text:
# Transforming ordinal logistic regression coefficients to beta weights

Ordinal logistic regression analysis result in coefficients which are log odds, and not b or beta weights, like in a linear regression. For example:

1. How can I compare the log odds of the DVs? Is it correct to say that DV1 effect on the IV is 11%, compared to DV2 (-0.071/-0.619)?
2. Is there any way to convert the log odds to beta weights?
• Just as a sidenote OLS refers to Ordinary Least Square. Not to Ordinal Logistic (Regression) en.wikipedia.org/wiki/Ordinary_least_squares May 20 at 8:13
• I am a bit confused w.r.t. your choice of abbreviations: If DV abbreviates "dependent variable", you talk about the effect that the dependent variable DV1 has on the independent variable IV? May 20 at 13:27
• Thanks for the corrections to the title and table May 20 at 18:39

Now, the "log odds"-function (or "logit") is nonlinear, and thus is its inverse, the logistic sigmoid function $$\sigma$$. Thus, the effect on the DV, of a unit change in an IV, is not constant but depends on the value of the IV.
So, if you want to know the effect of a change in the IV $$\mathbf x$$ on the DV $$y$$ at the point $$\mathbf x= \mathbf{x_0}$$, you could compute the gradient of $$\sigma(\beta\cdot\mathbf x)$$ at $$\mathbf{x_0}$$, which gives you the linear approximation of the effects of all your scalar IVs at this particular value $$\mathbf{x_0}$$. Recall, that, if you have $$k$$ IVs, then $$\mathbf x \in \mathbb{R}^{k+1}$$, because an extra dimension is added for the intercept.

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#### CHAPTER 15 COMMUNICATION SYSTEMS

Need for modulation

1. Size of the antenna or aerial

The antenna should have a size comparable to the wavelength of the signal (at least λ/4 in dimension) to sense the time variation of the signal. For an electromagnetic wave of frequency 20 kHz, the wavelength λ is 15 km. Hence direct transmission of such baseband signals is not practical due to large antenna requirement. We can transmit with reasonable antenna lengths if transmission frequency is high (for example, if ν is 1 MHz, then λ is 300 m). Therefore, there is a need of translating the information contained in the original low frequency baseband signal into high or radio frequencies before transmission.

2. Effective power radiated by an antenna

Power radiated by an antenna is related to length L of the antenna and wavelength λ as follows,

Therefore, for the same antenna length, the power radiated increases with decreasing λ, i.e., increasing frequency. Hence, the effective power radiated by a long wavelength baseband signal would be small. For a good transmission, we need high powers and hence the need of using high frequency transmission.

3. Mixing up of signals from different transmitters

If many people are talking at the same time or many transmitters are transmitting baseband information signals simultaneously, all these signals will get mixed up and there is no simple way to distinguish between them. Using communication at high frequencies and allotting a band of frequencies to each message signal for its transmission can solve the problem.


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• Corpus ID: 239615997

# Algebraic cycles and Fano threefolds of genus 8

```@inproceedings{Laterveer2021AlgebraicCA,
title={Algebraic cycles and Fano threefolds of genus 8},
author={<NAME>},
year={2021}
}```
We show that prime Fano threefolds Y of genus 8 have a multiplicative Chow– Künneth decomposition, in the sense of Shen–Vial. As a consequence, a certain tautological subring of the Chow ring of powers of Y injects into cohomology.
5 Citations
Some new Fano varieties with a multiplicative Chow-K\"unneth decomposition
Let Y be a smooth dimensionally transverse intersection of the GrassmannianGr(2, n) with 3 Plücker hyperplanes. We show that Y admits a multiplicative Chow–Künneth decomposition, in the sense of
Some Motivic Properties of Gushel-Mukai Sixfolds
• Mathematics
• 2022
Gushel-Mukai sixfolds are an important class of so-called FanoK3 varieties. In this paper we show that they admit a multiplicative ChowKünneth decomposition modulo algebraic equivalence and that they
Algebraic cycles and intersections of three quadrics
• R. Laterveer
• Mathematics
Mathematical Proceedings of the Cambridge Philosophical Society
• 2021
Let Y be a smooth complete intersection of three quadrics, and assume the dimension of Y is even. We show that Y has a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a
Algebraic cycles and intersections of a quadric and a cubic
Abstract Let Y be a smooth complete intersection of a quadric and a cubic in ℙn{\mathbb{P}^{n}}, with n even. We show that Y has a multiplicative Chow–Künneth decomposition, in the sense of
Algebraic Cycles and Intersections of 2 Quadrics
A smooth intersection Y of two quadrics in P has Hodge level 1. We show that such varieties Y have a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a consequence, a certain

## References

SHOWING 1-10 OF 51 REFERENCES
On the Chow ring of certain Fano fourfolds
We prove that certain Fano fourfolds of K3 type constructed by Fatighenti–Mongardi have a multiplicative Chow–Kunneth decomposition. We present some consequences for the Chow ring of these fourfolds.
ON THE CHOW RING OF A K3 SURFACE
We show that the Chow group of 0-cycles on a K3 surface contains a class of degree 1 with remarkable properties: any product of divisors is proportional to this class, and so is the second Chern
Derived categories of Fano threefolds
We consider the structure of the derived categories of coherent sheaves on Fano threefolds with Picard number 1 and describe a strange relation between derived categories of different threefolds. In
Algebraic cycles and Verra fourfolds
This note is about the Chow ring of Verra fourfolds. For a general Verra fourfold, we show that the Chow group of homologically trivial \$1\$-cycles is generated by conics. We also show that Verra
A REMARK ON THE CHOW RING OF KÜCHLE FOURFOLDS OF TYPE \$d3\$
• <NAME>
• Mathematics
Bulletin of the Australian Mathematical Society
• 2019
We prove that a Küchle fourfold \$X\$ of type d3 has a multiplicative Chow–Künneth decomposition. We present some consequences for the Chow ring of \$X\$ .
The Chow Ring of a Cubic Hypersurface
We study the product structure on the Chow ring (with rational coefficients) of a cubic hypersurface in projective space and prove that the image of the product map is as small as possible.
Finite-dimensionality and cycles on powers of K3 surfaces
For a K3 surface S, consider the subring of CH(S^n) generated by divisor and diagonal classes (with Q-coefficients). Voisin conjectures that the restriction of the cycle class map to this ring is
Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8
• Mathematics
• 2005
Let \$X\$ be a general complex Fano threefold of genus 8. We prove that the moduli space of rank two semistable sheaves on \$X\$ with Chern numbers \$c_1=1\$, \$c_2=6\$ and \$c_3=0\$ is isomorphic to the Fano


text:
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# All about LaTeX - PowerPoint PPT Presentation

All about LaTeX. <NAME> ( <EMAIL> ) <NAME> ( <EMAIL> ) <NAME> ( <EMAIL> ). Outline. Introduction Document Structure Mathematical Typesetting Spacing Accents and Font Style Tables, Arrays, and Lists

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<NAME>

(<EMAIL>)

Outline
• Introduction
• Document Structure
• Mathematical Typesetting
• Spacing
• Accents and Font Style
• Tables, Arrays, and Lists
• Multi-line Equations
• Text Formatting
• Bibliography and Compound Expressions
• Slides
• Including Graphics
Introduction
• Introduction to LaTeX
• Required Components of a LaTeX Document
• Error Messages
• Typing LaTeX Commands
1.1 Introduction to LaTeX
• The history of TeX
• Donald Knuth, 1978
• Everyone could easily use to typeset documents, particularly those that include formulae.
• Make it freely available.
• The history of LaTeX
• Leslie Lamport, wrote a variant of TEX called LaTeX.
• Focuses on document structure rather than TeX small details
• Strong when working with mathematical symbols
1.2 Documents Components
• Every LaTeX document must contain the following three components:
• \documentclass{article}
• \begin{document}
• \end{document}
• In general, required information is included in LaTeX commands in braces {}, while optional information is included in square brackets [].
• The default font size for each class is 10 point.
• The \documentclass command must appear at the very beginning of your LaTeX document, before any other LaTeX commands, or you will get an error message.
1.3 Error Messages
• A common error is not to close braces for a command.
• Another one that occurs frequently is to use math commands outside of math mode (described later).
• Since LaTeX will stop after any \end{document} command, a good strategy is to insert \end{document} temporarily to see if the error is above its location.
1.4 Typing LaTeX Commands
• Maybe, you having to type LaTeX commands as part of your text. How do you do that without LaTeX taking them seriously and following them?
• Surround any text that you want printed as is with a \begin{verbatim} and an \end{verbatim} command.
Document Structure
• Creating a Title Page
• Creating a Title Page, Continued
• Sections
• Cross-References
• Abstracts
• Footnote
• The command \pagestyle controls page numbering and headings. It can take the following forms:
• \pagestyle{plain}
• \pagestyle{empty}
• These commands can also be applied to a single page using \thispagestyle instead of \pagestyle.
2.2 Creating a Title Page
• (Remember that the preamble refers to any commands between the \documentclass command and the \begin{document} command.)
• Provide this information in the preamble of your document:
• \title{yourtitlehere}
• \author{yournamehere
• \date{currentdate}
2.3 Creating a Title Page (cont.)
• Place a \maketitle command immediately after the \begin{document} command.
• The \documentclass command can take a titlepage option: \documentclass[titlepage]{article}.
2.4 Sections
• One of the most important ways of creating structure in a document is to split it into logical sections.
• There are two related commands for creating sections:
• \section{sectiontitle}
• \section*{sectiontitle}.
2.5 Cross-References
• Use \label{name} to label the point in your document with some mnemonic.
• Section \ref{name} to refer to that point.
• \ref{name} will be replaced by the number of the section containing the corresponding \label command.
• You will need to run LaTeX twice to generate these references.
• If you have been using \section commands throughout your document, then LaTeX has all the information that it needs to construct one for you.
• Place the command \tableofcontents after your \begin{document} command.
• It may be necessary to run LaTeX twice on a document with a Table of Contents.
2.7 Abstracts
• To create an abstract, place your text in an abstract environment, i.e., between \begin{abstract} and \end{abstract} commands.
• The abstract should come immediately after your \maketitle command, but before any \tableofcontents command.
2.8 Footnote

For example:

… in ICMP\footnote{Internet Control Message Protocol} …

Mathematical Typesetting
• Mathematical Formulas
• Greek Letters
• Exponents and Subscripts
• Above and Below
• Fractions
• Functions
• Sums, Integrals, and Limits
• Roots
• Text in Math Displays
• Operators
• Relations
• Negated Symbols
• More Symbols
3.1 Mathematical Formulas
• There are two ways to insert mathematical formulas into your document with LaTeX:
• Is to have it appear in a paragraph with text($). • Is to have them appear in a separate paragraph($$). • \alpha is the first letter of the Greek alphabet. •$$ \frac{x^n-1}{x-1} = \sum_{k=0}^{n-1}x^k $$3.3 Exponents and Subscripts • Use the ^ character to create exponents: • If you have an exponent containing more than one character, group the exponent characters inside braces. x^21 \ne x^{21} • Similarly, subscripts are created using the _(underscore character). Again, for • subscripts of more than one character, use braces to indicate where the subscript starts and stops. x_21 \ne x_{21} \overline \overbrace \underline \underbrace$$ \left( \begin{array}{c} m+n\\ m \end{array} \right) = \frac{(m+n)!}{m!n!} = \frac {\overbrace{(m+n)(m+n-1)\cdots(n+1)}^\mbox{$m$factors} {\underbrace{m(m-1)\cdots 1}_\mbox{$m$factors}} $${ while \overline{x+\overline{y}} = \overline{x}+y 3.4 Above and Below 3.5 Fractions • Diagonal fraction bar • Horizontal fraction bar • a/b • written as \frac{numerator}{denominator}. •$$ \frac{a/b-c/d}{e/f-g/h} $$LaTeX uses italics in math mode. Roman (non-italic) for function names. Use a backslash in front of function names. Here is a list of function names: \arccos \arcsin \arctan \arg \cos \cosh \cot \coth \csc \deg \det \dim \exp \gcd \hom \inf \ker \lg \lim \liminf \limsup \ln \log \max \min \Pr \sec \sin \sinh \sup \tan \tanh 3.6 Functions 3.7 Sums, Integrals, and Limits • Summations and integrals both have lower and upper limits, and the commands are similar. • Limits usually have text with an arrow placed below them. •$$ \sum_{k=0}^\infty\frac{(-1)^k}{k+1} = \int_0^1\frac{dx}{1+x} $$•$$ \lim_{x\rightarrow 0} \frac{\sin x}{x} = 1 $$3.8 Roots • Use the \sqrt{} command to produce square roots: • \sqrt{\frac{a}{b}} • If you need an nth root, use \sqrt[n]{} instead. • \sqrt[10]{\frac{a}{b}} 3.9 Text in Math Displays • Use the command \mbox{your text here} to include short phrases in a formula. • (If your phrase isn't short, then you should consider embedding your formula in a text paragraph instead of your text in a formula paragraph.) •$$ \int_0^{2\pi}\cos(mx)\,dx = 0 \hspace{1cm} \mbox{if and only if} \hspace{1cm} m\ne 0 $$3.10 Operators • You will probably not need most of the binary operators listed here, but it should be a handy reference: 3.11 Relations • Again, here are more relations than you will ever need. You may want to print this for reference: 3.13 More Symbols • For \therefore you will need to include the line \usepackage{amssymb} in your preamble. • Similarly, for using \mathbb{Z}, etc., you will need to include the line \usepackage{amssymb} in your preamble. Spacing • Spacing Between Words • Fine-Tuning Spacing in Math-Mode • Double Spacing • Sloppy Line Breaks • Enlarging Pages 4.1 Spacing Between Words • LaTeX controls the spacing of your document, trying hard to break lines in places that are pleasing to the eye. • As a consequence, one blank space is the same as a million blank spaces. • Tabs are treated like blank spaces. • Blanks at the end of a line are ignored. • A single \Enter" is treated like a blank space. • More than one \Enter" marks the beginning of a new paragraph. 4.2 Spaces in Math-Mode • \, produces a small space • \: produces a medium space • \; produces a large space • \! produces a small negative space 4.3 Double Spacing • There will be times when you will need to submit a draft that is double-spaced, to permit a grader or editor to make comments. • To double-space a paper, put \renewcommand{\baselinestretch}{2} in your paper's preamble. 4.4 Sloppy Line Breaks • Surround the offending paragraph with \begin{sloppypar} and \end{sloppypar} commands. • Then LaTeX will not break words up but rather will allow more spacing between words in the given paragraph. 4.5 Enlarging Pages • LaTeX works very hard to find the best place to break between pages. If you are unhappy with the result, you can change it with the following two commands: • \newpage will force the start of a new page. • \enlargethispage{size} will increase the number of lines added to a page. Accents and Font Style • Accents • Hyphenation • The Logo • Quotation Marks • Changing the Appearance of Words 5.1 Accents • LaTeX can produce the following accents. (The letter \u" is only used for the purposes of this example. The accents work with any letter.) 5.2 Hyphenation • There are four hyphens in LaTeX : • - (a single dash) is for hyphenating words. • -- (two dashes) is for ranges of numbers. • --- (three dashes) is for an honest-to-goodness dash between words. • - is a minus sign in math mode. • For example: My cousin-in-law lived in Germany in 1995--6; he speaks French---really, he does. His favorite number is -2. 5.3 The LaTeX Logo • You can typeset the LATEX logo with the \LaTeX command. • As with most commands, it consumes any space behind it, so if it isn't at the end of a sentence, use \LaTeX\ instead. 5.4 Quotation Marks • Use  (usually on the left side of the keyboard) to begin a quotation • And '' (usually on the right side of the keyboard) to end a quotation: 5.5 Appearance of Words • \underline{phrase} to underline a phrase, • \textbf{phrase} to print a phrase in boldface, and • \emph{phrase} to italicize a phrase. Tables, Arrays, and Lists • Constructing Arrays • Constructing Tables 6.1 Constructing Arrays • Surround the entries with a \begin{array}{justification} command and an \end{array} command. • Separate column entries by an &. And end each line with a \\. • If your array is a matrix, you can surround it with large parentheses \left( and \right). • For example: •$$ • \left( • \begin{array}{rcl} • \alpha&\beta&\gamma\\ • \delta&\epsilon&\zeta\\ • \eta&\theta&\iota\\ • \end{array} • \right) • $$6.2 Constructing Tables • For example: \begin{tabular}{|r|c|l|} \hline Right & Center & Left\\ \hline alpha&beta&gamma\\ delta&epsilon&zeta\\ eta&theta&iota\\ \hline \end{tabular} Multi-line Equations • Multi-line Equations • Accents • Dots • Indenting 7.1 Multi-line Equations • Surround the equations by \begin{eqnarray*} and \end{eqnarray*}. • Surround the equals sign or inequality with &'s, and end each line with \\. • Note: you do not need to use$$'s with this environment. For example, \begin{eqnarray*} 1+2+\ldots+n &=& \frac{1}{2}((1+2+\ldots+n)+(n+\ldots+2+1))\\ &=& \frac{1}{2}\underbrace{(n+1)+(n+1)+\ldots+(n+1)}_{\mbox{$n$copies}}\\ &=& \frac{n(n+1)}{2}\\ \end{eqnarray*} 7.2 Accents • We use several different kinds of accents in mathematics: a hat, bar, dot, and arrow over a variable all have different meanings. LaTeX uses commands that surround the variable: •$\hat{a},

\dot{a},

\ddot{a},

\tilde{a},

\bar{a},

\vec{a}\$

7.3 Dots
• \cdots for center height dots.
• \ddots for diagonal dots, which occur in matrices.
• \ldots for lower height dots.
• \vdots for vertical dots.

For example:

$$\left( \begin{array}{ccc} a_{11}&\cdots&a_{1n}\\ \vdots&\ddots&\vdots\\ a_{m1}&\cdots&a_{mn} \end{array} \right)$$

7.4 Indenting
• The default for a LaTeX document is to indent new paragraphs unless the paragraph follows a section heading.
• If you want to change the indentation, use the \indent and \noindent commands respectively, at the beginning of the paragraph.
• If you wish to choose the amount of indentation for some reason, then use the command:

\setlength{\parindent}{size of indentation with unit}.

• Since this is a command that affects the whole document, it should go in the preamble, between the \documentclass and \begin{document} commands.
Text Formatting
• Centering Text
• Extended Quotation
• Bulleted Lists
• Numbered Lists
• Filling a Line
8.1 Centering Text
• By default, LaTeX will start all text at the left margin.
• If you want to center a title, a table, etc., surround what you want centered with the commands:

\begin{center} and \end{center}.

• A header is the text automatically included at the top of each document.

will do the job for you.

8.3 Extended Quotation
• If you are going to include an extended quotation from another source, it is important to indicate the difference between the quotation and your words.
• The least obtrusive way to do so is to indent.
• In LaTeX, surround the quotation with \begin{quote} and \end{quote}.
8.4 Bulleted Lists
• To create a bulleted list, surround the information with a \begin{itemize} and an \end{itemize}, and begin each item with an \item.

For example,

\begin{itemize}

\item A bulleted item.

\item Another bulleted item.

\begin{itemize}

\item A nested bulleted item.

\end{itemize}

\item You get the idea.

\end{itemize}

8.5 Numbered Lists
• To create a numbered list, surround the information with a \begin{enumerate} and an \end{enumerate}, and begin each item with an \item.

For example,

\begin{enumerate}

\item A numbered item.

\item Another numbered item.

\begin{enumerate}

\item A nested numbered item.

\end{enumerate}

\item You get the idea.

\end{enumerate}

8.6 Filling a Line
• You can insert an arbitrary amount of space into a line with the \hspace{length} command. Here the length must include a unit, such as 1.5in or 2.3cm.
• If you want a spacing in a line that will push the surrounding words to the left and right margins, use the \hfill command.
• If instead of spacing, you want either dots or a line, use \dotfill or \hrulefill, respectively.
9 Bibliography
• Bibliographies
• Using BibTex
9.1 Bibliographies
• LaTeX provides a mechanism for automatically linking citations with items in the bibliography.
• Surround the bibliography with \begin{thebibliography}{9} and \end{thebibliography}.
• With the bibliography in place, a citation in the body of the document is made with \cite{label}, where label is the same as what occurs in the corresponding \bibitem{label}.
• What is the 9 in \begin{thebibliography}{9} for? It is a dummy number indicating how many digits to leave space for in the numbering of the bibliography.
Slides
• The Slide Class
• How to Use the Slides Class
10.1 The Slide Class
• LaTeX does not want to be Microsoft PowerPoint.
• If you have mathematical formulae to display on transparencies, LaTeX is there to help with the slides document class.
• The slide class uses a larger font that is designed to be legible at a distance.
10.2 How to Use the Slides Class
• Surround the document with \begin{document} and \end{document} commands.
• Surround the text that you want to appear on each slide with \begin{slide} and \end{slide} commands.
• Preview the slides to see where best to break the material between slides.
Including Graphics
• Graphic File Formats
• Graphics Package
• Including Graphics Within Your Document
11.1 Graphic File Formats
• There are a number of graphics formats out there, such as:
• bmp
• eps
• Gif
• Jpg
• PDF
• ps
• LaTeX works best with the postscript formats (eps, ps) which were around
11.2 Graphics Package
• Picture environment \begin{picture} & \end{picture}
• If you are going to include graphics in your document, you will need to ask LaTeX to use a package of graphics commands:
• place \usepackage{graphicx} in the preamble.

For example:

11.3 Including Graphics
• You use the \includegraphics{graphicfile} command to include your graphic file in your document.
• If you wish to control the size of the document, you can also specify the height and width:

\includegraphics[height=2in, width =3in]{graphicfile}.

• The Letter Class
• Letter Commands for the Preamble
• Commands for Each Letter
12.1 The Letter Class
• Aside from the article class, LaTeX provides a letter class for formal letters.
• To use the class,
• Include the commands that apply to all letters in the file.
• Begin with a \begin{document} command.
• Include the commands for each letter.
• End with a \end{document} command.
12.2 Preamble’s Letter Commands
• The following commands apply to each letter in the file:
• \signature{yournameandtitle} for your printed name in the signature block.
• \date{letterdate} if you want to x the date on the letter; otherwise the date will default to the current date when the letter is printed.
12.3 Commands for Each Letter
• On the next line, type the addressee's address in braces. Separate lines with \\’s.
• Put your opening greeting in \opening{dearjohndoe}.
• Put the text of your letter.
• Put your closing in \closing{sincerely}.
• If their are carbon copies, use \cc{names}.
• If their are enclosures, use \encl{docs}.
• If their is a postscript, use \ps.
• End with \end{letter}.
Introduction

Document Structure

Mathematical Typesetting

Spacing

Accents and Font Style

Tables, Arrays, and Lists

Multiline Equations

Text Formatting

Bibliography and Compound Expressions

Slides


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#### DOCUMENTA MATHEMATICA, Vol. 2 (1997), 313-333

<NAME> and <NAME>

Remarks on the Darboux Transform of Isothermic Surfaces

We study Darboux and Christoffel transforms of isothermic surfaces in Euclidean space. Using quaternionic calculus we derive a Riccati type equation which characterizes all Darboux transforms of a given isothermic surface. Surfaces of constant mean curvature turn out to be special among all isothermic surfaces: their parallel surfaces of constant mean curvature are Christoffel and Darboux transforms at the same time. We prove --- as a generalization of Bianchi's theorem on minimal Darboux transforms of minimal surfaces --- that constant mean curvature surfaces in Euclidean space allow $\infty^3$ Darboux transforms into surfaces of constant mean curvature. We indicate the relation between these Darboux transforms and Bäcklund transforms of spherical surfaces.

1991 Mathematics Subject Classification: (Primary) 53A10, (Secondary) 53A50, 53C42.

Keywords: Isothermic surface, Darboux transformation, Christoffel transformation, Riccati equation, Constant mean curvature, Baecklund transformation.

--> This manuscript contains color graphics,
--> hence the dvi files will be incomplete.
Full text: dvi.gz 32 k, dvi 80 k, ps.gz 1402 k, pdf 1423 k

Home Page of DOCUMENTA MATHEMATICA


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# SHA256_HMAC for deriving session keys using a counter

I need to generate some session keys from a master key that was generated from an ECDH key exchange. The master key is 256 bits and I need 256 bit sessions keys.

Is it safe to use SHA256_HMAC with a counter as the HMAC input to get the session keys?

skey1 = SHA256_HMAC(master_key, 1);

skey2 = SHA256_HMAC(master_key, 2);

skeyN = SHA256_HMAC(master_key, N);

The counter is meaningful to the application to know which session key to use. I have also looked at Hashed Key Derivation Functions (HKDF) but it seems like that is more useful when you need a long random output from a given input. My output length is the same as the input length and I need to be able to generate the correct session key based on a counter value (might not be sequential calls). The counter is essentially an id.

Sure, that should be fine. It's probably more secure than KDF1 & 2 that use a normal hash method and a 4 byte counter. HKDF however can certainly be used for this, but it seems you only need to differentiate, rather than extract and expand.

• Anything missing from the answer, John? – <NAME> Jun 14 '15 at 11:47

Yes, it's fine.

However, you might as well use HKDF-Expand (with your counter as the context information 'info'), so that if you later need some session keys to be larger than 256 bits, the extension is already defined for you. So,

$$sk_1 = HMAC(mk, 1 || 0x01)\\ sk_2 = HMAC(mk, 2 || 0x01)\\ ...$$

And if you need a 512-bit $sk_3$ that's:

$$sk_3 = HMAC(mk, 3 || 0x01)\ ||\ HMAC(mk, HMAC(mk, 3 || 0x01) || 3 || 0x02)$$


text:
Chapter 130

Testicular torsion is a true urologic emergency. It occurs when a testicle rotates on its vascular pedicle resulting in vascular obstruction (Figure 130-1). Torsion is most common between the ages of 12 to 18.1 Age should not be considered when making the diagnosis, however, as torsion may occur in an antenate, neonate, or geriatric patient.2A history of prior orchiopexy does not negate the possibility of torsion. Presenting signs and symptoms frequently include acute and diffuse scrotal pain, scrotal swelling, a high-riding testicle, and an absent cremasteric reflex. If torsion is suspected, a Urologist should be consulted immediately and manual detorsion attempted.

###### Figure 130-1

Torsion of the right testicle. The testicle lies horizontally and in a higher position than the normal testicle.

The differential diagnosis of the acutely swollen or painful scrotum also includes torsion of the testicular appendage, epididymitis, orchitis, hernia, varicocele, tumor, trauma, idiopathic scrotal edema, fat necrosis, viral inflammation, and Henoch-Schönlein purpura.3,4As testicular torsion is the diagnosis requiring the most urgent action, it should be first on the differential diagnosis list. Testicular torsion may result in irreversible damage to the involved testis. It may also affect the contralateral testicle. Recent studies have examined the possible immunologic mechanism for this global effect on fertility but the exact pathophysiology has not been established.5,6

Testicular torsion results in the obstruction of the blood supply to the testis. The venous obstruction leads to edema. This is followed by arterial obstruction that leads to testicular ischemia. Because the degree of torsion or vascular compromise cannot be quantified by current methods, the time for torsion to result in irreversible testicular damage cannot be determined.2 A complete vascular occlusion will cause a testicle to develop permanent and irreversible damage earlier than a testicle with partial vascular occlusion. The literature is variable and cites a range of 6 to 24 hours of vascular occlusion required to cause irreversible ischemic damage to a testicle.7 Most authors agree that the best outcomes are obtained with detorsion within 6 hours of symptom onset.

Testicular torsion may be classified as extravaginal or intravaginal. Extravaginal torsion occurs primarily in neonates. The testis, epididymis, and tunica vaginalis twist together on their vertical axis because the gubernaculum has not yet become attached to the scrotal wall. It is caused by the free rotation of the testicle around the spermatic cord at a level above the tunica vaginalis. Intravaginal torsion occurs in peri- or postpubertal males and has been associated with the so-called bell-clapper deformity. In the normal scrotum, the tunica vaginalis only partially covers the epididymis and does not cover the spermatic cord. In the bell-clapper deformity, the tunica vaginalis encases the entire testicle, epididymis, and base of the spermatic cord. This allows the contents to twist and move within the ...

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## Building Gpg4win installer package

Learn how you can build the Gpg4win installer packages on your own.

## Conventional ".exe installer"

Building a new Gpg4win installer package is mostly automated. The build procedure can be executed on a GNU/Linux system or within a virtual machine on Windows and other systems.

What you need is:

• Build Gpg4win on GNU/Linux:

In principle, any current GNU/Linux system is sufficient as the base system. Some minor adaptations might be necessary though. The specific GNU/Linux guide is tested with a Debian GNU/Linux 'Etch' 4.0 system.

• Build Gpg4win on Windows:

In principle, any current Windows system is sufficient as the base system. Some minor adaptations might be necessary though. The specific Windows guide is tested with Windows XP SP2.

## MSI Installer

Attention: The Gpg4win MSI Installer is only supported since Gpg4win 1.9.0beta.

What you need is:

• A complete conventional installer as described above with the same version and contents as you want for the MSI package.
• Perl 5 on the GNU/Linux System.

On Debian GNU/Linux 4.0 you can install Perl 5 this way:
# apt-get install perl

• A Windows XP SP2 system, with the following tools installed.
• Windows Installer XML (WiX) toolset Version 3.0. This can be downloaded from http://wix.sourceforge.net/.
• WiX requires the .NET Framework. Successfully tested is .NET 2.0
• Finally, you need a method to access the file tree where your built your conventional installer from your Windows system This could done via an SMB network connection or simply by transferring the whole file tree to Windows (attention: it is several 100 MBytes). See also the section below.

Now you need to execute the following steps:

1. Change into the src/ directory of the Gpg4win source code where you built the conventional installer before (compare Build Gpg4win under GNU/Linux):
$cd src 2. Execute make-msi.pl to create the required WiX source files:$ make msi
3. Now switch to the same directory ("src") on the Windows system and execute script "make-msi.bat" to create the MSI package:
> make-msi.bat gpg4win-Version.wix
or
> make-msi.bat gpg4win-light-Version.wix

where "Version" is the complete version number of the just created installer, e.g. "1.9.0-svn595". You will find the resulting .wix files in the same directory.

This routine assumes that WiX is installed in a default location. In case it is not, you need to adapt the search path (PATH system variable).

4. The MSI package is now ready and stored as file "gpg4win.msi". You can install it in the following way:
> msiexec /i gpg4win.msi
and also de-install it:
> msiexec /x gpg4win.msi

### How to access the Gpg4win build files from Windows

The WiX software requires access to the file tree where the installer was created. Although this can be done in many ways, only three options are illustrated here. As these are not step-by-step procedures and they need to be adapted for your individual environment.
• Mounting a virtual ext3 build partition:

If you build Gpg4win as described on the special guide for Windows in a virtual GNU/Linux system, then the required file tree is located inside a hard disk image named build.img. It can be accessed directly from Windows with the free tools ext2fsd and FileDisk.

If ext2fsd and FileDisk are installed as described, you can mount the build partition after shutdown of the virtual GNU/Linux with this command:

filedisk /mount 0 C:\path\to\build.img H:

Of course 'C:\path\to\build.img' needs to be replaced with the actual path to the image file. Now the build partition is available as drive H: on your Windows system.

• Ubuntu with VirtualBox and Samba:

You can run Windows XP as a virtual machine under VirtualBox and access the file tree via SMB by running a Samba server on the Linux host system. The file tree is accessible as a so-called "Share" (e.g. via the right mouse button menu for the respective folder "gpg4win" in Nautilus). After this, the network share can be made available in Windows:
> net use H: \\10.0.2.2\gpg4win
Where H: is the drive letter to use and gpg4win the name of the network share.

• Using the archive tool "tar":

A list of all required files is stored in the file make-msi.files by the script make-msi.pl. This list can now be used to pack all required files for transport:
$cd gpg4win$ tar -T src/gpg4win-Version.files cjf gpg4win-msi.tar.bz2

where "Version" should be the complete version number of the current installer, e.g. "1.9.0-svn595". You will find the respective .files files in directory "src".

Additional to gpg4win-msi.tar.bz you need src/gpg4win-Version.wix and src/make-msi.bat on your Windows system. You should store them in the respective src/ directory.


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# ZZ Top and the Heros of Mathematics

My summer reading, $textrm{Primes of the form}, x^2 + ny^2"$, follows the mathematical discoveries and subsequent works of <NAME>, <NAME>, <NAME>, and <NAME>. My goal in mathematics is to make the kinds of significant discoveries that these mathematicians made.

Euler lived in the 18th century; he proved some theorems about primes of the form $x^2 + ny^2$ which had been conjectured in the 17th century by another famous mathematician, <NAME>, who succeeded Euler as the director of the Prussian Academy of Sciences, and Legendre both studied quadratic forms and their applications to Euler’s work. One of the applications of the theory of quadratic forms is to generalize Euler’s proofs. However, Legendre developed the theory in a much more modern and natural way. In addition, he made significant developments in the theory of quadratic reciprocity. Finally, Gauss synthesized all of the above ideas. He is widely considered to be the finest mathematician ever.

I am fascinated by who these famous mathematicians were, whereas during my engineering studies I was more interested in the how and why questions. For example, there is a famous result in algebraic number theory credited to <NAME>: the number field generated by the 23rd root of unity does not have unique factorization while the number fields generated by the nth root of unity for $n < 23$, had all been found to have unique factorization. My question was, “how the heck was Kummer able to figure this out?” to which my professor responded, “…he was some kind of genius.”

I may not be a genius in the same class as Kummer and Gauss, but I wouldn’t be studying mathematics if I didn’t enjoy it or if I didn’t think I could be successful in it. I hope one day, I will be in a position to make a significant mathematical discovery on par with the heroes of mathematics.

This entry was posted in General. Bookmark the permalink.


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시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 128 MB49821317443.069%

문제

A level is being designed for a new platform game. The locations of the platforms have been chosen. Contrary to popular opinion, platforms can't float in the air, but need pillars for support. More precisely, each of the two ends of the platform needs to be supported by a pillar standing on the floor or on a different platform.

You will be given the locations of the platforms in a coordinate system as in the left image below. Each platform's location is determined by its altitude (vertical distance from the ground) and the start and end coordinates in the horizontal direction. Each support pillar is placed half a unit from the end of a platform, as in the right image.

Determine the total length of pillars needed to support all the platforms.

 Example level with three platforms. The lowest platform is at altitude 1, the second lowest at altitude 3 and the third at altitude 5. The total length of pillars needed to support all platforms is 14.

입력

The first line contains the integer N, 1 ≤ N ≤ 100, the number of platforms.

Each of the following N lines contains the position of one platform, three coordinates Y, X1 and X2The first number is the altitude, the other two the horizontal coordinates. All coordinates will be positive integers less than 10000 satisfying X2 > X1+1 (i.e. the length of each platform will be at least 2).

The input will be such that no two platforms overlap.

출력

Output the total length of pillars needed to support all the platforms.

예제 입력 1

3
1 5 10
3 1 5
5 3 7

예제 출력 1

14

예제 입력 2

5
50 50 90
40 40 80
30 30 70
20 20 60
10 10 50

예제 출력 2

200


text:
# Math Help - binomial theorem

1. ## binomial theorem

can someone pls help me solve the following expansion?

a binomial expansion, (a+b)^n, has 15 terms altogether. what is the value of n?

this question is part of my combinatorics chapter assignment. i don't know where else to put it

2. Originally Posted by oryxncrake
can someone pls help me solve the following expansion?

a binomial expansion, (a+b)^n, has 15 terms altogether. what is the value of n?

this question is part of my combinatorics chapter assignment. i don't know where else to put it
Hello. We know that $(x+y)^n=\sum_{k=0}^{n}{n\choose k}x^{n-k}y^k$. We know that no two of these terms can be coalesced into a single term (since they all have differing powers of x and y). Thus the number of terms is $n+1$...............so

3. where does n+1 come from?

4. also, does the "15" go anywhere in the equation?

5. Originally Posted by oryxncrake
also, does the "15" go anywhere in the equation?
How many terms does $(a+b)^1$ have?

What about $(a+b)^2$?

$(a+b)^3$?

:
:

notice the pattern?

CB

6. Yes. A better way maybe just to notice what CaptainBlack said.

What I was getting at was that

$\left(x+y\right)^n=\sum_{\ell=0}^{n}{n\choose \ell}x^{n-\ell}y^\ell$

And noting that on the RHS no two terms can be coalesced into a single term we can deduce that $\left(x+y\right)^n$ has as many terms as $\sum_{\ell=0}^{n}x^{n-\ell}y^\ell$. But how many does that have?

Well it not only has the first term through the $n$th term (which is $n$ terms) but it has the $0$th term. So the number of terms in $\sum_{\ell=0}^{n}x^{n-\ell}y^\ell$ is $n+1$. Consequently the number of terms in $\left(x+y\right)^n$ is $n+1$


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# How to improve this table?

I'm looking for ideas to improve the layout of the following table.

• Is there a better way to separate ABC Metrics and XYZ Metrics (other than using separate table for each metric)?
• Should I convert Algorithms row into a column?
• Should I convert Dataset row into a column?

I would appreciate any ideas, thanks.

\documentclass{article}

\usepackage[margin=1in]{geometry}
\usepackage{tabularx,ragged2e,booktabs}

\begin{document}

\begin{table*}[!ht]
\caption{Evaluation results}
\centering
\setlength{\tabcolsep}{4pt}
\begin{tabularx}{\textwidth}{>{\hsize=1.9\hsize\bfseries\RaggedRight}X!{\extracolsep{\fill}}*{6}{>{\centering\arraybackslash\hsize=0.48\hsize}X}}
\toprule[1pt]\midrule[0.3pt]
\multicolumn{7}{c}{\textbf{ABC Metrics}} \\ \midrule[0.3pt]
\textbf{Algorithm}& \multicolumn{2}{c}{\textit{Algo 1}} & \multicolumn{2}{c}{\textit{Algo 2}} & \multicolumn{2}{c}{\textit{Algo 3}} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5} \cmidrule(lr){6-7}%
{Dataset} & $D_1$ & $D_2$ & $D_1$ & $D_2$ & $D_1$ & $D_2$ \\
{Matric 1} & 0 & 0 & 0 & 0 & 0 & 0 \\
{Matric 2} & 0 & 0 & 0 & 0 & 0 & 0 \\
{Matric 3} & 0 & 0 & 0 & 0 & 0 & 0 \\
{Matric 4} & 0 & 0 & 0 & 0 & 0 & 0 \\
\midrule
\multicolumn{7}{c}{\textbf{XYZ Metrics}} \\ \midrule[0.3pt]
\textbf{Algorithm}& \multicolumn{2}{c}{\textit{Algo 1}} & \multicolumn{2}{c}{\textit{Algo 2}} & \multicolumn{2}{c}{\textit{Algo 3}} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5} \cmidrule(lr){6-7}%
{Matric 5} & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} \\ \addlinespace
{Matric 6} & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} & \multicolumn{2}{c}{0} \\
\midrule[0.3pt]\bottomrule[1pt]
\end{tabularx}
\end{table*}

\end{document}

• I think this is off-topic because it is subjective. You should ask how to make changes to a table, not opinions on what improvements can you do. – manooooh Jan 3 '19 at 2:24
• @manooooh That's actually a good question for Meta, whether code review questions are accepted here. – <NAME> Jan 3 '19 at 4:42
• – Werner Jan 3 '19 at 5:55

i only repair some inconsistencies in your column width calculation. the sum of the defined widths is 4.78. but it should be an integer number. all other is opinion based ...

my suggestion for your table code (with some opinion based changes and simplification of writing) is:

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage[skip=1ex]{caption}

\usepackage{ragged2e}
\usepackage{booktabs,tabularx}
\newcommand\mcc[1]{\multicolumn{2}{c}{#1}}

\begin{document}
\begin{table}[!ht]
\caption{Evaluation results}
\centering
\begin{tabularx}{\textwidth}{
>{\hsize=0.4\hsize\bfseries\RaggedRight}X
*{6}{>{\hsize=0.1\hsize\centering\arraybackslash}X}}
\toprule
\multicolumn{7}{c}{\textbf{ABC Metrics}} \\
\midrule
\textbf{Algorithm}
& \mcc{\textit{Algo 1}} & \mcc{\textit{Algo 2}} & \mcc{\textit{Algo 3}} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5} \cmidrule(lr){6-7}%
Dataset     & $D_1$ & $D_2$ & $D_1$ & $D_2$ & $D_1$ & $D_2$ \\
\midrule
Matric 1   & 0 & 0 & 0 & 0 & 0 & 0 \\
Matric 2    & 0 & 0 & 0 & 0 & 0 & 0 \\
Matric 3    & 0 & 0 & 0 & 0 & 0 & 0 \\
Matric 4    & 0 & 0 & 0 & 0 & 0 & 0 \\
\midrule
\multicolumn{7}{c}{\textbf{XYZ Metrics}} \\ \midrule[0.3pt]
\textbf{Algorithm}
& \mcc{\textit{Algo 1}} & \mcc{\textit{Algo 2}} & \mcc{\textit{Algo 3}} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5} \cmidrule(lr){6-7}%
{Matric 5} & \mcc{0} & \mcc{0} & \mcc{0} \\
{Matric 6} & \mcc{0} & \mcc{0} & \mcc{0} \\
\bottomrule
\end{tabularx}
\end{table}
\end{document}

which gives:

• I don't understand why you're using 1 tabularx environment for two structures that don't look all that much connected. I'd use two separate environments.

• Since there appears to be no line-wrapping whatsoever, I don't understand why you'd be using a tabularx environment to begin with. Why not use a tabular* environment? For that matter, why not use tabular environments?

• Using bold-facing and/or italics in the header cells is a transparent attempt to compensate for the lack of clear visual structure. With such an approach, you are mostly going to come across as somebody who (a) isn't particularly well organized and (b) thinks it's ok to shout at people. The people I know, though, very much prefer not to be shouted at. Your experience may differ...

• Based on the information you've provided, the material can easily be presented in two separate, side-by-side tabular environments.

The following solution tries to present the material without any shouting, while still trying to be visually "open" and inviting.

PS. What's a "matric"?

\documentclass{article}
\usepackage[margin=1in,letterpaper]{geometry}
\usepackage[skip=0.5\baselineskip]{caption} % optional
\usepackage{array,booktabs}

\begin{document}
\begin{table}[!ht]
\setlength\tabcolsep{10pt} % default: 6pt
\caption{Evaluation results}

\begin{tabular}[t]{@{} l *{6}{c} @{}}
\multicolumn{7}{@{}l}{ABC Metrics, for datasets $D_1$ and $D_2$} \\
\toprule
& \multicolumn{6}{c@{}}{Algorithm}\\
\cmidrule(l){2-7}
& \multicolumn{2}{c}{Algo 1}
& \multicolumn{2}{c}{Algo 2}
& \multicolumn{2}{c@{}}{Algo 3} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5} \cmidrule(l){6-7}
& $D_1$ & $D_2$ & $D_1$ & $D_2$ & $D_1$ & $D_2$ \\
\midrule
Matric 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
Matric 2 & 0 & 0 & 0 & 0 & 0 & 0 \\
Matric 3 & 0 & 0 & 0 & 0 & 0 & 0 \\
Matric 4 & 0 & 0 & 0 & 0 & 0 & 0 \\
\bottomrule
\end{tabular}
\hspace{\fill}
\begin{tabular}[t]{@{} l ccc @{}}
\multicolumn{4}{@{}l}{XYZ Metrics} \\
\toprule
& \multicolumn{3}{c@{}}{Algorithm}\\
\cmidrule(l){2-4}
& Algo 1 & Algo 2 & Algo 3 \\
\midrule
Matric 5 & 0 & 0 & 0 \\
Matric 6 & 0 & 0 & 0 \\
\bottomrule
\end{tabular}
\end{table}
\end{document}

I propose this variant layout, with correct coefficients fòr \hsize=:

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage[skip=1ex]{caption}
\usepackage[table, svgnames]{xcolor}

\usepackage{ragged2e}
\usepackage{booktabs,tabularx}
\newcommand\mcc[1]{\multicolumn{2}{c}{#1}}

\begin{document}

\begin{table}[!ht]
\caption{Evaluation results}
\centering
\setlength{\extrarowheight}{2pt}
\setlength{\belowrulesep}{0pt}
\begin{tabularx}{\textwidth}{
>{\hsize=2.8\hsize\bfseries\RaggedRight}X
*{6}{>{\hsize=0.7\hsize\centering\arraybackslash}X}}
\toprule
& \multicolumn{6}{c}{\textbf{Algorithm}} \\
\cmidrule{2-7}
& \mcc{\textit{Algo 1}} & \mcc{\textit{Algo 2}} & \mcc{\textit{Algo 3}} \\
\rowcolor{WhiteSmoke} ABC Metrics\hfill Dataset & $D₁$ & $D₂$ & $D₁$ & $D₂$ & $D₁$ & $D₂$ \\
Metric 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
Metric 2 & 0 & 0 & 0 & 0 & 0 & 0 \\
Metric 3 & 0 & 0 & 0 & 0 & 0 & 0 \\