http://www.mdpi.com/journal/entropy/special_issues/entropy_information/ Submission All papers should be submitted to entropy@mdpi.org with copy to the guest editor. To be published continuously until the deadline and papers will be listed together at the special websites. Both, research articles and review articles are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editors for announcment on this website. Submitted papers should not have been published previously, nor be under consideration for publication elsewhere. All papers are refereed through a peer-review process. A guide for authors, sample copies and other relevant information for submitting papers are available on the Instructions for Authors page. Entropy is an international peer-reviewed quarterly journal published by Molecular Diversity Preservation International. Please visit the Instructions for Authors page before submitting a paper. Open Access publication fees are 800 CHF per paper. English correction fees (250 CHF) will be added in certain cases (1050 CHF per paper for those papers that require extensive additional formatting and/or English corrections.). http://www.mdpi.com/1099-4300/12/3/516/ In several socioeconomic applications, matrices containing information on flows-trade, income or migration flows, for example–are usually not constructed from direct observation but are rather estimated, since the compilation of the information required is often extremely expensive and time-consuming. The estimation process takes as point of departure another matrix which is adjusted until it optimizes some divergence criterion and simultaneously is consistent with some partial information-row and column margins–of the target matrix. Among all the possible criteria to be considered, one of the most popular is the Kullback-Leibler divergence [1], leading to the well-known Cross-Entropy technique. This paper proposes the use of a composite Cross-Entropy approach that allows for introducing a mixture of two types of a priori information–two possible matrices to be included as point of departure in the estimation process. By means of a Monte Carlo simulation experiment, we will show that under some circumstances this approach outperforms other competing estimators. Besides, a real-world case with a matrix of interregional trade is included to show the applicability of the suggested technique. http://www.mdpi.com/1099-4300/12/3/516/ Fri, 12 Mar 2010 00:00:00 CET Entropy 2010-03-12 12 3 Article 516 527 1099-4300 Recovering Matrices of Economic Flows from Incomplete Data and a Composite Prior 2010-03-12 doi: 10.3390/e12030516 Fernández-Vázquez http://www.mdpi.com/1099-4300/12/1/148/ We investigate the classical limit of the semiclassical evolution with reference to a well-known model that represents the interaction between matter and a given field. This is done by recourse to a special statistical quantifier called the “symbolic transfer entropy”. We encounter that the quantum-classical transition gets thereby described as the sign-reversal of the dominating direction of the information flow between classical and quantal variables. http://www.mdpi.com/1099-4300/12/1/148/ Tue, 26 Jan 2010 00:00:00 CET Entropy 2010-01-26 12 1 Article 148 160 1099-4300 The Quantum-Classical Transition as an Information Flow 2010-01-26 doi: 10.3390/e12010148 Andres M. Kowalski Maria T. Martin Luciano Zunino Angelo Plastino Montserrat Casas http://www.mdpi.com/1099-4300/12/1/80/ We discuss the possibility of a relativistic relationship between information and entropy, closely analogous to the classical Maxwell electro-magnetic wave equations. Inherent to the analysis is the description of information as residing in points of non-analyticity; yet ultimately also exhibiting a distributed characteristic: additionally analogous, therefore, to the wave-particle duality of light. At cosmological scales our vector differential equations predict conservation of information in black holes, whereas regular- and Z-DNA molecules correspond to helical solutions at microscopic levels. We further propose that regular- and Z-DNA are equivalent to the alternative words chosen from an alphabet to maintain the equilibrium of an information transmission system. http://www.mdpi.com/1099-4300/12/1/80/ Thu, 07 Jan 2010 00:00:00 CET Entropy 2010-01-07 12 1 Article 80 88 1099-4300 A Dynamic Model of Information and Entropy 2010-01-07 doi: 10.3390/e12010080 Michael C. Parker Stuart D. Walker http://www.mdpi.com/1099-4300/12/1/63/ Mutual information among three or more dimensions (μ* = –Q) has been considered as interaction information. However, Krippendorff [1,2] has shown that this measure cannot be interpreted as a unique property of the interactions and has proposed an alternative measure of interaction information based on iterative approximation of maximum entropies. Q can then be considered as a measure of the difference between interaction information and redundancy generated in a model entertained by an observer. I argue that this provides us with a measure of the imprint of a second-order observing system—a model entertained by the system itself—on the underlying information processing. The second-order system communicates meaning hyper-incursively; an observation instantiates this meaning-processing within the information processing. The net results may add to or reduce the prevailing uncertainty. The model is tested empirically for the case where textual organization can be expected to contain intellectual organization in terms of distributions of title words, author names, and cited references. http://www.mdpi.com/1099-4300/12/1/63/ Wed, 06 Jan 2010 00:00:00 CET Entropy 2010-01-06 12 1 Article 63 79 1099-4300 Redundancy in Systems Which Entertain a Model of Themselves: Interaction Information and the Self-Organization of Anticipation 2010-01-06 doi: 10.3390/e12010063 Loet Leydesdorff http://www.mdpi.com/1099-4300/11/4/1121/ The volume of the body enclosed by the n-dimensional Lamé curve defined by Ʃni=1 xbi = E is computed. http://www.mdpi.com/1099-4300/11/4/1121/ Tue, 22 Dec 2009 00:00:00 CET Entropy 2009-12-22 11 4 Discussion 1121 1122 1099-4300 Comment on “Equiprobability, Entropy, Gamma Distributions and Other Geometrical Questions in Multi-Agent Systems”, Entropy 2009, 11, 959-971 2009-12-22 doi: 10.3390/e11041121 Raúl Toral http://www.mdpi.com/1099-4300/11/4/1073/ A survey is given summarizing the state of the art of describing information processing in Quantum Decision Theory, which has been recently advanced as a novel variant of decision making, based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intended actions. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. The self-consistent procedure of decision making, in the frame of the quantum decision theory, takes into account both the available objective information as well as subjective contextual effects. This quantum approach avoids any paradox typical of classical decision theory. Conditional maximization of entropy, equivalent to the minimization of an information functional, makes it possible to connect the quantum and classical decision theories, showing that the latter is the limit of the former under vanishing interference terms. http://www.mdpi.com/1099-4300/11/4/1073/ Mon, 14 Dec 2009 00:00:00 CET Entropy 2009-12-14 11 4 Review 1073 1120 1099-4300 Processing Information in Quantum Decision Theory 2009-12-14 doi: 10.3390/e11041073 Vyacheslav I. Yukalov Didier Sornette http://www.mdpi.com/1099-4300/11/4/1025/ Systems do not elect thermodynamic pathways on their own. They operate in tandem with their surroundings. Pathway selection and traversal require coordinated work and heat exchanges along with parallel tuning of the system variables. Previous research by the author (Reference [1]) focused on the information expressed in thermodynamic pathways. Examined here is how spectral entropy is a by-product of information that depends intricately on the pathway structure. The spectral entropy has proven to be a valuable tool in diverse fields. This paper illustrates the contact between spectral entropy and the properties which distinguish ideal from non-ideal gases. The role of spectral entropy in the first and second laws of thermodynamics and heat → work conversions is also discussed. http://www.mdpi.com/1099-4300/11/4/1025/ Mon, 07 Dec 2009 00:00:00 CET Entropy 2009-12-07 11 4 Article 1025 1041 1099-4300 On the Spectral Entropy of Thermodynamic Paths for Elementary Systems 2009-12-07 doi: 10.3390/e11041025 Daniel J. Graham http://www.mdpi.com/1099-4300/11/4/993/ The objective of this essay is to reflect on a possible relation between entropy and emergence. A qualitative, relational approach is followed. We begin by highlighting that entropy includes the concept of dispersal, relevant to our enquiry. Emergence in complex systems arises from the coordinated behavior of their parts. Coordination in turn necessitates recognition between parts, i.e., information exchange. What will be argued here is that the scope of recognition processes between parts is increased when preceded by their dispersal, which multiplies the number of encounters and creates a richer potential for recognition. A process intrinsic to emergence is dissolvence (aka submergence or top-down constraints), which participates in the information-entropy interplay underlying the creation, evolution and breakdown of higher-level entities. http://www.mdpi.com/1099-4300/11/4/993/ Thu, 03 Dec 2009 00:00:00 CET Entropy 2009-12-03 11 4 Communication 993 1000 1099-4300 Dispersal (Entropy) and Recognition (Information) as Foundations of Emergence and Dissolvence 2009-12-03 doi: 10.3390/e11040993 Bernard Testa http://www.mdpi.com/1099-4300/11/4/959/ A set of many identical interacting agents obeying a global additive constraint is considered. Under the hypothesis of equiprobability in the high-dimensional volume delimited in phase space by the constraint, the statistical behavior of a generic agent over the ensemble is worked out. The asymptotic distribution of that statistical behavior is derived from geometrical arguments. This distribution is related with the Gamma distributions found in several multi-agent economy models. The parallelism with all these systems is established. Also, as a collateral result, a formula for the volume of high-dimensional symmetrical bodies is proposed. http://www.mdpi.com/1099-4300/11/4/959/ Wed, 02 Dec 2009 00:00:00 CET Entropy 2009-12-02 11 4 Article 959 971 1099-4300 Equiprobability, Entropy, Gamma Distributions and Other Geometrical Questions in Multi-Agent Systems 2009-12-02 doi: 10.3390/e11040959 Ricardo López-Ruiz Jaime Sañudo Xavier Calbet http://www.mdpi.com/1099-4300/11/4/634/ We show that the maximin average redundancy in pattern coding is eventually larger than 1.84 (n/log n)1/3 for messages of length n. This improves recent results on pattern redundancy, although it does not fill the gap between known lower- and upper-bounds. The pattern of a string is obtained by replacing each symbol by the index of its first occurrence. The problem of pattern coding is of interest because strongly universal codes have been proved to exist for patterns while universal message coding is impossible for memoryless sources on an infinite alphabet. The proof uses fine combinatorial results on partitions with small summands. http://www.mdpi.com/1099-4300/11/4/634/ Thu, 22 Oct 2009 00:00:00 CEST Entropy 2009-10-22 11 4 Article 634 642 1099-4300 A Lower-Bound for the Maximin Redundancy in Pattern Coding 2009-10-22 doi: 10.3390/e11040634 Aurélien Garivier http://www.mdpi.com/1099-4300/11/4/586/ Landauer’s principle is one of the pillars of the physics of information. It constitutes one of the foundations behind the idea that “information is physical”. Landauer’s principle establishes the smallest amount of energy that has to be dissipated when one bit of information is erased from a computing device. Here we explore an extended Landauerlike principle valid for general dynamical systems (not necessarily Hamiltonian) governed by divergenceless phase space flows. http://www.mdpi.com/1099-4300/11/4/586/ Tue, 13 Oct 2009 00:00:00 CEST Entropy 2009-10-13 11 4 Article 586 597 1099-4300 Landauer’s Principle and Divergenceless Dynamical Systems 2009-10-13 doi: 10.3390/e11040586 Claudia Zander Angel Ricardo Plastino Angelo Plastino Montserrat Casas Sergio Curilef http://www.mdpi.com/1099-4300/11/3/513/ By a “covering” we mean a Gaussian mixture model fit to observed data. Approximations of the Bayes factor can be availed of to judge model fit to the data within a given Gaussian mixture model. Between families of Gaussian mixture models, we propose the Rényi quadratic entropy as an excellent and tractable model comparison framework. We exemplify this using the segmentation of an MRI image volume, based (1) on a direct Gaussian mixture model applied to the marginal distribution function, and (2) Gaussian model fit through k-means applied to the 4D multivalued image volume furnished by the wavelet transform. Visual preference for one model over another is not immediate. The Rényi quadratic entropy allows us to show clearly that one of these modelings is superior to the other. http://www.mdpi.com/1099-4300/11/3/513/ Thu, 24 Sep 2009 00:00:00 CEST Entropy 2009-09-24 11 3 Article 513 528 1099-4300 Scale-Based Gaussian Coverings: Combining Intra and Inter Mixture Models in Image Segmentation 2009-09-24 doi: 10.3390/e11030513 Fionn Murtagh Pedro Contreras Jean-Luc Starck http://www.mdpi.com/1099-4300/11/1/32/ Semiclassical delocalization in phase space constitutes a manifestation of the Uncertainty Principle, one indispensable part of the present understanding of Nature and the Wehrl entropy is widely regarded as the foremost localization-indicator. We readdress the matter here within the framework of the celebrated semiclassical Husimi distributions and their associatedWehrl entropies, suitably қ-deformed. We are able to show that it is possible to significantly improve on the extant phase-space classical-localization power. http://www.mdpi.com/1099-4300/11/1/32/ Tue, 27 Jan 2009 00:00:00 CET Entropy 2009-01-27 11 1 Article 32 41 1099-4300 Information, Deformed қ-Wehrl Entropies and Semiclassical Delocalization 2009-01-27 doi: 10.3390/e11010032 Flavia Pennini Angelo Plastino Gustavo L. Ferri Felipe Olivares Montse Casas http://www.mdpi.com/1099-4300/10/4/776/ For 2 x 2 x K contingency tables, Tomizawa considered a Shannon entropy type measure to represent the degree of departure from a log-linear model of no three-factor interaction (the NOTFI model). This paper proposes a generalization of Tomizawa's measure for 2 x 2 x K tables. The measure proposed is expressed by using Patil-Taillie diversity index or Cressie-Read power-divergence. A special case of the proposed measure includes Tomizawa's measure. The proposed measure would be useful for comparing the degrees of departure from the NOTFI model in several tables. http://www.mdpi.com/1099-4300/10/4/776/ Mon, 22 Dec 2008 00:00:00 CET Entropy 2008-12-22 10 4 Article 776 785 1099-4300 Generalized Measure of Departure from No Three-Factor Interaction Model for 2 x 2 x K Contingency Tables 2008-12-22 doi: 10.3390/e10040776 Kouji Yamamoto Yohei Ban Sadao Tomizawa