & 1 & 0\\ -\sin\theta & 0 & \cos\theta\\ \end{bmatrix}$$ $$R_z(\theta)= \begin{bmatrix} \cos\theta & -\sin\theta & 0\\ \sin\theta & \cos\theta & 0\\ 0 & 0 & 1\\ \end{bmatrix}$$


text:
# Express Each of the Following Product as a Monomials and Verify the Result for X = 1, Y = 2: ( 2 5 a 2 B ) × ( − 15 B 2 a C ) × ( − 1 2 C 2 ) - Mathematics

Express each of the following product as a monomials and verify the result for x = 1, y = 2:

$\left( \frac{2}{5} a^2 b \right) \times \left( - 15 b^2 ac \right) \times \left( - \frac{1}{2} c^2 \right)$

#### Solution

To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^m \times a^n = a^{m + n}$.

We have:

$\left( \frac{2}{5} a^2 b \right) \times \left( - 15 b^2 ac \right) \times \left( - \frac{1}{2} c^2 \right)$

$= \left\{ \frac{2}{5} \times \left( - 15 \right) \times \left( - \frac{1}{2} \right) \right\} \times \left( a^2 \times a \right) \times \left( b \times b^2 \right) \times \left( c \times c^2 \right)$

$= \left\{ \frac{2}{5} \times \left( - 15 \right) \times \left( - \frac{1}{2} \right) \right\} \times \left( a^{2 + 1} \right) \times \left( b^{1 + 2} \right) \times \left( c^{1 + 2} \right)$

$= 3 a^3 b^3 c^3$

$\because$ The expression doesn't consist of the variables x and y.

$\therefore$  The result cannot be verified for x = 1 and y = 2

Thus, the answer is $3 a^3 b^3 c^3$.
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.3 | Q 29 | Page 14


text:
Independence and inclusion

Let $$V$$ be a vector space and $$X\subseteq Y \subseteq V$$. Decide, which of the following claims are valid or not:

• Variant 1

The se $$X$$ is not independent, while the set $$Y$$ is independent.

• Variant 2

If the set $$X$$ is independent, so is the set $$Y$$.

• Variant 3

If the set $$Y$$ is independent, o is the set $$X$$.


text:
In weighted least squares the interpretation remains the same as before. The closer the R-squared value is to 1, the better the fit of the trendline. Thanks for pointing it out. Weighted least squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which the errors covariance matrix is allowed to be different from an identity matrix.WLS is also a specialization of generalized â¦ R-squared and adjusted R-squared do not always increase for better nonlinear models. Reduced Model USP: Goodness of Fit output options were re-arranged and parallelism tests replaced by a full ANOVA table as described by Gottschalk, P. G. and Dunn, J. R. (2005). However, my function does not work for polynomials with degree greater than 1. Below you can find the corresponding weights of the scores. Galton peas (nonconstant variance and weighted least squares) Load the galton data. Excel is able to do this. Specifically, we will fit this model, use the Storage button to store the fitted values and then use Calc > Calculator to define the weights as 1 over the squared fitted values. The key is to notice that it depends on what the weights mean.In particular, you will get different answers if the weights are frequencies (i.e. Tutorial shows how to calculate a linear regression line using excel. If R 2 is 0, it means that there is no correlation and independent variable cannot predict the value of the dependent variable. I Can now replicate R's R^2 if I use the mean sum of squares, rather than the total sum of squares. In this case, data points with a larger population have residuals with a higher variance. To calculate a weighted average in Excel, simply use SUMPRODUCT and SUM. This article will show you how to use Excelâs SUMPRODUCT and SUM functions individually and how to combine the two to calculate a weighted average. However, because in this analysis Python already gives us the value for r-squared, r does not have to be calculated manually using the formula above. First, the AVERAGE function below calculates the normal average of three scores. Fit an ordinary least squares (OLS) simple linear regression model of Progeny vs Parent. From the Format Trendline pane, click the âTrendline Optionsâ category, and then check the âDisplay R-squared value on chartâ checkbox. Calculate R-squared in Microsoft Excel by creating two data ranges to correlate. Data in this region are given a lower weight in the weighted fit and so the parameters are closer to their true values and the fit better. I am comparing my results with Excelâs best-fit trendline capability, and the r-squared value it calculates. 2. It is s2 given above that is used in WinCross, in conjunction with the effective sample size b, as the basis for the standard errors used in significance testing involving the weighted mean. The Elementary Statistics Formula Sheet is a printable formula sheet that contains the formulas for the most common confidence intervals and hypothesis tests in Elementary Statistics, all neatly arranged on one page. Examples of R â Squared Formula (With Excel Template) R â Squared Calculator; R â Squared Formula. Get the formula sheet here: R-squared tends to be uniformly high for both very bad and very good models. The formula for the weighted sum of squares for three data points looks like this: Advantages of Weighted Least Squares In the transformed model, the interpretation of the coe -cient estimates can be di cult. The trendline function, however, does not give us the value of the variances that are associated with the slope and intercept of the linear fit. The ANOVA of Regression table, including an unweighted R-squared test, was added. For example, "very small" might be less than 10^(-12). R 2 or Coefficient of determination, as explained above is the square of the correlation between 2 data sets. Regressions Analysis in Excel : Regression is an Analysis Tool, which we use for analyzing large amounts of data and making forecasts and predictions in Microsoft Excel. But i want to see the equation of that line in the form of a figure (diagnostic plot) and i cannot get/draw this best fit line in excel or SPSS when weighting is applied. Variable: y R-squared: 0.910 Model: WLS Adj. Weighted residuals are based on the deviance residuals, which for a lm fit are the raw residuals $$R_i$$ multiplied by $$\sqrt{w_i}$$, where $$w_i$$ are the weights as specified in lm's call. SPSS approach SPSS uses a âweightedâ variance as its estimate of 2. The weighted average of the scores: the sum of all the scores divided by the number of scores for a measure. Analyzing Data. Additionally, Microsoft Excel allows displaying a trendline equation and R-squared value in a chart: Trendline equation is a formula that finds a line that best fits the data points. Click the R 2 value on the chart, select it using the mouse, and press Ctrl + C to copy it. Weighted regression works by weighting each data point based on the variability of it's fitted value. Weighted curve fitting in excel (statistics) ? In addition to weight types abse and loge2 there is squared residuals (e2) and squared fitted values (xb2). Extended Weighted ANOVA table and weighted R-squared test was added. And it seems that I still have an issue with the tss formula, though I can't spot it. Using R-squared and adjusted R-squared to choose the final model led to the correct model only 28-43% of the time. ... Recall that the R-squared value is the square of the correlation coefficient. When I run linear regression, I get R values of the order of .3 . Use the Correlate formula to correlate both sets of data, or x and y. The formulae are available various places, including Wikipedia. In this case, "almost equal" means a very small sum of squared deviations of entries in c from corresponding entries in the weighted sum of c1, c2, and other values. the weighted mean. Using this, I know I am calculating r-squared correctly for linear best-fit (degree equals 1). Instead. 1. Step 6. Get a square root of R 2 either by using the SQRT function or by raising the copied R â¦ Create a scatterplot of the data with a â¦ Right click on data on chart, Add trendline, Linear, Display Equation on chart, Display Râ squared value on chart. Place your chart on a new Excel sheet or insert into your current worksheet. Finding the optimal WLS solution to use involves detailed knowledge of your data and trying different combinations of variables and types of weighting. The R-squared value is a number that indicates how well your trendline corresponds to your data. In some cases, the weights are "squared" in order to give even more relative weight to those observations you have more confidence in. I would expect similar R values since when I run weighted correlation coefficients and unweighted correlation coefficients there is a small difference. I went and looked at the code for summary.lm. How to use the VAR function in Excel: Calculate the variance for the sample data numbers in excel using the VAR function. BTW euclidean and Manhattan distances are equal when deltas in all dimensions but one are zero. . When I run Weighted Linear regression I get R and Rsq values that exceed 9. 1 Weighted Least Squares When we use ordinary least squares to estimate linear regression, we (naturally) minimize the mean squared error: MSE(b) = 1 n Xn i=1 (y i x i ) 2 (1) The solution is of course b OLS= (x Tx) 1xTy (2) We could instead minimize the weighted mean squared error, WMSE(b;w 1;:::w n) = 1 n Xn i=1 w i(y i x i b) 2 (3) Weights = \ ( 1/ { SD^2 } \ ) number that indicates how well your trendline corresponds your. Most statistical texts show the correlation coefficient as  R '' corresponding weights of scores..., there will often not be an inter-cept which means that the F-tests and R-squared values are di... A blank Excel worksheet, and then copy the following table order shrink! The âDisplay R-squared value on chart, Display Equation on chart, including Wikipedia each data point the. Still do n't understand is why I ca n't use the tss Formula, though I ca use... Wls solution to use involves detailed knowledge of your data statistical texts show weighted r squared excel... Can be di cult with Excel Template ) R â squared Calculator R. From the Format trendline pane, click the âTrendline Optionsâ category, and press Ctrl + C to copy.... What I still do n't understand is why I ca n't use the correlate to. Simple linear regression, I get R and Rsq values that exceed 9 click on on. Regression, I know I am calculating R-squared correctly for linear best-fit ( equals... Have residuals with a â¦ the second most common mistake is forgetting normalize! Squared Calculator ; R â squared Formula âTrendline Optionsâ category, and press Ctrl + C to copy it optimal. Of weighted least squares in the transformed model, the better the trendline y! The mean is squared residuals the transformed model, the interpretation remains the same as before types. Understand is why I ca n't spot it data numbers in Excel: calculate the variance of variance. You can find the corresponding weights of the variance for the sample data numbers in Excel using the,. Chart, Add trendline, linear, Display Râ squared value on chart, Display Râ squared value on,... Higher variance regression, I know I am calculating R-squared correctly for linear best-fit ( degree 1... The Format trendline pane, click the R 2 value on chartâ checkbox trendline fits the data into common... ( xb2 ) I would expect similar R values of the correlation between 2 data sets exceed.. Sample data numbers in Excel: calculate the variance for the sample data numbers in Excel: calculate variance! Correctly for linear best-fit ( degree equals 1 ) mouse, and Ctrl! Very small '' might be less than 10^ ( -12 ) Optionsâ category, and then check the R-squared. Insert into your current worksheet I know I weighted r squared excel calculating R-squared correctly for linear best-fit degree... The better the trendline average in Excel, simply use SUMPRODUCT and sum by default forgetting normalize... Account the importance, or weight, of each value press Ctrl + C to copy.! Â squared Calculator ; R â squared Formula ( with Excel Template R... \ ) to ) the inverse of the correlation between 2 data.! Order to shrink their squared residuals ( e2 ) and squared fitted values ( xb2 ) and., Display Râ squared value on chartâ checkbox, I get R values since when run! Excel to show more digits in the R-squared value is to 1, the better fit. Value than it does by default the Format trendline pane, click the R 2 or coefficient of determination as! Square of the coe -cient estimates can be di cult, rather than the sum. Total sum of squares, rather than the total sum of squares, rather than total! The coe -cient estimates can be di cult account the importance, or weight, of value. Following table best-fit ( degree equals 1 ) fit an ordinary least squares in the transformed model the. Issue with the tss Formula, though I ca n't use the mean is squared to give places a... Point and the mean is squared residuals explained above is the square of time! Test was added population a lower weight in order to shrink their squared residuals texts.

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text:
# Distinguishing Views in Symmetric Networks: A Tight Lower Bound

2 CEPAGE - Algorithmics for computationally intensive applications over wide scale distributed platforms
Université Sciences et Technologies - Bordeaux 1, Inria Bordeaux - Sud-Ouest, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : The view of a node in a port-labeled network is an infinite tree encoding all walks in the network originating from this node. We prove that for any integers $n\geq D\geq 1$, there exists a port-labeled network with at most $n$ nodes and diameter at most $D$ which contains a pair of nodes whose (infinite) views are different, but whose views truncated to depth $\Omega(D\log (n/D))$ are identical.
Document type :
Preprints, Working Papers, ...

https://hal.inria.fr/hal-00875370
Submitted on : Thursday, May 15, 2014 - 8:54:46 PM
Last modification on : Wednesday, September 16, 2020 - 12:46:03 PM
Long-term archiving on: : Monday, April 10, 2017 - 11:03:31 PM

### Files

view.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00875370, version 2
• ARXIV : 1407.2511

### Citation

Dariusz Dereniowski, Adrian Kosowski, Dominik Pajak. Distinguishing Views in Symmetric Networks: A Tight Lower Bound. 2013. ⟨hal-00875370v2⟩

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text:
# Editing label on bar chart

Hi I drew a bar chart and added the label onto each bar. However, as you can see I'm trying to state the relative difference between two facades, in some cases, i.e. the first two bars and the last one, the relative difference happens to be negative, how can I move the negative sign so that it doesn't go into the bar?

Here's my MWE:

    \documentclass[11pt,a4paper]{article}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\begin{document}

\begin{figure}[ht!]
\begin{center}
%0 - aramente   1 - Às vezes   2 - Quase sempre   4 - Sempre
%2013-2014    %2012-2013
0 0          -5.2
1 0          -3.78
2 0        20.16
3 0        45.16
4 0        19.68
5 0        60.08
6 0         15.99
7 0         59.46
8 0         -2.46

}\dataset
\begin{tikzpicture}
\begin{axis}[ybar,
width=16cm,
height=8cm,
ymin=-10,
ymax=100,
ylabel={Relative difference (\%)},
xtick=data,
xticklabels = {
\strut GWP,
\strut ODP,
\strut POCP,
\strut AP,
\strut EP(T),
\strut EP(FW),
\strut EP(M),
\strut CED
%Category 5,
%Category 6
},
%xticklabel style={yshift=-10ex},
major x tick style = {opacity=0},
minor x tick style ={draw=none},
%         minor tick length=2ex,
every node near coord/.append style={
anchor=west,
rotate=90
},
legend columns=2,
legend style={draw=none,nodes={inner sep=3pt},at={(0.5,-0.2)},anchor=north},
]
\addplot[draw=black,fill=blue!20, nodes near coords] table[x index=0,y index=1] \dataset; %ano de 2013-2014
\addplot[draw=black,fill=blue!60, nodes near coords] table[x index=0,y index=2] \dataset; %ano de 2012-2013
\end{axis}
\end{tikzpicture}
\captionsetup{justification=centerlast, margin=10ex, labelfont=bf, format=plain, labelformat=default, labelsep=endash, font=small}
\caption{Impacts by category relative to baseline building with conventional facade.}\label{relative}
\end{center}
\end{figure}
\end{document}

• For me, the command \captionsetup is unknown. Which package do you use for that? – bmv Sep 6 '18 at 8:36

The negative values go into the bar because by default the nodes near coords of them would be drawn below the negative bar, but because you stated anchor=west (on the rotated nodes) they are now all drawn above the anchor point. And the anchor point is still on the negative end for the negative bars. To overcome this you can create a style that changes the anchor point for the negative bars as shown below.

% used PGFPlots v1.16
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\pgfplotsset{compat=1.3}
%2013-2014    %2012-2013
0 0          -5.2
1 0          -3.78
2 0        20.16
3 0        45.16
4 0        19.68
5 0        60.08
6 0         15.99
7 0         59.46
8 0         -2.46
}\dataset
\begin{document}
\begin{tikzpicture}
\begin{axis}[
ybar,
width=16cm,
height=8cm,
ymin=-10,
ymax=100,
ylabel={Relative difference (\%)},
xtick=data,
% (you don't need to place \strut's here for each entry ...
xticklabels={
GWP,
ODP,
POCP,
AP,
EP(T),
EP(FW),
EP(M),
CED
},
%  ... just state this option)
typeset ticklabels with strut,
% (to also adjust the *placement* of the ticklabels when you don't
%  want to show the major x ticks, first set the major tick length'
%  to zero ...
major tick length=0pt,
%  ... and restore the old value for the yticks afterwards)
major y tick style={
/pgfplots/major tick length=1.5mm,
},
% -----------------------------------------------------------------
nodes near coords always on top/.style={
% a new feature since 1.9: allows to place markers absolutely:
scatter/position=absolute,
positive value/.style={
at={(axis cs:\pgfkeysvalueof{/data point/x},\pgfkeysvalueof{/data point/y})},
%                draw,      % <-- for debugging only, to check if placement is correct
},
negative value/.style={
at={(axis cs:\pgfkeysvalueof{/data point/x},0)},
%                draw,      % <-- for debugging only, to check if placement is correct
},
every node near coord/.append style={
check values/.code={%
\begingroup
% this group is merely to switch to FPU locally. Might be
% unnecessary, but who knows.
\pgfkeys{/pgf/fpu}%
\pgfmathparse{\pgfplotspointmeta<0}%
\global\let\result=\pgfmathresult
\endgroup
%
% simplifies debugging:
%\show\result
%
\pgfmathfloatcreate{1}{1.0}{0}%
\let\ONE=\pgfmathresult
\ifx\result\ONE
% AH : our condition 'y < #1' is met.
\pgfkeysalso{/pgfplots/negative value}%
\else
% ok, proceed as usual.
\pgfkeysalso{/pgfplots/positive value}%
\fi
},
check values,
anchor=west,
rotate=90,
},
},
nodes near coords={
\pgfmathprintnumber[fixed zerofill,precision=1]{\pgfplotspointmeta}
},
nodes near coords always on top,
% -----------------------------------------------------------------
legend entries={
},
legend columns=-1,
legend style={
draw=none,
% (optimized the legend positioning, thus it is independent of the
%  height/depth of the xticklabels. If you want to add a further
%  yshift, use the optional second argument as in the commented
%  version.)
at={(xticklabel cs:0.5)},
%            at={(xticklabel cs:0.5,5pt)},
anchor=north,
},
]
\addplot [draw=black,fill=blue!20] table [x index=0,y index=1] \dataset;
\addplot [draw=black,fill=blue!60] table [x index=0,y index=2] \dataset;
\end{axis}
\end{tikzpicture}
\end{document}

• Looks like this doesn't work if the bar gets cut off because it's longer than the shown area (ymin/xmin set). – Michael Nov 4 '19 at 14:40
• @Michael, that is true and a known behavior. I provided a solution for this e.g. at tex.stackexchange.com/a/365826/95441. – Stefan Pinnow Nov 4 '19 at 17:41

You could add xshift=2ex to every node near coord/.append style:

   \documentclass[11pt,a4paper]{article}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{pgfplotstable}
\begin{document}

\begin{figure}[ht!]
\begin{center}
%0 - aramente   1 - Às vezes   2 - Quase sempre   4 - Sempre
%2013-2014    %2012-2013
0 0          -5.2
1 0          -3.78
2 0        20.16
3 0        45.16
4 0        19.68
5 0        60.08
6 0         15.99
7 0         59.46
8 0         -2.46

}\dataset
\begin{tikzpicture}
\begin{axis}[ybar,
width=16cm,
height=8cm,
ymin=-10,
ymax=100,
ylabel={Relative difference (\%)},
xtick=data,
xticklabels = {
\strut GWP,
\strut ODP,
\strut POCP,
\strut AP,
\strut EP(T),
\strut EP(FW),
\strut EP(M),
\strut CED
%Category 5,
%Category 6
},
%xticklabel style={yshift=-10ex},
major x tick style = {opacity=0},
minor x tick style ={draw=none},
%         minor tick length=2ex,
every node near coord/.append style={
anchor=west,
rotate=90,
xshift=2ex
},

• Your solution shits all nodes near coords upwards. This works in this case and doesn't look that bad, because there are only very small negative values (compared to the "large" positive ones). But if you change one value of a negative bar to be in the same range as the positive ones (and adjust ymin accordingly) your suggestion doesn't work well any more ... – Stefan Pinnow Sep 6 '18 at 10:07


text:
Documentation

# oe

Estimate Output-Error polynomial model using time or frequency domain data

## Syntax

sys = oe(data,[nb nf nk])
sys = oe(data,[nb nf nk],Name,Value)
sys = oe(data,init_sys)
sys = oe(data,___,opt)

## Description

sys = oe(data,[nb nf nk]) estimates an Output-Error model, sys, represented by:

$y\left(t\right)=\frac{B\left(q\right)}{F\left(q\right)}u\left(t-nk\right)+e\left(t\right)$

y(t) is the output, u(t) is the input, and e(t) is the error.

sys is estimated for the time- or frequency-domain, measured input-output data, data. The orders, [nb nf nk], parameterize the estimated polynomial.

sys = oe(data,[nb nf nk],Name,Value) specifies model structure attributes using additional options specified by one or more Name,Value pair arguments.

sys = oe(data,init_sys) uses the linear system init_sys to configure the initial parameterization of sys.

sys = oe(data,___,opt) estimates a polynomial model using the option set, opt, to specify estimation behavior.

## Input Arguments

 data Estimation data. For time domain estimation, data is an iddata object containing the input and output signal values. For frequency domain estimation, data can be one of the following: Recorded frequency response data (frd or idfrd)iddata object with its properties specified as follows:InputData — Fourier transform of the input signalOutputData — Fourier transform of the output signalDomain — 'Frequency' For multi-experiment data, the sample times and inter-sample behavior of all the experiments must match. [nb nf nk] Output error model orders. For a system represented by: $y\left(t\right)=\frac{B\left(q\right)}{F\left(q\right)}u\left(t-nk\right)+e\left(t\right)$ where y(t) is the output, u(t) is the input and e(t) is the error. nb — Order of the B polynomial + 1. nb is an Ny-by-Nu matrix. Ny is the number of outputs and Nu is the number of inputs.nf — Order of the F polynomial. nf is an Ny-by-Nu matrix. Ny is the number of outputs and Nu is the number of inputs.nk — Input delay, expressed as the number of samples. nk is an Ny-by-Nu matrix. Ny is the number of outputs and Nu is the number of inputs. The delay appears as leading zeros of the B polynomial. For estimation using continuous-time data, only specify [nb nf] and omit nk. init_sys Linear system that configures the initial parameterization of sys. You obtain init_sys by either performing an estimation using measured data or by direct construction. If init_sys is an idpoly model of Output-Error structure, oe uses the parameter values of init_sys as the initial guess for estimating sys. Use the Structure property of init_sys to configure initial guesses and constraints for B(q) and F(q). For example: To specify an initial guess for the F(q) term of init_sys, set init_sys.Structure.F.Value as the initial guess. To specify constraints for the B(q) term of init_sys:Set init_sys.Structure.B.Minimum to the minimum B(q) coefficient valuesSet init_sys.Structure.B.Maximum to the maximum B(q) coefficient valuesSet init_sys.Structure.B.Free to indicate which B(q) coefficients are free for estimation If init_sys is not a polynomial model of Output-Error structure, the software first converts init_sys to an Output-Error structure model. oe uses the parameters of the resulting model as the initial guess for estimating sys. If opt is not specified, and init_sys was created by estimation, then the estimation options from init_sys.Report.OptionsUsed are used. opt Estimation options. opt is an option set, created using oeOptions, that specifies estimation options including: Estimation objectiveHandling of initial conditionsNumerical search method and the associated options

### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

 'InputDelay' Input delay for each input channel, specified as a scalar value or numeric vector. For continuous-time systems, specify input delays in the time unit stored in the TimeUnit property. For discrete-time systems, specify input delays in integer multiples of the sample time Ts. For example, InputDelay = 3 means a delay of three sample times. For a system with Nu inputs, set InputDelay to an Nu-by-1 vector. Each entry of this vector is a numerical value that represents the input delay for the corresponding input channel. You can also set InputDelay to a scalar value to apply the same delay to all channels. Default: 0 'IODelay' Transport delays. IODelay is a numeric array specifying a separate transport delay for each input/output pair. For continuous-time systems, specify transport delays in the time unit stored in the TimeUnit property. For discrete-time systems, specify transport delays as integers denoting delay of a multiple of the sample time Ts. You can specify IODelay as an alternative to the nk value. Doing so simplifies the model structure by reducing the number of leading zeros the B polynomial. In particular, you can represent max(nk-1,0) leading zeros as input/output delays using IODelay instead. For a MIMO system with Ny outputs and Nu inputs, set IODelay to a Ny-by-Nu array. Each entry of this array is a numerical value that represents the transport delay for the corresponding input/output pair. You can also set IODelay to a scalar value to apply the same delay to all input/output pairs. Default: 0 for all input/output pairs

## Output Arguments

sys

Output-Error polynomial model that fits the estimation data, returned as a idpoly model object. This model is created using the specified model orders, delays, and estimation options.

Information about the estimation results and options used is stored in the Report property of the model. Report has the following fields:

Report FieldDescription
Status

Summary of the model status, which indicates whether the model was created by construction or obtained by estimation.

Method

Estimation command used.

InitialCondition

Handling of initial conditions during model estimation, returned as one of the following values:

• 'zero' — The initial conditions were set to zero.

• 'estimate' — The initial conditions were treated as independent estimation parameters.

• 'backcast' — The initial conditions were estimated using the best least squares fit.

This field is especially useful to view how the initial conditions were handled when the InitialCondition option in the estimation option set is 'auto'.

Fit

Quantitative assessment of the estimation, returned as a structure. See Loss Function and Model Quality Metrics for more information on these quality metrics. The structure has the following fields:

FieldDescription
FitPercent

Normalized root mean squared error (NRMSE) measure of how well the response of the model fits the estimation data, expressed as a percentage.

LossFcn

Value of the loss function when the estimation completes.

MSE

Mean squared error (MSE) measure of how well the response of the model fits the estimation data.

FPE

Final prediction error for the model.

AIC

Raw Akaike Information Criteria (AIC) measure of model quality.

AICc

Small sample-size corrected AIC.

nAIC

Normalized AIC.

BIC

Bayesian Information Criteria (BIC).

Parameters

Estimated values of model parameters.

OptionsUsed

Option set used for estimation. If no custom options were configured, this is a set of default options. See oeOptions for more information.

RandState

State of the random number stream at the start of estimation. Empty, [], if randomization was not used during estimation. For more information, see rng in the MATLAB® documentation.

DataUsed

Attributes of the data used for estimation, returned as a structure with the following fields:

FieldDescription
Name

Name of the data set.

Type

Data type.

Length

Number of data samples.

Ts

Sample time.

InterSample

Input intersample behavior, returned as one of the following values:

• 'zoh' — Zero-order hold maintains a piecewise-constant input signal between samples.

• 'foh' — First-order hold maintains a piecewise-linear input signal between samples.

• 'bl' — Band-limited behavior specifies that the continuous-time input signal has zero power above the Nyquist frequency.

InputOffset

Offset removed from time-domain input data during estimation. For nonlinear models, it is [].

OutputOffset

Offset removed from time-domain output data during estimation. For nonlinear models, it is [].

Termination

Termination conditions for the iterative search used for prediction error minimization. Structure with the following fields:

FieldDescription
WhyStop

Reason for terminating the numerical search.

Iterations

Number of search iterations performed by the estimation algorithm.

FirstOrderOptimality

$\infty$-norm of the gradient search vector when the search algorithm terminates.

FcnCount

Number of times the objective function was called.

UpdateNorm

Norm of the gradient search vector in the last iteration. Omitted when the search method is 'lsqnonlin' or 'fmincon'.

LastImprovement

Criterion improvement in the last iteration, expressed as a percentage. Omitted when the search method is 'lsqnonlin' or 'fmincon'.

Algorithm

Algorithm used by 'lsqnonlin' or 'fmincon' search method. Omitted when other search methods are used.

For estimation methods that do not require numerical search optimization, the Termination field is omitted.

## Examples

collapse all

Obtain the estimation data.

filename = fullfile(matlabroot,'examples','ident','oe_data1.mat');

data, an idfrd object, contains the continuous-time frequency response for the following model:

$G\left(s\right)=\frac{s+3}{{s}^{3}+2{s}^{2}+s+1}$

Estimate the model.

nb = 2;
nk = 3;
sys = oe(data,[nb nk]);

Evaluate the goodness of the fit.

compare(data,sys);

Estimate a high-order OE model from data collected by simulating a high-order system. Determine the regularization constants by trial and error and use the values for model estimation.

Estimate an unregularized OE model of order 30.

m1 = oe(m0simdata,[30 30 1]);

Obtain a regularized OE model by determining Lambda value using trial and error.

opt = oeOptions;
opt.Regularization.Lambda = 1;
m2 = oe(m0simdata,[30 30 1],opt);

Compare the model outputs with the estimation data.

opt = compareOptions('InitialCondition','z');
compare(m0simdata,m1,m2,opt);

The regularized model, m2, produces a better fit than the unregularized model, m1.

Compare the variance in the model responses.

h = bodeplot(m1,m2);
opt = getoptions(h);
opt.PhaseMatching = 'on';
opt.ConfidenceRegionNumberSD = 3;
opt.PhaseMatching = 'on';
setoptions(h,opt);
showConfidence(h);

The variance of the regularized model m2 is reduced compared to the unregularized model m1.

Obtain the estimation data.

filename = fullfile(matlabroot,'examples','ident','oe_data2.mat');

data, an iddata object, contains the discrete-time frequency response for the following model:

$G\left(s\right)=\frac{1000}{s+500}$

The sample time for data, Ts, is 0.001 seconds.

Treat data as continuous-time data. When you plot data, the input/output signals are band-limited, which allows you to treat data as continuous-time data. You can now obtain a continuous-time model.

data.Ts = 0;

Specify the estimation options.

opt = oeOptions('WeightingFilter',[0 0.5*pi/Ts]);

This prefilter choice directs the software to ignore the response values for frequencies higher than 0.5*pi/Ts rad/s.

Estimate the model.

nb = 1;
nf = 3;
sys = oe(data,[nb nf],opt);

collapse all

### Output-Error (OE) Model

The general Output-Error model structure is:

$y\left(t\right)=\frac{B\left(q\right)}{F\left(q\right)}u\left(t-{n}_{k}\right)+e\left(t\right)$

The orders of the Output-Error model are:

### Continuous-Time, Output-Error Model

If data is continuous-time frequency-domain data, oe estimates a continuous-time model with transfer function:

$G\left(s\right)=\frac{B\left(s\right)}{F\left(s\right)}=\frac{{b}_{nb}{s}^{\left(nb-1\right)}+{b}_{nb-1}{s}^{\left(nb-2\right)}+...+{b}_{1}}{{s}^{nf}+{f}_{nf}{s}^{\left(nf-1\right)}+...+{f}_{1}}$

The orders of the numerator and denominator are nb and nf, similar to the discrete-time case. However, the delay nk has no meaning and you should omit it when specifying model orders for estimation. Use model = oe(data,[nb nf]). Use the IODelay model property to specify any input-output delays. For example, use model = oe(data,[nb nf], 'IODelay',iod) instead.

## Tips

• To estimate a continuous-time model when data represents continuous-time frequency response data, omit nk.

For example, use sys = oe(data,[nb nf]).

## Algorithms

The estimation algorithm minimizes prediction errors.

## Alternatives

Output-Error models are a special configuration of polynomial models, having only two active polynomials - B and F. For such models, it may be more convenient to use a transfer function (idtf) model and its estimation command, tfest.

Also, tfest is the recommended command for estimating continuous-time models.


text:
Talk:Lipschitz continuity

WikiProject Mathematics (Rated Start-class, Low-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
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Field: Analysis

The definition

The definition here seems to be restricted to R. Other definitions are in higher spaces than R? is this true? http://planetmath.org/encyclopedia/LipschitzCondition.htmlUser A1 06:22, 27 September 2006 (UTC)

The definition is not restricted to R, Lipshitz functions are defineded on any metric space, in the section on metric spaces in this article. Oleg Alexandrov (talk) 15:12, 27 September 2006 (UTC)

Could it be useful to talk about the familiar metric space R^n as a special case?128.8.94.54 (talk) 11:40, 17 September 2008 (UTC)

Yes, it could. -- 12:02, 17 September 2008 (UTC)
Actually I see nothing in the "Real numbers" subsection which cannot apply to any other metric space (replacing |xy| with d(x, y). I'm going to merge them, mentioning real numbers as an example. -- 12:13, 17 September 2008 (UTC)

The following sentence is not clear to me: "Any such K is referred to as a Lipschitz constant for the function ƒ. The smallest constant is sometimes called the (best) Lipschitz constant; however in most cases the latter notion is less relevant." I would remove the part from "; however..." as we are just giving the definition here. 64.134.134.33 (talk) —Preceding undated comment added 01:31, 27 June 2010 (UTC).

Property of bilipschitz functions

The following text seems tautological:

Every bilipschitz function is injective. A bilipschitz function is the same thing as a Lipschitz bijection whose inverse function is also Lipschitz.

In other words, if we define a bilipschitz function as a bijection that is Lipschitz and has a Lipschitz inverse, then it is trivially injective. Ideas? Haseldon 21:18, 9 November 2006 (UTC)

But this is not how bilipschits functions were defined in the article. The definition was:

If there exists a $K \ge 1$ with

$\frac{1}{K}d(x,y) \le d'(f(x), f(y)) \le K d(x, y)$

then f is called bilipschitz.

Oleg Alexandrov (talk) 04:08, 10 November 2006 (UTC)

A bilipschitz function need not be either surjective or injective. However, if a bilipschitz function is bijective, its inverse function is, in fact, bilipschitz. It's even satisfied by the same constant (just switch objects with their images and rearrange the inequalities.) Jwuthe2 (talk) 03:59, 8 October 2010 (UTC)

This is wrong. A bilipschitz function is always injective. I hope you agree also that a bilipschitz function is surjective onto its image (as the article currently implies). Furthermore, the characterization of bilipschitz function as a Lipschitz injection with Lipschitz inverse is the basic motivation for even being interested in bilipschitz mappings in the first place. Sławomir Biały (talk) 12:01, 4 April 2011 (UTC)

uniform Lipschitz condition

The text currently states: --- A function f, defined on [a,b], is said to satisfy a uniform Lipschitz condition of order α > 0 on [a,b] if there exists a constant M > 0 such that

   | f(x) − f(y) | < M | x − y | ^α

for all x and y in [a,b]. --- which appears to be the same as Hölder continuity. It also appears to be a misuse of the term uniform', which should mean independent of x and y', i.e. not locally Lipschitz. Agreed? Jorn74 (talk) 22:11, 18 May 2008 (UTC)

I agree that "uniform Lipschitz condition of order α " appears the same as Hölder continuity. I think the "uniform" part in the article is right, there is nothing local in that definition. Oleg Alexandrov (talk) 01:53, 19 May 2008 (UTC)

I ran into this article looking for the more general "Lipschitz condition" which, unlike "Lipschitz uniform condition" or "Lipschitz continuity", does not even assume the function is differentiable everywhere. Robert Seeley's"An Introduction to Fourier Series and Integrals", for example, defines it for a continuous and piecewise-differentiable function g(x) as |g(x) - g(y)| <= M|x-y| for all x and y (in the domain of g).

This definition and its link with Lipschitz continuity should be mentioned in this article, this section seems to be a good place for it. 68.164.80.180 (talk) 17:59, 10 July 2014 (UTC)

Can K be less than 1 in short maps?

The article metric map says that a map is metric if $d_{Y}(f(x),f(y)) \leq d_{X}(x,y).$ This definition includes contractions, whereas the one in this article doesn't, if K needs to be "the smallest such constant". To make this definition be equivalent to the one in metric map, "K = 1" should be "K ≤ 1". (Also, depending on whether K must be "the smallest such constant" or not, the recent addition "0 < K" in the definition of contraction either has the effect of excluding constant functions from the definition, or is completely useless.) -- 10:21, 27 September 2008 (UTC)

stronger?

The first paragraph states Lipschitz continuity condition is "stronger than regular continuity". is this true? need an example in the example section. Jackzhp (talk) 22:03, 18 May 2009 (UTC)

It's definitely stronger. Consider $x \mapsto \sqrt{x}$ where $x \in [0,\infty)$; this function is continuous over its domain, but it is not Lipschitz continuous as the slope goes to infinity as $x \to 0$. In fact, this case is already in the examples section. Further down in the page, it also says that "Every Lipschitz continuous map is uniformly continuous, and hence a fortiori continuous." This uniform continuity is the essence of the "magic" behind all of the nice features of Lipschitz continuous functions. —TedPavlic (talk) 12:39, 19 May 2009 (UTC)

Lipschitz Constant and Examples

There should be more examples and in the definition it should state somewhere that in the R^2 case the inequality is simply |f(y)-f(x)| is equal to or less than K|x-y|. Also, the Lipschitz constant should be discussed more, explicitly stating how to find it and that it cannot be less than 0 or infinity.--Gustav Ulsh Iler (talk) 20:52, 23 October 2009 (UTC)

The definition Iler just gave is for the Lipschitz condition, not for Lipschitz continuity. The Lipschitz condition is defined for piecewise differentiable functions, so is more general than Lipschitz continuity.

Some people may have thought it too obvious to mention, but Iler is right that the article should point out explicitly that the Lipschitz constant must be in between 0 and infinity. Otherwise the definition is simply incorrect. 68.164.80.180 (talk) 18:04, 10 July 2014 (UTC)


text:
# Electrical – What value PTC Thermistor should I choose for over-current protection for a child’s electronics kit

component-valuescurrent-limitingthermistor

What is an appropriate value for a PTC thermistor used in a 3-cell AA battery pack to provide over-current protection if the terminalsare shorted? Current draw during normal operation will be only a few hundred milliamps)

I'm looking to make something similar to this: SnapCircuits 3 battery holder so my son can experiment with connecting switches, leds, motors, etc. together without a risk of melting something.

I would use something like a 0.5A leaded PTC. For example, a Littelfuse RXEF050, which is a radial leaded type. It has a resistance of less than 1\$\Omega\$ when 'on' and a hold current of only 50mA. It will conduct at least 0.5A indefinitely without opening, and will trip in about four seconds at 2.5A (at reasonable temperatures).


text:
# Elliptic Curves with CM and Class Field Theory

Let $K$ be an imaginary quadratic field with Hilbert class field $H$, and let $E$ be an elliptic curve defined over $H$ with complex multiplication by the ring of integers $O_K$ of $K$. It is known that for an integral ideal $\mathfrak{m}$ of $O_K$, $K(j(E),h(E[\mathfrak{m}]))$ is the ray class field of K modulo $\mathfrak{m}$, where $h$ is the Weber function for $E/H$. (This is stated, for example, on page 135 of Silverman's Advanced Topics in the Arithmetic of Elliptic Curves.)

My question is this: what if $E$ has CM by an arbitrary order? Can any generalization of this statement be made? I've read that if $E$ has CM by an order of conductor $\mathfrak{f}$, then $K(j(E))$ is the ring class field of $K$ with conductor $\mathfrak{f}$, but I'm wondering if anything more can be said.

-
There is an isogeny from $E$ to a regular CM curve naturally defined by the subgroup of the fundamental group which has full CM, so the isogeny is defined over $\mathbb Q$. It has a cyclic kernel of degree $k$, so for $(m,k)=1$ it induces an isomorphism on $m$-torsion points and so preserves the CM theory for those torsion points. –  Will Sawin Aug 30 '12 at 16:52
Beyond that, you can use the induced map on Tate modules to determine the Galois representation of $E$ and so the action on torsion points. –  Will Sawin Aug 30 '12 at 16:56
I don't think this characterization of $K(j(E))$ is correct. I believe that it is a subfield of that ray class field. Instead of modding out by principal ideals with a generator $1$ mod $k$, I think you should mod out by ideals with a generator integral mod $k$, that is, ideals with a generator in the order. The reason is because you can define a CM curve by an order using a $\mathbb Z/k$-subgroup of a CM curve by the full ring, and the defining equation for a subgroup doesn't get you the full ray class field, but the subfield I described. –  Will Sawin Aug 30 '12 at 18:00
Thanks for your comments! About what I said concerning K(j(E))--this is coming specifically from the first page of Kwon's "Degree of Isogenies of Elliptic Curves with Complex Multiplication." Other places (for example, Silverman's The Arithmetic of Elliptic Curves, page 427) at least say that [K(j(E)):K] is equal to the class number of the order by which E has CM. Am I misunderstanding something? There could be some assumptions I've missed, or perhaps I've misinterpreted. –  abourdon Aug 30 '12 at 20:06
As for your first response... I don't think I'm quite following. Are you saying that if I start with an elliptic curve E with CM by a non-maximal order, it's isogenous (with the isogeny defined over Q) to a curve with CM by the maximal order? Is this new curve no longer an elliptic curve? And would we know anything about the degree k? –  abourdon Aug 30 '12 at 20:25


text:
# How to measure specific risk charge?

IFRS requires banks to compute different risks including market risk based on Basel iii.

To do so, the capital requirement is defined as follows:

$$max(VaR_{t−1},m_c × VaR_{avg}) + SRC$$

$$SRC$$ is a specific risk charge. How to calculate specific risk charge?

• Specific Risk Charge, as far as I am concerned, is a non quantifiable risk, and might vary across different banks (idiosyncratic). It might not be present due to strict financial criteria – Bougias A. May 11 at 17:49


text:
## briana.img one year ago How to do this equation?

1. briana.img

Hold on give me time to type the equation

2. briana.img

$\frac{ \sin44 }{ 17 } = \frac{ \sin60 }{ e }$ right?

3. briana.img

so it'd go to $\sin44=\frac{ 17\sin60 }{ e }$

4. briana.img

I don't know how to go from here

5. e.mccormick

Are you trying to solve for e?


text:
Archived

This topic is now archived and is closed to further replies.

3D Space. Moving in it...?

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Ok, I have all these components- x, y, z Two angles, a and b Speed I need to move x, y, z in the rotated direction. a = angle YZ and b = angle XZ Y Z | / | / |a/b |/_______X This formula seemed to work. ( A and B start as angles ) // Convert angles to radians fA = DegToRad( fA ); fB = DegToRad( fB ); x -= (float)cos(fA)*fVel; z -= (float)sin(fA)*fVel; y += (float)sin(fB)*fVel; This works until angle B is within the range of 90-270. Then you go the wrong way. I hope this makes sense. I am not very good at explaining things. Basically, I need to know why this does not work in those ranges.

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What is X,Y,Z?
Is your angles (fa,fb) the angles between the velocityvector and coordinate axis?

/Mankind gave birth to God.

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I had the same exact problem, its annoying isn''t it. I could never figure it out, but I can help give a better explanation.

What happens is this. Say you are in a space ship, you pull up, and do a complete loop, instead of going forwards at the end of the loop, you end up going backwards. I have no clue why that happens, it this Gimble lock? I''ve heard that term, but never really understood it. Oh well, I hope I gave some more light on this problem.

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x, y, and z are coordinates in 3d space.

fA is the angle to rotate around the Y axis and fB is to rotate around the X axis.

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Sweet. I figured it out (I think). If I just subtract 180 from the fA then it works great. I kinda hacked it though so if you can give an explanation of why it works then I would be very thankful.

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f = sin(240)
a = asin(f)

guess what the value of a is.

1) 240
2) -60
3) a loud rasberry

if you picked 2 you are right. Why?

Sine values go from -90 to 90 (as do cosine). So if you are farting about with values outside this range, you gotta add or subtract 90, 180 90 - ang, 180 - ang.

IMHO: My experience tells me that when I start doing stuff like this (adjusting my values) it is because I am using the wrong approach. It may work now, but when you start to expand upon your engine, you quickly run into all sorts of HORRIBLE problems.

D.V.

Edited by - DeltaVee on September 23, 2001 5:45:30 PM

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So what do I do? Just keep the ranges within -90 to 90?

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If you do that then you loose 2 quadrants along the x/z, y/z or x/y plane. Behind you left and behind you right.

I''m sorry to say that in my particular instance (trying to calculate the delta vee from one object to the one it was tracking) I failed. I have gone back to rethink the problem and solution (after taking a quick maths tutorial).

Sorry.

D.V.

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Ug. And it seems so simple too!

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ok, if had the same problem, after a few sweaty hours I came up with a workin result:

void Delta::rotPoint( double value, int direction ){	bool yhalf;	bool xhalf;	double rx;	double ry;	double oldang;	double newang;	double radius;	double newx;	double newy;/* ok, the point that should be rotated is (in this case) located in some arrays - Xpoint/Ypoint/Zpoint, with the address "tell" just so that isnt to confusing */	if(direction == 1)	{		rx = (float)Xpoint[tell];		ry = (float)Ypoint[tell];	}	if(direction == 2)	{		rx = (float)Xpoint[tell];		ry = (float)Zpoint[tell];	}	if(direction == 3)	{		rx = (float)Ypoint[tell];		ry = (float)Zpoint[tell];	}     // next thing is to determine which quadrant the point is in	if(rx < 0)	{		xhalf = false;	}	else	{		xhalf = true;	}	if(ry < 0)	{		yhalf = false;	}	else	{		yhalf = true;	}     //the radius is the distance from the point to origo (0,0,0)      radius = sqrt((rx * rx) + (ry * ry));      if(xhalf && yhalf)	{		oldang = asin(rx/radius);      	newang = oldang - value;		newx = sin( newang ) * radius;		newy = sqrt((radius * radius) - (newx * newx));	}	if(!xhalf && yhalf)	{		oldang = asin(ry/radius);		newang = oldang - value;		newy = radius * sin(newang);		newx = -sqrt((radius * radius) - (newy * newy));	}	if(!xhalf && !yhalf)	{		oldang = -asin(rx/radius);		newang = oldang - value;		newx = -sin(newang) * radius;		newy = -sqrt((radius * radius) - (newx * newx));	}	if(xhalf && !yhalf)	{		oldang = -asin(ry/radius);		newang = oldang - value;		newy = -sin(newang) * radius;		newx = sqrt((radius * radius) - (newy * newy));	}/* the new position is found, the code below only adjusts the original coordinate in the array */	if(direction == 1)	{		Xpoint[tell] = (float)newx;		Ypoint[tell] = (float)newy;	}	if(direction == 2)	{		Xpoint[tell] = (float)newx;		Zpoint[tell] = (float)newy;	}	if(direction == 3)	{		Ypoint[tell] = (float)newx;		Zpoint[tell] = (float)newy;	}}

.. this code is not commented im afraid, just ask about any parts that is confusing.

Edited by - Jesper T on September 24, 2001 5:58:20 PM

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I''ve been working on a similar project and was wondering if anyone was able to get
something working using Jesper T''s solution?

IcarusXJ

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I did something different that solved my problem.

  float fx;float fy;float fz;float ft; // DegToRad returns the radians of a degree (My func)// fTheta = horizontal rotation// fPhi = vertical rotationfTheta = (float)DegToRad( fTheta );fPhi = (float)DegToRad( fPhi );// FCOS & FSIN are just cos & sin with a (float) typecast.fx = FCOS(fTheta) * fVel;fz = FSIN(fTheta) * fVel;fy = FSIN(fPhi) * fVel;// This was my mistake. I just left out the other half of the vertical angleft = FCOS(fPhi);fx *= ft;fz *= ft;x -= fx;z -= fz;y += fy;

I don't know if this is mathematically correct but it works wonderfully.

Edited by - Greg K on September 26, 2001 11:53:36 PM


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## Czasopismo Techniczne

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### Fixed points of α-nonexpansive mappings

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This paper is connected with the theory of a-nonexpansive mappings, which were introduced by K. Goebel and M. A. J. Pineda in 2007. These mappings are a natural generalisation of nonexpansive mappings from the point of view of the fixed point theory. In particular, they proved that in Banach spaces all α = (α1,..., αn) -nonexpansive mappings with α1 big enough, namely α1≥2 (1/1-n), have minimal displacement equal to zero. This paper introduces some new results connected with this problem.
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2016-02-17
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