Role of Colored Cross-Correlation in Additive and Multiplicative White Noises on Upper Bound of Time Derivative of Information Entropy[PACS numbers: 02.50.Ey, 05.40.-a

Energy Technology Data Exchange (ETDEWEB)

Goswami, Gurupada; Majee, Pradip; Bag, Bidhan Chandra [Department of Chemistry, Visva-Bharati, Santiniketan 731 235 (India); Barik, Debashis [Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032 (India)

2006-09-15

In this paper we have studied upper bound of time derivative of information entropy for colored cross-correlated noise driven open systems. The upper bound is calculated based on the Fokker-Planck equation and the Schwartz inequality principle. Our results consider the effect of the noise correlation strength and correlation time due to the correlation between additive and multiplicative white noises on the upper bound as well as relaxation time. The interplay of deterministic and random forces reveals extremal nature of the upper bound and its deviation from the time derivative of information entropy. (author)

A Lower Bound on the Differential Entropy of Log-Concave Random Vectors with Applications

Directory of Open Access Journals (Sweden)

Arnaud Marsiglietti

2018-03-01

Full Text Available We derive a lower bound on the differential entropy of a log-concave random variable X in terms of the p-th absolute moment of X. The new bound leads to a reverse entropy power inequality with an explicit constant, and to new bounds on the rate-distortion function and the channel capacity. Specifically, we study the rate-distortion function for log-concave sources and distortion measure d ( x , x ^ = | x − x ^ | r , with r ≥ 1 , and we establish that the difference between the rate-distortion function and the Shannon lower bound is at most log ( π e ≈ 1 . 5 bits, independently of r and the target distortion d. For mean-square error distortion, the difference is at most log ( π e 2 ≈ 1 bit, regardless of d. We also provide bounds on the capacity of memoryless additive noise channels when the noise is log-concave. We show that the difference between the capacity of such channels and the capacity of the Gaussian channel with the same noise power is at most log ( π e 2 ≈ 1 bit. Our results generalize to the case of a random vector X with possibly dependent coordinates. Our proof technique leverages tools from convex geometry.

A Dynamic and Adaptive Selection Radar Tracking Method Based on Information Entropy

Directory of Open Access Journals (Sweden)

Ge Jianjun

2017-12-01

Full Text Available Nowadays, the battlefield environment has become much more complex and variable. This paper presents a quantitative method and lower bound for the amount of target information acquired from multiple radar observations to adaptively and dynamically organize the detection of battlefield resources based on the principle of information entropy. Furthermore, for minimizing the given information entropy’s lower bound for target measurement at every moment, a method to dynamically and adaptively select radars with a high amount of information for target tracking is proposed. The simulation results indicate that the proposed method has higher tracking accuracy than that of tracking without adaptive radar selection based on entropy.

Entropy bound and causality violation in higher curvature gravity

International Nuclear Information System (INIS)

Neupane, Ishwaree P; Dadhich, Naresh

2009-01-01

In any quantum theory of gravity we do expect corrections to Einstein gravity to occur. Yet, at a fundamental level, it is not apparent what the most relevant corrections are. We argue that the generic curvature square corrections present in the lower dimensional actions of various compactified string theories provide a natural passage between the classical and quantum realms of gravity. The Gauss-Bonnet and (Riemann) 2 gravities, in particular, provide concrete examples in which inconsistency of a theory, such as a violation of microcausality, and a classical limit on black hole entropy are correlated. In such theories the ratio of the shear viscosity to the entropy density, η/s, can be smaller than for a boundary conformal field theory with Einstein gravity dual. This result is interesting from the viewpoint that nuclear matter or quark-gluon plasma produced (such as at RHIC) under extreme densities and temperatures may violate the conjectured KSS bound η/s ≥ 1/4π, albeit marginally so.

The optimal entropy bound and the self-energy of test objects in the vicinity of a black hole

OpenAIRE

Mayo, Avraham E.

1999-01-01

Recently Bekenstein and Mayo conjectured an entropy bound for charged rotating objects. On the basis of the No-Hair principle for black holes, they speculate that this bound cannot be improved generically based on knowledge of other ``quantum numbers'', e.g. baryon number, which may be borne by the object. Here we take a first step in the proof of this conjecture. The proof make use of a gedanken experiment in which a massive object endowed with a scalar charge is lowered adiabatically toward...

An Entropy-Based Upper Bound Methodology for Robust Predictive Multi-Mode RCPSP Schedules

Directory of Open Access Journals (Sweden)

Angela Hsiang-Ling Chen

2014-09-01

Full Text Available Projects are an important part of our activities and regardless of their magnitude, scheduling is at the very core of every project. In an ideal world makespan minimization, which is the most commonly sought objective, would give us an advantage. However, every time we execute a project we have to deal with uncertainty; part of it coming from known sources and part remaining unknown until it affects us. For this reason, it is much more practical to focus on making our schedules robust, capable of handling uncertainty, and even to determine a range in which the project could be completed. In this paper we focus on an approach to determine such a range for the Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP, a widely researched, NP-complete problem, but without adding any subjective considerations to its estimation. We do this by using a concept well known in the domain of thermodynamics, entropy and a three-stage approach. First we use Artificial Bee Colony (ABC—an effective and powerful meta-heuristic—to determine a schedule with minimized makespan which serves as a lower bound. The second stage defines buffer times and creates an upper bound makespan using an entropy function, with the advantage over other methods that it only considers elements which are inherent to the schedule itself and does not introduce any subjectivity to the buffer time generation. In the last stage, we use the ABC algorithm with an objective function that seeks to maximize robustness while staying within the makespan boundaries defined previously and in some cases even below the lower boundary. We evaluate our approach with two different benchmarks sets: when using the PSPLIB for the MRCPSP benchmark set, the computational results indicate that it is possible to generate robust schedules which generally result in an increase of less than 10% of the best known solutions while increasing the robustness in at least 20% for practically every

Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations.

Science.gov (United States)

Fogolari, Federico; Corazza, Alessandra; Fortuna, Sara; Soler, Miguel Angel; VanSchouwen, Bryan; Brancolini, Giorgia; Corni, Stefano; Melacini, Giuseppe; Esposito, Gennaro

2015-01-01

Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes. In particular: reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements;the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state;backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy);the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic.

Entropy bound of horizons for accelerating, rotating and charged Plebanski–Demianski black hole

International Nuclear Information System (INIS)

Debnath, Ujjal

2016-01-01

We first review the accelerating, rotating and charged Plebanski–Demianski (PD) black hole, which includes the Kerr–Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sums are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou–Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.

Entropy bound of horizons for accelerating, rotating and charged Plebanski–Demianski black hole

Energy Technology Data Exchange (ETDEWEB)

Debnath, Ujjal, E-mail: ujjaldebnath@yahoo.com

2016-09-15

We first review the accelerating, rotating and charged Plebanski–Demianski (PD) black hole, which includes the Kerr–Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sums are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou–Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.

Universal bounds on current fluctuations.

Science.gov (United States)

Pietzonka, Patrick; Barato, Andre C; Seifert, Udo

2016-05-01

For current fluctuations in nonequilibrium steady states of Markovian processes, we derive four different universal bounds valid beyond the Gaussian regime. Different variants of these bounds apply to either the entropy change or any individual current, e.g., the rate of substrate consumption in a chemical reaction or the electron current in an electronic device. The bounds vary with respect to their degree of universality and tightness. A universal parabolic bound on the generating function of an arbitrary current depends solely on the average entropy production. A second, stronger bound requires knowledge both of the thermodynamic forces that drive the system and of the topology of the network of states. These two bounds are conjectures based on extensive numerics. An exponential bound that depends only on the average entropy production and the average number of transitions per time is rigorously proved. This bound has no obvious relation to the parabolic bound but it is typically tighter further away from equilibrium. An asymptotic bound that depends on the specific transition rates and becomes tight for large fluctuations is also derived. This bound allows for the prediction of the asymptotic growth of the generating function. Even though our results are restricted to networks with a finite number of states, we show that the parabolic bound is also valid for three paradigmatic examples of driven diffusive systems for which the generating function can be calculated using the additivity principle. Our bounds provide a general class of constraints for nonequilibrium systems.

Large Field Inflation and Gravitational Entropy

DEFF Research Database (Denmark)

Kaloper, Nemanja; Kleban, Matthew; Lawrence, Albion

2016-01-01

species will lead to a violation of the covariant entropy bound at large $N$. If so, requiring the validity of the covariant entropy bound could limit the number of light species and their couplings, which in turn could severely constrain axion-driven inflation. Here we show that there is no such problem...... entropy of de Sitter or near-de Sitter backgrounds at leading order. Working in detail with $N$ scalar fields in de Sitter space, renormalized to one loop order, we show that the gravitational entropy automatically obeys the covariant entropy bound. Furthermore, while the axion decay constant is a strong...... in this light, and show that they are perfectly consistent with the covariant entropy bound. Thus, while quantum gravity might yet spoil large field inflation, holographic considerations in the semiclassical theory do not obstruct it....

Entropy Production of Stars

Directory of Open Access Journals (Sweden)

Leonid M. Martyushev

2015-06-01

Full Text Available The entropy production (inside the volume bounded by a photosphere of main-sequence stars, subgiants, giants, and supergiants is calculated based on B–V photometry data. A non-linear inverse relationship of thermodynamic fluxes and forces as well as an almost constant specific (per volume entropy production of main-sequence stars (for 95% of stars, this quantity lies within 0.5 to 2.2 of the corresponding solar magnitude is found. The obtained results are discussed from the perspective of known extreme principles related to entropy production.

Optimization and large scale computation of an entropy-based moment closure

Science.gov (United States)

Kristopher Garrett, C.; Hauck, Cory; Hill, Judith

2015-12-01

We present computational advances and results in the implementation of an entropy-based moment closure, MN, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as PN, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. These results show, in particular, load balancing issues in scaling the MN algorithm that do not appear for the PN algorithm. We also observe that in weak scaling tests, the ratio in time to solution of MN to PN decreases.

Effect of time delay on the upper bound of the time derivative of information entropy in a stochastic dynamical system

International Nuclear Information System (INIS)

Zhang Min-Min; Mei Dong-Cheng; Wang Can-Jun

2011-01-01

The effects of the time delay on the upper bound of the time derivative of information entropy are investigated in a time-delayed dynamical system driven by correlated noise. Using the Markov approximation of the stochastic delay differential equations and the Schwartz inequality principle, we obtain an analytical expression for the upper bound U B (t) of the time derivative of the information entropy. The results show that there is a critical value of τ (delay time), and U B (t) presents opposite behaviours on difference sides of the critical value. For the case of the weak additive noise, τ can induce a reentrance transition. Delay time τ also causes a reversal behaviour in U B (t)-λ plot, where λ denotes the degree of the correlation between the two noises. (general)

Coherent Behavior and the Bound State of Water and K(+) Imply Another Model of Bioenergetics: Negative Entropy Instead of High-energy Bonds.

Science.gov (United States)

Jaeken, Laurent; Vasilievich Matveev, Vladimir

2012-01-01

Observations of coherent cellular behavior cannot be integrated into widely accepted membrane (pump) theory (MT) and its steady state energetics because of the thermal noise of assumed ordinary cell water and freely soluble cytoplasmic K(+). However, Ling disproved MT and proposed an alternative based on coherence, showing that rest (R) and action (A) are two different phases of protoplasm with different energy levels. The R-state is a coherent metastable low-entropy state as water and K(+) are bound to unfolded proteins. The A-state is the higher-entropy state because water and K(+) are free. The R-to-A phase transition is regarded as a mechanism to release energy for biological work, replacing the classical concept of high-energy bonds. Subsequent inactivation during the endergonic A-to-R phase transition needs an input of metabolic energy to restore the low entropy R-state. Matveev's native aggregation hypothesis allows to integrate the energetic details of globular proteins into this view.

Quantum aspects of black hole entropy

Indian Academy of Sciences (India)

Quantum corrections to the semiclassical Bekenstein–Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramification for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black ...

A Note on the W-S Lower Bound of the MEE Estimation

Directory of Open Access Journals (Sweden)

Badong Chen

2014-02-01

Full Text Available The minimum error entropy (MEE estimation is concerned with the estimation of a certain random variable (unknown variable based on another random variable (observation, so that the entropy of the estimation error is minimized. This estimation method may outperform the well-known minimum mean square error (MMSE estimation especially for non-Gaussian situations. There is an important performance bound on the MEE estimation, namely the W-S lower bound, which is computed as the conditional entropy of the unknown variable given observation. Though it has been known in the literature for a considerable time, up to now there is little study on this performance bound. In this paper, we reexamine the W-S lower bound. Some basic properties of the W-S lower bound are presented, and the characterization of Gaussian distribution using the W-S lower bound is investigated.

On the Conditional Entropy of Wireless Networks

DEFF Research Database (Denmark)

Coon, Justin P.; Badiu, Mihai Alin; Gündüz, Deniz

2018-01-01

The characterization of topological uncertainty in wireless networks using the formalism of graph entropy has received interest in the spatial networks community. In this paper, we develop lower bounds on the entropy of a wireless network by conditioning on potential network observables. Two...... approaches are considered: 1) conditioning on subgraphs, and 2) conditioning on node positions. The first approach is shown to yield a relatively tight bound on the network entropy. The second yields a loose bound, in general, but it provides insight into the dependence between node positions (modelled using...

Statistical properties of entropy production derived from fluctuation theorems

International Nuclear Information System (INIS)

Merhav, Neri; Kafri, Yariv

2010-01-01

Several implications of well-known fluctuation theorems, on the statistical properties of entropy production, are studied using various approaches. We begin by deriving a tight lower bound on the variance of the entropy production for a given mean of this random variable. It is shown that the Evans–Searles fluctuation theorem alone imposes a significant lower bound on the variance only when the mean entropy production is very small. It is then nonetheless demonstrated that upon incorporating additional information concerning the entropy production, this lower bound can be significantly improved, so as to capture extensivity properties. Another important aspect of the fluctuation properties of the entropy production is the relationship between the mean and the variance, on the one hand, and the probability of the event where the entropy production is negative, on the other hand. Accordingly, we derive upper and lower bounds on this probability in terms of the mean and the variance. These bounds are tighter than previous bounds that can be found in the literature. Moreover, they are tight in the sense that there exist probability distributions, satisfying the Evans–Searles fluctuation theorem, that achieve them with equality. Finally, we present a general method for generating a wide class of inequalities that must be satisfied by the entropy production. We use this method to derive several new inequalities that go beyond the standard derivation of the second law

Combinatorial Image Entropy

DEFF Research Database (Denmark)

Yuri, Shtarkov; Justesen, Jørn

1997-01-01

The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions.......The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions....

Bound on viscosity and the generalized second law of thermodynamics

International Nuclear Information System (INIS)

Fouxon, Itzhak; Betschart, Gerold; Bekenstein, Jacob D.

2008-01-01

We describe a new paradox for ideal fluids. It arises in the accretion of an ideal fluid onto a black hole, where, under suitable boundary conditions, the flow can violate the generalized second law of thermodynamics. The paradox indicates that there is in fact a lower bound to the correlation length of any real fluid, the value of which is determined by the thermodynamic properties of that fluid. We observe that the universal bound on entropy, itself suggested by the generalized second law, puts a lower bound on the correlation length of any fluid in terms of its specific entropy. With the help of a new, efficient estimate for the viscosity of liquids, we argue that this also means that viscosity is bounded from below in a way reminiscent of the conjectured Kovtun-Son-Starinets lower bound on the ratio of viscosity to entropy density. We conclude that much light may be shed on the Kovtun-Son-Starinets bound by suitable arguments based on the generalized second law

Preimage entropy dimension of topological dynamical systems

OpenAIRE

Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao

2014-01-01

We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated system...

High Entropy Random Selection Protocols

NARCIS (Netherlands)

H. Buhrman (Harry); M. Christandl (Matthias); M. Koucky (Michal); Z. Lotker (Zvi); B. Patt-Shamir; M. Charikar; K. Jansen; O. Reingold; J. Rolim

2007-01-01

textabstractIn this paper, we construct protocols for two parties that do not trust each other, to generate random variables with high Shannon entropy. We improve known bounds for the trade off between the number of rounds, length of communication and the entropy of the outcome.

Black hole entropy, curved space and monsters

International Nuclear Information System (INIS)

Hsu, Stephen D.H.; Reeb, David

2008-01-01

We investigate the microscopic origin of black hole entropy, in particular the gap between the maximum entropy of ordinary matter and that of black holes. Using curved space, we construct configurations with entropy greater than the area A of a black hole of equal mass. These configurations have pathological properties and we refer to them as monsters. When monsters are excluded we recover the entropy bound on ordinary matter S 3/4 . This bound implies that essentially all of the microstates of a semiclassical black hole are associated with the growth of a slightly smaller black hole which absorbs some additional energy. Our results suggest that the area entropy of black holes is the logarithm of the number of distinct ways in which one can form the black hole from ordinary matter and smaller black holes, but only after the exclusion of monster states

Infinite Shannon entropy

International Nuclear Information System (INIS)

Baccetti, Valentina; Visser, Matt

2013-01-01

Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context. (paper)

Maximum entropy production rate in quantum thermodynamics

Energy Technology Data Exchange (ETDEWEB)

Beretta, Gian Paolo, E-mail: beretta@ing.unibs.i [Universita di Brescia, via Branze 38, 25123 Brescia (Italy)

2010-06-01

, well-behaved and intriguing, general closure of the dynamics, compatible with the nontrivial requirements of strong separability. Based on the time-energy Heisenberg uncertainty relation, we derive a lower bound to the internal-relaxation-time functionals that determine the rate of entropy generation. This bound entails an upper bound to the rate of entropy generation. By this extreme maximal-entropy-generation-rate ansatz, each indivisible subsystem follows the direction of steepest locally perceived entropy ascent at the highest rate compatible with the time- energy uncertainty principle.

Entropic Lower Bound for Distinguishability of Quantum States

Directory of Open Access Journals (Sweden)

Seungho Yang

2015-01-01

Full Text Available For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are all pure, acquiring the entropic lower bound requires only the density operator and the number of the possible states. This entropic bound shows a relation between the von Neumann entropy and the distinguishability.

The holographic entropy cone

Energy Technology Data Exchange (ETDEWEB)

Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology,Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Nezami, Sepehr [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Ooguri, Hirosi [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa 277-8583 (Japan); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Sully, James [Theory Group, SLAC National Accelerator Laboratory, Stanford University,Menlo Park, CA 94025 (United States); Walter, Michael [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)

2015-09-21

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

The holographic entropy cone

International Nuclear Information System (INIS)

Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael

2015-01-01

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices

Science.gov (United States)

Huang, Feimin; Li, Tianhong; Yu, Huimin; Yuan, Difan

2018-06-01

We are concerned with the global existence and large time behavior of entropy solutions to the one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations in a bounded interval. In this paper, we first prove the global existence of entropy solution by vanishing viscosity and compensated compactness framework. In particular, the solutions are uniformly bounded with respect to space and time variables by introducing modified Riemann invariants and the theory of invariant region. Based on the uniform estimates of density, we further show that the entropy solution converges to the corresponding unique stationary solution exponentially in time. No any smallness condition is assumed on the initial data and doping profile. Moreover, the novelty in this paper is about the unform bound with respect to time for the weak solutions of the isentropic Euler-Poisson system.

Relative entropy of steering: on its definition and properties

International Nuclear Information System (INIS)

Kaur, Eneet; Wilde, Mark M

2017-01-01

In Gallego and Aolita (2015 Phys. Rev . X 5 041008), the authors proposed a definition for the relative entropy of steering and showed that the resulting quantity is a convex steering monotone. Here we advocate for a different definition for relative entropy of steering, based on well grounded concerns coming from quantum Shannon theory. We prove that this modified relative entropy of steering is a convex steering monotone. Furthermore, we establish that it is uniformly continuous and faithful, in both cases giving quantitative bounds that should be useful in applications. We also consider a restricted relative entropy of steering which is relevant for the case in which the free operations in the resource theory of steering have a more restricted form (the restricted operations could be more relevant in practical scenarios). The restricted relative entropy of steering is convex, monotone with respect to these restricted operations, uniformly continuous, and faithful. (paper)

Shannon's information is not entropy

International Nuclear Information System (INIS)

Schiffer, M.

1990-01-01

In this letter we clear up the long-standing misidentification of Shannon's Information with Entropy. We show that Information, in contrast to Entropy, is not invariant under unitary transformations and that these quantities are only equivalent for representations consisting of Hamiltonian eigenstates. We illustrate this fact through a toy system consisting of a harmonic oscillator in a coherent state. It is further proved that the representations which maximize the information are those which are energy-eigenstates. This fact sets the entropy as an upper bound for Shannon's Information. (author)

Bounds on the Capacity of Weakly constrained two-dimensional Codes

DEFF Research Database (Denmark)

Forchhammer, Søren

2002-01-01

Upper and lower bounds are presented for the capacity of weakly constrained two-dimensional codes. The maximum entropy is calculated for two simple models of 2-D codes constraining the probability of neighboring 1s as an example. For given models of the coded data, upper and lower bounds...... on the capacity for 2-D channel models based on occurrences of neighboring 1s are considered....

Autonomous entropy-based intelligent experimental design

Science.gov (United States)

Malakar, Nabin Kumar

2011-07-01

The aim of this thesis is to explore the application of probability and information theory in experimental design, and to do so in a way that combines what we know about inference and inquiry in a comprehensive and consistent manner. Present day scientific frontiers involve data collection at an ever-increasing rate. This requires that we find a way to collect the most relevant data in an automated fashion. By following the logic of the scientific method, we couple an inference engine with an inquiry engine to automate the iterative process of scientific learning. The inference engine involves Bayesian machine learning techniques to estimate model parameters based upon both prior information and previously collected data, while the inquiry engine implements data-driven exploration. By choosing an experiment whose distribution of expected results has the maximum entropy, the inquiry engine selects the experiment that maximizes the expected information gain. The coupled inference and inquiry engines constitute an autonomous learning method for scientific exploration. We apply it to a robotic arm to demonstrate the efficacy of the method. Optimizing inquiry involves searching for an experiment that promises, on average, to be maximally informative. If the set of potential experiments is described by many parameters, the search involves a high-dimensional entropy space. In such cases, a brute force search method will be slow and computationally expensive. We develop an entropy-based search algorithm, called nested entropy sampling, to select the most informative experiment. This helps to reduce the number of computations necessary to find the optimal experiment. We also extended the method of maximizing entropy, and developed a method of maximizing joint entropy so that it could be used as a principle of collaboration between two robots. This is a major achievement of this thesis, as it allows the information-based collaboration between two robotic units towards a same

Entropy Stability and the No-Slip Wall Boundary Condition

KAUST Repository

Svä rd, Magnus; Carpenter, Mark H.; Parsani, Matteo

2018-01-01

We present an entropy stable numerical scheme subject to no-slip wall boundary conditions. To enforce entropy stability only the no-penetration boundary condition and a temperature condition are needed at a wall, and this leads to an L bound on the conservative variables. In this article, we take the next step and design a finite difference scheme that also bounds the velocity gradients. This necessitates the use of the full no-slip conditions.

Entropy Stability and the No-Slip Wall Boundary Condition

KAUST Repository

Svärd, Magnus

2018-01-18

We present an entropy stable numerical scheme subject to no-slip wall boundary conditions. To enforce entropy stability only the no-penetration boundary condition and a temperature condition are needed at a wall, and this leads to an L bound on the conservative variables. In this article, we take the next step and design a finite difference scheme that also bounds the velocity gradients. This necessitates the use of the full no-slip conditions.

Entropy Evaluation Based on Value Validity

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Tarald O. Kvålseth

2014-09-01

Full Text Available Besides its importance in statistical physics and information theory, the Boltzmann-Shannon entropy S has become one of the most widely used and misused summary measures of various attributes (characteristics in diverse fields of study. It has also been the subject of extensive and perhaps excessive generalizations. This paper introduces the concept and criteria for value validity as a means of determining if an entropy takes on values that reasonably reflect the attribute being measured and that permit different types of comparisons to be made for different probability distributions. While neither S nor its relative entropy equivalent S* meet the value-validity conditions, certain power functions of S and S* do to a considerable extent. No parametric generalization offers any advantage over S in this regard. A measure based on Euclidean distances between probability distributions is introduced as a potential entropy that does comply fully with the value-validity requirements and its statistical inference procedure is discussed.

Multiscale sample entropy and cross-sample entropy based on symbolic representation and similarity of stock markets

Science.gov (United States)

Wu, Yue; Shang, Pengjian; Li, Yilong

2018-03-01

A modified multiscale sample entropy measure based on symbolic representation and similarity (MSEBSS) is proposed in this paper to research the complexity of stock markets. The modified algorithm reduces the probability of inducing undefined entropies and is confirmed to be robust to strong noise. Considering the validity and accuracy, MSEBSS is more reliable than Multiscale entropy (MSE) for time series mingled with much noise like financial time series. We apply MSEBSS to financial markets and results show American stock markets have the lowest complexity compared with European and Asian markets. There are exceptions to the regularity that stock markets show a decreasing complexity over the time scale, indicating a periodicity at certain scales. Based on MSEBSS, we introduce the modified multiscale cross-sample entropy measure based on symbolic representation and similarity (MCSEBSS) to consider the degree of the asynchrony between distinct time series. Stock markets from the same area have higher synchrony than those from different areas. And for stock markets having relative high synchrony, the entropy values will decrease with the increasing scale factor. While for stock markets having high asynchrony, the entropy values will not decrease with the increasing scale factor sometimes they tend to increase. So both MSEBSS and MCSEBSS are able to distinguish stock markets of different areas, and they are more helpful if used together for studying other features of financial time series.

Entropy of Bit-Stuffing-Induced Measures for Two-Dimensional Checkerboard Constraints

DEFF Research Database (Denmark)

Forchhammer, Søren; Vaarby, Torben Strange

2007-01-01

A modified bit-stuffing scheme for two-dimensional (2-D) checkerboard constraints is introduced. The entropy of the scheme is determined based on a probability measure defined by the modified bit-stuffing. Entropy results of the scheme are given for 2-D constraints on a binary alphabet....... The constraints considered are 2-D RLL (d, infinity) for d = 2, 3 and 4 as well as for the constraint with a minimum 1-norm distance of 3 between Is. For these results the entropy is within 1-2% of an upper bound on the capacity for the constraint. As a variation of the scheme, periodic merging arrays are also...

Entropy of localized states and black hole evaporation

International Nuclear Information System (INIS)

Olum, K.D.

1997-01-01

We call a state 'vacuum bounded' if every measurement performed outside a specified interior region gives the same result as in the vacuum. We compute the maximum entropy of a vacuum-bounded state with a given energy for a one-dimensional model, with the aid of numerical calculations on a lattice. The maximum entropy is larger than it would be for rigid wall boundary conditions by an amount δS, which for large energies is approx-lt(1)/(6)ln(L in T), where L in is the length of the interior region. Assuming that the state resulting from the evaporation of a black hole is similar to a vacuum-bounded state, and that the similarity between vacuum-bounded and rigid-wall-bounded problems extends from 1 to 3 dimensions, we apply these results to the black hole information paradox. Under these assumptions we conclude that large amounts of information cannot be emitted in the final explosion of a black hole. copyright 1997 The American Physical Society

Entropy production of stationary diffusions on non-compact Riemannian manifolds

Institute of Scientific and Technical Information of China (English)

龚光鲁; 钱敏平

1997-01-01

The closed form of the entropy production of stationary diffusion processes with bounded Nelson’s current velocity is given.The limit of the entropy productions of a sequence of reflecting diffusions is also discussed.

Topological entropy of continuous functions on topological spaces

International Nuclear Information System (INIS)

Liu Lei; Wang Yangeng; Wei Guo

2009-01-01

Adler, Konheim and McAndrew introduced the concept of topological entropy of a continuous mapping for compact dynamical systems. Bowen generalized the concept to non-compact metric spaces, but Walters indicated that Bowen's entropy is metric-dependent. We propose a new definition of topological entropy for continuous mappings on arbitrary topological spaces (compactness, metrizability, even axioms of separation not necessarily required), investigate fundamental properties of the new entropy, and compare the new entropy with the existing ones. The defined entropy generates that of Adler, Konheim and McAndrew and is metric-independent for metrizable spaces. Yet, it holds various basic properties of Adler, Konheim and McAndrew's entropy, e.g., the entropy of a subsystem is bounded by that of the original system, topologically conjugated systems have a same entropy, the entropy of the induced hyperspace system is larger than or equal to that of the original system, and in particular this new entropy coincides with Adler, Konheim and McAndrew's entropy for compact systems

Entropy-based financial asset pricing.

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Mihály Ormos

Full Text Available We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.

Entropy-based financial asset pricing.

Science.gov (United States)

Ormos, Mihály; Zibriczky, Dávid

2014-01-01

We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.

On the Conditional Entropy of Wireless Networks

DEFF Research Database (Denmark)

Coon, Justin P.; Badiu, Mihai Alin; Gündüz, Deniz

2018-01-01

The characterization of topological uncertainty in wireless networks using the formalism of graph entropy has received interest in the spatial networks community. In this paper, we develop lower bounds on the entropy of a wireless network by conditioning on potential network observables. Two appr...... a homogeneous binomial point process in this work) and the network topology....

A simple method for estimating the entropy of neural activity

International Nuclear Information System (INIS)

Berry II, Michael J; Tkačik, Gašper; Dubuis, Julien; Marre, Olivier; Da Silveira, Rava Azeredo

2013-01-01

The number of possible activity patterns in a population of neurons grows exponentially with the size of the population. Typical experiments explore only a tiny fraction of the large space of possible activity patterns in the case of populations with more than 10 or 20 neurons. It is thus impossible, in this undersampled regime, to estimate the probabilities with which most of the activity patterns occur. As a result, the corresponding entropy—which is a measure of the computational power of the neural population—cannot be estimated directly. We propose a simple scheme for estimating the entropy in the undersampled regime, which bounds its value from both below and above. The lower bound is the usual ‘naive’ entropy of the experimental frequencies. The upper bound results from a hybrid approximation of the entropy which makes use of the naive estimate, a maximum entropy fit, and a coverage adjustment. We apply our simple scheme to artificial data, in order to check their accuracy; we also compare its performance to those of several previously defined entropy estimators. We then apply it to actual measurements of neural activity in populations with up to 100 cells. Finally, we discuss the similarities and differences between the proposed simple estimation scheme and various earlier methods. (paper)

Entropy-Based Algorithm for Supply-Chain Complexity Assessment

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Boris Kriheli

2018-03-01

Full Text Available This paper considers a graph model of hierarchical supply chains. The goal is to measure the complexity of links between different components of the chain, for instance, between the principal equipment manufacturer (a root node and its suppliers (preceding supply nodes. The information entropy is used to serve as a measure of knowledge about the complexity of shortages and pitfalls in relationship between the supply chain components under uncertainty. The concept of conditional (relative entropy is introduced which is a generalization of the conventional (non-relative entropy. An entropy-based algorithm providing efficient assessment of the supply chain complexity as a function of the SC size is developed.

Upper entropy axioms and lower entropy axioms

International Nuclear Information System (INIS)

Guo, Jin-Li; Suo, Qi

2015-01-01

The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak upper entropy axioms and weak lower entropy axioms. Their conditions are weaker than those of Shannon–Khinchin axioms and Tsallis axioms, while these conditions are stronger than those of the axiomatics based on the first three Shannon–Khinchin axioms. The subadditivity and strong subadditivity of entropy are obtained in the new axiomatics. Tsallis statistics is a special case of satisfying our axioms. Moreover, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics

Entropy-Based Clutter Rejection for Intrawall Diagnostics

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Raffaele Solimene

2012-01-01

Full Text Available The intrawall diagnostic problem of detecting localized inhomogeneities possibly present within the wall is addressed. As well known, clutter arising from masonry structure can impair detection of embedded scatterers due to high amplitude reflections that wall front face introduces. Moreover, internal multiple reflections also can make it difficult ground penetrating radar images (radargramms interpretation. To counteract these drawbacks, a clutter rejection method, properly tailored on the wall features, is mandatory. To this end, here we employ a windowing strategy based on entropy measures of temporal traces “similarity.” Accordingly, instants of time for which radargramms exhibit entropy values greater than a prescribed threshold are “silenced.” Numerical results are presented in order to show the effectiveness of the entropy-based clutter rejection algorithm. Moreover, a comparison with the standard average trace subtraction is also included.

Entropy of the Mixture of Sources and Entropy Dimension

OpenAIRE

Smieja, Marek; Tabor, Jacek

2011-01-01

We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based on measures instead of partitions.

Entropy of self-gravitating radiation

International Nuclear Information System (INIS)

Sorkin, R.D.; Wald, R.M.; Jiu, Z.Z.

1981-01-01

The entropy of self-gravitating radiation confined to a spherical box of radius R is examined in the context of general relativity. It is expected that configurations (i.e., initial data) which extremize total entropy will be spherically symmetric, time symmetric distributions of radiation in local thermodynamic equilibrium. Assuming this is the case, it is proved that extrema of S coincide precisely with static equilibrium configurations of the radiation fluid. Furthermore, dynamically stable equilibrium configurations are shown to coincide with local maxima of S. The equilibrium configurations and their entropies are calculated and their properties are discussed. However, it is shown that entropies higher than these local extrema can be achieved and, indeed, arbitrarily high entropies can be attained by configurations inside of or outside but arbitrarily near their own Schwarzschild radius. However, consideration is limited to configurations which are outside their own Schwarzschild radius by at least one radiation wavelength, then the entropy is bounded and it is found Ssub(max) < is approximately equal to MR, where M is the total mass. This supports the validity for self-gravitating systems of the Bekenstein upper limit on the entropy to energy ratio of material bodies. (author)

On the statistical-mechanical meaning of the Bousso bound

International Nuclear Information System (INIS)

Pesci, Alessandro

2008-01-01

The Bousso entropy bound, in its generalized form, is investigated for the case of perfect fluids at local thermodynamic equilibrium and evidence is found that the bound is satisfied if and only if a certain local thermodynamic property holds, emerging when the attempt is made to apply the bound to thin layers of matter. This property consists of the existence of an ultimate lower limit l* to the thickness of the slices for which a statistical-mechanical description is viable, depending l* on the thermodynamical variables which define the state of the system locally. This limiting scale, found to be in general much larger than the Planck scale (so that no Planck scale physics must be necessarily invoked to justify it), appears not related to gravity and this suggests that the generalized entropy bound is likely to be rooted on conventional flat-spacetime statistical mechanics, with the maximum admitted entropy being however actually determined also by gravity. Some examples of ideal fluids are considered in order to identify the mechanisms which can set a lower limit to the statistical-mechanical description and these systems are found to respect the lower limiting scale l*. The photon gas, in particular, appears to seemingly saturate this limiting scale and the consequence is drawn that for systems consisting of a single slice of a photon gas with thickness l*, the generalized Bousso bound is saturated. It is argued that this seems to open the way to a peculiar understanding of black hole entropy: if an entropy can meaningfully (i.e. with a second law) be assigned to a black hole, the value A/4 for it (where A is the area of the black hole) is required simply by (conventional) statistical mechanics coupled to general relativity

A holographic bound for D3-brane

Energy Technology Data Exchange (ETDEWEB)

Momeni, Davood; Myrzakul, Aizhan; Myrzakulov, Ratbay [Eurasian National University, Eurasian International Center for Theoretical Physics, Astana (Kazakhstan); Eurasian National University, Department of General Theoretical Physics, Astana (Kazakhstan); Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada); Bahamonde, Sebastian [University College London, Department of Mathematics, London (United Kingdom)

2017-06-15

In this paper, we will regularize the holographic entanglement entropy, holographic complexity and fidelity susceptibility for a configuration of D3-branes. We will also study the regularization of the holographic complexity from the action for a configuration of D3-branes. It will be demonstrated that for a spherical shell of D3-branes the regularized holographic complexity is always greater than or equal to the regularized fidelity susceptibility. Furthermore, we will also demonstrate that the regularized holographic complexity is related to the regularized holographic entanglement entropy for this system. Thus, we will obtain a holographic bound involving regularized holographic complexity, regularized holographic entanglement entropy and regularized fidelity susceptibility of a configuration of D3-brane. We will also discuss a bound for regularized holographic complexity from action, for a D3-brane configuration. (orig.)

Configurational entropy change of netropsin and distamycin upon DNA minor-groove binding.

Science.gov (United States)

Dolenc, Jozica; Baron, Riccardo; Oostenbrink, Chris; Koller, Joze; van Gunsteren, Wilfred F

2006-08-15

Binding of a small molecule to a macromolecular target reduces its conformational freedom, resulting in a negative entropy change that opposes the binding. The goal of this study is to estimate the configurational entropy change of two minor-groove-binding ligands, netropsin and distamycin, upon binding to the DNA duplex d(CGCGAAAAACGCG).d(CGCGTTTTTCGCG). Configurational entropy upper bounds based on 10-ns molecular dynamics simulations of netropsin and distamycin in solution and in complex with DNA in solution were estimated using the covariance matrix of atom-positional fluctuations. The results suggest that netropsin and distamycin lose a significant amount of configurational entropy upon binding to the DNA minor groove. The estimated changes in configurational entropy for netropsin and distamycin are -127 J K(-1) mol(-1) and -104 J K(-1) mol(-1), respectively. Estimates of the configurational entropy contributions of parts of the ligands are presented, showing that the loss of configurational entropy is comparatively more pronounced for the flexible tails than for the relatively rigid central body.

Entropy-Based Model for Interpreting Life Systems in Traditional Chinese Medicine

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Guo-lian Kang

2008-01-01

Full Text Available Traditional Chinese medicine (TCM treats qi as the core of the human life systems. Starting with a hypothetical correlation between TCM qi and the entropy theory, we address in this article a holistic model for evaluating and unveiling the rule of TCM life systems. Several new concepts such as acquired life entropy (ALE, acquired life entropy flow (ALEF and acquired life entropy production (ALEP are propounded to interpret TCM life systems. Using the entropy theory, mathematical models are established for ALE, ALEF and ALEP, which reflect the evolution of life systems. Some criteria are given on physiological activities and pathological changes of the body in different stages of life. Moreover, a real data-based simulation shows life entropies of the human body with different ages, Cold and Hot constitutions and in different seasons in North China are coincided with the manifestations of qi as well as the life evolution in TCM descriptions. Especially, based on the comparative and quantitative analysis, the entropy-based model can nicely describe the evolution of life entropies in Cold and Hot individuals thereby fitting the Yin–Yang theory in TCM. Thus, this work establishes a novel approach to interpret the fundamental principles in TCM, and provides an alternative understanding for the complex life systems.

Parameters Tuning of Model Free Adaptive Control Based on Minimum Entropy

Institute of Scientific and Technical Information of China (English)

Chao Ji; Jing Wang; Liulin Cao; Qibing Jin

2014-01-01

Dynamic linearization based model free adaptive control(MFAC) algorithm has been widely used in practical systems, in which some parameters should be tuned before it is successfully applied to process industries. Considering the random noise existing in real processes, a parameter tuning method based on minimum entropy optimization is proposed,and the feature of entropy is used to accurately describe the system uncertainty. For cases of Gaussian stochastic noise and non-Gaussian stochastic noise, an entropy recursive optimization algorithm is derived based on approximate model or identified model. The extensive simulation results show the effectiveness of the minimum entropy optimization for the partial form dynamic linearization based MFAC. The parameters tuned by the minimum entropy optimization index shows stronger stability and more robustness than these tuned by other traditional index,such as integral of the squared error(ISE) or integral of timeweighted absolute error(ITAE), when the system stochastic noise exists.

The Entropy of Co-Compact Open Covers

Directory of Open Access Journals (Sweden)

Steven Bourquin

2013-06-01

Full Text Available Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space (compactness and metrizability are not necessarily required. This is achieved through the consideration of co-compact covers of the space. The advantages of co-compact entropy include: (1 it does not require the space to be compact and, thus, generalizes Adler, Konheim and McAndrew’s topological entropy of continuous mappings on compact dynamical systems; and (2 it is an invariant of topological conjugation, compared to Bowen’s entropy, which is metric-dependent. Other properties of co-compact entropy are investigated, e.g., the co-compact entropy of a subsystem does not exceed that of the whole system. For the linear system, (R; f, defined by f(x = 2x, the co-compact entropy is zero, while Bowen’s entropy for this system is at least log 2. More generally, it is found that co-compact entropy is a lower bound of Bowen’s entropies, and the proof of this result also generates the Lebesgue Covering Theorem to co-compact open covers of non-compact metric spaces.

An Entropy-Based Measure for Assessing Fuzziness in Logistic Regression

Science.gov (United States)

Weiss, Brandi A.; Dardick, William

2016-01-01

This article introduces an entropy-based measure of data-model fit that can be used to assess the quality of logistic regression models. Entropy has previously been used in mixture-modeling to quantify how well individuals are classified into latent classes. The current study proposes the use of entropy for logistic regression models to quantify…

IN-cross Entropy Based MAGDM Strategy under Interval Neutrosophic Set Environment

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Shyamal Dalapati

2017-12-01

Full Text Available Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set (INS environment, which we call IN-cross entropy measure and prove its basic properties. We also develop weighted IN-cross entropy measure and investigats its basic properties. Based on the weighted IN-cross entropy measure, we develop a novel strategy for multi attribute group decision making (MAGDM strategy under interval neutrosophic environment. The proposed multi attribute group decision making strategy is compared with the existing cross entropy measure based strategy in the literature under interval neutrosophic set environment. Finally, an illustrative example of multi attribute group decision making problem is solved to show the feasibility, validity and efficiency of the proposed MAGDM strategy.

Entropy Rate of Time-Varying Wireless Networks

DEFF Research Database (Denmark)

Cika, Arta; Badiu, Mihai Alin; Coon, Justin P.

2018-01-01

In this paper, we present a detailed framework to analyze the evolution of the random topology of a time-varying wireless network via the information theoretic notion of entropy rate. We consider a propagation channel varying over time with random node positions in a closed space and Rayleigh...... fading affecting the connections between nodes. The existence of an edge between two nodes at given locations is modeled by a Markov chain, enabling memory effects in network dynamics. We then derive a lower and an upper bound on the entropy rate of the spatiotemporal network. The entropy rate measures...

Quantum engine efficiency bound beyond the second law of thermodynamics.

Science.gov (United States)

Niedenzu, Wolfgang; Mukherjee, Victor; Ghosh, Arnab; Kofman, Abraham G; Kurizki, Gershon

2018-01-11

According to the second law, the efficiency of cyclic heat engines is limited by the Carnot bound that is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. Quantum engines operating between a thermal and a squeezed-thermal bath have been shown to surpass this bound. Yet, their maximum efficiency cannot be determined by the reversibility condition, which may yield an unachievable efficiency bound above unity. Here we identify the fraction of the exchanged energy between a quantum system and a bath that necessarily causes an entropy change and derive an inequality for this change. This inequality reveals an efficiency bound for quantum engines energised by a non-thermal bath. This bound does not imply reversibility, unless the two baths are thermal. It cannot be solely deduced from the laws of thermodynamics.

Damage detection in rotating machinery by means of entropy-based parameters

Science.gov (United States)

Tocarciuc, Alexandru; Bereteu, Liviu; ǎgǎnescu, Gheorghe Eugen, Dr

2014-11-01

The paper is proposing two new entropy-based parameters, namely Renyi Entropy Index (REI) and Sharma-Mittal Entropy Index (SMEI), for detecting the presence of failures (or damages) in rotating machinery, namely: belt structural damage, belt wheels misalignment, failure of the fixing bolt of the machine to its baseplate and eccentricities (i.e.: due to detaching a small piece of material or bad mounting of the rotating components of the machine). The algorithms to obtain the proposed entropy-based parameters are described and test data is used in order to assess their sensitivity. A vibration test bench is used for measuring the levels of vibration while artificially inducing damage. The deviation of the two entropy-based parameters is compared in two states of the vibration test bench: not damaged and damaged. At the end of the study, their sensitivity is compared to Shannon Entropic Index.

Entropy estimates for simple random fields

DEFF Research Database (Denmark)

Forchhammer, Søren; Justesen, Jørn

1995-01-01

We consider the problem of determining the maximum entropy of a discrete random field on a lattice subject to certain local constraints on symbol configurations. The results are expected to be of interest in the analysis of digitized images and two dimensional codes. We shall present some examples...... of binary and ternary fields with simple constraints. Exact results on the entropies are known only in a few cases, but we shall present close bounds and estimates that are computationally efficient...

Fractal Image Compression Based on High Entropy Values Technique

Directory of Open Access Journals (Sweden)

Douaa Younis Abbaas

2018-04-01

Full Text Available There are many attempts tried to improve the encoding stage of FIC because it consumed time. These attempts worked by reducing size of the search pool for pair range-domain matching but most of them led to get a bad quality, or a lower compression ratio of reconstructed image. This paper aims to present a method to improve performance of the full search algorithm by combining FIC (lossy compression and another lossless technique (in this case entropy coding is used. The entropy technique will reduce size of the domain pool (i. e., number of domain blocks based on the entropy value of each range block and domain block and then comparing the results of full search algorithm and proposed algorithm based on entropy technique to see each of which give best results (such as reduced the encoding time with acceptable values in both compression quali-ty parameters which are C. R (Compression Ratio and PSNR (Image Quality. The experimental results of the proposed algorithm proven that using the proposed entropy technique reduces the encoding time while keeping compression rates and reconstruction image quality good as soon as possible.

Tight bounds on the size of neural networks for classification problems

Energy Technology Data Exchange (ETDEWEB)

Beiu, V. [Los Alamos National Lab., NM (United States); Pauw, T. de [Universite Catholique de Louvain, Louvain-la-Neuve (Belgium). Dept. de Mathematique

1997-06-01

This paper relies on the entropy of a data-set (i.e., number-of-bits) to prove tight bounds on the size of neural networks solving a classification problem. First, based on a sequence of geometrical steps, the authors constructively compute an upper bound of O(mn) on the number-of-bits for a given data-set - here m is the number of examples and n is the number of dimensions (i.e., R{sup n}). This result is used further in a nonconstructive way to bound the size of neural networks which correctly classify that data-set.

Syntactic Parameters and a Coding Theory Perspective on Entropy and Complexity of Language Families

Directory of Open Access Journals (Sweden)

Matilde Marcolli

2016-04-01

Full Text Available We present a simple computational approach to assigning a measure of complexity and information/entropy to families of natural languages, based on syntactic parameters and the theory of error correcting codes. We associate to each language a binary string of syntactic parameters and to a language family a binary code, with code words the binary string associated to each language. We then evaluate the code parameters (rate and relative minimum distance and the position of the parameters with respect to the asymptotic bound of error correcting codes and the Gilbert–Varshamov bound. These bounds are, respectively, related to the Kolmogorov complexity and the Shannon entropy of the code and this gives us a computationally simple way to obtain estimates on the complexity and information, not of individual languages but of language families. This notion of complexity is related, from the linguistic point of view to the degree of variability of syntactic parameter across languages belonging to the same (historical family.

Entropy-based critical reaction time for mixing-controlled reactive transport

DEFF Research Database (Denmark)

Chiogna, Gabriele; Rolle, Massimo

2017-01-01

Entropy-based metrics, such as the dilution index, have been proposed to quantify dilution and reactive mixing in solute transport problems. In this work, we derive the transient advection dispersion equation for the entropy density of a reactive plume. We restrict our analysis to the case where...... the concentration distribution of the transported species is Gaussian and we observe that, even in case of an instantaneous complete bimolecular reaction, dilution caused by dispersive processes dominates the entropy balance at early times and results in the net increase of the entropy density of a reactive species...

Stationary neutrino radiation transport by maximum entropy closure

International Nuclear Information System (INIS)

Bludman, S.A.

1994-11-01

The authors obtain the angular distributions that maximize the entropy functional for Maxwell-Boltzmann (classical), Bose-Einstein, and Fermi-Dirac radiation. In the low and high occupancy limits, the maximum entropy closure is bounded by previously known variable Eddington factors that depend only on the flux. For intermediate occupancy, the maximum entropy closure depends on both the occupation density and the flux. The Fermi-Dirac maximum entropy variable Eddington factor shows a scale invariance, which leads to a simple, exact analytic closure for fermions. This two-dimensional variable Eddington factor gives results that agree well with exact (Monte Carlo) neutrino transport calculations out of a collapse residue during early phases of hydrostatic neutron star formation

Multi-Level Wavelet Shannon Entropy-Based Method for Single-Sensor Fault Location

Directory of Open Access Journals (Sweden)

Qiaoning Yang

2015-10-01

Full Text Available In actual application, sensors are prone to failure because of harsh environments, battery drain, and sensor aging. Sensor fault location is an important step for follow-up sensor fault detection. In this paper, two new multi-level wavelet Shannon entropies (multi-level wavelet time Shannon entropy and multi-level wavelet time-energy Shannon entropy are defined. They take full advantage of sensor fault frequency distribution and energy distribution across multi-subband in wavelet domain. Based on the multi-level wavelet Shannon entropy, a method is proposed for single sensor fault location. The method firstly uses a criterion of maximum energy-to-Shannon entropy ratio to select the appropriate wavelet base for signal analysis. Then multi-level wavelet time Shannon entropy and multi-level wavelet time-energy Shannon entropy are used to locate the fault. The method is validated using practical chemical gas concentration data from a gas sensor array. Compared with wavelet time Shannon entropy and wavelet energy Shannon entropy, the experimental results demonstrate that the proposed method can achieve accurate location of a single sensor fault and has good anti-noise ability. The proposed method is feasible and effective for single-sensor fault location.

Constraining the mSUGRA parameter space through entropy and abundance criteria

International Nuclear Information System (INIS)

Cabral-Rosetti, Luis G.; Mondragon, Myriam; Nunez, Dario; Sussman, Roberto A.; Zavala, Jesus; Nellen, Lukas

2007-01-01

We explore the use of two criteria to constrain the allowed parameter space in mSUGRA models; both criteria are based in the calculation of the present density of neutralinos χ0 as Dark Matter in the Universe. The first one is the usual ''abundance'' criterion that requieres that present neutralino relic density complies with 0.0945 < ΩCDMh2 < 0.1287, which are the 2σ bounds according to WMAP. To calculate the relic density we use the public numerical code micrOMEGAS. The second criterion is the original idea presented in [3] that basically applies the microcanonical definition of entropy to a weakly interacting and self-gravitating gas, and then evaluate the change in entropy per particle of this gas between the freeze-out era and present day virialized structures. An 'entropy consistency' criterion emerges by comparing theoretical and empirical estimates of this entropy. One of the objetives of the work is to analyze the joint application of both criteria, already done in [3], to see if their results, using approximations for the calculations of the relic density, agree with the results coming from the exact numerical results of micrOMEGAS. The main objetive of the work is to use this method to constrain the parameter space in mSUGRA models that are inputs for the calculations of micrOMEGAS, and thus to get some bounds on the predictions for the SUSY spectra

The Bekenstein bound in strongly coupled O(N) scalar field theory

International Nuclear Information System (INIS)

Magalhaes, T. Santos; Svaiter, N.F.; Menezes, G.

2009-09-01

We discuss the O(N) self-interacting scalar field theory, in the strong-coupling regime and also in the limit of large N. Considering that the system is in thermal equilibrium with a reservoir at temperature β -1 , we assume the presence of macroscopic boundaries conning the field in a hypercube of side L. Using the strong-coupling perturbative expansion, we generalize previous results, i.e., we obtain the renormalized mean energy E and entropy S for the system in rst order of the strong-coupling perturbative expansion, presenting an analytical proof that the specific entropy also satisfies in some situations a quantum bound. When considering the low temperature behavior of the specific entropy, the sign of the renormalized zero-point energy can invalidate this quantum bound. If the renormalized zero point-energy is a positive quantity, at intermediate temperatures and in the low temperature limit, there is a quantum bound. (author)

On Landauer's Principle and Bound for Infinite Systems

Science.gov (United States)

Longo, Roberto

2018-04-01

Landauer's principle provides a link between Shannon's information entropy and Clausius' thermodynamical entropy. Here we set up a basic formula for the incremental free energy of a quantum channel, possibly relative to infinite systems, naturally arising by an Operator Algebraic point of view. By the Tomita-Takesaki modular theory, we can indeed describe a canonical evolution associated with a quantum channel state transfer. Such evolution is implemented both by a modular Hamiltonian and a physical Hamiltonian, the latter being determined by its functoriality properties. This allows us to make an intrinsic analysis, extending our QFT index formula, but without any a priori given dynamics; the associated incremental free energy is related to the logarithm of the Jones index and is thus quantised. This leads to a general lower bound for the incremental free energy of an irreversible quantum channel which is half of the Landauer bound, and to further bounds corresponding to the discrete series of the Jones index. In the finite dimensional context, or in the case of DHR charges in QFT, where the dimension is a positive integer, our lower bound agrees with Landauer's bound.

Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes

Science.gov (United States)

Liu, Yong; Shu, Chi-Wang; Zhang, Mengping

2018-02-01

We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi-discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by Godunov [32], the entropy stable DG framework with suitable quadrature rules [15], the entropy conservative flux in [14] inside each cell and the entropy dissipative approximate Godunov type numerical flux at cell interfaces to make the scheme entropy stable. The main difficulty in the generalization of the results in [15] is the appearance of the non-conservative "source terms" added in the modified MHD model introduced by Godunov [32], which do not exist in the general hyperbolic system studied in [15]. Special care must be taken to discretize these "source terms" adequately so that the resulting DG scheme satisfies entropy stability. Total variation diminishing / bounded (TVD/TVB) limiters and bound-preserving limiters are applied to control spurious oscillations. We demonstrate the accuracy and robustness of this new scheme on standard MHD examples.

A proof of the Bekenstein bound for any strength of gravity through holography

International Nuclear Information System (INIS)

Pesci, Alessandro

2010-01-01

The universal entropy bound of Bekenstein is considered at any strength of a gravitational interaction. A proof of it is given, provided the considered general-relativistic spacetimes allow for a meaningful and unequivocal definition of the quantities which participate in the bound (such as system energy and radius). This is done assuming as a starting point that, for assigned statistical-mechanical local conditions, a lower-limiting scale l* to system size definitely exists, it being required by holography through its semiclassical formulation as given by the generalized covariant entropy bound. An attempt is also made to draw some possible general consequences of the l* assumption with regard to the proliferation of species problem and to the viscosity to entropy density ratio. Concerning the latter, various fluids are considered including systems potentially relevant, to some extent, to the quark-gluon plasma case.

Entropy-based automated classification of independent components separated from fMCG

International Nuclear Information System (INIS)

Comani, S; Srinivasan, V; Alleva, G; Romani, G L

2007-01-01

Fetal magnetocardiography (fMCG) is a noninvasive technique suitable for the prenatal diagnosis of the fetal heart function. Reliable fetal cardiac signals can be reconstructed from multi-channel fMCG recordings by means of independent component analysis (ICA). However, the identification of the separated components is usually accomplished by visual inspection. This paper discusses a novel automated system based on entropy estimators, namely approximate entropy (ApEn) and sample entropy (SampEn), for the classification of independent components (ICs). The system was validated on 40 fMCG datasets of normal fetuses with the gestational age ranging from 22 to 37 weeks. Both ApEn and SampEn were able to measure the stability and predictability of the physiological signals separated with ICA, and the entropy values of the three categories were significantly different at p <0.01. The system performances were compared with those of a method based on the analysis of the time and frequency content of the components. The outcomes of this study showed a superior performance of the entropy-based system, in particular for early gestation, with an overall ICs detection rate of 98.75% and 97.92% for ApEn and SampEn respectively, as against a value of 94.50% obtained with the time-frequency-based system. (note)

The improvement of Clausius entropy and its application in entropy analysis

Institute of Scientific and Technical Information of China (English)

WU Jing; GUO ZengYuan

2008-01-01

The defects of Cleusius entropy which Include s premise of reversible process and a process quantlty of heat in Its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state funcllon. Unlike Clausius entropy, the improved deflnltion consists of system properties wlthout premise just like other state functions, for example, pressure p and enthalpy h, etc. it is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved deflnitlon of Clausius entropy provides a clear concept as well as a convenient method for en-tropy change calculation.

Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities

KAUST Repository

Nielsen, Frank

2016-12-09

Information-theoreticmeasures, such as the entropy, the cross-entropy and the Kullback-Leibler divergence between two mixture models, are core primitives in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using costly Monte Carlo stochastic integration, approximated or bounded using various techniques. We present a fast and generic method that builds algorithmically closed-form lower and upper bounds on the entropy, the cross-entropy, the Kullback-Leibler and the α-divergences of mixtures. We illustrate the versatile method by reporting our experiments for approximating the Kullback-Leibler and the α-divergences between univariate exponential mixtures, Gaussian mixtures, Rayleigh mixtures and Gamma mixtures.

Epoch-based Entropy for Early Screening of Alzheimer's Disease.

Science.gov (United States)

Houmani, N; Dreyfus, G; Vialatte, F B

2015-12-01

In this paper, we introduce a novel entropy measure, termed epoch-based entropy. This measure quantifies disorder of EEG signals both at the time level and spatial level, using local density estimation by a Hidden Markov Model on inter-channel stationary epochs. The investigation is led on a multi-centric EEG database recorded from patients at an early stage of Alzheimer's disease (AD) and age-matched healthy subjects. We investigate the classification performances of this method, its robustness to noise, and its sensitivity to sampling frequency and to variations of hyperparameters. The measure is compared to two alternative complexity measures, Shannon's entropy and correlation dimension. The classification accuracies for the discrimination of AD patients from healthy subjects were estimated using a linear classifier designed on a development dataset, and subsequently tested on an independent test set. Epoch-based entropy reached a classification accuracy of 83% on the test dataset (specificity = 83.3%, sensitivity = 82.3%), outperforming the two other complexity measures. Furthermore, it was shown to be more stable to hyperparameter variations, and less sensitive to noise and sampling frequency disturbances than the other two complexity measures.

Does horizon entropy satisfy a quantum null energy conjecture?

Science.gov (United States)

Fu, Zicao; Marolf, Donald

2016-12-01

A modern version of the idea that the area of event horizons gives 4G times an entropy is the Hubeny-Rangamani causal holographic information (CHI) proposal for holographic field theories. Given a region R of a holographic QFTs, CHI computes A/4G on a certain cut of an event horizon in the gravitational dual. The result is naturally interpreted as a coarse-grained entropy for the QFT. CHI is known to be finitely greater than the fine-grained Hubeny-Rangamani-Takayanagi (HRT) entropy when \\partial R lies on a Killing horizon of the QFT spacetime, and in this context satisfies other non-trivial properties expected of an entropy. Here we present evidence that it also satisfies the quantum null energy condition (QNEC), which bounds the second derivative of the entropy of a quantum field theory on one side of a non-expanding null surface by the flux of stress-energy across the surface. In particular, we show CHI to satisfy the QNEC in 1  +  1 holographic CFTs when evaluated in states dual to conical defects in AdS3. This surprising result further supports the idea that CHI defines a useful notion of coarse-grained holographic entropy, and suggests unprecedented bounds on the rate at which bulk horizon generators emerge from a caustic. To supplement our motivation, we include an appendix deriving a corresponding coarse-grained generalized second law for 1  +  1 holographic CFTs perturbatively coupled to dilaton gravity.

Financial time series analysis based on effective phase transfer entropy

Science.gov (United States)

Yang, Pengbo; Shang, Pengjian; Lin, Aijing

2017-02-01

Transfer entropy is a powerful technique which is able to quantify the impact of one dynamic system on another system. In this paper, we propose the effective phase transfer entropy method based on the transfer entropy method. We use simulated data to test the performance of this method, and the experimental results confirm that the proposed approach is capable of detecting the information transfer between the systems. We also explore the relationship between effective phase transfer entropy and some variables, such as data size, coupling strength and noise. The effective phase transfer entropy is positively correlated with the data size and the coupling strength. Even in the presence of a large amount of noise, it can detect the information transfer between systems, and it is very robust to noise. Moreover, this measure is indeed able to accurately estimate the information flow between systems compared with phase transfer entropy. In order to reflect the application of this method in practice, we apply this method to financial time series and gain new insight into the interactions between systems. It is demonstrated that the effective phase transfer entropy can be used to detect some economic fluctuations in the financial market. To summarize, the effective phase transfer entropy method is a very efficient tool to estimate the information flow between systems.

Driver Fatigue Detection System Using Electroencephalography Signals Based on Combined Entropy Features

Directory of Open Access Journals (Sweden)

Zhendong Mu

2017-02-01

Full Text Available Driver fatigue has become one of the major causes of traffic accidents, and is a complicated physiological process. However, there is no effective method to detect driving fatigue. Electroencephalography (EEG signals are complex, unstable, and non-linear; non-linear analysis methods, such as entropy, maybe more appropriate. This study evaluates a combined entropy-based processing method of EEG data to detect driver fatigue. In this paper, 12 subjects were selected to take part in an experiment, obeying driving training in a virtual environment under the instruction of the operator. Four types of enthrones (spectrum entropy, approximate entropy, sample entropy and fuzzy entropy were used to extract features for the purpose of driver fatigue detection. Electrode selection process and a support vector machine (SVM classification algorithm were also proposed. The average recognition accuracy was 98.75%. Retrospective analysis of the EEG showed that the extracted features from electrodes T5, TP7, TP8 and FP1 may yield better performance. SVM classification algorithm using radial basis function as kernel function obtained better results. A combined entropy-based method demonstrates good classification performance for studying driver fatigue detection.

Bounding species distribution models

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Thomas J. STOHLGREN, Catherine S. JARNEVICH, Wayne E. ESAIAS,Jeffrey T. MORISETTE

2011-10-01

Full Text Available Species distribution models are increasing in popularity for mapping suitable habitat for species of management concern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for “clamping” model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART and maximum entropy (Maxent models, and we tested a simple alteration of the model extrapolations, bounding extrapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suitable habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used [Current Zoology 57 (5: 642–647, 2011].

Bounding Species Distribution Models

Science.gov (United States)

Stohlgren, Thomas J.; Jarnevich, Cahterine S.; Morisette, Jeffrey T.; Esaias, Wayne E.

2011-01-01

Species distribution models are increasing in popularity for mapping suitable habitat for species of management concern. Many investigators now recognize that extrapolations of these models with geographic information systems (GIS) might be sensitive to the environmental bounds of the data used in their development, yet there is no recommended best practice for "clamping" model extrapolations. We relied on two commonly used modeling approaches: classification and regression tree (CART) and maximum entropy (Maxent) models, and we tested a simple alteration of the model extrapolations, bounding extrapolations to the maximum and minimum values of primary environmental predictors, to provide a more realistic map of suitable habitat of hybridized Africanized honey bees in the southwestern United States. Findings suggest that multiple models of bounding, and the most conservative bounding of species distribution models, like those presented here, should probably replace the unbounded or loosely bounded techniques currently used [Current Zoology 57 (5): 642-647, 2011].

On Uniform Decay of the Entropy for Reaction–Diffusion Systems

KAUST Repository

Mielke, Alexander

2014-09-10

This work provides entropy decay estimates for classes of nonlinear reaction–diffusion systems modeling reversible chemical reactions under the detailed-balance condition. We obtain explicit bounds for the exponential decay of the relative logarithmic entropy, being based essentially on the application of the Log-Sobolev estimate and a convexification argument only, making it quite robust to model variations. An important feature of our analysis is the interaction of the two different dissipative mechanisms: pure diffusion, forcing the system asymptotically to the homogeneous state, and pure reaction, forcing the solution to the (possibly inhomogeneous) chemical equilibrium. Only the interaction of both mechanisms provides the convergence to the homogeneous equilibrium. Moreover, we introduce two generalizations of the main result: (i) vanishing diffusion constants in some chemical components and (ii) usage of different entropy functionals. We provide a few examples to highlight the usability of our approach and shortly discuss possible further applications and open questions.

Improved Ordinary Measure and Image Entropy Theory based intelligent Copy Detection Method

Directory of Open Access Journals (Sweden)

Dengpan Ye

2011-10-01

Full Text Available Nowadays, more and more multimedia websites appear in social network. It brings some security problems, such as privacy, piracy, disclosure of sensitive contents and so on. Aiming at copyright protection, the copy detection technology of multimedia contents becomes a hot topic. In our previous work, a new computer-based copyright control system used to detect the media has been proposed. Based on this system, this paper proposes an improved media feature matching measure and an entropy based copy detection method. The Levenshtein Distance was used to enhance the matching degree when using for feature matching measure in copy detection. For entropy based copy detection, we make a fusion of the two features of entropy matrix of the entropy feature we extracted. Firstly,we extract the entropy matrix of the image and normalize it. Then, we make a fusion of the eigenvalue feature and the transfer matrix feature of the entropy matrix. The fused features will be used for image copy detection. The experiments show that compared to use these two kinds of features for image detection singly, using feature fusion matching method is apparent robustness and effectiveness. The fused feature has a high detection for copy images which have been received some attacks such as noise, compression, zoom, rotation and so on. Comparing with referred methods, the method proposed is more intelligent and can be achieved good performance.

Logarithmic black hole entropy corrections and holographic Renyi entropy

Energy Technology Data Exchange (ETDEWEB)

Mahapatra, Subhash [The Institute of Mathematical Sciences, Chennai (India); KU Leuven - KULAK, Department of Physics, Kortrijk (Belgium)

2018-01-15

The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G{sub D}{sup 0}. The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)

Logarithmic black hole entropy corrections and holographic Renyi entropy

International Nuclear Information System (INIS)

Mahapatra, Subhash

2018-01-01

The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G D 0 . The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)

The Grading Entropy-based Criteria for Structural Stability of Granular Materials and Filters

Directory of Open Access Journals (Sweden)

Janos Lőrincz

2015-05-01

Full Text Available This paper deals with three grading entropy-based rules that describe different soil structure stability phenomena: an internal stability rule, a filtering rule and a segregation rule. These rules are elaborated on the basis of a large amount of laboratory testing and from existing knowledge in the field. Use is made of the theory of grading entropy to derive parameters which incorporate all of the information of the grading curve into a pair of entropy-based parameters that allow soils with common behaviours to be grouped into domains on an entropy diagram. Applications of the derived entropy-based rules are presented by examining the reason of a dam failure, by testing against the existing filter rules from the literature, and by giving some examples for the design of non-segregating grading curves (discrete particle size distributions by dry weight. A physical basis for the internal stability rule is established, wherein the higher values of base entropy required for granular stability are shown to reflect the closeness between the mean and maximum grain diameters, which explains how there are sufficient coarser grains to achieve a stable grain skeleton.

The improvement of Clausius entropy and its application in entropy analysis

Institute of Scientific and Technical Information of China (English)

2008-01-01

The defects of Clausius entropy which include a premise of reversible process and a process quantity of heat in its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state function. Unlike Clausius entropy, the improved definition consists of system properties without premise just like other state functions, for example, pressure p and enthalpy h, etc. It is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved definition of Clausius entropy provides a clear concept as well as a convenient method for en- tropy change calculation.

An Entropy-Based Network Anomaly Detection Method

Directory of Open Access Journals (Sweden)

Przemysław Bereziński

2015-04-01

Full Text Available Data mining is an interdisciplinary subfield of computer science involving methods at the intersection of artificial intelligence, machine learning and statistics. One of the data mining tasks is anomaly detection which is the analysis of large quantities of data to identify items, events or observations which do not conform to an expected pattern. Anomaly detection is applicable in a variety of domains, e.g., fraud detection, fault detection, system health monitoring but this article focuses on application of anomaly detection in the field of network intrusion detection.The main goal of the article is to prove that an entropy-based approach is suitable to detect modern botnet-like malware based on anomalous patterns in network. This aim is achieved by realization of the following points: (i preparation of a concept of original entropy-based network anomaly detection method, (ii implementation of the method, (iii preparation of original dataset, (iv evaluation of the method.

Entropy-Based Privacy against Profiling of User Mobility

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Alicia Rodriguez-Carrion

2015-06-01

Full Text Available Location-based services (LBSs flood mobile phones nowadays, but their use poses an evident privacy risk. The locations accompanying the LBS queries can be exploited by the LBS provider to build the user profile of visited locations, which might disclose sensitive data, such as work or home locations. The classic concept of entropy is widely used to evaluate privacy in these scenarios, where the information is represented as a sequence of independent samples of categorized data. However, since the LBS queries might be sent very frequently, location profiles can be improved by adding temporal dependencies, thus becoming mobility profiles, where location samples are not independent anymore and might disclose the user’s mobility patterns. Since the time dimension is factored in, the classic entropy concept falls short of evaluating the real privacy level, which depends also on the time component. Therefore, we propose to extend the entropy-based privacy metric to the use of the entropy rate to evaluate mobility profiles. Then, two perturbative mechanisms are considered to preserve locations and mobility profiles under gradual utility constraints. We further use the proposed privacy metric and compare it to classic ones to evaluate both synthetic and real mobility profiles when the perturbative methods proposed are applied. The results prove the usefulness of the proposed metric for mobility profiles and the need for tailoring the perturbative methods to the features of mobility profiles in order to improve privacy without completely loosing utility.

Entropy Viscosity and L1-based Approximations of PDEs: Exploiting Sparsity

Science.gov (United States)

2015-10-23

AFRL-AFOSR-VA-TR-2015-0337 Entropy Viscosity and L1-based Approximations of PDEs: Exploiting Sparsity Jean-Luc Guermond TEXAS A & M UNIVERSITY 750...REPORT DATE (DD-MM-YYYY) 09-05-2015 2. REPORT TYPE Final report 3. DATES COVERED (From - To) 01-07-2012 - 30-06-2015 4. TITLE AND SUBTITLE Entropy ...conservation equations can be stabilized by using the so-called entropy viscosity method and we proposed to to investigate this new technique. We

On the Entropy Based Associative Memory Model with Higher-Order Correlations

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Masahiro Nakagawa

2010-01-01

Full Text Available In this paper, an entropy based associative memory model will be proposed and applied to memory retrievals with an orthogonal learning model so as to compare with the conventional model based on the quadratic Lyapunov functional to be minimized during the retrieval process. In the present approach, the updating dynamics will be constructed on the basis of the entropy minimization strategy which may be reduced asymptotically to the above-mentioned conventional dynamics as a special case ignoring the higher-order correlations. According to the introduction of the entropy functional, one may involve higer-order correlation effects between neurons in a self-contained manner without any heuristic coupling coefficients as in the conventional manner. In fact we shall show such higher order coupling tensors are to be uniquely determined in the framework of the entropy based approach. From numerical results, it will be found that the presently proposed novel approach realizes much larger memory capacity than that of the quadratic Lyapunov functional approach, e.g., associatron.

A Theoretical Basis for Entropy-Scaling Effects in Human Mobility Patterns.

Science.gov (United States)

Osgood, Nathaniel D; Paul, Tuhin; Stanley, Kevin G; Qian, Weicheng

2016-01-01

Characterizing how people move through space has been an important component of many disciplines. With the advent of automated data collection through GPS and other location sensing systems, researchers have the opportunity to examine human mobility at spatio-temporal resolution heretofore impossible. However, the copious and complex data collected through these logging systems can be difficult for humans to fully exploit, leading many researchers to propose novel metrics for encapsulating movement patterns in succinct and useful ways. A particularly salient proposed metric is the mobility entropy rate of the string representing the sequence of locations visited by an individual. However, mobility entropy rate is not scale invariant: entropy rate calculations based on measurements of the same trajectory at varying spatial or temporal granularity do not yield the same value, limiting the utility of mobility entropy rate as a metric by confounding inter-experimental comparisons. In this paper, we derive a scaling relationship for mobility entropy rate of non-repeating straight line paths from the definition of Lempel-Ziv compression. We show that the resulting formulation predicts the scaling behavior of simulated mobility traces, and provides an upper bound on mobility entropy rate under certain assumptions. We further show that this formulation has a maximum value for a particular sampling rate, implying that optimal sampling rates for particular movement patterns exist.

Entropy equilibrium equation and dynamic entropy production in environment liquid

Institute of Scientific and Technical Information of China (English)

无

2002-01-01

The entropy equilibrium equation is the basis of the nonequilibrium state thermodynamics. But the internal energy implies the kinetic energy of the fluid micelle relative to mass center in the classical entropy equilibrium equation at present. This internal energy is not the mean kinetic energy of molecular movement in thermodynamics. Here a modified entropy equilibrium equation is deduced, based on the concept that the internal energy is just the mean kinetic energy of the molecular movement. A dynamic entropy production is introduced into the entropy equilibrium equation to describe the dynamic process distinctly. This modified entropy equilibrium equation can describe not only the entropy variation of the irreversible processes but also the reversible processes in a thermodynamic system. It is more reasonable and suitable for wider applications.

Entropy considerations in constraining the mSUGRA parameter space

International Nuclear Information System (INIS)

Nunez, Dario; Sussman, Roberto A.; Zavala, Jesus; Nellen, Lukas; Cabral-Rosetti, Luis G.; Mondragon, Myriam

2006-01-01

We explore the use of two criteria to constraint the allowed parameter space in mSUGRA models. Both criteria are based in the calculation of the present density of neutralinos as dark matter in the Universe. The first one is the usual ''abundance'' criterion which is used to calculate the relic density after the ''freeze-out'' era. To compute the relic density we used the numerical public code micrOMEGAs. The second criterion applies the microcanonical definition of entropy to a weakly interacting and self-gravitating gas evaluating then the change in the entropy per particle of this gas between the ''freeze-out'' era and present day virialized structures (i.e systems in virial equilibrium). An ''entropy-consistency'' criterion emerges by comparing theoretical and empirical estimates of this entropy. The main objective of our work is to determine for which regions of the parameter space in the mSUGRA model are both criteria consistent with the 2σ bounds according to WMAP for the relic density: 0.0945 < ΩCDMh2 < 0.1287. As a first result, we found that for A0 = 0, sgnμ +, small values of tanβ are not favored; only for tanβ ≅ 50 are both criteria significantly consistent

A Method of Rotating Machinery Fault Diagnosis Based on the Close Degree of Information Entropy

Institute of Scientific and Technical Information of China (English)

GENG Jun-bao; HUANG Shu-hong; JIN Jia-shan; CHEN Fei; LIU Wei

2006-01-01

This paper presents a method of rotating machinery fault diagnosis based on the close degree of information entropy. In the view of the information entropy, we introduce four information entropy features of the rotating machinery, which describe the vibration condition of the machinery. The four features are, respectively, denominated as singular spectrum entropy, power spectrum entropy, wavelet space state feature entropy and wavelet power spectrum entropy. The value scopes of the four information entropy features of the rotating machinery in some typical fault conditions are gained by experiments, which can be acted as the standard features of fault diagnosis. According to the principle of the shorter distance between the more similar models, the decision-making method based on the close degree of information entropy is put forward to deal with the recognition of fault patterns. We demonstrate the effectiveness of this approach in an instance involving the fault pattern recognition of some rotating machinery.

Multiattribute Decision Making Based on Entropy under Interval-Valued Intuitionistic Fuzzy Environment

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Yingjun Zhang

2013-01-01

Full Text Available Multiattribute decision making (MADM is one of the central problems in artificial intelligence, specifically in management fields. In most cases, this problem arises from uncertainty both in the data derived from the decision maker and the actions performed in the environment. Fuzzy set and high-order fuzzy sets were proven to be effective approaches in solving decision-making problems with uncertainty. Therefore, in this paper, we investigate the MADM problem with completely unknown attribute weights in the framework of interval-valued intuitionistic fuzzy (IVIF set (IVIFS. We first propose a new definition of IVIF entropy and some calculation methods for IVIF entropy. Furthermore, we propose an entropy-based decision-making method to solve IVIF MADM problems with completely unknown attribute weights. Particular emphasis is put on assessing the attribute weights based on IVIF entropy. Instead of the traditional methods, which use divergence among attributes or the probabilistic discrimination of attributes to obtain attribute weights, we utilize the IVIF entropy to assess the attribute weights based on the credibility of the decision-making matrix for solving the problem. Finally, a supplier selection example is given to demonstrate the feasibility and validity of the proposed MADM method.

Logarithmic black hole entropy corrections and holographic Rényi entropy

Science.gov (United States)

Mahapatra, Subhash

2018-01-01

The entanglement and Rényi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Rényi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order GD^0. The entropic c-function and the inequalities of the Rényi entropy are also satisfied even with the correction terms.

Adaptive information-theoretic bounded rational decision-making with parametric priors

OpenAIRE

Grau-Moya, Jordi; Braun, Daniel A.

2015-01-01

Deviations from rational decision-making due to limited computational resources have been studied in the field of bounded rationality, originally proposed by Herbert Simon. There have been a number of different approaches to model bounded rationality ranging from optimality principles to heuristics. Here we take an information-theoretic approach to bounded rationality, where information-processing costs are measured by the relative entropy between a posterior decision strategy and a given fix...

Towards an entropy-based detached-eddy simulation

Science.gov (United States)

Zhao, Rui; Yan, Chao; Li, XinLiang; Kong, WeiXuan

2013-10-01

A concept of entropy increment ratio ( s¯) is introduced for compressible turbulence simulation through a series of direct numerical simulations (DNS). s¯ represents the dissipation rate per unit mechanical energy with the benefit of independence of freestream Mach numbers. Based on this feature, we construct the shielding function f s to describe the boundary layer region and propose an entropy-based detached-eddy simulation method (SDES). This approach follows the spirit of delayed detached-eddy simulation (DDES) proposed by Spalart et al. in 2005, but it exhibits much better behavior after their performances are compared in the following flows, namely, pure attached flow with thick boundary layer (a supersonic flat-plate flow with high Reynolds number), fully separated flow (the supersonic base flow), and separated-reattached flow (the supersonic cavity-ramp flow). The Reynolds-averaged Navier-Stokes (RANS) resolved region is reliably preserved and the modeled stress depletion (MSD) phenomenon which is inherent in DES and DDES is partly alleviated. Moreover, this new hybrid strategy is simple and general, making it applicable to other models related to the boundary layer predictions.

Characterization of complexity in the electroencephalograph activity of Alzheimer's disease based on fuzzy entropy.

Science.gov (United States)

Cao, Yuzhen; Cai, Lihui; Wang, Jiang; Wang, Ruofan; Yu, Haitao; Cao, Yibin; Liu, Jing

2015-08-01

In this paper, experimental neurophysiologic recording and statistical analysis are combined to investigate the nonlinear characteristic and the cognitive function of the brain. Fuzzy approximate entropy and fuzzy sample entropy are applied to characterize the model-based simulated series and electroencephalograph (EEG) series of Alzheimer's disease (AD). The effectiveness and advantages of these two kinds of fuzzy entropy are first verified through the simulated EEG series generated by the alpha rhythm model, including stronger relative consistency and robustness. Furthermore, in order to detect the abnormality of irregularity and chaotic behavior in the AD brain, the complexity features based on these two fuzzy entropies are extracted in the delta, theta, alpha, and beta bands. It is demonstrated that, due to the introduction of fuzzy set theory, the fuzzy entropies could better distinguish EEG signals of AD from that of the normal than the approximate entropy and sample entropy. Moreover, the entropy values of AD are significantly decreased in the alpha band, particularly in the temporal brain region, such as electrode T3 and T4. In addition, fuzzy sample entropy could achieve higher group differences in different brain regions and higher average classification accuracy of 88.1% by support vector machine classifier. The obtained results prove that fuzzy sample entropy may be a powerful tool to characterize the complexity abnormalities of AD, which could be helpful in further understanding of the disease.

Conformational entropy changes upon lactose binding to the carbohydrate recognition domain of galectin-3

International Nuclear Information System (INIS)

Diehl, Carl; Genheden, Samuel; Modig, Kristofer; Ryde, Ulf; Akke, Mikael

2009-01-01

The conformational entropy of proteins can make significant contributions to the free energy of ligand binding. NMR spin relaxation enables site-specific investigation of conformational entropy, via order parameters that parameterize local reorientational fluctuations of rank-2 tensors. Here we have probed the conformational entropy of lactose binding to the carbohydrate recognition domain of galectin-3 (Gal3), a protein that plays an important role in cell growth, cell differentiation, cell cycle regulation, and apoptosis, making it a potential target for therapeutic intervention in inflammation and cancer. We used 15 N spin relaxation experiments and molecular dynamics simulations to monitor the backbone amides and secondary amines of the tryptophan and arginine side chains in the ligand-free and lactose-bound states of Gal3. Overall, we observe good agreement between the experimental and computed order parameters of the ligand-free and lactose-bound states. Thus, the 15 N spin relaxation data indicate that the molecular dynamics simulations provide reliable information on the conformational entropy of the binding process. The molecular dynamics simulations reveal a correlation between the simulated order parameters and residue-specific backbone entropy, re-emphasizing that order parameters provide useful estimates of local conformational entropy. The present results show that the protein backbone exhibits an increase in conformational entropy upon binding lactose, without any accompanying structural changes

Sample Entropy-Based Approach to Evaluate the Stability of Double-Wire Pulsed MIG Welding

Directory of Open Access Journals (Sweden)

Ping Yao

2014-01-01

Full Text Available According to the sample entropy, this paper deals with a quantitative method to evaluate the current stability in double-wire pulsed MIG welding. Firstly, the sample entropy of current signals with different stability but the same parameters is calculated. The results show that the more stable the current, the smaller the value and the standard deviation of sample entropy. Secondly, four parameters, which are pulse width, peak current, base current, and frequency, are selected for four-level three-factor orthogonal experiment. The calculation and analysis of desired signals indicate that sample entropy values are affected by welding current parameters. Then, a quantitative method based on sample entropy is proposed. The experiment results show that the method can preferably quantify the welding current stability.

2D Tsallis Entropy for Image Segmentation Based on Modified Chaotic Bat Algorithm

Directory of Open Access Journals (Sweden)

Zhiwei Ye

2018-03-01

Full Text Available Image segmentation is a significant step in image analysis and computer vision. Many entropy based approaches have been presented in this topic; among them, Tsallis entropy is one of the best performing methods. However, 1D Tsallis entropy does not consider make use of the spatial correlation information within the neighborhood results might be ruined by noise. Therefore, 2D Tsallis entropy is proposed to solve the problem, and results are compared with 1D Fisher, 1D maximum entropy, 1D cross entropy, 1D Tsallis entropy, fuzzy entropy, 2D Fisher, 2D maximum entropy and 2D cross entropy. On the other hand, due to the existence of huge computational costs, meta-heuristics algorithms like genetic algorithm (GA, particle swarm optimization (PSO, ant colony optimization algorithm (ACO and differential evolution algorithm (DE are used to accelerate the 2D Tsallis entropy thresholding method. In this paper, considering 2D Tsallis entropy as a constrained optimization problem, the optimal thresholds are acquired by maximizing the objective function using a modified chaotic Bat algorithm (MCBA. The proposed algorithm has been tested on some actual and infrared images. The results are compared with that of PSO, GA, ACO and DE and demonstrate that the proposed method outperforms other approaches involved in the paper, which is a feasible and effective option for image segmentation.

Hierarchical Polygamy Inequality for Entanglement of Tsallis q-Entropy

Science.gov (United States)

Luo, Yu; Li, Yong-Ming

2018-05-01

In this paper, we study the polygamy inequality of quantum entanglement in terms of Tsallis q-entropy. We first give a lower bound of Tsallis q-entropy entanglement of assistance (TOA) in the 2 ⊗ d systems. The relation-ships between Tsallis q-entropy entanglement (TEE) and TOA are also given. Furthermore, we prove TOA follows a hierarchical polygamy inequality in a 2 ⊗ 2 ⊗ 2 N‑2 systems. Supported by the National Natural Science Foundation of China under Grant No. 11671244, the Higher School Doctoral Subject Foun- dation of Ministry of Education of China under Grant No. 20130202110001, and Fundamental Research Funds for the Central Universities under Grants Nos. 2016TS060 and 2016CBY003

On Uniform Decay of the Entropy for Reaction–Diffusion Systems

KAUST Repository

Mielke, Alexander; Haskovec, Jan; Markowich, Peter A.

2014-01-01

This work provides entropy decay estimates for classes of nonlinear reaction–diffusion systems modeling reversible chemical reactions under the detailed-balance condition. We obtain explicit bounds for the exponential decay of the relative

Bubble Entropy: An Entropy Almost Free of Parameters.

Science.gov (United States)

Manis, George; Aktaruzzaman, Md; Sassi, Roberto

2017-11-01

Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors. Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation

Upper bounds on entangling rates of bipartite Hamiltonians

International Nuclear Information System (INIS)

Bravyi, Sergey

2007-01-01

We discuss upper bounds on the rate at which unitary evolution governed by a nonlocal Hamiltonian can generate entanglement in a bipartite system. Given a bipartite Hamiltonian H coupling two finite dimensional particles A and B, the entangling rate is shown to be upper bounded by c log(d) parallel H parallel, where d is the smallest dimension of the interacting particles parallel H parallel is the operator norm of H, and c is a constant close to 1. Under certain restrictions on the initial state we prove an analogous upper bound for the ancilla-assisted entangling rate with a constant c that does not depend upon dimensions of local ancillas. The restriction is that the initial state has at most two distinct Schmidt coefficients (each coefficient may have arbitrarily large multiplicity). Our proof is based on analysis of a mixing rate - a functional measuring how fast entropy can be produced if one mixes a time-independent state with a state evolving unitarily

A Novel Entropy-Based Decoding Algorithm for a Generalized High-Order Discrete Hidden Markov Model

Directory of Open Access Journals (Sweden)

Jason Chin-Tiong Chan

2018-01-01

Full Text Available The optimal state sequence of a generalized High-Order Hidden Markov Model (HHMM is tracked from a given observational sequence using the classical Viterbi algorithm. This classical algorithm is based on maximum likelihood criterion. We introduce an entropy-based Viterbi algorithm for tracking the optimal state sequence of a HHMM. The entropy of a state sequence is a useful quantity, providing a measure of the uncertainty of a HHMM. There will be no uncertainty if there is only one possible optimal state sequence for HHMM. This entropy-based decoding algorithm can be formulated in an extended or a reduction approach. We extend the entropy-based algorithm for computing the optimal state sequence that was developed from a first-order to a generalized HHMM with a single observational sequence. This extended algorithm performs the computation exponentially with respect to the order of HMM. The computational complexity of this extended algorithm is due to the growth of the model parameters. We introduce an efficient entropy-based decoding algorithm that used reduction approach, namely, entropy-based order-transformation forward algorithm (EOTFA to compute the optimal state sequence of any generalized HHMM. This EOTFA algorithm involves a transformation of a generalized high-order HMM into an equivalent first-order HMM and an entropy-based decoding algorithm is developed based on the equivalent first-order HMM. This algorithm performs the computation based on the observational sequence and it requires OTN~2 calculations, where N~ is the number of states in an equivalent first-order model and T is the length of observational sequence.

Relation Entropy and Transferable Entropy Think of Aggregation on Group Decision Making

Institute of Scientific and Technical Information of China (English)

CHENG Qi-yue; QIU Wan-hua; LIU Xiao-feng

2002-01-01

In this paper, aggregation question based on group decision making and a single decision making is studied. The theory of entropy is applied to the sets pair analysis. The system of relation entropy and the transferable entropy notion are put. The character is studied. An potential by the relation entropy and transferable entropy are defined. It is the consistency measure on the group between a single decision making. We gained a new aggregation effective definition on the group misjudge.

Fuzzy 2-partition entropy threshold selection based on Big Bang–Big Crunch Optimization algorithm

Directory of Open Access Journals (Sweden)

Baljit Singh Khehra

2015-03-01

Full Text Available The fuzzy 2-partition entropy approach has been widely used to select threshold value for image segmenting. This approach used two parameterized fuzzy membership functions to form a fuzzy 2-partition of the image. The optimal threshold is selected by searching an optimal combination of parameters of the membership functions such that the entropy of fuzzy 2-partition is maximized. In this paper, a new fuzzy 2-partition entropy thresholding approach based on the technology of the Big Bang–Big Crunch Optimization (BBBCO is proposed. The new proposed thresholding approach is called the BBBCO-based fuzzy 2-partition entropy thresholding algorithm. BBBCO is used to search an optimal combination of parameters of the membership functions for maximizing the entropy of fuzzy 2-partition. BBBCO is inspired by the theory of the evolution of the universe; namely the Big Bang and Big Crunch Theory. The proposed algorithm is tested on a number of standard test images. For comparison, three different algorithms included Genetic Algorithm (GA-based, Biogeography-based Optimization (BBO-based and recursive approaches are also implemented. From experimental results, it is observed that the performance of the proposed algorithm is more effective than GA-based, BBO-based and recursion-based approaches.

Enthalpy-entropy compensation: the role of solvation.

Science.gov (United States)

Dragan, Anatoliy I; Read, Christopher M; Crane-Robinson, Colyn

2017-05-01

Structural modifications to interacting systems frequently lead to changes in both the enthalpy (heat) and entropy of the process that compensate each other, so that the Gibbs free energy is little changed: a major barrier to the development of lead compounds in drug discovery. The conventional explanation for such enthalpy-entropy compensation (EEC) is that tighter contacts lead to a more negative enthalpy but increased molecular constraints, i.e., a compensating conformational entropy reduction. Changes in solvation can also contribute to EEC but this contribution is infrequently discussed. We review long-established and recent cases of EEC and conclude that the large fluctuations in enthalpy and entropy observed are too great to be a result of only conformational changes and must result, to a considerable degree, from variations in the amounts of water immobilized or released on forming complexes. Two systems exhibiting EEC show a correlation between calorimetric entropies and local mobilities, interpreted to mean conformational control of the binding entropy/free energy. However, a substantial contribution from solvation gives the same effect, as a consequence of a structural link between the amount of bound water and the protein flexibility. Only by assuming substantial changes in solvation-an intrinsically compensatory process-can a more complete understanding of EEC be obtained. Faced with such large, and compensating, changes in the enthalpies and entropies of binding, the best approach to engineering elevated affinities must be through the addition of ionic links, as they generate increased entropy without affecting the enthalpy.

A new entropy based method for computing software structural complexity

CERN Document Server

Roca, J L

2002-01-01

In this paper a new methodology for the evaluation of software structural complexity is described. It is based on the entropy evaluation of the random uniform response function associated with the so called software characteristic function SCF. The behavior of the SCF with the different software structures and their relationship with the number of inherent errors is investigated. It is also investigated how the entropy concept can be used to evaluate the complexity of a software structure considering the SCF as a canonical representation of the graph associated with the control flow diagram. The functions, parameters and algorithms that allow to carry out this evaluation are also introduced. After this analytic phase follows the experimental phase, verifying the consistency of the proposed metric and their boundary conditions. The conclusion is that the degree of software structural complexity can be measured as the entropy of the random uniform response function of the SCF. That entropy is in direct relation...

Entropy and information causality in general probabilistic theories

International Nuclear Information System (INIS)

Barnum, Howard; Leifer, Matthew; Spekkens, Robert; Barrett, Jonathan; Clark, Lisa Orloff; Stepanik, Nicholas; Wilce, Alex; Wilke, Robin

2010-01-01

We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic. Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A: B)=H(A)+H(B)-H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC)< I(A:B). This is relevant to IC in the sense of Pawlowski et al: we show that any monoentropic non-signaling theory in which measurement entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu-Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.

A two-phase copula entropy-based multiobjective optimization approach to hydrometeorological gauge network design

Science.gov (United States)

Xu, Pengcheng; Wang, Dong; Singh, Vijay P.; Wang, Yuankun; Wu, Jichun; Wang, Lachun; Zou, Xinqing; Chen, Yuanfang; Chen, Xi; Liu, Jiufu; Zou, Ying; He, Ruimin

2017-12-01

Hydrometeorological data are needed for obtaining point and areal mean, quantifying the spatial variability of hydrometeorological variables, and calibration and verification of hydrometeorological models. Hydrometeorological networks are utilized to collect such data. Since data collection is expensive, it is essential to design an optimal network based on the minimal number of hydrometeorological stations in order to reduce costs. This study proposes a two-phase copula entropy- based multiobjective optimization approach that includes: (1) copula entropy-based directional information transfer (CDIT) for clustering the potential hydrometeorological gauges into several groups, and (2) multiobjective method for selecting the optimal combination of gauges for regionalized groups. Although entropy theory has been employed for network design before, the joint histogram method used for mutual information estimation has several limitations. The copula entropy-based mutual information (MI) estimation method is shown to be more effective for quantifying the uncertainty of redundant information than the joint histogram (JH) method. The effectiveness of this approach is verified by applying to one type of hydrometeorological gauge network, with the use of three model evaluation measures, including Nash-Sutcliffe Coefficient (NSC), arithmetic mean of the negative copula entropy (MNCE), and MNCE/NSC. Results indicate that the two-phase copula entropy-based multiobjective technique is capable of evaluating the performance of regional hydrometeorological networks and can enable decision makers to develop strategies for water resources management.

An entropy-based analysis of lane changing behavior: An interactive approach.

Science.gov (United States)

Kosun, Caglar; Ozdemir, Serhan

2017-05-19

As a novelty, this article proposes the nonadditive entropy framework for the description of driver behaviors during lane changing. The authors also state that this entropy framework governs the lane changing behavior in traffic flow in accordance with the long-range vehicular interactions and traffic safety. The nonadditive entropy framework is the new generalized theory of thermostatistical mechanics. Vehicular interactions during lane changing are considered within this framework. The interactive approach for the lane changing behavior of the drivers is presented in the traffic flow scenarios presented in the article. According to the traffic flow scenarios, 4 categories of traffic flow and driver behaviors are obtained. Through the scenarios, comparative analyses of nonadditive and additive entropy domains are also provided. Two quadrants of the categories belong to the nonadditive entropy; the rest are involved in the additive entropy domain. Driving behaviors are extracted and the scenarios depict that nonadditivity matches safe driving well, whereas additivity corresponds to unsafe driving. Furthermore, the cooperative traffic system is considered in nonadditivity where the long-range interactions are present. However, the uncooperative traffic system falls into the additivity domain. The analyses also state that there would be possible traffic flow transitions among the quadrants. This article shows that lane changing behavior could be generalized as nonadditive, with additivity as a special case, based on the given traffic conditions. The nearest and close neighbor models are well within the conventional additive entropy framework. In this article, both the long-range vehicular interactions and safe driving behavior in traffic are handled in the nonadditive entropy domain. It is also inferred that the Tsallis entropy region would correspond to mandatory lane changing behavior, whereas additive and either the extensive or nonextensive entropy region would

Entropy Based Analysis of DNS Query Traffic in the Campus Network

Directory of Open Access Journals (Sweden)

Dennis Arturo Ludeña Romaña

2008-10-01

Full Text Available We carried out the entropy based study on the DNS query traffic from the campus network in a university through January 1st, 2006 to March 31st, 2007. The results are summarized, as follows: (1 The source IP addresses- and query keyword-based entropies change symmetrically in the DNS query traffic from the outside of the campus network when detecting the spam bot activity on the campus network. On the other hand (2, the source IP addresses- and query keywordbased entropies change similarly each other when detecting big DNS query traffic caused by prescanning or distributed denial of service (DDoS attack from the campus network. Therefore, we can detect the spam bot and/or DDoS attack bot by only watching DNS query access traffic.

Entropy-based Probabilistic Fatigue Damage Prognosis and Algorithmic Performance Comparison

Data.gov (United States)

National Aeronautics and Space Administration — In this paper, a maximum entropy-based general framework for probabilistic fatigue damage prognosis is investigated. The proposed methodology is based on an...

Entropy-based probabilistic fatigue damage prognosis and algorithmic performance comparison

Data.gov (United States)

National Aeronautics and Space Administration — In this paper, a maximum entropy-based general framework for probabilistic fatigue damage prognosis is investigated. The proposed methodology is based on an...

Measuring the quality of a quantum reference frame: The relative entropy of frameness

International Nuclear Information System (INIS)

Gour, Gilad; Marvian, Iman; Spekkens, Robert W.

2009-01-01

In the absence of a reference frame for transformations associated with group G, any quantum state that is noninvariant under the action of G may serve as a token of the missing reference frame. We here present a measure of the quality of such a token: the relative entropy of frameness. This is defined as the relative entropy distance between the state of interest and the nearest G-invariant state. Unlike the relative entropy of entanglement, this quantity is straightforward to calculate, and we find it to be precisely equal to the G-asymmetry, a measure of frameness introduced by Vaccaro et al. It is shown to provide an upper bound on the mutual information between the group element encoded into the token and the group element that may be extracted from it by measurement. In this sense, it quantifies the extent to which the token successfully simulates a full reference frame. We also show that despite a suggestive analogy from entanglement theory, the regularized relative entropy of frameness is zero and therefore does not quantify the rate of interconversion between the token and some standard form of quantum reference frame. Finally, we show how these investigations yield an approach to bounding the relative entropy of entanglement.

Entropy based fingerprint for local crystalline order

Science.gov (United States)

Piaggi, Pablo M.; Parrinello, Michele

2017-09-01

We introduce a new fingerprint that allows distinguishing between liquid-like and solid-like atomic environments. This fingerprint is based on an approximate expression for the entropy projected on individual atoms. When combined with local enthalpy, this fingerprint acquires an even finer resolution and it is capable of discriminating between different crystal structures.

Emergent Geometry from Entropy and Causality

Science.gov (United States)

Engelhardt, Netta

In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum

Minimization under entropy conditions, with applications in lower bound problems

International Nuclear Information System (INIS)

Toft, Joachim

2004-01-01

We minimize the functional f->∫ afdμ under the entropy condition E(f)=-∫ f log fdμ≥E, ∫ fdμ=1 and f≥0, where E is a member of R is fixed. We prove that the minimum is attained for f=e -sa /∫ e -sa dμ, where s is a member of R is chosen such that E(f)=E. We apply the result on minimizing problems in pseudodifferential calculus, where we minimize the harmonic oscillator

Entropy Viscosity Method for High-Order Approximations of Conservation Laws

KAUST Repository

Guermond, J. L.

2010-09-17

A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.

Entropy Viscosity Method for High-Order Approximations of Conservation Laws

KAUST Repository

Guermond, J. L.; Pasquetti, R.

2010-01-01

A stabilization technique for conservation laws is presented. It introduces in the governing equations a nonlinear dissipation function of the residual of the associated entropy equation and bounded from above by a first order viscous term. Different two-dimensional test cases are simulated - a 2D Burgers problem, the "KPP rotating wave" and the Euler system - using high order methods: spectral elements or Fourier expansions. Details on the tuning of the parameters controlling the entropy viscosity are given. © 2011 Springer.

Global sensitivity analysis for fuzzy inputs based on the decomposition of fuzzy output entropy

Science.gov (United States)

Shi, Yan; Lu, Zhenzhou; Zhou, Yicheng

2018-06-01

To analyse the component of fuzzy output entropy, a decomposition method of fuzzy output entropy is first presented. After the decomposition of fuzzy output entropy, the total fuzzy output entropy can be expressed as the sum of the component fuzzy entropy contributed by fuzzy inputs. Based on the decomposition of fuzzy output entropy, a new global sensitivity analysis model is established for measuring the effects of uncertainties of fuzzy inputs on the output. The global sensitivity analysis model can not only tell the importance of fuzzy inputs but also simultaneously reflect the structural composition of the response function to a certain degree. Several examples illustrate the validity of the proposed global sensitivity analysis, which is a significant reference in engineering design and optimization of structural systems.

Conditional quantum entropy power inequality for d-level quantum systems

Science.gov (United States)

Jeong, Kabgyun; Lee, Soojoon; Jeong, Hyunseok

2018-04-01

We propose an extension of the quantum entropy power inequality for finite dimensional quantum systems, and prove a conditional quantum entropy power inequality by using the majorization relation as well as the concavity of entropic functions also given by Audenaert et al (2016 J. Math. Phys. 57 052202). Here, we make particular use of the fact that a specific local measurement after a partial swap operation (or partial swap quantum channel) acting only on finite dimensional bipartite subsystems does not affect the majorization relation for the conditional output states when a separable ancillary subsystem is involved. We expect our conditional quantum entropy power inequality to be useful, and applicable in bounding and analyzing several capacity problems for quantum channels.

The criteria for selecting a method for unfolding neutron spectra based on the information entropy theory

International Nuclear Information System (INIS)

Zhu, Qingjun; Song, Fengquan; Ren, Jie; Chen, Xueyong; Zhou, Bin

2014-01-01

To further expand the application of an artificial neural network in the field of neutron spectrometry, the criteria for choosing between an artificial neural network and the maximum entropy method for the purpose of unfolding neutron spectra was presented. The counts of the Bonner spheres for IAEA neutron spectra were used as a database, and the artificial neural network and the maximum entropy method were used to unfold neutron spectra; the mean squares of the spectra were defined as the differences between the desired and unfolded spectra. After the information entropy of each spectrum was calculated using information entropy theory, the relationship between the mean squares of the spectra and the information entropy was acquired. Useful information from the information entropy guided the selection of unfolding methods. Due to the importance of the information entropy, the method for predicting the information entropy using the Bonner spheres' counts was established. The criteria based on the information entropy theory can be used to choose between the artificial neural network and the maximum entropy method unfolding methods. The application of an artificial neural network to unfold neutron spectra was expanded. - Highlights: • Two neutron spectra unfolding methods, ANN and MEM, were compared. • The spectrum's entropy offers useful information for selecting unfolding methods. • For the spectrum with low entropy, the ANN was generally better than MEM. • The spectrum's entropy was predicted based on the Bonner spheres' counts

Upper bounds for reversible circuits based on Young subgroups

DEFF Research Database (Denmark)

Abdessaied, Nabila; Soeken, Mathias; Thomsen, Michael Kirkedal

2014-01-01

We present tighter upper bounds on the number of Toffoli gates needed in reversible circuits. Both multiple controlled Toffoli gates and mixed polarity Toffoli gates have been considered for this purpose. The calculation of the bounds is based on a synthesis approach based on Young subgroups...... that results in circuits using a more generalized gate library. Starting from an upper bound for this library we derive new bounds which improve the existing bound by around 77%....

Value at risk estimation with entropy-based wavelet analysis in exchange markets

Science.gov (United States)

He, Kaijian; Wang, Lijun; Zou, Yingchao; Lai, Kin Keung

2014-08-01

In recent years, exchange markets are increasingly integrated together. Fluctuations and risks across different exchange markets exhibit co-moving and complex dynamics. In this paper we propose the entropy-based multivariate wavelet based approaches to analyze the multiscale characteristic in the multidimensional domain and improve further the Value at Risk estimation reliability. Wavelet analysis has been introduced to construct the entropy-based Multiscale Portfolio Value at Risk estimation algorithm to account for the multiscale dynamic correlation. The entropy measure has been proposed as the more effective measure with the error minimization principle to select the best basis when determining the wavelet families and the decomposition level to use. The empirical studies conducted in this paper have provided positive evidence as to the superior performance of the proposed approach, using the closely related Chinese Renminbi and European Euro exchange market.

The singular minimum entropy $H_\\infty$ control problem

NARCIS (Netherlands)

Stoorvogel, A.A.

1990-01-01

In this paper we search for controllers which minimize an entropy function of the closed loop transfer matrix under the constraint of internal stability and under the constraint that the closed loop transfer matrix has $H_\\infty$ norm less than some a priori given bound $\\gamma$. We find an explicit

Quantum key distribution with finite resources: Secret key rates via Renyi entropies

Energy Technology Data Exchange (ETDEWEB)

Abruzzo, Silvestre; Kampermann, Hermann; Mertz, Markus; Bruss, Dagmar [Institute for Theoretical Physics III, Heinrich-Heine-universitaet Duesseldorf, D-40225 Duesseldorf (Germany)

2011-09-15

A realistic quantum key distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem over Renyi entropies. Under the assumption of collective attacks by an eavesdropper, a computable estimate of our bound for the six-state protocol is provided. This bound leads to improved key rates in comparison to previous results.

Quantum key distribution with finite resources: Secret key rates via Renyi entropies

International Nuclear Information System (INIS)

Abruzzo, Silvestre; Kampermann, Hermann; Mertz, Markus; Bruss, Dagmar

2011-01-01

A realistic quantum key distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem over Renyi entropies. Under the assumption of collective attacks by an eavesdropper, a computable estimate of our bound for the six-state protocol is provided. This bound leads to improved key rates in comparison to previous results.

SpatEntropy: Spatial Entropy Measures in R

OpenAIRE

Altieri, Linda; Cocchi, Daniela; Roli, Giulia

2018-01-01

This article illustrates how to measure the heterogeneity of spatial data presenting a finite number of categories via computation of spatial entropy. The R package SpatEntropy contains functions for the computation of entropy and spatial entropy measures. The extension to spatial entropy measures is a unique feature of SpatEntropy. In addition to the traditional version of Shannon's entropy, the package includes Batty's spatial entropy, O'Neill's entropy, Li and Reynolds' contagion index, Ka...

Symbolic transfer entropy-based premature signal analysis

International Nuclear Information System (INIS)

Wang Jun; Yu Zheng-Feng

2012-01-01

In this paper, we use symbolic transfer entropy to study the coupling strength between premature signals. Numerical experiments show that three types of signal couplings are in the same direction. Among them, normal signal coupling is the strongest, followed by that of premature ventricular contractions, and that of atrial premature beats is the weakest. The T test shows that the entropies of the three signals are distinct. Symbolic transfer entropy requires less data, can distinguish the three types of signals and has very good computational efficiency. (interdisciplinary physics and related areas of science and technology)

Maximizing Entropy over Markov Processes

DEFF Research Database (Denmark)

Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis

2013-01-01

The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of an system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code....

Maximizing entropy over Markov processes

DEFF Research Database (Denmark)

Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis

2014-01-01

The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of a system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code. © 2014 Elsevier...

Adjoint entropy vs topological entropy

OpenAIRE

Giordano Bruno, Anna

2012-01-01

Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...

On the joint entropy of d-wise-independent variables

Czech Academy of Sciences Publication Activity Database

Gavinsky, Dmitry; Pudlák, Pavel

2016-01-01

Roč. 57, č. 3 (2016), s. 333-343 ISSN 0010-2628 R&D Projects: GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : d-wise-independent variables * entropy * lower bound Subject RIV: BA - General Mathematics http://hdl.handle.net/10338.dmlcz/145838

Entropy localization and extensivity in the semiclassical black hole evaporation

International Nuclear Information System (INIS)

Casini, H.

2009-01-01

I aim to quantify the distribution of information in the Hawking radiation and inside the black hole in the semiclassical evaporation process. The structure of relativistic quantum field theory does not allow one to define a localized entropy unambiguously, but rather forces one to consider the shared information (mutual information) between two different regions of space-time. Using this tool, I first show that the entropy of a thermal gas at the Unruh temperature underestimates the actual amount of (shared) information present in a region of the Rindler space. Then, I analyze the mutual information between the black hole and the late time radiation region. A well-known property of the entropy implies that this is monotonically increasing with time. This means that in the semiclassical picture it is not possible to recover the eventual purity of the initial state in the final Hawking radiation through subtle correlations established during the whole evaporation period, no matter the interactions present in the theory. I find extensivity of the entropy as a consequence of a reduction to a two dimensional conformal problem in a simple approximation. However, the extensivity of information in the radiation region in a full four dimensional calculation seems not to be guaranteed on general grounds. I also analyze the localization of shared information inside the black hole finding that a large amount of it is contained in a small, approximately flat region of space-time near the point where the horizon begins. This gives place to large violations of the entropy bounds. I show that this problem is not eased by backscattering effects and argue that a breaking of conformal invariance is necessary to delocalize the entropy. Finally, I indicate that the mutual information could lead to a way to understand the Bekenstein-Hawking black hole entropy which does not require a drastic reduction in degrees of freedom in order to regulate the entanglement entropy. On the contrary

Generalized sample entropy analysis for traffic signals based on similarity measure

Science.gov (United States)

Shang, Du; Xu, Mengjia; Shang, Pengjian

2017-05-01

Sample entropy is a prevailing method used to quantify the complexity of a time series. In this paper a modified method of generalized sample entropy and surrogate data analysis is proposed as a new measure to assess the complexity of a complex dynamical system such as traffic signals. The method based on similarity distance presents a different way of signals patterns match showing distinct behaviors of complexity. Simulations are conducted over synthetic data and traffic signals for providing the comparative study, which is provided to show the power of the new method. Compared with previous sample entropy and surrogate data analysis, the new method has two main advantages. The first one is that it overcomes the limitation about the relationship between the dimension parameter and the length of series. The second one is that the modified sample entropy functions can be used to quantitatively distinguish time series from different complex systems by the similar measure.

Calculating the Entropy of Solid and Liquid Metals, Based on Acoustic Data

Science.gov (United States)

Tekuchev, V. V.; Kalinkin, D. P.; Ivanova, I. V.

2018-05-01

The entropies of iron, cobalt, rhodium, and platinum are studied for the first time, based on acoustic data and using the Debye theory and rigid-sphere model, from 298 K up to the boiling point. A formula for the melting entropy of metals is validated. Good agreement between the research results and the literature data is obtained.

Entropy and equilibrium via games of complexity

Science.gov (United States)

Topsøe, Flemming

2004-09-01

It is suggested that thermodynamical equilibrium equals game theoretical equilibrium. Aspects of this thesis are discussed. The philosophy is consistent with maximum entropy thinking of Jaynes, but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical principle. The games introduced are based on measures of complexity. Entropy is viewed as minimal complexity. It is demonstrated that Tsallis entropy ( q-entropy) and Kaniadakis entropy ( κ-entropy) can be obtained in this way, based on suitable complexity measures. A certain unifying effect is obtained by embedding these measures in a two-parameter family of entropy functions.

Non-Gaussian Systems Control Performance Assessment Based on Rational Entropy

Directory of Open Access Journals (Sweden)

Jinglin Zhou

2018-05-01

Full Text Available Control loop Performance Assessment (CPA plays an important role in system operations. Stochastic statistical CPA index, such as a minimum variance controller (MVC-based CPA index, is one of the most widely used CPA indices. In this paper, a new minimum entropy controller (MEC-based CPA method of linear non-Gaussian systems is proposed. In this method, probability density function (PDF and rational entropy (RE are respectively used to describe the characteristics and the uncertainty of random variables. To better estimate the performance benchmark, an improved EDA algorithm, which is used to estimate the system parameters and noise PDF, is given. The effectiveness of the proposed method is illustrated through case studies on an ARMAX system.

Nonsymmetric entropy and maximum nonsymmetric entropy principle

International Nuclear Information System (INIS)

Liu Chengshi

2009-01-01

Under the frame of a statistical model, the concept of nonsymmetric entropy which generalizes the concepts of Boltzmann's entropy and Shannon's entropy, is defined. Maximum nonsymmetric entropy principle is proved. Some important distribution laws such as power law, can be derived from this principle naturally. Especially, nonsymmetric entropy is more convenient than other entropy such as Tsallis's entropy in deriving power laws.

Towards an information extraction and knowledge formation framework based on Shannon entropy

Directory of Open Access Journals (Sweden)

Iliescu Dragoș

2017-01-01

Full Text Available Information quantity subject is approached in this paperwork, considering the specific domain of nonconforming product management as information source. This work represents a case study. Raw data were gathered from a heavy industrial works company, information extraction and knowledge formation being considered herein. Involved method for information quantity estimation is based on Shannon entropy formula. Information and entropy spectrum are decomposed and analysed for extraction of specific information and knowledge-that formation. The result of the entropy analysis point out the information needed to be acquired by the involved organisation, this being presented as a specific knowledge type.

Fault detection of the connection of lithium-ion power batteries based on entropy for electric vehicles

Science.gov (United States)

Yao, Lei; Wang, Zhenpo; Ma, Jun

2015-10-01

This paper proposes a method of fault detection of the connection of Lithium-Ion batteries based on entropy for electric vehicle. In electric vehicle operation process, some factors, such as road conditions, driving habits, vehicle performance, always affect batteries by vibration, which easily cause loosing or virtual connection between batteries. Through the simulation of the battery charging and discharging experiment under vibration environment, the data of voltage fluctuation can be obtained. Meanwhile, an optimal filtering method is adopted using discrete cosine filter method to analyze the characteristics of system noise, based on the voltage set when batteries are working under different vibration frequency. Experimental data processed by filtering is analyzed based on local Shannon entropy, ensemble Shannon entropy and sample entropy. And the best way to find a method of fault detection of the connection of lithium-ion batteries based on entropy is presented for electric vehicle. The experimental data shows that ensemble Shannon entropy can predict the accurate time and the location of battery connection failure in real time. Besides electric-vehicle industry, this method can also be used in other areas in complex vibration environment.

Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels

Directory of Open Access Journals (Sweden)

Benoît Collins

2010-06-01

Full Text Available Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additivity problems. Our main result is a classification of regimes for which the von Neumann entropy is lower on average than the elementary bounds that can be obtained with linear algebra techniques.

A Novel Entropy-Based Centrality Approach for Identifying Vital Nodes in Weighted Networks

Directory of Open Access Journals (Sweden)

Tong Qiao

2018-04-01

Full Text Available Measuring centrality has recently attracted increasing attention, with algorithms ranging from those that simply calculate the number of immediate neighbors and the shortest paths to those that are complicated iterative refinement processes and objective dynamical approaches. Indeed, vital nodes identification allows us to understand the roles that different nodes play in the structure of a network. However, quantifying centrality in complex networks with various topological structures is not an easy task. In this paper, we introduce a novel definition of entropy-based centrality, which can be applicable to weighted directed networks. By design, the total power of a node is divided into two parts, including its local power and its indirect power. The local power can be obtained by integrating the structural entropy, which reveals the communication activity and popularity of each node, and the interaction frequency entropy, which indicates its accessibility. In addition, the process of influence propagation can be captured by the two-hop subnetworks, resulting in the indirect power. In order to evaluate the performance of the entropy-based centrality, we use four weighted real-world networks with various instance sizes, degree distributions, and densities. Correspondingly, these networks are adolescent health, Bible, United States (US airports, and Hep-th, respectively. Extensive analytical results demonstrate that the entropy-based centrality outperforms degree centrality, betweenness centrality, closeness centrality, and the Eigenvector centrality.

Fault Diagnosis Method Based on Information Entropy and Relative Principal Component Analysis

Directory of Open Access Journals (Sweden)

Xiaoming Xu

2017-01-01

Full Text Available In traditional principle component analysis (PCA, because of the neglect of the dimensions influence between different variables in the system, the selected principal components (PCs often fail to be representative. While the relative transformation PCA is able to solve the above problem, it is not easy to calculate the weight for each characteristic variable. In order to solve it, this paper proposes a kind of fault diagnosis method based on information entropy and Relative Principle Component Analysis. Firstly, the algorithm calculates the information entropy for each characteristic variable in the original dataset based on the information gain algorithm. Secondly, it standardizes every variable’s dimension in the dataset. And, then, according to the information entropy, it allocates the weight for each standardized characteristic variable. Finally, it utilizes the relative-principal-components model established for fault diagnosis. Furthermore, the simulation experiments based on Tennessee Eastman process and Wine datasets demonstrate the feasibility and effectiveness of the new method.

Entropy, neutro-entropy and anti-entropy for neutrosophic information

OpenAIRE

Vasile Patrascu

2017-01-01

This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: e...

Physical entropy, information entropy and their evolution equations

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.

Explaining the entropy concept and entropy components

Directory of Open Access Journals (Sweden)

Marko Popovic

2018-04-01

Full Text Available Total entropy of a thermodynamic system consists of two components: thermal entropy due to energy, and residual entropy due to molecular orientation. In this article, a three-step method for explaining entropy is suggested. Step one is to use a classical method to introduce thermal entropy STM as a function of temperature T and heat capacity at constant pressure Cp: STM = ∫(Cp/T dT. Thermal entropy is the entropy due to uncertainty in motion of molecules and vanishes at absolute zero (zero-point energy state. It is also the measure of useless thermal energy that cannot be converted into useful work. The next step is to introduce residual entropy S0 as a function of the number of molecules N and the number of distinct orientations available to them in a crystal m: S0 = N kB ln m, where kB is the Boltzmann constant. Residual entropy quantifies the uncertainty in molecular orientation. Residual entropy, unlike thermal entropy, is independent of temperature and remains present at absolute zero. The third step is to show that thermal entropy and residual entropy add up to the total entropy of a thermodynamic system S: S = S0 + STM. This method of explanation should result in a better comprehension of residual entropy and thermal entropy, as well as of their similarities and differences. The new method was tested in teaching at Faculty of Chemistry University of Belgrade, Serbia. The results of the test show that the new method has a potential to improve the quality of teaching.

Rényi-Fisher entropy product as a marker of topological phase transitions

Science.gov (United States)

Bolívar, J. C.; Nagy, Ágnes; Romera, Elvira

2018-05-01

The combined Rényi-Fisher entropy product of electrons plus holes displays a minimum at the charge neutrality points. The Stam-Rényi difference and the Stam-Rényi uncertainty product of the electrons plus holes, show maxima at the charge neutrality points. Topological quantum numbers capable of detecting the topological insulator and the band insulator phases, are defined. Upper and lower bounds for the position and momentum space Rényi-Fisher entropy products are derived.

Entropy, neutro-entropy and anti-entropy for neutrosophic information

OpenAIRE

Vasile Patrascu

2017-01-01

This article shows a deca-valued representation of neutrosophic information in which are defined the following features: truth, falsity, weak truth, weak falsity, ignorance, contradiction, saturation, neutrality, ambiguity and hesitation. Using these features, there are constructed computing formulas for entropy, neutro-entropy and anti-entropy.

Using heteroclinic orbits to quantify topological entropy in fluid flows

International Nuclear Information System (INIS)

Sattari, Sulimon; Chen, Qianting; Mitchell, Kevin A.

2016-01-01

Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or “ghost,” rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding of ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.

Multiscale Permutation Entropy Based Rolling Bearing Fault Diagnosis

Directory of Open Access Journals (Sweden)

Jinde Zheng

2014-01-01

Full Text Available A new rolling bearing fault diagnosis approach based on multiscale permutation entropy (MPE, Laplacian score (LS, and support vector machines (SVMs is proposed in this paper. Permutation entropy (PE was recently proposed and defined to measure the randomicity and detect dynamical changes of time series. However, for the complexity of mechanical systems, the randomicity and dynamic changes of the vibration signal will exist in different scales. Thus, the definition of MPE is introduced and employed to extract the nonlinear fault characteristics from the bearing vibration signal in different scales. Besides, the SVM is utilized to accomplish the fault feature classification to fulfill diagnostic procedure automatically. Meanwhile, in order to avoid a high dimension of features, the Laplacian score (LS is used to refine the feature vector by ranking the features according to their importance and correlations with the main fault information. Finally, the rolling bearing fault diagnosis method based on MPE, LS, and SVM is proposed and applied to the experimental data. The experimental data analysis results indicate that the proposed method could identify the fault categories effectively.

EXISTENCE AND UNIQUENESS OF THE ENTROPY SOLUTION TO A NONLINEAR HYPERBOLIC EQUATION

Institute of Scientific and Technical Information of China (English)

R.EYMARD; T.Gallouёt; R.Herbin

1995-01-01

This work is concerned with the proof of the existence and uniqueness of the entropy weak solution to the following nonlinear hyperbolic equation: ut+div(vf(u)） = 0 in IRN×（0, T）, with initial data u(-, 0) = u0(-) in IRN, where u0 ∈ L∞（IRN) is a given function, v is a divergence-free bounded fnnction of class C1 from IRN × [0, T] to IRN, and f is a 5motion of class C1 from IR to IR. It also gives a result of convergence of a numerical scheme for the discretization of this equation. The authors first show the existence of a “process” solution (which generalizes the concept of entropy weak solutions, and can be obtained by passing to the limit of solutions ofthe numerical scheme). The uniqueness of this entropy process solution is then proven; it isalso proven that the entropy process solution is in fact an entropy weak solution. Hence the existence and uniqueness of the entropy weak solution are proven.

Viscosity bound violation in holographic solids and the viscoelastic response

Energy Technology Data Exchange (ETDEWEB)

Alberte, Lasma [Abdus Salam International Centre for Theoretical Physics (ICTP),Strada Costiera 11, 34151, Trieste (Italy); Baggioli, Matteo [Institut de Física d’Altes Energies (IFAE),The Barcelona Institute of Science and Technology (BIST),Campus UAB, 08193 Bellaterra, Barcelona (Spain); Department of Physics, Institute for Condensed Matter Theory, University of Illinois,1110 W. Green Street, Urbana, IL 61801 (United States); Pujolàs, Oriol [Institut de Física d’Altes Energies (IFAE),The Barcelona Institute of Science and Technology (BIST),Campus UAB, 08193 Bellaterra, Barcelona (Spain)

2016-07-14

We argue that the Kovtun-Son-Starinets (KSS) lower bound on the viscosity to entropy density ratio holds in fluid systems but is violated in solid materials with a non-zero shear elastic modulus. We construct explicit examples of this by applying the standard gauge/gravity duality methods to massive gravity and show that the KSS bound is clearly violated in black brane solutions whenever the massive gravity theories are of solid type. We argue that the physical reason for the bound violation relies on the viscoelastic nature of the mechanical response in these materials. We speculate on whether any real-world materials can violate the bound and discuss a possible generalization of the bound that involves the ratio of the shear elastic modulus to the pressure.

Viscosity bound violation in holographic solids and the viscoelastic response

International Nuclear Information System (INIS)

Alberte, Lasma; Baggioli, Matteo; Pujolàs, Oriol

2016-01-01

We argue that the Kovtun-Son-Starinets (KSS) lower bound on the viscosity to entropy density ratio holds in fluid systems but is violated in solid materials with a non-zero shear elastic modulus. We construct explicit examples of this by applying the standard gauge/gravity duality methods to massive gravity and show that the KSS bound is clearly violated in black brane solutions whenever the massive gravity theories are of solid type. We argue that the physical reason for the bound violation relies on the viscoelastic nature of the mechanical response in these materials. We speculate on whether any real-world materials can violate the bound and discuss a possible generalization of the bound that involves the ratio of the shear elastic modulus to the pressure.

Risk Contagion in Chinese Banking Industry: A Transfer Entropy-Based Analysis

Directory of Open Access Journals (Sweden)

Jianping Li

2013-12-01

Full Text Available What is the impact of a bank failure on the whole banking industry? To resolve this issue, the paper develops a transfer entropy-based method to determine the interbank exposure matrix between banks. This method constructs the interbank market structure by calculating the transfer entropy matrix using bank stock price sequences. This paper also evaluates the stability of Chinese banking system by simulating the risk contagion process. This paper contributes to the literature on interbank contagion mainly in two ways: it establishes a convincing connection between interbank market and transfer entropy, and exploits the market information (stock price rather than presumptions to determine the interbank exposure matrix. Second, the empirical analysis provides an in depth understanding of the stability of the current Chinese banking system.

Comment on ''Proof of the quantum bound on specific entropy for free fields''

International Nuclear Information System (INIS)

Unruh, W.G.

1990-01-01

The effect of zero modes on the arguments of Bekenstein and Schiffer are analyzed, and it is shown that, if a system has such zero modes, an arbitrarily large entropy can be stored in the system for any given cost in energy

Entropy of Iterated Function Systems and Their Relations with Black Holes and Bohr-Like Black Holes Entropies

Directory of Open Access Journals (Sweden)

Christian Corda

2018-01-01

Full Text Available In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein–Hawking entropies and its subleading corrections. More precisely, we consider the recent model of a Bohr-like black hole that has been recently analysed in some papers in the literature, obtaining the intriguing result that the metric entropies of a black hole are created by the metric entropies of the functions, created by the black hole principal quantum numbers, i.e., by the black hole quantum levels. We present a new type of topological entropy for general iterated function systems based on a new kind of the inverse of covers. Then the notion of metric entropy for an Iterated Function System ( I F S is considered, and we prove that these definitions for topological entropy of IFS’s are equivalent. It is shown that this kind of topological entropy keeps some properties which are hold by the classic definition of topological entropy for a continuous map. We also consider average entropy as another type of topological entropy for an I F S which is based on the topological entropies of its elements and it is also an invariant object under topological conjugacy. The relation between Axiom A and the average entropy is investigated.

Biological Aging and Life Span Based on Entropy Stress via Organ and Mitochondrial Metabolic Loading

Directory of Open Access Journals (Sweden)

Kalyan Annamalai

2017-10-01

Full Text Available The energy for sustaining life is released through the oxidation of glucose, fats, and proteins. A part of the energy released within each cell is stored as chemical energy of Adenosine Tri-Phosphate molecules, which is essential for performing life-sustaining functions, while the remainder is released as heat in order to maintain isothermal state of the body. Earlier literature introduced the availability concepts from thermodynamics, related the specific irreversibility and entropy generation rates to metabolic efficiency and energy release rate of organ k, computed whole body specific entropy generation rate of whole body at any given age as a sum of entropy generation within four vital organs Brain, Heart, Kidney, Liver (BHKL with 5th organ being the rest of organs (R5 and estimated the life span using an upper limit on lifetime entropy generated per unit mass of body, σM,life. The organ entropy stress expressed in terms of lifetime specific entropy generated per unit mass of body organs (kJ/(K kg of organ k was used to rank organs and heart ranked highest while liver ranked lowest. The present work includes the effects of (1 two additional organs: adipose tissue (AT and skeletal muscles (SM which are of importance to athletes; (2 proportions of nutrients oxidized which affects blood temperature and metabolic efficiencies; (3 conversion of the entropy stress from organ/cellular level to mitochondrial level; and (4 use these parameters as metabolism-based biomarkers for quantifying the biological aging process in reaching the limit of σM,life. Based on the 7-organ model and Elia constants for organ metabolic rates for a male of 84 kg steady mass and using basic and derived allometric constants of organs, the lifetime energy expenditure is estimated to be 2725 MJ/kg body mass while lifetime entropy generated is 6050 kJ/(K kg body mass with contributions of 190; 1835.0; 610; 290; 700; 1470 and 95 kJ/K contributed by AT-BHKL-SM-R7 to 1 kg body

Contour entropy: a new determinant of perceiving ground or a hole.

Science.gov (United States)

Gillam, Barbara J; Grove, Philip M

2011-06-01

Figure-ground perception is typically described as seeing one surface occluding another. Figure properties, not ground properties, are considered the significant factors. In scenes, however, a near surface will often occlude multiple contours and surfaces, often at different depths, producing alignments that are improbable except under conditions of occlusion. We thus hypothesized that unrelated (high entropy) lines would tend to appear as ground in a figure-ground paradigm more often than similarly aligned ordered (low entropy) lines. We further hypothesized that for lines spanning a closed area, high line entropy should increase the hole-like appearance of that area. These predictions were confirmed in three experiments. The probability that patterned rectangles were seen as ground when alternated with blank rectangles increased with pattern entropy. A single rectangular shape appeared more hole-like when the entropy of the enclosed contours increased. Furthermore, these same contours, with the outline shape removed, gave rise to bounding illusory contours whose strength increased with contour entropy. We conclude that figure-ground and hole perception can be determined by properties of ground in the absence of any figural shape, or surround, factors.

Image coding based on maximum entropy partitioning for identifying ...

Indian Academy of Sciences (India)

A new coding scheme based on maximum entropy partitioning is proposed in our work, particularly to identify the improbable intensities related to different emotions. The improbable intensities when used as a mask decode the facial expression correctly, providing an effectiveplatform for future emotion categorization ...

Using entropy measures to characterize human locomotion.

Science.gov (United States)

Leverick, Graham; Szturm, Tony; Wu, Christine Q

2014-12-01

Entropy measures have been widely used to quantify the complexity of theoretical and experimental dynamical systems. In this paper, the value of using entropy measures to characterize human locomotion is demonstrated based on their construct validity, predictive validity in a simple model of human walking and convergent validity in an experimental study. Results show that four of the five considered entropy measures increase meaningfully with the increased probability of falling in a simple passive bipedal walker model. The same four entropy measures also experienced statistically significant increases in response to increasing age and gait impairment caused by cognitive interference in an experimental study. Of the considered entropy measures, the proposed quantized dynamical entropy (QDE) and quantization-based approximation of sample entropy (QASE) offered the best combination of sensitivity to changes in gait dynamics and computational efficiency. Based on these results, entropy appears to be a viable candidate for assessing the stability of human locomotion.

Towards an entropy-based analysis of log variability

DEFF Research Database (Denmark)

Back, Christoffer Olling; Debois, Søren; Slaats, Tijs

2017-01-01

the development of hybrid miners: given a (sub-)log, can we determine a priori whether the log is best suited for imperative or declarative mining? We propose using the concept of entropy, commonly used in information theory. We consider different measures for entropy that could be applied and show through...... experimentation on both synthetic and real-life logs that these entropy measures do indeed give insights into the complexity of the log and can act as an indicator of which mining paradigm should be used....

Towards an Entropy-based Analysis of Log Variability

DEFF Research Database (Denmark)

Back, Christoffer Olling; Debois, Søren; Slaats, Tijs

2018-01-01

the development of hybrid miners: given a log, can we determine a priori whether the log is best suited for imperative or declarative mining? We propose using the concept of entropy, commonly used in information theory. We consider different measures for entropy that could be applied and show through...... experimentation on both synthetic and real-life logs that these entropy measures do indeed give insights into the complexity of the log and can act as an indicator of which mining paradigm should be used....

The holographic bound in the scalar-tensor and f(R) gravities

International Nuclear Information System (INIS)

Firouzjaee, J.T.

2013-01-01

The holographic bound has been extended to the different theory of gravities such as scalar-tensor gravity and f(R) gravity according to the Noether charge definition of the entropy for a black hole surface. We have introduced some popular examples of the flat FRW cosmology in order to investigate holographic bound in scalar-tensor and f(R) gravity. Using the holographic bound, we put an additional constraint on scalar-tensor gravity and the f(R) gravity parameters. We also discuss the transformation from Jordan frame to Einstein frame. (orig.)

Dynamical noise filter and conditional entropy analysis in chaos synchronization.

Science.gov (United States)

Wang, Jiao; Lai, C-H

2006-06-01

It is shown that, in a chaotic synchronization system whose driving signal is exposed to channel noise, the estimation of the drive system states can be greatly improved by applying the dynamical noise filtering to the response system states. If the noise is bounded in a certain range, the estimation errors, i.e., the difference between the filtered responding states and the driving states, can be made arbitrarily small. This property can be used in designing an alternative digital communication scheme. An analysis based on the conditional entropy justifies the application of dynamical noise filtering in generating quality synchronization.

Giant irreversible positive to large reversible negative magnetic entropy change evolution in Tb-based bulk metallic glass

International Nuclear Information System (INIS)

Luo Qiang; Schwarz, Bjoern; Mattern, Norbert; Eckert, Juergen

2010-01-01

We study the effects of amorphous structure and random anisotropy on the magnetic entropy change in a series of Tb-based amorphous alloys. The amorphous structure broadens the peak of magnetic entropy change and facilitates the adjustment of properties. The peak magnetic entropy change above the spin freezing temperature first depends on the average magnetic moment approximately linearly and second on the exchange interaction and random anisotropy. Large and broad reversible negative magnetic entropy changes are observed above the spin freezing temperature and giant positive irreversible magnetic entropy changes which associate with the internal entropy production are obtained well below.

Entropy-based implied volatility and its information content

NARCIS (Netherlands)

X. Xiao (Xiao); C. Zhou (Chen)

2016-01-01

markdownabstractThis paper investigates the maximum entropy approach on estimating implied volatility. The entropy approach also allows to measure option implied skewness and kurtosis nonparametrically, and to construct confidence intervals. Simulations show that the en- tropy approach outperforms

Bounds on topological Abelian string-vortex and string-cigar from information-entropic measure

Energy Technology Data Exchange (ETDEWEB)

Correa, R.A.C., E-mail: rafael.couceiro@ufabc.edu.br [CCNH, Universidade Federal do ABC (UFABC), 09210-580, Santo André, SP (Brazil); Dantas, D.M., E-mail: davi@fisica.ufc.br [Universidade Federal do Ceará (UFC), 60455-760, Fortaleza, CE (Brazil); Almeida, C.A.S., E-mail: carlos@fisica.ufc.br [Universidade Federal do Ceará (UFC), Departamento de Física, 60455-760, Fortaleza, CE (Brazil); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), 09210-580, Santo André, SP (Brazil)

2016-04-10

In this work we obtain bounds on the topological Abelian string-vortex and on the string-cigar, by using a new measure of configurational complexity, known as configurational entropy. In this way, the information-theoretical measure of six-dimensional braneworlds scenarios is capable to probe situations where the parameters responsible for the brane thickness are arbitrary. The so-called configurational entropy (CE) selects the best value of the parameter in the model. This is accomplished by minimizing the CE, namely, by selecting the most appropriate parameters in the model that correspond to the most organized system, based upon the Shannon information theory. This information-theoretical measure of complexity provides a complementary perspective to situations where strictly energy-based arguments are inconclusive. We show that the higher the energy the higher the CE, what shows an important correlation between the energy of the a localized field configuration and its associated entropic measure.

Optimizing an estuarine water quality monitoring program through an entropy-based hierarchical spatiotemporal Bayesian framework

Science.gov (United States)

Alameddine, Ibrahim; Karmakar, Subhankar; Qian, Song S.; Paerl, Hans W.; Reckhow, Kenneth H.

2013-10-01

The total maximum daily load program aims to monitor more than 40,000 standard violations in around 20,000 impaired water bodies across the United States. Given resource limitations, future monitoring efforts have to be hedged against the uncertainties in the monitored system, while taking into account existing knowledge. In that respect, we have developed a hierarchical spatiotemporal Bayesian model that can be used to optimize an existing monitoring network by retaining stations that provide the maximum amount of information, while identifying locations that would benefit from the addition of new stations. The model assumes the water quality parameters are adequately described by a joint matrix normal distribution. The adopted approach allows for a reduction in redundancies, while emphasizing information richness rather than data richness. The developed approach incorporates the concept of entropy to account for the associated uncertainties. Three different entropy-based criteria are adopted: total system entropy, chlorophyll-a standard violation entropy, and dissolved oxygen standard violation entropy. A multiple attribute decision making framework is adopted to integrate the competing design criteria and to generate a single optimal design. The approach is implemented on the water quality monitoring system of the Neuse River Estuary in North Carolina, USA. The model results indicate that the high priority monitoring areas identified by the total system entropy and the dissolved oxygen violation entropy criteria are largely coincident. The monitoring design based on the chlorophyll-a standard violation entropy proved to be less informative, given the low probabilities of violating the water quality standard in the estuary.

Research on Sustainable Development Level Evaluation of Resource-based Cities Based on Shapely Entropy and Chouqet Integral

Science.gov (United States)

Zhao, Hui; Qu, Weilu; Qiu, Weiting

2018-03-01

In order to evaluate sustainable development level of resource-based cities, an evaluation method with Shapely entropy and Choquet integral is proposed. First of all, a systematic index system is constructed, the importance of each attribute is calculated based on the maximum Shapely entropy principle, and then the Choquet integral is introduced to calculate the comprehensive evaluation value of each city from the bottom up, finally apply this method to 10 typical resource-based cities in China. The empirical results show that the evaluation method is scientific and reasonable, which provides theoretical support for the sustainable development path and reform direction of resource-based cities.

Entropy-Based Video Steganalysis of Motion Vectors

Directory of Open Access Journals (Sweden)

Elaheh Sadat Sadat

2018-04-01

Full Text Available In this paper, a new method is proposed for motion vector steganalysis using the entropy value and its combination with the features of the optimized motion vector. In this method, the entropy of blocks is calculated to determine their texture and the precision of their motion vectors. Then, by using a fuzzy cluster, the blocks are clustered into the blocks with high and low texture, while the membership function of each block to a high texture class indicates the texture of that block. These membership functions are used to weight the effective features that are extracted by reconstructing the motion estimation equations. Characteristics of the results indicate that the use of entropy and the irregularity of each block increases the precision of the final video classification into cover and stego classes.

Characterizing brain structures and remodeling after TBI based on information content, diffusion entropy.

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Fozouni, Niloufar; Chopp, Michael; Nejad-Davarani, Siamak P; Zhang, Zheng Gang; Lehman, Norman L; Gu, Steven; Ueno, Yuji; Lu, Mei; Ding, Guangliang; Li, Lian; Hu, Jiani; Bagher-Ebadian, Hassan; Hearshen, David; Jiang, Quan

2013-01-01

To overcome the limitations of conventional diffusion tensor magnetic resonance imaging resulting from the assumption of a Gaussian diffusion model for characterizing voxels containing multiple axonal orientations, Shannon's entropy was employed to evaluate white matter structure in human brain and in brain remodeling after traumatic brain injury (TBI) in a rat. Thirteen healthy subjects were investigated using a Q-ball based DTI data sampling scheme. FA and entropy values were measured in white matter bundles, white matter fiber crossing areas, different gray matter (GM) regions and cerebrospinal fluid (CSF). Axonal densities' from the same regions of interest (ROIs) were evaluated in Bielschowsky and Luxol fast blue stained autopsy (n = 30) brain sections by light microscopy. As a case demonstration, a Wistar rat subjected to TBI and treated with bone marrow stromal cells (MSC) 1 week after TBI was employed to illustrate the superior ability of entropy over FA in detecting reorganized crossing axonal bundles as confirmed by histological analysis with Bielschowsky and Luxol fast blue staining. Unlike FA, entropy was less affected by axonal orientation and more affected by axonal density. A significant agreement (r = 0.91) was detected between entropy values from in vivo human brain and histologically measured axonal density from post mortum from the same brain structures. The MSC treated TBI rat demonstrated that the entropy approach is superior to FA in detecting axonal remodeling after injury. Compared with FA, entropy detected new axonal remodeling regions with crossing axons, confirmed with immunohistological staining. Entropy measurement is more effective in distinguishing axonal remodeling after injury, when compared with FA. Entropy is also more sensitive to axonal density than axonal orientation, and thus may provide a more accurate reflection of axonal changes that occur in neurological injury and disease.

Characterizing Brain Structures and Remodeling after TBI Based on Information Content, Diffusion Entropy

Science.gov (United States)

Fozouni, Niloufar; Chopp, Michael; Nejad-Davarani, Siamak P.; Zhang, Zheng Gang; Lehman, Norman L.; Gu, Steven; Ueno, Yuji; Lu, Mei; Ding, Guangliang; Li, Lian; Hu, Jiani; Bagher-Ebadian, Hassan; Hearshen, David; Jiang, Quan

2013-01-01

Background To overcome the limitations of conventional diffusion tensor magnetic resonance imaging resulting from the assumption of a Gaussian diffusion model for characterizing voxels containing multiple axonal orientations, Shannon's entropy was employed to evaluate white matter structure in human brain and in brain remodeling after traumatic brain injury (TBI) in a rat. Methods Thirteen healthy subjects were investigated using a Q-ball based DTI data sampling scheme. FA and entropy values were measured in white matter bundles, white matter fiber crossing areas, different gray matter (GM) regions and cerebrospinal fluid (CSF). Axonal densities' from the same regions of interest (ROIs) were evaluated in Bielschowsky and Luxol fast blue stained autopsy (n = 30) brain sections by light microscopy. As a case demonstration, a Wistar rat subjected to TBI and treated with bone marrow stromal cells (MSC) 1 week after TBI was employed to illustrate the superior ability of entropy over FA in detecting reorganized crossing axonal bundles as confirmed by histological analysis with Bielschowsky and Luxol fast blue staining. Results Unlike FA, entropy was less affected by axonal orientation and more affected by axonal density. A significant agreement (r = 0.91) was detected between entropy values from in vivo human brain and histologically measured axonal density from post mortum from the same brain structures. The MSC treated TBI rat demonstrated that the entropy approach is superior to FA in detecting axonal remodeling after injury. Compared with FA, entropy detected new axonal remodeling regions with crossing axons, confirmed with immunohistological staining. Conclusions Entropy measurement is more effective in distinguishing axonal remodeling after injury, when compared with FA. Entropy is also more sensitive to axonal density than axonal orientation, and thus may provide a more accurate reflection of axonal changes that occur in neurological injury and disease

Improved Minimum Entropy Filtering for Continuous Nonlinear Non-Gaussian Systems Using a Generalized Density Evolution Equation

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Jinliang Xu

2013-06-01

Full Text Available This paper investigates the filtering problem for multivariate continuous nonlinear non-Gaussian systems based on an improved minimum error entropy (MEE criterion. The system is described by a set of nonlinear continuous equations with non-Gaussian system noises and measurement noises. The recently developed generalized density evolution equation is utilized to formulate the joint probability density function (PDF of the estimation errors. Combining the entropy of the estimation error with the mean squared error, a novel performance index is constructed to ensure the estimation error not only has small uncertainty but also approaches to zero. According to the conjugate gradient method, the optimal filter gain matrix is then obtained by minimizing the improved minimum error entropy criterion. In addition, the condition is proposed to guarantee that the estimation error dynamics is exponentially bounded in the mean square sense. Finally, the comparative simulation results are presented to show that the proposed MEE filter is superior to nonlinear unscented Kalman filter (UKF.

A new entropy based method for computing software structural complexity

International Nuclear Information System (INIS)

Roca, Jose L.

2002-01-01

In this paper a new methodology for the evaluation of software structural complexity is described. It is based on the entropy evaluation of the random uniform response function associated with the so called software characteristic function SCF. The behavior of the SCF with the different software structures and their relationship with the number of inherent errors is investigated. It is also investigated how the entropy concept can be used to evaluate the complexity of a software structure considering the SCF as a canonical representation of the graph associated with the control flow diagram. The functions, parameters and algorithms that allow to carry out this evaluation are also introduced. After this analytic phase follows the experimental phase, verifying the consistency of the proposed metric and their boundary conditions. The conclusion is that the degree of software structural complexity can be measured as the entropy of the random uniform response function of the SCF. That entropy is in direct relationship with the number of inherent software errors and it implies a basic hazard failure rate for it, so that a minimum structure assures a certain stability and maturity of the program. This metric can be used, either to evaluate the product or the process of software development, as development tool or for monitoring the stability and the quality of the final product. (author)

Universal bounds in even-spin CFTs

Energy Technology Data Exchange (ETDEWEB)

Qualls, Joshua D. [Department of Physics, National Taiwan University,Taipei, Taiwan (China)

2015-12-01

We prove using invariance under the modular S− and ST−transformations that every unitary two-dimensional conformal field theory (CFT) having only even-spin primary operators (with no extended chiral algebra and with right- and left-central charges c,c̃>1) contains a primary operator with dimension Δ{sub 1} satisfying 0<Δ{sub 1}<((c+c̃)/24)+0.09280…. After deriving both analytical and numerical bounds, we discuss how to extend our methods to bound higher conformal dimensions before deriving lower and upper bounds on the number of primary operators in a given energy range. Using the AdS{sub 3}/CFT{sub 2} dictionary, the bound on Δ{sub 1} proves the lightest massive excitation in appropriate theories of 3D matter and gravity with cosmological constant Λ<0 can be no heavier than 1/8G{sub N}+O(√(−Λ)); the bounds on the number of operators are related via AdS/CFT to the entropy of states in the dual gravitational theory. In the flat-space approximation, the limiting mass is exactly that of the lightest BTZ black hole.

Multidimensional scaling analysis of financial time series based on modified cross-sample entropy methods

Science.gov (United States)

He, Jiayi; Shang, Pengjian; Xiong, Hui

2018-06-01

Stocks, as the concrete manifestation of financial time series with plenty of potential information, are often used in the study of financial time series. In this paper, we utilize the stock data to recognize their patterns through out the dissimilarity matrix based on modified cross-sample entropy, then three-dimensional perceptual maps of the results are provided through multidimensional scaling method. Two modified multidimensional scaling methods are proposed in this paper, that is, multidimensional scaling based on Kronecker-delta cross-sample entropy (MDS-KCSE) and multidimensional scaling based on permutation cross-sample entropy (MDS-PCSE). These two methods use Kronecker-delta based cross-sample entropy and permutation based cross-sample entropy to replace the distance or dissimilarity measurement in classical multidimensional scaling (MDS). Multidimensional scaling based on Chebyshev distance (MDSC) is employed to provide a reference for comparisons. Our analysis reveals a clear clustering both in synthetic data and 18 indices from diverse stock markets. It implies that time series generated by the same model are easier to have similar irregularity than others, and the difference in the stock index, which is caused by the country or region and the different financial policies, can reflect the irregularity in the data. In the synthetic data experiments, not only the time series generated by different models can be distinguished, the one generated under different parameters of the same model can also be detected. In the financial data experiment, the stock indices are clearly divided into five groups. Through analysis, we find that they correspond to five regions, respectively, that is, Europe, North America, South America, Asian-Pacific (with the exception of mainland China), mainland China and Russia. The results also demonstrate that MDS-KCSE and MDS-PCSE provide more effective divisions in experiments than MDSC.

A High-Precision Time-Frequency Entropy Based on Synchrosqueezing Generalized S-Transform Applied in Reservoir Detection

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Hui Chen

2018-06-01

Full Text Available According to the fact that high frequency will be abnormally attenuated when seismic signals travel across reservoirs, a new method, which is named high-precision time-frequency entropy based on synchrosqueezing generalized S-transform, is proposed for hydrocarbon reservoir detection in this paper. First, the proposed method obtains the time-frequency spectra by synchrosqueezing generalized S-transform (SSGST, which are concentrated around the real instantaneous frequency of the signals. Then, considering the characteristics and effects of noises, we give a frequency constraint condition to calculate the entropy based on time-frequency spectra. The synthetic example verifies that the entropy will be abnormally high when seismic signals have an abnormal attenuation. Besides, comparing with the GST time-frequency entropy and the original SSGST time-frequency entropy in field data, the results of the proposed method show higher precision. Moreover, the proposed method can not only accurately detect and locate hydrocarbon reservoirs, but also effectively suppress the impact of random noises.

Entropy in molecular recognition by proteins.

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Caro, José A; Harpole, Kyle W; Kasinath, Vignesh; Lim, Jackwee; Granja, Jeffrey; Valentine, Kathleen G; Sharp, Kim A; Wand, A Joshua

2017-06-20

Molecular recognition by proteins is fundamental to molecular biology. Dissection of the thermodynamic energy terms governing protein-ligand interactions has proven difficult, with determination of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quantitatively obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein-ligand complexes are used to show a quantitative relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodynamic variable to modulate protein-ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biologically meaningless. The dynamical proxy for conformational entropy or "entropy meter" also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water-protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity molecular recognition by proteins.

The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

KAUST Repository

Di Francesco, M.

2008-12-08

We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.

On the quantum information entropies and squeezing associated with the eigenstates of the isotonic oscillator

International Nuclear Information System (INIS)

Ghasemi, A; Hooshmandasl, M R; Tavassoly, M K

2011-01-01

In this paper we calculate the position and momentum space information entropies for the quantum states associated with a particular physical system, i.e. the isotonic oscillator Hamiltonian. We present our results for its ground states, as well as for its excited states. We observe that the lower bound of the sum of the position and momentum entropies expressed by the Beckner, Bialynicki-Birula and Mycielski (BBM) inequality is satisfied. Moreover, there exist eigenstates that exhibit squeezing in the position information entropy. In fact, entropy squeezing, which occurs in position, will be compensated for by an increase in momentum entropy, such that the BBM inequality is guaranteed. To complete our study we investigate the amplitude squeezing in x and p-quadratures corresponding to the eigenstates of the isotonic oscillator and show that amplitude squeezing, again in x, will be revealed as expected, while the Heisenberg uncertainty relationship is also satisfied. Finally, our numerical calculations of the entropy densities will be presented graphically.

Structured chaos shapes spike-response noise entropy in balanced neural networks

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Guillaume eLajoie

2014-10-01

Full Text Available Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. For many models of these networks, a striking feature is that their dynamics are chaotic and thus, are sensitive to small perturbations. How does this chaos manifest in the neural code? Specifically, how variable are the spike patterns that such a network produces in response to an input signal? To answer this, we derive a bound for a general measure of variability -- spike-train entropy. This leads to important insights on the variability of multi-cell spike pattern distributions in large recurrent networks of spiking neurons responding to fluctuating inputs. The analysis is based on results from random dynamical systems theory and is complemented by detailed numerical simulations. We find that the spike pattern entropy is an order of magnitude lower than what would be extrapolated from single cells. This holds despite the fact that network coupling becomes vanishingly sparse as network size grows -- a phenomenon that depends on ``extensive chaos, as previously discovered for balanced networks without stimulus drive. Moreover, we show how spike pattern entropy is controlled by temporal features of the inputs. Our findings provide insight into how neural networks may encode stimuli in the presence of inherently chaotic dynamics.

Fault Detection and Diagnosis for Gas Turbines Based on a Kernelized Information Entropy Model

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Weiying Wang

2014-01-01

Full Text Available Gas turbines are considered as one kind of the most important devices in power engineering and have been widely used in power generation, airplanes, and naval ships and also in oil drilling platforms. However, they are monitored without man on duty in the most cases. It is highly desirable to develop techniques and systems to remotely monitor their conditions and analyze their faults. In this work, we introduce a remote system for online condition monitoring and fault diagnosis of gas turbine on offshore oil well drilling platforms based on a kernelized information entropy model. Shannon information entropy is generalized for measuring the uniformity of exhaust temperatures, which reflect the overall states of the gas paths of gas turbine. In addition, we also extend the entropy to compute the information quantity of features in kernel spaces, which help to select the informative features for a certain recognition task. Finally, we introduce the information entropy based decision tree algorithm to extract rules from fault samples. The experiments on some real-world data show the effectiveness of the proposed algorithms.

Fault detection and diagnosis for gas turbines based on a kernelized information entropy model.

Science.gov (United States)

Wang, Weiying; Xu, Zhiqiang; Tang, Rui; Li, Shuying; Wu, Wei

2014-01-01

Gas turbines are considered as one kind of the most important devices in power engineering and have been widely used in power generation, airplanes, and naval ships and also in oil drilling platforms. However, they are monitored without man on duty in the most cases. It is highly desirable to develop techniques and systems to remotely monitor their conditions and analyze their faults. In this work, we introduce a remote system for online condition monitoring and fault diagnosis of gas turbine on offshore oil well drilling platforms based on a kernelized information entropy model. Shannon information entropy is generalized for measuring the uniformity of exhaust temperatures, which reflect the overall states of the gas paths of gas turbine. In addition, we also extend the entropy to compute the information quantity of features in kernel spaces, which help to select the informative features for a certain recognition task. Finally, we introduce the information entropy based decision tree algorithm to extract rules from fault samples. The experiments on some real-world data show the effectiveness of the proposed algorithms.

An entropy-based improved k-top scoring pairs (TSP) method for ...

African Journals Online (AJOL)

An entropy-based improved k-top scoring pairs (TSP) (Ik-TSP) method was presented in this study for the classification and prediction of human cancers based on gene-expression data. We compared Ik-TSP classifiers with 5 different machine learning methods and the k-TSP method based on 3 different feature selection ...

Membrane-based ethylene/ethane separation: The upper bound and beyond

KAUST Repository

Rungta, Meha

2013-08-02

Ethylene/ethane separation via cryogenic distillation is extremely energy-intensive, and membrane separation may provide an attractive alternative. In this paper, ethylene/ethane separation performance using polymeric membranes is summarized, and an experimental ethylene/ethane polymeric upper bound based on literature data is presented. A theoretical prediction of the ethylene/ethane upper bound is also presented, and shows good agreement with the experimental upper bound. Further, two ways to overcome the ethylene/ethane upper bound, based on increasing the sorption or diffusion selectivity, is also discussed, and a review on advanced membrane types such as facilitated transport membranes, zeolite and metal organic framework based membranes, and carbon molecular sieve membranes is presented. Of these, carbon membranes have shown the potential to surpass the polymeric ethylene/ethane upper bound performance. Furthermore, a convenient, potentially scalable method for tailoring the performance of carbon membranes for ethylene/ethane separation based on tuning the pyrolysis conditions has also been demonstrated. © 2013 American Institute of Chemical Engineers.

Feedback structure based entropy approach for multiple-model estimation

Institute of Scientific and Technical Information of China (English)

Shen-tu Han; Xue Anke; Guo Yunfei

2013-01-01

The variable-structure multiple-model (VSMM) approach, one of the multiple-model (MM) methods, is a popular and effective approach in handling problems with mode uncertainties. The model sequence set adaptation (MSA) is the key to design a better VSMM. However, MSA methods in the literature have big room to improve both theoretically and practically. To this end, we propose a feedback structure based entropy approach that could find the model sequence sets with the smallest size under certain conditions. The filtered data are fed back in real time and can be used by the minimum entropy (ME) based VSMM algorithms, i.e., MEVSMM. Firstly, the full Markov chains are used to achieve optimal solutions. Secondly, the myopic method together with particle filter (PF) and the challenge match algorithm are also used to achieve sub-optimal solutions, a trade-off between practicability and optimality. The numerical results show that the proposed algorithm provides not only refined model sets but also a good robustness margin and very high accuracy.

Entropy-based derivation of generalized distributions for hydrometeorological frequency analysis

Science.gov (United States)

Chen, Lu; Singh, Vijay P.

2018-02-01

Frequency analysis of hydrometeorological and hydrological extremes is needed for the design of hydraulic and civil infrastructure facilities as well as water resources management. A multitude of distributions have been employed for frequency analysis of these extremes. However, no single distribution has been accepted as a global standard. Employing the entropy theory, this study derived five generalized distributions for frequency analysis that used different kinds of information encoded as constraints. These distributions were the generalized gamma (GG), the generalized beta distribution of the second kind (GB2), and the Halphen type A distribution (Hal-A), Halphen type B distribution (Hal-B) and Halphen type inverse B distribution (Hal-IB), among which the GG and GB2 distribution were previously derived by Papalexiou and Koutsoyiannis (2012) and the Halphen family was first derived using entropy theory in this paper. The entropy theory allowed to estimate parameters of the distributions in terms of the constraints used for their derivation. The distributions were tested using extreme daily and hourly rainfall data. Results show that the root mean square error (RMSE) values were very small, which indicated that the five generalized distributions fitted the extreme rainfall data well. Among them, according to the Akaike information criterion (AIC) values, generally the GB2 and Halphen family gave a better fit. Therefore, those general distributions are one of the best choices for frequency analysis. The entropy-based derivation led to a new way for frequency analysis of hydrometeorological extremes.

Prediction of Protein Configurational Entropy (Popcoen).

Science.gov (United States)

Goethe, Martin; Gleixner, Jan; Fita, Ignacio; Rubi, J Miguel

2018-03-13

A knowledge-based method for configurational entropy prediction of proteins is presented; this methodology is extremely fast, compared to previous approaches, because it does not involve any type of configurational sampling. Instead, the configurational entropy of a query fold is estimated by evaluating an artificial neural network, which was trained on molecular-dynamics simulations of ∼1000 proteins. The predicted entropy can be incorporated into a large class of protein software based on cost-function minimization/evaluation, in which configurational entropy is currently neglected for performance reasons. Software of this type is used for all major protein tasks such as structure predictions, proteins design, NMR and X-ray refinement, docking, and mutation effect predictions. Integrating the predicted entropy can yield a significant accuracy increase as we show exemplarily for native-state identification with the prominent protein software FoldX. The method has been termed Popcoen for Prediction of Protein Configurational Entropy. An implementation is freely available at http://fmc.ub.edu/popcoen/ .

Strong converse theorems using Rényi entropies

Energy Technology Data Exchange (ETDEWEB)

Leditzky, Felix; Datta, Nilanjana [Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WB (United Kingdom); Wilde, Mark M. [Department of Physics and Astronomy, Center for Computation and Technology, Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)

2016-08-15

We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint http://arxiv.org/abs/1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.

Entropy Coherent and Entropy Convex Measures of Risk

NARCIS (Netherlands)

Laeven, R.J.A.; Stadje, M.A.

2011-01-01

We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences,

A review of entropy generation in microchannels

Directory of Open Access Journals (Sweden)

Mohamed M Awad

2015-12-01

Full Text Available In this study, a critical review of thermodynamic optimum of microchannels based on entropy generation analysis is presented. Using entropy generation analysis as evaluation parameter of microchannels has been reported by many studies in the literature. In these studies, different working fluids such as nanofluids, air, water, engine oil, aniline, ethylene glycol, and non-Newtonian fluids have been used. For the case of nanofluids, “nanoparticles” has been used in various kinds such as Al2O3 and Cu, and “base fluid” has been used in various kinds such as water and ethylene glycol. Furthermore, studies on thermodynamic optimum of microchannels based on entropy generation analysis are summarized in a table. At the end, recommendations of future work for thermodynamic optimum of microchannels based on entropy generation analysis are given. As a result, this article can not only be used as the starting point for the researcher interested in entropy generation in microchannels, but it also includes recommendations for future studies on entropy generation in microchannels.

Particle swarm optimization-based local entropy weighted histogram equalization for infrared image enhancement

Science.gov (United States)

Wan, Minjie; Gu, Guohua; Qian, Weixian; Ren, Kan; Chen, Qian; Maldague, Xavier

2018-06-01

Infrared image enhancement plays a significant role in intelligent urban surveillance systems for smart city applications. Unlike existing methods only exaggerating the global contrast, we propose a particle swam optimization-based local entropy weighted histogram equalization which involves the enhancement of both local details and fore-and background contrast. First of all, a novel local entropy weighted histogram depicting the distribution of detail information is calculated based on a modified hyperbolic tangent function. Then, the histogram is divided into two parts via a threshold maximizing the inter-class variance in order to improve the contrasts of foreground and background, respectively. To avoid over-enhancement and noise amplification, double plateau thresholds of the presented histogram are formulated by means of particle swarm optimization algorithm. Lastly, each sub-image is equalized independently according to the constrained sub-local entropy weighted histogram. Comparative experiments implemented on real infrared images prove that our algorithm outperforms other state-of-the-art methods in terms of both visual and quantized evaluations.

New Fault Recognition Method for Rotary Machinery Based on Information Entropy and a Probabilistic Neural Network.

Science.gov (United States)

Jiang, Quansheng; Shen, Yehu; Li, Hua; Xu, Fengyu

2018-01-24

Feature recognition and fault diagnosis plays an important role in equipment safety and stable operation of rotating machinery. In order to cope with the complexity problem of the vibration signal of rotating machinery, a feature fusion model based on information entropy and probabilistic neural network is proposed in this paper. The new method first uses information entropy theory to extract three kinds of characteristics entropy in vibration signals, namely, singular spectrum entropy, power spectrum entropy, and approximate entropy. Then the feature fusion model is constructed to classify and diagnose the fault signals. The proposed approach can combine comprehensive information from different aspects and is more sensitive to the fault features. The experimental results on simulated fault signals verified better performances of our proposed approach. In real two-span rotor data, the fault detection accuracy of the new method is more than 10% higher compared with the methods using three kinds of information entropy separately. The new approach is proved to be an effective fault recognition method for rotating machinery.

Entropy coherent and entropy convex measures of risk

NARCIS (Netherlands)

Laeven, Roger; Stadje, M.A.

2010-01-01

We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized

Entropy: From Thermodynamics to Hydrology

Directory of Open Access Journals (Sweden)

Demetris Koutsoyiannis

2014-02-01

Full Text Available Some known results from statistical thermophysics as well as from hydrology are revisited from a different perspective trying: (a to unify the notion of entropy in thermodynamic and statistical/stochastic approaches of complex hydrological systems and (b to show the power of entropy and the principle of maximum entropy in inference, both deductive and inductive. The capability for deductive reasoning is illustrated by deriving the law of phase change transition of water (Clausius-Clapeyron from scratch by maximizing entropy in a formal probabilistic frame. However, such deductive reasoning cannot work in more complex hydrological systems with diverse elements, yet the entropy maximization framework can help in inductive inference, necessarily based on data. Several examples of this type are provided in an attempt to link statistical thermophysics with hydrology with a unifying view of entropy.

Harmonic analysis of electric locomotive and traction power system based on wavelet singular entropy

Science.gov (United States)

Dun, Xiaohong

2018-05-01

With the rapid development of high-speed railway and heavy-haul transport, the locomotive and traction power system has become the main harmonic source of China's power grid. In response to this phenomenon, the system's power quality issues need timely monitoring, assessment and governance. Wavelet singular entropy is an organic combination of wavelet transform, singular value decomposition and information entropy theory, which combines the unique advantages of the three in signal processing: the time-frequency local characteristics of wavelet transform, singular value decomposition explores the basic modal characteristics of data, and information entropy quantifies the feature data. Based on the theory of singular value decomposition, the wavelet coefficient matrix after wavelet transform is decomposed into a series of singular values that can reflect the basic characteristics of the original coefficient matrix. Then the statistical properties of information entropy are used to analyze the uncertainty of the singular value set, so as to give a definite measurement of the complexity of the original signal. It can be said that wavelet entropy has a good application prospect in fault detection, classification and protection. The mat lab simulation shows that the use of wavelet singular entropy on the locomotive and traction power system harmonic analysis is effective.

Beyond the classical theory of heat conduction: a perspective view of future from entropy

Science.gov (United States)

Lai, Xiang; Zhu, Pingan

2016-01-01

Energy is conserved by the first law of thermodynamics; its quality degrades constantly due to entropy generation, by the second law of thermodynamics. It is thus important to examine the entropy generation regarding the way to reduce its magnitude and the limit of entropy generation as time tends to infinity regarding whether it is bounded or not. This work initiates such an analysis with one-dimensional heat conduction. The work not only offers some fundamental insights of universe and its future, but also builds up the relation between the second law of thermodynamics and mathematical inequalities via developing the latter of either new or classical nature. A concise review of entropy is also included for the interest of performing the analysis in this work and the similar analysis for other processes in the future. PMID:27843400

A Real-Time Analysis Method for Pulse Rate Variability Based on Improved Basic Scale Entropy

Directory of Open Access Journals (Sweden)

Yongxin Chou

2017-01-01

Full Text Available Base scale entropy analysis (BSEA is a nonlinear method to analyze heart rate variability (HRV signal. However, the time consumption of BSEA is too long, and it is unknown whether the BSEA is suitable for analyzing pulse rate variability (PRV signal. Therefore, we proposed a method named sliding window iterative base scale entropy analysis (SWIBSEA by combining BSEA and sliding window iterative theory. The blood pressure signals of healthy young and old subjects are chosen from the authoritative international database MIT/PhysioNet/Fantasia to generate PRV signals as the experimental data. Then, the BSEA and the SWIBSEA are used to analyze the experimental data; the results show that the SWIBSEA reduces the time consumption and the buffer cache space while it gets the same entropy as BSEA. Meanwhile, the changes of base scale entropy (BSE for healthy young and old subjects are the same as that of HRV signal. Therefore, the SWIBSEA can be used for deriving some information from long-term and short-term PRV signals in real time, which has the potential for dynamic PRV signal analysis in some portable and wearable medical devices.

Entropy coherent and entropy convex measures of risk

NARCIS (Netherlands)

Laeven, R.J.A.; Stadje, M.

2013-01-01

We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex

Properties of Risk Measures of Generalized Entropy in Portfolio Selection

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Rongxi Zhou

2017-12-01

Full Text Available This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the following properties, which various scholars have associated with effective risk measures: Monotonicity, Translation Invariance, Sub-additivity, Positive Homogeneity, Consistency and Convexity. Measures based on Fuzzy Entropy, Credibility Entropy, and Sine Entropy all exhibit the same properties: Sub-additivity, Positive Homogeneity, Consistency, and Convexity. These measures based on Information Entropy and Hybrid Entropy, meanwhile, only exhibit Sub-additivity and Consistency. Cumulative Residual Entropy satisfies just Sub-additivity, Positive Homogeneity, and Convexity. After identifying these properties, we develop seven portfolio models based on different risk measures and made empirical comparisons using samples from both the Shenzhen Stock Exchange of China and the New York Stock Exchange of America. The comparisons show that the Mean Fuzzy Entropy Model performs the best among the seven models with respect to both daily returns and relative cumulative returns. Overall, these results could provide an important reference for both constructing effective risk measures and rationally selecting the appropriate risk measure under different portfolio selection conditions.

Enthalpy-entropy compensation in protein unfolding

Institute of Scientific and Technical Information of China (English)

无

2000-01-01

Enthalpy-entropy compensation was found to be a universal law in protein unfolding based on over 3 000 experimental data. Water molecular reorganization accompanying the protein unfolding was suggested as the origin of the enthalpy-entropy compensation in protein unfolding. It is indicated that the enthalpy-entropy compensation constitutes the physical foundation that satisfies the biological need of the small free energy changes in protein unfolding, without the sacrifice of the bio-diversity of proteins. The enthalpy-entropy compensation theory proposed herein also provides valuable insights into the Privalov's puzzle of enthalpy and entropy convergence in protein unfolding.

Black hole entropy functions and attractor equations

International Nuclear Information System (INIS)

Lopes Cardoso, Gabriel; Wit, Bernard de; Mahapatra, Swapna

2007-01-01

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N = 2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions

Information-entropic method for studying the stability bound of nonrelativistic polytropic stars within modified gravity theories

Science.gov (United States)

Wibisono, C.; Sulaksono, A.

We study the stability of nonrelativistic polytropic stars within two modified gravity theories, i.e. beyond Horndeski gravity and Eddington-inspired Born-Infeld theories, using the configuration entropy method. We use the spatially localized bounded function of energy density as solutions from stellar effective equations to construct the corresponding configuration entropy. We use the same argument as the one used by Gleiser and coworkers [M. Gleiser and D. Sowinski, Phys. Lett. B 727 (2013) 272; M. Gleiser and N. Jiang, Phys. Rev. D 92 (2015) 044046] that the stars are stable if there is a peak in configuration entropy as a function of adiabatic index curve. Specifically, the boundary between stable and unstable regions which corresponds to Chandrasekhar stability bound is indicated from the existence of the maximum peak while the most stable polytropic stars are indicated by the minimum peak in the corresponding curve. We have found that the values of critical adiabatic indexes of Chandrasekhar stability bound and the most stable polytropic stars predicted by the nonrelativistic limits of beyond Horndeski gravity and Eddington-inspired Born-Infeld theories are different to those predicted by general relativity where the corresponding differences depend on the free parameters of both theories.

Multivariate refined composite multiscale entropy analysis

International Nuclear Information System (INIS)

Humeau-Heurtier, Anne

2016-01-01

Multiscale entropy (MSE) has become a prevailing method to quantify signals complexity. MSE relies on sample entropy. However, MSE may yield imprecise complexity estimation at large scales, because sample entropy does not give precise estimation of entropy when short signals are processed. A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. Nevertheless, RCMSE is for univariate signals only. The simultaneous analysis of multi-channel (multivariate) data often over-performs studies based on univariate signals. We therefore introduce an extension of RCMSE to multivariate data. Applications of multivariate RCMSE to simulated processes reveal its better performances over the standard multivariate MSE. - Highlights: • Multiscale entropy quantifies data complexity but may be inaccurate at large scale. • A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. • Nevertheless, RCMSE is adapted to univariate time series only. • We herein introduce an extension of RCMSE to multivariate data. • It shows better performances than the standard multivariate multiscale entropy.

Activity-Based Approach for Teaching Aqueous Solubility, Energy, and Entropy

Science.gov (United States)

Eisen, Laura; Marano, Nadia; Glazier, Samantha

2014-01-01

We describe an activity-based approach for teaching aqueous solubility to introductory chemistry students that provides a more balanced presentation of the roles of energy and entropy in dissolution than is found in most general chemistry textbooks. In the first few activities, students observe that polar substances dissolve in water, whereas…

Trajectories entropy in dynamical graphs with memory

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Francesco eCaravelli

2016-04-01

Full Text Available In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.

Time Dependence of Entropy Flux and Entropy Production of a Dissipative Dynamical System Driven by Non-Gaussian Noise

International Nuclear Information System (INIS)

Guo Yongfeng; Xu Wei; Li Dongxi; Xie Wenxian

2008-01-01

A stochastic dissipative dynamical system driven by non-Gaussian noise is investigated. A general approximate Fokker-Planck equation of the system is derived through a path-integral approach. Based on the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production of the system is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculation can be used to interpret the interplay of the dissipative constant and non-Gaussian noise on the entropy flux and entropy production

Application of the entropy generation minimization method to a solar heat exchanger: A pseudo-optimization design process based on the analysis of the local entropy generation maps

International Nuclear Information System (INIS)

Giangaspero, Giorgio; Sciubba, Enrico

2013-01-01

This paper presents an application of the entropy generation minimization method to the pseudo-optimization of the configuration of the heat exchange surfaces in a Solar Rooftile. An initial “standard” commercial configuration is gradually improved by introducing design changes aimed at the reduction of the thermodynamic losses due to heat transfer and fluid friction. Different geometries (pins, fins and others) are analysed with a commercial CFD (Computational Fluid Dynamics) code that also computes the local entropy generation rate. The design improvement process is carried out on the basis of a careful analysis of the local entropy generation maps and the rationale behind each step of the process is discussed in this perspective. The results are compared with other entropy generation minimization techniques available in the recent technical literature. It is found that the geometry with pin-fins has the best performance among the tested ones, and that the optimal pin array shape parameters (pitch and span) can be determined by a critical analysis of the integrated and local entropy maps and of the temperature contours. - Highlights: ► An entropy generation minimization method is applied to a solar heat exchanger. ► The approach is heuristic and leads to a pseudo-optimization process with CFD as main tool. ► The process is based on the evaluation of the local entropy generation maps. ► The geometry with pin-fins in general outperforms all other configurations. ► The entropy maps and temperature contours can be used to determine the optimal pin array design parameters

Dynamic Garment Simulation based on Hybrid Bounding Volume Hierarchy

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Zhu Dongyong

2016-12-01

Full Text Available In order to solve the computing speed and efficiency problem of existing dynamic clothing simulation, this paper presents a dynamic garment simulation based on a hybrid bounding volume hierarchy. It firstly uses MCASG graph theory to do the primary segmentation for a given three-dimensional human body model. And then it applies K-means cluster to do the secondary segmentation to collect the human body’s upper arms, lower arms, upper legs, lower legs, trunk, hip and woman’s chest as the elementary units of dynamic clothing simulation. According to different shapes of these elementary units, it chooses the closest and most efficient hybrid bounding box to specify these units, such as cylinder bounding box and elliptic cylinder bounding box. During the process of constructing these bounding boxes, it uses the least squares method and slices of the human body to get the related parameters. This approach makes it possible to use the least amount of bounding boxes to create close collision detection regions for the appearance of the human body. A spring-mass model based on a triangular mesh of the clothing model is finally constructed for dynamic simulation. The simulation result shows the feasibility and superiority of the method described.

Minimization of entropy production in separate and connected process units

Energy Technology Data Exchange (ETDEWEB)

Roesjorde, Audun

2004-08-01

production of a heat-integrated distillation column separating benzene and toluene was influenced by changing two important system parameters. The two parameters were the ratio between the pressure in the rectifying and stripping section and the total rate of heat transfer per Kelvin (UA{sub total}). In Chapter 4, UA{sub total} was evenly distributed in the column. The results showed that there was an upper and a lower bound on the pressure ratio, for which the heat-integrated column had a lower entropy production than the adiabatic column. A lower bound was also found on UA{sub total}. In Chapter 5, we allowed the UA{sub total} to distribute itself in an optimal way. This enabled even lower entropy productions and widened the range of the two parameters for which the heat-integrated distillation column performed better than the adiabatic. As in Chapter 3, we found that heat exchange was most important close to the condenser and re boiler. This made us propose a new design for the heat-integrated distillation column, with heat transfer between the topmost and bottommost trays only. This enabled further reductions in the entropy production. The next step in the development was to study several units in connection. In Chapter 6, we minimized the entropy production of a heat exchanger, a plug-flow reactor, and a heat exchanger in series. This was a preparatory study for the larger process optimization in Chapter 7. By shifting heat transfer from the reactor to the heat exchanger up-front, the entropy production was reduced. It was also found that the ambient temperature profile along the reactor was of less important to the entropy production. Finally, in Chapter 7, we were able to minimize the entropy production of a process, producing propylene from propane. We showed that it is meaningful to use the entropy production in a chemical process as objective function in an optimization that aims to find the most energy efficient state of operation and, in some aspects, design. By

Microscopic insights into the NMR relaxation based protein conformational entropy meter

Science.gov (United States)

Kasinath, Vignesh; Sharp, Kim A.; Wand, A. Joshua

2013-01-01

Conformational entropy is a potentially important thermodynamic parameter contributing to protein function. Quantitative measures of conformational entropy are necessary for an understanding of its role but have been difficult to obtain. An empirical method that utilizes changes in conformational dynamics as a proxy for changes in conformational entropy has recently been introduced. Here we probe the microscopic origins of the link between conformational dynamics and conformational entropy using molecular dynamics simulations. Simulation of seven pro! teins gave an excellent correlation with measures of side-chain motion derived from NMR relaxation. The simulations show that the motion of methyl-bearing side-chains are sufficiently coupled to that of other side chains to serve as excellent reporters of the overall side-chain conformational entropy. These results tend to validate the use of experimentally accessible measures of methyl motion - the NMR-derived generalized order parameters - as a proxy from which to derive changes in protein conformational entropy. PMID:24007504

ENTROPY FUNCTIONAL FOR CONTINUOUS SYSTEMS OF FINITE ENTROPY

Institute of Scientific and Technical Information of China (English)

M. Rahimi A. Riazi

2012-01-01

In this article,we introduce the concept of entropy functional for continuous systems on compact metric spaces,and prove some of its properties.We also extract the Kolmogorov entropy from the entropy functional.

COLLAGE-BASED INVERSE PROBLEMS FOR IFSM WITH ENTROPY MAXIMIZATION AND SPARSITY CONSTRAINTS

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Herb Kunze

2013-11-01

Full Text Available We consider the inverse problem associated with IFSM: Given a target function f, find an IFSM, such that its invariant fixed point f is sufficiently close to f in the Lp distance. In this paper, we extend the collage-based method developed by Forte and Vrscay (1995 along two different directions. We first search for a set of mappings that not only minimizes the collage error but also maximizes the entropy of the dynamical system. We then include an extra term in the minimization process which takes into account the sparsity of the set of mappings. In this new formulation, the minimization of collage error is treated as multi-criteria problem: we consider three different and conflicting criteria i.e., collage error, entropy and sparsity. To solve this multi-criteria program we proceed by scalarization and we reduce the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented. Numerical studies indicate that a maximum entropy principle exists for this approximation problem, i.e., that the suboptimal solutions produced by collage coding can be improved at least slightly by adding a maximum entropy criterion.

Entropy type complexity of quantum processes

International Nuclear Information System (INIS)

Watanabe, Noboru

2014-01-01

von Neumann entropy represents the amount of information in the quantum state, and this was extended by Ohya for general quantum systems [10]. Umegaki first defined the quantum relative entropy for σ-finite von Neumann algebras, which was extended by Araki, and Uhlmann, for general von Neumann algebras and *-algebras, respectively. In 1983 Ohya introduced the quantum mutual entropy by using compound states; this describes the amount of information correctly transmitted through the quantum channel, which was also extended by Ohya for general quantum systems. In this paper, we briefly explain Ohya's S-mixing entropy and the quantum mutual entropy for general quantum systems. By using structure equivalent class, we will introduce entropy type functionals based on quantum information theory to improve treatment for the Gaussian communication process. (paper)

Topological nearly entropy

Science.gov (United States)

Gulamsarwar, Syazwani; Salleh, Zabidin

2017-08-01

The purpose of this paper is to generalize the notions of Adler's topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f-1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.

A numerically research on energy loss evaluation in a centrifugal pump system based on local entropy production method

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Hou Hucan

2017-01-01

Full Text Available Inspired by wide application of the second law of thermodynamics to flow and heat transfer devices, local entropy production analysis method was creatively introduced into energy assessment system of centrifugal water pump. Based on Reynolds stress turbulent model and energy equation model, the steady numerical simulation of the whole flow passage of one IS centrifugal pump was carried out. The local entropy production terms were calculated by user defined functions, mainly including wall entropy production, turbulent entropy production, and viscous entropy production. The numerical results indicated that the irreversible energy loss calculated by the local entropy production method agreed well with that calculated by the traditional method but with some deviations which were probably caused by high rotatability and high curvature of impeller and volute. The wall entropy production and turbulent entropy production took up large part of the whole entropy production about 48.61% and 47.91%, respectively, which indicated that wall friction and turbulent fluctuation were the major factors in affecting irreversible energy loss. Meanwhile, the entropy production rate distribution was discussed and compared with turbulent kinetic energy dissipation rate distribution, it showed that turbulent entropy production rate increased sharply at the near wall regions and both distributed more uniformly. The blade region in leading edge near suction side, trailing edge and volute tongue were the main regions to generate irreversible exergy loss. This research broadens a completely new view in evaluating energy loss and further optimizes pump using entropy production minimization.

A novel evaluation of heat-electricity cost allocation in cogenerations based on entropy change method

International Nuclear Information System (INIS)

Ye, Xuemin; Li, Chunxi

2013-01-01

As one of the most significant measures to improve energy utilization efficiency and save energy, cogeneration or combined heat and power (CHP) has been widely applied and promoted with positive motivations in many countries. A rational cost allocation model should indicate the performance of cogenerations and balance the benefits between electricity generation and heat production. Based on the second law of thermodynamics, the present paper proposes an entropy change method for cost allocation by choosing exhaust steam entropy as a datum point, and the new model works in conjunction with entropy change and irreversibility during energy conversion processes. The allocation ratios of heat cost with the present and existing methods are compared for different types of cogenerations. Results show that the allocation ratios with the entropy change method are more rational and the cost allocation model can make up some limitations involved in other approaches. The future energy policies and innovational directions for cogenerations and heat consumers should be developed. - Highlights: • A rational model of cogeneration cost allocation is established. • Entropy change method integrates the relation of entropy change and exergy losses. • The unity of measuring energy quality and quantity is materialized. • The benefits between electricity generation and heat production are balanced

Entanglement entropy and differential entropy for massive flavors

International Nuclear Information System (INIS)

Jones, Peter A.R.; Taylor, Marika

2015-01-01

In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.

Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation

Institute of Scientific and Technical Information of China (English)

Xie Wen-Xian; Xu Wei; Cai Li

2007-01-01

This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.

Dynamic Cross-Entropy.

Science.gov (United States)

Aur, Dorian; Vila-Rodriguez, Fidel

2017-01-01

Complexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical systems are spatially distributed multidimensional systems. We introduced Dynamic Cross-Entropy (DCE) a novel multidimensional complexity measure that quantifies the degree of regularity of EEG signals in selected frequency bands. Time series generated by discrete logistic equations with varying control parameter r are used to test DCE measures. Sliding window DCE analyses are able to reveal specific period doubling bifurcations that lead to chaos. A similar behavior can be observed in seizures triggered by electroconvulsive therapy (ECT). Sample entropy data show the level of signal complexity in different phases of the ictal ECT. The transition to irregular activity is preceded by the occurrence of cyclic regular behavior. A significant increase of DCE values in successive order from high frequencies in gamma to low frequencies in delta band reveals several phase transitions into less ordered states, possible chaos in the human brain. To our knowledge there are no reliable techniques able to reveal the transition to chaos in case of multidimensional times series. In addition, DCE based on sample entropy appears to be robust to EEG artifacts compared to DCE based on Shannon entropy. The applied technique may offer new approaches to better understand nonlinear brain activity. Copyright © 2016 Elsevier B.V. All rights reserved.

Chatter detection in milling process based on VMD and energy entropy

Science.gov (United States)

Liu, Changfu; Zhu, Lida; Ni, Chenbing

2018-05-01

This paper presents a novel approach to detect the milling chatter based on Variational Mode Decomposition (VMD) and energy entropy. VMD has already been employed in feature extraction from non-stationary signals. The parameters like number of modes (K) and the quadratic penalty (α) need to be selected empirically when raw signal is decomposed by VMD. Aimed at solving the problem how to select K and α, the automatic selection method of VMD's based on kurtosis is proposed in this paper. When chatter occurs in the milling process, energy will be absorbed to chatter frequency bands. To detect the chatter frequency bands automatically, the chatter detection method based on energy entropy is presented. The vibration signal containing chatter frequency is simulated and three groups of experiments which represent three cutting conditions are conducted. To verify the effectiveness of method presented by this paper, chatter feather extraction has been successfully employed on simulation signals and experimental signals. The simulation and experimental results show that the proposed method can effectively detect the chatter.

Confidence bounds of recurrence-based complexity measures

International Nuclear Information System (INIS)

Schinkel, Stefan; Marwan, N.; Dimigen, O.; Kurths, J.

2009-01-01

In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real-life data.

Epileptic seizure detection using DWT-based approximate entropy, Shannon entropy and support vector machine: a case study.

Science.gov (United States)

Sharmila, A; Aman Raj, Suman; Shashank, Pandey; Mahalakshmi, P

2018-01-01

In this work, we have used a time-frequency domain analysis method called discrete wavelet transform (DWT) technique. This method stand out compared to other proposed methods because of its algorithmic elegance and accuracy. A wavelet is a mathematical function based on time-frequency analysis in signal processing. It is useful particularly because it allows a weak signal to be recovered from a noisy signal without much distortion. A wavelet analysis works by analysing the image and converting it to mathematical function which is decoded by the receiver. Furthermore, we have used Shannon entropy and approximate entropy (ApEn) for extracting the complexities associated with electroencephalographic (EEG) signals. The ApEn is a suitable feature to characterise the EEGs because its value drops suddenly due to excessive synchronous discharge of neurons in the brain during epileptic activity in this study. EEG signals are decomposed into six EEG sub-bands namely D1-D5 and A5 using DWT technique. Non-linear features such as ApEn and Shannon entropy are calculated from these sub-bands and support vector machine classifiers are used for classification purpose. This scheme is tested using EEG data recorded from five healthy subjects and five epileptic patients during the inter-ictal and ictal periods. The data are acquired from University of Bonn, Germany. The proposed method is evaluated through 15 classification problems, and obtained high classification accuracy of 100% for two cases and it indicates the good classifying performance of the proposed method.

Symplectic entropy

International Nuclear Information System (INIS)

De Nicola, Sergio; Fedele, Renato; Man'ko, Margarita A; Man'ko, Vladimir I

2007-01-01

The tomographic-probability description of quantum states is reviewed. The symplectic tomography of quantum states with continuous variables is studied. The symplectic entropy of the states with continuous variables is discussed and its relation to Shannon entropy and information is elucidated. The known entropic uncertainty relations of the probability distribution in position and momentum of a particle are extended and new uncertainty relations for symplectic entropy are obtained. The partial case of symplectic entropy, which is optical entropy of quantum states, is considered. The entropy associated to optical tomogram is shown to satisfy the new entropic uncertainty relation. The example of Gaussian states of harmonic oscillator is studied and the entropic uncertainty relations for optical tomograms of the Gaussian state are shown to minimize the uncertainty relation

Time-dependent entropy evolution in microscopic and macroscopic electromagnetic relaxation

International Nuclear Information System (INIS)

Baker-Jarvis, James

2005-01-01

This paper is a study of entropy and its evolution in the time and frequency domains upon application of electromagnetic fields to materials. An understanding of entropy and its evolution in electromagnetic interactions bridges the boundaries between electromagnetism and thermodynamics. The approach used here is a Liouville-based statistical-mechanical theory. I show that the microscopic entropy is reversible and the macroscopic entropy satisfies an H theorem. The spectral entropy development can be very useful for studying the frequency response of materials. Using a projection-operator based nonequilibrium entropy, different equations are derived for the entropy and entropy production and are applied to the polarization, magnetization, and macroscopic fields. I begin by proving an exact H theorem for the entropy, progress to application of time-dependent entropy in electromagnetics, and then apply the theory to relevant applications in electromagnetics. The paper concludes with a discussion of the relationship of the frequency-domain form of the entropy to the permittivity, permeability, and impedance

Crane Safety Assessment Method Based on Entropy and Cumulative Prospect Theory

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Aihua Li

2017-01-01

Full Text Available Assessing the safety status of cranes is an important problem. To overcome the inaccuracies and misjudgments in such assessments, this work describes a safety assessment method for cranes that combines entropy and cumulative prospect theory. Firstly, the proposed method transforms the set of evaluation indices into an evaluation vector. Secondly, a decision matrix is then constructed from the evaluation vectors and evaluation standards, and an entropy-based technique is applied to calculate the index weights. Thirdly, positive and negative prospect value matrices are established from reference points based on the positive and negative ideal solutions. Thus, this enables the crane safety grade to be determined according to the ranked comprehensive prospect values. Finally, the safety status of four general overhead traveling crane samples is evaluated to verify the rationality and feasibility of the proposed method. The results demonstrate that the method described in this paper can precisely and reasonably reflect the safety status of a crane.

Controlling the Shannon Entropy of Quantum Systems

Science.gov (United States)

Xing, Yifan; Wu, Jun

2013-01-01

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking. PMID:23818819

Controlling the Shannon Entropy of Quantum Systems

Directory of Open Access Journals (Sweden)

Yifan Xing

2013-01-01

Full Text Available This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

Entropy for Mechanically Vibrating Systems

Science.gov (United States)

Tufano, Dante

, which demonstrates the applicability of entropy-based approaches to real-world systems. Three systems are considered to demonstrate these findings: 1) a rod end-coupled to a simple oscillator, 2) two end-coupled rods, and 3) two end-coupled beams. The aforementioned work utilizes the weak coupling assumption to determine the entropy of composite systems. Following this discussion, a direct method of finding entropy is developed which does not rely on this limiting assumption. The resulting entropy provides a useful benchmark for evaluating the accuracy of the weak coupling approach, and is validated using systems of coupled oscillators. The later chapters of this work discuss Khinchin's entropy as applied to nonlinear and nonconservative systems, respectively. The discussion of entropy for nonlinear systems is motivated by the desire to expand the applicability of SEA techniques beyond the linear regime. The discussion of nonconservative systems is also crucial, since real-world systems interact with their environment, and it is necessary to confirm the validity of an entropy approach for systems that are relevant in the context of SEA. Having developed a mathematical framework for determining entropy under a number of previously unexplored cases, the relationship between thermodynamics and statistical vibroacoustics can be better understood. Specifically, vibroacoustic temperatures can be obtained for systems that are not necessarily linear or weakly coupled. In this way, entropy provides insight into how the power flow proportionality of statistical energy analysis (SEA) can be applied to a broader class of vibroacoustic systems. As such, entropy is a useful tool for both justifying and expanding the foundational results of SEA.

Entanglement entropy in top-down models

Energy Technology Data Exchange (ETDEWEB)

Jones, Peter A.R.; Taylor, Marika [Mathematical Sciences and STAG Research Centre, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom)

2016-08-26

We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.

Entanglement entropy in top-down models

International Nuclear Information System (INIS)

Jones, Peter A.R.; Taylor, Marika

2016-01-01

We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.

Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach

Directory of Open Access Journals (Sweden)

Ning-Cong Xiao

2013-12-01

Full Text Available In this paper the combinations of maximum entropy method and Bayesian inference for reliability assessment of deteriorating system is proposed. Due to various uncertainties, less data and incomplete information, system parameters usually cannot be determined precisely. These uncertainty parameters can be modeled by fuzzy sets theory and the Bayesian inference which have been proved to be useful for deteriorating systems under small sample sizes. The maximum entropy approach can be used to calculate the maximum entropy density function of uncertainty parameters more accurately for it does not need any additional information and assumptions. Finally, two optimization models are presented which can be used to determine the lower and upper bounds of systems probability of failure under vague environment conditions. Two numerical examples are investigated to demonstrate the proposed method.

Problems in black-hole entropy interpretation

International Nuclear Information System (INIS)

Liberati, S.

1997-01-01

In this work some proposals for black-hole entropy interpretation are exposed and investigated. In particular, the author will firstly consider the so-called 'entanglement entropy' interpretation, in the framework of the brick wall model and the divergence problem arising in the one-loop calculations of various thermodynamical quantities, like entropy, internal energy and heat capacity. It is shown that the assumption of equality of entanglement entropy and Bekenstein-Hawking one appears to give inconsistent results. These will be a starting point for a different interpretation of black.hole entropy based on peculiar topological structures of manifolds with 'intrinsic' thermodynamical features. It is possible to show an exact relation between black-hole gravitational entropy and topology of these Euclidean space-times. the expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for entropy for gravitational instantons are proposed in a form which makes the relation between these self-evident. Using this relation he propose a generalization of the Bekenstein-Hawking entropy in which the former and Euler characteristic are related in the equation S = χA / 8. Finally, he try to expose some conclusions and hypotheses about possible further development of this research

Entropy Measurement for Biometric Verification Systems.

Science.gov (United States)

Lim, Meng-Hui; Yuen, Pong C

2016-05-01

Biometric verification systems are designed to accept multiple similar biometric measurements per user due to inherent intrauser variations in the biometric data. This is important to preserve reasonable acceptance rate of genuine queries and the overall feasibility of the recognition system. However, such acceptance of multiple similar measurements decreases the imposter's difficulty of obtaining a system-acceptable measurement, thus resulting in a degraded security level. This deteriorated security needs to be measurable to provide truthful security assurance to the users. Entropy is a standard measure of security. However, the entropy formula is applicable only when there is a single acceptable possibility. In this paper, we develop an entropy-measuring model for biometric systems that accepts multiple similar measurements per user. Based on the idea of guessing entropy, the proposed model quantifies biometric system security in terms of adversarial guessing effort for two practical attacks. Excellent agreement between analytic and experimental simulation-based measurement results on a synthetic and a benchmark face dataset justify the correctness of our model and thus the feasibility of the proposed entropy-measuring approach.

An Integrated Dictionary-Learning Entropy-Based Medical Image Fusion Framework

Directory of Open Access Journals (Sweden)

Guanqiu Qi

2017-10-01

Full Text Available Image fusion is widely used in different areas and can integrate complementary and relevant information of source images captured by multiple sensors into a unitary synthetic image. Medical image fusion, as an important image fusion application, can extract the details of multiple images from different imaging modalities and combine them into an image that contains complete and non-redundant information for increasing the accuracy of medical diagnosis and assessment. The quality of the fused image directly affects medical diagnosis and assessment. However, existing solutions have some drawbacks in contrast, sharpness, brightness, blur and details. This paper proposes an integrated dictionary-learning and entropy-based medical image-fusion framework that consists of three steps. First, the input image information is decomposed into low-frequency and high-frequency components by using a Gaussian filter. Second, low-frequency components are fused by weighted average algorithm and high-frequency components are fused by the dictionary-learning based algorithm. In the dictionary-learning process of high-frequency components, an entropy-based algorithm is used for informative blocks selection. Third, the fused low-frequency and high-frequency components are combined to obtain the final fusion results. The results and analyses of comparative experiments demonstrate that the proposed medical image fusion framework has better performance than existing solutions.

Strong Law of Large Numbers for Hidden Markov Chains Indexed by an Infinite Tree with Uniformly Bounded Degrees

Directory of Open Access Journals (Sweden)

Huilin Huang

2014-01-01

Full Text Available We study strong limit theorems for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees. We mainly establish the strong law of large numbers for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees and give the strong limit law of the conditional sample entropy rate.

Wavelet entropy characterization of elevated intracranial pressure.

Science.gov (United States)

Xu, Peng; Scalzo, Fabien; Bergsneider, Marvin; Vespa, Paul; Chad, Miller; Hu, Xiao

2008-01-01

Intracranial Hypertension (ICH) often occurs for those patients with traumatic brain injury (TBI), stroke, tumor, etc. Pathology of ICH is still controversial. In this work, we used wavelet entropy and relative wavelet entropy to study the difference existed between normal and hypertension states of ICP for the first time. The wavelet entropy revealed the similar findings as the approximation entropy that entropy during ICH state is smaller than that in normal state. Moreover, with wavelet entropy, we can see that ICH state has the more focused energy in the low wavelet frequency band (0-3.1 Hz) than the normal state. The relative wavelet entropy shows that the energy distribution in the wavelet bands between these two states is actually different. Based on these results, we suggest that ICH may be formed by the re-allocation of oscillation energy within brain.

Characterizing time series via complexity-entropy curves

Science.gov (United States)

Ribeiro, Haroldo V.; Jauregui, Max; Zunino, Luciano; Lenzi, Ervin K.

2017-06-01

The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only capture a single aspect of the system dynamics. Here, we propose a family of complexity measures for time series based on a generalization of the complexity-entropy causality plane. By replacing the Shannon entropy by a monoparametric entropy (Tsallis q entropy) and after considering the proper generalization of the statistical complexity (q complexity), we build up a parametric curve (the q -complexity-entropy curve) that is used for characterizing and classifying time series. Based on simple exact results and numerical simulations of stochastic processes, we show that these curves can distinguish among different long-range, short-range, and oscillating correlated behaviors. Also, we verify that simulated chaotic and stochastic time series can be distinguished based on whether these curves are open or closed. We further test this technique in experimental scenarios related to chaotic laser intensity, stock price, sunspot, and geomagnetic dynamics, confirming its usefulness. Finally, we prove that these curves enhance the automatic classification of time series with long-range correlations and interbeat intervals of healthy subjects and patients with heart disease.

Permutation Entropy: New Ideas and Challenges

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Karsten Keller

2017-03-01

Full Text Available Over recent years, some new variants of Permutation entropy have been introduced and applied to EEG analysis, including a conditional variant and variants using some additional metric information or being based on entropies that are different from the Shannon entropy. In some situations, it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data.

Robust bounds on risk-sensitive functionals via Renyi divergence

OpenAIRE

Atar, Rami; Chowdhary, Kamaljit; Dupuis, Paul

2013-01-01

We extend the duality between exponential integrals and relative entropy to a variational formula for exponential integrals involving the Renyi divergence. This formula characterizes the dependence of risk-sensitive functionals and related quantities determined by tail behavior to perturbations in the underlying distributions, in terms of the Renyi divergence. The characterization gives rise to upper and lower bounds that are meaningful for all values of a large deviation scaling parameter, a...

Rolling Bearing Fault Diagnosis Based on ELCD Permutation Entropy and RVM

Directory of Open Access Journals (Sweden)

Jiang Xingmeng

2016-01-01

Full Text Available Aiming at the nonstationary characteristic of a gear fault vibration signal, a recognition method based on permutation entropy of ensemble local characteristic-scale decomposition (ELCD and relevance vector machine (RVM is proposed. First, the vibration signal was decomposed by ELCD; then a series of intrinsic scale components (ISCs were obtained. Second, according to the kurtosis of ISCs, principal ISCs were selected and then the permutation entropy of principal ISCs was calculated and they were combined into a feature vector. Finally, the feature vectors were input in RVM classifier to train and test and identify the type of rolling bearing faults. Experimental results show that this method can effectively diagnose four kinds of working condition, and the effect is better than local characteristic-scale decomposition (LCD method.

Measuring time series regularity using nonlinear similarity-based sample entropy

International Nuclear Information System (INIS)

Xie Hongbo; He Weixing; Liu Hui

2008-01-01

Sampe Entropy (SampEn), a measure quantifying regularity and complexity, is believed to be an effective analyzing method of diverse settings that include both deterministic chaotic and stochastic processes, particularly operative in the analysis of physiological signals that involve relatively small amount of data. However, the similarity definition of vectors is based on Heaviside function, of which the boundary is discontinuous and hard, may cause some problems in the validity and accuracy of SampEn. Sigmoid function is a smoothed and continuous version of Heaviside function. To overcome the problems SampEn encountered, a modified SampEn (mSampEn) based on nonlinear Sigmoid function was proposed. The performance of mSampEn was tested on the independent identically distributed (i.i.d.) uniform random numbers, the MIX stochastic model, the Rossler map, and the Hennon map. The results showed that mSampEn was superior to SampEn in several aspects, including giving entropy definition in case of small parameters, better relative consistency, robust to noise, and more independence on record length when characterizing time series generated from either deterministic or stochastic system with different regularities

Gradient Dynamics and Entropy Production Maximization

Science.gov (United States)

Janečka, Adam; Pavelka, Michal

2018-01-01

We compare two methods for modeling dissipative processes, namely gradient dynamics and entropy production maximization. Both methods require similar physical inputs-how energy (or entropy) is stored and how it is dissipated. Gradient dynamics describes irreversible evolution by means of dissipation potential and entropy, it automatically satisfies Onsager reciprocal relations as well as their nonlinear generalization (Maxwell-Onsager relations), and it has statistical interpretation. Entropy production maximization is based on knowledge of free energy (or another thermodynamic potential) and entropy production. It also leads to the linear Onsager reciprocal relations and it has proven successful in thermodynamics of complex materials. Both methods are thermodynamically sound as they ensure approach to equilibrium, and we compare them and discuss their advantages and shortcomings. In particular, conditions under which the two approaches coincide and are capable of providing the same constitutive relations are identified. Besides, a commonly used but not often mentioned step in the entropy production maximization is pinpointed and the condition of incompressibility is incorporated into gradient dynamics.

Entropy and information

CERN Document Server

Volkenstein, Mikhail V

2009-01-01

The book "Entropy and Information" deals with the thermodynamical concept of entropy and its relationship to information theory. It is successful in explaining the universality of the term "Entropy" not only as a physical phenomenon, but reveals its existence also in other domains. E.g., Volkenstein discusses the "meaning" of entropy in a biological context and shows how entropy is related to artistic activities. Written by the renowned Russian bio-physicist Mikhail V. Volkenstein, this book on "Entropy and Information" surely serves as a timely introduction to understand entropy from a thermodynamic perspective and is definitely an inspiring and thought-provoking book that should be read by every physicist, information-theorist, biologist, and even artist.

Option price calibration from Renyi entropy

International Nuclear Information System (INIS)

Brody, Dorje C.; Buckley, Ian R.C.; Constantinou, Irene C.

2007-01-01

The calibration of the risk-neutral density function for the future asset price, based on the maximisation of the entropy measure of Renyi, is proposed. Whilst the conventional approach based on the use of logarithmic entropy measure fails to produce the observed power-law distribution when calibrated against option prices, the approach outlined here is shown to produce the desired form of the distribution. Procedures for the maximisation of the Renyi entropy under constraints are outlined in detail, and a number of interesting properties of the resulting power-law distributions are also derived. The result is applied to efficiently evaluate prices of path-independent derivatives

Entropy generation of nanofluid flow in a microchannel heat sink

Science.gov (United States)

Manay, Eyuphan; Akyürek, Eda Feyza; Sahin, Bayram

2018-06-01

Present study aims to investigate the effects of the presence of nano sized TiO2 particles in the base fluid on entropy generation rate in a microchannel heat sink. Pure water was chosen as base fluid, and TiO2 particles were suspended into the pure water in five different particle volume fractions of 0.25%, 0.5%, 1.0%, 1.5% and 2.0%. Under laminar, steady state flow and constant heat flux boundary conditions, thermal, frictional, total entropy generation rates and entropy generation number ratios of nanofluids were experimentally analyzed in microchannel flow for different channel heights of 200 μm, 300 μm, 400 μm and 500 μm. It was observed that frictional and total entropy generation rates increased as thermal entropy generation rate were decreasing with an increase in particle volume fraction. In microchannel flows, thermal entropy generation could be neglected due to its too low rate smaller than 1.10e-07 in total entropy generation. Higher channel heights caused higher thermal entropy generation rates, and increasing channel height yielded an increase from 30% to 52% in thermal entropy generation. When channel height decreased, an increase of 66%-98% in frictional entropy generation was obtained. Adding TiO2 nanoparticles into the base fluid caused thermal entropy generation to decrease about 1.8%-32.4%, frictional entropy generation to increase about 3.3%-21.6%.

Parametric Bayesian Estimation of Differential Entropy and Relative Entropy

OpenAIRE

Gupta; Srivastava

2010-01-01

Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian est...

Maximum Entropy Fundamentals

Directory of Open Access Journals (Sweden)

F. Topsøe

2001-09-01

Full Text Available Abstract: In its modern formulation, the Maximum Entropy Principle was promoted by E.T. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play by also focusing on the "observer" and on coding. This view was brought forward by the second named author in the late seventies and is the view we will follow-up on here. It leads to the consideration of a certain game, the Code Length Game and, via standard game theoretical thinking, to a principle of Game Theoretical Equilibrium. This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy. In the present paper we offer a self-contained and comprehensive treatment of fundamentals of both principles mentioned, based on a study of the Code Length Game. Though new concepts and results are presented, the reading should be instructional and accessible to a rather wide audience, at least if certain mathematical details are left aside at a rst reading. The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy". This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory. But our approach reaches further, especially regarding the study of continuity properties of the entropy function, and this leads to new results which allow a discussion of models with so-called entropy loss. These results have tempted us to speculate over

A New Method of Reliability Evaluation Based on Wavelet Information Entropy for Equipment Condition Identification

International Nuclear Information System (INIS)

He, Z J; Zhang, X L; Chen, X F

2012-01-01

Aiming at reliability evaluation of condition identification of mechanical equipment, it is necessary to analyze condition monitoring information. A new method of reliability evaluation based on wavelet information entropy extracted from vibration signals of mechanical equipment is proposed. The method is quite different from traditional reliability evaluation models that are dependent on probability statistics analysis of large number sample data. The vibration signals of mechanical equipment were analyzed by means of second generation wavelet package (SGWP). We take relative energy in each frequency band of decomposed signal that equals a percentage of the whole signal energy as probability. Normalized information entropy (IE) is obtained based on the relative energy to describe uncertainty of a system instead of probability. The reliability degree is transformed by the normalized wavelet information entropy. A successful application has been achieved to evaluate the assembled quality reliability for a kind of dismountable disk-drum aero-engine. The reliability degree indicates the assembled quality satisfactorily.

Entropy, baryon asymmetry and dark matter from heavy neutrino decays

International Nuclear Information System (INIS)

Buchmueller, W.; Schmitz, K.; Vertongen, G.

2011-01-01

The origin of the hot phase of the early universe remains so far an unsolved puzzle. A viable option is entropy production through the decays of heavy Majorana neutrinos whose lifetimes determine the initial temperature. We show that baryogenesis and the production of dark matter are natural by-products of this mechanism. As is well known, the cosmological baryon asymmetry can be accounted for by leptogenesis for characteristic neutrino mass parameters. We find that thermal gravitino production then automatically yields the observed amount of dark matter, for the gravitino as the lightest superparticle and typical gluino masses. As an example, we consider the production of heavy Majorana neutrinos in the course of tachyonic preheating associated with spontaneous B-L breaking. A quantitative analysis leads to constraints on the superparticle masses in terms of neutrino masses: For a light neutrino mass of 10 -5 eV the gravitino mass can be as small as 200 MeV, whereas a lower neutrino mass bound of 0.01 eV implies a lower bound of 9 GeV on the gravitino mass. The measurement of a light neutrino mass of 0.1 eV would rule out heavy neutrino decays as the origin of entropy, visible and dark matter.

Entropy, baryon asymmetry and dark matter from heavy neutrino decays

Energy Technology Data Exchange (ETDEWEB)

Buchmueller, W.; Schmitz, K.; Vertongen, G.

2011-04-15

The origin of the hot phase of the early universe remains so far an unsolved puzzle. A viable option is entropy production through the decays of heavy Majorana neutrinos whose lifetimes determine the initial temperature. We show that baryogenesis and the production of dark matter are natural by-products of this mechanism. As is well known, the cosmological baryon asymmetry can be accounted for by lepto- genesis for characteristic neutrino mass parameters. We nd that thermal gravitino production then automatically yields the observed amount of dark matter, for the gravitino as the lightest superparticle and typical gluino masses. As an example, we consider the production of heavy Majorana neutrinos in the course of tachyonic preheating associated with spontaneous B-L breaking. A quantitative analysis leads to contraints on the superparticle masses in terms of neutrino masses: For a light neutrino mass of 10{sup -5} eV the gravitino mass can be as small as 200 MeV, whereas a lower neutrino mass bound of 0.01 eV implies a lower bound of 9 GeV on the gravitino mass. The measurement of a light neutrino mass of 0.1 eV would rule out heavy neutrino decays as the origin of entropy, visible and dark matter. (orig.)

Entropy and wigner functions

Science.gov (United States)

Manfredi; Feix

2000-10-01

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such a definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive-definite probability distributions which are also admissible Wigner functions.

Entropy and Wigner Functions

OpenAIRE

Manfredi, G.; Feix, M. R.

2002-01-01

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive definite probability distributions which are also admissible Wigner functions

Quantum dynamical entropy revisited

International Nuclear Information System (INIS)

Hudetz, T.

1996-10-01

We define a new quantum dynamical entropy, which is a 'hybrid' of the closely related, physically oriented entropy introduced by Alicki and Fannes in 1994, and of the mathematically well-developed, single-argument entropy introduced by Connes, Narnhofer and Thirring in 1987. We show that this new quantum dynamical entropy has many properties similar to the ones of the Alicki-Fannes entropy, and also inherits some additional properties from the CNT entropy. In particular, the 'hybrid' entropy interpolates between the two different ways in which both the AF and the CNT entropy of the shift automorphism on the quantum spin chain agree with the usual quantum entropy density, resulting in even better agreement. Also, the new quantum dynamical entropy generalizes the classical dynamical entropy of Kolmogorov and Sinai in the same way as does the AF entropy. Finally, we estimate the 'hybrid' entropy both for the Powers-Price shift systems and for the noncommutative Arnold map on the irrational rotation C * -algebra, leaving some interesting open problems. (author)

Entropy resistance minimization: An alternative method for heat exchanger analyses

International Nuclear Information System (INIS)

Cheng, XueTao

2013-01-01

In this paper, the concept of entropy resistance is proposed based on the entropy generation analyses of heat transfer processes. It is shown that smaller entropy resistance leads to larger heat transfer rate with fixed thermodynamic force difference and smaller thermodynamic force difference with fixed heat transfer rate, respectively. For the discussed two-stream heat exchangers in which the heat transfer rates are not given and the three-stream heat exchanger with prescribed heat capacity flow rates and inlet temperatures of the streams, smaller entropy resistance leads to larger heat transfer rate. For the two-stream heat exchangers with fixed heat transfer rate, smaller entropy resistance leads to larger effectiveness. Furthermore, it is shown that smaller values of the concepts of entropy generation numbers and modified entropy generation number do not always correspond to better performance of the discussed heat exchangers. - Highlights: • The concept of entropy resistance is defined for heat exchangers. • The concepts based on entropy generation are used to analyze heat exchangers. • Smaller entropy resistance leads to better performance of heat exchangers. • The applicability of entropy generation minimization is conditional

Microscopic entropy and nonlocality

International Nuclear Information System (INIS)

Karpov, E.; Ordonets, G.; Petroskij, T.; Prigozhin, I.

2003-01-01

We have obtained a microscopic expression for entropy in terms of H function based on nonunitary Λ transformation which leads from the time evolution as a unitary group to a Markovian dynamics and unifies the reversible and irreversible aspects of quantum mechanics. This requires a new representation outside the Hilbert space. In terms of H, we show the entropy production and the entropy flow during the emission and absorption of radiation by an atom. Analyzing the time inversion experiment, we emphasize the importance of pre- and postcollisional correlations, which break the symmetry between incoming and outgoing waves. We consider the angle dependence of the H function in a three-dimensional situation. A model including virtual transitions is discussed in a subsequent paper

Entropy in bimolecular simulations: A comprehensive review of atomic fluctuations-based methods.

Science.gov (United States)

Kassem, Summer; Ahmed, Marawan; El-Sheikh, Salah; Barakat, Khaled H

2015-11-01

Entropy of binding constitutes a major, and in many cases a detrimental, component of the binding affinity in biomolecular interactions. While the enthalpic part of the binding free energy is easier to calculate, estimating the entropy of binding is further more complicated. A precise evaluation of entropy requires a comprehensive exploration of the complete phase space of the interacting entities. As this task is extremely hard to accomplish in the context of conventional molecular simulations, calculating entropy has involved many approximations. Most of these golden standard methods focused on developing a reliable estimation of the conformational part of the entropy. Here, we review these methods with a particular emphasis on the different techniques that extract entropy from atomic fluctuations. The theoretical formalisms behind each method is explained highlighting its strengths as well as its limitations, followed by a description of a number of case studies for each method. We hope that this brief, yet comprehensive, review provides a useful tool to understand these methods and realize the practical issues that may arise in such calculations. Copyright © 2015 Elsevier Inc. All rights reserved.

Some Comments on the Entropy-Based Criteria for Piping

Directory of Open Access Journals (Sweden)

Emöke Imre

2015-04-01

Full Text Available This paper is an extension of previous work which characterises soil behaviours using the grading entropy diagram. The present work looks at the piping process in granular soils, by considering some new data from flood-protection dikes. The piping process is divided into three parts here: particle movement at the micro scale to segregate free water; sand boil development (which is the initiation of the pipe, and pipe growth. In the first part of the process, which occurs during the rising flood, the increase in shear stress along the dike base may cause segregation of water into micro pipes if the subsoil in the dike base is relatively loose. This occurs at the maximum dike base shear stress level (ratio of shear stress and strength zone which is close to the toe. In the second part of the process, the shear strain increment causes a sudden, asymmetric slide and cracking of the dike leading to the localized excess pore pressure, liquefaction and the formation of a sand boil. In the third part of the process, the soil erosion initiated through the sand boil continues, and the pipe grows. The piping in the Hungarian dikes often occurs in a two-layer system; where the base layer is coarser with higher permeability and the cover layer is finer with lower permeability. The new data presented here show that the soils ejected from the sand boils are generally silty sands and sands, which are prone to both erosion (on the basis of the entropy criterion and liquefaction. They originate from the cover layer which is basically identical to the soil used in the Dutch backward erosion experiments.

Entropy of Vaidya-deSitter Spacetime

Institute of Scientific and Technical Information of China (English)

LI Xiang; ZHAO Zheng

2001-01-01

As a statistical model of black hole entropy, the brick-wall method based on the thermal equilibrium in a large scale cannot be applied to the cases out of equilibrium, such as the non-static hole or the case with two horizons.However, the leading term of hole entropy called the Bekenstein-Hawking entropy comes from the contribution of the field near the horizon. According to this idea, the entropy of Vaidya-deSitter spacetime is calculated. A difference from the static case is that the result proportional to the area of horizon relies on a time-dependent cut-off. The condition of local equilibrium near the horizon is used as a working postulate.

Bounds and asymptotics for orthogonal polynomials for varying weights

CERN Document Server

Levin, Eli

2018-01-01

This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals.  Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics.  This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices. .

An estimator for the relative entropy rate of path measures for stochastic differential equations

Energy Technology Data Exchange (ETDEWEB)

Opper, Manfred, E-mail: manfred.opper@tu-berlin.de

2017-02-01

We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.

Entropy Coding in HEVC

OpenAIRE

Sze, Vivienne; Marpe, Detlev

2014-01-01

Context-Based Adaptive Binary Arithmetic Coding (CABAC) is a method of entropy coding first introduced in H.264/AVC and now used in the latest High Efficiency Video Coding (HEVC) standard. While it provides high coding efficiency, the data dependencies in H.264/AVC CABAC make it challenging to parallelize and thus limit its throughput. Accordingly, during the standardization of entropy coding for HEVC, both aspects of coding efficiency and throughput were considered. This chapter describes th...

Information Entropy Measures for Stand Structural Diversity:Joint Entropy

Institute of Scientific and Technical Information of China (English)

Lei Xiangdong; Lu Yuanchang

2004-01-01

Structural diversity is the key attribute of a stand. A set of biodiversity measures in ecology was introduced in forest management for describing stand structure, of which Shannon information entropy (Shannon index) has been the most widely used measure of species diversity. It is generally thought that tree size diversity could serve as a good proxy for height diversity. However, tree size diversity and height diversity for stand structure is not completely consistent. Stand diameter cannot reflect height information completely. Either tree size diversity or height diversity is one-dimensional information entropy measure. This paper discussed the method of multiple-dimensional information entropy measure with the concept of joint entropy. It is suggested that joint entropy is a good measure for describing overall stand structural diversity.

On Using Entropy for Enhancing Handwriting Preprocessing

Directory of Open Access Journals (Sweden)

Bernhard Peischl

2012-11-01

Full Text Available 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.

Quantum chaos: entropy signatures

International Nuclear Information System (INIS)

Miller, P.A.; Sarkar, S.; Zarum, R.

1998-01-01

A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)

Bivariate Rainfall and Runoff Analysis Using Shannon Entropy Theory

Science.gov (United States)

Rahimi, A.; Zhang, L.

2012-12-01

Rainfall-Runoff analysis is the key component for many hydrological and hydraulic designs in which the dependence of rainfall and runoff needs to be studied. It is known that the convenient bivariate distribution are often unable to model the rainfall-runoff variables due to that they either have constraints on the range of the dependence or fixed form for the marginal distributions. Thus, this paper presents an approach to derive the entropy-based joint rainfall-runoff distribution using Shannon entropy theory. The distribution derived can model the full range of dependence and allow different specified marginals. The modeling and estimation can be proceeded as: (i) univariate analysis of marginal distributions which includes two steps, (a) using the nonparametric statistics approach to detect modes and underlying probability density, and (b) fitting the appropriate parametric probability density functions; (ii) define the constraints based on the univariate analysis and the dependence structure; (iii) derive and validate the entropy-based joint distribution. As to validate the method, the rainfall-runoff data are collected from the small agricultural experimental watersheds located in semi-arid region near Riesel (Waco), Texas, maintained by the USDA. The results of unviariate analysis show that the rainfall variables follow the gamma distribution, whereas the runoff variables have mixed structure and follow the mixed-gamma distribution. With this information, the entropy-based joint distribution is derived using the first moments, the first moments of logarithm transformed rainfall and runoff, and the covariance between rainfall and runoff. The results of entropy-based joint distribution indicate: (1) the joint distribution derived successfully preserves the dependence between rainfall and runoff, and (2) the K-S goodness of fit statistical tests confirm the marginal distributions re-derived reveal the underlying univariate probability densities which further

Tight Bounds for Communication-Assisted Agreement Distillation

OpenAIRE

Guruswami, Venkatesan; Radhakrishnan, Jaikumar

2016-01-01

Suppose Alice holds a uniformly random string X in {0,1}^N and Bob holds a noisy version Y of X where each bit of X is flipped independently with probability epsilon in [0,1/2]. Alice and Bob would like to extract a common random string of min-entropy at least k. In this work, we establish the communication versus success probability trade-off for this problem by giving a protocol and a matching lower bound (under the restriction that the string to be agreed upon is determined by Alice's inpu...

Gravitational entropies in LTB dust models

International Nuclear Information System (INIS)

Sussman, Roberto A; Larena, Julien

2014-01-01

We consider generic Lemaître–Tolman–Bondi (LTB) dust models to probe the gravitational entropy proposals of Clifton, Ellis and Tavakol (CET) and of Hosoya and Buchert (HB). We also consider a variant of the HB proposal based on a suitable quasi-local scalar weighted average. We show that the conditions for entropy growth for all proposals are directly related to a negative correlation of similar fluctuations of the energy density and Hubble scalar. While this correlation is evaluated locally for the CET proposal, it must be evaluated in a non-local domain dependent manner for the two HB proposals. By looking at the fulfilment of these conditions at the relevant asymptotic limits we are able to provide a well grounded qualitative description of the full time evolution and radial asymptotic scaling of the three entropies in generic models. The following rigorous analytic results are obtained for the three proposals: (i) entropy grows when the density growing mode is dominant, (ii) all ever-expanding hyperbolic models reach a stable terminal equilibrium characterized by an inhomogeneous entropy maximum in their late time evolution; (iii) regions with decaying modes and collapsing elliptic models exhibit unstable equilibria associated with an entropy minimum (iv) near singularities the CET entropy diverges while the HB entropies converge; (v) the CET entropy converges for all models in the radial asymptotic range, whereas the HB entropies only converge for models asymptotic to a Friedmann–Lemaître–Robertson–Walker background. The fact that different independent proposals yield fairly similar conditions for entropy production, time evolution and radial scaling in generic LTB models seems to suggest that their common notion of a ‘gravitational entropy’ may be a theoretically robust concept applicable to more general spacetimes. (paper)

Multiscale multifractal multiproperty analysis of financial time series based on Rényi entropy

Science.gov (United States)

Yujun, Yang; Jianping, Li; Yimei, Yang

This paper introduces a multiscale multifractal multiproperty analysis based on Rényi entropy (3MPAR) method to analyze short-range and long-range characteristics of financial time series, and then applies this method to the five time series of five properties in four stock indices. Combining the two analysis techniques of Rényi entropy and multifractal detrended fluctuation analysis (MFDFA), the 3MPAR method focuses on the curves of Rényi entropy and generalized Hurst exponent of five properties of four stock time series, which allows us to study more universal and subtle fluctuation characteristics of financial time series. By analyzing the curves of the Rényi entropy and the profiles of the logarithm distribution of MFDFA of five properties of four stock indices, the 3MPAR method shows some fluctuation characteristics of the financial time series and the stock markets. Then, it also shows a richer information of the financial time series by comparing the profile of five properties of four stock indices. In this paper, we not only focus on the multifractality of time series but also the fluctuation characteristics of the financial time series and subtle differences in the time series of different properties. We find that financial time series is far more complex than reported in some research works using one property of time series.

Boundary entropy of one-dimensional quantum systems at low temperature

International Nuclear Information System (INIS)

Friedan, Daniel; Konechny, Anatoly

2004-01-01

The boundary β function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula for the boundary β function, expressing it as the gradient of the boundary entropy s at fixed nonzero temperature. The gradient formula implies that s decreases under renormalization, except at critical points (where it stays constant). At a critical point, the number exp(s) is the 'ground-state degeneracy', g, of Affleck and Ludwig, so we have proved their long-standing conjecture that g decreases under renormalization, from critical point to critical point. The gradient formula also implies that s decreases with temperature, except at critical points, where it is independent of temperature. It remains open whether the boundary entropy is always bounded below

Measurement Uncertainty Relations for Discrete Observables: Relative Entropy Formulation

Science.gov (United States)

Barchielli, Alberto; Gregoratti, Matteo; Toigo, Alessandro

2018-02-01

We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate joint measurement of two target discrete observables, we define the entropic divergence as the maximal total loss of information occurring in the approximation at hand. For fixed target observables, we study the joint measurements minimizing the entropic divergence, and we prove the general properties of its minimum value. Such a minimum is our uncertainty lower bound: the total information lost by replacing the target observables with their optimal approximations, evaluated at the worst possible state. The bound turns out to be also an entropic incompatibility degree, that is, a good information-theoretic measure of incompatibility: indeed, it vanishes if and only if the target observables are compatible, it is state-independent, and it enjoys all the invariance properties which are desirable for such a measure. In this context, we point out the difference between general approximate joint measurements and sequential approximate joint measurements; to do this, we introduce a separate index for the tradeoff between the error of the first measurement and the disturbance of the second one. By exploiting the symmetry properties of the target observables, exact values, lower bounds and optimal approximations are evaluated in two different concrete examples: (1) a couple of spin-1/2 components (not necessarily orthogonal); (2) two Fourier conjugate mutually unbiased bases in prime power dimension. Finally, the entropic incompatibility degree straightforwardly generalizes to the case of many observables, still maintaining all its relevant properties; we explicitly compute it for three orthogonal spin-1/2 components.

Fault detection in nonlinear chemical processes based on kernel entropy component analysis and angular structure

Energy Technology Data Exchange (ETDEWEB)

Jiang, Qingchao; Yan, Xuefeng; Lv, Zhaomin; Guo, Meijin [East China University of Science and Technology, Shanghai (China)

2013-06-15

Considering that kernel entropy component analysis (KECA) is a promising new method of nonlinear data transformation and dimensionality reduction, a KECA based method is proposed for nonlinear chemical process monitoring. In this method, an angle-based statistic is designed because KECA reveals structure related to the Renyi entropy of input space data set, and the transformed data sets are produced with a distinct angle-based structure. Based on the angle difference between normal status and current sample data, the current status can be monitored effectively. And, the confidence limit of the angle-based statistics is determined by kernel density estimation based on sample data of the normal status. The effectiveness of the proposed method is demonstrated by case studies on both a numerical process and a simulated continuous stirred tank reactor (CSTR) process. The KECA based method can be an effective method for nonlinear chemical process monitoring.

Fault detection in nonlinear chemical processes based on kernel entropy component analysis and angular structure

International Nuclear Information System (INIS)

Jiang, Qingchao; Yan, Xuefeng; Lv, Zhaomin; Guo, Meijin

2013-01-01

Considering that kernel entropy component analysis (KECA) is a promising new method of nonlinear data transformation and dimensionality reduction, a KECA based method is proposed for nonlinear chemical process monitoring. In this method, an angle-based statistic is designed because KECA reveals structure related to the Renyi entropy of input space data set, and the transformed data sets are produced with a distinct angle-based structure. Based on the angle difference between normal status and current sample data, the current status can be monitored effectively. And, the confidence limit of the angle-based statistics is determined by kernel density estimation based on sample data of the normal status. The effectiveness of the proposed method is demonstrated by case studies on both a numerical process and a simulated continuous stirred tank reactor (CSTR) process. The KECA based method can be an effective method for nonlinear chemical process monitoring

Self-adjusting entropy-stable scheme for compressible Euler equations

Institute of Scientific and Technical Information of China (English)

程晓晗; 聂玉峰; 封建湖; LuoXiao-Yu; 蔡力

2015-01-01

In this work, a self-adjusting entropy-stable scheme is proposed for solving compressible Euler equations. The entropy-stable scheme is constructed by combining the entropy conservative flux with a suitable diffusion operator. The entropy has to be preserved in smooth solutions and be dissipated at shocks. To achieve this, a switch function, based on entropy variables, is employed to make the numerical diffusion term added around discontinuities automatically. The resulting scheme is still entropy-stable. A number of numerical experiments illustrating the robustness and accuracy of the scheme are presented. From these numerical results, we observe a remarkable gain in accuracy.

Tsallis Entropy Theory for Modeling in Water Engineering: A Review

Directory of Open Access Journals (Sweden)

Vijay P. Singh

2017-11-01

Full Text Available Water engineering is an amalgam of engineering (e.g., hydraulics, hydrology, irrigation, ecosystems, environment, water resources and non-engineering (e.g., social, economic, political aspects that are needed for planning, designing and managing water systems. These aspects and the associated issues have been dealt with in the literature using different techniques that are based on different concepts and assumptions. A fundamental question that still remains is: Can we develop a unifying theory for addressing these? The second law of thermodynamics permits us to develop a theory that helps address these in a unified manner. This theory can be referred to as the entropy theory. The thermodynamic entropy theory is analogous to the Shannon entropy or the information theory. Perhaps, the most popular generalization of the Shannon entropy is the Tsallis entropy. The Tsallis entropy has been applied to a wide spectrum of problems in water engineering. This paper provides an overview of Tsallis entropy theory in water engineering. After some basic description of entropy and Tsallis entropy, a review of its applications in water engineering is presented, based on three types of problems: (1 problems requiring entropy maximization; (2 problems requiring coupling Tsallis entropy theory with another theory; and (3 problems involving physical relations.

Special Issue on Entropy-Based Applied Cryptography and Enhanced Security for Ubiquitous Computing

Directory of Open Access Journals (Sweden)

James (Jong Hyuk Park

2016-09-01

Full Text Available Entropy is a basic and important concept in information theory. It is also often used as a measure of the unpredictability of a cryptographic key in cryptography research areas. Ubiquitous computing (Ubi-comp has emerged rapidly as an exciting new paradigm. In this special issue, we mainly selected and discussed papers related with ore theories based on the graph theory to solve computational problems on cryptography and security, practical technologies; applications and services for Ubi-comp including secure encryption techniques, identity and authentication; credential cloning attacks and countermeasures; switching generator with resistance against the algebraic and side channel attacks; entropy-based network anomaly detection; applied cryptography using chaos function, information hiding and watermark, secret sharing, message authentication, detection and modeling of cyber attacks with Petri Nets, and quantum flows for secret key distribution, etc.

ENTROPY FLOW CHARACTERISTICS ANALYSIS OF TYPHOON MATSA (0509)

Institute of Scientific and Technical Information of China (English)

XU Hui; LIU Chong-jian

2008-01-01

The evolution of Typhoon Matsa (0509) is examined in terms of entropy flow through an entropy balance equation derived from the Gibbs relation, according to the second law of thermodynamics. The entropy flows in the various significant stages of (genesis, development and decaying) during its evolution are diagnosed based on the outputs of the PSU/NCAR mesoscale model (known as MM5). The results show that: (1) the vertical spatial distribution of entropy flow for Matsa is characterized by a predominantly negative entropy flow in a large portion of the troposphere and a positive flow in the upper levels; (2) the fields of entropy flows at the middle troposphere (500 hPa) show that the growth of the typhoon is greatly dependent on the negative entropy flows from its surroundings; and (3) the simulated centres of heavy rainfall associated with the typhoon match well with the zones of large negative entropy flows, suggesting that they may be a significant indicator for severe weather events.

Cooperative Localization for Multi-AUVs Based on GM-PHD Filters and Information Entropy Theory

Directory of Open Access Journals (Sweden)

Lichuan Zhang

2017-10-01

Full Text Available Cooperative localization (CL is considered a promising method for underwater localization with respect to multiple autonomous underwater vehicles (multi-AUVs. In this paper, we proposed a CL algorithm based on information entropy theory and the probability hypothesis density (PHD filter, aiming to enhance the global localization accuracy of the follower. In the proposed framework, the follower carries lower cost navigation systems, whereas the leaders carry better ones. Meanwhile, the leaders acquire the followers’ observations, including both measurements and clutter. Then, the PHD filters are utilized on the leaders and the results are communicated to the followers. The followers then perform weighted summation based on all received messages and obtain a final positioning result. Based on the information entropy theory and the PHD filter, the follower is able to acquire a precise knowledge of its position.

[Identification of special quality eggs with NIR spectroscopy technology based on symbol entropy feature extraction method].

Science.gov (United States)

Zhao, Yong; Hong, Wen-Xue

2011-11-01

Fast, nondestructive and accurate identification of special quality eggs is an urgent problem. The present paper proposed a new feature extraction method based on symbol entropy to identify near infrared spectroscopy of special quality eggs. The authors selected normal eggs, free range eggs, selenium-enriched eggs and zinc-enriched eggs as research objects and measured the near-infrared diffuse reflectance spectra in the range of 12 000-4 000 cm(-1). Raw spectra were symbolically represented with aggregation approximation algorithm and symbolic entropy was extracted as feature vector. An error-correcting output codes multiclass support vector machine classifier was designed to identify the spectrum. Symbolic entropy feature is robust when parameter changed and the highest recognition rate reaches up to 100%. The results show that the identification method of special quality eggs using near-infrared is feasible and the symbol entropy can be used as a new feature extraction method of near-infrared spectra.

Refined multiscale fuzzy entropy based on standard deviation for biomedical signal analysis.

Science.gov (United States)

Azami, Hamed; Fernández, Alberto; Escudero, Javier

2017-11-01

Multiscale entropy (MSE) has been a prevalent algorithm to quantify the complexity of biomedical time series. Recent developments in the field have tried to alleviate the problem of undefined MSE values for short signals. Moreover, there has been a recent interest in using other statistical moments than the mean, i.e., variance, in the coarse-graining step of the MSE. Building on these trends, here we introduce the so-called refined composite multiscale fuzzy entropy based on the standard deviation (RCMFE σ ) and mean (RCMFE μ ) to quantify the dynamical properties of spread and mean, respectively, over multiple time scales. We demonstrate the dependency of the RCMFE σ and RCMFE μ , in comparison with other multiscale approaches, on several straightforward signal processing concepts using a set of synthetic signals. The results evidenced that the RCMFE σ and RCMFE μ values are more stable and reliable than the classical multiscale entropy ones. We also inspect the ability of using the standard deviation as well as the mean in the coarse-graining process using magnetoencephalograms in Alzheimer's disease and publicly available electroencephalograms recorded from focal and non-focal areas in epilepsy. Our results indicated that when the RCMFE μ cannot distinguish different types of dynamics of a particular time series at some scale factors, the RCMFE σ may do so, and vice versa. The results showed that RCMFE σ -based features lead to higher classification accuracies in comparison with the RCMFE μ -based ones. We also made freely available all the Matlab codes used in this study at http://dx.doi.org/10.7488/ds/1477 .

Towards operational interpretations of generalized entropies

Science.gov (United States)

Topsøe, Flemming

2010-12-01

The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.

Towards operational interpretations of generalized entropies

International Nuclear Information System (INIS)

Topsoee, Flemming

2010-01-01

The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.

Common approximations for density operators may lead to imaginary entropy

International Nuclear Information System (INIS)

Lendi, K.; Amaral Junior, M.R. do

1983-01-01

The meaning and validity of usual second order approximations for density operators are illustrated with the help of a simple exactly soluble two-level model in which all relevant quantities can easily be controlled. This leads to exact upper bound error estimates which help to select more precisely permissible correlation times as frequently introduced if stochastic potentials are present. A final consideration of information entropy reveals clearly the limitations of this kind of approximation procedures. (Author) [pt

Angular momentum independence of the entropy sum and entropy product for AdS rotating black holes in all dimensions

Directory of Open Access Journals (Sweden)

Hang Liu

2016-08-01

Full Text Available In this paper, we investigate the angular momentum independence of the entropy sum and product for AdS rotating black holes based on the first law of thermodynamics and a mathematical lemma related to Vandermonde determinant. The advantage of this method is that the explicit forms of the spacetime metric, black hole mass and charge are not needed but the Hawking temperature and entropy formula on the horizons are necessary for static black holes, while our calculations require the expressions of metric and angular velocity formula. We find that the entropy sum is always independent of angular momentum for all dimensions and the angular momentum-independence of entropy product only holds for the dimensions d>4 with at least one rotation parameter ai=0, while the mass-free of entropy sum and entropy product for rotating black holes only stand for higher dimensions (d>4 and for all dimensions, respectively. On the other hand, we find that the introduction of a negative cosmological constant does not affect the angular momentum-free of entropy sum and product but the criterion for angular momentum-independence of entropy product will be affected.

Minimal entropy approximation for cellular automata

International Nuclear Information System (INIS)

Fukś, Henryk

2014-01-01

We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)

New Definition and Properties of Fuzzy Entropy

Institute of Scientific and Technical Information of China (English)

Qing Ming; Qin Yingbing

2006-01-01

Let X = (x1,x2 ,…,xn ) and F(X) be a fuzzy set on a universal set X. A new definition of fuzzy entropy about a fuzzy set A on F(X), e*, is defined based on the order relation "≤" on [0,1/2] n. It is proved that e* is a σ-entropy under an additional requirement. Besides, some entropy formulas are presented and related properties are discussed.

Properties of Fuzzy Entropy Based on the Shape Change of Membership Function

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore, play a significant role in analysis of the change of fuzziness of a fuzzy system because a fuzzy partition consists of a set of fuzzy sets which satisfy some special constraints. This paper has shown several results about entropy changes of a fuzzy set. First, the entropies of two same type of fuzzy sets have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Second, as for Triangular Fuzzy Numbers (TFNs), the entropies of any two TFNs which can not be always the same type, also,have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Hence, any two TFNs with the same sizes of support intervals have the same entropies. Third, concerning two Triangular Fuzzy Sets (TFSs) with same sizes of support intervals and different heights, the relationship of their entropies lies on their height.Finally, we point it out a mistake that Chen's assertion that the entropy of resultant fuzzy set of elevation operation is directly proportional to that of the original one while elevation factor just acts as a proportional factor. These results should contribute to the analysis and design of a fuzzy system.

An Algorithm of Traffic Perception of DDoS Attacks against SOA Based on Time United Conditional Entropy

Directory of Open Access Journals (Sweden)

Yuntao Zhao

2016-01-01

Full Text Available DDoS attacks can prevent legitimate users from accessing the service by consuming resource of the target nodes, whose availability of network and service is exposed to a significant threat. Therefore, DDoS traffic perception is the premise and foundation of the whole system security. In this paper the method of DDoS traffic perception for SOA network based on time united conditional entropy was proposed. According to many-to-one relationship mapping between the source IP address and destination IP addresses of DDoS attacks, traffic characteristics of services are analyzed based on conditional entropy. The algorithm is provided with perception ability of DDoS attacks on SOA services by introducing time dimension. Simulation results show that the novel method can realize DDoS traffic perception with analyzing abrupt variation of conditional entropy in time dimension.

Wavelet Entropy-Based Traction Inverter Open Switch Fault Diagnosis in High-Speed Railways

Directory of Open Access Journals (Sweden)

Keting Hu

2016-03-01

Full Text Available In this paper, a diagnosis plan is proposed to settle the detection and isolation problem of open switch faults in high-speed railway traction system traction inverters. Five entropy forms are discussed and compared with the traditional fault detection methods, namely, discrete wavelet transform and discrete wavelet packet transform. The traditional fault detection methods cannot efficiently detect the open switch faults in traction inverters because of the low resolution or the sudden change of the current. The performances of Wavelet Packet Energy Shannon Entropy (WPESE, Wavelet Packet Energy Tsallis Entropy (WPETE with different non-extensive parameters, Wavelet Packet Energy Shannon Entropy with a specific sub-band (WPESE3,6, Empirical Mode Decomposition Shannon Entropy (EMDESE, and Empirical Mode Decomposition Tsallis Entropy (EMDETE with non-extensive parameters in detecting the open switch fault are evaluated by the evaluation parameter. Comparison experiments are carried out to select the best entropy form for the traction inverter open switch fault detection. In addition, the DC component is adopted to isolate the failure Isolated Gate Bipolar Transistor (IGBT. The simulation experiments show that the proposed plan can diagnose single and simultaneous open switch faults correctly and timely.

Self-adjusting entropy-stable scheme for compressible Euler equations

International Nuclear Information System (INIS)

Cheng Xiao-Han; Nie Yu-Feng; Cai Li; Feng Jian-Hu; Luo Xiao-Yu

2015-01-01

In this work, a self-adjusting entropy-stable scheme is proposed for solving compressible Euler equations. The entropy-stable scheme is constructed by combining the entropy conservative flux with a suitable diffusion operator. The entropy has to be preserved in smooth solutions and be dissipated at shocks. To achieve this, a switch function, which is based on entropy variables, is employed to make the numerical diffusion term be automatically added around discontinuities. The resulting scheme is still entropy-stable. A number of numerical experiments illustrating the robustness and accuracy of the scheme are presented. From these numerical results, we observe a remarkable gain in accuracy. (paper)

Entropy of the system formed in heavy ion collision

International Nuclear Information System (INIS)

Gudima, K.K.; Schulz, H.; Toneev, V.D.

1985-01-01

In frames of a cascade model the entropy evolution in a system producted in heavy ion collisions is investigated. Entropy calculation is based on smoothing of the distribution function over the momentum space by the temperature field introduction. The resulting entropy per one nucleon is shown to be rather sensitive to phase space subdivision into cells at the stage of free scattering of reaction products. Compared to recent experimental results for specific entropy values inferred from the composite particle yield of 4π measurements, it is found that cascade calculations do not favour some particular entropy model treatments and suggest smaller entropy values than following from consideration within equilibrium statistics

Entropy and cosmology.

Science.gov (United States)

Zucker, M. H.

This paper is a critical analysis and reassessment of entropic functioning as it applies to the question of whether the ultimate fate of the universe will be determined in the future to be "open" (expanding forever to expire in a big chill), "closed" (collapsing to a big crunch), or "flat" (balanced forever between the two). The second law of thermodynamics declares that entropy can only increase and that this principle extends, inevitably, to the universe as a whole. This paper takes the position that this extension is an unwarranted projection based neither on experience nonfact - an extrapolation that ignores the powerful effect of a gravitational force acting within a closed system. Since it was originally presented by Clausius, the thermodynamic concept of entropy has been redefined in terms of "order" and "disorder" - order being equated with a low degree of entropy and disorder with a high degree. This revised terminology more subjective than precise, has generated considerable confusion in cosmology in several critical instances. For example - the chaotic fireball of the big bang, interpreted by Stephen Hawking as a state of disorder (high entropy), is infinitely hot and, thermally, represents zero entropy (order). Hawking, apparently focusing on the disorderly "chaotic" aspect, equated it with a high degree of entropy - overlooking the fact that the universe is a thermodynamic system and that the key factor in evaluating the big-bang phenomenon is the infinitely high temperature at the early universe, which can only be equated with zero entropy. This analysis resolves this confusion and reestablishes entropy as a cosmological function integrally linked to temperature. The paper goes on to show that, while all subsystems contained within the universe require external sources of energization to have their temperatures raised, this requirement does not apply to the universe as a whole. The universe is the only system that, by itself can raise its own

Structural contributions to the third-law entropy of uranyl phases

International Nuclear Information System (INIS)

Chen, F.; Ewing, R.C.

1999-01-01

Entropies that are used in geochemical calculations are usually based on calorimetric measurements. However, because of the contributions of neglected residual entropies which cannot be determined by calorimetric measurements, the true third-law entropies for many phases may be quite different from those derived from thermal data. The residual entropies are caused by site-mixing, structural disorder and magnetic spin disorder and may result in a considerable contribution to the third-law entropy of solid phases. Magnetic spin-configurational entropy is not expected to be significant in uranyl phases. However, because most uranyl phases are based on sheet or chain structures and usually contain several molecular water groups, site-mixing, vacancies, as well as disorder in the orientation of hydrogen bonds and the polar H 2 O molecules may occur. Calculations of the ideal site-mixing configurational entropy for some uranyl phases indicate that the residual contributions that arise from substitution and vacancies to the third-law entropies of uranyl phases may be large. A brief examination of the crystal chemistry of water molecules in uranyl phases suggests that considerable residual entropy may be caused by the disorder of hydrogen bonds associated with interstitial H 2 O groups

ENTROPIES AND FLUX-SPLITTINGS FOR THE ISENTROPIC EULER EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

The authors establish the existence of a large class of mathematical entropies (the so-called weak entropies) associated with the Euler equations for an isentropic, compressible fluid governed by a general pressure law. A mild assumption on the behavior of the pressure law near the vacuum is solely required. The analysis is based on an asymptotic expansion of the fundamental solution (called here the entropy kernel) of a highly singular Euler-Poisson-Darboux equation. The entropy kernel is only H lder continuous and its regularity is carefully investigated. Relying on a notion introduced earlier by the authors, it is also proven that, for the Euler equations, the set of entropy flux-splittings coincides with the set of entropies-entropy fluxes. These results imply the existence of a flux-splitting consistent with all of the entropy inequalities.

The Conditional Entropy Power Inequality for Bosonic Quantum Systems

DEFF Research Database (Denmark)

de Palma, Giacomo; Trevisan, Dario

2018-01-01

We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally...... independent given the memory and have given quantum conditional entropies. We also prove that, for any couple of values of the quantum conditional entropies of the two inputs, the minimum of the quantum conditional entropy of the output given by the conditional Entropy Power Inequality is asymptotically...... achieved by a suitable sequence of quantum Gaussian input states. Our proof of the conditional Entropy Power Inequality is based on a new Stam inequality for the quantum conditional Fisher information and on the determination of the universal asymptotic behaviour of the quantum conditional entropy under...

Universality of the Volume Bound in Slow-Roll Eternal Inflation

Energy Technology Data Exchange (ETDEWEB)

Dubovsky, Sergei; Senatore, Leonardo; Villadoro, Giovanni

2012-03-28

It has recently been shown that in single field slow-roll inflation the total volume cannot grow by a factor larger than e{sup S{sub dS}/2} without becoming infinite. The bound is saturated exactly at the phase transition to eternal inflation where the probability to produce infinite volume becomes non zero. We show that the bound holds sharply also in any space-time dimensions, when arbitrary higher-dimensional operators are included and in the multi-field inflationary case. The relation with the entropy of de Sitter and the universality of the bound strengthen the case for a deeper holographic interpretation. As a spin-off we provide the formalism to compute the probability distribution of the volume after inflation for generic multi-field models, which might help to address questions about the population of vacua of the landscape during slow-roll inflation.

Trustworthiness Measurement Algorithm for TWfMS Based on Software Behaviour Entropy

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Qiang Han

2018-03-01

Full Text Available As the virtual mirror of complex real-time business processes of organisations’ underlying information systems, the workflow management system (WfMS has emerged in recent decades as a new self-autonomous paradigm in the open, dynamic, distributed computing environment. In order to construct a trustworthy workflow management system (TWfMS, the design of a software behaviour trustworthiness measurement algorithm is an urgent task for researchers. Accompanying the trustworthiness mechanism, the measurement algorithm, with uncertain software behaviour trustworthiness information of the WfMS, should be resolved as an infrastructure. Based on the framework presented in our research prior to this paper, we firstly introduce a formal model for the WfMS trustworthiness measurement, with the main property reasoning based on calculus operators. Secondly, this paper proposes a novel measurement algorithm from the software behaviour entropy of calculus operators through the principle of maximum entropy (POME and the data mining method. Thirdly, the trustworthiness measurement algorithm for incomplete software behaviour tests and runtime information is discussed and compared by means of a detailed explanation. Finally, we provide conclusions and discuss certain future research areas of the TWfMS.

Combined Forecasting of Rainfall Based on Fuzzy Clustering and Cross Entropy

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Baohui Men

2017-12-01

Full Text Available Rainfall is an essential index to measure drought, and it is dependent upon various parameters including geographical environment, air temperature and pressure. The nonlinear nature of climatic variables leads to problems such as poor accuracy and instability in traditional forecasting methods. In this paper, the combined forecasting method based on data mining technology and cross entropy is proposed to forecast the rainfall with full consideration of the time-effectiveness of historical data. In view of the flaws of the fuzzy clustering method which is easy to fall into local optimal solution and low speed of operation, the ant colony algorithm is adopted to overcome these shortcomings and, as a result, refine the model. The method for determining weights is also improved by using the cross entropy. Besides, the forecast is conducted by analyzing the weighted average rainfall based on Thiessen polygon in the Beijing–Tianjin–Hebei region. Since the predictive errors are calculated, the results show that improved ant colony fuzzy clustering can effectively select historical data and enhance the accuracy of prediction so that the damage caused by extreme weather events like droughts and floods can be greatly lessened and even kept at bay.

Secondary structural entropy in RNA switch (Riboswitch) identification.

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Manzourolajdad, Amirhossein; Arnold, Jonathan

2015-04-28

RNA regulatory elements play a significant role in gene regulation. Riboswitches, a widespread group of regulatory RNAs, are vital components of many bacterial genomes. These regulatory elements generally function by forming a ligand-induced alternative fold that controls access to ribosome binding sites or other regulatory sites in RNA. Riboswitch-mediated mechanisms are ubiquitous across bacterial genomes. A typical class of riboswitch has its own unique structural and biological complexity, making de novo riboswitch identification a formidable task. Traditionally, riboswitches have been identified through comparative genomics based on sequence and structural homology. The limitations of structural-homology-based approaches, coupled with the assumption that there is a great diversity of undiscovered riboswitches, suggests the need for alternative methods for riboswitch identification, possibly based on features intrinsic to their structure. As of yet, no such reliable method has been proposed. We used structural entropy of riboswitch sequences as a measure of their secondary structural dynamics. Entropy values of a diverse set of riboswitches were compared to that of their mutants, their dinucleotide shuffles, and their reverse complement sequences under different stochastic context-free grammar folding models. Significance of our results was evaluated by comparison to other approaches, such as the base-pairing entropy and energy landscapes dynamics. Classifiers based on structural entropy optimized via sequence and structural features were devised as riboswitch identifiers and tested on Bacillus subtilis, Escherichia coli, and Synechococcus elongatus as an exploration of structural entropy based approaches. The unusually long untranslated region of the cotH in Bacillus subtilis, as well as upstream regions of certain genes, such as the sucC genes were associated with significant structural entropy values in genome-wide examinations. Various tests show that there

Parametric Bayesian Estimation of Differential Entropy and Relative Entropy

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Maya Gupta

2010-04-01

Full Text Available Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian estimates, depend on the accuracy of the prior parameters, but example simulations show that the performance can be substantially improved compared to maximum likelihood or state-of-the-art nonparametric estimators.

A gravitational entropy proposal

International Nuclear Information System (INIS)

Clifton, Timothy; Tavakol, Reza; Ellis, George F R

2013-01-01

We propose a thermodynamically motivated measure of gravitational entropy based on the Bel–Robinson tensor, which has a natural interpretation as the effective super-energy–momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein–Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson–Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein’s field equations. It is also in keeping with Penrose’s Weyl curvature hypothesis. (paper)

Entropy? Honest!

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Tommaso Toffoli

2016-06-01

Full Text Available Here we deconstruct, and then in a reasoned way reconstruct, the concept of “entropy of a system”, paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a count associated with a description; this count (traditionally expressed in logarithmic form for a number of good reasons is in essence the number of possibilities—specific instances or “scenarios”—that match that description. Very natural (and virtually inescapable generalizations of the idea of description are the probability distribution and its quantum mechanical counterpart, the density operator. We track the process of dynamically updating entropy as a system evolves. Three factors may cause entropy to change: (1 the system’s internal dynamics; (2 unsolicited external influences on it; and (3 the approximations one has to make when one tries to predict the system’s future state. The latter task is usually hampered by hard-to-quantify aspects of the original description, limited data storage and processing resource, and possibly algorithmic inadequacy. Factors 2 and 3 introduce randomness—often huge amounts of it—into one’s predictions and accordingly degrade them. When forecasting, as long as the entropy bookkeping is conducted in an honest fashion, this degradation will always lead to an entropy increase. To clarify the above point we introduce the notion of honest entropy, which coalesces much of what is of course already done, often tacitly, in responsible entropy-bookkeping practice. This notion—we believe—will help to fill an expressivity gap in scientific discourse. With its help, we shall prove that any dynamical system—not just our physical universe—strictly obeys Clausius’s original formulation of the second law of thermodynamics if and only if it is invertible. Thus this law is a tautological property of invertible systems!

EEG entropy measures in anesthesia

Science.gov (United States)

Liang, Zhenhu; Wang, Yinghua; Sun, Xue; Li, Duan; Voss, Logan J.; Sleigh, Jamie W.; Hagihira, Satoshi; Li, Xiaoli

2015-01-01

Highlights: ► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents. Methods: Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared. Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R2) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation

Optimized Kernel Entropy Components.

Science.gov (United States)

Izquierdo-Verdiguier, Emma; Laparra, Valero; Jenssen, Robert; Gomez-Chova, Luis; Camps-Valls, Gustau

2017-06-01

This brief addresses two main issues of the standard kernel entropy component analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of variance, as in the kernel principal components analysis. In this brief, we propose an extension of the KECA method, named optimized KECA (OKECA), that directly extracts the optimal features retaining most of the data entropy by means of compacting the information in very few features (often in just one or two). The proposed method produces features which have higher expressive power. In particular, it is based on the independent component analysis framework, and introduces an extra rotation to the eigen decomposition, which is optimized via gradient-ascent search. This maximum entropy preservation suggests that OKECA features are more efficient than KECA features for density estimation. In addition, a critical issue in both the methods is the selection of the kernel parameter, since it critically affects the resulting performance. Here, we analyze the most common kernel length-scale selection criteria. The results of both the methods are illustrated in different synthetic and real problems. Results show that OKECA returns projections with more expressive power than KECA, the most successful rule for estimating the kernel parameter is based on maximum likelihood, and OKECA is more robust to the selection of the length-scale parameter in kernel density estimation.

Irreversible entropy model for damage diagnosis in resistors

Energy Technology Data Exchange (ETDEWEB)

Cuadras, Angel, E-mail: angel.cuadras@upc.edu; Crisóstomo, Javier; Ovejas, Victoria J.; Quilez, Marcos [Instrumentation, Sensor and Interfaces Group, Electronic Engineering Department, Escola d' Enginyeria de Telecomunicació i Aeronàutica de Castelldefels EETAC, Universitat Politècnica de Catalunya, Barcelona Tech (UPC), Castelldefels-Barcelona (Spain)

2015-10-28

We propose a method to characterize electrical resistor damage based on entropy measurements. Irreversible entropy and the rate at which it is generated are more convenient parameters than resistance for describing damage because they are essentially positive in virtue of the second law of thermodynamics, whereas resistance may increase or decrease depending on the degradation mechanism. Commercial resistors were tested in order to characterize the damage induced by power surges. Resistors were biased with constant and pulsed voltage signals, leading to power dissipation in the range of 4–8 W, which is well above the 0.25 W nominal power to initiate failure. Entropy was inferred from the added power and temperature evolution. A model is proposed to understand the relationship among resistance, entropy, and damage. The power surge dissipates into heat (Joule effect) and damages the resistor. The results show a correlation between entropy generation rate and resistor failure. We conclude that damage can be conveniently assessed from irreversible entropy generation. Our results for resistors can be easily extrapolated to other systems or machines that can be modeled based on their resistance.

Irreversible entropy model for damage diagnosis in resistors

International Nuclear Information System (INIS)

Cuadras, Angel; Crisóstomo, Javier; Ovejas, Victoria J.; Quilez, Marcos

2015-01-01

We propose a method to characterize electrical resistor damage based on entropy measurements. Irreversible entropy and the rate at which it is generated are more convenient parameters than resistance for describing damage because they are essentially positive in virtue of the second law of thermodynamics, whereas resistance may increase or decrease depending on the degradation mechanism. Commercial resistors were tested in order to characterize the damage induced by power surges. Resistors were biased with constant and pulsed voltage signals, leading to power dissipation in the range of 4–8 W, which is well above the 0.25 W nominal power to initiate failure. Entropy was inferred from the added power and temperature evolution. A model is proposed to understand the relationship among resistance, entropy, and damage. The power surge dissipates into heat (Joule effect) and damages the resistor. The results show a correlation between entropy generation rate and resistor failure. We conclude that damage can be conveniently assessed from irreversible entropy generation. Our results for resistors can be easily extrapolated to other systems or machines that can be modeled based on their resistance

Local curvature entropy-based 3D terrain representation using a comprehensive Quadtree

Science.gov (United States)

Chen, Qiyu; Liu, Gang; Ma, Xiaogang; Mariethoz, Gregoire; He, Zhenwen; Tian, Yiping; Weng, Zhengping

2018-05-01

Large scale 3D digital terrain modeling is a crucial part of many real-time applications in geoinformatics. In recent years, the improved speed and precision in spatial data collection make the original terrain data more complex and bigger, which poses challenges for data management, visualization and analysis. In this work, we presented an effective and comprehensive 3D terrain representation based on local curvature entropy and a dynamic Quadtree. The Level-of-detail (LOD) models of significant terrain features were employed to generate hierarchical terrain surfaces. In order to reduce the radical changes of grid density between adjacent LODs, local entropy of terrain curvature was regarded as a measure of subdividing terrain grid cells. Then, an efficient approach was presented to eliminate the cracks among the different LODs by directly updating the Quadtree due to an edge-based structure proposed in this work. Furthermore, we utilized a threshold of local entropy stored in each parent node of this Quadtree to flexibly control the depth of the Quadtree and dynamically schedule large-scale LOD terrain. Several experiments were implemented to test the performance of the proposed method. The results demonstrate that our method can be applied to construct LOD 3D terrain models with good performance in terms of computational cost and the maintenance of terrain features. Our method has already been deployed in a geographic information system (GIS) for practical uses, and it is able to support the real-time dynamic scheduling of large scale terrain models more easily and efficiently.

RNA Thermodynamic Structural Entropy.

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Juan Antonio Garcia-Martin

Full Text Available Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs. However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http

RNA Thermodynamic Structural Entropy.

Science.gov (United States)

Garcia-Martin, Juan Antonio; Clote, Peter

2015-01-01

Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http

Research of Planetary Gear Fault Diagnosis Based on Permutation Entropy of CEEMDAN and ANFIS

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Moshen Kuai

2018-03-01

Full Text Available For planetary gear has the characteristics of small volume, light weight and large transmission ratio, it is widely used in high speed and high power mechanical system. Poor working conditions result in frequent failures of planetary gear. A method is proposed for diagnosing faults in planetary gear based on permutation entropy of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN Adaptive Neuro-fuzzy Inference System (ANFIS in this paper. The original signal is decomposed into 6 intrinsic mode functions (IMF and residual components by CEEMDAN. Since the IMF contains the main characteristic information of planetary gear faults, time complexity of IMFs are reflected by permutation entropies to quantify the fault features. The permutation entropies of each IMF component are defined as the input of ANFIS, and its parameters and membership functions are adaptively adjusted according to training samples. Finally, the fuzzy inference rules are determined, and the optimal ANFIS is obtained. The overall recognition rate of the test sample used for ANFIS is 90%, and the recognition rate of gear with one missing tooth is relatively high. The recognition rates of different fault gears based on the method can also achieve better results. Therefore, the proposed method can be applied to planetary gear fault diagnosis effectively.

Research of Planetary Gear Fault Diagnosis Based on Permutation Entropy of CEEMDAN and ANFIS.

Science.gov (United States)

Kuai, Moshen; Cheng, Gang; Pang, Yusong; Li, Yong

2018-03-05

For planetary gear has the characteristics of small volume, light weight and large transmission ratio, it is widely used in high speed and high power mechanical system. Poor working conditions result in frequent failures of planetary gear. A method is proposed for diagnosing faults in planetary gear based on permutation entropy of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) Adaptive Neuro-fuzzy Inference System (ANFIS) in this paper. The original signal is decomposed into 6 intrinsic mode functions (IMF) and residual components by CEEMDAN. Since the IMF contains the main characteristic information of planetary gear faults, time complexity of IMFs are reflected by permutation entropies to quantify the fault features. The permutation entropies of each IMF component are defined as the input of ANFIS, and its parameters and membership functions are adaptively adjusted according to training samples. Finally, the fuzzy inference rules are determined, and the optimal ANFIS is obtained. The overall recognition rate of the test sample used for ANFIS is 90%, and the recognition rate of gear with one missing tooth is relatively high. The recognition rates of different fault gears based on the method can also achieve better results. Therefore, the proposed method can be applied to planetary gear fault diagnosis effectively.

Prediction Model of Collapse Risk Based on Information Entropy and Distance Discriminant Analysis Method

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Hujun He

2017-01-01

Full Text Available The prediction and risk classification of collapse is an important issue in the process of highway construction in mountainous regions. Based on the principles of information entropy and Mahalanobis distance discriminant analysis, we have produced a collapse hazard prediction model. We used the entropy measure method to reduce the influence indexes of the collapse activity and extracted the nine main indexes affecting collapse activity as the discriminant factors of the distance discriminant analysis model (i.e., slope shape, aspect, gradient, and height, along with exposure of the structural face, stratum lithology, relationship between weakness face and free face, vegetation cover rate, and degree of rock weathering. We employ postearthquake collapse data in relation to construction of the Yingxiu-Wolong highway, Hanchuan County, China, as training samples for analysis. The results were analyzed using the back substitution estimation method, showing high accuracy and no errors, and were the same as the prediction result of uncertainty measure. Results show that the classification model based on information entropy and distance discriminant analysis achieves the purpose of index optimization and has excellent performance, high prediction accuracy, and a zero false-positive rate. The model can be used as a tool for future evaluation of collapse risk.

Density estimation by maximum quantum entropy

International Nuclear Information System (INIS)

Silver, R.N.; Wallstrom, T.; Martz, H.F.

1993-01-01

A new Bayesian method for non-parametric density estimation is proposed, based on a mathematical analogy to quantum statistical physics. The mathematical procedure is related to maximum entropy methods for inverse problems and image reconstruction. The information divergence enforces global smoothing toward default models, convexity, positivity, extensivity and normalization. The novel feature is the replacement of classical entropy by quantum entropy, so that local smoothing is enforced by constraints on differential operators. The linear response of the estimate is proportional to the covariance. The hyperparameters are estimated by type-II maximum likelihood (evidence). The method is demonstrated on textbook data sets

Transfer Entropy as a Log-Likelihood Ratio

Science.gov (United States)

Barnett, Lionel; Bossomaier, Terry

2012-09-01

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology, and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic χ2 distribution is established for the transfer entropy estimator. The result generalizes the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense.

Heavy-quark free energies, internal-energy and entropy contributions

International Nuclear Information System (INIS)

Kaczmarek, O.

2009-01-01

We present lattice QCD results on heavy-quark free energies, extract from its temperature dependence the entropy and internal-energy contributions, and discuss the onset of medium effects that lead to screening of static quark-antiquark sources in a thermal medium. The detailed analysis of the temperature and distance dependence of the different contributions indicate the complex non-perturbative nature of strongly interacting matter. We shall discuss the necessity to include those effects in studies on the behavior of heavy quarks, heavy-quark bound states and their dissociation in the quark-gluon plasma phase. (orig.)

Entropy In the Universe: A New Approach

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Antonio Alfonso-Faus

2000-09-01

Full Text Available Abstract: We propose a new definition of entropy for any mass m, based on gravitation and through the concept of a gravitational cross section. It turns out to be proportional to mass, and therefore extensive, and to the age of the Universe. It is a Machian approach. It is also the number of gravity quanta the mass has emitted through its age. The entropy of the Uni-verse is so determined and the cosmological entropy problem solved.

Statistical region based active contour using a fractional entropy descriptor: Application to nuclei cell segmentation in confocal \\ud microscopy images

OpenAIRE

Histace, A; Meziou, B J; Matuszewski, Bogdan; Precioso, F; Murphy, M F; Carreiras, F

2013-01-01

We propose an unsupervised statistical region based active contour approach integrating an original fractional entropy measure for image segmentation with a particular application to single channel actin tagged fluorescence confocal microscopy image segmentation. Following description of statistical based active contour segmentation and the mathematical definition of the proposed fractional entropy descriptor, we demonstrate comparative segmentation results between the proposed approach and s...

Constraining the mSUGRA (minimal supergravity) parameter space using the entropy of dark matter halos

Energy Technology Data Exchange (ETDEWEB)

Nunez, Dario; Zavala, Jesus; Nellen, Lukas; Sussman, Roberto A [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico (ICN-UNAM), AP 70-543, Mexico 04510 DF (Mexico); Cabral-Rosetti, Luis G [Departamento de Posgrado, Centro Interdisciplinario de Investigacion y Docencia en Educacion Tecnica (CIIDET), Avenida Universidad 282 Pte., Col. Centro, Apartado Postal 752, C. P. 76000, Santiago de Queretaro, Qro. (Mexico); Mondragon, Myriam, E-mail: nunez@nucleares.unam.mx, E-mail: jzavala@nucleares.unam.mx, E-mail: jzavala@shao.ac.cn, E-mail: lukas@nucleares.unam.mx, E-mail: sussman@nucleares.unam.mx, E-mail: lgcabral@ciidet.edu.mx, E-mail: myriam@fisica.unam.mx [Instituto de Fisica, Universidad Nacional Autonoma de Mexico (IF-UNAM), Apartado Postal 20-364, 01000 Mexico DF (Mexico); Collaboration: For the Instituto Avanzado de Cosmologia, IAC

2008-05-15

We derive an expression for the entropy of a dark matter halo described using a Navarro-Frenk-White model with a core. The comparison of this entropy with that of dark matter in the freeze-out era allows us to constrain the parameter space in mSUGRA models. Moreover, combining these constraints with the ones obtained from the usual abundance criterion and demanding that these criteria be consistent with the 2{sigma} bounds for the abundance of dark matter: 0.112{<=}{Omega}{sub DM}h{sup 2}{<=}0.122, we are able to clearly identify validity regions among the values of tan{beta}, which is one of the parameters of the mSUGRA model. We found that for the regions of the parameter space explored, small values of tan{beta} are not favored; only for tan {beta} Asymptotically-Equal-To 50 are the two criteria significantly consistent. In the region where the two criteria are consistent we also found a lower bound for the neutralino mass, m{sub {chi}}{>=}141 GeV.

Constraining the mSUGRA (minimal supergravity) parameter space using the entropy of dark matter halos

International Nuclear Information System (INIS)

Núñez, Darío; Zavala, Jesús; Nellen, Lukas; Sussman, Roberto A; Cabral-Rosetti, Luis G; Mondragón, Myriam

2008-01-01

We derive an expression for the entropy of a dark matter halo described using a Navarro–Frenk–White model with a core. The comparison of this entropy with that of dark matter in the freeze-out era allows us to constrain the parameter space in mSUGRA models. Moreover, combining these constraints with the ones obtained from the usual abundance criterion and demanding that these criteria be consistent with the 2σ bounds for the abundance of dark matter: 0.112≤Ω DM h 2 ≤0.122, we are able to clearly identify validity regions among the values of tanβ, which is one of the parameters of the mSUGRA model. We found that for the regions of the parameter space explored, small values of tanβ are not favored; only for tan β ≃ 50 are the two criteria significantly consistent. In the region where the two criteria are consistent we also found a lower bound for the neutralino mass, m χ ≥141 GeV

Energy and entropy analysis of closed adiabatic expansion based trilateral cycles

International Nuclear Information System (INIS)

Garcia, Ramon Ferreiro; Carril, Jose Carbia; Gomez, Javier Romero; Gomez, Manuel Romero

2016-01-01

Highlights: • The adiabatic expansion based TC surpass Carnot factor at low temperatures. • The fact of surpassing Carnot factor doesn’t violate the 2nd law. • An entropy analysis is applied to verify the fulfilment of the second law. • Correction of the exergy transfer associated with heat transferred to a cycle. - Abstract: A vast amount of heat energy is available at low cost within the range of medium and low temperatures. Existing thermal cycles cannot make efficient use of such available low grade heat because they are mainly based on conventional organic Rankine cycles which are limited by Carnot constraints. However, recent developments related to the performance of thermal cycles composed of closed processes have led to the exceeding of the Carnot factor. Consequently, once the viability of closed process based thermal cycles that surpass the Carnot factor operating at low and medium temperatures is globally accepted, research work will aim at looking into the consequences that lead from surpassing the Carnot factor while fulfilling the 2nd law, its impact on the 2nd law efficiency definition as well as the impact on the exergy transfer from thermal power sources to any heat consumer, including thermal cycles. The methodology used to meet the proposed objectives involves the analysis of energy and entropy on trilateral closed process based thermal cycles. Thus, such energy and entropy analysis is carried out upon non-condensing mode trilateral thermal cycles (TCs) characterised by the conversion of low grade heat into mechanical work undergoing closed adiabatic path functions: isochoric heat absorption, adiabatic heat to mechanical work conversion and isobaric heat rejection. Firstly, cycle energy analysis is performed to determine the range of some relevant cycle parameters, such as the operating temperatures and their associated pressures, entropies, internal energies and specific volumes. In this way, the ranges of temperatures within which

Change of entropy in the martensitic transformation and its dependence in Cu-based shape memory alloys

International Nuclear Information System (INIS)

Romero, R.; Pelegrina, J.L.

2003-01-01

A study of the entropy change ΔS between the β phase and the martensite in Cu-based shape memory alloys is presented. From a compilation of available experimental data, the composition dependence of ΔS was studied. The experimental data were analyzed within the frame of a simple model, which is based on the specific heats of the phases. It was demonstrated that the dependence of ΔS with composition comes only through the lattice parameter and the effective mass of the alloy. For the studied composition range, the greater vibrational entropy of β phase is mainly controlled by the high-mass Cu atoms

Gravel Image Segmentation in Noisy Background Based on Partial Entropy Method

Institute of Scientific and Technical Information of China (English)

无

2000-01-01

Because of wide variation in gray levels and particle dimensions and the presence of many small gravel objects in the background, as well as corrupting the image by noise, it is difficult o segment gravel objects. In this paper, we develop a partial entropy method and succeed to realize gravel objects segmentation. We give entropy principles and fur calculation methods. Moreover, we use minimum entropy error automaticly to select a threshold to segment image. We introduce the filter method using mathematical morphology. The segment experiments are performed by using different window dimensions for a group of gravel image and demonstrates that this method has high segmentation rate and low noise sensitivity.

A Note of Caution on Maximizing Entropy

Directory of Open Access Journals (Sweden)

Richard E. Neapolitan

2014-07-01

Full Text Available The Principle of Maximum Entropy is often used to update probabilities due to evidence instead of performing Bayesian updating using Bayes’ Theorem, and its use often has efficacious results. However, in some circumstances the results seem unacceptable and unintuitive. This paper discusses some of these cases, and discusses how to identify some of the situations in which this principle should not be used. The paper starts by reviewing three approaches to probability, namely the classical approach, the limiting frequency approach, and the Bayesian approach. It then introduces maximum entropy and shows its relationship to the three approaches. Next, through examples, it shows that maximizing entropy sometimes can stand in direct opposition to Bayesian updating based on reasonable prior beliefs. The paper concludes that if we take the Bayesian approach that probability is about reasonable belief based on all available information, then we can resolve the conflict between the maximum entropy approach and the Bayesian approach that is demonstrated in the examples.

EEG entropy measures in anesthesia

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Zhenhu eLiang

2015-02-01

Full Text Available Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs’ effect is lacking. In this study, we compare the capability of twelve entropy indices for monitoring depth of anesthesia (DoA and detecting the burst suppression pattern (BSP, in anesthesia induced by GA-BAergic agents.Methods: Twelve indices were investigated, namely Response Entropy (RE and State entropy (SE, three wavelet entropy (WE measures (Shannon WE (SWE, Tsallis WE (TWE and Renyi WE (RWE, Hilbert-Huang spectral entropy (HHSE, approximate entropy (ApEn, sample entropy (SampEn, Fuzzy entropy, and three permutation entropy (PE measures (Shannon PE (SPE, Tsallis PE (TPE and Renyi PE (RPE. Two EEG data sets from sevoflurane-induced and isoflu-rane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, phar-macokinetic / pharmacodynamic (PK/PD modeling and prediction probability analysis were applied. The multifractal detrended fluctuation analysis (MDFA as a non-entropy measure was compared.Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline vari-ability, higher coefficient of determination and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an ad-vantage in computation efficiency compared with MDFA.Conclusion: Each entropy index has its advantages and disadvantages in estimating DoA. Overall, it is suggested that the RPE index was a superior measure.Significance: Investigating the advantages and disadvantages of these entropy indices could help improve current clinical indices for monitoring DoA.

CoFea: A Novel Approach to Spam Review Identification Based on Entropy and Co-Training

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Wen Zhang

2016-11-01

Full Text Available With the rapid development of electronic commerce, spam reviews are rapidly growing on the Internet to manipulate online customers’ opinions on goods being sold. This paper proposes a novel approach, called CoFea (Co-training by Features, to identify spam reviews, based on entropy and the co-training algorithm. After sorting all lexical terms of reviews by entropy, we produce two views on the reviews by dividing the lexical terms into two subsets. One subset contains odd-numbered terms and the other contains even-numbered terms. Using SVM (support vector machine as the base classifier, we further propose two strategies, CoFea-T and CoFea-S, embedded with the CoFea approach. The CoFea-T strategy uses all terms in the subsets for spam review identification by SVM. The CoFea-S strategy uses a predefined number of terms with small entropy for spam review identification by SVM. The experiment results show that the CoFea-T strategy produces better accuracy than the CoFea-S strategy, while the CoFea-S strategy saves more computing time than the CoFea-T strategy with acceptable accuracy in spam review identification.

EEG-Based Computer Aided Diagnosis of Autism Spectrum Disorder Using Wavelet, Entropy, and ANN

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Ridha Djemal

2017-01-01

Full Text Available Autism spectrum disorder (ASD is a type of neurodevelopmental disorder with core impairments in the social relationships, communication, imagination, or flexibility of thought and restricted repertoire of activity and interest. In this work, a new computer aided diagnosis (CAD of autism ‎based on electroencephalography (EEG signal analysis is investigated. The proposed method is based on discrete wavelet transform (DWT, entropy (En, and artificial neural network (ANN. DWT is used to decompose EEG signals into approximation and details coefficients to obtain EEG subbands. The feature vector is constructed by computing Shannon entropy values from each EEG subband. ANN classifies the corresponding EEG signal into normal or autistic based on the extracted features. The experimental results show the effectiveness of the proposed method for assisting autism diagnosis. A receiver operating characteristic (ROC curve metric is used to quantify the performance of the proposed method. The proposed method obtained promising results tested using real dataset provided by King Abdulaziz Hospital, Jeddah, Saudi Arabia.

Another short and elementary proof of strong subadditivity of quantum entropy

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Ruskai, Mary Beth

2007-08-01

A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz inequality in elementary courses. Several consequences are proved in a way which allows an elementary proof of strong subadditivity in a few more lines. Some expository material on Schwarz inequalities for operators and the Holevo bound for partial measurements is also included.

Entropy-Based Block Processing for Satellite Image Registration

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Ikhyun Lee

2012-11-01

Full Text Available Image registration is an important task in many computer vision applications such as fusion systems, 3D shape recovery and earth observation. Particularly, registering satellite images is challenging and time-consuming due to limited resources and large image size. In such scenario, state-of-the-art image registration methods such as scale-invariant feature transform (SIFT may not be suitable due to high processing time. In this paper, we propose an algorithm based on block processing via entropy to register satellite images. The performance of the proposed method is evaluated using different real images. The comparative analysis shows that it not only reduces the processing time but also enhances the accuracy.

Applying Improved Multiscale Fuzzy Entropy for Feature Extraction of MI-EEG

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Ming-ai Li

2017-01-01

Full Text Available Electroencephalography (EEG is considered the output of a brain and it is a bioelectrical signal with multiscale and nonlinear properties. Motor Imagery EEG (MI-EEG not only has a close correlation with the human imagination and movement intention but also contains a large amount of physiological or disease information. As a result, it has been fully studied in the field of rehabilitation. To correctly interpret and accurately extract the features of MI-EEG signals, many nonlinear dynamic methods based on entropy, such as Approximate Entropy (ApEn, Sample Entropy (SampEn, Fuzzy Entropy (FE, and Permutation Entropy (PE, have been proposed and exploited continuously in recent years. However, these entropy-based methods can only measure the complexity of MI-EEG based on a single scale and therefore fail to account for the multiscale property inherent in MI-EEG. To solve this problem, Multiscale Sample Entropy (MSE, Multiscale Permutation Entropy (MPE, and Multiscale Fuzzy Entropy (MFE are developed by introducing scale factor. However, MFE has not been widely used in analysis of MI-EEG, and the same parameter values are employed when the MFE method is used to calculate the fuzzy entropy values on multiple scales. Actually, each coarse-grained MI-EEG carries the characteristic information of the original signal on different scale factors. It is necessary to optimize MFE parameters to discover more feature information. In this paper, the parameters of MFE are optimized independently for each scale factor, and the improved MFE (IMFE is applied to the feature extraction of MI-EEG. Based on the event-related desynchronization (ERD/event-related synchronization (ERS phenomenon, IMFE features from multi channels are fused organically to construct the feature vector. Experiments are conducted on a public dataset by using Support Vector Machine (SVM as a classifier. The experiment results of 10-fold cross-validation show that the proposed method yields

Maximum Entropy Methods as the Bridge Between Microscopic and Macroscopic Theory

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Taylor, Jamie M.

2016-09-01

This paper is concerned with an investigation into a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability distributions on a state space, defined so that it corresponds to the maximum possible entropy given known observed statistical averages, although non-classical entropy-like objective functions will also be considered. First the set of admissible moments must be established, and under the conditions presented in this work the set is open, bounded and convex allowing a description in terms of supporting hyperplanes, which provides estimates on the development of singularities for related probability distributions. Under appropriate conditions it is shown that the singular potential is strictly convex, as differentiable as the microscopic entropy, and blows up uniformly as the macroscopic variable tends to the boundary of the set of admissible moments. Applications of the singular potential are then discussed, and particular consideration will be given to certain free-energy functionals typical in mean-field theory, demonstrating an equivalence between certain microscopic and macroscopic free-energy functionals. This allows statements about L^1-local minimisers of Onsager's free energy to be obtained which cannot be given by two-sided variations, and overcomes the need to ensure local minimisers are bounded away from zero and +∞ before taking L^∞ variations. The analysis also permits the definition of a dual order parameter for which Onsager's free energy allows an explicit representation. Also, the difficulties in approximating the singular potential by everywhere defined functions, in particular by polynomial functions, are addressed, with examples demonstrating the failure of the Taylor approximation to preserve relevant shape properties of the singular potential.

Entropy of black holes with multiple horizons

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He, Yun; Ma, Meng-Sen; Zhao, Ren

2018-05-01

We examine the entropy of black holes in de Sitter space and black holes surrounded by quintessence. These black holes have multiple horizons, including at least the black hole event horizon and a horizon outside it (cosmological horizon for de Sitter black holes and "quintessence horizon" for the black holes surrounded by quintessence). Based on the consideration that the two horizons are not independent each other, we conjecture that the total entropy of these black holes should not be simply the sum of entropies of the two horizons, but should have an extra term coming from the correlations between the two horizons. Different from our previous works, in this paper we consider the cosmological constant as the variable and employ an effective method to derive the explicit form of the entropy. We also try to discuss the thermodynamic stabilities of these black holes according to the entropy and the effective temperature.

Three faces of entropy for complex systems: Information, thermodynamics, and the maximum entropy principle

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Thurner, Stefan; Corominas-Murtra, Bernat; Hanel, Rudolf

2017-09-01

There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, H (p ) =-∑ipilogpi . For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as SEXT for extensive entropy, SIT for the source information rate in information theory, and SMEP for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.

Exploring the effects of climatic variables on monthly precipitation variation using a continuous wavelet-based multiscale entropy approach.

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Roushangar, Kiyoumars; Alizadeh, Farhad; Adamowski, Jan

2018-08-01

Understanding precipitation on a regional basis is an important component of water resources planning and management. The present study outlines a methodology based on continuous wavelet transform (CWT) and multiscale entropy (CWME), combined with self-organizing map (SOM) and k-means clustering techniques, to measure and analyze the complexity of precipitation. Historical monthly precipitation data from 1960 to 2010 at 31 rain gauges across Iran were preprocessed by CWT. The multi-resolution CWT approach segregated the major features of the original precipitation series by unfolding the structure of the time series which was often ambiguous. The entropy concept was then applied to components obtained from CWT to measure dispersion, uncertainty, disorder, and diversification of subcomponents. Based on different validity indices, k-means clustering captured homogenous areas more accurately, and additional analysis was performed based on the outcome of this approach. The 31 rain gauges in this study were clustered into 6 groups, each one having a unique CWME pattern across different time scales. The results of clustering showed that hydrologic similarity (multiscale variation of precipitation) was not based on geographic contiguity. According to the pattern of entropy across the scales, each cluster was assigned an entropy signature that provided an estimation of the entropy pattern of precipitation data in each cluster. Based on the pattern of mean CWME for each cluster, a characteristic signature was assigned, which provided an estimation of the CWME of a cluster across scales of 1-2, 3-8, and 9-13 months relative to other stations. The validity of the homogeneous clusters demonstrated the usefulness of the proposed approach to regionalize precipitation. Further analysis based on wavelet coherence (WTC) was performed by selecting central rain gauges in each cluster and analyzing against temperature, wind, Multivariate ENSO index (MEI), and East Atlantic (EA) and

The concept of entropy. Relation between action and entropy

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J.-P.Badiali

2005-01-01

Full Text Available The Boltzmann expression for entropy represents the traditional link between thermodynamics and statistical mechanics. New theoretical developments like the Unruh effect or the black hole theory suggest a new definition of entropy. In this paper we consider the thermodynamics of black holes as seriously founded and we try to see what we can learn from it in the case of ordinary systems for which a pre-relativistic description is sufficient. We introduce a space-time model and a new definition of entropy considering the thermal equilibrium from a dynamic point of view. Then we show that for black hole and ordinary systems we have the same relation relating a change of entropy to a change of action.

Maximum-entropy clustering algorithm and its global convergence analysis

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

Constructing a batch of differentiable entropy functions touniformly approximate an objective function by means of the maximum-entropy principle, a new clustering algorithm, called maximum-entropy clustering algorithm, is proposed based on optimization theory. This algorithm is a soft generalization of the hard C-means algorithm and possesses global convergence. Its relations with other clustering algorithms are discussed.

Ergodicity, Maximum Entropy Production, and Steepest Entropy Ascent in the Proofs of Onsager's Reciprocal Relations

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Benfenati, Francesco; Beretta, Gian Paolo

2018-04-01

We show that to prove the Onsager relations using the microscopic time reversibility one necessarily has to make an ergodic hypothesis, or a hypothesis closely linked to that. This is true in all the proofs of the Onsager relations in the literature: from the original proof by Onsager, to more advanced proofs in the context of linear response theory and the theory of Markov processes, to the proof in the context of the kinetic theory of gases. The only three proofs that do not require any kind of ergodic hypothesis are based on additional hypotheses on the macroscopic evolution: Ziegler's maximum entropy production principle (MEPP), the principle of time reversal invariance of the entropy production, or the steepest entropy ascent principle (SEAP).

Self-Similar Solutions of Rényi’s Entropy and the Concavity of Its Entropy Power

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Agapitos N. Hatzinikitas

2015-08-01

Full Text Available We study the class of self-similar probability density functions with finite mean and variance, which maximize Rényi’s entropy. The investigation is restricted in the Schwartz space S(Rd and in the space of l-differentiable compactly supported functions Clc (Rd. Interestingly, the solutions of this optimization problem do not coincide with the solutions of the usual porous medium equation with a Dirac point source, as occurs in the optimization of Shannon’s entropy. We also study the concavity of the entropy power in Rd with respect to time using two different methods. The first one takes advantage of the solutions determined earlier, while the second one is based on a setting that could be used for Riemannian manifolds.

Nonequilibrium entropies

International Nuclear Information System (INIS)

Maes, Christian

2012-01-01

In contrast to the quite unique entropy concept useful for systems in (local) thermodynamic equilibrium, there is a variety of quite distinct nonequilibrium entropies, reflecting different physical points. We disentangle these entropies as they relate to heat, fluctuations, response, time asymmetry, variational principles, monotonicity, volume contraction or statistical forces. However, not all of those extensions yield state quantities as understood thermodynamically. At the end we sketch how aspects of dynamical activity can take over for obtaining an extended Clausius relation.

Carbon emission analysis and evaluation of industrial departments in China: An improved environmental DEA cross model based on information entropy.

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Han, Yongming; Long, Chang; Geng, Zhiqiang; Zhang, Keyu

2018-01-01

Environmental protection and carbon emission reduction play a crucial role in the sustainable development procedure. However, the environmental efficiency analysis and evaluation based on the traditional data envelopment analysis (DEA) cross model is subjective and inaccurate, because all elements in a column or a row of the cross evaluation matrix (CEM) in the traditional DEA cross model are given the same weight. Therefore, this paper proposes an improved environmental DEA cross model based on the information entropy to analyze and evaluate the carbon emission of industrial departments in China. The information entropy is applied to build the entropy distance based on the turbulence of the whole system, and calculate the weights in the CEM of the environmental DEA cross model in a dynamic way. The theoretical results show that the new weight constructed based on the information entropy is unique and optimal globally by using the Monte Carlo simulation. Finally, compared with the traditional environmental DEA and DEA cross model, the improved environmental DEA cross model has a better efficiency discrimination ability based on the data of industrial departments in China. Moreover, the proposed model can obtain the potential of carbon emission reduction of industrial departments to improve the energy efficiency. Copyright © 2017 Elsevier Ltd. All rights reserved.

Permutation Entropy for Random Binary Sequences

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Lingfeng Liu

2015-12-01

Full Text Available In this paper, we generalize the permutation entropy (PE measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other randomness measures, such as Shannon’s entropy and Lempel–Ziv complexity. The results show that PE is consistent with these two measures. Furthermore, we use PE as one of the randomness measures to evaluate the randomness of chaotic binary sequences.

Scale-invariant entropy-based theory for dynamic ordering

International Nuclear Information System (INIS)

Mahulikar, Shripad P.; Kumari, Priti

2014-01-01

Dynamically Ordered self-organized dissipative structure exists in various forms and at different scales. This investigation first introduces the concept of an isolated embedding system, which embeds an open system, e.g., dissipative structure and its mass and/or energy exchange with its surroundings. Thereafter, scale-invariant theoretical analysis is presented using thermodynamic principles for Order creation, existence, and destruction. The sustainability criterion for Order existence based on its structured mass and/or energy interactions with the surroundings is mathematically defined. This criterion forms the basis for the interrelationship of physical parameters during sustained existence of dynamic Order. It is shown that the sufficient condition for dynamic Order existence is approached if its sustainability criterion is met, i.e., its destruction path is blocked. This scale-invariant approach has the potential to unify the physical understanding of universal dynamic ordering based on entropy considerations

Structure of a Global Network of Financial Companies Based on Transfer Entropy

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Leonidas Sandoval

2014-08-01

Full Text Available This work uses the stocks of the 197 largest companies in the world, in terms of market capitalization, in the financial area, from 2003 to 2012. We study the causal relationships between them using Transfer Entropy, which is calculated using the stocks of those companies and their counterparts lagged by one day. With this, we can assess which companies influence others according to sub-areas of the financial sector, which are banks, diversified financial services, savings and loans, insurance, private equity funds, real estate investment companies, and real estate trust funds. We also analyze the exchange of information between those stocks as seen by Transfer Entropy and the network formed by them based on this measure, verifying that they cluster mainly according to countries of origin, and then by industry and sub-industry. Then we use data on the stocks of companies in the financial sector of some countries that are suffering the most with the current credit crisis, namely Greece, Cyprus, Ireland, Spain, Portugal, and Italy, and assess, also using Transfer Entropy, which companies from the largest 197 are most affected by the stocks of these countries in crisis. The aim is to map a network of influences that may be used in the study of possible contagions originating in those countries in financial crisis.

Differential effects of gender on entropy perception

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Satcharoen, Kleddao

2017-12-01

The purpose of this research is to examine differences in perception of entropy (color intensity) between male and female computer users. The objectives include identifying gender-based differences in entropy intention and exploring the potential effects of these differences (if any) on user interface design. The research is an effort to contribute to an emerging field of interest in gender as it relates to science, engineering and technology (SET), particularly user interface design. Currently, there is limited evidence on the role of gender in user interface design and in use of technology generally, with most efforts at gender-differentiated or customized design based on stereotypes and assumptions about female use of technology or the assumption of a default position based on male preferences. Image entropy was selected as a potential characteristic where gender could be a factor in perception because of known differences in color perception acuity between male and female individuals, even where there is no known color perception abnormality (which is more common with males). Although the literature review suggested that training could offset differences in color perception and identification, tests in untrained subject groups routinely show that females are more able to identify, match, and differentiate colors, and that there is a stronger emotional and psychosocial association of color for females. Since image entropy is associated with information content and image salience, the ability to identify areas of high entropy could make a difference in user perception and technological capabilities.

Empirical study on entropy models of cellular manufacturing systems

Institute of Scientific and Technical Information of China (English)

Zhifeng Zhang; Renbin Xiao

2009-01-01

From the theoretical point of view,the states of manufacturing resources can be monitored and assessed through the amount of information needed to describe their technological structure and operational state.The amount of information needed to describe cellular manufacturing systems is investigated by two measures:the structural entropy and the operational entropy.Based on the Shannon entropy,the models of the structural entropy and the operational entropy of cellular manufacturing systems are developed,and the cognizance of the states of manufacturing resources is also illustrated.Scheduling is introduced to measure the entropy models of cellular manufacturing systems,and the feasible concepts of maximum schedule horizon and schedule adherence are advanced to quantitatively evaluate the effectiveness of schedules.Finally,an example is used to demonstrate the validity of the proposed methodology.

Entropy of black holes with multiple horizons

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Yun He

2018-05-01

Full Text Available We examine the entropy of black holes in de Sitter space and black holes surrounded by quintessence. These black holes have multiple horizons, including at least the black hole event horizon and a horizon outside it (cosmological horizon for de Sitter black holes and “quintessence horizon” for the black holes surrounded by quintessence. Based on the consideration that the two horizons are not independent each other, we conjecture that the total entropy of these black holes should not be simply the sum of entropies of the two horizons, but should have an extra term coming from the correlations between the two horizons. Different from our previous works, in this paper we consider the cosmological constant as the variable and employ an effective method to derive the explicit form of the entropy. We also try to discuss the thermodynamic stabilities of these black holes according to the entropy and the effective temperature.

An Entropy-Based Adaptive Hybrid Particle Swarm Optimization for Disassembly Line Balancing Problems

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Shanli Xiao

2017-11-01

Full Text Available In order to improve the product disassembly efficiency, the disassembly line balancing problem (DLBP is transformed into a problem of searching for the optimum path in the directed and weighted graph by constructing the disassembly hierarchy information graph (DHIG. Then, combining the characteristic of the disassembly sequence, an entropy-based adaptive hybrid particle swarm optimization algorithm (AHPSO is presented. In this algorithm, entropy is introduced to measure the changing tendency of population diversity, and the dimension learning, crossover and mutation operator are used to increase the probability of producing feasible disassembly solutions (FDS. Performance of the proposed methodology is tested on the primary problem instances available in the literature, and the results are compared with other evolutionary algorithms. The results show that the proposed algorithm is efficient to solve the complex DLBP.

Application of entropy measurement technique in grey based ...

African Journals Online (AJOL)

For this study, four control variables are selected current, voltage, gas flow rate and ... Keywords: Metal Inert Gas (MIG) Welding, Grey-Taguchi Method, Entropy ...... of metal inert gas welding on the corrosion and mechanical behaviour of.

The Conditional Entropy Power Inequality for Bosonic Quantum Systems

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De Palma, Giacomo; Trevisan, Dario

2018-06-01

We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally independent given the memory and have given quantum conditional entropies. We also prove that, for any couple of values of the quantum conditional entropies of the two inputs, the minimum of the quantum conditional entropy of the output given by the conditional Entropy Power Inequality is asymptotically achieved by a suitable sequence of quantum Gaussian input states. Our proof of the conditional Entropy Power Inequality is based on a new Stam inequality for the quantum conditional Fisher information and on the determination of the universal asymptotic behaviour of the quantum conditional entropy under the heat semigroup evolution. The beam-splitter and the squeezing are the central elements of quantum optics, and can model the attenuation, the amplification and the noise of electromagnetic signals. This conditional Entropy Power Inequality will have a strong impact in quantum information and quantum cryptography. Among its many possible applications there is the proof of a new uncertainty relation for the conditional Wehrl entropy.

Theoretical Bound of CRLB for Energy Efficient Technique of RSS-Based Factor Graph Geolocation

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Kahar Aziz, Muhammad Reza; Heriansyah; Saputra, EfaMaydhona; Musa, Ardiansyah

2018-03-01

To support the increase of wireless geolocation development as the key of the technology in the future, this paper proposes theoretical bound derivation, i.e., Cramer Rao lower bound (CRLB) for energy efficient of received signal strength (RSS)-based factor graph wireless geolocation technique. The theoretical bound derivation is crucially important to evaluate whether the energy efficient technique of RSS-based factor graph wireless geolocation is effective as well as to open the opportunity to further innovation of the technique. The CRLB is derived in this paper by using the Fisher information matrix (FIM) of the main formula of the RSS-based factor graph geolocation technique, which is lied on the Jacobian matrix. The simulation result shows that the derived CRLB has the highest accuracy as a bound shown by its lowest root mean squared error (RMSE) curve compared to the RMSE curve of the RSS-based factor graph geolocation technique. Hence, the derived CRLB becomes the lower bound for the efficient technique of RSS-based factor graph wireless geolocation.

High-order computer-assisted estimates of topological entropy

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Grote, Johannes

The concept of Taylor Models is introduced, which offers highly accurate C0-estimates for the enclosures of functional dependencies, combining high-order Taylor polynomial approximation of functions and rigorous estimates of the truncation error, performed using verified interval arithmetic. The focus of this work is on the application of Taylor Models in algorithms for strongly nonlinear dynamical systems. A method to obtain sharp rigorous enclosures of Poincare maps for certain types of flows and surfaces is developed and numerical examples are presented. Differential algebraic techniques allow the efficient and accurate computation of polynomial approximations for invariant curves of certain planar maps around hyperbolic fixed points. Subsequently we introduce a procedure to extend these polynomial curves to verified Taylor Model enclosures of local invariant manifolds with C0-errors of size 10-10--10 -14, and proceed to generate the global invariant manifold tangle up to comparable accuracy through iteration in Taylor Model arithmetic. Knowledge of the global manifold structure up to finite iterations of the local manifold pieces enables us to find all homoclinic and heteroclinic intersections in the generated manifold tangle. Combined with the mapping properties of the homoclinic points and their ordering we are able to construct a subshift of finite type as a topological factor of the original planar system to obtain rigorous lower bounds for its topological entropy. This construction is fully automatic and yields homoclinic tangles with several hundred homoclinic points. As an example rigorous lower bounds for the topological entropy of the Henon map are computed, which to the best knowledge of the authors yield the largest such estimates published so far.

Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme

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Burton, D. E.; Morgan, N. R.; Charest, M. R. J.; Kenamond, M. A.; Fung, J.

2018-02-01

From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian-Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. In particular, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. The paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.

Application of SNODAS and hydrologic models to enhance entropy-based snow monitoring network design

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Keum, Jongho; Coulibaly, Paulin; Razavi, Tara; Tapsoba, Dominique; Gobena, Adam; Weber, Frank; Pietroniro, Alain

2018-06-01

Snow has a unique characteristic in the water cycle, that is, snow falls during the entire winter season, but the discharge from snowmelt is typically delayed until the melting period and occurs in a relatively short period. Therefore, reliable observations from an optimal snow monitoring network are necessary for an efficient management of snowmelt water for flood prevention and hydropower generation. The Dual Entropy and Multiobjective Optimization is applied to design snow monitoring networks in La Grande River Basin in Québec and Columbia River Basin in British Columbia. While the networks are optimized to have the maximum amount of information with minimum redundancy based on entropy concepts, this study extends the traditional entropy applications to the hydrometric network design by introducing several improvements. First, several data quantization cases and their effects on the snow network design problems were explored. Second, the applicability the Snow Data Assimilation System (SNODAS) products as synthetic datasets of potential stations was demonstrated in the design of the snow monitoring network of the Columbia River Basin. Third, beyond finding the Pareto-optimal networks from the entropy with multi-objective optimization, the networks obtained for La Grande River Basin were further evaluated by applying three hydrologic models. The calibrated hydrologic models simulated discharges using the updated snow water equivalent data from the Pareto-optimal networks. Then, the model performances for high flows were compared to determine the best optimal network for enhanced spring runoff forecasting.

Efficiency bounds for nonequilibrium heat engines

International Nuclear Information System (INIS)

Mehta, Pankaj; Polkovnikov, Anatoli

2013-01-01

We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodic engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples. -- Highlights: ► Derived efficiency bounds for heat engines working with a single reservoir. ► Analyzed both ergodic and non-ergodic engines. ► Showed that non-ergodic engines can be more efficient. ► Extended fundamental thermodynamic relation to arbitrary nonequilibrium processes

On the dimension of subspaces with bounded Schmidt rank

International Nuclear Information System (INIS)

Cubitt, Toby; Montanaro, Ashley; Winter, Andreas

2008-01-01

We consider the question of how large a subspace of a given bipartite quantum system can be when the subspace contains only highly entangled states. This is motivated in part by results of Hayden et al. [e-print arXiv:quant-ph/0407049; Commun. Math. Phys., 265, 95 (2006)], which show that in large dxd-dimensional systems there exist random subspaces of dimension almost d 2 , all of whose states have entropy of entanglement at least log d-O(1). It is also a generalization of results on the dimension of completely entangled subspaces, which have connections with the construction of unextendible product bases. Here we take as entanglement measure the Schmidt rank, and determine, for every pair of local dimensions d A and d B , and every r, the largest dimension of a subspace consisting only of entangled states of Schmidt rank r or larger. This exact answer is a significant improvement on the best bounds that can be obtained using the random subspace techniques in Hayden et al. We also determine the converse: the largest dimension of a subspace with an upper bound on the Schmidt rank. Finally, we discuss the question of subspaces containing only states with Schmidt equal to r

Entropy-Based Voltage Fault Diagnosis of Battery Systems for Electric Vehicles

Directory of Open Access Journals (Sweden)

Peng Liu

2018-01-01

Full Text Available The battery is a key component and the major fault source in electric vehicles (EVs. Ensuring power battery safety is of great significance to make the diagnosis more effective and predict the occurrence of faults, for the power battery is one of the core technologies of EVs. This paper proposes a voltage fault diagnosis detection mechanism using entropy theory which is demonstrated in an EV with a multiple-cell battery system during an actual operation situation. The preliminary analysis, after collecting and preprocessing the typical data periods from Operation Service and Management Center for Electric Vehicle (OSMC-EV in Beijing, shows that overvoltage fault for Li-ion batteries cell can be observed from the voltage curves. To further locate abnormal cells and predict faults, an entropy weight method is established to calculate the objective weight, which reduces the subjectivity and improves the reliability. The result clearly identifies the abnormity of cell voltage. The proposed diagnostic model can be used for EV real-time diagnosis without laboratory testing methods. It is more effective than traditional methods based on contrastive analysis.

On the Conditional Rényi Entropy

NARCIS (Netherlands)

S. Fehr (Serge); S. Berens (Stefan)

2014-01-01

htmlabstractThe Rényi entropy of general order unifies the well-known Shannon entropy with several other entropy notions, like the min-entropy or the collision entropy. In contrast to the Shannon entropy, there seems to be no commonly accepted definition for the conditional Rényi entropy: several

An Alternative to Chaid Segmentation Algorithm Based on Entropy.

Directory of Open Access Journals (Sweden)

María Purificación Galindo Villardón

2010-07-01

Full Text Available The CHAID (Chi-Squared Automatic Interaction Detection treebased segmentation technique has been found to be an effective approach for obtaining meaningful segments that are predictive of a K-category (nominal or ordinal criterion variable. CHAID was designed to detect, in an automatic way, the  nteraction between several categorical or ordinal predictors in explaining a categorical response, but, this may not be true when Simpson’s paradox is present. This is due to the fact that CHAID is a forward selection algorithm based on the marginal counts. In this paper we propose a backwards elimination algorithm that starts with the full set of predictors (or full tree and eliminates predictors progressively. The elimination procedure is based on Conditional Independence contrasts using the concept of entropy. The proposed procedure is compared to CHAID.

Tsallis-like entropies in quantum scattering

International Nuclear Information System (INIS)

Ion, D.B.; Ion, M.L.

1998-01-01

In this work, the following entropies in quantum scattering are defined: the informational angular entropy, S θ ; Tsallis-like angular entropies, S q (θ); the angular momentum entropy, S L ; the Tsallis-like angular momentum entropies, S q (L); the angle-angular momentum entropy, S θL . These entropies are defined as natural measures of the uncertainties corresponding to the distribution probabilities. If we are interested in obtaining a measure of uncertainty of the simultaneous realization of the probability distributions, than, we have to calculate the entropy corresponding to these distributions. The expression of angle-angular momentum entropy is given. The relation between the Tsallis entropies and the angle-angular momentum entropy is derived

Thermodynamics based on the principle of least abbreviated action: Entropy production in a network of coupled oscillators

International Nuclear Information System (INIS)

Garcia-Morales, Vladimir; Pellicer, Julio; Manzanares, Jose A.

2008-01-01

We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several examples are worked out to show that this formalism yields the right microcanonical (equilibrium) quantities. The relevance of this approach to nonequilibrium situations is illustrated with an application to a network of coupled oscillators (Kuramoto model). We provide an expression for the entropy production in this system finding that its positive value is directly related to dissipation at the steady state in attaining order through synchronization

Entropy generation method to quantify thermal comfort

Science.gov (United States)

Boregowda, S. C.; Tiwari, S. N.; Chaturvedi, S. K.

2001-01-01

The present paper presents a thermodynamic approach to assess the quality of human-thermal environment interaction and quantify thermal comfort. The approach involves development of entropy generation term by applying second law of thermodynamics to the combined human-environment system. The entropy generation term combines both human thermal physiological responses and thermal environmental variables to provide an objective measure of thermal comfort. The original concepts and definitions form the basis for establishing the mathematical relationship between thermal comfort and entropy generation term. As a result of logic and deterministic approach, an Objective Thermal Comfort Index (OTCI) is defined and established as a function of entropy generation. In order to verify the entropy-based thermal comfort model, human thermal physiological responses due to changes in ambient conditions are simulated using a well established and validated human thermal model developed at the Institute of Environmental Research of Kansas State University (KSU). The finite element based KSU human thermal computer model is being utilized as a "Computational Environmental Chamber" to conduct series of simulations to examine the human thermal responses to different environmental conditions. The output from the simulation, which include human thermal responses and input data consisting of environmental conditions are fed into the thermal comfort model. Continuous monitoring of thermal comfort in comfortable and extreme environmental conditions is demonstrated. The Objective Thermal Comfort values obtained from the entropy-based model are validated against regression based Predicted Mean Vote (PMV) values. Using the corresponding air temperatures and vapor pressures that were used in the computer simulation in the regression equation generates the PMV values. The preliminary results indicate that the OTCI and PMV values correlate well under ideal conditions. However, an experimental study

The determination of nuclear charge distributions using a Bayesian maximum entropy method

International Nuclear Information System (INIS)

Macaulay, V.A.; Buck, B.

1995-01-01

We treat the inference of nuclear charge densities from measurements of elastic electron scattering cross sections. In order to get the most reliable information from expensively acquired, incomplete and noisy measurements, we use Bayesian probability theory. Very little prior information about the charge densities is assumed. We derive a prior probability distribution which is a generalization of a form used widely in image restoration based on the entropy of a physical density. From the posterior distribution of possible densities, we select the most probable one, and show how error bars can be evaluated. These have very reasonable properties, such as increasing without bound as hypotheses about finer scale structures are included in the hypothesis space. The methods are demonstrated by using data on the nuclei 4 He and 12 C. (orig.)

Inhomogeneity of epidemic spreading with entropy-based infected clusters.

Science.gov (United States)

Wen-Jie, Zhou; Xing-Yuan, Wang

2013-12-01

Considering the difference in the sizes of the infected clusters in the dynamic complex networks, the normalized entropy based on infected clusters (δ*) is proposed to characterize the inhomogeneity of epidemic spreading. δ* gives information on the variability of the infected clusters in the system. We investigate the variation in the inhomogeneity of the distribution of the epidemic with the absolute velocity v of moving agent, the infection density ρ, and the interaction radius r. By comparing δ* in the dynamic networks with δH* in homogeneous mode, the simulation experiments show that the inhomogeneity of epidemic spreading becomes smaller with the increase of v, ρ, r.

Statistical-mechanical entropy by the thin-layer method

International Nuclear Information System (INIS)

Feng, He; Kim, Sung Won

2003-01-01

G. Hooft first studied the statistical-mechanical entropy of a scalar field in a Schwarzschild black hole background by the brick-wall method and hinted that the statistical-mechanical entropy is the statistical origin of the Bekenstein-Hawking entropy of the black hole. However, according to our viewpoint, the statistical-mechanical entropy is only a quantum correction to the Bekenstein-Hawking entropy of the black-hole. The brick-wall method based on thermal equilibrium at a large scale cannot be applied to the cases out of equilibrium such as a nonstationary black hole. The statistical-mechanical entropy of a scalar field in a nonstationary black hole background is calculated by the thin-layer method. The condition of local equilibrium near the horizon of the black hole is used as a working postulate and is maintained for a black hole which evaporates slowly enough and whose mass is far greater than the Planck mass. The statistical-mechanical entropy is also proportional to the area of the black hole horizon. The difference from the stationary black hole is that the result relies on a time-dependent cutoff

Entropy viscosity method for nonlinear conservation laws

KAUST Repository

Guermond, Jean-Luc

2011-05-01

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

Entropy viscosity method for nonlinear conservation laws

KAUST Repository

Guermond, Jean-Luc; Pasquetti, Richard; Popov, Bojan

2011-01-01

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.

A Review of Solid-Solution Models of High-Entropy Alloys Based on Ab Initio Calculations

Directory of Open Access Journals (Sweden)

Fuyang Tian

2017-11-01

Full Text Available Similar to the importance of XRD in experiments, ab initio calculations, as a powerful tool, have been applied to predict the new potential materials and investigate the intrinsic properties of materials in theory. As a typical solid-solution material, the large degree of uncertainty of high-entropy alloys (HEAs results in the difficulty of ab initio calculations application to HEAs. The present review focuses on the available ab initio based solid-solution models (virtual lattice approximation, coherent potential approximation, special quasirandom structure, similar local atomic environment, maximum-entropy method, and hybrid Monte Carlo/molecular dynamics and their applications and limits in single phase HEAs.

A Roller Bearing Fault Diagnosis Method Based on LCD Energy Entropy and ACROA-SVM

Directory of Open Access Journals (Sweden)

HungLinh Ao

2014-01-01

Full Text Available This study investigates a novel method for roller bearing fault diagnosis based on local characteristic-scale decomposition (LCD energy entropy, together with a support vector machine designed using an Artificial Chemical Reaction Optimisation Algorithm, referred to as an ACROA-SVM. First, the original acceleration vibration signals are decomposed into intrinsic scale components (ISCs. Second, the concept of LCD energy entropy is introduced. Third, the energy features extracted from a number of ISCs that contain the most dominant fault information serve as input vectors for the support vector machine classifier. Finally, the ACROA-SVM classifier is proposed to recognize the faulty roller bearing pattern. The analysis of roller bearing signals with inner-race and outer-race faults shows that the diagnostic approach based on the ACROA-SVM and using LCD to extract the energy levels of the various frequency bands as features can identify roller bearing fault patterns accurately and effectively. The proposed method is superior to approaches based on Empirical Mode Decomposition method and requires less time.

Generalized composite multiscale permutation entropy and Laplacian score based rolling bearing fault diagnosis

Science.gov (United States)

Zheng, Jinde; Pan, Haiyang; Yang, Shubao; Cheng, Junsheng

2018-01-01

Multiscale permutation entropy (MPE) is a recently proposed nonlinear dynamic method for measuring the randomness and detecting the nonlinear dynamic change of time series and can be used effectively to extract the nonlinear dynamic fault feature from vibration signals of rolling bearing. To solve the drawback of coarse graining process in MPE, an improved MPE method called generalized composite multiscale permutation entropy (GCMPE) was proposed in this paper. Also the influence of parameters on GCMPE and its comparison with the MPE are studied by analyzing simulation data. GCMPE was applied to the fault feature extraction from vibration signal of rolling bearing and then based on the GCMPE, Laplacian score for feature selection and the Particle swarm optimization based support vector machine, a new fault diagnosis method for rolling bearing was put forward in this paper. Finally, the proposed method was applied to analyze the experimental data of rolling bearing. The analysis results show that the proposed method can effectively realize the fault diagnosis of rolling bearing and has a higher fault recognition rate than the existing methods.

The prediction of engineering cost for green buildings based on information entropy

Science.gov (United States)

Liang, Guoqiang; Huang, Jinglian

2018-03-01

Green building is the developing trend in the world building industry. Additionally, construction costs are an essential consideration in building constructions. Therefore, it is necessary to investigate the problems of cost prediction in green building. On the basis of analyzing the cost of green building, this paper proposes the forecasting method of actual cost in green building based on information entropy and provides the forecasting working procedure. Using the probability density obtained from statistical data, such as labor costs, material costs, machinery costs, administration costs, profits, risk costs a unit project quotation and etc., situations can be predicted which lead to cost variations between budgeted cost and actual cost in constructions, through estimating the information entropy of budgeted cost and actual cost. The research results of this article have a practical significance in cost control of green building. Additionally, the method proposed in this article can be generalized and applied to a variety of other aspects in building management.

Out-of-Bounds Hydrodynamics in Anisotropic Dirac Fluids

Science.gov (United States)

Link, Julia M.; Narozhny, Boris N.; Kiselev, Egor I.; Schmalian, Jörg

2018-05-01

We study hydrodynamic transport in two-dimensional, interacting electronic systems with merging Dirac points at charge neutrality. The dispersion along one crystallographic direction is Dirac-like, while it is Newtonian-like in the orthogonal direction. As a result, the electrical conductivity is metallic in one and insulating in the other direction. The shear viscosity tensor contains six independent components, which can be probed by measuring an anisotropic thermal flow. One of the viscosity components vanishes at zero temperature leading to a generalization of the previously conjectured lower bound for the shear viscosity to entropy density ratio.

Distinguishing Stationary/Nonstationary Scaling Processes Using Wavelet Tsallis q-Entropies

Directory of Open Access Journals (Sweden)

Julio Ramirez Pacheco

2012-01-01

Full Text Available Classification of processes as stationary or nonstationary has been recognized as an important and unresolved problem in the analysis of scaling signals. Stationarity or nonstationarity determines not only the form of autocorrelations and moments but also the selection of estimators. In this paper, a methodology for classifying scaling processes as stationary or nonstationary is proposed. The method is based on wavelet Tsallis q-entropies and particularly on the behaviour of these entropies for scaling signals. It is demonstrated that the observed wavelet Tsallis q-entropies of 1/f signals can be modeled by sum-cosh apodizing functions which allocates constant entropies to a set of scaling signals and varying entropies to the rest and that this allocation is controlled by q. The proposed methodology, therefore, differentiates stationary signals from non-stationary ones based on the observed wavelet Tsallis entropies for 1/f signals. Experimental studies using synthesized signals confirm that the proposed method not only achieves satisfactorily classifications but also outperforms current methods proposed in the literature.

Entropy of the electroencephalogram as applied in the M-Entropy S ...

African Journals Online (AJOL)

Background: It has been suggested that spectral entropy of the electroencephalogram as applied in the M-Entropy S/5TM Module (GE Healthcare) does not detect the effects of nitrous oxide (N2O). The aim of this study was to investigate the effect on entropy by graded increases in N2O concentrations in the presence of a ...

Entropy of Baker's Transformation

Institute of Scientific and Technical Information of China (English)

栾长福

2003-01-01

Four theorems about four different kinds of entropies for Baker's transformation are presented. The Kolmogorov entropy of Baker's transformation is sensitive to the initial flips by the time. The topological entropy of Baker's transformation is found to be log k. The conditions for the state of Baker's transformation to be forbidden are also derived. The relations among the Shanonn, Kolmogorov, topological and Boltzmann entropies are discussed in details.

Modeling Electric Discharges with Entropy Production Rate Principles

Directory of Open Access Journals (Sweden)

Thomas Christen

2009-12-01

Full Text Available Under which circumstances are variational principles based on entropy production rate useful tools for modeling steady states of electric (gas discharge systems far from equilibrium? It is first shown how various different approaches, as Steenbeck’s minimum voltage and Prigogine’s minimum entropy production rate principles are related to the maximum entropy production rate principle (MEPP. Secondly, three typical examples are discussed, which provide a certain insight in the structure of the models that are candidates for MEPP application. It is then thirdly argued that MEPP, although not being an exact physical law, may provide reasonable model parameter estimates, provided the constraints contain the relevant (nonlinear physical effects and the parameters to be determined are related to disregarded weak constraints that affect mainly global entropy production. Finally, it is additionally conjectured that a further reason for the success of MEPP in certain far from equilibrium systems might be based on a hidden linearity of the underlying kinetic equation(s.

The Dynameomics Entropy Dictionary: A Large-Scale Assessment of Conformational Entropy across Protein Fold Space.

Science.gov (United States)

Towse, Clare-Louise; Akke, Mikael; Daggett, Valerie

2017-04-27

Molecular dynamics (MD) simulations contain considerable information with regard to the motions and fluctuations of a protein, the magnitude of which can be used to estimate conformational entropy. Here we survey conformational entropy across protein fold space using the Dynameomics database, which represents the largest existing data set of protein MD simulations for representatives of essentially all known protein folds. We provide an overview of MD-derived entropies accounting for all possible degrees of dihedral freedom on an unprecedented scale. Although different side chains might be expected to impose varying restrictions on the conformational space that the backbone can sample, we found that the backbone entropy and side chain size are not strictly coupled. An outcome of these analyses is the Dynameomics Entropy Dictionary, the contents of which have been compared with entropies derived by other theoretical approaches and experiment. As might be expected, the conformational entropies scale linearly with the number of residues, demonstrating that conformational entropy is an extensive property of proteins. The calculated conformational entropies of folding agree well with previous estimates. Detailed analysis of specific cases identifies deviations in conformational entropy from the average values that highlight how conformational entropy varies with sequence, secondary structure, and tertiary fold. Notably, α-helices have lower entropy on average than do β-sheets, and both are lower than coil regions.

The maximum entropy production and maximum Shannon information entropy in enzyme kinetics

Science.gov (United States)

Dobovišek, Andrej; Markovič, Rene; Brumen, Milan; Fajmut, Aleš

2018-04-01

We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.

Entropy feature extraction on flow pattern of gas/liquid two-phase flow based on cross-section measurement

International Nuclear Information System (INIS)

Han, J; Dong, F; Xu, Y Y

2009-01-01

This paper introduces the fundamental of cross-section measurement system based on Electrical Resistance Tomography (ERT). The measured data of four flow regimes of the gas/liquid two-phase flow in horizontal pipe flow are obtained by an ERT system. For the measured data, five entropies are extracted to analyze the experimental data according to the different flow regimes, and the analysis method is examined and compared in three different perspectives. The results indicate that three different perspectives of entropy-based feature extraction are sensitive to the flow pattern transition in gas/liquid two-phase flow. By analyzing the results of three different perspectives with the changes of gas/liquid two-phase flow parameters, the dynamic structures of gas/liquid two-phase flow is obtained, and they also provide an efficient supplementary to reveal the flow pattern transition mechanism of gas/liquid two-phase flow. Comparison of the three different methods of feature extraction shows that the appropriate entropy should be used for the identification and prediction of flow regimes.

Tight Bounds for Beacon-Based Coverage in Simple Rectilinear Polygons

KAUST Repository

Bae, Sang Won

2016-03-21

We establish tight bounds for beacon-based coverage problems. In particular, we show that $$\\\\lfloor \\\\frac{n}{6} \\ floor $$⌊n6⌋ beacons are always sufficient and sometimes necessary to cover a simple rectilinear polygon P with n vertices. When P is monotone and rectilinear, we prove that this bound becomes $$\\\\lfloor \\\\frac{n+4}{8} \\ floor $$⌊n+48⌋. We also present an optimal linear-time algorithm for computing the beacon kernel of P.

Tight Bounds for Beacon-Based Coverage in Simple Rectilinear Polygons

KAUST Repository

Bae, Sang Won; Shin, Chan-Su; Vigneron, Antoine E.

2016-01-01

We establish tight bounds for beacon-based coverage problems. In particular, we show that $$\\lfloor \\frac{n}{6} \\rfloor $$⌊n6⌋ beacons are always sufficient and sometimes necessary to cover a simple rectilinear polygon P with n vertices. When P is monotone and rectilinear, we prove that this bound becomes $$\\lfloor \\frac{n+4}{8} \\rfloor $$⌊n+48⌋. We also present an optimal linear-time algorithm for computing the beacon kernel of P.

Entropy production in a cell and reversal of entropy flow as an anticancer therapy

Institute of Scientific and Technical Information of China (English)

Liao-fu LUO

2009-01-01

The entropy production rate of cancer cells is always higher than healthy cells in the case where no external field is applied. Different entropy production between two kinds of cells determines the direction of entropy flow among cells. The entropy flow is the carrier of information flow. The entropy flow from cancerous cells to healthy cells takes along the harmful information of cancerous cells, propagating its toxic action to healthy tissues. We demonstrate that a low-frequency and low- intensity electromagnetic field or ultrasound irradiation may increase the entropy production rate of a cell in normal tissue than that in cancer and consequently re- verse the direction of entropy current between two kinds of cells. The modification of the PH value of cells may also cause the reversal of the direction of entropy flow between healthy and cancerous cells. Therefore, the bio- logical tissue under the irradiation of an electromagnetic field or ultrasound or under the appropriate change of cell acidity can avoid the propagation of harmful infor- marion from cancer cells. We suggest that this entropy mechanism possibly provides a basis for a novel approach to anticancer therapy.

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

International Nuclear Information System (INIS)

Schaerer, Roman Pascal; Bansal, Pratyuksh; Torrilhon, Manuel

2017-01-01

We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) , we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

Science.gov (United States)

Schaerer, Roman Pascal; Bansal, Pratyuksh; Torrilhon, Manuel

2017-07-01

We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) [13], we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

Energy Technology Data Exchange (ETDEWEB)

Schaerer, Roman Pascal, E-mail: schaerer@mathcces.rwth-aachen.de; Bansal, Pratyuksh; Torrilhon, Manuel

2017-07-01

We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) , we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

Methods for calculating nonconcave entropies

International Nuclear Information System (INIS)

Touchette, Hugo

2010-01-01

Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and techniques: (i) microcanonical contraction, (ii) metastable branches of the free energy, (iii) generalized canonical ensembles with specific illustrations involving the so-called Gaussian and Betrag ensembles, (iv) the restricted canonical ensemble, and (v) the inverse Laplace transform. A simple long-range spin model having a nonconcave entropy is used to illustrate each method

The different paths to entropy

International Nuclear Information System (INIS)

Benguigui, L

2013-01-01

In order to understand how the complex concept of entropy emerged, we propose a trip into the past, reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since Gibbs's work is not very well known we present a detailed analysis, recalling the three definitions of entropy that Gibbs gives. The introduction of entropy in quantum mechanics gives in a compact form all the classical definitions of entropy. Perhaps one of the most important aspects of entropy is to see it as a thermodynamic potential like the others proposed by Callen. The calculation of fluctuations in thermodynamic quantities is thus naturally related to entropy. We close with some remarks on entropy and irreversibility. (paper)

Linking entropy flow with typhoon evolution: a case-study

International Nuclear Information System (INIS)

Liu, C; Xu, H; Liu, Y

2007-01-01

This paper is mainly aimed at investigating the relationship of entropy flow with an atmospheric system (typhoon), based on the observational analyses covering its whole life-cycle. The formula for calculating entropy flow is derived starting with the Gibbs relation with data from the NCEP/NCAR reanalysis. The results show that: (i) entropy flow characteristics at different vertical layers of the system are heterogeneous with predominant negative entropy flow in the large portion of the troposphere and positive ones at upper levels during its development; (ii) changes in the maximum surface wind velocity or the intensity of a typhoon are synchronous with the total entropy flow around the typhoon centre and its neighbourhood, suggesting that the growth of a severe atmospheric system relies greatly upon the negative entropy flow being strong enough, and that entropy flow analysis might provide a particular point of view and a powerful tool to understand the mechanism responsible for the life-cycle of an atmospheric system and associated weather events; and (iii) the horizontal pattern of negative entropy flow near the surface might contain some significant information conducive to the track forecast of typhoons

ENTROPY - OUR BEST FRIEND

Directory of Open Access Journals (Sweden)

Urban Kordes

2005-10-01

Full Text Available The paper tries to tackle the question of connection between entropy and the living. Definitions of life as the phenomenon that defies entropy are overviewed and the conclusion is reached that life is in a way dependant on entropy - it couldn't exist without it. Entropy is a sort of medium, a fertile soil, that gives life possibility to blossom. Paper ends with presenting some consequences for the field of artificial intelligence.

Entropy factor for randomness quantification in neuronal data.

Science.gov (United States)

Rajdl, K; Lansky, P; Kostal, L

2017-11-01

A novel measure of neural spike train randomness, an entropy factor, is proposed. It is based on the Shannon entropy of the number of spikes in a time window and can be seen as an analogy to the Fano factor. Theoretical properties of the new measure are studied for equilibrium renewal processes and further illustrated on gamma and inverse Gaussian probability distributions of interspike intervals. Finally, the entropy factor is evaluated from the experimental records of spontaneous activity in macaque primary visual cortex and compared to its theoretical behavior deduced for the renewal process models. Both theoretical and experimental results show substantial differences between the Fano and entropy factors. Rather paradoxically, an increase in the variability of spike count is often accompanied by an increase of its predictability, as evidenced by the entropy factor. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Physicochemical attack against solid tumors based on the reversal of direction of entropy flow: an attempt to introduce thermodynamics in anticancer therapy

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Lv Xiaogui

2006-11-01

Full Text Available Abstract Background There are many differences between healthy tissue and growing tumor tissue, including metabolic, structural and thermodynamic differences. Both structural and thermodynamic differences can be used to follow the entropy differences in cancerous and normal tissue. Entropy production is a bilinear form of the rates of irreversible processes and the corresponding "generalized forces". Entropy production due to various dissipation mechanisms based on temperature differences, chemical potential gradient, chemical affinity, viscous stress and exerted force is a promising tool for calculations relating to potential targets for tumor isolation and demarcation. Methods The relative importance of five forms of entropy production was assessed through mathematical estimation. Using our mathematical model we demonstrated that the rate of entropy production by a cancerous cell is always higher than that of a healthy cell apart from the case of the application of external energy. Different rates of entropy production by two kinds of cells influence the direction of entropy flow between the cells. Entropy flow from a cancerous cell to a healthy cell transfers information regarding the cancerous cell and propagates its invasive action to the healthy tissues. To change the direction of entropy flow, in addition to designing certain biochemical pathways to reduce the rate of entropy production by cancerous cells, we suggest supplying external energy to the tumor area, changing the relative rate of entropy production by the two kinds of cells and leading to a higher entropy accumulation in the surrounding normal cells than in the tumorous cells. Conclusion Through the use of mathematical models it was quantitatively demonstrated that when no external force field is applied, the rate of entropy production of cancerous cells is always higher than that of healthy cells. However, when the external energy of square wave electric pulses is applied to

Temporal Entropy Generation in the Viscous Layers of Laterally-converging Duct Flows

International Nuclear Information System (INIS)

McEligot, Donald M.; Brodkey, Robert S.; Eckelmann, Helmut

2008-01-01

Since insight into entropy generation is a key to increasing efficiency and thereby reducing fuel consumption and/or waste and--for wall-bounded flows--most entropy is generated in the viscous layer, we examine the transient behavior of its dominant contributor there for a non-canonical flow. New measurements in oil flow are presented for the effects of favorable streamwise mean pressure gradients on temporal entropy generation rates and, in the process, on key Reynolds-stress-producing events such as sweep front passage and on the deceleration/outflow phase of the overall bursting process. Two extremes have been considered: (1) a high pressure gradient, nearing 'laminarization', and (2), for comparison, a low pressure gradient corresponding to many earlier experiments. In both cases, the peak temporal entropy generation rate occurs shortly after passage of the ejection/sweep interface. Whether sweep and ejection rates appear to decrease or increase with the pressure gradient depends on the feature examined and the manner of sampling. When compared using wall coordinates for velocities, distances and time, the trends and magnitudes of the transient behaviors are mostly the same. The main effects of the higher pressure gradient are (1) changes in the time lag between detections--representing modification of the shape of the sweep front and the sweep angle with the wall, (2) modification of the magnitude of an instantaneous Reynolds shear stress with wall distance and (3) enlarging the sweeps and ejections. Results new for both low and high pressure gradients are the temporal behaviors of the dominant contribution to entropy generation; it is found to be much more sensitive to distance from the wall than to streamwise pressure gradient

Configurational entropy of hydrogen-disordered ice polymorphs

International Nuclear Information System (INIS)

Herrero, Carlos P.; Ramírez, Rafael

2014-01-01

The configurational entropy of several H-disordered ice polymorphs is calculated by means of a thermodynamic integration along a path between a totally H-disordered state and one fulfilling the Bernal-Fowler ice rules. A Monte Carlo procedure based on a simple energy model is used, so that the employed thermodynamic path drives the system from high temperatures to the low-temperature limit. This method turns out to be precise enough to give reliable values for the configurational entropy s th of different ice phases in the thermodynamic limit (number of molecules N → ∞). The precision of the method is checked for the ice model on a two-dimensional square lattice. Results for the configurational entropy are given for H-disordered arrangements on several polymorphs, including ices Ih, Ic, II, III, IV, V, VI, and XII. The highest and lowest entropy values correspond to ices VI and XII, respectively, with a difference of 3.3% between them. The dependence of the entropy on the ice structures has been rationalized by comparing it with structural parameters of the various polymorphs, such as the mean ring size. A particularly good correlation has been found between the configurational entropy and the connective constant derived from self-avoiding walks on the ice networks

Editorial: Entropy in Landscape Ecology

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Samuel A. Cushman

2018-04-01

Full Text Available Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are poorly developed in landscape ecology. The purpose of this Special Issue “Entropy in Landscape Ecology” in Entropy is to bring together current research on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. The special issue contains six articles, which cover a broad range of topics including relationships between entropy and evolution, connections between fractal geometry and entropy, new approaches to calculate configurational entropy of landscapes, example analyses of computing entropy of landscapes, and using entropy in the context of optimal landscape planning. Collectively these papers provide a broad range of contributions to the nascent field of ecological thermodynamics. Formalizing the connections between entropy and ecology are in a very early stage, and that this special issue contains papers that address several centrally important ideas, and provides seminal work that will be a foundation for the future development of ecological and evolutionary thermodynamics.

A Pilot Directional Protection for HVDC Transmission Line Based on Relative Entropy of Wavelet Energy

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Sheng Lin

2015-07-01

Full Text Available On the basis of analyzing high-voltage direct current (HVDC transmission system and its fault superimposed circuit, the direction of the fault components of the voltage and the current measured at one end of transmission line is certified to be different for internal faults and external faults. As an estimate of the differences between two signals, relative entropy is an effective parameter for recognizing transient signals in HVDC transmission lines. In this paper, the relative entropy of wavelet energy is applied to distinguish internal fault from external fault. For internal faults, the directions of fault components of voltage and current are opposite at the two ends of the transmission line, indicating a huge difference of wavelet energy relative entropy; for external faults, the directions are identical, indicating a small difference. The simulation results based on PSCAD/EMTDC show that the proposed pilot protection system acts accurately for faults under different conditions, and its performance is not affected by fault type, fault location, fault resistance and noise.

Atomistic-level non-equilibrium model for chemically reactive systems based on steepest-entropy-ascent quantum thermodynamics

International Nuclear Information System (INIS)

Li, Guanchen; Al-Abbasi, Omar; Von Spakovsky, Michael R

2014-01-01

This paper outlines an atomistic-level framework for modeling the non-equilibrium behavior of chemically reactive systems. The framework called steepest- entropy-ascent quantum thermodynamics (SEA-QT) is based on the paradigm of intrinsic quantum thermodynamic (IQT), which is a theory that unifies quantum mechanics and thermodynamics into a single discipline with wide applications to the study of non-equilibrium phenomena at the atomistic level. SEA-QT is a novel approach for describing the state of chemically reactive systems as well as the kinetic and dynamic features of the reaction process without any assumptions of near-equilibrium states or weak-interactions with a reservoir or bath. Entropy generation is the basis of the dissipation which takes place internal to the system and is, thus, the driving force of the chemical reaction(s). The SEA-QT non-equilibrium model is able to provide detailed information during the reaction process, providing a picture of the changes occurring in key thermodynamic properties (e.g., the instantaneous species concentrations, entropy and entropy generation, reaction coordinate, chemical affinities, reaction rate, etc). As an illustration, the SEA-QT framework is applied to an atomistic-level chemically reactive system governed by the reaction mechanism F + H 2 ↔ FH + H

Fast concurrent array-based stacks, queues and deques using fetch-and-increment-bounded, fetch-and-decrement-bounded and store-on-twin synchronization primitives

Science.gov (United States)

Chen, Dong; Gara, Alana; Heidelberger, Philip; Kumar, Sameer; Ohmacht, Martin; Steinmacher-Burow, Burkhard; Wisniewski, Robert

2014-09-16

Implementation primitives for concurrent array-based stacks, queues, double-ended queues (deques) and wrapped deques are provided. In one aspect, each element of the stack, queue, deque or wrapped deque data structure has its own ticket lock, allowing multiple threads to concurrently use multiple elements of the data structure and thus achieving high performance. In another aspect, new synchronization primitives FetchAndIncrementBounded (Counter, Bound) and FetchAndDecrementBounded (Counter, Bound) are implemented. These primitives can be implemented in hardware and thus promise a very fast throughput for queues, stacks and double-ended queues.

An entropy-assisted musculoskeletal shoulder model.

Science.gov (United States)

Xu, Xu; Lin, Jia-Hua; McGorry, Raymond W

2017-04-01

Optimization combined with a musculoskeletal shoulder model has been used to estimate mechanical loading of musculoskeletal elements around the shoulder. Traditionally, the objective function is to minimize the summation of the total activities of the muscles with forces, moments, and stability constraints. Such an objective function, however, tends to neglect the antagonist muscle co-contraction. In this study, an objective function including an entropy term is proposed to address muscle co-contractions. A musculoskeletal shoulder model is developed to apply the proposed objective function. To find the optimal weight for the entropy term, an experiment was conducted. In the experiment, participants generated various 3-D shoulder moments in six shoulder postures. The surface EMG of 8 shoulder muscles was measured and compared with the predicted muscle activities based on the proposed objective function using Bhattacharyya distance and concordance ratio under different weight of the entropy term. The results show that a small weight of the entropy term can improve the predictability of the model in terms of muscle activities. Such a result suggests that the concept of entropy could be helpful for further understanding the mechanism of muscle co-contractions as well as developing a shoulder biomechanical model with greater validity. Copyright © 2017 Elsevier Ltd. All rights reserved.

Persistence-Based Branch Misprediction Bounds for WCET Analysis

DEFF Research Database (Denmark)

Puffitsch, Wolfgang

2015-01-01

Branch prediction is an important feature of pipelined processors to achieve high performance. However, it can lead to overly pessimistic worst-case execution time (WCET) bounds when being modeled too conservatively. This paper presents bounds on the number of branch mispredictions for local...... dynamic branch predictors. To handle interferences between branch instructions we use the notion of persistence, a concept that is also found in cache analyses. The bounds apply to branches in general, not only to branches that close a loop. Furthermore, the bounds can be easily integrated into integer...... linear programming formulations of the WCET problem. An evaluation on a number of benchmarks shows that with these bounds, dynamic branch prediction does not necessarily lead to higher WCET bounds than static prediction schemes....

On quantum Rényi entropies

DEFF Research Database (Denmark)

Müller-Lennert, Martin; Dupont-Dupuis, Fréderic; Szehr, Oleg

2013-01-01

The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in in...

Proposed Empirical Entropy and Gibbs Energy Based on Observations of Scale Invariance in Open Nonequilibrium Systems.

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