Information theory

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.

Information revolution A visualization of the various routes through a portion of the Internet. The Information Age (also known as the Computer Age, Digital Age, or New Media Age) is a period in human history characterized by the shift from traditional industry that the industrial revolution brought through industrialization, to an economy based on information computerization. The onset of the Information Age is associated with the Digital Revolution, just as the Industrial Revolution marked the onset of the Industrial Age. During the information age, the phenomenon is that the digital industry creates a knowledge-based society surrounded by a high-tech global economy that spans over its influence on how the manufacturing throughput and the service sector operate in an efficient and convenient way. The Internet[edit] The Internet was conceived as a fail-proof network that could connect computers together and be resistant to any single point of failure. Progression[edit] Library expansion[edit] Computation[edit]

Density matrix Explicitly, suppose a quantum system may be found in state with probability p1, or it may be found in state with probability p2, or it may be found in state with probability p3, and so on. The density operator for this system is[1] By choosing a basis (which need not be orthogonal), one may resolve the density operator into the density matrix, whose elements are[1] For an operator (which describes an observable is given by[1] In words, the expectation value of A for the mixed state is the sum of the expectation values of A for each of the pure states Mixed states arise in situations where the experimenter does not know which particular states are being manipulated. Pure and mixed states[edit] In quantum mechanics, a quantum system is represented by a state vector (or ket) . is called a pure state. and a 50% chance that the state vector is . A mixed state is different from a quantum superposition. Example: Light polarization[edit] An example of pure and mixed states is light polarization. . and . . .

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]

Intelligence amplification Use of information technology to augment human intelligence Intelligence amplification (IA) (also referred to as cognitive augmentation, machine augmented intelligence and enhanced intelligence) refers to the effective use of information technology in augmenting human intelligence. The idea was first proposed in the 1950s and 1960s by cybernetics and early computer pioneers. Major contributions[edit] William Ross Ashby: Intelligence Amplification[edit] ... J. "Man-Computer Symbiosis" is a key speculative paper published in 1960 by psychologist/computer scientist J.C.R. Man-computer symbiosis is a subclass of man-machine systems. In Licklider's vision, many of the pure artificial intelligence systems envisioned at the time by over-optimistic researchers would prove unnecessary. Douglas Engelbart: Augmenting Human Intellect[edit] Licklider's research was similar in spirit to his DARPA contemporary and protégé Douglas Engelbart. Later contributions[edit] Levels of Human Cognitive Augmentation

Quantum teleportation Quantum teleportation is a process by which quantum information (e.g. the exact state of an atom or photon) can be transmitted (exactly, in principle) from one location to another, with the help of classical communication and previously shared quantum entanglement between the sending and receiving location. Because it depends on classical communication, which can proceed no faster than the speed of light, it cannot be used for superluminal transport or communication of classical bits. It also cannot be used to make copies of a system, as this violates the no-cloning theorem. Although the name is inspired by the teleportation commonly used in fiction, current technology provides no possibility of anything resembling the fictional form of teleportation. Non-technical summary[edit] Quantum teleportation provides a mechanism of moving a qubit from one location to another, without having to physically transport the underlying particle that a qubit is normally attached to. Protocol[edit] and