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Topic: Entropy information theory

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	math lessons - Information entropy
		Entropy is a measure of this randomness, suggested by Claude E. Shannon in his 1949 paper A Mathematical Theory of Communication.
		Entropy effectively bounds the performance of the strongest non-lossy (or nearly non-lossy) compression possible, which can be realized in theory by using the typical set or in practice using Huffman, Lempel-Ziv or arithmetic coding.
		Thus, the entropy of the source alphabet, with its given empiric probability distribution, is a number equal to the number (possibly fractional) of symbols of the "ideal alphabet", with an optimal probability distribution, necessary to encode for each symbol of the source alphabet.
	www.mathdaily.com /lessons/Information_entropy (1401 words)

	More on Information Theory
		Information theory is a branch of the mathematical theory of probability and mathematical statistics, that quantifies the concept of information.
		The transmission part of the theory is not concerned with the meaning (semantics) of the message conveyed, though the complementary wing of information theory concerns itself with content through lossy compression of messages subject to a fidelity criterion.
		These two wings of information theory are joined together and mutually justified by the information transmission theorems, or source-channel separation theorems that justify the use of bits as the universal currency for information in many contexts.
	www.artilifes.com /information-theory.htm (1143 words)

	Wikinfo \| Information theory (Site not responding. Last check: 2007-10-20)
		Information theory is a branch of the mathematical theory of probability and mathematical statistics, that deals with the concepts of information and information entropy, communication systems, data transmission and rate distortion theory, cryptography, signal-to-noise ratios, data compression, and related topics.
		His theory "considered the transmission of information as a statistical phenomenon" and gave communications engineers a way to determine the capacity of a communication channel in terms of the common currency of bits.
		The transmission part of the theory is not "concerned with the content of information or the message itself," though the complementary wing of information theory concerns itself with content through lossy compression of messages subject to a fidelity criterion.
	www.wikinfo.org /wiki.php?title=Information_theory (576 words)

	Information Theory Demystified
		Note that in communication theory, this uncertainty is taken as a measure of the amount of “information” transmitted by the source and that this amount of information is called “the entropy” or for the sake of clarity “Shannon entropy”.
		With respect to information theory, it doesn’t matter whether the content of a message is random or recognizable because the average number of bits is the same.
		Moreover, the word’s “information”, “entropy” and “uncertainty” are synonymous and correspond to increasing randomness or uncertainty as the number of bits increases i.e.
	www.ideacenter.org /contentmgr/showdetails.php/id/1236 (2865 words)

	The Paradox of Truth, the Truth of Entropy
		Thermodynamic entropy is the measure of this disorganization in the universe.
		Information theory is the mathematical theory of communication that is used to find out the speed and quantity of information transmission.
		In statistical terms, information theory entropy measures the probability of a system arriving at its present state, thus the higher the entropy, the higher the probability.
	www.pynchon.pomona.edu /entropy/paradox.html (2297 words)

	Information Theory: Entropy and Huffman Codes
		Information Theory is a mathematical model of communication that specifically deals with the transmission of information.
		Information Theory aims to describe data transmission in the language of mathematics to find realistic bounds for transmission rates over communication lines.
		Entropy is a measure of the uncertainty of the outcome of a an event.
	www.arches.uga.edu /~dfalke/Infotheory/infotheory/infotheory.html (941 words)

	Entropy and Information
		Statistical entropy is a probabilistic measure of uncertainty or ignorance; information is a measure of a reduction in that uncertainty
		Entropy (or uncertainty) and its complement, information, are perhaps the most fundamental quantitive measures in cybernetics, extending the more qualitative concepts of variety and constraint to the probabilistic domain.
		Entropies, correlates to entropies, and correlates to such important results as Shannon's 10th Theorem and the Second Law of Thermodynamics have been sought in biology, ecology, psychology, sociology, and economics.
	pespmc1.vub.ac.be /ENTRINFO.html (471 words)

	What is Entropy?
		In Shannon information theory, the entropy is a measure of the uncertainty over the true content of a message, but the task is complicated by the fact that successive bits in a string are not random, and therefore not mutually independent, in a real message.
		In classical thermodynamics, the entropy of a system is the ratio of heat content to temperature (equation 1), and the change in entropy represents the amount of energy input to the system which does not participate in mechanical work done by the system (equation 3).
		In that case the entropy is a measure of the probability for a givem macrostate, so that a high entropy indicates a high probability state, and a low entropy indicates a low probability state (equation 6).
	www.tim-thompson.com /entropy1.html (2609 words)

	On information theory, entropy, and phonology (Site not responding. Last check: 2007-10-20)
		It is this: the notions of information theory (entropy, and the notions derived from entropy) are the natural quantitative measures of many of the concepts used by phonologists, and by linguists more generally.
		Information theory has the reputation, I think, of being obsessed with reducing all messages to sequences of 0s and 1s, and of producing a compressed encoding along those lines, where compressed could be equated with the term non-redundant.
		The reduction of a message (or a linguistic passage, a corpus) to 0s and 1s is performed in information theory on the basis of a probabilistic model for the language, and it is the user (not the information theorist, in general) who is responsible for coming up with the model.
	humanities.uchicago.edu /faculty/goldsmith/Royaumont98/InfoTheory.html (3677 words)

	Information theory
		Entropy is an expression of the fundamental law of the tendency in nature to obliterate structures and wipe out forms.
		He described himself as a behavioral scientist and his critical use of the information theory in his field work and in his many publications is outstanding, since he as a true scientist with a very broad, impartial view, investigated the natural communication between living organisms such as humans and mammals.
		The theory of dis-continuity between categories and their elements is also called "the theory of logical types", which Bateson used as the fundament for his theory of communication.
	home22.inet.tele.dk /hightower/information.htm (5502 words)

	Information Theory and Creationism: Classical Information Theory (Shannon)
		Modern digital communication depends on Information Theory, which was invented in the 1940's by Claude E.
		The use of a logarithm to measure information is owed to Ralph V.L. Hartley whose 1928 paper is cited by Shannon.
		That is, the information source is assumed to be a random process, outputing a sequence of symbols from a fixed symbol set, where the probability of each new symbol depends on only on the preceding symbol.
	home.mira.net /~reynella/debate/shannon.htm (2565 words)

	Recent Developments in Information and Entropy Econometrics (IEE) – Theory and Applications – A Proposed ... (Site not responding. Last check: 2007-10-20)
		Information and Entropy Econometrics (IEE) is research that directly or indirectly builds on the foundations of Information Theory (IT) and the principle of Maximum Entropy (ME).
		The interrelationship between Information Theory (IT), statistics and inference, and the ME principle started to become clear in the early work of Kullback and Lindley.
		In that way, he was able to apply Shannon’s ideas to statistical theory by referring to the information in an experiment rather than in a message.
	www.american.edu /cas/econ/faculty/golan/conference2.htm (742 words)

	Entropy of FDI for Redundant Structures (Site not responding. Last check: 2007-10-20)
		This decision tree also represents explicitly the discrete communication or information channel for a redundant structure where: the input (X) is the prior information, the output (Y) is the system states, and the channel is the decision paths between input and output as dictated by the conditional knowledge of the FDI scheme.
		The rate of information transmission (R) across this discrete channel is optimized by maximizing the mutual information between the input and output states of the decision tree.
		The entropy of the system state set H(S t) is formulated directly from Shannon's equation for discrete events (Equation 5) and exhibits a characteristic, "humped" curve (Figure 2).
	www.ececs.uc.edu /~vhunt/journal2.htm (4142 words)

	Information entropy - Wikipedia, the free encyclopedia
		Information entropy is occasionally called Shannon's entropy in honor of Claude E. Shannon, who formulated many of the key ideas of information theory.
		Entropy effectively bounds the performance of the strongest lossless (or nearly lossless) compression possible, which can be realized in theory by using the typical set or in practice using Huffman, Lempel-Ziv or arithmetic coding.
		Information is not entropy, information is not uncertainty !
	en.wikipedia.org /wiki/Information_entropy (2379 words)

	Entropy in Information and Coding Theory
		In 1948, motivated by the problem of efficiently transmitting information over a noisy communication channel, Claude Shannon introduced a revolutionary new probabilistic way of thinking about communication and simultaneously created the first truly mathematical theory of entropy.
		His ideas created a sensation and were rapidly developed along two main lines of development: information theory, which employs probability and ergodic theory to study the statistical characteristics of data and communication systems, and coding theory, which uses mainly algebraic and geometric tools to contrive efficient codes for various situations.
		Focuses on the contrast between the traditional interpretation of the entropy of a stationary ergodic source in terms of the number of typical sequences of a given length and the interpretation in terms of the recurrence of blocks of symbols ("patterns") in a single typical sequence.
	www.math.uni-hamburg.de /home/gunesch/Entropy/infcode.html (1024 words)

	Information Theory
		The real justification for regarding the entropy as the amount of information is that, unsightly though it is, though it's abstracted away all the content of the message and almost all of the context (except for the distribution over messages), it works.
		Two problems with this, however, are that Badino assumes the theory completely specifies the probability of observations, i.e., no free parameters can be estimated from data, and he doesn't seem to be aware of any of the work relating information theory to hypothesis testing, which goes back at least to Kullback in the 1950s.
		Timpson, "On the Supposed Conceptual Inadequacy of the Shannon Information," quant-ph/0112178
	cscs.umich.edu /~crshalizi/notebooks/information-theory.html (4321 words)

	Entropy - Search Results - MSN Encarta
		Entropy, S, measure of the disorderliness with which energy is stored in a system: the greater the disorder, the greater the entropy.
		In most practical applications, one must choose among messages that have different probabilities of being sent.
		His had always been a vigorous, Italian sort of pessimism: like Machiavelli, he allowed the forces of virtù and fortuna to be about 50/50.
	uk.encarta.msn.com /Entropy.html (162 words)

	Information Theory (Site not responding. Last check: 2007-10-20)
		As such, the mutual information can be intuitively considered the amount of uncertainty in X that is eliminated by observations of Y and vice versa.
		Mutual information is closely related to the log-likelihood ratio test in the context of contingency tables and the Multinomial distribution and to Pearson's χ
		test: mutual information can be considered a statistic for assessing independence between a pair of variables, and has a well-specified asymptotic distribution.
	shennonlegacy.org.ru (856 words)

	Lucent \| Information Theory (Site not responding. Last check: 2007-10-20)
		Information Theory regards information as only those symbols that are uncertain to the receiver.
		The amount of information, or uncertainty, output by an information source is a measure of its entropy.
		In turn, a source's entropy determines the amount of bits per symbol required to encode the source's information.
	www.lucent.com /minds/infotheory/what1.html (120 words)

	CF005: 2nd law of thermodynamics and information theory
		While statistical information theory has a quantity called "entropy", it does not have anything equivalent to the second law of thermodynamics.
		Information theory does sort of have a principle of degradation, but it is only applicable in certain situations (which evolution isn't one of).
		In a communication or information storage system, where the goal is to transmit or replay the original message intact, change is necessarily bad, so this corresponds to degradation.
	www.talkorigins.org /indexcc/CF/CF005.html (264 words)

	Pitfalls in Information Theory and Molecular Information Theory (Site not responding. Last check: 2007-10-20)
		Information theory and molecular biology touch on a huge number of topics, as shown by the icon to the right.
		Entropy is not "disorder"; it is a measure of the dispersal of energy by Dr. Frank L. Lambert.
		Rsequence (the information content of a binding site) is a measure of the residue of energy dissipation left as a pattern in the DNA (by mutation and selection) when a protein binds to DNA.
	www.lecb.ncifcrf.gov /~toms/pitfalls.html (2709 words)

	Entropy (Site not responding. Last check: 2007-10-20)
		Claude Shannon, the inventor of information theory, devised an experiment aimed at determining the entropy of an English letter (the amount of information in bits that we obtain on the average when we learn one letter of English).
		He uses the entropy of the resulting random variable as an estimate for the entropy of an English letter.
		Perhaps we should mention that large scale experiments of this kind yield that the amount of information we gain when we learn a letter of English, within a sentence, is aproximately 1.1 bits.
	www.math.psu.edu /dlittle/java/informationtheory/entropy/index.html (356 words)

	The KLI Theory Lab - keywords - information theory
		Yockey, H.P. A study of aging, thermal killing and radiation damage by information theory.
		In Yockey/Platzman/Quastler, Symposium on Information Theory in Biology, 297—316.
		Yockey, H.P. An application of information theory to the Central Dogma and the sequence hypothesis.
	www.kli.ac.at /theorylab/Keyword/I/InfoTh.html (220 words)

	Publisher description for Library of Congress control number 84023108
		A number of scientists and information theorists have maintained that entropy is a subjective concept and is a measure of human ignorance.
		Whilst the present volume is not a treatise on thermodynamics or statistical mechanics, all relevant steps in the building up of these disciplines are carefully scrutinised and it is concluded that the charge of subjectivity cannot be upheld.
		The widely adopted view that entropy is a measure of disorder, or of lack of information, is shown to be ambiguous, although it may be of use in certain contexts.
	www.loc.gov /catdir/description/cam031/84023108.html (210 words)

	Elements of Information Theory
		Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory.
		All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing.
		Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications
	www.elementsofinformationtheory.com (158 words)

	Molecular Information Theory and the Theory of Molecular Machines (Site not responding. Last check: 2007-10-20)
		This is a general purpose method for using information theory to analyze sequences.
		Molecular Information Theory: Flippers, Flappers and Flip-Flops in DNA Binding, 2006 Feb 22 4:00 pm, at the Department of Chemistry and Biochemistry,
		Information theory-based analysis of CYP2C19, CYP2D6 and CYP3A5 splicing mutations, Pharmacogenetics 2003 13(4): 207-18.
	www.lecb.ncifcrf.gov /~toms (2160 words)

	Publisher description for Library of Congress control number 85121434 (Site not responding. Last check: 2007-10-20)
		Publisher description for Mathematical theory of entropy / Nathaniel F.G. Martin, James W. England ; foreword by James K. Brooks.
		This excellent treatment of the mathematical theory of entropy gives an accessible exposition of the ways in which this idea has been applied to information theory, ergodic theory, topological dynamics and statistical mechanics.
		Scientists who want a quick understanding of how entropy is applied in disciplines not their own, or simply desire a better understanding of the mathematical foundation of the entropy function will find this to be a valuable book.
	www.loc.gov /catdir/description/cam031/85121434.html (139 words)

	The KLI Theory Lab - keywords - entropy
		Keywords: Determinism • Entropy • Historical-determinism • Indeterminism • Philosophy of Science • Structural-determinism.
		Wagensberg, J. /Valls, J. The (extended) maximum entropy formalism and the statistical structure of ecosystems.
		Keywords: complexity • entropy • information • physics.
	www.kli.ac.at /theorylab/Keyword/E/Entropy.html (122 words)

	The world of Entropy, Information Theory
		The Laboratory of Information Theory (LTHI) was established in 1999 as part of the Communication Systems department at the Swiss Federal Institute of Technology, Lausanne
		The laboratory focuses on exploring the fundamental limits of communication, multi-user information theory and coding theory.
		Quantum Information Theory course: A 4 credit course offered by Prof.Erdal Arikan, this winter semester.
	lthiwww.epfl.ch /index_oct04.html (166 words)

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