Entropy

195 KiB

Open AccessArticle

Periodic Cosmological Evolutions of Equation of State for Dark Energy

by Kazuharu Bamba, Ujjal Debnath, Kuralay Yesmakhanova, Petr Tsyba, Gulgasyl Nugmanova and Ratbay Myrzakulov

Entropy 2012, 14(11), 2351-2374; https://doi.org/10.3390/e14112351 - 20 Nov 2012

Cited by 15 | Viewed by 6379

Abstract

We demonstrate two periodic or quasi-periodic generalizations of the Chaplygin gas (CG) type models to explain the origins of dark energy as well as dark matter by using the Weierstrass ξ(t), σ(t) and ζ (t) functions with two periods being infinite. If the [...] Read more.

We demonstrate two periodic or quasi-periodic generalizations of the Chaplygin gas (CG) type models to explain the origins of dark energy as well as dark matter by using the Weierstrass ξ(t), σ(t) and ζ (t) functions with two periods being infinite. If the universe can evolve periodically, a non-singular universe can be realized. Furthermore, we examine the cosmological evolution and nature of the equation of state (EoS) of dark energy in the Friedmann–Lemaître–Robertson–Walker cosmology. It is explicitly illustrated that there exist three type models in which the universe always stays in the non-phantom (quintessence) phase, whereas it always evolves in the phantom phase, or the crossing of the phantom divide can be realized. The scalar fields and the corresponding potentials are also analyzed for different types of models. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

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1746 KiB

Open AccessArticle

On Using Entropy for Enhancing Handwriting Preprocessing

by Andreas Holzinger, Christof Stocker, Bernhard Peischl and Klaus-Martin Simonic

Entropy 2012, 14(11), 2324-2350; https://doi.org/10.3390/e14112324 - 19 Nov 2012

Cited by 22 | Viewed by 12666

Abstract

Handwriting is an important modality for Human-Computer Interaction. For medical professionals, handwriting is (still) the preferred natural method of documentation. Handwriting recognition has long been a primary research area in Computer Science. With the tremendous ubiquity of smartphones, along with the renaissance of [...] Read more.

Handwriting is an important modality for Human-Computer Interaction. For medical professionals, handwriting is (still) the preferred natural method of documentation. Handwriting recognition has long been a primary research area in Computer Science. With the tremendous ubiquity of smartphones, along with the renaissance of the stylus, handwriting recognition has become a new impetus. However, recognition rates are still not 100% perfect, and researchers still are constantly improving handwriting algorithms. In this paper we evaluate the performance of entropy based slant- and skew-correction, and compare the results to other methods. We selected 3700 words of 23 writers out of the Unipen-ICROW-03 benchmark set, which we annotated with their associated error angles by hand. Our results show that the entropy-based slant correction method outperforms a window based approach with an average precision of ±6.02° for the entropy-based method, compared with the ±7.85° for the alternative. On the other hand, the entropy-based skew correction yields a lower average precision of ±2:86°, compared with the average precision of ±2.13° for the alternative LSM based approach. Full article

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228 KiB

Open AccessArticle

On the Smoothed Minimum Error Entropy Criterion

by Badong Chen and Jose C. Principe

Entropy 2012, 14(11), 2311-2323; https://doi.org/10.3390/e14112311 - 12 Nov 2012

Cited by 18 | Viewed by 6093

Abstract

Recent studies suggest that the minimum error entropy (MEE) criterion can outperform the traditional mean square error criterion in supervised machine learning, especially in nonlinear and non-Gaussian situations. In practice, however, one has to estimate the error entropy from the samples since in [...] Read more.

Recent studies suggest that the minimum error entropy (MEE) criterion can outperform the traditional mean square error criterion in supervised machine learning, especially in nonlinear and non-Gaussian situations. In practice, however, one has to estimate the error entropy from the samples since in general the analytical evaluation of error entropy is not possible. By the Parzen windowing approach, the estimated error entropy converges asymptotically to the entropy of the error plus an independent random variable whose probability density function (PDF) corresponds to the kernel function in the Parzen method. This quantity of entropy is called the smoothed error entropy, and the corresponding optimality criterion is named the smoothed MEE (SMEE) criterion. In this paper, we study theoretically the SMEE criterion in supervised machine learning where the learning machine is assumed to be nonparametric and universal. Some basic properties are presented. In particular, we show that when the smoothing factor is very small, the smoothed error entropy equals approximately the true error entropy plus a scaled version of the Fisher information of error. We also investigate how the smoothing factor affects the optimal solution. In some special situations, the optimal solution under the SMEE criterion does not change with increasing smoothing factor. In general cases, when the smoothing factor tends to infinity, minimizing the smoothed error entropy will be approximately equivalent to minimizing error variance, regardless of the conditional PDF and the kernel. Full article

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193 KiB

Open AccessArticle

Viscosity in Modified Gravity

by Iver Brevik

Entropy 2012, 14(11), 2302-2310; https://doi.org/10.3390/e14112302 - 12 Nov 2012

Cited by 15 | Viewed by 5213

Abstract

A bulk viscosity is introduced in the formalism of modified gravity. It is shownthat, based on a natural scaling law for the viscosity, a simple solution can be found forquantities such as the Hubble parameter and the energy density. These solutions mayincorporate a [...] Read more.

A bulk viscosity is introduced in the formalism of modified gravity. It is shownthat, based on a natural scaling law for the viscosity, a simple solution can be found forquantities such as the Hubble parameter and the energy density. These solutions mayincorporate a viscosity-induced Big Rip singularity. By introducing a phase transition inthe cosmic fluid, the future singularity can nevertheless in principle be avoided. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

205 KiB

Open AccessArticle

Violation of the Third Law of Black Hole Thermodynamics inHigher Curvature Gravity

by Takashi Torii

Entropy 2012, 14(11), 2291-2301; https://doi.org/10.3390/e14112291 - 12 Nov 2012

Cited by 4 | Viewed by 5358

Abstract

We examine the weak version of the third law of black hole thermodynamics inthe n-dimensional Einstein–Gauss–Bonnet system with a negative cosmological constant.To see whether the extreme black hole solution with zero temperature is formed, weinvestigate the motion of the thin shell that [...] Read more.

We examine the weak version of the third law of black hole thermodynamics inthe n-dimensional Einstein–Gauss–Bonnet system with a negative cosmological constant.To see whether the extreme black hole solution with zero temperature is formed, weinvestigate the motion of the thin shell that has the equal mass to the extreme black holein the background described by the non-GR branch solutions. The interior of the shell isempty. Our analysis using the generalized Israel's junction condition shows that the shellcan contract beyond a certain radius and the degenerate horizon is formed for same range ofparameters. Hence, this model can be a counterexample of the third law. Full article

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447 KiB

Open AccessReview

Is Cholesterol Sulfate Deficiency a Common Factor in Preeclampsia, Autism, and Pernicious Anemia?

by Stephanie Seneff, Robert M. Davidson and Jingjing Liu

Entropy 2012, 14(11), 2265-2290; https://doi.org/10.3390/e14112265 - 8 Nov 2012

Cited by 7 | Viewed by 16967

Abstract

In a recent paper, we proposed that a contributing factor in autism is a deficiency in cholesterol sulfate supply. In this paper, we investigate a link between preeclampsia and subsequent autism in the child, and we hypothesize that both conditions can be attributed [...] Read more.

In a recent paper, we proposed that a contributing factor in autism is a deficiency in cholesterol sulfate supply. In this paper, we investigate a link between preeclampsia and subsequent autism in the child, and we hypothesize that both conditions can be attributed to a severe depletion of cholesterol sulfate. Through studies on the Vaccine Adverse Event Reporting System (VAERS) database, we demonstrate a strong statistical relationship among the signs and symptoms associated with autism and those associated with preeclampsia, pernicious anemia, and serious adverse reactions to vaccines. We show that VAERS reports associated with symptoms typical of pernicious anemia produce both a set of symptoms that are highly correlated with preeclampsia and another set highly correlated with autism. We explain this observation via an argument that, in a severe reaction, the cascade of events subsequent to vaccination reflects a profuse production of nitric oxide (NO) and consequential destruction of both red blood cells (RBCs) and cobalamin. This may explain the diverse signs and symptoms associated with both preeclampsia and severe vaccine adverse reactions. We argue that excess NO synthesis, induced by the aluminum and antigen in vaccines, results in hemolysis of RBCs, which allows hemoglobin to scavenge the excess NO, converting it to nitrate. The NO is also scavenged by cobalamin, leading to its inactivation and contributing to subsequent pernicious anemia. Finally, we demonstrate that severe adverse reactions to vaccines can be associated with life-threatening conditions related to the heart and brain, as well as stillbirth, when the vaccine is administered to a woman in the third-trimester of pregnancy, as demonstrated by statistical analysis of the Gardasil records. Full article

(This article belongs to the Special Issue Biosemiotic Entropy: Disorder, Disease, and Mortality)

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203 KiB

Open AccessArticle

Statistical Information: A Bayesian Perspective

by Rafael B. Stern and Carlos A. de B. Pereira

Entropy 2012, 14(11), 2254-2264; https://doi.org/10.3390/e14112254 - 7 Nov 2012

Cited by 2 | Viewed by 6005

Abstract

We explore the meaning of information about quantities of interest. Our approach is divided in two scenarios: the analysis of observations and the planning of an experiment. First, we review the Sufficiency, Conditionality and Likelihood principles and how they relate to trivial experiments. [...] Read more.

We explore the meaning of information about quantities of interest. Our approach is divided in two scenarios: the analysis of observations and the planning of an experiment. First, we review the Sufficiency, Conditionality and Likelihood principles and how they relate to trivial experiments. Next, we review Blackwell Sufficiency and show that sampling without replacement is Blackwell Sufficient for sampling with replacement. Finally, we unify the two scenarios presenting an extension of the relationship between Blackwell Equivalence and the Likelihood Principle. Full article

441 KiB

Open AccessArticle

Empirical Data Confirm Autism Symptoms Related to Aluminum and Acetaminophen Exposure

by Stephanie Seneff, Robert M. Davidson and Jingjing Liu

Entropy 2012, 14(11), 2227-2253; https://doi.org/10.3390/e14112227 - 7 Nov 2012

Cited by 33 | Viewed by 143137

Abstract

Autism is a condition characterized by impaired cognitive and social skills, associated with compromised immune function. The incidence is alarmingly on the rise, and environmental factors are increasingly suspected to play a role. This paper investigates word frequency patterns in the U.S. CDC [...] Read more.

Autism is a condition characterized by impaired cognitive and social skills, associated with compromised immune function. The incidence is alarmingly on the rise, and environmental factors are increasingly suspected to play a role. This paper investigates word frequency patterns in the U.S. CDC Vaccine Adverse Events Reporting System (VAERS) database. Our results provide strong evidence supporting a link between autism and the aluminum in vaccines. A literature review showing toxicity of aluminum in human physiology offers further support. Mentions of autism in VAERS increased steadily at the end of the last century, during a period when mercury was being phased out, while aluminum adjuvant burden was being increased. Using standard log-likelihood ratio techniques, we identify several signs and symptoms that are significantly more prevalent in vaccine reports after 2000, including cellulitis, seizure, depression, fatigue, pain and death, which are also significantly associated with aluminum-containing vaccines. We propose that children with the autism diagnosis are especially vulnerable to toxic metals such as aluminum and mercury due to insufficient serum sulfate and glutathione. A strong correlation between autism and the MMR (Measles, Mumps, Rubella) vaccine is also observed, which may be partially explained via an increased sensitivity to acetaminophen administered to control fever. Full article

(This article belongs to the Special Issue Biosemiotic Entropy: Disorder, Disease, and Mortality)

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396 KiB

Open AccessArticle

Shannon’s Sampling Theorem for Bandlimited Signals and Their Hilbert Transform, Boas-Type Formulae for Higher Order Derivatives—The Aliasing Error Involved by Their Extensions from Bandlimited to Non-Bandlimited Signals

by Paul L. Butzer, Gerhard Schmeisser and Rudolf L. Stens

Entropy 2012, 14(11), 2192-2226; https://doi.org/10.3390/e14112192 - 5 Nov 2012

Cited by 29 | Viewed by 8651

Abstract

The paper is concerned with Shannon sampling reconstruction formulae of derivatives of bandlimited signals as well as of derivatives of their Hilbert transform, and their application to Boas-type formulae for higher order derivatives. The essential aim is to extend these results to non-bandlimited [...] Read more.

The paper is concerned with Shannon sampling reconstruction formulae of derivatives of bandlimited signals as well as of derivatives of their Hilbert transform, and their application to Boas-type formulae for higher order derivatives. The essential aim is to extend these results to non-bandlimited signals. Basic is the fact that by these extensions aliasing error terms must now be added to the bandlimited reconstruction formulae. These errors will be estimated in terms of the distance functional just introduced by the authors for the extensions of basic relations valid for bandlimited functions to larger function spaces. This approach can be regarded as a mathematical foundation of aliasing error analysis of many applications. Full article

(This article belongs to the Special Issue Information Theory Applied to Communications and Networking)

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316 KiB

Open AccessArticle

Life as Thermodynamic Evidence of Algorithmic Structure in Natural Environments

by Hector Zenil, Carlos Gershenson, James A. R. Marshall and David A. Rosenblueth

Entropy 2012, 14(11), 2173-2191; https://doi.org/10.3390/e14112173 - 5 Nov 2012

Cited by 19 | Viewed by 25526

Abstract

In evolutionary biology, attention to the relationship between stochastic organisms and their stochastic environments has leaned towards the adaptability and learning capabilities of the organisms rather than toward the properties of the environment. This article is devoted to the algorithmic aspects of the [...] Read more.

In evolutionary biology, attention to the relationship between stochastic organisms and their stochastic environments has leaned towards the adaptability and learning capabilities of the organisms rather than toward the properties of the environment. This article is devoted to the algorithmic aspects of the environment and its interaction with living organisms. We ask whether one may use the fact of the existence of life to establish how far nature is removed from algorithmic randomness. The paper uses a novel approach to behavioral evolutionary questions, using tools drawn from information theory, algorithmic complexity and the thermodynamics of computation to support an intuitive assumption about the near optimal structure of a physical environment that would prove conducive to the evolution and survival of organisms, and sketches the potential of these tools, at present alien to biology, that could be used in the future to address different and deeper questions. We contribute to the discussion of the algorithmic structure of natural environments and provide statistical and computational arguments for the intuitive claim that living systems would not be able to survive in completely unpredictable environments, even if adaptable and equipped with storage and learning capabilities by natural selection (brain memory or DNA). Full article

(This article belongs to the Special Issue Selected Papers from Symposium on Natural/Unconventional Computing and Its Philosophical Significance)

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437 KiB

Open AccessArticle

Multivariate Multiscale Entropy Applied to Center of Pressure Signals Analysis: An Effect of Vibration Stimulation of Shoes

by Qin Wei, Dong-Hai Liu, Kai-Hong Wang, Quan Liu, Maysam F. Abbod, Bernard C. Jiang, Ku-Ping Chen, Chuan Wu and Jiann-Shing Shieh

Entropy 2012, 14(11), 2157-2172; https://doi.org/10.3390/e14112157 - 2 Nov 2012

Cited by 40 | Viewed by 8968

Abstract

Falls are unpredictable accidents and resulting injuries can be serious to the elderly. A preventative solution can be the use of vibration stimulus of white noise to improve the sense of balance. In this work, a pair of vibration shoes were developed and [...] Read more.

Falls are unpredictable accidents and resulting injuries can be serious to the elderly. A preventative solution can be the use of vibration stimulus of white noise to improve the sense of balance. In this work, a pair of vibration shoes were developed and controlled by a touch-type switch which can generate mechanical vibration noise to stimulate the patient’s feet while wearing the shoes. In order to evaluate the balance stability and treatment effect of vibrating insoles in these shoes, multivariate multiscale entropy (MMSE) algorithm is applied to calculate the relative complexity index of reconstructed center of pressure (COP) signals in antero-posterior and medio-lateral directions by the multivariate empirical mode decomposition (MEMD). The results show that the balance stability of 61.5% elderly subjects is improved after wearing the developed shoes, which is more than 30.8% using multiscale entropy. In conclusion, MEMD-enhanced MMSE is able to distinguish the smaller differences between before and after the use of vibration shoes in both two directions, which is more powerful than the empirical mode decomposition (EMD)-enhanced MSE in each individual direction. Full article

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201 KiB

Open AccessArticle

Dark Energy Problem, Physics of Early Universe and Some New Approaches in Gravity

by Alexander Shalyt-Margolin

Entropy 2012, 14(11), 2143-2156; https://doi.org/10.3390/e14112143 - 2 Nov 2012

Cited by 2 | Viewed by 5588

Abstract

The dark energy problem is studied based on the approach associated with the cosmological term in General Relativity that is considered as a dynamic quantity. It is shown that a quantum field theory of the Early Universe (Planck scales) and its limiting transition [...] Read more.

The dark energy problem is studied based on the approach associated with the cosmological term in General Relativity that is considered as a dynamic quantity. It is shown that a quantum field theory of the Early Universe (Planck scales) and its limiting transition at low energy play a significant role. Connection of this problem with Verlinde’s new (entropic) approach to gravity is revealed within the frame of such statement as well as the Generalized Uncertainty Principle (GUP) and Extended Uncertainty Principle (EUP). The implications from the obtained results are presented, and a more rigorous statement of the Concordance Problem in cosmology is treated. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)

352 KiB

Open AccessArticle

Optimization of MIMO Systems Capacity Using Large Random Matrix Methods

by Florian Dupuy and Philippe Loubaton

Entropy 2012, 14(11), 2122-2142; https://doi.org/10.3390/e14112122 - 1 Nov 2012

Viewed by 6456

Abstract

This paper provides a comprehensive introduction of large random matrix methods for input covariance matrix optimization of mutual information of MIMO systems. It is first recalled informally how large system approximations of mutual information can be derived. Then, the optimization of the approximations [...] Read more.

This paper provides a comprehensive introduction of large random matrix methods for input covariance matrix optimization of mutual information of MIMO systems. It is first recalled informally how large system approximations of mutual information can be derived. Then, the optimization of the approximations is discussed, and important methodological points that are not necessarily covered by the existing literature are addressed, including the strict concavity of the approximation, the structure of the argument of its maximum, the accuracy of the large system approach with regard to the number of antennas, or the justification of iterative water-filling optimization algorithms. While the existing papers have developed methods adapted to a specific model, this contribution tries to provide a unified view of the large system approximation approach. Full article

(This article belongs to the Special Issue Information Theory Applied to Communications and Networking)

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434 KiB

Open AccessArticle

A Free Energy Principle for Biological Systems

by Friston Karl

Entropy 2012, 14(11), 2100-2121; https://doi.org/10.3390/e14112100 - 31 Oct 2012

Cited by 231 | Viewed by 23423

Abstract

This paper describes a free energy principle that tries to explain the ability of biological systems to resist a natural tendency to disorder. It appeals to circular causality of the sort found in synergetic formulations of self-organization (e.g., the slaving principle) and models [...] Read more.

This paper describes a free energy principle that tries to explain the ability of biological systems to resist a natural tendency to disorder. It appeals to circular causality of the sort found in synergetic formulations of self-organization (e.g., the slaving principle) and models of coupled dynamical systems, using nonlinear Fokker Planck equations. Here, circular causality is induced by separating the states of a random dynamical system into external and internal states, where external states are subject to random fluctuations and internal states are not. This reduces the problem to finding some (deterministic) dynamics of the internal states that ensure the system visits a limited number of external states; in other words, the measure of its (random) attracting set, or the Shannon entropy of the external states is small. We motivate a solution using a principle of least action based on variational free energy (from statistical physics) and establish the conditions under which it is formally equivalent to the information bottleneck method. This approach has proved useful in understanding the functional architecture of the brain. The generality of variational free energy minimisation and corresponding information theoretic formulations may speak to interesting applications beyond the neurosciences; e.g., in molecular or evolutionary biology. Full article

(This article belongs to the Special Issue The Information Bottleneck Method)

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178 KiB

Open AccessArticle

Temperature Effects, Frieden–Hawkins’ Order-Measure, and Wehrl Entropy

by Flavia Pennini, Angelo Plastino and Gustavo L. Ferri

Entropy 2012, 14(11), 2081-2099; https://doi.org/10.3390/e14112081 - 26 Oct 2012

Cited by 5 | Viewed by 5445

Abstract

We revisit the Frieden–Hawkins’ Fisher order measure with a consideration of temperature effects. To this end, we appeal to the semiclassical approach. The order-measure’s appropriateness is validated in the semiclassical realm with regard to two physical systems. Insight is thereby gained with respect [...] Read more.

We revisit the Frieden–Hawkins’ Fisher order measure with a consideration of temperature effects. To this end, we appeal to the semiclassical approach. The order-measure’s appropriateness is validated in the semiclassical realm with regard to two physical systems. Insight is thereby gained with respect to the relationships amongst semiclassical quantifiers. In particular, it is seen that Wehrl’s entropy is as good a disorder indicator as the Frieden–Hawkins’ one. Full article

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194 KiB

Open AccessArticle

Unconventional Algorithms: Complementarity of Axiomatics and Construction

by Gordana Dodig Crnkovic and Mark Burgin

Entropy 2012, 14(11), 2066-2080; https://doi.org/10.3390/e14112066 - 25 Oct 2012

Cited by 4 | Viewed by 6909

Abstract

In this paper, we analyze axiomatic and constructive issues of unconventional computations from a methodological and philosophical point of view. We explain how the new models of algorithms and unconventional computations change the algorithmic universe, making it open and allowing increased flexibility and [...] Read more.

In this paper, we analyze axiomatic and constructive issues of unconventional computations from a methodological and philosophical point of view. We explain how the new models of algorithms and unconventional computations change the algorithmic universe, making it open and allowing increased flexibility and expressive power that augment creativity. At the same time, the greater power of new types of algorithms also results in the greater complexity of the algorithmic universe, transforming it into the algorithmic multiverse and demanding new tools for its study. That is why we analyze new powerful tools brought forth by local mathematics, local logics, logical varieties and the axiomatic theory of algorithms, automata and computation. We demonstrate how these new tools allow efficient navigation in the algorithmic multiverse. Further work includes study of natural computation by unconventional algorithms and constructive approaches. Full article

(This article belongs to the Special Issue Selected Papers from Symposium on Natural/Unconventional Computing and Its Philosophical Significance)

467 KiB

Open AccessReview

The Completed Self: An Immunological View of the Human-Microbiome Superorganism and Risk of Chronic Diseases

by Rodney Dietert and Janice Dietert

Entropy 2012, 14(11), 2036-2065; https://doi.org/10.3390/e14112036 - 25 Oct 2012

Cited by 21 | Viewed by 19792

Abstract

In this review, we discuss an immunological-driven sign termed the Completed Self, which is related to a holistic determination of health vs. disease. This sign (human plus commensal microbiota) forms the human superorganism. The worldwide emergence of an epidemic of chronic [...] Read more.

In this review, we discuss an immunological-driven sign termed the Completed Self, which is related to a holistic determination of health vs. disease. This sign (human plus commensal microbiota) forms the human superorganism. The worldwide emergence of an epidemic of chronic diseases has caused increased healthcare costs, increased premature mortality and reduced quality of life for a majority of the world’s population. In addition, it has raised questions concerning the interactions between humans and their environment and potential imbalances. Misregulated inflammation, a host defense-homeostasis disorder, appears to be a key biomarker connecting a majority of chronic diseases. We consider the apparent contributors to this disorder that promote a web of interlinked comorbid conditions. Three key events are suggested to play a role: (1) altered epigenetic programming (AEP) that may span multiple generations, (2) developmental immunotoxicity (DIT), and (3) failure to adequately incorporate commensal microbes as a newborn (i.e., the incomplete self). We discuss how these three events can combine to determine whether the human superorganism is able to adequately and completely form during early childhood. We also discuss how corruption of this event can affect the risk of later-life diseases. Full article

(This article belongs to the Special Issue Biosemiotic Entropy: Disorder, Disease, and Mortality)

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Entropy, Volume 14, Issue 11 (November 2012) – 17 articles , Pages 2036-2374

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