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	ONLamp.com -- Calculating Entropy for Data Mining
		You will learn how to compute entropy for a single database column of values (i.e., univariate entropy) and what the resulting entropy score means.
		The actual entropy of well-formed English text passages will be lower than 4.76 bits because there is structure in the signal distribution, as indicated by the unequal signal probabilities for real English text streams.
		This code outputs a human-readable depiction of the instantiated entropy object, along with the computed entropy of the supplied clickstream data.
	www.onlamp.com /pub/a/php/2005/01/06/entropy.html (1333 words)

	state, second, microscopic, concept, measure, macroscopic, caloric, always, total, small, shown, possible, physics - ...
		Entropy is one of the factors that determines the free energy in the system and appears in the second law of thermodynamics.
		In 1877, thermodynamicist Ludwig Boltzmann visualized a probabilistic way to measure the entropy of an ensemble of ideal gas particles, in which he defined entropy to be proportional to the logarithm of the number of microstates such a gas could occupy.
		Entropy is the only quantity in the physical sciences that "picks" a particular direction for time, sometimes called an arrow of time.
	www.alphasearch.org /Entropy.html (2942 words)

	Signal entropy and the thermodynamics of computation.(MIT Media Lab) - HighBeam Encyclopedia
		The investigation of low-power computing is currently being done by two relatively disjoint camps: physicists who study the limits of single gates, but do not consider whole systems, and engineers who are making evolutionary improvements on existing designs, without considering the fundamental limits.
		Bennett[6] went further and showed that it is possible to compute reversibly with arbitrarily little dissipation per operation, and that the apparent paradox of Maxwell's Demon can be explained by the erasure in the Demon's brain of previous measurements of the state of the gas (that is when the combined Demon-gas system becomes irreversible).
		This entropy is not associated with a heat current if the bit is at the same temperature as the chip (remember that entropy is additive).
	www.encyclopedia.com /doc/1G1-18891264.html (4374 words)

	[No title] (Site not responding. Last check: )
		Lowest entropy (on 30 sequences) received at position 166 in sequence #4: 15.682 Highest entropy (on 30 sequences) received at position 244 in sequence #47: 42.342 Computing entropy of best 2500 base primers according to all 50 sequences.
		Lowest entropy (on 30 sequences) received at position 853 in sequence #39: 17.337 Highest entropy (on 30 sequences) received at position 592 in sequence #33: 42.626 Computing entropy of best 2500 base primers according to all 46 sequences.
		Lowest entropy (on 16 sequences) received at position 168 in sequence #0: 22.746 Highest entropy (on 16 sequences) received at position 94 in sequence #3: 39.822 Computing entropy of best 2090 base primers according to all 16 sequences.
	www.math.tau.ac.il /~rshamir/hyden/output.txt (679 words)

	[No title]
		The investigation of low-power computing is currently being done by two relatively disjoint camps: physicists who study the limits of single gates, but do not consider whole systems, and engineers who are making evolutionary improvements on existing designs, without considering the fundamental limits.
		Bennett6 went further and showed that it is possible to compute reversibly with arbitrarily little dissipation per operation, and that the apparent paradox of Maxwell's Demon can be explained by the erasure in the Demon's brain of previous measurements of the state of the gas (that is when the combined Demon-gas system becomes irreversible).
		It is a very good approximation to calculate this electronic entropy per bit in the Sommerfeld approximation for temperatures that are low compared to the Fermi temperature:15 (8) This entropy is not associated with a heat current if the bit is at the same temperature as the chip (remember that entropy is additive).
	www.research.ibm.com /journal/sj/mit/sectione/gershenfeld.txt (3815 words)

	Signal entropy and the thermodynamics of computation
		Bennett [6] went further and showed that it is possible to compute reversibly with arbitrarily little dissipation per operation, and that the apparent paradox of Maxwell's Demon can be explained by the erasure in the Demon's brain of previous measurements of the state of the gas (that is when the combined Demon-gas system becomes irreversible).
		This entropy is not associated with a heat current if the bit is at the same temperature as the chip (remember that entropy is additive).
		This situation is analogous to the role of entropy in a communications channel.
	www.research.ibm.com /journal/sj/353/sectione/gershenfeld.html (3991 words)

	Thermodynamic Entropy and Information
		thermodynamic entropy is best understood not as a property or macroscopic state of matter (like mass, temperature, or pressure), but as a lack of knowledge of the detailed configuration of matter.
		Entropy refers to the uncertainty of an unknown message, and information refers to the probability of a known message occurring by chance alone.
		More accurately, entropy is a measure of uncertainty due to the unknown part of a message/particle system, and information is a measure of reduction of uncertainty due to the known part of a message/particle system.
	lcni.uoregon.edu /~mark/Stat_mech/thermodynamic_entropy_and_information.html (1464 words)

	Laws of Computing, Version 2
		A computable function is represented by a linear sequence of instructions with occasional branching and looping.
		There are so many different computers, computer architecture, languages, operating systems, software development tools, and applications, it is impossible to summarize "computer science" in simple and general laws to describe our understanding of computers and the computational processes.
		Computers differ by details in their instruction sets, the bit width of words in memory, and the addressable memory space, etc. Nevertheless, with an instruction set including a minimum number of instructions in the above list, all computable functions can be represented as sequences of instructions.
	www.offete.com /files/LawsofComputing.htm (5318 words)

	Entropy laboratory, numerical computation of Kolmogorov-Sinai entropy of the Chirikov Standard map
		Entropy laboratory, numerical computation of Kolmogorov-Sinai entropy of the Chirikov Standard map
		The sequence f(n) converges in the limit n to infinity to the Kolmogorov-Sinai entropy of the map (Pesin formula).
		The computation done on your computer will so help to test the hypothesis.
	www.dynamical-systems.org /twist/Entropy/Entropy.html (102 words)

	Entropy Gradient Reversals - The Rise of the Stupid Network
		In those days, computers, including those that controlled switching, were still considered expensive, scarce resources.
		But in the 70s it was not generally known to be a `law' - to most telecommunications engineers (and to humanity in general), it has become the most game-changing wild card played in recent times.
		For example, as computer power got cheaper and cheaper in the 1980s, there was much talk of a shift in value from hardware to software, but it was not easy to see how the shift would unfold.
	www.rageboy.com /stupidnet.html (3722 words)

	Computing science Encyclopedia (Site not responding. Last check: )
		The Indian Association for Research in Computing Science (IARCS) is an institution run by a group of persons engaged in computer science in one way or the other.
		Its members are leading researchers in Computer Science drawn from major institutions from all over the country.
		It also recognizes a role for itself in correcting the biases in the current curriculum for computer science in the country.
	www.hallencyclopedia.com /topic/Computing_science.html (615 words)

	Reversible Agents (Site not responding. Last check: )
		A computer's task is often taken to be that of starting with some input, grinding for a while, and eventually returning an output.
		Theoretical computer science often focuses on devices like Turing machines, which start with some input string, and are then left undisturbed to take as long as they like to compute some output string.
		The number of bits of entropy an agent must "waste" to erase some data is given by the probability the agent would guess, after the erasure, that this was the information erased.
	hanson.gmu.edu /reverse.html (3732 words)

	Entropy-based Pruning of Backoff Language Models
		A criterion for pruning parameters from N-gram backoff language models is developed, based on the relative entropy between the original and the pruned model.
		Relative entropy minimization (sometimes in the guise of likelihood maximization) is the basis of many model optimization techniques proposed in the past, e.g., for text compression [1], Markov model induction [10, 7].
		Specifically, the algorithm of [6] assumes that backoff weights are unchanged by the pruning, and [9] does not consider the effect that a changed backoff weight has on N-gram probabilities other than the pruned one (this effect is discussed in more detail in Section 5).
	www.nist.gov /speech/publications/darpa98/html/lm20/lm20.htm (2303 words)

	[No title]
		Entropy can be viewed as a measure of how compressible or predictable a language is, and it can be estimated by building a model of the language from a large corpus and computing the cross-entropy between this model and a representative sample of text.
		While their upper bound for entropy of 1.75 is higher than previous estimates, the authors claim their estimate to be statistically more sound, based on the amount of training data on which their model was based, and the size of the test sample.
		The estimate for the entropy bound is based upon the fact that the cross-entropy of a stochastic process as measured by a model is an upper bound on the entropy of the process.
	www.cs.wisc.edu /~apirak/cs/cs838/reviews_score_6.html (7304 words)

	Conclusions from this research
		Using their formula, for instance, it turns out that the computed entropy for the Same feature displays (entropy value=1) is actually larger than for any of the Different displays of the other three display types (values between.59 and.65).
		This greater entropy in the feature displays is directly due to the presence of the irrelevant local variation in its elements.
		But for the Different displays, the entropy is greatest in the 3 x 1 array (1 target and 2 distractors; entropy =.91), intermediate for the 2 x 2 array (1 target and 3 distractors; entropy =.81), and smallest for the 3 x 2 array (1 target and 5 distractors, entropy =.65).
	www.pigeon.psy.tufts.edu /jep/sdclass/sdmsc_conclusions.htm (1383 words)

	Bambooweb: Entropy (computing)
		ENTROPY (which stands for Emerging Network To Reduce Orwellian Potency Yield) was developed as a response to increased censorship and surveillance of the internet.
		It is a computer program that allows users to access the "Entropy-Network" (or "Entropy-net"), wherein the intent of its architect(s) is to allow secure, encrypted, and potentially anonymous communication.
		ENTROPY is licensed with a GNU General Public License.
	www.bambooweb.com /articles/e/n/Entropy_(computing).html (120 words)

	Ideal Gas
		Willard Gibbs tried computing the entropy of an ideal gas using his version of statistical mechanics, which was based on classical mechanics.
		In fact, the amount of entropy of an ideal gas at fixed temperature and pressure is calculated to have a non-linear dependence on the number of gas molecules.
		The failure of Gibbs to obtain the proper entropy was an early indication that classical mechanics had problems on the atomic scale.
	www.physics.nmt.edu /~raymond/classes/ph13xbook/node240.html (564 words)

	Alibris: Entropy
		Led by Il Maestro, the evil Sons of Entropy are assaulting the mansion that holds back the realm of monsters and stealing the life force from the besieged Gatekeeper.
		This essay is an attempt to reconcile the disturbing contradiction between the striving for order in nature and in man and the principle of entropy implicit in the second law of thermodynamics; between the tendency toward greater organization and the general trend of the material universe toward death and disorder.
		Dr. John Sanford, a retired Cornell Professor, shows in Genetic Entropy and the Mystery of the Genome that the "Primary Axiom" is false.
	www.alibris.com /search/books/subject/Entropy (734 words)

	Information theory Summary
		This is because all the components used to construct computing machines are imperfect; they tend to distort the electrical signals they process as a side effect of their operation.
		The measure of data, known as information entropy, is usually expressed by the average number of bits needed for storage or communication.
		The entropy of a discrete message space M is a measure of the amount of uncertainty one has about which message will be chosen.
	www.bookrags.com /Information_theory (6169 words)

	The Talk.Origins Archive Post of the Month: October 2000
		Put another way: if thermodymanic entropy were the relevant constraint, it should be easier for a completely novel organism to appear, than for an existing organism to be replicated; it's not, therefore thermodynamic entropy is not the relevant constraint.
		Bennett (1973) found a way around this: by running the entire computation (keeping piles of intermediate results), copying the desired part of the result, then running the compatation in reverse to eat up those unwanted intermediate results, it would be possible to wind up with just the input data and desired output data.
		It's still entropy, mind you -- the entropy of the demon's memory banks increases with the amount of information stored there, so all we've really accomplished is to move entropy from the gas to the demon's memory, and change its form somewhat.
	www.talkorigins.org /origins/postmonth/oct00.html (4178 words)

	Ideal Gas
		Willard Gibbs tried computing the entropy of an ideal gas using his version of statistical mechanics, which was based on classical mechanics.
		In fact, the amount of entropy of an ideal gas at fixed temperature and pressure is calculated to have a non-linear dependence on the number of gas molecules.
		The failure of Gibbs to obtain the proper entropy was an early indication that classical mechanics had problems on the atomic scale.
	kestrel.nmt.edu /~raymond/classes/ph13xbook/node240.html (564 words)

	Evolution, Entropy, and Parallel Computation
		During these experiments evolving parallel computation, it was discovered that detectable changes in the entropy of instruction sequences would correspond to changes in self-reproduction efficiency.
		This was done by generating an instruction histogram for each creature’s genome and computing the entropy for the distribution contained in the histogram.
		To compute the entropy associated with this program, each instruction in the instruction set is enumerated and the total number of instances of each instruction in the program must be counted.
	www.thearling.com /text/physcomp94/physcomp94.htm (3116 words)

	Zenarchery.com » Quantum Computing, Entropy and Cocaine (Site not responding. Last check: )
		In information theory, however, entropy is the amount of information contained in a transmission from source to recipient.
		What I realized last night is that informational entropy, in a sense, is also literal entropy: that it takes a certain amount of energy to convey information from point A to point B, and that — generally speaking — the more complex the information, the more entropy is generated.
		My computer is relatively fast, but it’s crap, for example, at playing 3D shooter games (which is, essentally, an extremely dense simulation of optics and physics, if you think about it).
	www.zenarchery.com /2006/07/30/quantum-computing-entropy-and-cocaine (1162 words)

	entropy - Definitions from Dictionary.com
		The amount of entropy is often thought of as the amount of disorder in a system.
		Note: In the nineteenth century, a popular scientific notion suggested that entropy was gradually increasing, and therefore the universe was running down and eventually all motion would cease.
		The entropy of a system is related to the amount of information it contains.
	dictionary.reference.com /browse/entropy (789 words)

	From digraph entropy to word entropy in the Voynich MS
		Source texts in various languages will be analysed by computing entropy values for word-initial sequences of various lengths (I am restricting to 1-, 2-, 3- and 4-character sequences) and the full word entropy.
		The conditional entropies are denoted as hw2, hw3, hw4 and hW and computed as the difference between two absolute entropies.
		Word counts and entropies are the same in the two transliteration alphabets used for the Voynich MS, but the information per n-graph is lower in EVA than in Curva, as expected.
	www.voynich.nu /extra/wordent.html (1865 words)

	Dublin Workshop Speaker Abstracts
		Quantum theory of computation gives us not only the key to a new technology but also, more importantly, much deeper understanding of the foundations of quantum physics, computer science and mathematics.
		I review the spintronics proposal for quantum computing, in which electron spins in quantum confined structures play the role of the quantum bits (qubits), and discuss the essential requirements for such an implementation.
		It roughly states that if the relative entropy of two quantum states is small, then the first state "sits inside" the second state as a "substate".
	www.quiprocone.org /Dublin/dublinabstracts.htm (1861 words)

	Introduction to Alignment Scoring Statistics
		Relative entropy, H, is a measure of the expected coding inefficiency per letter, when describing a message with an assumed letter distribution P, when the true distribution is Q.
		Whereas Shannon's entropy, I, is the expected log-likelihood for a single distribution, relative entropy is the expected logarithm of the likelihood ratio (log-likelihood ratio or LLR) between two distributions.
		Relative entropy is symbolized in the present text by H and should not be confused with Shannon's entropy, which is represented in some texts by H, as well.
	blast.wustl.edu /doc/infotheory.html (3895 words)

	Quantum Computing
		Later on, in 1985, David Deutsch attempted to define a computational device that would be capable of efficiently simulating an arbitrary physical system.
		The action of demon would cause a transition from disorder to order in the gas, that is, a decrease in entropy [consider a thought experiment].
		The entropy of the system is reduced by the amount of information about the state of the system.
	www.iohk.com /UserPages/erictang/qcomputing.html (1980 words)

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