text:
J E L L Y E N T

It’s a holdover from the Netscape days:

Missing digits are dealt with as 0[…]. An vulgar digit is merely interpreted as 0. Shall we embrace the values #F0F0F0, F0F0F0, F0F0F, #FxFxFx and FxFxFx are the ultimate an identical.

Or no longer it is a protracted manner from the weblog put up A tiny bit of rant about Microsoft Files superhighway Explorer’s color parsing which covers it in fat ingredient, including diverse lengths of color values, and a lot of others.

If we attach collectively the foundations in flip from the weblog put up, we buy the next:

1. Change all nonvalid hexadecimal characters with 0’s:

chucknorris turns into c00c0000000

2. Pad out to the next total sequence of characters divisible by 3 (11 → 12):

c00c 0000 0000

3. Rupture up into three equal groups, with every fragment representing the corresponding color fragment of an RGB color:

RGB (c00c, 0000, 0000)

4. Truncate every of the arguments from the expansive manufacture correct down to 2 characters.

Which, for the length of the shatter, affords the next end result:

RGB (c0, 00, 00) = #C00000 or RGB(192, 0, 0)

Right here’s an instance demonstrating the bgcolor attribute in action, to originate this “pleasant” color swatch:

chuck norris
Mr T
ninjaturtle

in unhappy health
crap
grass

This furthermore answers the different fragment of the quiz: Why does bgcolor="chucknorr" originate a yellow color? Neatly, if we attach collectively the foundations, the string is:

c00c00000 => c00 c00 000 => c0 c0 00 [RGB(192, 192, 0)]

Which offers a gentle-weight yellow gold color. Because the string begins off as 9 characters, we retain the 2nd ‘C’ this time spherical, hence it finally ends up for the length of the ultimate color rate.

I first and most beneficial encountered this when somebody identified that it is useful to presumably plot color="crap" and, successfully, it comes out brown.


text:
### 7.6. The \signaturepage command

Place a \signaturepage command just before the \end{document} that ends your file. Each member of your committee must sign this page to certify they are satisfied with your work.

format: plain


text:
In: Physics

# Salaries for teachers in a particular elementary school district are normally distributed with a mean of...

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $46,000 and a standard deviation of$4,900. We randomly survey ten teachers from that district. (Round your answers to the nearest dollar.)

(a) Find the 90th percentile for an individual teacher's salary.

(b) Find the 90th percentile for the average teacher's salary.

## Solutions

##### Expert Solution

let,

if a random sample of size n is drawn from the population, then as n increases, the random variable which consists of sample means, tends to be normally distributed and

According to central limit theorem for sample means or averages, when larger and larger samples are drawn from the population and their means are calculated, it is found that the sample means form their own normal distribution and the normal distribution has mean same as the original distribution and the variance equal to original variance divided by n.

(note: variance is the square of standard deviation)

The random variable has different values of z scores associated with it, which is given as follows:

where is the value of in one sample

Note that,

whereas,

and is given by

a) For an individual teacher's salary, the sample size is 1

The mean and standard deviation for the distribution are:

Now for calculating the 90th percentile, we use NORM.INV function of Excel which has format NORM.INV(probability,mean,standard deviation)

Here, we have to calculate the 90th percentile for an individual teacher's salary, which indicates the salary below which 90% of the individual teachers fall.

Thus we have to find

we make the use of excel for finding value of Z

thus using NORM.INV(probability,mean,standard deviation) = NORM.INV(0.90,46000,4900), we get the required value of salary as 52280 i.e $52,280 Thus the 90th percentile for individual teacher's salary is$ 52,280

b) For the average teacher's salary, the sample size is 10

Thus the mean and standard deviation for the distribution are:

Now using NORM.INV function of Excel to calculate 90th percentile as in part a),

NORM.INV(probability,mean,standard deviation) = NORM.INV(0.90,46000,1550) we get required value of salary as 47986 i.e $47,986 Thus the 90th percentile for the average teacher's salary is$ 47,986.

## Related Solutions

##### Salaries for teachers in a particular elementary school district are normally distributed with a mean of...
Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of$6,500. We randomly survey ten teachers from that district. 1.Find the probability that the teachers earn a total of over $400,000 2.If we surveyed 70 teachers instead of ten, graphically, how would that change the distribution in part d? 3.If each of the 70 teachers received a$3,000 raise, graphically, how would that change the distribution in part...
##### Salaries for teachers in a particular elementary school district are normally distributed with a mean of...
Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of$6,500. We randomly survey ten teachers from that district. Find the 85th percentile for the sum of the sampled teacher's salaries to 2 decimal places.
##### A researcher claims that the mean of the salaries of elementary school teachers is greater than...
A researcher claims that the mean of the salaries of elementary school teachers is greater than the mean of the salaries of secondary school teachers in a large school district. The mean of the salaries of a random sample of 26 elementary school teachers is $48,250 and the sample standard deviation is$3900. The mean of the salaries of 24 randomly selected secondary school teachers is $45,630 with a sample standard deviation of$5530. At ? = 0.05, can it...
##### A study was conducted to estimate the difference in the mean salaries of elementary school teachers...
A study was conducted to estimate the difference in the mean salaries of elementary school teachers from two neighboring states. A sample of 10 teachers from the Indiana had a mean salary of $28,900 with a standard deviation of$2300. A sample of 14 teachers from Michigan had a mean salary of $30,300 with a standard deviation of$2100. Determine a 95% confidence interval for the difference between the mean salary in Indiana and Michigan.(Assume population variances are different.) *Include...
##### A study was conducted to determine if the salaries of elementary school teachers from two neighboring...
A study was conducted to determine if the salaries of elementary school teachers from two neighboring districts were equal. A sample of 15 teachers from each district was randomly selected. The mean from the first district was $28,900 with a standard deviation of$2300. The mean from the second district was $30,300 with a standard deviation of$2100. Assume the samples are random, independent, and come from populations that are normally distributed. Construct a 95% confidence interval for μ1 -...
##### In one school district, there are 89 elementary school (K-5) teachers, of which 18 are male (or male-identifying).
In one school district, there are 89 elementary school (K-5) teachers, of which 18 are male (or male-identifying). In a neighboring school district, there are 102 elementary teachers, of which 17 are male. A policy researcher would like to calculate the 99% confidence interval for the difference in proportions of male teachers.To keep the signs consistent for this problem, we will calculate all differences as p1−p2. That is, start with the percentage from the first school district and then subtract...


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# How to disprove this fallacy that derivatives of $x^2$ and $x+x+x+\cdots\ (x\text{ times})$ are not same. [duplicate]

$$x^2=\underbrace{{x+x+x+\cdots+x}}_{x \text{ times}}$$

$$\therefore \frac {dy}{ dx}\\ =\frac{d}{dx} \left( \underbrace{{x+x+x+\cdots+x}}_{x \text{ times}} \right) \\ = \underbrace{{1+1+1+\cdots+1}}_{x \text{ times}} \\ =x$$

but we know, $$\frac{dy}{dx} =2x$$ So what is the problem ?

My take :

We cannot derivate both sides because the terms $\underbrace{{x+x+x+\cdots+x}}_{x \text{ times}}$ is not finite and thus $1$ is not equal to $2$.

-

## marked as duplicate by Nate Eldredge, Douglas S. Stones, Rahul, Hans Lundmark, Zev ChonolesJun 29 '12 at 7:17

What do you mean by $x$ times? –  Frank Science Jun 29 '12 at 3:55
Adding x, x times x+x+x+x....(x times x) –  Bazinga Jun 29 '12 at 3:56
Worth reading. (maa.org/devlin/devlin_0708_08.html) –  user17762 Jun 29 '12 at 4:03
Note that the terms will be finite for any finite value of $x$ –  Pedro Tamaroff Jun 29 '12 at 4:05
$x^2 = \lfloor x\rfloor x + (x-\lfloor x\rfloor)x$. The first part, $\lfloor x\rfloor x$, is roughly like adding $x$ "$x$ times" while still adding an integer number of $x$s. The derivative of $\lfloor x\rfloor x$ is $\lfloor x\rfloor$ where it is defined. –  Jonas Meyer Jun 29 '12 at 4:40
show 1 more comment

Simply because "$x \text{ times}$" is also a "function" of $x$. One mistake is not considering that in the derivation.

-
Besides, it's also not clear what it means to add a number to itself a non-integer number of times. That interpretation of multiplication breaks down when you move beyond integers to fractions. –  Neal Jun 29 '12 at 4:06
@Neal True. I'm thinking about it from the differentiation perspective. –  Pedro Tamaroff Jun 29 '12 at 4:20
I'm sure that Neal is also thinking about it from a differentiation perspective. You can't take the derivative of a function with no definition, or that is defined only at the integers, in the context of calculus on the real line. –  Jonas Meyer Jun 29 '12 at 4:27
You say "$x\text{ times}$". The number of "times" you add it up---the number of terms in the sum---keeps changing as $x$ changes. An what if $x=1.6701$? How do you add up $x$ $1.6701$ times?
The arrangement of math equations in the question is very ugly. Help to edit it, such as $\underbrace{x+x+\cdots+x}_{x\textrm{ times}}$ instead of the one in the question, and displaymath is not necessary. His $dy/dx$ can be arranged with inline math. –  Frank Science Jun 29 '12 at 4:21
Concerning defining repeated addition for the reals, was your question for the OP's author's consideration? I think the problem is not with defining such addition, but with using the definition for $x^2$ that has been used in the OP. –  ThisIsNotAnId Jul 27 '12 at 3:36


text:
## CryptoDB

### Paper: Improved Rectangle Attacks on SKINNY and CRAFT

Authors: Hosein Hadipour , Department of Mathematics and Computer Science, University of Tehran, Tehran, Iran Nasour Bagheri , Electrical Engineering Department, Shahid Rajaee Teacher Training University, Tehran, Iran; School of Computer Science (SCS), Institute for Research in Fundamental Sciences (IPM),Tehran, Iran Ling Song , Jinan University, Guangzhou, China DOI: 10.46586/tosc.v2021.i2.140-198 URL: https://tosc.iacr.org/index.php/ToSC/article/view/8908 Search ePrint Search Google The boomerang and rectangle attacks are adaptions of differential cryptanalysis that regard the target cipher E as a composition of two sub-ciphers, i.e., E = E1 ∘ E0, to construct a distinguisher for E with probability p2q2 by concatenating two short differential trails for E0 and E1 with probability p and q respectively. According to the previous research, the dependency between these two differential characteristics has a great impact on the probability of boomerang and rectangle distinguishers. Dunkelman et al. proposed the sandwich attack to formalise such dependency that regards E as three parts, i.e., E = E1 ∘ Em ∘ E0, where Em contains the dependency between two differential trails, satisfying some differential propagation with probability r. Accordingly, the entire probability is p2q2r. Recently, Song et al. have proposed a general framework to identify the actual boundaries of Em and systematically evaluate the probability of Em with any number of rounds, and applied their method to accurately evaluate the probabilities of the best SKINNY’s boomerang distinguishers. In this paper, using a more advanced method to search for boomerang distinguishers, we show that the best previous boomerang distinguishers for SKINNY can be significantly improved in terms of probability and number of rounds. More precisely, we propose related-tweakey boomerang distinguishers for up to 19, 21, 23, and 25 rounds of SKINNY-64-128, SKINNY-128-256, SKINNY-64-192 and SKINNY-128-384 respectively, which improve the previous boomerang distinguishers of these variants of SKINNY by 1, 2, 1, and 1 round respectively. Based on the improved boomerang distinguishers for SKINNY, we provide related-tweakey rectangle attacks on 23 rounds of SKINNY-64-128, 24 rounds of SKINNY-128-256, 29 rounds of SKINNY-64-192, and 30 rounds of SKINNY-128-384. It is worth noting that our improved related-tweakey rectangle attacks on SKINNY-64-192, SKINNY-128-256 and SKINNY-128-384 can be directly applied for the same number of rounds of ForkSkinny-64-192, ForkSkinny-128-256 and ForkSkinny-128-384 respectively. CRAFT is another SKINNY-like tweakable block cipher for which we provide the security analysis against rectangle attack for the first time. As a result, we provide a 14-round boomerang distinguisher for CRAFT in the single-tweak model based on which we propose a single-tweak rectangle attack on 18 rounds of this cipher. Moreover, following the previous research regarding the evaluation of switching in multiple rounds of boomerang distinguishers, we also introduce new tools called Double Boomerang Connectivity Table (DBCT), LBCT⫤, and UBCT⊨ to evaluate the boomerang switch through the multiple rounds more accurately.
##### BibTeX
@article{tosc-2021-31083,
title={Improved Rectangle Attacks on SKINNY and CRAFT},
journal={IACR Transactions on Symmetric Cryptology},
publisher={Ruhr-Universität Bochum},
volume={2021, Issue 2},
pages={140-198},
url={https://tosc.iacr.org/index.php/ToSC/article/view/8908},
doi={10.46586/tosc.v2021.i2.140-198},
author={Hosein Hadipour and Nasour Bagheri and Ling Song},
year=2021
}


text:
# teTeX 3.0 and psfig

teTeX v3.0 (the distribution containing TeX, LaTeX, dvips etc.) has been recently installed in IAC's Linux and Sun Solaris machines. While it seems to be working well, there is a small problem with the psfig package, which has been removed and replaced by epsfig. To ensure that the compilation of your latex file run smoothly, do the following.

Check out the header of your latex file, and replace psfig with epsfig in the \usepackage or \documentstyle commands. For instance, replace:
\usepackage{psfig}  by  \usepackage{epsfig}
or, if you still have some older latex files:
\documentstyle[twoside,psfig]{article}  by   \documentstyle[twoside,epsfig]{article}

Notice that the command: \psfig is still valid, though you may replace it by \epsfig (these two commands really are synonymous).

As for CAT proposals, you should download the latest version of the (template) file cat_exam.tex, where the above fix has already been applied. There is no need to download the cat.sty file too, as it has already been updated in the texmf-local tree of our teTeX v3.0 distribution.


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# stat946f10

## June 2nd Maximum Variance Unfolding (Semidefinite Embedding)

Maximum Variance Unfolding (MVU) is a variation of Kernel PCA in which the kernel matrix is also obtained from the data. The main proposal of this technique is not to choose a kernel function a priori like classical kernel PCA or construct a kernel matrix by algorithm like LLE and ISOMAP, but instead learn a kernel $K$ optimizing an objective function with several constraints when the data set is given.

First, we give the constraints for the kernel.

### Constraints

1. Semipositive definiteness
Kernel PCA is a kind of spectral decomposition in Hilbert space. The kernel matrix stores the inner products of vectors in a Hilbert space, hence it must be positive semidefinite. The semipositive definiteness means all eigenvalues are non-negative, i.e. $K\gt =0$.

2. Centering
Considering the centering process in Kernel PCA, it is also required here. The condition is given by
$\sum_i \Phi\left(x_i\right) =0 .$
Equivalently,
$0 = \left|\sum_i \Phi(x_i)\right|^2 = \sum_{ij}\Phi(x_i)\Phi(x_j)=\sum_{ij}K_{ij}.$

3. Isometry
The local distance between a pairwise of data $x_i, x_j$, under neighbourhood relation $\eta$ (i.e. $\eta_{ij}=1$ indicates data $x_i, x_j$ are neighbours), should be preserved in new space after mapping $\Phi(\cdot)$. In other words, for all $\eta_{ij}\gt 0$,
$\left|\Phi(x_i) - \Phi(x_j)\right|^2 = \left|x_i - x_j\right|^2.$
Additonally, for the consider of conformal map, the pairwise distance between two points having a common neighbour point should also be preserved. Two data points having a common neighbour can be identified as $[\eta^T\eta]_{ij}\gt 0.$ This ensures that if two points have a common neighbour, we preserve their pairwise distances and angles.

$\left|\Phi(x_i) - \Phi(x_j)\right|^2 = \left(\Phi(x_i) - \Phi(x_j)\right)^{T}\left(\Phi(x_i) - \Phi(x_j)\right)$
$\left|\Phi(x_i) - \Phi(x_j)\right|^2 = \Phi(x_i)^{T}\Phi(x_i) - \Phi(x_j)^{T}\Phi(x_j) - 2 \Phi(x_i)^{T}\Phi(x_j)$

Thus, $K_{ii}+K_{jj}-2K_{ij}=\left|x_i - x_j\right|^2$ for all ij $\eta_{ij}\gt 0$ or $[\eta^T\eta]_{ij}\gt 0.$

### Objective Functions

Given the conditions, the objective functions should be considered. The aim of dimensional reduction is to map high dimension data into a low dimension space with the minimum information losing cost. Recall the fact that the dimension of new space depends on the rank of the kernel. Hence, the best ideal kernel is the one which has minimum rank. So the ideal objective function should be
$\min\quad rank(K).$
However, minimizing the rank of a matrix is a hard problem. So we look at the question in another way. When doing dimensional reduction, we try to maximize the distance between non-neighbour data. In other words, we want to maximize the variance between non-neighbour datas, and it is the same as maximizing the sum of the eigenvalues. In such sense, we can change the objective function to
$\max \quad Trace(K)$ .

Note that it is an interesting question that whether these two objective functions can be equivalent to each other. Although they are not totally equivallent, it can be shown that they usually converge to each other.

### Algorithm for Optimization Problem

The objective function with linear constraints form a typical semidefinite programming problem. The optimization is convex and globally. We already have methods to slove such kind of optimization problem.

### Colored Maximum Variance Unfolding .<ref>Song, L. and colleagues; Proceedings of the 2007 Conference, 1385-1392.</ref>

MVU is based on maximizing the overall variance while the local distances between neighbor points are preserved and it uses only one source of information. Colored MVU uses more than one source of information, i.e it reducing the dimension satisfying a combination of to goals
1- preserving the local distance (as first information)
2- optimum alignment with second information (side information)

##### Examples of how Colored MVU can leverage the side information
• Given text data from a newsgroup as first information, a hierarchy of topics can be used as side information to guide the embedding.
• Given term-frequency and inverse-document-frequency representation of academic papers as first information, co-author relationship can be used as side information to guide the embedding.
##### Rationale of separating the side information from the data
• We cannot merge all kind of information in one distance metric because the data(first information) and the side information may be heterogeneous
• The side information may be a feature of similarity(papers with the same co-authors tend to be more similar) rather than difference(papers with different co-authors are not necessarily far apart).
• When inserting new information, usually only new data but not new side information is added.

#### Algorithmic Modification

In Colored MVU, $Trace(KL)$ is maximized instead of $K$, where $L$ is the matrix of covariance of first and side information.

#### Application

One of the drawback of MVU is that its statistical interpretation is not always clear. However one of the application of Colored MVU, which has great statistical interpretation is to be used as a criterion to for measuring the Hilbert-Schmidt Independence.

### Steps for SDE algorithm

• Generate a K nearest neighbor graph. It should be a connected graph and so if K is too small it would be an unbounded problem, having no solution.
• Semidefinite programming: Maximize $Tr(K)$ subject to the above mentioned constraints.
• Do kernel PCA with this learned kernel.

• The kernel that is learned from the data can actually reflect the intrinsic dimensionality of the data. More specifically, the eigen-spectrum of the kernel matrix K provides an estimation.
The dimension needed to preserve local distance while maximizing variance is dependent on the number of dominant eigenvalues of K. That is, if top r eigenvalues of K account for 90% of the trace then an r dimensional representation can reveal about 90% of the unfolded data's variance.
• MVU is a convex problem which guarantees a unique solution.
• Distance-preserving constraints can be easily expressed and enforced in the semi-definite programming framework. This flexibility allows tailor-made constraints to be imposed on particular applications, for example analyzing robot motions(ARE).

• SDE can be solved efficiently in polynomial time but still has a high computational complexity. (O(matrix_size ^ 3 + number_of_constraints ^ 3))
• SDE is limited to a isometric map

### Application in SVM classification

The optimized kernel replaces the popular kernels using in SVM (i.e. linear kernel) for classification. It actually performs worse than other kernel functions chose in priori.

## June 4th

### Action Respecting Embedding (ARE)

It is a variation of Maximum Variance Unfolding.
The data here is temporal or ordered, i.e we move from one point to another by taking an action. In other words action $a_i$ is taken between data points $x_i$ and $x_{i+1}$.
Action labels,even with no interpretation or implied meaning,provide more information about the underlying generation of the data.It is natural to expect that the actions correspond to some simple operator on the generator's own degrees of freedom.For example,a camera that is being panned left and then right,has actions that correspond to a simple translation in the camera's actuator space.We therefore want to constrain the learned representation so that the labeled actions correspond to simple transformations in that space.In particular,we can require all actions to be a simple rotation plus translation in the resulting low-dimensional representation.<ref> M.Bowling, A.Ghodsi, and D.Wilkinson. Action respecting embedding. In International Conferenceon Machine Learning,2005. </ref>
Consider action $a$ taken between the points $x_i , x_{i+1}$, and the points $x_j , x_{j+1}$, in the original data space, it may not be a simple transformation (Rotation, Translation or combination of both).

A transformation $T$ is called simple or distance preserving if and only if

$\forall x, x'$ $\left \Vert T(x)-T(x') \right \|=\left \Vert x - x' \right \|$

Notice that $T_a(x_i)=x_{i+1}$ and $T_a(x_j)=x_{j+1}$

In the low dimension space, as in the camera case where actions corresponds to a simple translation in the camera's actuator space, the action can become a simple transformation. Therefore constraining the action to be a simple transformation in dimension reduction would help us to find a low dimension representation close to the true one, if the action indeed corresponds to a simple transformation in the intrinsic dimension space.

The goal here is not only to reduce the dimensionality of the data but also reducing the complexity of actions in the sense that actions in this low dimension representation is a simple transformation. Therefore to obtain a low dimensional embedding of the high dimensional temporal data, the action in low dimension must be represented by a constraint that preserves the distance. This constraint is called action respecting constraint.

### Constraint

For any two data points $x_i$,$x_j$ if the same action a $\left(a_{i}=a_{j}\right)$ is carried out, transforming them into $x_{i+1}$ and $x_{j+1}$ respectively, then the distance between $y_i$ and $y_j$ must be equal to the distance between $y_{i+1}$ and $y_{j+1}$ where $y_i$ , $y_j$ , $y_{i+1}$ , $y_{j+1}$ are the corresponding points in the low dimension. This constraint is given as:
$\left|y_i - y_j\right|^2=\left|y_{i+1} - y_{j+1}\right|^2 \rightarrow \left|\Phi(x_i) - \Phi(x_j)\right|^2=\left|\Phi(x_{i+1}) - \Phi(x_{j+1})\right|^2$
The kernel form of the above constarint is:
$\forall i, j a_{i}=a_{j} \Rightarrow K_{ii}+K_{jj}-2K_{ij}=K_{(i+1)(i+1)}+K_{(j+1)(j+1)}-2K_{(i+1)(j+1)}$

The above, action respecting constraint is added to the constraints of MVU and the algorithm of MVU is run to obtain a low dimension embedding for the temporal data.

### Example

This example is extracted from the "Action Respecting Embedding" paper listed in the references.

Consider a virtual robot that observe a 100 by 100 patch of a 2048 by 1536 image. The actions of the robot consists of four translations(rightward/leftward/upward/downward). In this example, we consider two action sequences and compare their representations by SDE and ARE.

File:image2.jpg
This is the 2048 by 1536 image.The rectangular box corresponds to the area covered by the first sequence of actions. The square box corresponds to the area covered by the second sequence of actions.
File:image1.jpg
This is the first sequence of actions which consists of 40 rightward translations followed by 20 leftward translations.
File:image3.jpg
This is the second sequence of actions which consists of translations in all the four directions.

It is obvious that the first sequence of actions lie in a one-dimensional subspace and the second sequence lies in a two-dimensional subspace. Although both SDE and ARE succeed in capturing this low dimensionality, the embedding achieved by ARE is much smoother and corresponds much better(almost exactly) to the actual actions.

File:image4.jpg
Representations of the first sequence of actions.
File:image5.jpg
Representations of the second sequence of actions.

## June 9th

### Applications of ARE

• Planning: To find a sequence of events to achieve a desired goal i.e. we want to find a path that leads us to the desired goal given the initial point and the set of all possible actions.

In ARE, the action is constrained to be a simple transformation in the low dimension space. After obtaining the low dimension representation through ARE, we have a set a points $\lbrace y_t \rbrace$.

Consider a collection of data point pairs $\lbrace (y_t$, $y_{t+1}) \rbrace$ such that $y_t \xrightarrow{a} y_{t+1}$, We can learn the action a as a simple transformation $f_a$ such that

$f_a(y_t)=A_ay_t+b_a$ subject to $A_a^TA_a=I$
we can do breath-first expansion for a tree starting from root (represents the intial point)by considering all possible actions(simple transformation) until the desired goal is reached.

• Robot loaization: It is accomplished by using the motion and sensor probabilistic model. But using ARE, we can do robot localization in the low dimensional map rather than in the original space. This has the advantage that it becomes independent of the environmental constraints.

### Metric Learning

Metric Learning is a supervised algorithm used for dimensionality reduction, in which class related side information are used. Two types of class-related information are brought in consideration, given a set of points $\{x_i, i=1, \cdots, m\}$. The first one is the similar set or class-equivalent set.

Similar Set
a set of pairs of similar points, denoted by $S$
$S : (x_i, x_j) \in S$ if $x_i$ and $x_j$ are similar;

The second one is the dissimilar set or class-inequivalent set
Dissimilar Set
a set of pairs of dissimilar points, denoted by $D$
$D : (x_i, x_j) \in D$ if $x_i$ and $x_j$ are dissimilar.

Note that pairs of points, which may not be known to be similar or dissimilar, will not be placed in either set. These two sets can come from knowing the class label or just the similarity or dissimilarity of some data. Some algorithms like Maximally Collapsing Metric Learning may require knowing the class label of data.

We want to learn a distance metric
$d_A(x_i, x_j) = \|x_i - x_j\|_A = \sqrt{(x_i-x_j)^T A(x_i-x_j)}$, where $\|x_i - x_j\|_A$ is not the euclidean distance but the mahalanobis distance determined by semi-definite matrix $A$.
Equivalently, we want to learn semi-definite matrix $A$ from the given data such that similiar points are close but dissimilar points are far apart.
$A= WW^T$ where $W$ is the transformation that maps data to the other space. The euclidean distance between the points in the transformed space is represented by mahalanobis distance in the oringinal space.

Such idea comes from firstly in 2004. After that, several different approaches are given to find the metric.

### 1. Original Optimization Problem

It is given by Eric P. Xing, Andrew Y. Ng, Michael I. Jordan and Stuart Russell in 2004 .<ref name="Xing">Eric P. Xing, Andrew Y. Ng, Michael I. Jordan and Stuart Russell, Distance metric learning, with application to clustering with side-information, </ref> . The authors give the optimization problem in following form:
$\min_A \sum_{(x_i , x_j) \in S} \|x_i - x_j\|^2_A$
$s.t. \sum_{(x_i , x_j) \in D} \|x_i - x_j\|_A \ge 1 ,(*)$
$A \ge 0 .$

The constraint is given to keep the distance between dissimilar points. If the constraint is ignored, $A = 0$ will be a trivial but not useful solution, which means all points collapse to a single point. The choice of constant $1$ is not important, and can be changed to any other positive number. In the paper, it is also shown that it is a convex optimization problem. Hence, we can solve it by some efficient algoritms without getting stuck at local minimas. In this paper, the author also notes that some possible alternatives to (*) would not be a good choice. For example, if this constraint is changed to $s.t. \sum_{(x_i , x_j) \in D} \|x_i - x_j\|^2_A \ge 1$, though it maintains a linear constraint, it would result in A always being rank 1 (i.e., the data are always projected onto a line).

#### Algorithms to Find A

Since no analytical formula is known for solving $A$ in the above formulation, iterative algorithms are developed to approximate $A$. During the iterative process, the algorithms have to ensure that $A \ge 0$.

##### Algorithm to find a full matrix diagonal A

In the general case where we seek a full matrix $A$, the constraint $A \ge 0$ is tricky to enforce and brute-force Newton method's is prohibitively expensive. An algorithm which uses the ideas of gradient descent and iterative projections is given in the aforementioned paper as follows:

Iterate
Iterate
$A := \arg \min_{A'} \{ \| A' - A \|_F : A' \in C_1 \}$(first projection)
$A := \arg \min_{A'} \{ \| A' - A \|_F : A' \in C_2 \}$(second projection)
until $A$ converges
$A := A + \alpha \nabla_A(g(A))_{\perp \nabla_A f}$(gradient ascent)
until convergence

where $\| \cdot \|_F$ is the Frobenium norm,
$C_1 = \{A:\sum_{(x_i, x_j) \in S}\| x_i - x_j \|^2_A \le 1\}$ and $C_2 = \{A:A \ge 0 \}$

##### Efficient Algorithm to find a diagonal A

In the special case where we seek a diagonal matrix $A$, the authors have derived a much more efficient algorithm, as explained below.

Obviously, letting A = I gives Euclidean distance. Now, let us suppose we want to learn a diagonal, that is $A=diag(A_{11},A_{22},...,A_{nn})$

Define $g(A)=g(A_{11},A_{22},...,A_{nn})=\sum_{(x_i , x_j) \in S} \|x_i - x_j\|^2_A-log(\sum_{(x_i , x_j) \in D} \|x_i - x_j\|_A)$

We can use Newton-Raphson algorithm to optimize $g(A)$.

### 2. Maximally Collapsing Metric Learning

Globerson & Roweis <ref> Globerson, A., and Roweis, S. 2006. Metric learning by collapsing classes. In Weiss, Y.; Sch¨olkopf, B.; and Platt, J., eds., Advances in Neural Information Processing Systems 18, 451–458. Cambridge, MA: MIT Press.</ref> proposed another metric learning method which considerably overperforms the original technique suggested by Xing, et. al. Based on a distance metric matrix $A$, they define a conditional probability distribution function as
$P^A(j|i)=\frac{e^{-({d_{ij}^A})^2}}{\sum_{k\neq i} e^{-({d_{ik}^A})^2}}$
Ideally, we expect all the points in the same class collapse to one point and all the points in different classes get infinitely far apart from each other. In this ideal situation the conditional probabilty distributions would be
$p_0(j|i)\propto \left\{\begin{matrix} 1 & y_i=y_j \\ 0 & yi \neq y_j \end{matrix}\right.$

To learn a distance metric, Globerson & Roweis find the value of the matrix $A$ such that the conditional probability distribution introduced above gets as close as possible to the ideal conditional distribution. To this end, they minimize the KL divergence between the two distributions (As known, KL divergence is a measure of difference between two probability distributions):
$\min_A \sum_{i} \textbf{KL}\left[ p_0(j|i)p^A(j|i)\right]$
subject to $A\succeq 0$. This is a convex optimization problem and may be solved by a projected gradient approach similar to the one used in Xing, et. al. <ref name="Xing"/>.

### 3. PSD formulation

Another approach is given in <ref name="Ali Ghodsi"> Ali Ghodsi, Dana Wilkinson, Finnegan Southey, Improving Embeddings by Flexible Exploitation of Side Information</ref>, in which the loss function is given by

$L(A) = \sum_{(x_i, x_j) \in S } \|x_i - x_j\|^2_A - \sum_{(x_i, x_j)\in D} \|x_i - x_j\|_A^2.$

Motivation for using this loss function is that, it is minimized equivalently if its first component (sum of the differences between points in similarity class) is minimized while, its second component (sum of the differences between points in dissimilarity class) is maximized.
The optimization problem is
$\min_A L(A); s.t. A \ge 0, Tr(A) = 1 (1)$.
The Positive semi-definiteness ($A \ge 0$) constrain guarantees a valid Euclidean metric and the trace constraints is to prevent the solution $A =0$. In order to be able to use standard semidefinite programing software $L(A)$ must be linearized. To do so function $vec()$ (which rearranges a matrix by concatenating its columns) which gives quite useful results like,

$vec(ABC)=(C^{T}*A)vec(B)$.
in which $*$ is the Kroneker product.

since $(x_{i}-x_{j})^{T}A(x_{i}-x_{j})$ is a scalar we can write

$(x_{i}-x_{j})^{T}A(x_{i}-x_{j})=vec((x_{i}-x_{j})^{T}A(x_{i}-x_{j}))$

also from Kroneker product for any two (same size) vectors $a , b$ we have

$(a^{T}*b^{T})=vec(ba^{T})^{T}$

using the two results above it is easy to drive the following conclusion.

$L(A) = \sum_{(x_i, x_j) \in S } (x_i - x_j)^T A (x_i - x_j) - \sum_{(x_i, x_j)\in D} (x_i - x_j)^T A (x_i - x_j)$
$= \sum_{(x_i, x_j) \in S } vec(A)^T vec((x_i - x_j)(x_i - x_j)^T) - \sum_{(x_i, x_j)\in D} vec(A)^T vec((x_i - x_j)(x_i - x_j)^T)$
$= vec(A)^T \left[ \sum_{(x_i, x_j) \in S } vec((x_i - x_j)(x_i - x_j)^T) - \sum_{(x_i, x_j)\in D} vec((x_i - x_j)(x_i - x_j)^T) \right]$

"This form along with the two linear constraints given in (1), makes a semidefinite positive problem that can be easily solved by a SDP solver, called SeDumi in Matlab. Therefore, it is a more convenient form than that used by Xing et all. Furthermore, in the original form, at least one dissimilar pair is required, while it is not necessary in the form given by Ali Ghodsi et al., because of the trace constraint. There can be only similar pairs, only dissimilar pairs, or any combination of the two, and the method will still avoid the trivial solution. Furthermore, in the absence of specific information regarding dissimilarities, Xing et al. assume that all points not explicitly identified as similar are dissimilar. This information may be misleading, forcing the algorithm to separate points that should be in fact be similar. The formulation presented by Ali Ghodsi et al. allows one to specify only the side information one actually has, partitioning the pairing into similar, dissimilar, and unknown."<ref name="Lecture notes by Ali Ghodsi"/>

## June 11th

### Closed form Metric learning (CFML)

As, $(x_i-x_j)^TA(x_i-x_j)=Tr((x_i-x_j)^T WW^T(x_i-x_j))=Tr(W^T(x_i-x_j)(x_i-x_j)^T W)$
The cost function to be minimized is:
$\min \frac 1S \operatorname{trace}(W^TM_SW)- \frac1D \operatorname{trace}(W^TM_DW)$
s.t. $\operatorname{trace}(A)=1$ or $\operatorname{trace}(WW^T)=1$
Solving this as a lagrange multiplier problem we get,
$\mathbf {(M_S-M_D)} \mathbf W = \lambda \mathbf W$
This results in matrix$\mathbf W$ being rank 1 i.e it consists of eigenvectors (as its columns) each having the same eigenvalue and therefore A is also rank 1. As a result all the data points are projected on a line.
Projection of the data points on a line is due to the constraint imposed on the cost function and therefore to avoid that we need to change our constarint. There are two alternative constraints that can be imposed on the cost function:

• The constraint imposed is: $\mathbf W^T\mathbf W= \mathbf I_m$.
So, the objective function is:
$\min_{\mathbf W}\operatorname {trace}(\mathbf W^T(\mathbf M_S-\mathbf M_D)\mathbf W)$ s.t $\mathbf W^T\mathbf W=\mathbf I_m$.

$\mathbf W$ is the eigenvectors of $(\mathbf M_S-\mathbf M_D)$.

• The constraint is: $\mathbf W^T\mathbf M_S\mathbf W= \mathbf I_m$.
So, the objective function is:

$\min_{\mathbf W}\operatorname {trace}(\mathbf W^T(\mathbf M_S-\mathbf M_D)\mathbf W)$
s.t. $\mathbf W^T\mathbf M_S\mathbf W=\mathbf I_m$
this alternative algorithm is called CFML-II.
To solve this new form of optimization problem, let $\mathbf M_S=\mathbf {HH^T}$. Substituing this in our constraint and also considering$\mathbf {H^TW}=\mathbf Q$, we get our cost function as:
$\min\operatorname {trace}(\mathbf Q^T(\mathbf I-\mathbf {H^{-1}M_DH^{-1^T}})\mathbf Q)$ s.t $\mathbf Q^T\mathbf Q=\mathbf I$
$\mathbf Q$ is the eigenvectors of $(\mathbf I-\mathbf {H^{-1}M_DH^{-1^T}})$.
That is, $(\mathbf I-\mathbf {H^{-1}M_DH^{-1^T}})\mathbf Q=\lambda\mathbf Q$

    ie, $\mathbf {H^{T^{-1}}H^{-1}}\mathbf M_D\mathbf W=\lambda\mathbf W$
ie, $\mathbf {M_S^{-1}}\mathbf M_D\mathbf W=\lambda\mathbf W$

This optimization problem is related to an old technique called Fischer discriminant analysis(FDA)

### Comparison

So far , we have discussed a number of algorithms in metric learning. Xing et al., MCML, CFML, CFML-II, and FDA. Compared to the others, Xing doesn't give a good result, CFML and MCML compete with each other, CFML has a closed form and runs pretty fast, and FDA has a restriction on the rank such that given the number of classes as k, the rank is always equal to k-1.

### Using partial distance side information <ref name="Ali Ghodsi"/>

In this case, only partial distances are known i.e. we are given exact distances between some pairs of points.
Suppose a set of similarities is given: $S : (x_i, x_j) \in S$ if the target distance $d_{ij}$ is known, then the cost function that preserves the local distnces is:
$\min_{\mathbf A} \sum_S\|\|x_i-x_j\|_A^2-d_{ij}\|^2$ s.t $\mathbf A \succeq 0$
The above function can be written as:
$L(A)=\min_{\mathbf A} \sum_S\|vec(A)^T vec(B_{ij})-d_{ij}\|^2$
$L(A)=\min_{\mathbf A} \sum_S(vec(A)^T vec(B_{ij})vec(B_{ij})vec(A)+d_{ij}^2)-2d_{ij}vec(A)^Tvec(B_{ij})$
where, $B_{ij}=(x_i-x_j)(x_i-x_j)^T$ and as $d_{ij}^2$ is independent of A, it can be dropped.
Therefore, the loss function is:
$L(A)=vec(A)^T[Qvec(A)-2R]$ where, $Q=\sum_S vec(B_{ij})vec(B_{ij})^T$ and $\sum_SR=2d_{ij}vec(B_{ij})$

The above loss function being in the quadratic form, semi definite programming can not be applied. It can be converted to a linear function using 'Shur Complement.'

Shur Complement
$\begin{bmatrix} \mathbf X & \mathbf Y \\ \mathbf {Y^T} & \mathbf Z\end{bmatrix}\succeq 0$ if and only if $\mathbf {Z-Y^TX^{-1}Y}\succeq 0$
By decomposing $\mathbf {Q = S^TS}$, a matrix of the form
$J =\begin{bmatrix} I & Svec(A)\\(Svec(A))^T &2vec(A)^TR + t\end{bmatrix}$ is constructed. By the Schur complement, if $J \succeq 0$, then the following relation holds
$\mathbf {2vec(A)^TR + t}- \mathbf {vec(A)^T S^T Svec(A)} \succeq 0$
Scalar $\mathbf t$ is an upper bound on the loss and therefore,
$\mathbf {vec(A)^T S^T Svec(A) }-\mathbf { 2vec(A)^TR} = \mathbf {vec(A)^TQvec(A)}-\mathbf{ 2vec(A)^TR} \lt = \mathbf t$
Therefore, minimizing t subject to $J \succeq 0$also minimizes the objective. This optimization problem can be readily solved by standard semidefinite programming software
$\min_A \mathbf t$ s.t. $\mathbf A \succeq 0$and $\mathbf J \succeq 0$

## June 16th

### Nonnegative Matrix Factorization (NMF)

Assume $A$ is our data matrix with columns representing each data point. A matrix factorization of $A_{m\times n} \approx W_{m\times k}H_{k\times n}$, in general, can be thought as a way of expressing columns of A as a weighted sum of $k$ bases. The $k$ bases are, in fact, columns of $W$ and the weights corresponding to the $i$th data point are located in the $i$th column of matrix $H$.
As known, PCA or equivalently SVD gives matrices $W$ and $H$ satisfying the following optimiztion constraint:
$\min_{W,H} |A-WH|_F$

In the above factorization, matrix $A$ and the output matrices $W$ and $H$ in general may have negative or non-negative entries.
However, there are many applications in which matrix $A$ has only non-negative entries. Examples are images, word frequency vector of texts, DNA microarrays and music notes. In these applications, it would helpful to impose non-negative constrains on the $W$ and $H$ matrices above. Summarily speaking, we want to factorize nonnegative matrix A into two non-negative matrices, $W$ and $H$, such that $A \approx WH$. Nonnegative means all entries in the matrix are non-negative. So NMF, in a sense, is similar to Singular Value Decomposition (SVD), but SVD does not guarantee non-negative entries.

As mentioned, for some applications we may require/prefer non-negative entries. e.g. in face/image data we may want our image intensities to be non-negative. It makes sense to interpret an image reconstruction as adding a set of images with non-negative intensities.

Nonnegative rank - Started from 1989 (Gregory and Pullman).

### History

NMF became popular with the publication of the work of Lee and Seung in 1999 <ref> D. Lee, and H. S. Seung, Learning the parts of objects by non-negative matrix factorization. Nature 401, 788-791 (21 October 1999). </ref>. They presented an algorithm for NMF capable of learning parts of faces and semantic features of text, which is in contrast to other methods, such as PCA and vector quantization, that learn holistic, not parts-based, representations.

#### Applications

DNA microarray experiments (Ilmels and Barkai, 2003) using gene expression data.

Retrieve notes from an audio recording of polyphonic music (Smaragdis and Brown, 2003).

#### NMF Algorithms

Alternate updates to $W$ and $H^T$ using an ascent direction (Lee and Seung).

Want to minimise $||A - WH^T||_F$ - linear least squares for either $W$ or $H$ if the other is fixed.

Alternatively use an $L^1$ penalty term to enhance sparsity (Kim and Park).

#### Observations

Leading singular vectors of a nonnegative matrix are nonnegative. Used as the basis for R1D (rank-1 downdate).

Simple rank-1 NMF using SVD. Gives rank-1 approximation of $A$.

Rows and columns of $A$ can be clustered using singular vectors. If there are similar entries in $U$, there will be corresponding similar rows in $A$. Likewise, similar entries in $V$ correspond to similar columns of $A$. i.e. $U$ and $V$ can be though of as lower dimensional representations of the rows and columns, respectively, of $A$.

<references/>


text:
68 views

| 68 views
0
60??

20*3 FF
0
60
0
request  =

everyone should add the test series name
0
Gateforum
0
if the clock is directly connected to all three FF then it should be 20

but here the output of one FF connected as the clock of next FF and so

it should be 3*20=60 ??
0

please add test-series name in $\underline{title}$


text:
### On the Security of Iterated Hashing based on Forgery-resistant Compression Functions

Charles Bouillaguet, Orr Dunkelman, Pierre-Alain Fouque, and Antoine Joux

##### Abstract

In this paper we re-examine the security notions suggested for hash functions, with an emphasis on the delicate notion of second preimage resistance. We start by showing that, in the random oracle model, both Merkle-Damgaard and HAIFA achieve second preimage resistance beyond the birthday bound, and actually up to the level of known generic attacks, hence demonstrating the optimality of HAIFA in this respect. We then try to distill a more elementary requirement out of the compression function to get some insight on the properties it should have to guarantee the second preimage resistance of its iteration. We show that if the (keyed) compression function is a secure FIL-MAC then the Merkle-Damgaard mode of iteration (or HAIFA) still maintains the same level of second preimage resistance. We conclude by showing that this new'' assumption (or security notion) implies the recently introduced Preimage-Awareness while ensuring all other classical security notions for hash functions.

##### Metadata
Available format(s)
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Contact author(s)
charles bouillaguet @ ens fr
History
2009-02-16: received
Short URL
https://ia.cr/2009/077
License

CC BY

BibTeX

@misc{cryptoeprint:2009/077,
author = {Charles Bouillaguet and Orr Dunkelman and Pierre-Alain Fouque and Antoine Joux},
title = {On the Security of Iterated Hashing based on Forgery-resistant Compression Functions},
howpublished = {Cryptology ePrint Archive, Paper 2009/077},
year = {2009},
note = {\url{https://eprint.iacr.org/2009/077}},
url = {https://eprint.iacr.org/2009/077}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.


text:
## The simplest illustration of Bell's error

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### Re: The simplest illustration of Bell's error

gill1109 wrote:
Joy Christian wrote:Much is made in the critique [1] of the so-called "theorem" of Bell that claims that the models such as the one presented in [2 -- 6] are impossible. But mathematically a theorem with loopholes [13] is an oxymoron, while physically we know that the bounds on Bell inequalities are not respected by Nature. The consequent conclusion that therefore Nature must be non-local, non-realistic, or conspiratorial is not justified. For Bell's theorem depends on a number of assumptions [4], in addition to those of locality and realism. And, in fact, Bell inequalities can be derived without assuming either locality or realism, as shown, for example, in Section 4.2 of [4].

The word “loophole” in this context does not refer to a loophole in a theorem, but to a loophole in an attempt to apply a logical argument to a practical situation.

Joy is 100% right. There is no such thing as a mathematical theorem with loopholes. Richard is wrong, the so-called "loopholes" in Bell's theorem are directly related to oversights in Bell's analysis. In other words, the "loopholes" disprove the theorem. Why else will Richard (and Larsson) try to create a new theorem if the original one was valid? Notwithstanding the fact that Fine first identified the time synchronization flaw in Bell's theorem.

It is not simply a problem with practical application.
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The simplest illustration of Bell's errortt

minkwe wrote:
gill1109 wrote:Michel, you ignored a crucial sentence. *You* are talking about functions which take values in {-1, +1, “undefined”}.

Wow Richard, you are a mathematician don't make such stupid statements. Next you will tell me the range of tan(x) is $\{ \mathbb{R}, undefined \}$

Yes. I will tell you that. It’s very convenient indeed to think of the function “tan” as a mapping from the real line to the union of the real line and a disjoint one-point set {“undefined”}.

The alternative is to define it as a function from the real line with an infinite series of points removed to the real line.

Wikipedia: “Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane from which some isolated points are removed.”

The simple parts of the wikipedia page on trigonometric functions (the parts for school children) uses an old fashioned definition, making it “+infinity” on those points.

minkwe wrote:Joy is 100% right. There is no such thing as a mathematical theorem with loopholes. Richard is wrong, the so-called "loopholes" in Bell's theorem are directly related to oversights in Bell's analysis. In other words, the "loopholes" disprove the theorem. Why else will Richard (and Larsson) try to create a new theorem if the original one was valid? Notwithstanding the fact that Fine first identified the time synchronization flaw in Bell's theorem.

It is not simply a problem with practical application.

Joy is not 100% right. There can be a loophole in an attempt to apply a mathematical theorem to a practical matter.

Larsson and my theorem is a different theorem to the “Bell theorem seen as a math theorem”. The conditions are different, and the conclusion is different.

The theorem of Lasrsson and myself, for instance, applies to the computer simulation “epr-simple”.

Bell’s theorem doesn’t. See https://arxiv.org/abs/1507.00106

[Submitted on 1 Jul 2015 (v1), last revised 10 Apr 2021 (this version, v10)]
Event based simulation of an EPR-B experiment by local hidden variables: epr-simple and epr-clocked

Richard D. Gill
In this note, I analyze the data generated by M. Fodje's (2013, 2014) simulation programs "epr-simple" and "epr-clocked". They were written in Python and published on Github. Inspection of the program descriptions showed that they made use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signalling. His coincidence-loophole model is actually a clever modification of his detection-loophole model. Because of this, however, it cannot lead to optimal efficiency.
Comments: This is version 11 of this preprint. Earlier versions incorrectly stated that documentation of Michel Fodje's simulation was inexistent. This version also contains better explanation of my terminology. It is also posted on Researchers.one, article 2020-01-1. Another version on this http URL, preprints202001.0045, is being updated
gill1109
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### Re: The simplest illustration of Bell's error

local wrote:Joy, Arthur Fine is a traditional gentleman and would respond politely to any correspondent. I wouldn't take that against him. I do agree with your assessment of Gill as there is ample evidence.

Arthur approached me. Indeed, he is a traditional gentleman. I used to admire “local” for being much the same but he suddenly dramatically changed personality, as well as nickname. I suppose he prefers to be ungentlemanly anonymously. Clearly a case of a split personality.
gill1109
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### Re: The simplest illustration of Bell's errortt

gill1109 wrote:
minkwe wrote:
gill1109 wrote:Michel, you ignored a crucial sentence. *You* are talking about functions which take values in {-1, +1, “undefined”}.

Wow Richard, you are a mathematician don't make such stupid statements. Next you will tell me the range of tan(x) is $\{ \mathbb{R}, undefined \}$

Yes. I will tell you that. It’s very convenient indeed to think of the function “tan” as a mapping from the real line to the union of the real line and a disjoint one-point set {“undefined”}.

Now I know it's just polemics to you. You are not serious at all.
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The simplest illustration of Bell's errortt

minkwe wrote:
gill1109 wrote:
minkwe wrote:
gill1109 wrote:Michel, you ignored a crucial sentence. *You* are talking about functions which take values in {-1, +1, “undefined”}.

Wow Richard, you are a mathematician don't make such stupid statements. Next you will tell me the range of tan(x) is $\{ \mathbb{R}, undefined \}$

Yes. I will tell you that. It’s very convenient indeed to think of the function “tan” as a mapping from the real line to the union of the real line and a disjoint one-point set {“undefined”}.

Now I know it's just polemics to you. You are not serious at all.

I’m a very serious mathematician. We are talking about mathematics, and I mention its application to computer science (distributed computing). Did you read my paper on Gull’s theorem yet?

What do you think is the definition of the mathematical function “tan”? What is the definition of “function”?
gill1109
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### Re: The simplest illustration of Bell's error

Sorry, Richard. That was the last straw, I'm done with you.

The domain of tan(x) is $\mathbb{R} - (n\pi + \frac{\pi}{2}), n \in \mathbb{Z}$
The range of tan(x) is $\mathbb{R}$
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The simplest illustration of Bell's error

minkwe wrote:The domain of tan(x) is $\mathbb{R} - (n\pi + \frac{\pi}{2}), n \in \mathbb{Z}$
The range of tan(x) is $\mathbb{R}$

That's indeed a common definition. Read the Wikipedia page on the trigonometric functions: it is not the only common definition.

It is also legitimate to define domain and range a bit differently. You are saying yourself that tan(x) is not defined for x = (n pi + pi/2), n an integer. I say the same thing in a different way. Wikipedia says it is equal to +infty for those values! That is also a common convention. You can find out yourself what Mathematica does, or Python, or R, or C. They too must all build in some convention. No doubt, IEEE has established some conventions. But different computer languages have different concept of "number". Some allow values "+infty", "-infty" or "not a number".

You are avoiding the issue which was about Bell's theorem as a mathematical theorem, and about Larsson and my theorems. Different mathematical theorems. Different mathematical assumptions. Different mathematical conclusions. One can sometimes apply them to computer simulation programs.
gill1109
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### Re: The simplest illustration of Bell's error

gill1109 wrote:You are avoiding the issue which was about Bell's theorem as a mathematical theorem, and about Larsson and my theorems. Different mathematical theorems. Different mathematical assumptions. Different mathematical conclusions. One can sometimes apply them to computer simulation programs.

I'm definitely not. The issue is that I provided two functions that beat your challenge and you start relying on word games to change the goalposts. It's very obvious what you are doing. I'm not surprised.

But this is all off-topic in anycase. I noticed you don't have anything to say on the actual topic of this thread.
minkwe

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### Re: The simplest illustration of Bell's error

minkwe wrote:
gill1109 wrote:You are avoiding the issue which was about Bell's theorem as a mathematical theorem, and about Larsson and my theorems. Different mathematical theorems. Different mathematical assumptions. Different mathematical conclusions. One can sometimes apply them to computer simulation programs.

I'm definitely not. The issue is that I provided two functions that beat your challenge and you start relying on word games to change the goalposts. It's very obvious what you are doing. I'm not surprised.

Michel, you did not provide two functions which beat my challenge. You thought you did, but apparently you did not read the challenge carefully.

No problem!

So please do answer the following question. Suppose A and B are two functions programmed in some programming language such as R or Python, with range {-1, +1} and domain [0, 2 pi) x [0, 1]. We generate a long stream of pseudo-random numbers u_1, ..., u_N, supposed to behave like independent realisations of a random number uniformly distributed on [0, 1]. We compute the average of the N numbers A(a, u_n) * B(b, u_n). Is it possible that this will very well approximate -cos(a - b) for say all a, b, , for instance corresponding to half degree steps between 0 and 360 degrees. Take N equal to a million.
This is actually strongly related to the original question you asked in this thread, though perhaps you don't quite see how, at the moment.
gill1109
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### Re: The simplest illustration of Bell's error

gill1109 wrote:So please do answer the following question. Suppose A and B are two functions programmed in some programming language such as R or Python, with range {-1, +1} and domain [0, 2 pi) x [0, 1]. We generate a long stream of pseudo-random numbers u_1, ..., u_N, supposed to behave like independent realisations of a random number uniformly distributed on [0, 1]. We compute the average of the N numbers A(a, u_n) * B(b, u_n). Is it possible that this will very well approximate -cos(a - b) for say all a, b, , for instance corresponding to half degree steps between 0 and 360 degrees. Take N equal to a million.
This is actually strongly related to the original question you asked in this thread, though perhaps you don't quite see how, at the moment.

I answered your challenge already. It is off-topic and unrelated to this thread please start a new one since you want to kee changing the rules. Start a new thread and I will provide any additional answers I have there if I change my mind.

This thread is about the fact that Bell used the wrong QM prediction for the "franken-correlation" P(b,c). He used -b.c when he should have used 0.
minkwe

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### Re: The simplest illustration of Bell's error

minkwe wrote:
gill1109 wrote:So please do answer the following question. Suppose A and B are two functions programmed in some programming language such as R or Python, with range {-1, +1} and domain [0, 2 pi) x [0, 1]. We generate a long stream of pseudo-random numbers u_1, ..., u_N, supposed to behave like independent realisations of a random number uniformly distributed on [0, 1]. We compute the average of the N numbers A(a, u_n) * B(b, u_n). Is it possible that this will very well approximate -cos(a - b) for say all a, b, , for instance corresponding to half degree steps between 0 and 360 degrees. Take N equal to a million.
This is actually strongly related to the original question you asked in this thread, though perhaps you don't quite see how, at the moment.

I answered your challenge already. It is off-topic and unrelated to this thread please start a new one since you want to kee changing the rules. Start a new thread and I will provide any additional answers I have there if I change my mind.

This thread is about the fact that Bell used the wrong QM prediction for the "franken-correlation" P(b,c). He used -b.c when he should have used 0.

Michel, I’ve started a new thread at http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=491&p=14467#p14467
gill1109
Mathematical Statistician

Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

### Re: The simplest illustration of Bell's error

@gill1109 Irrelevant rubbish!
.
FrediFizzx
Independent Physics Researcher

Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

### Re: The simplest illustration of Bell's error

By the way, here are links to the two Fine papers which were mentioned earlier, thanks to "local".

Some Local Models for Correlation Experiments. Synthese 50 (1982), pp 279-94
Arthur Fine
https://www.jstor.org/stable/20115716

Correlations and Physical Locality. In P. Asquith & R. Giere (eds.) PSA 1980, Volume 2. E. Lansing, MI: Philosophy of Science Association, 1981, pp. 535-56.
Arthur Fine
https://www.jstor.org/stable/192609

I can send you pdf's by email if you can't get through the paywall or don't find them on SciHub.
gill1109
Mathematical Statistician

Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

### Re: The simplest illustration of Bell's error

@gill1109 More old irrelevant stuff!
.
FrediFizzx
Independent Physics Researcher

Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Previous


text:
## Friday, 4 September 2020

### Does this covariant function belong to some 2d CFT?

In conformal field theory, correlation functions of primary fields are covariant functions of the fields’ positions. For example, in two dimensions, a correlation function of N diagonal primary fields must be such that
\begin{aligned} F(z_1,z_2,\cdots , z_N) = \prod_{j=1}^N {|cz_j+d|^{-4\Delta_j}} F\left(\tfrac{az_1+b}{cz_1+d},\tfrac{az_2+b}{cz_2+d},\cdots , \tfrac{az_N+b}{cz_N+d}\right) \ , \end{aligned}
where zj ∈ ℂ are the fields’ positions, Δj ∈ ℂ their conformal dimensions, and $\left(\begin{smallmatrix} a& b \\ c& d \end{smallmatrix}\right)\in SL_2(\mathbb{C})$ is a global conformal transformation. In addition, there are nontrivial relations between different correlation functions, such as crossing symmetry. But given just one covariant function, do we know whether it belongs to a CFT, and what can we say about that CFT?

In particular, in two dimensions, do we know whether the putative CFT has local conformal symmetry, and if so what is the Virasoro algebra’s central charge?

Since covariance completely fixes three-point functions up to an overall constant, we will focus on four-point functions i.e. N = 4. The stimulus for addressing these questions came from the correlation functions in the Brownian loop soup, recently computed by Camia, Foit, Gandolfi and Kleban. (Let me thank the authors for interesting correspondence, and Raoul Santachiara for bringing their article to my attention.)

#### Doesn’t any covariant function belong to multiple 2d CFTs?

In conformal field theory, any correlation function can be written as a linear combination of s-channel conformal blocks. These conformal blocks are a particular basis of smooth covariant functions, labelled by a conformal dimension and a conformal spin. (I will not try to say preciely what smooth means.) In two dimensions, we actually have a family of bases, parametrized by the central charge c, with the limit c = ∞ corresponding to global conformal symmetry rather than local conformal symmetry.

## Thursday, 27 August 2020

### (2/2) Open access mystery: why did ERC backstab Plan S?

In my first post about the ERC’s recent withdrawal from supporting Plan S, I tried to explain ERC’s announcement using publicly available information on the ERC, Plan S, and their recent news. The potential dangers of this approach were to miss relevant pieces of information, and to give too much weight to calendar coincidences.

We are still waiting for a detailed and convincing explanation from the ERC, and for a description of their open access strategy if they still have one. Meanwhile, I would like to complete the picture based on informal contacts with a few well-informed colleagues. There emerge two potential lines of explanation.

## Wednesday, 22 July 2020

### (1/2) Open access mystery: why did the ERC backstab Plan S?

The European Research Council (ERC) just announced that they would withdraw their support for Coalition S, the consortium of research funders behind Plan S. Plan S is the valiant but not universally welcome attempt to impose strong open access requirements to research articles, without paying more money to publishers.

The ERC is Europe’s most prestigious research funder, and a main backer of Plan S. Without Plan S, the ERC has no open access strategy, and without the backing of ERC, Coalition S may not be big enough for succeeding. Why would ERC make this U-turn? I do not know, but let me gather a few potentially relevant pieces of the puzzle. The pieces are of three types:
• some context on the ERC and more generally on Europe’s research plans,
• the recently announced rights retention strategy by Coalition S,
• ERC’s meager and not very credible justification for their withdrawal.

## Tuesday, 3 March 2020

### With open peer review, open is just the beginning

#### Abstract

Open peer review does not just mean publishing existing reviewer reports, but should also lead to writing reports primarily for the public. We make a specific proposal for structured reviewer reports, based on the three criteria validity, interest and clarity.
This post is partly based on a joint proposal with Anton Akhmerov for improving the structure of reviewer reports at SciPost. Feedback from Jean-Sébastien Caux on that proposal is gratefully acknowledged.

#### Benefits of open peer review: the obvious and the less obvious

In the traditional model of academic peer review, reviewers’ reports on the submitted article are kept confidential, and this is a big source of inefficiency and waste. If the article is published, the readers can neither assess how rigorous the process was, nor benefit directly from the reviewers’ insights. If it is rejected, the work has to start all over again at another journal.

Open peer review, defined here as making the reports public, could help journals remedy the penury of reviewers: if applied to rejected articles, by avoiding duplicating effort, and if coupled with naming reviewers, by giving them better incentives to do the work. However, the consequences of open peer review may be more far-reaching. Published reports can indeed be used for evaluating the article’s interest and quality. In aggregate, they could be used for evaluating journals and researchers. For these purposes, they would certainly be better than citation counts.


text:
Chapter 8, Problem 34CE

### Cornerstones of Financial Accounti...

4th Edition
Jay Rich + 1 other
ISBN: 9781337690881

Chapter
Section

### Cornerstones of Financial Accounti...

4th Edition
Jay Rich + 1 other
ISBN: 9781337690881
Textbook Problem
1 views

# Liquidity RatiosGER’s financial statements contain the following information: Note: Round answers to two decimal places.Required:1. What is the current ratio?2. What is the quick ratio?3. What is the cash ratio?4. Discuss GER’s liquidity using these ratios.

To determine

Concept introduction:

Current Ratio:

Current Ratio is measure of the company’s ability to pay off its current liabilities using its current assets. It is calculated by dividing the total current assets by total current liabilities. The formula of the current ratio is as follows:

Current Ratio=Current assetsCurrent liabilities

Acid test ratio:

Acid test ration is also called Quick ratio. This ratio is calculated by dividing the quick assets (Cash, Cash equivalents, Short term investments and current receivables) by total current liabilities for the year. The formula for Acid test ratio is as follows:

Acid test ratio = (Cash + Cash equivalents + Short term investments + Accounts receivables) Current Liabilities

Cash ratio:

Cash ratio is calculated by dividing and cash and cash equivalents by the total current liabilities. The formula for Cash ratio is as follows:

Cash Ratio = Cash and cash equivalents/ Current liabilities

Requirement 1:

To calculate:

The Current Ratio.

Explanation

The Current Ratio is calculated as follows:

 Cash $3,125,000 Marketable Securities$ 1,850,000 Accounts Receivables $3,150,000 Inventory$ 4,200,000 Total Current Assets (A) \$ 12,325,0...
To determine

Concept introduction:

Current Ratio:

Current Ratio is measure of the company’s ability to pay off its current liabilities using its current assets. It is calculated by dividing the total current assets by total current liabilities. The formula of the current ratio is as follows:

Current Ratio=Current assetsCurrent liabilities

Acid test ratio:

Acid test ration is also called Quick ratio. This ratio is calculated by dividing the quick assets (Cash, Cash equivalents, Short term investments and current receivables) by total current liabilities for the year. The formula for Acid test ratio is as follows:

Acid test ratio = (Cash + Cash equivalents + Short term investments + Accounts receivables) Current Liabilities

Cash ratio:

Cash ratio is calculated by dividing and cash and cash equivalents by the total current liabilities. The formula for Cash ratio is as follows:

Cash Ratio = Cash and cash equivalents/ Current liabilities

Requirement 2:

To calculate:

The Quick Ratio.

To determine

Concept introduction:

Current Ratio:

Current Ratio is measure of the company’s ability to pay off its current liabilities using its current assets. It is calculated by dividing the total current assets by total current liabilities. The formula of the current ratio is as follows:

Current Ratio=Current assetsCurrent liabilities

Acid test ratio:

Acid test ration is also called Quick ratio. This ratio is calculated by dividing the quick assets (Cash, Cash equivalents, Short term investments and current receivables) by total current liabilities for the year. The formula for Acid test ratio is as follows:

Acid test ratio = (Cash + Cash equivalents + Short term investments + Accounts receivables) Current Liabilities

Cash ratio:

Cash ratio is calculated by dividing and cash and cash equivalents by the total current liabilities. The formula for Cash ratio is as follows:

Cash Ratio = Cash and cash equivalents/ Current liabilities

Requirement 3:

To calculate:

The Cash Ratio.

To determine

Concept introduction:

Current Ratio:

Current Ratio is measure of the company’s ability to pay off its current liabilities using its current assets. It is calculated by dividing the total current assets by total current liabilities. The formula of the current ratio is as follows:

Current Ratio=Current assetsCurrent liabilities

Acid test ratio:

Acid test ration is also called Quick ratio. This ratio is calculated by dividing the quick assets (Cash, Cash equivalents, Short term investments and current receivables) by total current liabilities for the year. The formula for Acid test ratio is as follows:

Acid test ratio = (Cash + Cash equivalents + Short term investments + Accounts receivables) Current Liabilities

Cash ratio:

Cash ratio is calculated by dividing and cash and cash equivalents by the total current liabilities. The formula for Cash ratio is as follows:

Cash Ratio = Cash and cash equivalents/ Current liabilities

Requirement 4:

To discuss:

Liquidity of the company.

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text:
# Constructing ramified covers with prescribed multiplicities at ramification points

Let $Y$ be a smooth projective curve defined over number field $K$. Let $P_1,\dots ,P_m$ be some $K$-points to which we will associate "multiplicities" $m_i\in\{ 2,3,\dots \}$ for $i=1,\dots ,m$. The other $K$ points (and even those not defined over $K$ ) are considered with "multiplicities" $1$. We want to find a smooth projective curve $X$ defined over some number field $M$, and a morphism $\phi :X\to Y$ such that $e_{T}=m_{\phi (T)}$ for all closed points $T$ of $X$. Here $e_T$ is the ramification at the point $T$. We assume the "characteristics" of $Y$ is negative, that is $2-2g-\sum _P(1-\frac{1}{m_P})<0$. Here $g$ is the genus.

In Serre's Topics in Galois theory, he solves the problem for the Riemann surfaces. He doesn't require that the first curve is projective. The universal cover is $\mathbb{H}$, the Poincaré half-plane, if the "characteristics" is negative.

The cover here is infinite. Of course, I need a finite. Therefore somehow I should quotient it by some group and get a smooth projective curve. Then I know how to use GAGA to finish the problem.

Any ideas how to make the missing step?

• The Riemann-Hurwitz formula is a numerical constraint on existence of such a cover. By the Riemann-Hurwitz formula, for a finite cover, the sum over all points $P$ of $m_P-1$ must be even. Thus, for instance (and this is obvious topologically), there is no cover of $\mathbb{P}^1$ that is branched simply over a single point. Jun 2, 2017 at 9:13
• I assume the characteristics is negative. I don't understand your argument on the RH formula. The sum goes over $e_P$ when $P$ in the cover not in $Y$. Hence, one may have many points lying over the same poins and having the same ramification. Jun 2, 2017 at 9:49
• Over $\mathbb{C}$, this amounts to find a transitive representation of the fundamental group of the complement of the points into the simmetric group $\mathbb{S}_n$, for a suitable $n$. Jun 2, 2017 at 11:05
• I misunderstood your question. As Francesco Polizzi points out, you are asking for a transitive representation of the fundamental group of the punctured Riemann surface in the symmetric group $\mathfrak{S}_n$, $n$ divisible by every $m_P$, such that the homotopy class of a loop around $P$ maps to an element of cycle type $(m_P^{n/m_P})$ with the standard notation for cycle types. For instance, when $Y$ is $\mathbb{P}^1$ and there are three points with $m_P=4$, this seems difficult . . . Jun 2, 2017 at 12:11
• If you allow a "few" simple branch points with branching $(2,1^{n-2})$ in $Y$ in addition to the points $P$ with branching $(m_P^{n/m_P})$, existence follows from work of Deligne, cf. Kluitman's article in the Braids volume. Jun 2, 2017 at 12:15

Theorem A of the following article of Pete Clark and Jon Voight seems to prove the existence of $X\to Y$ when $Y$ is $\mathbb{P}^1$ with three special points with multiplicities $(a,b,c)$.


text:
## Le Monde puzzle [#1111]

Posted in R, Statistics with tags , , , , , , on September 18, 2019 by xi'an

Another low-key arithmetic problem as Le Monde current mathematical puzzle:

Notice that there are 10 numbers less than, and prime with 11, 100 less than and prime with 101, 1000 less than, and prime with 1111? What is the smallest integer N such that the cardinal of the set of M<N prime with N is 10⁴? What is the smallest multiple of 1111 using only different digits? And what is the largest?

As it is indeed a case for brute force resolution as in the following R code

library(numbers)
homanycoprim=function(n){
many=1
for (i in 2:(n-1)) many=many+coprime(i,n)
return(many)}

smallest=function(){
n=1e4
many=homanycoprim(n)
while (many!=1e4) many=homanycoprim(n<-n+1)
return(n)}

which returns n=10291 as the smallest value of N.  For the other two questions, the usual integer2digit function is necessary

smalldiff=function(){
n=1111;mul=1
while (mul<1e6) {
x=as.numeric(strsplit(as.character(n*mul), "")[[1]])
while (sum(duplicated(x))!=0){
mul=mul+1
x=as.numeric(strsplit(as.character(n*mul), "")[[1]])}
print(n*mul);mul=mul+1}}

leading to 241,087 as the smallest and 9,875,612,340 as the largest (with 10 digits).

## Le Monde puzzle [#1110]

Posted in Books, Kids, R, Travel with tags , , , , , , , , , on September 16, 2019 by xi'an

A low-key sorting problem as Le Monde current mathematical puzzle:

If the numbers from 1 to 67 are randomly permuted and if the sorting algorithm consists in picking a number i with a position higher than its rank i and moving it at the correct i-th position, what is the maximal number of steps to sort this set of integers when the selected integer is chosen optimaly?

As the question does not clearly state what happens to the number j that stood in the i-th position, I made the assumption that the entire sequence from position i to position n is moved one position upwards (rather than having i and j exchanged). In which case my intuition was that moving the smallest moveable number was optimal, resulting in the following R code

sorite<-function(permu){ n=length(permu) p=0 while(max(abs(permu-(1:n)))>0){
j=min(permu[permu<(1:n)])
p=p+1
permu=unique(c(permu[(1:n)<j],j,permu[j:n]))}
return(p)}

which takes at most n-1 steps to reorder the sequence. I however checked this insertion sort was indeed the case through a recursive function

resorite<-function(permu){ n=length(permu);p=0 while(max(abs(permu-(1:n)))>0){
j=cand=permu[permu<(1:n)]
if (length(cand)==1){
p=p+1
permu=unique(c(permu[(1:n)<j],j,permu[j:n]))
}else{
sol=n^3
for (i in cand){
qermu=unique(c(permu[(1:n)<i],i,permu[i:n]))
rol=resorite(qermu)
if (rol<sol)sol=rol}
p=p+1+sol;break()}}
return(p)}

which did confirm my intuition.

## Le Monde puzzle [#1109]

Posted in Kids, R with tags , , , , , on September 4, 2019 by xi'an

A digital problem as Le Monde current mathematical puzzle:

Noble numbers are such that they only involve different digits and are multiple of all their digits. What is the largest noble number?

Hmmmm…. Brute force? Since the maximal number of digits is 10, one may as well try:

k=soz=9
for (t in 1:1e3){
sol=1
while (sol<10^(k-1)){
u=sample(0:8,k);i=digit2int(u)
if (max(i%%u[u>0])==0) soz=max(soz,sol<-i)}}

which returns 9875643120… (I made the conscious choice to exclude zero from the dividers. Which was not a choice spelled out in the original question.)

## Le Monde puzzle [#818]

Posted in Books, Kids, R with tags , , , , on May 1, 2013 by xi'an

The current puzzle is as follows:

Define the symmetric of an integer as the integer obtained by inverting the order of its digits, eg 4321 is the symmetric of 1234. What are the numbers for which the square is equal to the symmetric of the square of the symmetric?

I first consulted stackexchange to find a convenient R function to create the symmetric:

int2digit=function(x){
as.numeric(sapply(sequence(nchar(x)),
function(y) substr(x, y, y)))}

digit2int=function(a){
as.numeric(paste(a,collapse=""))}

flip=function(x){
digit2int(rev(int2digit(x)))}

and then found that all integers but the multiples of 10 are symmetric! only some integers involving 1,2,3 and sometimes zero would work:

> for (i in 1:1000){
+   if (i^2==flip(flip(i)^2)) print(i)}
[1] 1
[1] 2
[1] 3
[1] 11
[1] 12
[1] 13
[1] 21
[1] 22
[1] 31
[1] 101
[1] 102
[1] 103
[1] 111
[1] 112
[1] 113
[1] 121
[1] 122
[1] 201
[1] 202
[1] 211
[1] 212
[1] 221
[1] 301
[1] 311

If I am not (again) confused, the symmetric integers would be those (a) not ending with zero and (b) only involving digits whose products are all less than 10.

## Anomalies in the Iranian election

Posted in Statistics with tags , , on June 17, 2009 by xi'an

While the results of the recent Iranian presidential election are currently severely contested, with accusations of fraud and manipulations, and with an level of protest unheard of in Iran, I had not so far seen a statistical analysis of the votes. This is over: Boudewijn Roukema, a cosmologist with the University of Toruń (Poland), has produced an analysis of the figures published by the Iranian Ministry of the Interior, based on Benford’s Law for the repartition of the first digit i in decimal representations of real numbers, which should be

$f(i) \propto \log_{10}(1+\frac{1}{i})$

for the proportion of votes for a candidate among the four in competition. Roukema exhibits a very unlikely discrepancy on Mehdi Karoubi’s votes, with an extremely high occurence of the digit 7. There is also a discrepancy for Mahmoud Ahmadinejad’s frequencies of 1’s and 2’s that is harder to detect because of the higher frequency of votes for this candidate in the Iranian Ministry of the Interior data. But looking at the most populous districts, Roukema concludes that several million votes could have been added to Ahmadinejad’s votes in those areas, if Benford’s Law holds…

I find this analysis produced merely five days after the election quite astounding, even though the validity of applying Benford’s Law in those circumstances needs more backup…


text:
# Homework Help: Conducting hollow tube

1. Feb 11, 2009

### jimbo71

1. The problem statement, all variables and given/known data
A very long conducting tube (hollow cylinder) has inner radius a and outer radius b. It carries charge per unit length + \alpha , where \alpha is a positive constant with units of C/m. A line of charge lies along the axis of the tube. The line of charge has charge per unit length + \alpha .

Calculate the electric field in terms of \alpha and the distance r from the axis of the tube for r<a.
Express your answer in terms of the variables \alpha, r, and constant \epsilon_0.

Calculate the electric field in terms of \alpha and the distance r from the axis of the tube for a<r<b.
Express your answer in terms of the variables \alpha, r, and constant \epsilon_0.

Calculate the electric field in terms of \alpha and the distance r from the axis of the tube for r>b.
Express your answer in terms of the variables \alpha, r, and constant \epsilon_0.

What is the charge per unit length on the inner surface of the tube?

What is the charge per unit length on the outer surface of the tube?

2. Relevant equations
E=(1/4*pi-epsilon_0)(q/R^2)

3. The attempt at a solution
No idea where to start or how to set up problem

2. Feb 11, 2009


text:
# Medicine:Relative survival

Relative survival of a disease, in survival analysis, is calculated by dividing the overall survival after diagnosis by the survival as observed in a similar population not diagnosed with that disease. A similar population is composed of individuals with at least age and gender similar to those diagnosed with the disease.

When describing the survival experience of a group of people or patients typically the method of overall survival is used, and it presents estimates of the proportion of people or patients alive at a certain point in time. The problem with measuring overall survival by using the Kaplan-Meier or actuarial survival methods is that the estimates include two causes of death: deaths from the disease of interest and deaths from all other causes, which includes old age, other cancers, trauma and any other possible cause of death. In general, survival analysis is interested in the deaths by a disease rather than all causes. Thus, a "cause-specific survival analysis" is employed to measure disease-specific survival. Thus, there are two ways in performing a cause-specific survival analysis "competing risks survival analysis" and "relative survival."

## Competing risks survival analysis

This form of analysis is known by its use of death certificates. In traditional overall survival analysis, the cause of death is irrelevant to the analysis. In a competing risks survival analyses, each death certificate is reviewed. If the disease of interest is cancer, and the patient dies of a car accident, the patient is labelled as censored at death instead of being labelled as having died. Issues with this method arise, as each hospital and or registry may code for causes of death differently.

For example, there is variability in the way a patient who has cancer and commits suicide is coded/labelled. In addition, if a patient has an eye removed from an ocular cancer and dies getting hit while crossing the road because he did not see the car, he would often be considered to be censored rather than having died from the cancer or its subsequent effects.

## Hazard rate

The relative survival form of analysis is more complex than "competing risks" but is considered the gold-standard for performing a cause-specific survival analysis. It is based on two rates: the overall hazard rate observed in a diseased population and the background or expected hazard rate in the general or background population.

Deaths from the disease in a single time period are the total number of deaths (overall number of deaths) minus the expected number of deaths in the general population. If a population of cancer sufferers suffer 10 deaths per hundred population but only 1 death occurs per hundred general population, the disease specific number of deaths (excess hazard rate) is 9 deaths per hundred population. The classic equation for the excess hazard rate is as follows:

$\lambda = \lambda^*+\nu\,\!$

$\lambda = \text{Overall Death Rate},~\lambda^*=\text{Expected death rate},~\nu=\text{Disease-specific death rate}$

The equation does not define a survival proportion but simply describes the relationships between disease-specific death (excess hazard) rates, background mortality rates (expected death rate) and the overall observed mortality rates. The excess hazard rate is related to relative survival, just as hazard rates are related to overall survival.

## Cancer survival

Relative survival is typically used in the analysis of cancer registry data.[1] Cause-specific survival estimation using the coding of death certificates has considerable inaccuracy and inconsistency and does not permit the comparison of rates across registries.

The diagnosis of cause-of-death is varied between practitioners. How does one code for a patient who dies of heart failure after receiving a chemotherapeutic agent with known deleterious cardiac side-effects? In essence, what really matters is not why the population dies but if the rate of death is higher than that of the general population.

If all patients are dying of car crashes, perhaps the tumour or treatment predisposes them to have visual or perceptual disturbances, which lead them to be more likely to die in a car crash. In addition, it has been shown that patients coded in a large US cancer registry as suffering from a non-cancer death are 1.37 times as likely to die than does a member of the general population.[2]

If the coding was accurate, this figure should approximate 1.0 as the rate of those dying of non-cancer deaths (in a population of cancer sufferers) should approximate that of the general population. Thus, the use of relative survival provides an accurate way to measure survival rates that are associated with the cancer in question.

## Epidemiology

In epidemiology, relative survival (as opposed to overall survival and associated with excess hazard rates) is defined as the ratio of observed survival in a population to the expected or background survival rate.[3] It can be thought of as the kaplan-meier survivor function for a particular year, divided by the expected survival rate in that particular year. That is typically known as the relative survival (RS).

If five consecutive years are multiplied, the resulting figure would be known as cumulative relative survival (CRS). It is analogous to the five-year overall survival rate, but it is a way of describing cancer-specific risk of death over five years after diagnosis.

## Software

There are several software suites available to estimate relative survival rates. Regression modelling can be performed using maximum likelihood estimation methods by using Stata or R.[4][5]


text:
# Overview

TigerGraph GraphStudio™ is a graphic user interface that provides an intuitive, browser-based interface to easily accomplish graph-based application development tasks.

## Feature Overview

GraphStudio provides the following features:

### 1. Design Schema

The Design Schema page is where users edit their graph schema. Users will be able to add and specify the attributes and fields of every vertex and edge they add to the schema and also customize the colors and icons displayed on each vertex or edge. Users will also be able to edit existing vertices and edges in the existing schema in this page.

For more details, see Design Schema

### 2. Map Data To Graph

The Map Data To Graph page is where users will add data files and map it to the corresponding vertices or edges in the schema. In this page users will be able to add data files as the data source to load their data into the database. Users will also be able to specify the delimiter used to separate the fields in each file. This page also provides the tools that users can use to map each data file to the corresponding vertices and edges that the data should be loaded to. Users will also be able to map each data field in each data file to the corresponding attributes within each vertex or edge.

For more details, see Map Data To Graph

For more details, see Load Data

### 4. Explore Graph

The Explore Graph page is where users can explore their graph data and uncover insights based on their data. Here users can search for vertices in a graph, discover nearby vertices, find paths between vertices, and run gsql queries. Users will also be able to use the Graph Exploration panel in this page to modify and augment the visualization of their exploration results.

For more details, see Explore Graph

### 5. Build Graph Patterns

The Build Graph Patterns page is where users can build graph business logic queries visually. In this page we provide tools that users can use to build visual patterns visually in drag and drop fashion. In this way, users will not need to understand any gsql to build business logic queries. The users will be able to run these visual patterns, and check out the results. Users will also have the option to see, copy and save the corresponding generated gsql code if they want to do so.

For more details, see Visual Query Builder

### 6. Write Queries

The Write Queries page is where users can write and test out their gsql queries. In this page we provide users a query editor where the users can write their gsql code on. The query editor also validates the user’s query syntax and will let the user know if the syntax is wrong. Users can also install their queries on this page and run it to see the results of their queries. If the user does not install their queries first, the queries will be run on interpreted mode.

For more details, see Write Queries

## GraphStudio Online Test Drive

Visit TigerGraph Test Drive demos at: https://testdrive.tigergraph.com/

The GraphStudio online Test Drive features several instances of the TigerGraph system, each one targeting a different use case. Each copy of TigerGraph has a GraphStudio interface and is preloaded with application-specific queries and synthetic data. These demo applications are provided in a read-only mode. Users can explore and play with pre-installed queries. Users on these demo systems cannot save changes to the graph schema, the loading job, or queries. The corresponding buttons are disabled.

## GraphStudio Availability

### Cloud

If you are using GraphStudio in the TigerGraph Cloud environment, you can directly access GraphStudio via your browser.

### On-Prem

For on-prem deployment, the server by default is listening on port 14240. Any machine connected to the server can access GraphStudio from a browser with the following address:

``http://<your_tigergraph_server_ip_address>:<your_tigergraph_server_port>``

If you cannot access GraphStudio, check your firewall rules and open 14240 port to public. For example, if your Linux OS uses firewall-cmd:

``$firewall-cmd –zone=public –add-port=14240/tcp –permanent`` If you see the error message "Oops, looks like something went wrong" on the login page, the GUI service might be off.  This error might also be caused by an IP range block rule from your ad blocker. Please try turning off your ad blocker for the GraphStudio page and try again. To verify, in a linux shell of the server, run the following: `$ gadmin status gui`

If it is off, turn it on by running:

## Browser Support

As of Jan 2020, the GraphStudio UI is certified on following browsers:

Browser Chrome Safari Firefox Opera Edge Internet Explorer

Supported version

54.0+

11.1+

59.0+

52.0+

80.0+

10+

Not all features are guaranteed to work on other browsers.

## GraphStudio Limitations

Some features which are available in GSQL are not available in GraphStudio.

### Design Schema

• Fixed binary data types are not supported.

• PRIMARY KEY and composite key are not supported.


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# Error Message: 'Constant Already Defined' When using PHPUnit

Last updated:

If you are using PHPUnit to run many tests each of which defines constants, you might run into errors, namely "Constant CONSTANT_NAME already defined" when you try to run them together.

This happens because PHPUnit runs all tests in the same PHP process by default so, after you run your first test (and define a constant therein) PHP will complain because you've already set it - in another test, yes, but all in the same process.

To fiz this you need to tell PHPUnit not to preserve global state between tests and to run each test in a separate process. This is how you'd do it:

class RecurringReportTest extends \PHPUnit_Framework_TestCase {

protected $preserveGlobalState = FALSE; protected$runTestInSeparateProcess = TRUE;

//setup and teardown functions
protected function setUp() { }
protected function tearDown() { }

If you use bootstrap files (as is the case with many modern frameworks), you will probably want to place the bootstrap code in PHPUnit's setUp() function (before each test) instead.