Entropy and Information Theory 3 March 2013 This site provides the current version of the first edition of the book Entropy and Information Theory by R.M. Gray in the Adobe portable document format (PDF). This format can be read from a Web browser by using the Acrobat Reader helper application, which is available for free downloading from Adobe. The current version is a corrected and slightly revised version of the second printing (1991) of the Springer-Verlag book of the same name, which is now out of print. Permission is hereby given to freely print and circulate copies of this book so long as it is left intact and not reproduced for commercial purposes.

Gambling and information theory Statistical inference might be thought of as gambling theory applied to the world around. The myriad applications for logarithmic information measures tell us precisely how to take the best guess in the face of partial information.[1] In that sense, information theory might be considered a formal expression of the theory of gambling. It is no surprise, therefore, that information theory has applications to games of chance.[2] Kelly Betting[edit] Kelly betting or proportional betting is an application of information theory to investing and gambling. Its discoverer was John Larry Kelly, Jr. Part of Kelly's insight was to have the gambler maximize the expectation of the logarithm of his capital, rather than the expected profit from each bet. Side information[edit] where Y is the side information, X is the outcome of the betable event, and I is the state of the bookmaker's knowledge. The nature of side information is extremely finicky. Doubling rate[edit] where there are th horse winning being

The Traditional Four-Step Method | Bean Institute Dry beans are an incredibly nutritious, versatile and inexpensive ingredient. The cost of one ½ cup serving of dry beans is about one-third the cost of canned beans. Cooking with dry beans is easy and rewarding, but to cook with dry beans versus canned beans you need to follow four simple steps. For best results, follow these tips! Keep cooking water at a gentle simmer to prevent split skins.Since beans expand as they cook, add warm water periodically during the cooking process to keep the beans covered.Stir beans occasionally throughout the cooking process to prevent sticking.You can “bite test” beans for tenderness.

Welcome, take my hand Entropy (information theory) 2 bits of entropy. A single toss of a fair coin has an entropy of one bit. A series of two fair coin tosses has an entropy of two bits. The number of fair coin tosses is its entropy in bits. This random selection between two outcomes in a sequence over time, whether the outcomes are equally probable or not, is often referred to as a Bernoulli process. The entropy of such a process is given by the binary entropy function. This definition of "entropy" was introduced by Claude E. Entropy is a measure of unpredictability of information content. Now consider the example of a coin toss. English text has fairly low entropy. If a compression scheme is lossless—that is, you can always recover the entire original message by decompressing—then a compressed message has the same quantity of information as the original, but communicated in fewer characters. Shannon's theorem also implies that no lossless compression scheme can compress all messages. . The average uncertainty , with

Harlan County War The Harlan County War, or Bloody Harlan, was a series of coal mining-related skirmishes, executions, bombings, and strikes (both attempted and realized) that took place in Harlan County, Kentucky during the 1930s. The incidents involved coal miners and union organizers on one side, and coal firms and law enforcement officials on the other.[1] The question at hand: the rights of Harlan County coal miners to organize their workplaces and better their wages and working conditions. It was a nearly decade-long conflict, lasting from 1931 to 1939. Before its conclusion, an indeterminate number of miners, deputies, and bosses would be killed, state and federal troops would occupy the county more than half a dozen times, two acclaimed folk singers would emerge, union membership would oscillate wildly, and workers in the nation's most anti-labor coal county would ultimately be represented by a union. History[edit] "Sheriff J.H. Impact[edit] See also[edit] References[edit] External links[edit]

History of mathematical notation: Facts, Discussion Forum, and E Mathematical notation comprises the symbol A symbol is something which represents an idea, a physical entity or a process but is distinct from it. The purpose of a symbol is to communicate meaning. For example, a red octagon may be a symbol for "STOP". On a map, a picture of a tent might represent a campsite. Numerals are symbols for... s used to write mathematical equation An equation is a mathematical statement that asserts the equality of two expressions. s and formula In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language.... s. The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . , Hebrew The Hebrew alphabet , known variously by scholars as the Jewish script, square script, block script, or more historically, the Assyrian script, is used in the writing of the Hebrew language, as well as other Jewish languages, most notably Yiddish, Ladino, and Judeo-Arabic. , and German . . .

Latent Dirichlet allocation In natural language processing, latent Dirichlet allocation (LDA) is a generative model that allows sets of observations to be explained by unobserved groups that explain why some parts of the data are similar. For example, if observations are words collected into documents, it posits that each document is a mixture of a small number of topics and that each word's creation is attributable to one of the document's topics. LDA is an example of a topic model and was first presented as a graphical model for topic discovery by David Blei, Andrew Ng, and Michael Jordan in 2003.[1] Topics in LDA[edit] In LDA, each document may be viewed as a mixture of various topics. For example, an LDA model might have topics that can be classified as CAT_related and DOG_related. Each document is assumed to be characterized by a particular set of topics. Model[edit] With plate notation, the dependencies among the many variables can be captured concisely. is the topic distribution for document i, The 1. , where .

Castor and Pollux Castor[a] and Pollux[b] (or in Greek, Polydeuces[c]) were twin half-brothers in Greek and Roman mythology, known together as the Dioscuri.[d] Birth and functions[edit] Castor depicted on a calyx krater of c. 460–450 BC, holding a horse's reins and spears and wearing a pilos-style helmet Castor and Pollux are sometimes both mortal, sometimes both divine. One consistent point is that if only one of them is immortal, it is Pollux. The Dioscuri were regarded as helpers of humankind and held to be patrons of travellers and of sailors in particular, who invoked them to seek favourable winds.[3] Their role as horsemen and boxers also led to them being regarded as the patrons of athletes and athletic contests.[4] They characteristically intervened at the moment of crisis, aiding those who honoured or trusted them.[5] Classical sources[edit] Pair of Roman statuettes (3rd century AD) depicting the Dioscuri as horsemen, with their characteristic skullcaps (Metropolitan Museum of Art) Mythology[edit]

An Atlas of Cyberspaces- Historical Maps USENET in 1981. The topology of the BITNET in 1981 (partial map) The NSFNET infrastructure and topology in 1991. (Source : NSFNET postscript maps from | Introduction | Whats New | Conceptual | Artistic | Geographic | Cables & Satellites | Traceroutes | | Census | Topology | Info Maps | Info Landscapes | Info Spaces | ISP Maps | Weather Maps | | Wireless | Web Site Maps | Surf Maps | MUDs & Virtual Worlds | Historical | (© Copyright - Martin Dodge, 2007)

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Codognet states, "Information theory can be thought of as a sort of simplified or idealized semiotics: a ciphering/deciphering algorithm represents the interpretation process used to decode some signifier (encoded information) into some computable signified (meaningful information) to be fed to a subsequent processing step. This process, like semiosis itself, is, of course unlimted." by arlene Mar 24