Journal articles: 'SHANONS LAW'

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Shental, O., and I. Kanter. "Shannon meets Carnot: Generalized second thermodynamic law." EPL (Europhysics Letters) 85, no. 1 (January 2009): 10006. http://dx.doi.org/10.1209/0295-5075/85/10006.

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Khan, Khuram Ali, Tasadduq Niaz, Đilda Pečarić, and Josip Pečarić. "Estimation of different entropies via Abel–Gontscharoff Green functions and Fink’s identity using Jensen type functionals." Arab Journal of Mathematical Sciences 26, no. 1/2 (December 31, 2018): 15–39. http://dx.doi.org/10.1016/j.ajmsc.2018.12.002.

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In this work, we estimated the different entropies like Shannon entropy, Rényi divergences, Csiszár divergence by using Jensen’s type functionals. The Zipf’s–Mandelbrot law and hybrid Zipf’s–Mandelbrot law are used to estimate the Shannon entropy. The Abel–Gontscharoff Green functions and Fink’s Identity are used to construct new inequalities and generalized them for m-convex function.

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Corral, Álvaro, and Montserrat García del Muro. "From Boltzmann to Zipf through Shannon and Jaynes." Entropy 22, no. 2 (February 5, 2020): 179. http://dx.doi.org/10.3390/e22020179.

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The word-frequency distribution provides the fundamental building blocks that generate discourse in natural language. It is well known, from empirical evidence, that the word-frequency distribution of almost any text is described by Zipf’s law, at least approximately. Following Stephens and Bialek (2010), we interpret the frequency of any word as arising from the interaction potentials between its constituent letters. Indeed, Jaynes’ maximum-entropy principle, with the constrains given by every empirical two-letter marginal distribution, leads to a Boltzmann distribution for word probabilities, with an energy-like function given by the sum of the all-to-all pairwise (two-letter) potentials. The so-called improved iterative-scaling algorithm allows us finding the potentials from the empirical two-letter marginals. We considerably extend Stephens and Bialek’s results, applying this formalism to words with length of up to six letters from the English subset of the recently created Standardized Project Gutenberg Corpus. We find that the model is able to reproduce Zipf’s law, but with some limitations: the general Zipf’s power-law regime is obtained, but the probability of individual words shows considerable scattering. In this way, a pure statistical-physics framework is used to describe the probabilities of words. As a by-product, we find that both the empirical two-letter marginal distributions and the interaction-potential distributions follow well-defined statistical laws.

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Kreiner, Welf Alfred. "First Digits’ Shannon Entropy." Entropy 24, no. 10 (October 3, 2022): 1413. http://dx.doi.org/10.3390/e24101413.

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Related to the letters of an alphabet, entropy means the average number of binary digits required for the transmission of one character. Checking tables of statistical data, one finds that, in the first position of the numbers, the digits 1 to 9 occur with different frequencies. Correspondingly, from these probabilities, a value for the Shannon entropy H can be determined as well. Although in many cases, the Newcomb–Benford Law applies, distributions have been found where the 1 in the first position occurs up to more than 40 times as frequently as the 9. In this case, the probability of the occurrence of a particular first digit can be derived from a power function with a negative exponent p > 1. While the entropy of the first digits following an NB distribution amounts to H = 2.88, for other data distributions (diameters of craters on Venus or the weight of fragments of crushed minerals), entropy values of 2.76 and 2.04 bits per digit have been found.

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Tenreiro Machado, J. A. "Shannon Information and Power Law Analysis of the Chromosome Code." Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/439089.

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This paper studies the information content of the chromosomes of twenty-three species. Several statistics considering different number of bases for alphabet character encoding are derived. Based on the resulting histograms, word delimiters and character relative frequencies are identified. The knowledge of this data allows moving along each chromosome while evaluating the flow of characters and words. The resulting flux of information is captured by means of Shannon entropy. The results are explored in the perspective of power law relationships allowing a quantitative evaluation of the DNA of the species.

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Beltaos, L. "A critique of Brookes' logarithmic 'law'." Journal of Information Science 11, no. 3 (September 1985): 109–12. http://dx.doi.org/10.1177/016555158501100302.

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An examination of Brookes' mathematical expression of his logarithmic 'law' yields inconsistencies and mathematical er rors. Brookes' 'tunnel' model of perception incorrectly repre sents perception of physical distance. Brookes' 'affinity' with Shannon is shown to be nonexistent. The most significant result is that Brookes' logarithmic 'law' applies to only one communication system which has properties as defined and assumed by Brookes and can not be generalized to any com munication system with properties different from the Brookes' system.

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Murray, Cara. "Cultivating Chaos: Entropy, Information, and the Making of the Dictionary of National Biography." Victorian Literature and Culture 50, no. 1 (October 18, 2021): 87–116. http://dx.doi.org/10.1017/s1060150320000121.

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The Dictionary of National Biography, published between 1885 and 1900, was one of Britain's biggest cyclopedia projects. The rampant expansion of the nation's archives, private collections, and museums produced an abundance of materials that frustrated the dictionary's editors, Leslie Stephen and Sidney Lee, especially because methodologies for making order of such materials were underdeveloped. Adding to their frustration was the sense of impending doom felt generally in Britain after the discovery of the second law of thermodynamics in 1859. Entropy put an end to the presiding belief in the infinite energy that fueled Britain's economic development and therefore challenged Victorian biography's premise that the capacity for self-development was boundless. Like the physicists of the era, these dictionary makers searched for ways to circumvent entropy's deadening force and reenergize their world. This project would not actually be achieved, however, until the twentieth century when Claude Shannon published his “Information Theory” in 1948. I argue that in an attempt to get out from under the chaos of information overload, the editors of the DNB invented new methods to organize information that anticipated Shannon's revolutionary theory and changed the way that we think, write, and work.

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Turan, Cemal, and Servet Ahmet Doğdu. "Preliminary Assessment of Invasive Lionfish Pterois miles Using Underwater Visual Census Method in the Northeastern Mediterranean." Croatian Journal of Fisheries 80, no. 1 (February 27, 2022): 38–46. http://dx.doi.org/10.2478/cjf-2022-0005.

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Abstract Underwater visual census (UVC) is a commonly used approach for assessing fish density and biomass. Iskenderun Bay, comprising the Samandağ coast in Turkey, is the most important introduction pathway of alien species in the northeastern Mediterranean. In this study, the density, abundance, distribution and interaction of invasive lionfish or devil firefish Pterois miles were assessed using the UVC method on the Samandağ coast. The total transect area monitored on the Samandağ coast was 4.500 m2. Species richness, Shannon’s diversity index and rate of biomass were 25, 1.81 and 73.5 m2, respectively. Reduced diversity was observed with increasing depths. The sandy seafloor was a limiting factor for lionfish distribution. There was a significant positive correlation between lionfish total density and both the Shannon diversity index (r = 0.99, P<0.001) and Shannon evenness index (r = 0.99, P<0.05). A high number of significant positive correlations (P<0.05) were detected between the occurrence of lionfish and the occurrence of both the native species and other alien species. The first stock assessment study of lionfish by the UVC method in Turkish marine waters revealed that native species are under very high pressure from lionfish species, especially Chromis, Sparids and Wrasses, indicating negative effects of lionfish on regional native biodiversity.

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Singh, Vijay P. "Derivation of Power Law and Logarithmic Velocity Distributions Using the Shannon Entropy." Journal of Hydrologic Engineering 16, no. 5 (May 2011): 478–83. http://dx.doi.org/10.1061/(asce)he.1943-5584.0000335.

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Khan, Khuram Ali, Tasadduq Niaz, Đilda Pečarić, and Josip Pečarić. "Estimation of different entropies via Lidstone polynomial using Jensen-type functionals." Arabian Journal of Mathematics 9, no. 3 (February 18, 2020): 613–31. http://dx.doi.org/10.1007/s40065-020-00277-y.

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Abstract In this work, some new functional of Jensen-type inequalities are constructed using Shannon entropy, f-divergence, and Rényi divergence, and some estimates are obtained for these new functionals. Also using the Zipf–Mandelbrot law and hybrid Zipf–Mandelbrot law, we investigate some bounds for these new functionals. Furthermore, we generalize these new functionals for m-convex function using Lidstone polynomial.

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Vopson, Melvin M., and S. Lepadatu. "Second law of information dynamics." AIP Advances 12, no. 7 (July 1, 2022): 075310. http://dx.doi.org/10.1063/5.0100358.

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One of the most powerful laws in physics is the second law of thermodynamics, which states that the entropy of any system remains constant or increases over time. In fact, the second law is applicable to the evolution of the entire universe and Clausius stated, “The entropy of the universe tends to a maximum.” Here, we examine the time evolution of information systems, defined as physical systems containing information states within Shannon’s information theory framework. Our observations allow the introduction of the second law of information dynamics (infodynamics). Using two different information systems, digital data storage and a biological RNA genome, we demonstrate that the second law of infodynamics requires the information entropy to remain constant or to decrease over time. This is exactly the opposite to the evolution of the physical entropy, as dictated by the second law of thermodynamics. The surprising result obtained here has massive implications for future developments in genomic research, evolutionary biology, computing, big data, physics, and cosmology.

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12

Mancani, Salvatore. "Entropy Area Law in Quantum Field Theories and Spin Systems." Proceedings 12, no. 1 (June 3, 2019): 5. http://dx.doi.org/10.3390/proceedings2019012005.

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The entanglement entropy measures quantum correlations and it can be seen as the uncertainty on a quantum state. In one spatial dimension, the entanglement entropy scales as the boundary that divides two subsystems, so an area law has been proposed. However, the entanglement entropy diverges logarithmically at conformally invariant critical points, so the area law does not hold. The purpose of the work is to find a way to get more information about a critical state. The ground state of the Heisenberg XXZ model at criticality is analyzed by means of critical Ising eigenstates. Two ways of analysis are followed: a basis made of Ising eigenstates is built up and used to represent the XXZ ground state, then the Shannon entropy in the new basis is computed; the adiabatic evolution from the Ising ground state to the XXZ ground state. The result is that the Shannon entropy in the Ising basis scales linearly with the length of the system, while a phase transition is encountered during the adiabatic evolution. The conclusion is that there is no net gain in information after the procedure and possibly it is related to the fact the two systems stand in different phases.

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Huang, Huilin. "Strong Law of Large Numbers of the Offspring Empirical Measure for Markov Chains Indexed by Homogeneous Tree." ISRN Applied Mathematics 2012 (April 3, 2012): 1–9. http://dx.doi.org/10.5402/2012/536530.

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We study the limit law of the offspring empirical measure and for Markov chains indexed by homogeneous tree with almost everywhere convergence. Then we prove a Shannon-McMillan theorem with the convergence almost everywhere.

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Puzachenko, Andrey Yuryevich. "The Shannon–Hartley Law and the limit of self-ordering of biological systems." Principles of the Ecology 37, no. 3 (September 2020): 28–44. http://dx.doi.org/10.15393/j1.art.2020.10822.

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15

Fujikawa, Kazuo. "Remarks on Shannon's Statistical Inference and the Second Law in Quantum Statistical Mechanics." Journal of the Physical Society of Japan 71, no. 1 (January 2002): 67–74. http://dx.doi.org/10.1143/jpsj.71.67.

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16

Kennington, Roger. "Reviews : Tom Shannon and Christopher Morgan Black Swan, 1997; £6.99 pbk." Probation Journal 44, no. 1 (March 1997): 47–48. http://dx.doi.org/10.1177/026455059704400110.

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Bright, Sarah. "Reviews : Tom Shannon and Christopher Morgan Black Swan, 1997; £6.99 pbk." Probation Journal 44, no. 1 (March 1997): 48–49. http://dx.doi.org/10.1177/026455059704400111.

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18

Canton, Rob. "Reviews : Tom Shannon and Christopher Morgan Black Swan, 1997; £6.99 pbk." Probation Journal 44, no. 1 (March 1997): 49–50. http://dx.doi.org/10.1177/026455059704400112.

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19

Corominas-Murtra, Bernat, Luís F. Seoane, and Ricard Solé. "Zipf’s Law, unbounded complexity and open-ended evolution." Journal of The Royal Society Interface 15, no. 149 (December 2018): 20180395. http://dx.doi.org/10.1098/rsif.2018.0395.

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A major problem for evolutionary theory is understanding the so-called open-ended nature of evolutionary change, from its definition to its origins. Open-ended evolution (OEE) refers to the unbounded increase in complexity that seems to characterize evolution on multiple scales. This property seems to be a characteristic feature of biological and technological evolution and is strongly tied to the generative potential associated with combinatorics, which allows the system to grow and expand their available state spaces. Interestingly, many complex systems presumably displaying OEE, from language to proteins, share a common statistical property: the presence of Zipf’s Law. Given an inventory of basic items (such as words or protein domains) required to build more complex structures (sentences or proteins) Zipf’s Law tells us that most of these elements are rare whereas a few of them are extremely common. Using algorithmic information theory, in this paper we provide a fundamental definition for open-endedness, which can be understood as postulates . Its statistical counterpart, based on standard Shannon information theory, has the structure of a variational problem which is shown to lead to Zipf’s Law as the expected consequence of an evolutionary process displaying OEE. We further explore the problem of information conservation through an OEE process and we conclude that statistical information (standard Shannon information) is not conserved, resulting in the paradoxical situation in which the increase of information content has the effect of erasing itself. We prove that this paradox is solved if we consider non-statistical forms of information. This last result implies that standard information theory may not be a suitable theoretical framework to explore the persistence and increase of the information content in OEE systems.

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Krivovichev, Sergey V., and Vladimir G. Krivovichev. "The Fedorov–Groth law revisited: complexity analysis using mineralogical data." Acta Crystallographica Section A Foundations and Advances 76, no. 3 (April 28, 2020): 429–31. http://dx.doi.org/10.1107/s2053273320004209.

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The Fedorov–Groth law points out that, on average, chemical simplicity corresponds to higher symmetry, and chemically complex compounds usually have lower symmetry than chemically simple compounds. Using mineralogical data, it is demonstrated that the Fedorov–Groth law is valid and statistically meaningful, when chemical complexity is expressed as the amount of Shannon chemical information per atom and the degree of symmetry as the order of the point group of a mineral.

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Khan, Muhammad, Zaid Al-sahwi, and Yu-Ming Chu. "New Estimations for Shannon and Zipf–Mandelbrot Entropies." Entropy 20, no. 8 (August 16, 2018): 608. http://dx.doi.org/10.3390/e20080608.

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The main purpose of this paper is to find new estimations for the Shannon and Zipf–Mandelbrot entropies. We apply some refinements of the Jensen inequality to obtain different bounds for these entropies. Initially, we use a precise convex function in the refinement of the Jensen inequality and then tamper the weight and domain of the function to obtain general bounds for the Shannon entropy (SE). As particular cases of these general bounds, we derive some bounds for the Shannon entropy (SE) which are, in fact, the applications of some other well-known refinements of the Jensen inequality. Finally, we derive different estimations for the Zipf–Mandelbrot entropy (ZME) by using the new bounds of the Shannon entropy for the Zipf–Mandelbrot law (ZML). We also discuss particular cases and the bounds related to two different parametrics of the Zipf–Mandelbrot entropy. At the end of the paper we give some applications in linguistics.

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Pennini, F., and A. Plastino. "Quantum Purity as an Information Measure and Nernst Law." Entropy 25, no. 8 (July 26, 2023): 1113. http://dx.doi.org/10.3390/e25081113.

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We propose to re-express Nernst law in terms of a suitable information measure (IM) parameter. This is achieved by dwelling on the idea of adapting the notion of purity in the case of a thermal Gibbs environment, yielding what we might call the “purity” indicator (which we denote by the symbol D in the text). We find it interesting to define an extension of this D−IM indicator in a classical context. This generalization turns out to have useful conceptual consequences when used in conjunction with the classical Shannon entropy S. Implications for the Nernst law are discussed.

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Huang, Huilin. "The asymptotic behavior for Markov chains in a finite i.i.d random environment indexed by cayley trees." Filomat 31, no. 2 (2017): 273–83. http://dx.doi.org/10.2298/fil1702273h.

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We firstly define a Markov chain indexed by a homogeneous tree in a finite i.i.d random environment. Then, we prove the strong law of large numbers and Shannon-McMillan theorem for finite Markov chains indexed by a homogeneous tree in the finite i.i.d random environment.

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Коверда, В. П., and В. Н. Скоков. "Характеристическая функция самоподобного случайного процесса." Письма в журнал технической физики 48, no. 14 (2022): 7. http://dx.doi.org/10.21883/pjtf.2022.14.52861.19221.

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A stochastic differential equation is proposed for a characteristic function whose inverse function describes a self-similar random process with a power-law behavior of power spectra in a wide frequency range and a power-law amplitude distribution function. Gaussian “tails” for the characteristic distribution make it possible to evaluate its stability according to the formulas of classical statistics using the maximum of the Gibbs-Shannon entropy and, therefore, the stability of a random process given by an inverse function.

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Vu, Dinh Duy, Quoc Khanh Nguyen, and Mai Phuong Pham. "Genetic structure in natural populations of Dacrydium elatum (Roxb.) Wall. (Podocarpaceae) in the Central Highlands of Vietnam inferred by Microsatellites." E3S Web of Conferences 265 (2021): 01030. http://dx.doi.org/10.1051/e3sconf/202126501030.

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To provide a reference for the conservation and application of breeding parentallines resource of Dacrydium elatum (Roxb.). Genetic diversity and population structure of eighty individuals from four populations (Kon Tum, Gia Lai, Dak Lak and Lam Dong) in Central Highlands were evaluated using eight SSR markers. Based on the SSR data, 21 alleles were detected by eight SSR with high polymorphism. The genetic diversity of levels within the populations were moderately high (Ho = 0.555, He = 0.429). The average number of shannon information index were 0.618 and genetic differentiation among populations was low (Fst=0.097). The AMOVA revealed high genetic variation within individuals (87%) compared among populations (13%). The UPGMA phenogram showed that the results of molecular clustering largely agreed with the pedigree and geographic origin. Three populations (NL, KCR and BDNB) were clustered together and CYS population was separated. The maximum quantity ΔK was observed for K=2 in population structure analysis, indicating that the entire collection could be divided into two main groups of genes. This study can provide a theoretical basis for genetic resource management and varieties identification of D. elatum resources, and provide reference basis for breeding.

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Vigo, Ronaldo, Charles A. Doan, Jay Wimsatt, and Cody B. Ross. "A Context-Sensitive Alternative to Hick’s Law of Choice Reaction Times: A Mathematical and Computational Unification of Conceptual Complexity and Choice Behavior." Mathematics 11, no. 11 (May 23, 2023): 2422. http://dx.doi.org/10.3390/math11112422.

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Hick’s law describes the time that individuals take to make a preference decision when presented with a set of possible choices. Basically speaking, the law states that decision time is a logarithmic function of the number of choices when the choices are equiprobable. However, the evidence examined here suggests that this, and a variant of the law for non-equiprobable choices based on Shannon entropy, are not effective at predicting decision reaction times involving structured sets of alternatives. The purpose of this report is to communicate a theoretical alternative to Hick’s law that is derived from a mathematical law of invariance for conceptual behavior at the heart of Generalized Invariance Structure Theory (Vigo, 2013, 2015). We argue that such an alternative accounts more precisely for decision reaction times on structured sets. Furthermore, we argue that Hick’s law is a special case of this more general law of choice reaction times for categories with zero degree of invariance.

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JIANG, JIAN, FRÉDÉRIC METZ, CHRISTOPHE BECK, SÉBASTIEN LEFEVRE, JINCAN CHEN, QIUPING A. WANG, and MICHEL PEZERIL. "DOUBLE POWER-LAW DEGREE DISTRIBUTION AND INFORMATIONAL ENTROPY IN URBAN ROAD NETWORKS." International Journal of Modern Physics C 22, no. 01 (January 2011): 13–20. http://dx.doi.org/10.1142/s0129183111016075.

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The double power-law function, p(x) ~ 1/(xb + cxd) where x is the degree of one node, and b, c, d are parameters, is used to fit the degree distribution of urban road network of Le Mans city in France. It is called "double power-law" since it behaves as two power laws respectively, in large and small degree region with a crossing in-between. The position of the crossing point is derived as a function of the three parameters. The probabilistic uncertainty of this law is studied with two possible information measures: a generalized measure called varentropy and the Shannon entropy formula.

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Hatton, Les, and Gregory Warr. "Strong evidence of an information-theoretical conservation principle linking all discrete systems." Royal Society Open Science 6, no. 10 (October 2019): 191101. http://dx.doi.org/10.1098/rsos.191101.

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Diverse discrete systems share common global properties that lack a unifying theoretical explanation. However, constraining the simplest measure of total information (Hartley–Shannon) in a statistical mechanics framework reveals a principle, the conservation of Hartley–Shannon information (CoHSI) that directly predicts both known and unsuspected common properties of discrete systems, as borne out in the diverse systems of computer software, proteins and music. Discrete systems fall into two categories distinguished by their structure: heterogeneous systems in which there is a distinguishable order of assembly of the system’s components from an alphabet of unique tokens (e.g. proteins assembled from an alphabet of amino acids), and homogeneous systems in which unique tokens are simply binned, counted and rank ordered. Heterogeneous systems are characterized by an implicit distribution of component lengths, with sharp unimodal peak (containing the majority of components) and a power-law tail, whereas homogeneous systems reduce naturally to Zipf’s Law but with a drooping tail in the distribution. We also confirm predictions that very long components are inevitable for heterogeneous systems; that discrete systems can exhibit simultaneously both heterogeneous and homogeneous behaviour; and that in systems with more than one consistent token alphabet (e.g. digital music), the alphabets themselves show a power-law relationship.

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Koverda V. P. and Skokov V. N. "Characteristic function of a self-similar random process." Technical Physics Letters 48, no. 7 (2022): 47. http://dx.doi.org/10.21883/tpl.2022.07.54038.19221.

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A stochastic differential equation is proposed for a characteristic function whose inverse function describes a self-similar random process with a power-law behavior of power spectra in a wide frequency range and a power-law amplitude distribution function. Gaussian "tails" for the characteristic distribution make it possible to evaluate its stability according to the formulas of classical statistics using the maximum of the Gibbs-Shannon entropy and, therefore, the stability of a random process given by an inverse function. Keywords: self-similar random processes, stochastic equations, power spectrum, 1/f-noise, maximum entropy.

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Jing, Cui. "Improving Public Service Delivery in Qingdao Municipality of Shandong Province." Chinese Public Administration Review 6, no. 1-2 (September 2009): 41–54. http://dx.doi.org/10.22140/cpar.v6i1.2.86.

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This paper will assess the effectiveness of the reform of improving public service delivery and identify the factors responsible for the improvements in public service delivery in Qingdao municipality of Shandong province in the People's Republic of China. This paper begins with a description of the policy context and discusses how the policy context affects the improvement of public service delivery in Qingdao municipality. It then discusses the efforts of improving the delivery of public service through enhancing human service delivery, reforming the administrative approval system and increasing government transparency and public participation in Qingdao municipality. Finally, this paper will identify the factors affecting the improvement of public service delivery in Qingdao municipality in terms of the decentralization of economic management, tax profit sharing with the local government, political control, the delegation of law-making and the local leadership.

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Jing, Cui. "Improving Public Service Delivery in Qingdao Municipality of Shandong Province." Chinese Public Administration Review 6, no. 1/2 (November 5, 2016): 41. http://dx.doi.org/10.22140/cpar.v6i1/2.86.

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This paper will assess the effectiveness of the reform of improving public service delivery and identify the factors responsible for the improvements in public service delivery in Qingdao municipality of Shandong province in the People’s Republic of China. This paper begins with a description of the policy context and discusses how the policy context affects the improvement of public service delivery in Qingdao municipality. It then discusses the efforts of improving the delivery of public service through enhancing human service delivery, reforming the administrative approval system and increasing government transparency and public participation in Qingdao municipality. Finally, this paper will identify the factors affecting the improvement of public service delivery in Qingdao municipality in terms of the decentralization of economic management, tax profit sharing with the local government, political control, the delegation of law-making and the local leadership.

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Sohrab, Siavash H. "Some Implications of a Scale Invariant Model of Statistical Mechanics to Boltzmann versus Shannon Entropy in Thermodynamics and Information Theory." WSEAS TRANSACTIONS ON COMPUTERS 20 (April 27, 2021): 56–65. http://dx.doi.org/10.37394/23205.2021.20.7.

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A scale invariant model of statistical mechanics is applied for a comparative study of Boltzmann’s entropy in thermodynamics versus Shannon’s entropy in information theory. The implications of the model to the objective versus subjective aspects of entropy as well as Nernst-Planck statement of the third law of thermodynamics are also discussed

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Reeves, Caroline. "Sovereignty and the Chinese Red Cross Society: The Differentiated Practice of International Law in Shandong, 1914–1916." Journal of the History of International Law / Revue d'histoire du droit international 13, no. 1 (2011): 155–77. http://dx.doi.org/10.1163/157180511x552072.

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AbstractThis article looks at the strategic manipulation of national Red Cross Societies as markers of sovereignty during a period of heightened world nationalism in the early twentieth century. Using Chinese archival materials, it examines how in 1916, on China's much contested Shandong Peninsula, a Japanese delegation set up a Japanese Red Cross chapter and hospital in the Chinese port city of Longkou, in flagrant disregard of widely recognized principles of sovereignty and international law. Occurring just as the larger “Shandong Question” was roiling the international legal community, this incident shows how the local practice of international legal statutes diverged from a more publicized, transnational discussion of those same principles. The article explores this disjuncture, and considers one instance of what I term the differentiated practice of international law: the early twentiethcentury Japanese “double policy” – “one policy for the East and another for the West.” Revealing much about the use of humanitarian activity and the laws of war to further national agendas, the Longkou Incident was later used by the Chinese Red Cross Society as precedent for checking further incursions into China's sovereignty.

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Kazemian-Kale-Kale, Amin, Azadeh Gholami, Mohammad Rezaie-Balf, Amir Mosavi, Ahmed A. Sattar, Amir H. Azimi, Bahram Gharabaghi, and Hossein Bonakdari. "Uncertainty Assessment of Entropy-Based Circular Channel Shear Stress Prediction Models Using a Novel Method." Geosciences 11, no. 8 (July 24, 2021): 308. http://dx.doi.org/10.3390/geosciences11080308.

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Entropy models have been recently adopted in many studies to evaluate the shear stress distribution in open-channel flows. Although the uncertainty of Shannon and Tsallis entropy models were analyzed separately in previous studies, the uncertainty of other entropy models and comparisons of their reliability remain an open question. In this study, a new method is presented to evaluate the uncertainty of four entropy models, Shannon, Shannon-Power Law (PL), Tsallis, and Renyi, in shear stress prediction of the circular channels. In the previous method, the model with the largest value of the percentage of observed data within the confidence bound (Nin) and the smallest value of Forecasting Range of Error Estimation (FREE) is the most reliable. Based on the new method, using the effect of Optimized Forecasting Range of Error Estimation (FREEopt) and Optimized Confidence Bound (OCB), a new statistic index called FREEopt-based OCB (FOCB) is introduced. The lower the value of FOCB, the more certain the model. Shannon and Shannon PL entropies had close values of the FOCB equal to 8.781 and 9.808, respectively, and had the highest certainty, followed by ρgRs and Tsallis models with close values of 14.491 and 14.895, respectively. However, Renyi entropy, with the value of FOCB equal to 57.726, had less certainty.

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Barter, Susan. "Reviews : Invisible Crying Tree Tom Shannon and Christopher Morgan Black Swan, 1997; £6.99 pbk." Probation Journal 44, no. 1 (March 1997): 46–47. http://dx.doi.org/10.1177/026455059704400109.

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Weiguo Yang and Wen Liu. "Strong law of large numbers and Shannon-McMillan theorem for Markov chain fields on trees." IEEE Transactions on Information Theory 48, no. 1 (2002): 313–18. http://dx.doi.org/10.1109/18.971762.

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Zhu, Zhongfan, Jingshan Yu, Jie Dou, and Dingzhi Peng. "An Expression for Velocity Lag in Sediment-Laden Open-Channel Flows Based on Tsallis Entropy Together with the Principle of Maximum Entropy." Entropy 21, no. 5 (May 23, 2019): 522. http://dx.doi.org/10.3390/e21050522.

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In the context of river dynamics, some experimental results have shown that particle velocity is different from fluid velocity along the stream-wise direction for uniform sediment-laden open-channel flows; this velocity difference has been termed velocity lag in the literature. In this study, an analytical expression for estimating the velocity lag in open-channel flows was derived based on the Tsallis entropy theory together with the principle of maximum entropy. The derived expression represents the velocity lag as a function of a non-dimensional entropy parameter depending on the average and maximum values of velocity lag from experimental measurements. The derived expression was tested against twenty-two experimental datasets collected from the literature with three deterministic models and the developed Shannon entropy-based model. The Tsallis entropy-based model agreed better with the experimental datasets than the deterministic models for eighteen out of the twenty-two total real cases, and the prediction accuracy for the eighteen experimental datasets was comparable to that of the developed Shannon entropy-based model (the Tsallis entropy-based expression agreed slightly better than the Shannon entropy-based model for twelve out of eighteen test cases, whereas for the other six test cases, the Shannon entropy-based model had a slightly higher prediction accuracy). Finally, the effects of the friction velocity of the flow, the particle diameter, and the particles’ specific gravity on the velocity lag were analyzed based on the Tsallis entropy-based model. This study shows the potential of the Tsallis entropy theory together with the principle of maximum entropy to predict the stream-wise velocity lag between a particle and the surrounding fluid in sediment-laden open-channel flows.

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Weicai, Peng, Yang Weiguo, and Shi Zhiyan. "STRONG LAW OF LARGE NUMBERS FOR MARKOV CHAINS INDEXED BY SPHERICALLY SYMMETRIC TREES." Probability in the Engineering and Informational Sciences 29, no. 3 (April 16, 2015): 473–81. http://dx.doi.org/10.1017/s0269964815000108.

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In this paper, we main consider spherically symmetric tree T. First, under the condition lim supn→∞ |T(n)|/|Ln|<∞, we investigate the strong law of large numbers (SLLNs) for T-indexed Markov chains on the nth level of T. Then, combining the Stolz theorem, we obtain the SLLNs on T. Finally, we get Shannon–McMillan theorem for T-indexed Markov chains. The obtained theorems are generalizations of some known results on Cayley tree TC, N and Bethe tree TB, N.

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Meng, Yan Ru, Nan Jiang, Wen Feng Ning, Chong Qiu Zhong, Kun Peng Gao, and Yue Feng Men. "Geological Factors Analysis of Gas Unusual Area in Southwest of Shandong Province." Advanced Materials Research 734-737 (August 2013): 106–10. http://dx.doi.org/10.4028/www.scientific.net/amr.734-737.106.

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Gas geological law in southwest of Shandong province was studied with theoretical foundation and method of gas geology in this paper. It finds that the area in southwest of Shandong province is mostly low gas mining area. But Fucun coal mine of Tengnan mining area, Sanhekou coal mine, Jinyuan coal mine, Tangkou coal mine of Jining mining area and Zhaoguan coal mine of Huanghebei mining area are all gas unusual area. Among them, Fucun coal mine, Sanhekou coal mine and Jinyuan coal mine appear high gas unusual which are mainly affected by magma intrusion, Tangkou and Zhaoguan coal mine form gas unusual area which are mainly affected by thickness of upper bedrock.

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Shi, Zhiyan, Pingping Zhong, and Yan Fan. "THE SHANNON–MCMILLAN THEOREM FOR MARKOV CHAINS INDEXED BY A CAYLEY TREE IN RANDOM ENVIRONMENT." Probability in the Engineering and Informational Sciences 32, no. 4 (December 29, 2017): 626–39. http://dx.doi.org/10.1017/s0269964817000444.

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In this paper, we give the definition of tree-indexed Markov chains in random environment with countable state space, and then study the realization of Markov chain indexed by a tree in random environment. Finally, we prove the strong law of large numbers and Shannon–McMillan theorem for Markov chains indexed by a Cayley tree in a Markovian environment with countable state space.

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Thomas, Marc Simon, and Nina Holm Vohnsen. "Book Reviews." Journal of Legal Anthropology 1, no. 2 (September 1, 2010): 259–62. http://dx.doi.org/10.3167/jla.2010.010207.

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Pitarch, Pedro, Shannon Speed and Xochitl Leyva Solano (eds.). 2008. Human rights in the Maya region: Global politics, cultural contentions, and moral engagements. Durham and London: Duke University Press. ISBN: 978-0-8223-4313-4, x + 377 pp, $23.95Latour, Bruno (2010 [2002]) The Making of Law. An Ethnography of the Counseil d’État. Polity Press. ISBN-13: 978-0-7456-3985-7

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Xu, Haoran, Lingen Chen, Yanlin Ge, and Huijun Feng. "Four-Objective Optimization of an Irreversible Stirling Heat Engine with Linear Phenomenological Heat-Transfer Law." Entropy 24, no. 10 (October 19, 2022): 1491. http://dx.doi.org/10.3390/e24101491.

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This paper combines the mechanical efficiency theory and finite time thermodynamic theory to perform optimization on an irreversible Stirling heat-engine cycle, in which heat transfer between working fluid and heat reservoir obeys linear phenomenological heat-transfer law. There are mechanical losses, as well as heat leakage, thermal resistance, and regeneration loss. We treated temperature ratio x of working fluid and volume compression ratio λ as optimization variables, and used the NSGA-II algorithm to carry out multi-objective optimization on four optimization objectives, namely, dimensionless shaft power output P¯s, braking thermal efficiency ηs, dimensionless efficient power E¯p and dimensionless power density P¯d. The optimal solutions of four-, three-, two-, and single-objective optimizations are reached by selecting the minimum deviation indexes D with the three decision-making strategies, namely, TOPSIS, LINMAP, and Shannon Entropy. The optimization results show that the D reached by TOPSIS and LINMAP strategies are both 0.1683 and better than the Shannon Entropy strategy for four-objective optimization, while the Ds reached for single-objective optimizations at maximum P¯s, ηs, E¯p, and P¯d conditions are 0.1978, 0.8624, 0.3319, and 0.3032, which are all bigger than 0.1683. This indicates that multi-objective optimization results are better when choosing appropriate decision-making strategies.

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Tsallis, Constantino. "Beyond Boltzmann–Gibbs–Shannon in Physics and Elsewhere." Entropy 21, no. 7 (July 15, 2019): 696. http://dx.doi.org/10.3390/e21070696.

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The pillars of contemporary theoretical physics are classical mechanics, Maxwell electromagnetism, relativity, quantum mechanics, and Boltzmann–Gibbs (BG) statistical mechanics –including its connection with thermodynamics. The BG theory describes amazingly well the thermal equilibrium of a plethora of so-called simple systems. However, BG statistical mechanics and its basic additive entropy S B G started, in recent decades, to exhibit failures or inadequacies in an increasing number of complex systems. The emergence of such intriguing features became apparent in quantum systems as well, such as black holes and other area-law-like scenarios for the von Neumann entropy. In a different arena, the efficiency of the Shannon entropy—as the BG functional is currently called in engineering and communication theory—started to be perceived as not necessarily optimal in the processing of images (e.g., medical ones) and time series (e.g., economic ones). Such is the case in the presence of generic long-range space correlations, long memory, sub-exponential sensitivity to the initial conditions (hence vanishing largest Lyapunov exponents), and similar features. Finally, we witnessed, during the last two decades, an explosion of asymptotically scale-free complex networks. This wide range of important systems eventually gave support, since 1988, to the generalization of the BG theory. Nonadditive entropies generalizing the BG one and their consequences have been introduced and intensively studied worldwide. The present review focuses on these concepts and their predictions, verifications, and applications in physics and elsewhere. Some selected examples (in quantum information, high- and low-energy physics, low-dimensional nonlinear dynamical systems, earthquakes, turbulence, long-range interacting systems, and scale-free networks) illustrate successful applications. The grounding thermodynamical framework is briefly described as well.

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Botet, Robert, and Bernard Cabane. "Simple inversion formula for the small-angle X-ray scattering intensity from polydisperse systems of spheres." Journal of Applied Crystallography 45, no. 3 (May 4, 2012): 406–16. http://dx.doi.org/10.1107/s0021889812012812.

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A practical inversion method to calculate the size distribution of colloidal homogeneous particles from small-angle scattering experiments is presented. It is based on the analysis of the deviations of the scattering signal from the Porod law. The resulting inversion formula provides a reliable way to assess complex size distributions such as power-law, multimodal or very broad distributions. It is particularly suitable for colloidal dispersions that have a substantial fraction of very small particles. These cases correspond to large deviations from the Porod law over a broad range of scattering vector values,q. Shannon's theorem gives a way to obtain the maximum amount of information concerning the size distribution, without requiring an arbitrary extrapolation of the data beyond the availableqrange. It is demonstrated that this protocol yields a calculated distribution of particle sizes that is stable.

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Balocco, Carla, and Daniele Verdesca. "Shannon entropy for energy technologies ex-ante evaluation." International Journal of Environmental Technology and Management 7, no. 1/2 (2007): 197. http://dx.doi.org/10.1504/ijetm.2007.013245.

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Cui, Yujing, Luc Hens, Yongguan Zhu, and Jingzhu Zhao. "Environmental sustainability index of Shandong Province, China." International Journal of Sustainable Development & World Ecology 11, no. 3 (September 2004): 227–33. http://dx.doi.org/10.1080/13504500409469827.

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Yang, Weiguo, and Wen Liu. "strong law of large numbers and Shannon-McMillan theorem for Markov chains field on Cayley tree." Acta Mathematica Scientia 21, no. 4 (October 2001): 495–502. http://dx.doi.org/10.1016/s0252-9602(17)30438-1.

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HAYDN, NICOLAI, and SANDRO VAIENTI. "FLUCTUATIONS OF THE METRIC ENTROPY FOR MIXING MEASURES." Stochastics and Dynamics 04, no. 04 (December 2004): 595–627. http://dx.doi.org/10.1142/s021949370400119x.

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It is known from the theorem of Shannon–McMillan–Breiman that the measure of cylinder sets decays in the limit exponentially with a rate which is given by the metric entropy. Here we prove that the measure of cylinders satisfies a Central Limit Theorem for a wide class of mixing measures which do not necessarily have the Gibbs property. We, moreover, provide the rate of convergence (which is algebraic). As a consequence we can then also prove that the distribution of the first return time in cylinder sets is log-normally distributed and give the speed of convergence. We also show that the weak invariance principle and the law of the iterated logarithm hold for the convergence to the entropy in the Shannon–McMillan–Breiman and for the distribution of the first return time.

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Shi, Xin, Xiangyu Cui, Lianke Xie, Jianguang Yin, Lefeng Li, Yuwei Zang, and Xiaobang Hou. "Experimental Study on Wind Noise Distribution Law of Transmission Lines." Journal of Physics: Conference Series 2488, no. 1 (May 1, 2023): 012040. http://dx.doi.org/10.1088/1742-6596/2488/1/012040.

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Abstract Aiming at the problem of wind noise generated by transmission lines under windy weather conditions, this paper selects three groups of transmission lines in Shandong Province, China. Through the fixed-point measurement of the wind noise pressure of the conductor at the ground projection point of the side, phase conductor sags as the starting point, and the outward extension of 50 m as the endpoint, the frequency spectrum curve characteristics of the wind noise of the transmission line, the predominant frequency, the cut-off frequency, and the overall A sound level are analyzed. The results show that the transmission line conductor wind noise is mainly concentrated in the range of 500 - 2000 Hz, and its predominant frequency is around 650 Hz, which belongs to low-frequency noise. The wire wind noise attenuates with the increase of the distance from the projection point, and the attenuation is completed at 50m, and the wind noise fixed-point measurement decreases by 8 dB.

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Liu, Jia, Fengshan Ma, Jie Guo, Guang Li, Yewei Song, and Yang Wan. "A Field Study on the Law of Spatiotemporal Development of Rock Movement of Under-Sea Mining, Shandong, China." Sustainability 14, no. 10 (May 12, 2022): 5864. http://dx.doi.org/10.3390/su14105864.

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The phenomenon of rock movement in mining areas has always been a difficult problem in mining engineering, especially under complicated geological conditions. Although the backfilling method mitigates the destruction of the surrounding rock, deformation can still exist in the mining area. In order to ensure the safety of under-sea mining, it is necessary to study the rock movement laws and the mechanisms. This paper focuses on a settlement analysis of the monitoring data of the No. 55 prospecting profile. By analyzing the shape of the settlement curves, the spatial distribution characteristics of settlements of different mining sublevels are summarized. Additionally, the fractal characteristics of the settlement rate under different space–time conditions are studied. We also discuss the relationship between the fractal phenomenon and the self-organized criticality (SOC) theory. The findings are of great theoretical value for the further study of mining settlements to better understand the physical mechanisms of internal movement and rock mass failures through the fractal law of the settlement. Furthermore, elucidating the rock movement law is an urgent task for the safety of seabed mining.

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Journal articles on the topic 'SHANONS LAW'

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