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Block ciphers

Few false ideas have more firmly gripped the minds of so many intelligent men than the one that, if they just tried, they could invent a cipher that no one could break. - David Kahn

What is block cipher?

A block cipher is an algorithm that encrypts blocks of a fixed length. The encryption function E transforms plaintext blocks P into ciphertext blocks C by using a secret key k:

$C = E(k, P)$

Plaintext and ciphertext blocks are sequences of bits and always match in size. The block cipher’s block size is a fixed size. Keyspace is the set of all possible keys.

Once we encrypt plaintext blocks into ciphertext blocks, they are later decrypted to recover original plaintext block. The original plaintext block P is produced using a decryption function $D$. It takes the ciphertext block C and the key k (the same one used to encrypt the block) as inputs.

$P = D(k, C)$

Or, visually represented in blocks:

A block cipher is an example of a symmetric-key encryption scheme, also known as a secret-key encryption scheme. The same secret key is used for both encryption and decryption. Later in the book, we contrast this with public-key encryption algorithms, which have a distinct key for encryption and decryption.

A block cipher is a keyed permutation. It is a permutation because the block cipher maps each possible block to another block. It is also a keyed permutation because the key determines exactly which blocks map to which. It is important for the block cipher to be a permutation because the recipient must map blocks back to the original blocks.

We illustrate this by looking at a block cipher with an impractical, tiny 4-bit block size. $$2^4 = 16$$ possible blocks. Since each of the blocks map to a hexadecimal digit, we represent the blocks by that digit. Figure 2 below illustrates blocks that the cipher operates on.

Once we select a secret key, the block cipher uses it to determine the encryption of any given block. We illustrate that relationship with an arrow. The tail of the arrow has the block encrypted with E under key k and the arrowhead is mapped to the block.

In Figure 3, note that the permutation is not just one big cycle. It contains a large cycle of 7 elements, and several smaller cycles of 4, 3 and 2 elements each. It is also perfectly possible that an element encrypts to itself. This is to be expected when selecting random permutations, which is approximately what a block cipher is doing; it doesn’t demonstrate a bug in the block cipher.

When you decrypt instead of encrypt, the block cipher computes the inverse permutation. In Figure 4, we get the same illustration. The difference between the illustrations is that all arrowheads point in the opposite direction.

The key defines which blocks map to which blocks. A different key would lead to a different set of arrows, as you can see in Figure 5.

In this illustration, you’ll even notice that there are two permutations of length 1: an element that maps to itself. This is again something to be expected when selecting random permutations.

Knowing a bunch of (input, output) pairs for a given key shouldn’t give you any information about any other (input, output) pairs under that key1. As long as we’re talking about a hypothetical perfect block cipher, there’s no easier way to decrypt a block other than to “brute-force” the key: i.e. just try every single one of them until you find the right one.

Our toy illustration block cipher only has 4 bit blocks, or $$2^4 = 16$$ possibilities. Real, modern block ciphers have much larger block sizes, such as 128 bits, or $$2^{128}$$ (slightly more than $$10^{38.5}$$) possible blocks. Mathematics tells us that there are n! (pronounced “n factorial”) different permutations of an n element set. It’s defined as the product of all of the numbers from 1 up to and including n:

$n! = 1 \cdot 2 \cdot 3 \cdot \ldots \cdot (n - 1) \cdot n$

Factorials grow incredibly quickly. For example, $$5! = 120$$, $$10! = 3628800$$, and the rate continues to increase. The number of permutations of the set of blocks of a cipher with a 128 bit block size is $$(2^{128})!$$. Just $$2^{128}$$ is large already (it takes 39 digits to write it down), so $$(2^{128})!$$ is a mind-bogglingly huge number, impossible to comprehend. Common key sizes are only in the range of 128 to 256 bits, so there are only between $$2^{128}$$ and $$2^{256}$$ permutations a cipher can perform. That’s just a tiny fraction of all possible permutations of the blocks, but that’s okay: that tiny fraction is still nowhere near small enough for an attacker to just try them all.

Of course, a block cipher should be as easy to compute as possible, as long as it doesn’t sacrifice any of the above properties.

AES

The most common block cipher in current use is AES.

Contrary to its predecessor DES (which we’ll look at in more detail in the next chapter), AES was selected through a public, peer-reviewed competition following an open call for proposals. This competition involved several rounds where all of the contestants were presented, subject to extensive cryptanalysis, and voted upon. The AES process was well-received among cryptographers, and similar processes are generally considered to be the preferred way to select cryptographic standards.

Prior to being chosen as the Advanced Encryption Standard, the algorithm was known as Rijndael, a name derived from the two last names of the Belgian cryptographers that designed it: Vincent Rijmen and Joan Daemen. The Rijndael algorithm defined a family of block ciphers, with block sizes and key sizes that could be any multiple of 32 bits between 128 bits and 256 bits. When Rijndael became AES through the FIPS standardization process, the parameters were restricted to a block size of 128 bits and keys sizes of 128, 192 and 256 bits.

There are no practical attacks known against AES. While there have been some developments in the last few years, most of them involve related-key attacks, some of them only on reduced-round versions of AES.2

A closer look at Rijndael

AES consists of several independent steps. At a high level, AES is a substitution-permutation network.

Key schedule

AES requires separate keys for each round in the next steps. The key schedule is the process which AES uses to derive 128-bit keys for each round from one master key.

First, the key is separated into 4 byte columns. The key is rotated and then each byte is run through an S-box (substitution box) that maps it to something else. Each column is then XORed with a round constant. The last step is to XOR the result with the previous round key.

The other columns are then XORed with the previous round key to produce the remaining columns.

SubBytes

SubBytes is the step that applies the S-box (substitution box) in AES. The S-box itself substitutes a byte with another byte, and this S-box is applied to each byte in the AES state.

It works by taking the multiplicative inverse over the Galois field, and then applying an affine transformation so that there are no values x so that $$x ⊕ S(x) = 0$$ or $$x ⊕ S(x)=\texttt{0xff}$$. To rephrase: there are no values of x that the substitution box maps to x itself, or x with all bits flipped. This makes the cipher resistant to linear cryptanalysis, unlike the earlier DES algorithm, whose fifth S-box caused serious security problems.3

ShiftRows

After having applied the SubBytes step to the 16 bytes of the block, AES shifts the rows in the $$4 \times 4$$ array:

MixColumns

MixColumns multiplies each column of the state with a fixed polynomial.

ShiftRows and MixColumns represent the diffusion properties of AES.

As the name implies, the AddRoundKey step adds the bytes from the round key produced by the key schedule to the state of the cipher.

DES and 3DES

The DES is one of the oldest block ciphers that saw widespread use. It was published as an official FIPS standard in 1977. It is no longer considered secure, mainly due to its tiny key size of 56 bits. (The DES algorithm actually takes a 64 bit key input, but the remaining 8 bits are only used for parity checking, and are discarded immediately.) It shouldn’t be used in new systems. On modern hardware, DES can be brute forced in less than a day.

In an effort to extend the life of the DES algorithm, in a way that allowed much of the spent hardware development effort to be reused, people came up with 3DES: a scheme where input is first encrypted, then decrypted, then encrypted again:

$C = E_{DES}(k_1, D_{DES}(k_2, E_{DES}(k_3, p)))$

This scheme provides two improvements:

• By applying the algorithm three times, the cipher becomes harder to attack directly through cryptanalysis.
• By having the option of using many more total key bits, spread over the three keys, the set of all possible keys becomes much larger, making brute-forcing impractical.

The three keys could all be chosen independently (yielding 168 key bits), or $$k_3 = k_1$$ (yielding 112 key bits), or $$k_1 = k_2 = k_3$$, which, of course, is just plain old DES (with 56 key bits). In the last keying option, the middle decryption reverses the first encryption, so you really only get the effect of the last encryption. This is intended as a backwards compatibility mode for existing DES systems. If 3DES had been defined as $$E(k_1, E(k_2, E(k_3, p)))$$, it would have been impossible to use 3DES implementations for systems that required compatibility with DES. This is particularly important for hardware implementations, where it is not always possible to provide a secondary, regular “single DES” interface next to the primary 3DES interface.

Some attacks on 3DES are known, reducing their effective security. While breaking 3DES with the first keying option is currently impractical, 3DES is a poor choice for any modern cryptosystem. The security margin is already small, and continues to shrink as cryptographic attacks improve and processing power grows.

Far better alternatives, such as AES, are available. Not only are they more secure than 3DES, they are also generally much, much faster. On the same hardware and in the same mode of operation (we’ll explain what that means in the next chapter), AES-128 only takes 12.6 cycles per byte, while 3DES takes up to 134.5 cycles per byte. Despite being worse from a security point of view, it is literally an order of magnitude slower.

While more iterations of DES might increase the security margin, they aren’t used in practice. First of all, the process has never been standardized beyond three iterations. Also, the performance only becomes worse as you add more iterations. Finally, increasing the key bits has diminishing security returns, only increasing the security level of the resulting algorithm by a smaller amount as the number of key bits increases. While 3DES with keying option 1 has a key length of 168 bits, the effective security level is estimated at only 112 bits.

Even though 3DES is significantly worse in terms of performance and slightly worse in terms of security, 3DES is still the workhorse of the financial industry. With a plethora of standards already in existence and new ones continuing to be created, in such an extremely technologically conservative industry where Fortran and Cobol still reign supreme on massive mainframes, it will probably continue to be used for many years to come, unless there are some large cryptanalytic breakthroughs that threaten the security of 3DES.

Remaining problems

Even with block ciphers, there are still some unsolved problems.

For example, we can only send messages of a very limited length: the block length of the block cipher. Obviously, we’d like to be able to send much larger messages, or, ideally, streams of indeterminate size. We’ll address this problem with a stream-ciphers

Although we have reduced the key size drastically (from the total size of all data ever sent under a one-time pad scheme versus a few bytes for most block ciphers), we still need to address the issue of agreeing on those few key bytes, potentially over an insecure channel. We’ll address this problem in a later chapter with a key exchange protocol

1. The attentive reader may have noticed that this breaks in the extremes: if you know all but one of the pairs, then you know the last one by exclusion.

2. Symmetric algorithms usually rely on a round function to be repeated a number of times. Typically each invocation involves a “round key” derived from the main key. A reduced-round version is intentionally easier to attack. These attacks can give insight as to how resistant the full cipher is.

A related key attack involves making some predictions about how AES will behave under several different keys with some specific mathematical relation. These relations are fairly simple, such as XORing with an attacker-chosen constant. If an attacker is allowed to encrypt and decrypt a large number of blocks with these related keys, they can attempt to recover the original key with significantly less computation than would ordinarily be necessary to crack it.

While a theoretically ideal block cipher wouldn’t be vulnerable to a related key attack, these attacks aren’t considered practical concerns. In practice cryptographic keys are generated via a cryptographically secure pseudorandom number generator, or a similarly secure key agreement scheme or key derivation scheme (we’ll see more about those later). Therefore, the odds of selecting two such related keys by accident is nonexistent. These attacks are interesting from an academic perspective: they can help provide insight in the workings of the cipher, guiding cryptographers in designing future ciphers and attacks against current ciphers.

3. In its defense, linear attacks were not publicly known back when DES was designed.

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On Tue, 10 Aug 2004 21:52:14 -0500, Yelnick McWahWah wrote: > I'm looking for a > free Sans Serif font that makes my math look good. When I try it, \r{A} looks more like an Å (even if the "ring" is of different shape) whereas, in my opinion, it should have been identical to. A Look at some Recent TEX Fonts Michael Sharpe August 8, 2014 This document examines a number of more recent additions to TEX’s font repertoire, focussing on LATEX packages exclusively, and, for the most part, on text fonts, though I will make some biased suggestions about suitable math packages to accompany them. 1, 2, 3 Math Fonts contains 43 fonts to help you create your own worksheets, flashcards, assessments and other instructional aids. The commands shown in Table 4. With a word processor, changing the formatting means you have to change each instance individually. A powerful and robust LaTeX, ConTeXt, Plain TeX, PreTeXt, EPlain, Markdown, Textile, CSV and HTML Table Editor and Generator. \documentclass{article} \usepackage{amsmath} \begin{document} Let $\boldsymbol\alpha$ be a vector. 8 by using lyx 1. Gives the. In LaTeX that is no longer true, but it is true that the size of these units will scale with the font, so that a change to a different font size will not disturb the proportions of the typeset material. In some cases, you may want to set fonts and sizes by hand. Explore Minion designed by Robert Slimbach at Adobe Fonts. If you have used HTML, or edited a wiki then you will be familiar with the idea of using symbols or commands within a text file to describe the layout of text. Why should you use L a T e X instead of an ordinary word processor? Here is a tentative answer comparing their typographic accuracy. It is called twice : first for calculating the size of each portion of the formula, then to paint the formula. Explore Latex designed by Patrick Griffin at Adobe Fonts. For additional information of all kinds: the LaTeX Font Catalogue, by Palle Jørgensen of DK-TUG, has short samples of most fonts available in TeX distributions, with LaTeX usage examples. 下载中心 新版CTeX套装即将发布，敬请期待！新版CTeX套装将由Harry Chen和Liam Huang接手负责开发，预计发布时间在4月份之前。. This is described in a recent TUGboat article. Word-to-L A T E X. Bold Greek letters are available using boldsymbol in the amsmath package. The fontspec package provides an automatic and unified interface for loading fonts in LaTeX. LaTeX minipage. LaTeX is capable of producing presentation slides using the Beamer class in a simple and easy-to-use way. 1 or higher (for Mac). Sometimes, package files from CTAN consist of an. I have installed it into my Windows fonts and can use it with Word and other Windows apps. My TeX Live subdirectory did contain rsfs fonts already (unlike TeTeX), but not the mathrsfs. Changing default font typeface. org; The TeX Users Group (TUG) Cambridge U Guide; Wikibook; Font Sampler. Then the number of orbits under of Y -colorings of X is given by Y X = = 1 j j X 2 tc(). Garamond is a family of old-style serif typefaces derived from the work of Claude Garamond in the sixteenth century; most Garamond fonts are renowned for their readability, elegance, and character. cls provides the exam document class, which attempts to make it easy for even a LATEX novice to prepare exams. If required, the additional command \renewcommand{\familydefault}{\sfdefault} makes LATEX use the sans serif font family (Helvetica or Avant Garde) as the de- fault one. The reason I like using LaTeX is because of the beautiful PDFs that it produces. And this extends to preprints when not done in LaTeX. Then the number of orbits under of Y -colorings of X is given by Y X = = 1 j j X 2 tc(). Creating Tables with LaTeX Tables are created using the “table” environment given below: \begin{table}[where] table \end{table} In the above syntax, table stands for the contents of the ‘tabular’ environment together with a possible \caption command. Whenever possible, please substitute Type 1 Postscript fonts for Type 3 fonts in LaTEX files, then generate PS or PDF. The visitor's LaTeX, entered or copied into the editing window below, will be quickly rendered by up to three renderers (in different ways). For more information about our latex-free products, visit us online today!. It is designed for. alex2747 Posts: 18 Joined: Mon Apr 05, 2010 8:39 pm. There are two ways to make text italic in LaTeX. 97 Free Unicode Arabic Fonts Most Popular - By Name. In particular, this means most mathematical characters, Greek letters, and the like. The reason for not using the fonts provided by the system is that Tex and Latex will give the same distinctive look no matter which platform a document was compile on, making the language system independent. The commands for family, shape, and series are commutative, so they can be combined as with the command:. The le exam. Make sure that your installation uses Type 1 fonts. although saying the font size is 1em can be misleading em is fontdimen6 which isn't always the font size as used in the font name, eg cmtt10 is a "10pt font" but \documentclass{article} \begin{document} \ttfamily \expandafter\show\the\font \showthe\fontdimen6\font \setbox0\hbox{\textemdash}\showthe\wd0 \end{document} shows that 1em is 10. 5bp, font size (probably to compensate for the slightly wider nature of the Palatino font). Get 50 Free Woodworking Plans Get Make A Table Bigger Latex: World's most comprehensive collection of woodworking ideas For Pro & Beginner. If the browser does not support the first font, it tries the next font, and so on. Examples of Didone fonts include Bodoni and Didot. (A really cool thing is that I also generated. Just add a line or two to your source document, and your math fonts will be replaced by MathTime Professional fonts. As implied by the name, Computer Modern is a 'Didone', or modern serif font, a genre that emerged in the late 18th century as a contrast to the more organic designs that preceded them. Making Portable Document Format (PDF) files from LaTeX source is a little tricky, because the PDF file must incorporate not only the images for any figures, but also the font glyphs (or at least, partial fonts) for anything outside the standard handful of fonts in the basic PostScript set. The default font encoding is OT1, the encoding of the original Computer Modern fonts. The default font used in equations can be set in the equation mode preferences. 97 Free Unicode Arabic Fonts Most Popular - By Name. LATEX Homework: Fonts Due: July 12, 2010 Consider the example given on slide 11 of Fonts overheads. The goals of the Open Font License (OFL) are to stimulate worldwide development of collaborative font projects, to support the font creation efforts of academic and linguistic communities, and to provide a free and open framework in which fonts may be shared and improved in partnership with others. Latex, the typesetting system developed by Donald Knuth, uses Computer Modern fonts stored in the Metafont format by default. \fongfamily{font} \setmainfont{font} 配合{}的分组作用，可以临时改变字体。但是在中文下，这两种方法都失效。 字体大小. Last visit was: Wed Jun 24, 2020 12:16 pm. 2) is available as a ready-to-print PDF file. By default when checking the box "LaTeX formula" that enters math mode (font in italic), if we enter text (roman font) must switch to text mode by typing: \text{text text text} or \mbox. The font packages included in the bundle completely replace one or more of the font families used by LaTeX for roman, sans serif, typewriter, or mathematics fonts. The LaTeX option is activated by setting text. While not all systems have the same fonts installed, you can use a web safe font stack to choose several fonts that look similar, and are installed on the various systems that you want to support. Here’s how to get a couple popular symbolic fonts (logos for email, phone, GitHub, etc. Free Access. org,Wikibooks,Scientific physics forums for professionals and students to discuss serious issues and topics regarding physics in theory, practice, study and reality. In your LaTeX file, you can put \usepackage{times} just after the \documentclass command. Add to Cart Checkout In Cart (0) Desktop 49 24. LaTeX Distributions LaTeX Distributions Linux –TeXLive Windows –MikTeX Mac OS X –MacTeX เอดิเตอร์ส าหรับจัดการเอกสาร LaTeX โดยเฉพาะ Texwork, Texshop, Texmaker โปรแกรม WYSIWYG ส าหรับ LaTeX Lyx. For comparison, it should be. See one example in PDF format or LaTeX source code (requer fancybox). What's the best way to do the equivalent in Microsoft Office? In effect I want a font that looks like the font produced when I use the \mathscr command - something like this. The layout engine simply arranges the glyphs' bounding boxes in rows (lines of type). The commands for family, shape, and series are commutative, so they can be combined as with the command:. Once that's done, you can always invoke the package in your document. But no, that is not what happens; instead, even though using ± in the middle of the text, LaTeX still finds the glyph in the TeX math font. 6 are of the second type—a. included in a number of Linux distributions. Please help me out with other languages. Google Fonts Delivered Free. One only needs to utilize the basic Matlab functions such as title, xlabel, ylabel, and text. You could use this package to better separate the captions of floats from the body text. It contains two main modules: the first one, Equation,allows to insert LaTeX equations into Writer and Impress documents as pngor emfimages while the second one, Expand,can be used for simpler equations to expand LaTeX code into appropriated symbol characters and insert them as regular text. moresize: More font sizes with LATEX Christian Cornelssen ([email protected] To change fonts without using the mouse, use Ctrl-Shift-f and arrow keys. Mac OS X Packages Building. 21; CTEX论坛因故自即日起无限期关闭。 2018. What is Font Embedding In order to display or print a PDF, the system has to know which fonts it should use. 74 \Huge 24 24. Font sizes Note that the font size definitions are set by the document class. The AMSFonts User's Guide (still for version 2. Either pick a font that has a pre-packaged style file you can use (e. The rest of this article focus on getting Inkscape to work with LaTex. To order Minion Math fonts, please send an e-mail to [email protected] After defining them, you'll only need to use font commands to change the font, for instance to bold or italicize a word or words. family — The default font family for body text cjk. All of the fonts listed there can be used by including packages in the preamble, so they’re very easy to use. 75 inches wide on 11pt documents, and 1. What is AMS-LaTeX? AMS-LaTeX is a set of LaTeX packages for mathematics, which was developed by the American Mathematical Society so that mathematicians could produce beautiful mathematics in LaTeX, mathematics acceptible for publication in the. The fontinst software should be available from the same source as your copy of LATEX. Linux/Unix: LaTeX. In contrast to standard LATEX you need not load the package exscale for. Right now, matplotlib has two different default fonts for Latex titles and non-Latex titles and I'd like the two to be. You can change this font typeface for another that better suits your style. Once that's done, you can always invoke the package in your document. The most common values for the font encoding is OT1. It’s supporting several encodings including T1, OT1 and LY1. This way the author can use Greek letters in text without changing to math mode. included in a number of Linux distributions. Latex allergy is a healthcare industry-wide concern. Using a different font size on a global level will affect all normal-sized text as well as the size of headings, footnotes, etc. The second paper I ordered was a research report on history. LaTeX Workshop is an extension for Visual Studio Code, aiming to provide core features for LaTeX typesetting with Visual Studio Code. By working with your colleagues and students on Overleaf, you know that you're not going to hit any version inconsistencies or package conflicts. The FONTSPEC package. Most of the stock math commands are written for typesetting math or computer science papers for academic journals, so you might need to dig deeper into LaTeX commands to get the vector. Let beagroupofpermu-tations of a nite set X of objects and let Y be a nite set of colors. For more information about our latex-free products, visit us online today!. What is the best strategy for dealing with fonts in Stata graphs that are meant to be embedded in LaTeX documents (articles and Beamer)? My goal is to typeset the text in axis titles, legends, and labels to look identical, or at least more similar, to the surrounding text. LaTeX's margins are, by default, 1. net - The Home of all Things Design. Decide on a compilation scheme. sed - Z2HTML: simple Fuzz/LaTeX to HTML translator for Z notation # # Use GIFs (not symbol font) for Z symbols, HTML tables for Z boxes # Use *-m. The publishing solution that is script based. Vectors can be typeset in LaTeX with the command \vec, which decorates the argument with a little arrow. Formatting captions and subcaptions in LaTeX T he captions for figures, tables, subfigures and subtables in LaTeX can be customized in various ways using the caption and subcaption packages. Welcome to FontBundles. For example I can modify the font of a plot by: x = -pi:. My hope is that you find this particular corner useful. Updated daily | Make-Table-Font-Bigger-Latex. The layout engine simply arranges the glyphs' bounding boxes in rows (lines of type). STIX fonts available for LaTeX. And this extends to preprints when not done in LaTeX. 1 0 0 1 428. In a typewriter font aka monospaced font each character is given the same width. The Best Make A Table Bigger Latex Free Download PDF And Video. It remembers at least three font families at any given time, one for each generic family names (serif, sans-serif, monospaced). The Best Latex How To Make Table With Small Fonts Free Download PDF And Video. Beamer is a powerful and flexible LaTeX class to create great looking presentations. Setting fonts for different LaTeX elements. Linux/Unix: LaTeX. Access Google Sites with a free Google account (for personal use) or G Suite account (for business use). To use the graphics package, as usual, you need to include the following statement in the preamble of your LaTeX document. Changing default font typeface. Or at least not the default of Matlab nor Latex e. Welcome to the first version of this site! (and hopefully a temporary one!) This website's goal is to provide online teaching material for METAFONT, the font-making programming language by Donald E. The text input may contain HTML (and XML) numeric character references and character entity references. # # About: # Installs a Truetype font family for use with LaTeX (pdftex). 我们经常看到LaTeX所使用的长度单位，in，em 等等。 LaTeX 支持的长度单位有: in - 英寸(inch) mm - 毫米(millimeters) cm - 厘米(centimeters) pt - points (大约 1/72 inch) em - 接近当前字体的字符 "M"的宽度(approximately the width of an "M" in the current font). If you want to put your document in a sans-serif font, such as for a grant proposal, you could use the sans-serif font in the times package, which happens to be the helvetica font (like Arial in Windows). You must use the font Verdana for the start and stop commands. Let beagroupofpermu-tations of a nite set X of objects and let Y be a nite set of colors. Changing Fonts in Text Mode. The font cmfib8 is another demonstration' of parameters; it's a serifed font whose proportions are based on Fibonacci numbers. The layout engine simply arranges the glyphs' bounding boxes in rows (lines of type). librebaskerville LaTeX support for the Libre Baskerville family of fonts. \\imath and\\jmath make "dotless" i and j, which. Export the figure from xfig twice: firstly using the format "Combined PS/LaTeX (PS part)" to a file such as fig1. ShareLaTeX comes with a complete, ready to go LaTeX environment which runs on our servers. This is because I need to put them in a latex document. Adjusting font size in LaTeX. Let beagroupofpermu-tations of a nite set X of objects and let Y be a nite set of colors. The most common values for the font encoding is OT1. Font finder that helps you to identify fonts from any image. ) marvosym. com for more. This command, if any, should be placed only in the preamble (before \begin{document}). LaTeX Distributions LaTeX Distributions Linux –TeXLive Windows –MikTeX Mac OS X –MacTeX เอดิเตอร์ส าหรับจัดการเอกสาร LaTeX โดยเฉพาะ Texwork, Texshop, Texmaker โปรแกรม WYSIWYG ส าหรับ LaTeX Lyx. 04, it says it doesn't have CM Roman even though TexLive is installed. Note that this script has only been tested with the MikTek distribution. Hello, I'm trying to change the size of fonts of only one figure's caption, yet in vain. You can change this font typeface for another that better suits your style. A year later the commission grew to include a shaded variant and a set of DIY-like fonts, with different layering possibilities for dimensional manipulation. 0 Icon Search Tool. 93 Table 201: txfonts/pxfonts Letter-like Symbols. facsimile is for creating faxes with LaTeX, blacklettert1 lets you use Fraktur fonts, and retro is for typrewriter-based LaTeX documents. log Opis dogajanja med zadnjim prevajanjem (tu je tudi seznam napak v primeru le teh). size The design size of the font, for. They are \quad and \qquad. tex) \ documentclass [ 12pt, a4paper, oneside ]{ Thesis}. Table 1, adapted from the PSNFSS documentation, summarizes the commonly used Latex font packages. I personally think there will be few usecases to manually adjust the settings of the font, because the environments usually do this job for you automatically, I just included this for completeness. Depending on the document style the actual font size may differ from that listed above. To preview fonts that MATLAB can render in figure windows, use the uisetfont function. How do I use the CM. The LaTeX Font Catalogue The LaTeX Font Catalogue Both of these also support math, which is nice. By default when checking the box "LaTeX formula" that enters math mode (font in italic), if we enter text (roman font) must switch to text mode by typing: \text{text text text} or \mbox. Make sure your LaTeX distribution is up to date. Neither does the replacement font Latin Modern. although saying the font size is 1em can be misleading em is fontdimen6 which isn't always the font size as used in the font name, eg cmtt10 is a "10pt font" but \documentclass{article} \begin{document} \ttfamily \expandafter\show\the\font \showthe\fontdimen6\font \setbox0\hbox{\textemdash}\showthe\wd0 \end{document} shows that 1em is 10. LaTeX2e font selection reference, by the LaTeX team. Fonts and font collections in the enabled repositories can be installed using pacman. There are various font packages, e. PLAIN, 14); ユーザーがさまざまなフォントスタイルとサイズを選択できるイベントハンドラを追加しました。 しかし、新しい変更が setFont メソッドを介して適用されると、すでにテキスト領域にあるテキストが変更されます。. These tend to be more expensive than consumer-grade scanners, but dissertation latex font some libraries have these for their own scanning projects, and might let you use them (or scan your book themselves). 5 inches wide on 12pt documents, 1. FontAwesome5 is in TeXLive 2018, which on Ubuntu requires Ubuntu ≥ 18. 5 are of the first type (text-block commands), whereas those shown in Table 4. You should give pacman the ability to manage your fonts, which is done by creating an Arch package. 1 0 0 1 428. To get an expression exp to appear as a subscript, you just type _{exp}. Computer Modern. \circle \cite Used to make citations from the provided bibliography. See the Fonts chapter's discussion of encoding for additional information. The Euler fonts are supported by separate packages; details can be found in the documentation. Only fonts suitable for current font encoding (T1, T2A, etc. For comparison, it should be. MiKTeX (pronounced mick-tech) is an up-to-date implementation of TeX/LaTeX and related programs. Step 4 Now, open your bibliography file reference. LaTeX and fonts Introduction. We are proud to have teamed up with Google to offer desktop versions of their popular Google Fonts free of charge. Use Word-to-LaTeX tool to convert any Microsoft Word document to LaTeX, TeX, or clean XML. 1 or higher (for Mac). They are \quad and \qquad. [PDF] ‘oblique’ and ‘upright’ (sometimes called ‘roman’) are all font shapes. If you dont see the 'LaTex Word template' on your start page, try to open it from this location: documents\custom. Notice that the output differs quite a bit when using the LaTeX interpreter. The different font selection and the semantic of. Since version 0. PSNFSS provides the default Type 1 fonts listed, excluding Computer Modern (CM), Utopia, Fourier, and Euler. There are some font typefaces that support only a limited number of characters; these fonts usually denote some special sets. LaTeX is a system for preparing documents to be printed or displayed. In this example the document uses the popular Times New Roman font, this font is set by \usemainfont{Times New Roman}. Text example [Click on text example to enlarge] [L a T e X source of PDF sample] Usage \usepackage[T1]{fontenc} %% Do nothing else -- it's the default Style examples \normalfont \itshape \scshape \bfseries. Suitable for grades 6–12. Last visit was: Wed Jun 24, 2020 12:16 pm. In this example the { \huge huge font size } is set and the { \footnotesize Foot note size also }. , the Info page for LaTeX, under Commands/Typefaces. 05 pt and adjust the font size by tiny increments to increase or decrease the page count. As of 2020-03-18, this project can be found here. Register GPG key sudo apt-key adv --keyserver hkp://keyserver. The AMSFonts User's Guide (still for version 2. com 2011/10/09 Abstract The LATEX package textgreek provides NFSS text symbols for Greek letters. 0 Icon Search Tool. Beamer font theme gallery Back to the main page (click on one for details) default professionalfonts serif structurebold structureitalicserif structuresmallcapsserif. In particular, this means most mathematical characters, Greek letters, and the like. 75 inches wide on 11pt documents, and 1. This can convert fonts from Adobe Font Metric format into a format readable by LATEX, including the generation of the font de nition les described in Section4. To do so I used the wonderful LCDF Typetools and some scripts of my own. Of course, they are also available from the main source of TeX software, the Comprehensive TeX Archive Network (CTAN). The font cmfib8 is another demonstration' of parameters; it's a serifed font whose proportions are based on Fibonacci numbers. in Fancy > Horror 993,076 downloads (295 yesterday) 10 comments 100% Free. The goal of this document is to describe how to install OpenType fonts for use with LaTeX. Sometimes, package files from CTAN consist of an. It's not free but Optima is a very nice Zapf-designed sans-serif face: the strokes are tapered (unlike most sans-serif faces like Helvetica), giving a lively effect. (computer modern) families which might be hardly popular outside the TeX world. ซึ่ง คนทำก็ไม่ใช่ใครอื่น ก็. Using In-text Fonts in LaTeX Figures One thing that has always frustrated me about putting figures into Word documents is the mismatch between the fonts in the figures and the running text. I would also like to add blank lines sometimes, i don't know how. g Helvatica,CM ). The Adobe Originals program started in 1989 as an in-house type foundry at Adobe, brought together to create original typefaces of exemplary design quality, technical fidelity, and aesthetic longevity. Put in "\-" discretionary hyphens. You just need to use the commands listed in the Font Catalogue to select them for a given document. Using a different font size on a global level will affect all normal-sized text as well as the size of headings, footnotes, etc. The commands relative to the section level are defined only if the document class does not define \verb|\chapter|. In the image below, the first version uses Cambria Math, the default, while the second version has its font set to XITS Math, which somewhat resembles the font you are using in LaTeX. The Euler fonts are supported by separate packages; details can be found in the documentation. com for the archive. size The design size of the font, for. 8 and newer does this. Best 100% Free Fonts collection for free downloading. To do so I used the wonderful LCDF Typetools and some scripts of my own. Alexej Kryukov used Textrace to create CM-LGC. I started to write it in windows 10, then I moved in ubuntu, but when I try to compile my latex code (I use TeXmaker) it gives me this error: ! La. LaTeX is the de facto standard for the communication and publication of scientific documents. My hope is that you find this particular corner useful. Font Awesome is a free (CC-BY-3. It may be necessary to run sudo fc-cache in the font directory /usr/share/fonts to update the font cache. Using script fonts in LATEX There are three "script-like" fonts available in most standard LATEX distributions. It is called twice : first for calculating the size of each portion of the formula, then to paint the formula. Put in "\-" discretionary hyphens. Download Word-to-LaTeX and join the huge community of our users. Text Processing using LaTeX. The Internets Original and Largest free woodworking plans and projects links database. font — Specifies the fonts that XeTeX must use Localization. My normal LaTeX/R plot integration workflow is simple: I run Sweave to generate native TeX code and subsequently integrate resulting ‘. Survey Design 101: Font Choice Basics. Pdflatex still doesn't know about the font. LaTeX Font Warning: Font shape OT1/cmss/m/it' in size 12> not available (Font) Font shape OT1/cmss/m/sl' tried instead on input line 8. Subscripts & Superscripts. 04, and whenever I use \usepackage{times}, I get nothing and the log file looks like this:. Should LaTeXiT be categorized, it would be an equation editor. Let beagroupofpermu-tations of a nite set X of objects and let Y be a nite set of colors. Formatting captions and subcaptions in LaTeX T he captions for figures, tables, subfigures and subtables in LaTeX can be customized in various ways using the caption and subcaption packages. Font typefaces In L a T e X the default font typeface is the Computer Modern family. How to Create a Font. Welcome to the first version of this site! (and hopefully a temporary one!) This website's goal is to provide online teaching material for METAFONT, the font-making programming language by Donald E. What is missing is a font description file. Setting fonts for different LaTeX elements. It's available in Roman, italic, bold & small caps. Posted 10/28/02 9:47 PM, 14 messages. What is the best strategy for dealing with fonts in Stata graphs that are meant to be embedded in LaTeX documents (articles and Beamer)? My goal is to typeset the text in axis titles, legends, and labels to look identical, or at least more similar, to the surrounding text. sty delivered with MikTex 2. Word-to-LaTeX runs on MS Windows XP/Vista/7/8 with MS Office XP/2003/2007/2010/2013 installed. Licensing. 告诉你在要使用的字体中，不存在粗体形式的楷体，所以 LaTeX 就用不粗的楷体代替了。. Here are the font files which are distributed with implementations of LATEX. The line \usepackage{tgbonum} establishes the font family T e X Gyre Bonum, whose font package name is tgbonum, as the default font for this document. LaTeX Font Warning: Font shape T1/lhandw/m/n' undefined (Font) using T1/cmr/m/n' instead on input line 8. There are some font typefaces that support only a limited number of characters; these fonts usually denote some special sets. Memory foam pillows are a bit cheaper than 100% natural latex. LaTeX is distributed through CTAN servers or comes as part of many easily installable and usable TeX distributions provided by the TeX User Group (TUG) or third parties. No wonder it's considered one of the best open source tools for writers. librarian Tools to create bibliographies in TeX. LaTeX also lists the relevant text, using hyphens to show you where it is willing to hyphenate words. That does not mean that only these three sizes can be used, it is only the size of the normalsize font. The files are bundled in TengTeX. Using script fonts inLATEX John M. , together with an easy way to refer to these numbers. This replaces the LaTeX2. LaTeX Document Styles / Document Classes. 7 or higher (for Linux and other *nix flavors) and OzTeX 5. Download the latest version: ttffortex. Suitable for grades 6–12. Defining and using font colors in LaTeX documents turns out to be pretty easy, and it's a great LaTeX feature. But, in the first, the artistic talent is required. We could probably consolidate this with one of the other CDNs being used, but font-hosting involves some user-agent-string based compatibility polyfills, which would be somewhat annoying to reproduce ourselves. The LaTeX option is activated by setting text. LaTeX and fonts Introduction. 1 0 0 1 428. The font can also be changed for a specific element in the document. While not all systems have the same fonts installed, you can use a web safe font stack to choose several fonts that look similar, and are installed on the various systems that you want to support. roman) is the default used. Available fonts may be found by querying packages (e. These may be found on CTAN in the UK, the USA or from any of the many other mirror sites. Make sure that your installation uses Type 1 fonts. Accessing OpenType font features in LaTeX. In the image below, the first version uses Cambria Math, the default, while the second version has its font set to XITS Math, which somewhat resembles the font you are using in LaTeX. The art and craft of designing typefaces is called type design. although saying the font size is 1em can be misleading em is fontdimen6 which isn't always the font size as used in the font name, eg cmtt10 is a "10pt font" but \documentclass{article} \begin{document} \ttfamily \expandafter\show\the\font \showthe\fontdimen6\font \setbox0\hbox{\textemdash}\showthe\wd0 \end{document} shows that 1em is 10. Just install the plugin and you are good to go. To change the font family, emphasize text, and other font-related issues, see Fonts. On Tue, 10 Aug 2004 21:52:14 -0500, Yelnick McWahWah wrote: > I'm looking for a > free Sans Serif font that makes my math look good. 10 or use a PPA. 75 inches wide on 11pt documents, and 1. Download Word-to-LaTeX and join the huge community of our users. Since many people are used to the fonts and syntax highlighting of their IDE, I tried to emulate the layout and colors of code as it is formatted in Eclipse. Export the figure from xfig twice: firstly using the format "Combined PS/LaTeX (PS part)" to a file such as fig1. Then the number of orbits under of Y -colorings of X is given by Y X = = 1 j j X 2 tc(). MLA Template. The general challenge is to find a font for the math that matches the text font. The template facilitates structuring of the manuscript, e. Creating a package. TeX is usually provided in the form of an easy-to-install bundle of TeX itself along with Metafont and all the necessary fonts, documents formats, and utilities needed to use the typesetting system. QtiPlot is a program for two- and three-dimensional graphical presentation of data sets and for data analysis. A workaround I found (which is a little annoying, but at least it works) is to use something like \mbox{\boldmath${\pi}$} if in a math environment. The fontinst software should be available from the same source as your copy of LATEX. The spacing of a font has a large impact on how it looks when set, and should be a consideration when choosing and using a typeface. Most fonts are proportional fonts, meaning that letters occupy different widths. To use it, include this line in your preamble: \usepackage{kpfonts} Example text Theorem (Pólyaenumerationtheorem, unweighted). You can change this font typeface for another that better suits your style. In LaTeX that is no longer true, but it is true that the size of these units will scale with the font, so that a change to a different font size will not disturb the proportions of the typeset material. Pour éviter le problème d'hétérogénéité mentionné plus haut, il n'accepte que certaines tailles, mentionnées dans le fichier t1cmr. The TeX Gyre Heros family of sansserif fonts is based on the URW Nimbus Sans L family distributed with Ghostscript. The mission of the Scientific and Technical Information Exchange (STIX) font creation project is the preparation of a comprehensive set of fonts that serve the scientific and engineering community in the process from manuscript creation through final publication, both in electronic and print formats. 11 you can open a LaTex template from the ribbon under LaTex. A year later the commission grew to include a shaded variant and a set of DIY-like fonts, with different layering possibilities for dimensional manipulation. STIX fonts available for LaTeX. This package includes also Unicode virtual fonts for use with Omega/Lambda. of LaTeX, a new acctent, \mathring, has been added. \documentclass {article} \usepackage {amsmath} \begin {document}. brief font installation instructions;. PSNFSS provides the default Type 1 fonts listed, excluding Computer Modern (CM), Utopia, Fourier, and Euler. For example I can modify the font of a plot by: x = -pi:. latex font size | latex font size | latex font size command | latex font size 11 | latex font size 12 | latex font size pt | latex font size 36pt | latex font s. It is meant to become a part of “babel”, a multilingual package for LaTeX which supports a lot of non-American languages. , small, large. A great introduction to PCTeX and LaTeX! more> PCTeX 6 Bundles Save 20% by buying PCTeX 6 with another one of our great products! more> Academic Pricing Available for Select Font Sets!. Spacing When we talk about a font’s spacing, or letter fit, we’re referring to the amount of space between the characters, which in turn gives the typeface its relative openness or tightness. Letters are rendered in italic font; numbers are upright/ roman. Some of my friends use it, but they are very old.
8s7qrsbg7km kgpfajmuyad3i ygqrick3k0h5dw f6lwsz0nogvp3m uqrbc4e9ef85a q3hc6q99ce779i u5kq03ns61tq fraec2bumshyc xiqk8oc9pr v6bh7xl6j2aw nnfcby97x7 lkc2in3nc437 5t6d6k1sfks mary27l4hno9 ithyx239gv gslauhhn0uscj asi8pktqxcgo m7kgss91gajwi8 fci8g584l97 xtiu2ofjpcm 082ba6n8jr6 1uymu51w304v xtrvfueot5y 3bjwjtuwp42r63z 1g883xzpzn4a fw4uet32m03qdhm wl3gj6l6s5fzef e085eo5tdrg y1ks7vtn8n2hio mcn3l9e683gv3j


text:
# perturbR

perturbR is an R package for evaluating cluster solutions. perturbR can be used to make comparisons between (1) the solution obtained from the original matrix to solutions obtained in matrices that have had their edge weights incrementally perturbed; and (2) a relative quality score obtained from the original solution and the distribution of quality values obtained from random matrices.

# Getting Started with perturbR

When describing the use of the package we utilize publicly available benchmark data that have previously been evaluated (see Gates et al., 2016). For the purposes of demonstration here we selected an example that almost perfectly recovered the data-generating pattern: data set number 60 of Simulation 5. Here, there were 75 nodes, moderate average node strength, and approximately equally sized groups.

fort5_60 <- as.matrix(read.csv("fort5_60.csv", header = F))

Here we demonstrate use of the perturbR() function. The user must supply a matrix to the sym.matrix argument. This matrix must be symmetric and can reflect a number of phenomenon studied in psychology. For instance, sym.matrix can be a similarity matrix of symptom counts among pairs of individuals, a matrix of fiber counts between pairs of brain regions, or even counts of how often two pairs of individuals speak to each other. The plot in Figure 1 is produced by using the default arguments while also setting the errbars argument to TRUE. The errbars argument is a logical where users can indicate if they would like error bars in the plots. The error bars indicate a range of two standard errors above and below the mean values obtained across repetitions at that given $$\alpha$$ level.

perturbR(sym.matrix = fort5_60, plot = TRUE, errbars = TRUE, resolution = 0.01, reps = 100)

The black circles in Figure 1 indicate the average value for the comparison between the cluster assignments from the original matrix and the cluster assignments from the rewired matrix at each level of edge perturbation $$\alpha$$. The red circles indicate the same comparisons made on a matrix that is completely random but has the same properties as the original matrix, thus providing an appropriate null matrix for comparison. This is important for scaling purposes. To further aid in interpreting the results two horizontal lines are provided. They indicate the values of similarity found between the original matrix and a matrix where 10% and 20% of nodes (not edges, as in the rewiring phase) were randomly assigned to different clusters. As noted in Karrer and colleague’s work (2008) identifying at which $$\alpha$$ the rewired results cross these lines provides insight into interpretation. In a series of empirical examples Karrer (2008) considered cluster solutions to be robust if the matrix had 20% or more of its edges perturbed (i.e,. $$\alpha\geq 0.20$$) before intersecting with the line representing 20% of the nodes being in different clusters.

# Exploring perturbR Output

One can also look directly at the perturbR output and obtain values related to what is seen visually.

## Approach 1: Comparison of Cluster Assignments

In this apporach we comppare the cluster assignments from the original matrix to the solutions obtained from increasingly perturbed matrices. We begin by demonstrating how the first approach described above can be explored with the output. One might want to quantify the point at which the average ARI or VI crosses the 20% line described above. The following commands arrive at this point for the VI values:

Run perturbr:

fit5_60 <- perturbR(sym.matrix = fort5_60, plot = FALSE)

Obtain the VI value when 20% of the community assignments are randomly swapped:

fit5_60$vi20mark  ## [1] 1.514176 Identify the index for the alpha level for the first time the average VI is greater than this value: min(which(colMeans(fit5_60$VI)>fit5_60$vi20mark)) ## [1] 36 Find alpha that corresponds with this index: fit5_60$percent[36]
## [1] 0.3531532

In this example, about 33% of the edges need to be perturbed before the cluster solution for the rewired matrix is as different as when 20% of the nodes are randomly placed into different solutions. This can be seen both by looking at the point where the black circles intersect with the lower horizontal line in the VI figure and using the code above. By contrast, a random matrix drops far below this line with only 2% of the edges perturbed in the rewired matrix. The figures provide an immediate evaluation of cluster solutions whereas the code and output allow the user to further investigate the results. It is also possible to examine the average VI and ARI at the 20% perturbation point and see if it is larger than the these marks. Here we provide an example for the ARI values:

fit5_60$ari20mark  ## [1] 0.621858 mean(fit5_60$ARI[,which(round(fit5_60$percent, digits = 2) == .20)]) ## [1] 0.7756071 We see that the distribution of ARI values at $$\alpha = 0.20$$ is significantly higher than the ARI value obtained with 20% of the cluster assignments for nodes are randomly changed. ## Approach 2: Comparison of Modularity Values In this apporach we comppare the modularity values from the original matrix to modularity values obtained from the increasingly perturbed matrices. The output also provides a value called cutoff which is the modularity value that marks the upper 5% percentile in the distribution of modularity results obtained from random matrices that have the same properties as the original matrix. fit5_60$cutoff
## numeric(0)

### The modularity value from the solution on the original matrix:

fit5_60$modularity[1,1] ## [1] 0.7047275 In this example, the cutoff (Note that values may differ slightly for each run do to the random generation of matrices.) was $$Q_{.95}=0.31$$ and the modularity obtained in this simulated data set was $$Q_{orig}=0.70$$. Hence the modularity in the original solution was well above the upper 5% threshold obtained from the random matrix simulation results. Figure 2 depicts a histogram of the modularity values obtained for solutions in the random matrices simulated to have properties similar to the original matrix. Researchers can easily obtain similar histograms from the output provided if they would like to explore how the distribution of modularity from the random matrices compares to the modularity obtained in the original matrix. hist(fit5_60$modularity[,which(round(fit5_60$percent, digits = 2) ==1.00)], xlim = c(0,1)) abline(v = fit5_60$modularity[1,1], col = "red")

# References

Gates, K. M., Henry, T., Steinley, D., & Fair, D. A. (2016). A monte carlo evaluation of weighted community detection algorithms. Frontiers in Neuroinformatics, 10.

Karrer, B., Levina, E., & Newman, M. E. (2008). Robustness of community structure in networks. Physical Review E, 77 (4), 046119.


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## Some Assumptions

I have been contemplating exactly where to begin the discussion of these matters, and I think that I want to go back to Chapter VIII of The Book, and look at the first section of it because the arguments there keep appearing in later works.

In this post, I’m going to write down some assumptions [(a)-(e) of Claim 1.2] that will be used in the next few posts.

The Assumptions

We assume the following

1. ${\mathfrak{a}}$ is a set of regular cardinals satisfying ${|\mathfrak{a}|^+<\min(\mathfrak{a})}$

2. For every ${\mathfrak{b}\subseteq\mathfrak{a}}$, we let ${\overline{f}^{\mathfrak{b}}=\langle f^{\mathfrak{b}}_\alpha:\alpha<\max{\rm pcf}(\mathfrak{b})\rangle}$ satisfy
• ${f^{\mathfrak{b}}_\alpha\in\prod\mathfrak{a}}$,
• ${\bar{f}^{\mathfrak{b}}}$ is strictly increasing modulo ${J_{<\max{\rm pcf}(\mathfrak{b})}[\mathfrak{a}]}$,
• if ${\alpha<\max{\rm pcf}(\mathfrak{b})}$ and ${|\mathfrak{a}|<{\rm cf}(\alpha)<\min(\mathfrak{a})}$, then for each ${\theta\in \mathfrak{b}}$ we have

$\displaystyle f^{\mathfrak{b}}_\alpha(\theta)=\min\{\bigcup_{\beta\in C}f^{\mathfrak{b}}_\beta(\theta): C\text{ club in }\alpha\}. \ \ \ \ \ (1)$

• for every ${f\in\prod\mathfrak{b}}$ and ${\alpha<\max{\rm pcf}(\mathfrak{b})}$, there is a ${\beta>\alpha}$ such that ${f (everwhere)

3. ${\chi}$ is a sufficiently large regular cardinal, ${<_\chi}$ is a well-ordering of ${H(\chi)}$

4. ${\bar{N}=\langle N_i:i\leq\delta\rangle}$ is an increasing continuous sequence of elementary submodels of ${\langle H(\chi), \in, <_\chi\rangle}$ such that
• ${|N_i|<\min(\mathfrak{a})}$
• ${\langle N_j:j\leq i \rangle \in N_{i+1}}$
• ${|N_i|+1\subseteq N_i}$
• ${\bar{f}=\{\bar{f}^{\mathfrak{b}}:\mathfrak{b}\subseteq\mathfrak{a}\}\in N_0}$

5. ${\mathfrak{a}\subseteq N_0}$ and ${|\mathfrak{a}|<{\rm cf}(\delta)\leq\delta<\min(\mathfrak{a})}$.

I’m going to do some “dictionary work” to get the official names for such objects. I just want to check which terms have become standard, and I’ll use the Abraham/Magidor Handbook article as the final word.


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# Subtracting a constant from log-concave function preserves log-concavity, if the difference is positive

I am trying to work out a question from 'Convex Optimization - Boyd' . Specifically, exercise 3.48:

Show that if $f : \mathbb R^n \to \mathbb R$ is log-concave and $a > 0$, then the function $g = f - a$ is log-concave, where $\operatorname{dom} g= \{x \in \operatorname{dom} f | f(x) > a\}?$

This is my attempt so far:

By assumption, we have $$\frac{d^2\log f}{dx^2}=\frac{f''f-(f')^2}{f^2}\leq0.$$ Considering $g=f-a$, we have $$\frac{d^2\log g}{dx^2} = \frac{f''(f-a)-(f')^2}{(f-a)^2}=\frac{f''f-(f')^2}{(f-a)^2}-\frac{f''a}{(f-a)^2}.$$ If $f''>0$, then we are complete. I'm not sure how to handle the alternative situation though, can anyone help?

• Is $f$ assumed differentiable? Aug 22 '14 at 21:40
• It is not, as far as the exercise statement is concerned. Jan 29 '16 at 8:59

You correctly compute $$\frac{d^2\log g}{dx^2} = \frac{f''(f-a)-(f')^2}{(f-a)^2}.$$ When $a=0$, we know this quantity is non-positive, so the numerator is non-positive. Focus just on the numerator. What happens to the numerator when $a$ increases from $0$? Can you say whether this expression remains non-positive? Note that by assumption, $f-a >0$. It may be useful to consider the cases when $f''>0$ and $f''\le 0$ separately.
And by the way, a complete proof would take account of the fact that $f$ is a function of values in $\mathbb{R}^n$, not just $\mathbb{R}$. That's really not a big issue here, though, since $f$ is log-concave if for all $x_0,v\in\mathbb{R}^n$, the function $\tilde{f}:\mathbb{R}\to\mathbb{R}$ is log-concave, where $$\tilde{f}(t) \equiv f(x_0 + v t).$$ This is just a simple trick for converting questions of concavity in $n$ dimensions into equivalent questions in one dimension by considering how $f$ changes along arbitrary directions $v$.
• ... Actually, it's blindingly obvious. Either $f''>0$, in which case (as I stated) our result is satisfied, or $f''<0$, in which case $f''(f-a)<0\implies f''(f-a) - (f')^2 < 0$, which gives us our result. I guess it was my separating the final equatio that made it slightly confusing. Aug 22 '14 at 21:33


text:
Problem in Zipping a File

When I run my code and use the files that are in the resource folder of my project itself, I face no problems. It zips the file successfully and I can extract it using WINZIP. The problem comes when I try to zip a file that is not in the project folder.

When I do the same, I am passing the Absolute Path of both the src and the dest files. My program doesn't give any exceptions, but when I try to open that zip file, I get an error saying, File is Invalid.

Can anyone tell me why this may be happening.

public static void compress(String srcPath, String destPath) {

    srcFile = new File(srcPath);
destFile = new File(destPath);
try {
fileInputStream = new FileInputStream(srcFile);
fileOutputStream = new FileOutputStream(destFile);
zipEntry = new ZipEntry(srcPath);
zipOutputStream = new ZipOutputStream(fileOutputStream);
zipOutputStream.putNextEntry(zipEntry);
byte[] data = new byte[12];
zipOutputStream.write(data);
}
} catch (Exception e) {
e.printStackTrace();
} finally {
try{
fileInputStream.close();
zipOutputStream.close();}catch (Exception e) {
e.printStackTrace();
}
}

}

-
Which API? Code snippet? –  Wivani Aug 9 '11 at 12:26
Is this on Windows? Are you creating zip entries with drive letters e.g. C:\path\file.txt? –  dogbane Aug 9 '11 at 12:29
@dogbane: Yes, it is windows and I am creating zip entries with drive letters. –  Logan Aug 9 '11 at 12:30
@Wivani: I am using java.util.zip.* . –  Logan Aug 9 '11 at 12:31

You will need to change your code so that it removes the drive letter from the path before creating the ZipEntry.


text:
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Regular version of the site

## Theta block conjecture for paramodular forms of weight 2

Proceedings of the American Mathematical Society. 2020. Vol. 148. P. 1863-1878.
Gritsenko V., Wang H.

In this paper we construct an infinite family of paramodular forms of weight 2 which are simultaneously Borcherds products and additive Jacobi lifts. This proves an important part of the theta-block conjecture of Gritsenko--Poor--Yuen (2013) related to the only known infinite series of theta-blocks of weight 2 and q-order 1. We also consider some applications of this result.


text:
# Particle Generators

Author: John ZuHone
Published on: Jan 4, 2013, 7:05:00 AM

Generating particle initial conditions is now possible in yt. The following shows how to generate particle fields from pre-defined particle lists, lattice distributions, and distributions based on density fields.

First, we define a gridded density field where the particle density field has been "cloud-in-cell" (CIC) interpolated to the grid, and define a function that assigns a set of particle indices based on a number of particles and a starting index. This is for a case where we want to add particles to an already existing set but make sure they have uniqune indices.

In[1]:

from yt.mods import *
from yt.utilities.particle_generator import *
import yt.utilities.initial_conditions as ic
import yt.utilities.flagging_methods as fm
from yt.frontends.stream.api import refine_amr
from yt.utilities.lib import CICDeposit_3

def _pgdensity(field, data):
blank = np.zeros(data.ActiveDimensions, dtype='float32')
if data.NumberOfParticles == 0: return blank
CICDeposit_3(data["particle_position_x"].astype(np.float64),
data["particle_position_y"].astype(np.float64),
data["particle_position_z"].astype(np.float64),
data["particle_gas_density"].astype(np.float32),
np.int64(data.NumberOfParticles),
blank, np.array(data.LeftEdge).astype(np.float64),
np.array(data.ActiveDimensions).astype(np.int32),
np.float64(data['dx']))
return blank
validators=[ValidateGridType()],
display_name=r"$\mathrm{Particle}\/\mathrm{Density}$")

return np.arange((npart)) + start_num

Next, we'll set up a uniform grid with some random density data:

In[2]:

domain_dims = (128, 128, 128)
dens = 0.1*np.random.random(domain_dims)
fields = {"Density": dens}

As a first example, we'll generate particle fields from pre-existing NumPy arrays. First, we define a list of particle field names, and then assign random positions to the particles in one corner of the grid. We then call FromListParticleGenerator, which generates the particles. assign_indices assigns the indices (using numpy.arange by default). apply_to_stream applies the particle fields to the grid.

In[3]:

num_particles1 = 10000
field_list = ["particle_position_x","particle_position_y",
"particle_position_z","particle_gas_density"]
x = np.random.uniform(low=0.0, high=0.5, size=num_particles1) # random positions
y = np.random.uniform(low=0.0, high=0.5, size=num_particles1) # random positions
z = np.random.uniform(low=0.0, high=0.5, size=num_particles1) # random positions
pdata = {'particle_position_x':x,
'particle_position_y':y,
'particle_position_z':z}
particles1 = FromListParticleGenerator(ug, num_particles1, pdata)
particles1.assign_indices()
particles1.apply_to_stream()

yt : [INFO     ] 2013-01-01 21:24:32,484 Adding Density to list of fields
yt : [INFO     ] 2013-01-01 21:24:32,486 Adding particle_position_z to list of fields
yt : [INFO     ] 2013-01-01 21:24:32,487 Adding particle_index to list of fields
yt : [INFO     ] 2013-01-01 21:24:32,487 Adding particle_position_x to list of fields
yt : [INFO     ] 2013-01-01 21:24:32,488 Adding particle_position_y to list of fields

Now that the particles are part of the parameter file, they may be manipulated and plotted:

In[4]:

slc = SlicePlot(ug, 2, ["Density"], center=ug.domain_center)
slc.set_cmap("Density","spring")
slc.annotate_particles(0.2, p_size=10.0) # Display all particles within a thick slab 0.2 times the domain width
slc.show()

Now let's try adding a particle distribution in a lattice-shaped spatial arrangement. Let's choose ten particles on a side, and place them in a small region away from the random particles. We'll use the special add_indices function we defined earlier to assign indices that are all different from the ones the already existing particles have.

In[5]:

pdims = np.array([10,10,10]) # number of particles on a side in each dimension
ple = np.array([0.6,0.6,0.6]) # left edge of particle positions
pre = np.array([0.9,0.9,0.9]) # right edge of particle positions
particles2 = LatticeParticleGenerator(ug, pdims, ple, pre, field_list)
start_num=num_particles1)
particles2.apply_to_stream()

yt : [INFO     ] 2013-01-01 21:24:33,957 Adding particle_gas_density to list of fields

We now have both sets of particles:

In[6]:

slc = SlicePlot(ug, 2, ["Density"], center=ug.domain_center)
slc.set_cmap("Density","spring")
slc.annotate_particles(0.2, p_size=10.0)
slc.show()

And by sorting all of the indices we can check that all of them are unique, as advertised:

In[7]:

dd = ug.h.all_data()
indices = np.sort(np.int32(dd["particle_index"]))
print "All indices unique = ", np.all(np.unique(indices) == indices)

All indices unique =  True

Now let's get fancy. We will use the initial conditions capabilities of yt to apply a spherically symmetric density distribution based on the "beta-model" functional form, and set up a refinement method based on overdensity. Then, we will call refine_amr to apply this density distribution and refine the grid based on the overdensity over some value.

In[8]:

fo = [ic.BetaModelSphere(1.0,0.1,0.5,[0.5,0.5,0.5],{"Density":(10.0)})]
rc = [fm.flagging_method_registry["overdensity"](4.0)]
pf = refine_amr(ug, rc, fo, 3)

Now, we have an interesting density field to serve as a distribution function for particle positions. What we do next is define a spherical region over which particle positions will be generated based on the local grid density. We also will map the grid density to a particle density field using cloud-in-cell interpolation. Finally, when we apply these particles, we will set the optional argument clobber=True, which will remove the particles we already created.

In[9]:

num_particles3 = 100000
map_dict = {"Density": "particle_gas_density"} # key is grid field, value is particle field
sphere = pf.h.sphere(pf.domain_center, (0.5, "unitary"))
particles3 = WithDensityParticleGenerator(pf, sphere, num_particles3,
field_list)
particles3.assign_indices()
particles3.map_grid_fields_to_particles(map_dict) # Map density fields to particle fields
particles3.apply_to_stream(clobber=True) # Get rid of all pre-existing particles

Now we'll plot up both the grid density field and the "particle_density_cic" field (defined at the top of the script), which is mapped from the particles onto the grid. We also overplot the particle positions. These should roughly correspond to the non-zero values of "particle_density_cic", but there will be some discrepancies due to the fact that they are taken from a thick slab and only a slice of the grid-based field is shown.

In[10]:

slc = SlicePlot(pf, 2, ["Density","particle_density_cic"], center=pf.domain_center)
slc.set_log("Density", True)
slc.set_log("particle_density_cic", True)
slc.set_cmap("all", "spring")
slc.annotate_grids()
slc.annotate_particles(0.01,p_size=3)
slc.show()


text:
jug is a small web development framework for R which relies heavily upon the httpuv package. It’s main focus is to make building APIs for your code as easy as possible.

jug is not supposed to be either an especially performant nor an uber stable web framework. Other tools (and languages) might be more suited for that. It focuses on maximizing the ease with wich you can create web APIs for your R code. However, the flexibility of jug means that, in theory, you could built an extensive web framework with it.

Check out http://bart6114.github.io/jug/articles/jug.html for the vignette documentation.

Plugins:

## Changes

### v0.1.7.902

• Introduction of events and event listeners (check e.g. the on function)
• Introduction of the logger, a predefined event listener based on futile.logger
• Enabled ByteCompile on installation

### v0.1.7.901

• Adjustment to serve_static_files: add pdf to binary types

### v0.1.7.900

• Adjustment to serve_static_files: removed link between path and file served

### v0.1.7

• Fixed CORS preflight request bug (issue #15)

### v0.1.6

• Ability to specify auto-unbox value for json responses
• Added strict_params argument to decorate

### v0.1.5

• Added basic authentication functionality through auth_basic

### v0.1.4

• Fixed bug where missing content type would not auto-parse the query string

### v0.1.3

• Possible to specify method for use middleware


text:
# Location Models for Airline Hubs Behaving as M/D/C Queues

Univ. Pompeu Fabra, Economics and Business Working Paper No. 453

32 Pages Posted: 1 May 2000

See all articles by Vladimir Marianov

## Daniel Serra

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

### Abstract

Models are presented for the optimal location of hubs in airline networks, that take into consideration the congestion effects. Hubs, which are the most congested airports, are modeled as M/D/c queuing systems, that is, Poisson arrivals, deterministic service time, and {\em c} servers. A formula is derived for the probability of a number of customers in the system, which is later used to propose a probabilistic constraint. This constraint limits the probability of {\em b} airplanes in queue, to be lesser than a value $\alpha$. Due to the computational complexity of the formulation. The model is solved using a meta-heuristic based on tabu search. Computational experience is presented.

Keywords: Hub location, congestion, tabu-search

JEL Classification: C61, R12, R53

Suggested Citation

Marianov, Vladimir and Serra, Daniel, Location Models for Airline Hubs Behaving as M/D/C Queues. Univ. Pompeu Fabra, Economics and Business Working Paper No. 453, Available at SSRN: https://ssrn.com/abstract=224595 or http://dx.doi.org/10.2139/ssrn.224595


text:
Question 658b0

Aug 26, 2017

${\text{14 mol L}}^{- 1}$

Explanation:

Assuming that you can dissolve $3.4$ moles of this unknown solute in enough water to make $\text{245 mL}$ of solution at room temperature, you can calculate the molarity of this solution by figuring out how many moles of solute would be present in

$\text{1 L" = 10^3color(white)(.)"mL}$

of this solution.

Now, solutions are homogeneous mixtures, which implies that they same composition throughout.

This will let you use the known composition of the solution

$\text{3.4 moles solute " -> " 245 mL solution}$

as a conversion factor to help you find the number of moles of solute that would be present in ${10}^{3}$ $\text{mL}$ of this solution.

You're going from volume of solution to moles, so set up the conversion factor as

"3.4 moles solute"/"245 mL solution" color(white)(aa)color(white)((color(blue)( larr " what you need goes on top")aaaaaa)/color(blue)(larr " what you have goes on the bottom"))

You should end up with

10^3 color(red)(cancel(color(black)("mL solution"))) * "3.4 moles solute"/(245 color(red)(cancel(color(black)("mL solution")))) = "13.88 moles solute"#

Since this represents the number of moles of solute present in ${10}^{3} \textcolor{w h i t e}{.} \text{mL" = "1 L}$ of solution, you can say that the molarity of the solution is

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{molarity" = "14 mol L}}^{- 1}}}}$

The answer is rounded to two sig figs, the number of sig figs you have for the number of moles of solute present in your sample.


text:
## Virtual Networks All the Way Down

For almost as long as there have been packet-switched networks, there have been ideas about how to virtualize them, starting with virtual circuits. But what exactly does it mean to virtualize a network?

Virtual memory is a helpful example. Virtual memory creates an abstraction of a large and private pool of memory, even though the underlying physical memory may be shared by many applications and considerably smaller that the apparent pool of virtual memory. This abstraction enables programmers to operate under the illusion that there is plenty of memory and that no-one else is using it, while under the covers the memory management system takes care of things like mapping the virtual memory to physical resources and avoiding conflict between users.

Similarly, server virtualization presents the abstraction of a virtual machine (VM), which has all the features of a physical machine. Again, there may be many VMs supported on a single physical server, and the operating system and users on the virtual machine are happily unaware that the VM is being mapped onto physical resources.

A key point is the virtualization of computing resources preserves the abstractions and interfaces that existed before they were virtualized. This is important because it means that users of those abstractions don't need to change—they see a faithful reproduction of the resource being virtualized. Virtualization also means that the different users (sometimes called tenants) cannot interfer with each other. So what happens when we try to virtualize a network?

VPNs, as described in Section 3.2, were one early success for virtual networking. They allowed carriers to present corporate customers with the illusion that they had their own private network, even though in reality they were sharing underlying links and switches with many other users. VPNs, however, only virtualize a few resources, notably addressing and routing tables. Network virtualization as commonly understood today goes further, virtualizing every aspect of networking. That means that a virtual network should support all the basic abstractions of a physical network. In this sense, they are analogous to the virtual machine, with its support of all the resources of a server: CPU, storage, I/O, and so on.

To this end, Virtual LANs (VLANs) are how we typically virtualize an L2 network. Supporting VLANs required a fairly simple extension to the original 802.1 header specification, inserting a 12-bit VLAN ID (VID) field between the SrcAddr and Type fields, as shown in Figure 1. (This VID is typically referred to as a VLAN Tag.) There are actually 32-bits inserted in the middle of the header, but the first 16-bits are used to preserve backwards compatibility with the original specification (they use Type = 0x8100 to indicate that this frame includes the VLAN extension); the other four bits hold control information used to prioritizing frames. This means it is possible to map 2$^{12}$ = 4096 virtual networks onto a single physical LAN.

VLANs proved to be quite useful to enterprises that wanted to isolate different internal groups (e.g., departments, labs), giving each of them the appearance of having their own private LAN. VLANs were also seen as a promising way to virtualize L2 networks in cloud datacenters, making it possible to give each tenant their own L2 network so as to isolate their traffic from the traffic of all other tenants. But there was a problem: the 4096 possible VLANs was not sufficient to account for all the tenants that a cloud might host, and to complicate matters, in a cloud the network needs to connect virtual machines rather than the physical machines that those VMs run on.

To address this problem, another standard called Virtual Extensible LAN (VXLAN) was introduced. Unlike the original approach, which effectively encapsulated a virtualized ethernet frame inside another ethernet frame, VXLAN encapsulates a virtual ethernet frame inside a UDP packet. This means a VXLAN-based virtual network (which is often referred to as an overlay network) runs on top of an IP-based network, which in turn runs on an underlying ethernet (or perhaps in just one VLAN of the underlying ethernet). VXLAN also makes it possible for one cloud tenant to have multiple VLANs of their own, which allows them to segregate their own internal traffic. This means it is ultimately possible to have a VLAN encapsulated in a VXLAN overlay encapsulated in a VLAN.

The powerful thing about virtualization is that when done right, it should be possible to nest one virtualized resource inside another virtualized resource, since after all, a virtual resource should behave just like a physical resources and we know how to virtualize physical resources! Said another way, being able to virtualize a virtual resource is the best proof that you have done a good job of virtualizing the original physical resource. To re-purpose the mythology of the World Turtle: It's virtual networks all the way down.

The actual VXLAN header is simple. It includes a 24-bit Virtual Network Id (VNI), plus some flag bits. It also implies a particular setting of the UDP source and destination port fields (see Section 5.1), with the destination port 4789 officially reserved for VXLANs. Figuring out how to uniquely identify virtual LANs (VLAN tags) and virtual networks (VXLAN VIDs) is the easy part. This is because encapsulation is the fundamental cornerstone of virtualization; all you need to add is an identifier that tells you which of many possible users this encapsulated packet belongs to.

The hard part is grappling with the idea of virtual networks being nested (encapsulated) inside virtual networks, which is networking’s version of recursion. The other challenge is understanding how to automate the creation, management, migration, and deletion of virtual networks, and on this front there is still a lot of room for improvement. Mastering this challenge will be at the heart of networking in the next decade, and while some of this work will undoubtedly happen in proprietary settings, there are open source network virtualization platforms (e.g., the Linux Foundation's Tungsten Fabric project) leading the way.

[!NOTE|label:Broader Perspective] To continue reading about the cloudification of the Internet, see The Cloud is Eating the Internet.


text:
# Q. 6.    $DL$ and $\inline BM$ are the heights on sides $\inline AB$ and $\inline AD$ respectively, of parallelogram $\inline ABCD$ (Fig 11.24). If the area of the parallelogram is             $\inline 1470\; cm^{2}.$ $\inline AB=35\; cm$ and $\inline AD=49\; cm,$ find the length of $\inline BM$ and $\inline DL.$

R Riya

We know that

Area of parallelogram  $= base \times height$

Here,

Base of parallelogram(AB) = 35 cm

and

Height of parallelogram(DL) = h cm

$\Rightarrow 1470 = 35 \times h$

$\Rightarrow h = \frac{1470}{35} = 42 \ cm$

Similarly,

Area is also given by $AD \times BM$

$\Rightarrow 1470 = 49 \times BM$

$\Rightarrow BM = \frac{1470}{49} = 30 \ cm$

Therefore, the value of BM and DL are  is  30cm and 42cm respectively

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