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Entropy, Volume 14, Issue 9 (September 2012), Pages 1606-1812

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Research

Open AccessArticle Kullback–Leibler Divergence Measure for Multivariate Skew-Normal Distributions
Entropy 2012, 14(9), 1606-1626; doi:10.3390/e14091606
Received: 16 July 2012 / Revised: 25 August 2012 / Accepted: 27 August 2012 / Published: 4 September 2012
Cited by 10 | PDF Full-text (2213 KB) | HTML Full-text | XML Full-text
Abstract
The aim of this work is to provide the tools to compute the well-known Kullback–Leibler divergence measure for the flexible family of multivariate skew-normal distributions. In particular, we use the Jeffreys divergence measure to compare the multivariate normal distribution with the skew-multivariate [...] Read more.
The aim of this work is to provide the tools to compute the well-known Kullback–Leibler divergence measure for the flexible family of multivariate skew-normal distributions. In particular, we use the Jeffreys divergence measure to compare the multivariate normal distribution with the skew-multivariate normal distribution, showing that this is equivalent to comparing univariate versions of these distributions. Finally, we applied our results on a seismological catalogue data set related to the 2010 Maule earthquake. Specifically, we compare the distributions of the local magnitudes of the regions formed by the aftershocks. Full article
(This article belongs to the Special Issue Distance in Information and Statistical Physics Volume 2)
Open AccessArticle Cosmology of F(T) Gravity and k-Essence
Entropy 2012, 14(9), 1627-1651; doi:10.3390/e14091627
Received: 20 July 2012 / Revised: 17 August 2012 / Accepted: 21 August 2012 / Published: 4 September 2012
Cited by 20 | PDF Full-text (353 KB) | HTML Full-text | XML Full-text
Abstract
This a brief review on F(T) gravity and its relation with k-essence. Modified teleparallel gravity theory with the torsion scalar has recently gained a lot of attention as a possible explanation of dark energy. We perform a thorough reconstruction analysis on the [...] Read more.
This a brief review on F(T) gravity and its relation with k-essence. Modified teleparallel gravity theory with the torsion scalar has recently gained a lot of attention as a possible explanation of dark energy. We perform a thorough reconstruction analysis on the so-called F(T) models, where F(T) is some general function of the torsion term, and deduce the required conditions for the equivalence between of F(T) models with pure kinetic k-essence models. We present a new class of models of F(T)-gravity and k-essence. Full article
(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)
Open AccessArticle On the Information Transmission Ability of Nonlinear Stochastic Dynamic Networks
Entropy 2012, 14(9), 1652-1670; doi:10.3390/e14091652
Received: 10 August 2012 / Revised: 27 August 2012 / Accepted: 30 August 2012 / Published: 6 September 2012
Cited by 1 | PDF Full-text (422 KB) | HTML Full-text | XML Full-text
Abstract
The major function of dynamic networks is to sense information from the environment and process the information to the downstream. Therefore how to measure the information transmission ability of a dynamic network is an important topic to evaluate network performance. However, the [...] Read more.
The major function of dynamic networks is to sense information from the environment and process the information to the downstream. Therefore how to measure the information transmission ability of a dynamic network is an important topic to evaluate network performance. However, the dynamic behavior of a dynamic network is complex and, despite knowledge of network components, interactions and noises, it is a challenge to measure the information transmission ability of a dynamic network, especially a nonlinear stochastic dynamic network. Based on nonlinear stochastic dynamic system theory, the information transmission ability can be investigated by solving a Hamilton-Jacobi inequality (HJI)-constrained optimization problem. To avoid difficulties associated with solving a complex HJI-constrained optimization problem for information transmission ability, the Takagi-Sugeno (T-S) fuzzy model is introduced to approximate the nonlinear stochastic dynamic network by interpolating several local linear stochastic dynamic networks so that a HJI-constrained optimization problem can be replaced by the linear matrix inequalities (LMIs)-constrained optimization problem. The LMI problem can then be efficiently solved for measuring information transmission ability. We found that a more stable (robust) dynamic network has less information transmission ability, and vice versa. Finally, an example of a biochemical network in cellular communication is given to illustrate the measurement of information transmission ability and to confirm the results by using Monte Carlo simulations. Full article
(This article belongs to the Special Issue Information Theory Applied to Communications and Networking)
Open AccessArticle Some New Results on the Wiretap Channel with Side Information
Entropy 2012, 14(9), 1671-1702; doi:10.3390/e14091671
Received: 17 July 2012 / Revised: 20 August 2012 / Accepted: 30 August 2012 / Published: 7 September 2012
Cited by 15 | PDF Full-text (444 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, the model of wiretap channel has been reconsidered for the case that the main channel is controlled by channel state information (side information), and it is available at the transmitter in a noncausal manner (termed here noncausal side information) [...] Read more.
In this paper, the model of wiretap channel has been reconsidered for the case that the main channel is controlled by channel state information (side information), and it is available at the transmitter in a noncausal manner (termed here noncausal side information) or causal manner (termed here causal side information). Inner and outer bounds are derived on the capacity-equivocation regions for the noncausal and causal manners, and the secrecy capacities for both manners are described and bounded, which provide the best transmission rate with perfect secrecy. Moreover, for the case that the side information is available at the transmitter in a memoryless manner (termed here memoryless side information), both the capacity-equivocation region and the secrecy capacity are determined. The results of this paper extend the previous work on wiretap channel with noncausal side information by providing an outer bound on the capacity-equivocation region. In addition, we find that the memoryless side information can not help to obtain the same secrecy capacity as that of the causal case, and this is different from the well known fact that the memoryless manner can achieve the capacity of the channel with causal side information. Full article
(This article belongs to the Special Issue Information Theory Applied to Communications and Networking)
Open AccessArticle MENS, an Info-Computational Model for (Neuro-)cognitive Systems Capable of Creativity
Entropy 2012, 14(9), 1703-1716; doi:10.3390/e14091703
Received: 2 August 2012 / Revised: 30 August 2012 / Accepted: 5 September 2012 / Published: 7 September 2012
Cited by 4 | PDF Full-text (368 KB) | HTML Full-text | XML Full-text
Abstract
MENS is a bio-inspired model for higher level cognitive systems; it is an application of the Memory Evolutive Systems developed with Vanbremeersch to model complex multi-scale, multi-agent self-organized systems, such as biological or social systems. Its development resorts to an info-computationalism: first [...] Read more.
MENS is a bio-inspired model for higher level cognitive systems; it is an application of the Memory Evolutive Systems developed with Vanbremeersch to model complex multi-scale, multi-agent self-organized systems, such as biological or social systems. Its development resorts to an info-computationalism: first we characterize the properties of the human brain/mind at the origin of higher order cognitive processes up to consciousness and creativity, then we ‘abstract’ them in a MENS mathematical model for natural or artificial cognitive systems. The model, based on a ‘dynamic’ Category Theory incorporating Time, emphasizes the computability problems which are raised. Full article
Figures

Open AccessArticle Black Holes, Cosmological Solutions, Future Singularities, and Their Thermodynamical Properties in Modified Gravity Theories
Entropy 2012, 14(9), 1717-1770; doi:10.3390/e14091717
Received: 12 July 2012 / Revised: 14 August 2012 / Accepted: 24 August 2012 / Published: 18 September 2012
Cited by 83 | PDF Full-text (1458 KB) | HTML Full-text | XML Full-text
Abstract
Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann–Lemaˆıtre–Robertson–Walker metrics. The thermodynamical properties of fourth order gravity theories are [...] Read more.
Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann–Lemaˆıtre–Robertson–Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy–Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied. Full article
(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)
Open AccessArticle Exact Solution and Exotic Fluid in Cosmology
Entropy 2012, 14(9), 1771-1783; doi:10.3390/e14091771
Received: 21 August 2012 / Revised: 13 September 2012 / Accepted: 17 September 2012 / Published: 20 September 2012
Cited by 1 | PDF Full-text (538 KB) | HTML Full-text | XML Full-text
Abstract
We investigate cosmological consequences of nonlinear sigma model coupled with a cosmological fluid which satisfies the continuity equation. The target space action is of the de Sitter type and is composed of four scalar fields. The potential which is a function of only one of the scalar fields is also introduced. We perform a general analysis of the ensuing cosmological equations and give various critical points and their properties. Then, we show that the model exhibits an exact cosmological solution which yields a transition from matter domination into dark energy epoch and compare it with the Λ-CDM behavior. Especially, we calculate the age of the Universe and show that it is consistent with the observational value if the equation of the state ωf of the cosmological fluid is within the range of 0.13 < ωf < 0.22. Some implication of this result is also discussed. Full article
(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)
Open AccessArticle Bivariate Rainfall and Runoff Analysis Using Entropy and Copula Theories
Entropy 2012, 14(9), 1784-1812; doi:10.3390/e14091784
Received: 1 August 2012 / Revised: 15 September 2012 / Accepted: 17 September 2012 / Published: 24 September 2012
Cited by 9 | PDF Full-text (711 KB) | HTML Full-text | XML Full-text
Abstract
Multivariate hydrologic frequency analysis has been widely studied using: (1) commonly known joint distributions or copula functions with the assumption of univariate variables being independently identically distributed (I.I.D.) random variables; or (2) directly applying the entropy theory-based framework. However, for the I.I.D. [...] Read more.
Multivariate hydrologic frequency analysis has been widely studied using: (1) commonly known joint distributions or copula functions with the assumption of univariate variables being independently identically distributed (I.I.D.) random variables; or (2) directly applying the entropy theory-based framework. However, for the I.I.D. univariate random variable assumption, the univariate variable may be considered as independently distributed, but it may not be identically distributed; and secondly, the commonly applied Pearson’s coefficient of correlation (g) is not able to capture the nonlinear dependence structure that usually exists. Thus, this study attempts to combine the copula theory with the entropy theory for bivariate rainfall and runoff analysis. The entropy theory is applied to derive the univariate rainfall and runoff distributions. It permits the incorporation of given or known information, codified in the form of constraints and results in a universal solution of univariate probability distributions. The copula theory is applied to determine the joint rainfall-runoff distribution. Application of the copula theory results in: (i) the detection of the nonlinear dependence between the correlated random variables-rainfall and runoff, and (ii) capturing the tail dependence for risk analysis through joint return period and conditional return period of rainfall and runoff. The methodology is validated using annual daily maximum rainfall and the corresponding daily runoff (discharge) data collected from watersheds near Riesel, Texas (small agricultural experimental watersheds) and Cuyahoga River watershed, Ohio. Full article

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