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위키데이터

• ID : Q204570

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1. A formal way of putting that is to say the game of Russian roulette has more ‘entropy’ than crossing the street.
2. Above is the formula for calculating the entropy of a probability distribution.
3. The English language has 26 letters, if you assume each letter has a probability of 1/26 of being next, the language has an entropy of 4.7 bits.
4. Experiments by Shannon showed that English has an entropy between 0.6 and 1.3 bits.
5. In addition, we calculate the Kullback-Leibler relative entropy, the Jensen-Shannon divergence, Onicescu’s information energy, and a complexity measure recently proposed.
6. Calculating the information for a random variable is called “information entropy,” “Shannon entropy,” or simply “entropy“.
7. the Shannon entropy of a distribution is the expected amount of information in an event drawn from that distribution.
8. The lowest entropy is calculated for a random variable that has a single event with a probability of 1.0, a certainty.
9. We can consider a roll of a fair die and calculate the entropy for the variable.
10. The maximum surprise is for p = 1/2, when there is no reason to expect one outcome over another, and in this case a coin flip has an entropy of one bit.
11. The minimum surprise is when p = 0 or p = 1, when the event is known and the entropy is zero bits.
12. The definition can be derived from a set of axioms establishing that entropy should be a measure of how "surprising" the average outcome of a variable is.
13. If the probability of heads is the same as the probability of tails, then the entropy of the coin toss is as high as it could be for a two-outcome trial.
14. Claude Shannon calls this measure of average uncertainty "entropy", and he uses the letter H to represent it.
15. The unit of entropy Shannon chooses, is based on the uncertainty of a fair coin flip, and he calls this "the bit", which is equivalent to a fair bounce.
16. Entropy or H is the summation for each symbol, of the probability of that symbol times the number of bounces.
17. Entropy or H, is the summation for each symbol of the probability of that symbol times the logarithm base two of one over the probability of that symbol.
18. We have deduced a general formula for information entropy of mixing, which is the change in information entropy when two or more molecules form an ensemble.
19. This implies a striking difference from thermodynamic entropy, which cannot be nonzero when mixing different particles.
20. The information entropy of a molecular ensemble has been expressed through the information entropies of the constituting molecules and exemplified with real chemical systems.
21. This Research Topic is focused on what the characterization of entropy and information could tell us about life and survival.
22. Entropy is commonly interpreted as a measure of disorder.
23. The book explains with minimum amount of mathematics what information theory is and how it is related to thermodynamic entropy.
24. Shannon’s concept of entropy can now be taken up.
25. His thought experiment was intended to demonstrate the possibility of a gas evolving from a higher to a lower entropy state.
26. Although they show the law of entropy increase is not absolute, we might still be surprised to actually witness a large decrease in entropy happen through these means.
27. He argued that in order to achieve the entropy reduction, the intelligent being must acquire knowledge of which fluctuation occurs and so must perform a measurement.
28. Szilard argued that the second law would be saved if the acquisition of knowledge by the demon came with a compensating entropy cost.
29. This is just...entropy, he said, thinking that this explained everything, and he repeated the strange word a few times.
30. We can compute or measure the quantity of energy contained in this sheet of paper, and the same is true of its entropy.
31. Our galaxy, the solar system, and the biosphere all take their being from entropy, as a result of its transferenceto the surrounding medium.
32. This article aims at giving an overview of the scientific production about Entropy and Information Theory in national periodical publications in Qualis/CAPES.
33. The concept of Entropy emerged from Physics and started expanding to many other areas.
34. Mattos and Veiga (2002, p.3) emphasize that "Entropy in Information Theory corresponds to probabilistic uncertainty associated with a probability distribution.
35. For answering this question, we aim at giving an overview of the scientific production on Entropy and Information Theory in articles in periodical publications listed in Qualis/CAPES.
36. The pertinence of information entropy to such diverse fields lies in its ability to encapsulate not only the number of subcategories but also the relative quantities observed.
37. We propose the use of a modified version of the information entropy equation to accurately evaluate dispersity.
38. Information entropy () was first proposed by Claude Shannon in 1948 to quantify the amount of information produced by a given process.
39. The entropy is often described as being analogous to the amount of information conveyed when the outcome of an event is observed.
40. Statistical entropy was introduced by Shannon as a basic concept in information theory measuring the average missing information in a random source.
41. Extended into an entropy rate, it gives bounds in coding and compression theorems.
42. The relevance of entropy beyond the realm of physics, in particular for living systems and ecosystems, is yet to be demonstrated.
43. Thus it is natural that in this case entropy H reduces to variety V. Like variety, H expresses our uncertainty or ignorance about the system's state.
44. Information and entropy theory for the sustainability of coupled human and natural systems.
45. Here, we briefly review feedbacks as they have been observed in CHANS and then discuss the use of information theory to study system entropy and Fisher information.
46. Information is quantifiable as the amount of order or organization provided by a message (Haken 2006); entropy is one measure.
47. In this case, high Shannon entropy actually signals high redundancy in function, therefore conveying resilience to the ecosystem (MacDougall et al.
48. The spatial and temporal complexity of solute transport process was characterized and evaluated using spatial moment and information entropy.
49. Results indicated that the entropy increased as the increase of complexity of solute transport process.
50. For the point source, the one-dimensional entropy of solute concentration increased at first and then decreased along X and Y directions.
51. As time increased, entropy peak value basically unchanged, peak position migrated along the flow direction (X direction) and approximately coincided with the centroid position.
52. The molecules in ice have to stay in a lattice, as it is a rigid system, so ice has low entropy.
53. The molecules in water have more positions to move around, so water in liquid state has medium entropy.
54. To introduce the notion of entropy in probability, we’ll use an example throughout this whole article.
55. In the next section, we’ll cook up a formula for entropy.
56. Herein, we propose the use of information entropy as an alternative and assumption-free method for describing nanoparticle size distributions.
57. The average information entropy of the population \(\bar{H}\), reflects the level of information noise in the entire system.
58. The evolution of the average entropy of the network over time is shown for several different values of β and K in Fig.
59. It can be observed from the Figure that in most cases, an entropy explosion occurs sometime between t = 10 and t = 100, with the average information entropy shooting upward rapidly.
60. In the case where β = −3, the average entropy stabilizes at a higher level than in the other two cases.

메타데이터

위키데이터

• ID : Q204570

Spacy 패턴 목록

• [{'LOWER': 'information'}, {'LEMMA': 'entropy'}]
• [{'LEMMA': 'entropy'}]
• [{'LOWER': 'shannon'}, {'LEMMA': 'entropy'}]

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말뭉치

1. He captured it in a formula that calculates the minimum number of bits — a threshold later called the Shannon entropy — required to communicate a message.
2. The term “entropy” is borrowed from physics, where entropy is a measure of disorder.
3. A cloud has higher entropy than an ice cube, since a cloud allows for many more ways to arrange water molecules than a cube’s crystalline structure does.
4. In an analogous way, a random message has a high Shannon entropy — there are so many possibilities for how its information can be arranged — whereas one that obeys a strict pattern has low entropy.
5. Shannon entropy allows to estimate the average minimum number of bits needed to encode a string of symbols based on the alphabet size and the frequency of the symbols.
6. The concepts of entropy, as used in information theory and in various scientific disciplines, are now countless (Shannon, 1948).
7. Based on this fact, Shannon proposed measuring the average of this flux of information called entropy.
8. (7.79) can be a log 2 or an ln, with the entropy units in bits (binary units) or nats (natural units), respectively.
9. In general, the probability distribution for a given stochastic process is not known, and, in most situations, only small datasets from which to infer the entropy are available.
10. Shannon entropy, also known as information entropy or the Shannon entropy index, is a measure of the degree of randomness in a set of data.
11. The more characters there are, or the more proportional are the frequencies of occurrence, the harder it will be to predict what will come next - resulting in an increased entropy.
12. Apart from information theory, Shannon entropy is used in many fields.
13. In the Shannon entropy equation, p i is the probability of a given symbol.
14. The number of bits per character can be calculated from this frequency set using the Shannon entropy equation.
15. Shannon entropy provides a lower bound for the compression that can be achieved by the data representation (coding) compression step.
16. Shannon entropy makes no statement about the compression efficiency that can be achieved by predictive compression.
17. For anyone who wants to be fluent in Machine Learning, understanding Shannon’s entropy is crucial.
18. A little more formally, the entropy of a variable is the “amount of information” contained in the variable.
19. The analogy results when the values of the random variable designate energies of microstates, so Gibbs formula for the entropy is formally identical to Shannon's formula.
20. Entropy has relevance to other areas of mathematics such as combinatorics and machine learning.
21. The definition can be derived from a set of axioms establishing that entropy should be a measure of how "surprising" the average outcome of a variable is.
22. In this case a coin flip has an entropy of one bit.
23. Some details: We treat Shannon (discrete) and differential (continuous) entropy separately.
24. For example, you wouldn’t calculate nutrition in the same way you calculate entropy in thermodynamics.
25. Shannon entropy for imprecise and under-defined or over-defined information.
26. In the general case Arithmetic coding results in a near optimal encoding of messages that is very close to the number obtained from the Shannon entropy equation.
27. Statistical entropy was introduced by Shannon as a basic concept in information theory measuring the average missing information in a random source.
28. Extended into an entropy rate, it gives bounds in coding and compression theorems.
29. The relevance of entropy beyond the realm of physics, in particular for living systems and ecosystems, is yet to be demonstrated.
30. My goal is to really understand the concept of entropy, and I always try to explain complicated concepts using fun games, so that’s what I do in this post.
31. In colloquial terms, if the particles inside a system have many possible positions to move around, then the system has high entropy, and if they have to stay rigid, then the system has low entropy.
32. The molecules in ice have to stay in a lattice, as it is a rigid system, so ice has low entropy.
33. The molecules in water have more positions to move around, so water in liquid state has medium entropy.
34. In physics, the word entropy has important physical implications as the amount of "disorder" of a system.
35. But what properties single out Shannon entropy as special?
36. Instead of focusing on the entropy of a probability measure on a finite set, it can help to focus on the "information loss", or change in entropy, associated with a measure-preserving function.
37. Shannon entropy then gives the only concept of information loss that is functorial, convex-linear and continuous.
38. The entropy H is correspondingly reduced in the posterior relative to the prior distribution.
39. In this case a measurement yields a posterior PDF with no change in the expected value but a significant increase in the spread and in the Shannon entropy.
40. 2.6 Entropy Rate Revisited . . . . . . . . . . . . . . . . . . . . . . .
41. 105 5.4 Limiting Entropy Densities 5.5 Information for General Alphabets . . . . . . . . . . . . . . . . .
42. Instead of focusing on the entropy of a probability measure on a finite set, it can help to focus on the “information loss”, or change in entropy, associated with a measure-preserving function.
43. Thus, whenever you pick something out, you have absolutely no doubt (entropy is zero for Container 3) that it will be a circle.
44. As you can see, entropy (doubt, surprise, uncertainty) for Container 1 is less (56%), but more for Container 2 (99%).
45. For Container 3, there is no (0%) entropy - you have 100% chance to pick a circle.
46. The electroencephalographic Shannon entropy increased continuously over the observed concentration range of desflurane.
47. Recently, approximate entropy, a measure of the “amount of order” of the electroencephalographic signal has been shown to correlate well with the concentration of desflurane at the effect site.
48. The Shannon entropy 2 is a standard measure for the order state of sequences and has been applied previously to DNA sequences.
49. In this investigation, we applied the Shannon entropy to electroencephalographic data from anesthetized patients and correlated the concentration of anesthetic agent and entropy value.
50. KEYWORDS: Monte Carlo, keff, convergence, Shannon entropy, MCNP 1.
51. Line-plots of Shannon entropy vs. batch are easier to interpret and assess than are 2D or 3D plots of the source distribution vs. batch.
52. When running criticality calculations with MCNP5, it is essential that users examine the convergence of both keff and the fission source distribution (using Shannon entropy).
53. A number of theoretical approaches based on, e.g., conditional Shannon entropy and Fisher information have been developed, along with some experimental validations.
54. Shannon’s concept of entropy can now be taken up.
55. Thus, the bound computed using entropy cannot be attained with simple encodings.
56. This is better than the 2.0 obtained earlier, although still not equal to the entropy.
57. Because the entropy is not exactly equal to any fraction, no code exists whose average length is exactly equal to the entropy.
58. Pintacuda, N.: Shannon entropy: A more general derivation.
59. In this Letter, we report a comparative analysis of the Shannon entropy and qTIR using model series and real-world heartbeats.
60. We find that the permutation-based Shannon entropy (PEn) and time irreversibility (PYs) detect nonlinearities in the model series differently according to the surrogate theory.
61. In classical physics, the entropy of a physical system is proportional to the quantity of energy no longer available to do physical work.
62. In quantum mechanics, von Neumann entropy extends the notion of entropy to quantum systems by means of the density matrix.
63. In the theory of dynamical systems, entropy quantifies the exponential complexity of a dynamical system or the average flow of information per unit of time.
64. The term entropy is now used in many other sciences (such as sociology), sometimes distant from physics or mathematics, where it no longer maintains its rigorous quantitative character.
65. Shannon (the man, not the entropy) was one of those annoying people that excels at everything he touches.
66. Like the number of questions we need to arrive at the correct suit, Shannon Entropy decreases when order is imposed on a system and increases when the system is more random.
67. Once the (p)’s are known, Zorro simply implements the Shannon Entropy equation and returns the calculated value for (H), in bits.
68. A fair coin has an entropy of one bit.
69. However, if the coin is not fair, then the uncertainty is lower (if asked to bet on the next outcome, we would bet preferentially on the most frequent result), and thus the Shannon entropy is lower.
70. A long string of repeating characters has an entropy of 0, since every character is predictable.
71. Additivity The amount of entropy should be the same independently of how the process is regarded as being divided into parts.