Maximum and minimum entropy states yielding local continuity bounds
Hanson, Eric P.; Datta, Nilanjana
2018-04-01
Given an arbitrary quantum state (σ), we obtain an explicit construction of a state ρɛ * ( σ ) [respectively, ρ * , ɛ ( σ ) ] which has the maximum (respectively, minimum) entropy among all states which lie in a specified neighborhood (ɛ-ball) of σ. Computing the entropy of these states leads to a local strengthening of the continuity bound of the von Neumann entropy, i.e., the Audenaert-Fannes inequality. Our bound is local in the sense that it depends on the spectrum of σ. The states ρɛ * ( σ ) and ρ * , ɛ (σ) depend only on the geometry of the ɛ-ball and are in fact optimizers for a larger class of entropies. These include the Rényi entropy and the minimum- and maximum-entropies, providing explicit formulas for certain smoothed quantities. This allows us to obtain local continuity bounds for these quantities as well. In obtaining this bound, we first derive a more general result which may be of independent interest, namely, a necessary and sufficient condition under which a state maximizes a concave and Gâteaux-differentiable function in an ɛ-ball around a given state σ. Examples of such a function include the von Neumann entropy and the conditional entropy of bipartite states. Our proofs employ tools from the theory of convex optimization under non-differentiable constraints, in particular Fermat's rule, and majorization theory.
Maximum Quantum Entropy Method
Sim, Jae-Hoon; Han, Myung Joon
2018-01-01
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input matrix. As a result, the continuation of off-diagonal elements becomes straightforward. Without introducing any further ambiguity, the Bayesian probabilistic interpretation is maintained just as in the conventional maximum entropy method. The applications o...
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.
International Nuclear Information System (INIS)
Davis, Sergio
2013-01-01
In this work we develop a method for inferring the underlying configurational density of states of a molecular system by combining information from several microcanonical molecular dynamics or Monte Carlo simulations at different energies. This method is based on Jaynes' Maximum Entropy formalism (MaxEnt) for Bayesian statistical inference under known expectation values. We present results of its application to measure thermodynamic entropy and free energy differences in embedded-atom models of metals.
Hydrodynamic Relaxation of an Electron Plasma to a Near-Maximum Entropy State
International Nuclear Information System (INIS)
Rodgers, D. J.; Servidio, S.; Matthaeus, W. H.; Mitchell, T. B.; Aziz, T.; Montgomery, D. C.
2009-01-01
Dynamical relaxation of a pure electron plasma in a Malmberg-Penning trap is studied, comparing experiments, numerical simulations and statistical theories of weakly dissipative two-dimensional (2D) turbulence. Simulations confirm that the dynamics are approximated well by a 2D hydrodynamic model. Statistical analysis favors a theoretical picture of relaxation to a near-maximum entropy state with constrained energy, circulation, and angular momentum. This provides evidence that 2D electron fluid relaxation in a turbulent regime is governed by principles of maximum entropy.
International Nuclear Information System (INIS)
Ponman, T.J.
1984-01-01
For some years now two different expressions have been in use for maximum entropy image restoration and there has been some controversy over which one is appropriate for a given problem. Here two further entropies are presented and it is argued that there is no single correct algorithm. The properties of the four different methods are compared using simple 1D simulations with a view to showing how they can be used together to gain as much information as possible about the original object. (orig.)
Maximum entropy tokamak configurations
International Nuclear Information System (INIS)
Minardi, E.
1989-01-01
The new entropy concept for the collective magnetic equilibria is applied to the description of the states of a tokamak subject to ohmic and auxiliary heating. The condition for the existence of steady state plasma states with vanishing entropy production implies, on one hand, the resilience of specific current density profiles and, on the other, severe restrictions on the scaling of the confinement time with power and current. These restrictions are consistent with Goldston scaling and with the existence of a heat pinch. (author)
Directory of Open Access Journals (Sweden)
F. TopsÃƒÂ¸e
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
Introduction to maximum entropy
International Nuclear Information System (INIS)
Sivia, D.S.
1988-01-01
The maximum entropy (MaxEnt) principle has been successfully used in image reconstruction in a wide variety of fields. We review the need for such methods in data analysis and show, by use of a very simple example, why MaxEnt is to be preferred over other regularizing functions. This leads to a more general interpretation of the MaxEnt method, and its use is illustrated with several different examples. Practical difficulties with non-linear problems still remain, this being highlighted by the notorious phase problem in crystallography. We conclude with an example from neutron scattering, using data from a filter difference spectrometer to contrast MaxEnt with a conventional deconvolution. 12 refs., 8 figs., 1 tab
Introduction to maximum entropy
International Nuclear Information System (INIS)
Sivia, D.S.
1989-01-01
The maximum entropy (MaxEnt) principle has been successfully used in image reconstruction in a wide variety of fields. The author reviews the need for such methods in data analysis and shows, by use of a very simple example, why MaxEnt is to be preferred over other regularizing functions. This leads to a more general interpretation of the MaxEnt method, and its use is illustrated with several different examples. Practical difficulties with non-linear problems still remain, this being highlighted by the notorious phase problem in crystallography. He concludes with an example from neutron scattering, using data from a filter difference spectrometer to contrast MaxEnt with a conventional deconvolution. 12 refs., 8 figs., 1 tab
Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection
Directory of Open Access Journals (Sweden)
Stuart Bartlett
2016-12-01
Full Text Available Multiple authors have claimed that the natural convection of a fluid is a process that exhibits maximum entropy production (MEP. However, almost all such investigations were limited to fixed temperature boundary conditions (BCs. It was found that under those conditions, the system tends to maximize its heat flux, and hence it was concluded that the MEP state is a dynamical attractor. However, since entropy production varies with heat flux and difference of inverse temperature, it is essential that any complete investigation of entropy production allows for variations in heat flux and temperature difference. Only then can we legitimately assess whether the MEP state is the most attractive. Our previous work made use of negative feedback BCs to explore this possibility. We found that the steady state of the system was far from the MEP state. For any system, entropy production can only be maximized subject to a finite set of physical and material constraints. In the case of our previous work, it was possible that the adopted set of fluid parameters were constraining the system in such a way that it was entirely prevented from reaching the MEP state. Hence, in the present work, we used a different set of boundary parameters, such that the steady states of the system were in the local vicinity of the MEP state. If MEP was indeed an attractor, relaxing those constraints of our previous work should have caused a discrete perturbation to the surface of steady state heat flux values near the value corresponding to MEP. We found no such perturbation, and hence no discernible attraction to the MEP state. Furthermore, systems with fixed flux BCs actually minimize their entropy production (relative to the alternative stable state, that of pure diffusive heat transport. This leads us to conclude that the principle of MEP is not an accurate indicator of which stable steady state a convective system will adopt. However, for all BCs considered, the quotient of
Credal Networks under Maximum Entropy
Lukasiewicz, Thomas
2013-01-01
We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution of a Bayesian tree coincides with the maximum entropy model of its conditional distributions. This result, however, does not hold anymore for general Bayesian networks. We thus present a new kind of maximum entropy models, which are computed sequentially. ...
Feasible Histories, Maximum Entropy
International Nuclear Information System (INIS)
Pitowsky, I.
1999-01-01
We consider the broadest possible consistency condition for a family of histories, which extends all previous proposals. A family that satisfies this condition is called feasible. On each feasible family of histories we choose a probability measure by maximizing entropy, while keeping the probabilities of commuting histories to their quantum mechanical values. This procedure is justified by the assumption that decoherence increases entropy. Finally, a criterion for identifying the nearly classical families is proposed
Combined analysis of steady state and transient transport by the maximum entropy method
Energy Technology Data Exchange (ETDEWEB)
Giannone, L.; Stroth, U; Koellermeyer, J [Association Euratom-Max-Planck-Institut fuer Plasmaphysik, Garching (Germany); and others
1996-04-01
A new maximum entropy approach has been applied to analyse three types of transient transport experiments. For sawtooth propagation experiments in the ASDEX Upgrade and ECRH power modulation and power-switching experiments in the Wendelstein 7-AS Stellarator, either the time evolution of the temperature perturbation or the phase and amplitude of the modulated temperature perturbation are used as non-linear constraints to the {chi}{sub e} profile to be fitted. Simultaneously, the constraints given by the equilibrium temperature profile for steady-state power balance are fitted. In the maximum entropy formulation, the flattest {chi}{sub e} profile consistent with the constraints is found. It was found that {chi}{sub e} determined from sawtooth propagation was greater than the power balance value by a factor of five in the ASDEX Upgrade. From power modulation experiments, employing the measurements of four modulation frequencies simultaneously, the power deposition profile as well as the {chi}{sub e} profile could be determined. A comparison of the predictions of a time-independent {chi}{sub e} model and a power-dependent {chi}{sub e} model is made. The power-switching experiments show that the {chi}{sub e} profile must change within a millisecond to a new value consistent with the power balance value at the new input power. Neither power deposition broadening due to suprathermal electrons nor temperature or gradient dependences of {chi}{sub e} can explain this observation. (author).
Maximum Entropy in Drug Discovery
Directory of Open Access Journals (Sweden)
Chih-Yuan Tseng
2014-07-01
Full Text Available Drug discovery applies multidisciplinary approaches either experimentally, computationally or both ways to identify lead compounds to treat various diseases. While conventional approaches have yielded many US Food and Drug Administration (FDA-approved drugs, researchers continue investigating and designing better approaches to increase the success rate in the discovery process. In this article, we provide an overview of the current strategies and point out where and how the method of maximum entropy has been introduced in this area. The maximum entropy principle has its root in thermodynamics, yet since Jaynes’ pioneering work in the 1950s, the maximum entropy principle has not only been used as a physics law, but also as a reasoning tool that allows us to process information in hand with the least bias. Its applicability in various disciplines has been abundantly demonstrated. We give several examples of applications of maximum entropy in different stages of drug discovery. Finally, we discuss a promising new direction in drug discovery that is likely to hinge on the ways of utilizing maximum entropy.
Directory of Open Access Journals (Sweden)
Adom Giffin
2014-09-01
Full Text Available In this paper, we continue our efforts to show how maximum relative entropy (MrE can be used as a universal updating algorithm. Here, our purpose is to tackle a joint state and parameter estimation problem where our system is nonlinear and in a non-equilibrium state, i.e., perturbed by varying external forces. Traditional parameter estimation can be performed by using filters, such as the extended Kalman filter (EKF. However, as shown with a toy example of a system with first order non-homogeneous ordinary differential equations, assumptions made by the EKF algorithm (such as the Markov assumption may not be valid. The problem can be solved with exponential smoothing, e.g., exponentially weighted moving average (EWMA. Although this has been shown to produce acceptable filtering results in real exponential systems, it still cannot simultaneously estimate both the state and its parameters and has its own assumptions that are not always valid, for example when jump discontinuities exist. We show that by applying MrE as a filter, we can not only develop the closed form solutions, but we can also infer the parameters of the differential equation simultaneously with the means. This is useful in real, physical systems, where we want to not only filter the noise from our measurements, but we also want to simultaneously infer the parameters of the dynamics of a nonlinear and non-equilibrium system. Although there were many assumptions made throughout the paper to illustrate that EKF and exponential smoothing are special cases ofMrE, we are not “constrained”, by these assumptions. In other words, MrE is completely general and can be used in broader ways.
Maximum entropy beam diagnostic tomography
International Nuclear Information System (INIS)
Mottershead, C.T.
1985-01-01
This paper reviews the formalism of maximum entropy beam diagnostic tomography as applied to the Fusion Materials Irradiation Test (FMIT) prototype accelerator. The same formalism has also been used with streak camera data to produce an ultrahigh speed movie of the beam profile of the Experimental Test Accelerator (ETA) at Livermore. 11 refs., 4 figs
Maximum entropy beam diagnostic tomography
International Nuclear Information System (INIS)
Mottershead, C.T.
1985-01-01
This paper reviews the formalism of maximum entropy beam diagnostic tomography as applied to the Fusion Materials Irradiation Test (FMIT) prototype accelerator. The same formalism has also been used with streak camera data to produce an ultrahigh speed movie of the beam profile of the Experimental Test Accelerator (ETA) at Livermore
The maximum entropy production and maximum Shannon information entropy in enzyme kinetics
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.
On Maximum Entropy and Inference
Directory of Open Access Journals (Sweden)
Luigi Gresele
2017-11-01
Full Text Available Maximum entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a model from data, that affords predictions on all other (dependent variables. Conversely, maximum entropy can be invoked to retrieve the relevant variables (sufficient statistics directly from the data, once a model is identified by Bayesian model selection. We explore this approach in the case of spin models with interactions of arbitrary order, and we discuss how relevant interactions can be inferred. In this perspective, the dimensionality of the inference problem is not set by the number of parameters in the model, but by the frequency distribution of the data. We illustrate the method showing its ability to recover the correct model in a few prototype cases and discuss its application on a real dataset.
Maximum entropy and Bayesian methods
International Nuclear Information System (INIS)
Smith, C.R.; Erickson, G.J.; Neudorfer, P.O.
1992-01-01
Bayesian probability theory and Maximum Entropy methods are at the core of a new view of scientific inference. These 'new' ideas, along with the revolution in computational methods afforded by modern computers allow astronomers, electrical engineers, image processors of any type, NMR chemists and physicists, and anyone at all who has to deal with incomplete and noisy data, to take advantage of methods that, in the past, have been applied only in some areas of theoretical physics. The title workshops have been the focus of a group of researchers from many different fields, and this diversity is evident in this book. There are tutorial and theoretical papers, and applications in a very wide variety of fields. Almost any instance of dealing with incomplete and noisy data can be usefully treated by these methods, and many areas of theoretical research are being enhanced by the thoughtful application of Bayes' theorem. Contributions contained in this volume present a state-of-the-art overview that will be influential and useful for many years to come
Receiver function estimated by maximum entropy deconvolution
Institute of Scientific and Technical Information of China (English)
吴庆举; 田小波; 张乃铃; 李卫平; 曾融生
2003-01-01
Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than 1, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.
Maximum-entropy description of animal movement.
Fleming, Chris H; Subaşı, Yiğit; Calabrese, Justin M
2015-03-01
We introduce a class of maximum-entropy states that naturally includes within it all of the major continuous-time stochastic processes that have been applied to animal movement, including Brownian motion, Ornstein-Uhlenbeck motion, integrated Ornstein-Uhlenbeck motion, a recently discovered hybrid of the previous models, and a new model that describes central-place foraging. We are also able to predict a further hierarchy of new models that will emerge as data quality improves to better resolve the underlying continuity of animal movement. Finally, we also show that Langevin equations must obey a fluctuation-dissipation theorem to generate processes that fall from this class of maximum-entropy distributions when the constraints are purely kinematic.
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
In the framework of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, a recent paper [Gheorghiu-Svirschevski 2001 Phys. Rev. A 63 054102] reproposes the nonlinear equation of motion proposed by the present author [see Beretta G P 1987 Found. Phys. 17 365 and references therein] for quantum (thermo)dynamics of a single isolated indivisible constituent system, such as a single particle, qubit, qudit, spin or atomic system, or a Bose-Einstein or Fermi-Dirac field. As already proved, such nonlinear dynamics entails a fundamental unifying microscopic proof and extension of Onsager's reciprocity and Callen's fluctuation-dissipation relations to all nonequilibrium states, close and far from thermodynamic equilibrium. In this paper we propose a brief but self-contained review of the main results already proved, including the explicit geometrical construction of the equation of motion from the steepest-entropy-ascent ansatz and its exact mathematical and conceptual equivalence with the maximal-entropy-generation variational-principle formulation presented in Gheorghiu-Svirschevski S 2001 Phys. Rev. A 63 022105. Moreover, we show how it can be extended to the case of a composite system to obtain the general form of the equation of motion, consistent with the demanding requirements of strong separability and of compatibility with general thermodynamics principles. The irreversible term in the equation of motion describes the spontaneous attraction of the state operator in the direction of steepest entropy ascent, thus implementing the maximum entropy production principle in quantum theory. The time rate at which the path of steepest entropy ascent is followed has so far been left unspecified. As a step towards the identification of such rate, here we propose a possible
Two-dimensional maximum entropy image restoration
International Nuclear Information System (INIS)
Brolley, J.E.; Lazarus, R.B.; Suydam, B.R.; Trussell, H.J.
1977-07-01
An optical check problem was constructed to test P LOG P maximum entropy restoration of an extremely distorted image. Useful recovery of the original image was obtained. Comparison with maximum a posteriori restoration is made. 7 figures
Maximum entropy principal for transportation
International Nuclear Information System (INIS)
Bilich, F.; Da Silva, R.
2008-01-01
In this work we deal with modeling of the transportation phenomenon for use in the transportation planning process and policy-impact studies. The model developed is based on the dependence concept, i.e., the notion that the probability of a trip starting at origin i is dependent on the probability of a trip ending at destination j given that the factors (such as travel time, cost, etc.) which affect travel between origin i and destination j assume some specific values. The derivation of the solution of the model employs the maximum entropy principle combining a priori multinomial distribution with a trip utility concept. This model is utilized to forecast trip distributions under a variety of policy changes and scenarios. The dependence coefficients are obtained from a regression equation where the functional form is derived based on conditional probability and perception of factors from experimental psychology. The dependence coefficients encode all the information that was previously encoded in the form of constraints. In addition, the dependence coefficients encode information that cannot be expressed in the form of constraints for practical reasons, namely, computational tractability. The equivalence between the standard formulation (i.e., objective function with constraints) and the dependence formulation (i.e., without constraints) is demonstrated. The parameters of the dependence-based trip-distribution model are estimated, and the model is also validated using commercial air travel data in the U.S. In addition, policy impact analyses (such as allowance of supersonic flights inside the U.S. and user surcharge at noise-impacted airports) on air travel are performed.
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
Energy Technology Data Exchange (ETDEWEB)
Funakoshi, Satoshi; Sato, Tomoyoshi; Miyazaki, Takeshi, E-mail: funakosi@miyazaki.mce.uec.ac.jp, E-mail: miyazaki@mce.uec.ac.jp [Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications, 1-5-1, Chofugaoka, Chofu, Tokyo 182-8585 (Japan)
2012-06-01
We investigate the statistical mechanics of quasi-geostrophic point vortices of mixed sign (bi-disperse system) numerically and theoretically. Direct numerical simulations under periodic boundary conditions are performed using a fast special-purpose computer for molecular dynamics (GRAPE-DR). Clustering of point vortices of like sign is observed and two-dimensional (2D) equilibrium states are formed. It is shown that they are the solutions of the 2D mean-field equation, i.e. the sinh-Poisson equation. The sinh-Poisson equation is generalized to study the 3D nature of the equilibrium states, and a new mean-field equation with the 3D Laplace operator is derived based on the maximum entropy theory. 3D solutions are obtained at very low energy level. These solution branches, however, cannot be traced up to the higher energy level at which the direct numerical simulations are performed, and transitions to 2D solution branches take place when the energy is increased. (paper)
Maximum Entropy: Clearing up Mysteries
Directory of Open Access Journals (Sweden)
Marian GrendÃƒÂ¡r
2001-04-01
Full Text Available Abstract: There are several mystifications and a couple of mysteries pertinent to MaxEnt. The mystifications, pitfalls and traps are set up mainly by an unfortunate formulation of Jaynes' die problem, the cause cÃƒÂ©lÃƒÂ¨bre of MaxEnt. After discussing the mystifications a new formulation of the problem is proposed. Then we turn to the mysteries. An answer to the recurring question 'Just what are we accomplishing when we maximize entropy?' [8], based on MaxProb rationale of MaxEnt [6], is recalled. A brief view on the other mystery: 'What is the relation between MaxEnt and the Bayesian method?' [9], in light of the MaxProb rationale of MaxEnt suggests that there is not and cannot be a conflict between MaxEnt and Bayes Theorem.
Topics in Bayesian statistics and maximum entropy
International Nuclear Information System (INIS)
Mutihac, R.; Cicuttin, A.; Cerdeira, A.; Stanciulescu, C.
1998-12-01
Notions of Bayesian decision theory and maximum entropy methods are reviewed with particular emphasis on probabilistic inference and Bayesian modeling. The axiomatic approach is considered as the best justification of Bayesian analysis and maximum entropy principle applied in natural sciences. Particular emphasis is put on solving the inverse problem in digital image restoration and Bayesian modeling of neural networks. Further topics addressed briefly include language modeling, neutron scattering, multiuser detection and channel equalization in digital communications, genetic information, and Bayesian court decision-making. (author)
Zipf's law, power laws and maximum entropy
International Nuclear Information System (INIS)
Visser, Matt
2013-01-01
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines—from astronomy to demographics to software structure to economics to linguistics to zoology, and even warfare. A recent model of random group formation (RGF) attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present paper I argue that the specific cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified. (paper)
The maximum-entropy method in superspace
Czech Academy of Sciences Publication Activity Database
van Smaalen, S.; Palatinus, Lukáš; Schneider, M.
2003-01-01
Roč. 59, - (2003), s. 459-469 ISSN 0108-7673 Grant - others:DFG(DE) XX Institutional research plan: CEZ:AV0Z1010914 Keywords : maximum-entropy method, * aperiodic crystals * electron density Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.558, year: 2003
Objective Bayesianism and the Maximum Entropy Principle
Directory of Open Access Journals (Sweden)
Jon Williamson
2013-09-01
Full Text Available Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities; they should be calibrated to our evidence of physical probabilities; and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective Bayesianism are usually justified in different ways. In this paper, we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem.
Maximum entropy decomposition of quadrupole mass spectra
International Nuclear Information System (INIS)
Toussaint, U. von; Dose, V.; Golan, A.
2004-01-01
We present an information-theoretic method called generalized maximum entropy (GME) for decomposing mass spectra of gas mixtures from noisy measurements. In this GME approach to the noisy, underdetermined inverse problem, the joint entropies of concentration, cracking, and noise probabilities are maximized subject to the measured data. This provides a robust estimation for the unknown cracking patterns and the concentrations of the contributing molecules. The method is applied to mass spectroscopic data of hydrocarbons, and the estimates are compared with those received from a Bayesian approach. We show that the GME method is efficient and is computationally fast
Maximum entropy PDF projection: A review
Baggenstoss, Paul M.
2017-06-01
We review maximum entropy (MaxEnt) PDF projection, a method with wide potential applications in statistical inference. The method constructs a sampling distribution for a high-dimensional vector x based on knowing the sampling distribution p(z) of a lower-dimensional feature z = T (x). Under mild conditions, the distribution p(x) having highest possible entropy among all distributions consistent with p(z) may be readily found. Furthermore, the MaxEnt p(x) may be sampled, making the approach useful in Monte Carlo methods. We review the theorem and present a case study in model order selection and classification for handwritten character recognition.
Pareto versus lognormal: a maximum entropy test.
Bee, Marco; Riccaboni, Massimo; Schiavo, Stefano
2011-08-01
It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units.
Discontinuity of maximum entropy inference and quantum phase transitions
International Nuclear Information System (INIS)
Chen, Jianxin; Ji, Zhengfeng; Yu, Nengkun; Zeng, Bei; Li, Chi-Kwong; Poon, Yiu-Tung; Shen, Yi; Zhou, Duanlu
2015-01-01
In this paper, we discuss the connection between two genuinely quantum phenomena—the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit. (paper)
Maximum entropy analysis of liquid diffraction data
International Nuclear Information System (INIS)
Root, J.H.; Egelstaff, P.A.; Nickel, B.G.
1986-01-01
A maximum entropy method for reducing truncation effects in the inverse Fourier transform of structure factor, S(q), to pair correlation function, g(r), is described. The advantages and limitations of the method are explored with the PY hard sphere structure factor as model input data. An example using real data on liquid chlorine, is then presented. It is seen that spurious structure is greatly reduced in comparison to traditional Fourier transform methods. (author)
Automatic maximum entropy spectral reconstruction in NMR
International Nuclear Information System (INIS)
Mobli, Mehdi; Maciejewski, Mark W.; Gryk, Michael R.; Hoch, Jeffrey C.
2007-01-01
Developments in superconducting magnets, cryogenic probes, isotope labeling strategies, and sophisticated pulse sequences together have enabled the application, in principle, of high-resolution NMR spectroscopy to biomolecular systems approaching 1 megadalton. In practice, however, conventional approaches to NMR that utilize the fast Fourier transform, which require data collected at uniform time intervals, result in prohibitively lengthy data collection times in order to achieve the full resolution afforded by high field magnets. A variety of approaches that involve nonuniform sampling have been proposed, each utilizing a non-Fourier method of spectrum analysis. A very general non-Fourier method that is capable of utilizing data collected using any of the proposed nonuniform sampling strategies is maximum entropy reconstruction. A limiting factor in the adoption of maximum entropy reconstruction in NMR has been the need to specify non-intuitive parameters. Here we describe a fully automated system for maximum entropy reconstruction that requires no user-specified parameters. A web-accessible script generator provides the user interface to the system
Maximum entropy analysis of EGRET data
DEFF Research Database (Denmark)
Pohl, M.; Strong, A.W.
1997-01-01
EGRET data are usually analysed on the basis of the Maximum-Likelihood method \\cite{ma96} in a search for point sources in excess to a model for the background radiation (e.g. \\cite{hu97}). This method depends strongly on the quality of the background model, and thus may have high systematic unce...... uncertainties in region of strong and uncertain background like the Galactic Center region. Here we show images of such regions obtained by the quantified Maximum-Entropy method. We also discuss a possible further use of MEM in the analysis of problematic regions of the sky....
Maximum entropy method in momentum density reconstruction
International Nuclear Information System (INIS)
Dobrzynski, L.; Holas, A.
1997-01-01
The Maximum Entropy Method (MEM) is applied to the reconstruction of the 3-dimensional electron momentum density distributions observed through the set of Compton profiles measured along various crystallographic directions. It is shown that the reconstruction of electron momentum density may be reliably carried out with the aid of simple iterative algorithm suggested originally by Collins. A number of distributions has been simulated in order to check the performance of MEM. It is shown that MEM can be recommended as a model-free approach. (author). 13 refs, 1 fig
Dynamical maximum entropy approach to flocking.
Cavagna, Andrea; Giardina, Irene; Ginelli, Francesco; Mora, Thierry; Piovani, Duccio; Tavarone, Raffaele; Walczak, Aleksandra M
2014-04-01
We derive a new method to infer from data the out-of-equilibrium alignment dynamics of collectively moving animal groups, by considering the maximum entropy model distribution consistent with temporal and spatial correlations of flight direction. When bird neighborhoods evolve rapidly, this dynamical inference correctly learns the parameters of the model, while a static one relying only on the spatial correlations fails. When neighbors change slowly and the detailed balance is satisfied, we recover the static procedure. We demonstrate the validity of the method on simulated data. The approach is applicable to other systems of active matter.
Neutron spectra unfolding with maximum entropy and maximum likelihood
International Nuclear Information System (INIS)
Itoh, Shikoh; Tsunoda, Toshiharu
1989-01-01
A new unfolding theory has been established on the basis of the maximum entropy principle and the maximum likelihood method. This theory correctly embodies the Poisson statistics of neutron detection, and always brings a positive solution over the whole energy range. Moreover, the theory unifies both problems of overdetermined and of underdetermined. For the latter, the ambiguity in assigning a prior probability, i.e. the initial guess in the Bayesian sense, has become extinct by virtue of the principle. An approximate expression of the covariance matrix for the resultant spectra is also presented. An efficient algorithm to solve the nonlinear system, which appears in the present study, has been established. Results of computer simulation showed the effectiveness of the present theory. (author)
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.
Weak scale from the maximum entropy principle
Hamada, Yuta; Kawai, Hikaru; Kawana, Kiyoharu
2015-03-01
The theory of the multiverse and wormholes suggests that the parameters of the Standard Model (SM) are fixed in such a way that the radiation of the S3 universe at the final stage S_rad becomes maximum, which we call the maximum entropy principle. Although it is difficult to confirm this principle generally, for a few parameters of the SM, we can check whether S_rad actually becomes maximum at the observed values. In this paper, we regard S_rad at the final stage as a function of the weak scale (the Higgs expectation value) vh, and show that it becomes maximum around vh = {{O}} (300 GeV) when the dimensionless couplings in the SM, i.e., the Higgs self-coupling, the gauge couplings, and the Yukawa couplings are fixed. Roughly speaking, we find that the weak scale is given by vh ˜ T_{BBN}2 / (M_{pl}ye5), where ye is the Yukawa coupling of electron, T_BBN is the temperature at which the Big Bang nucleosynthesis starts, and M_pl is the Planck mass.
Maximum-Entropy Inference with a Programmable Annealer
Chancellor, Nicholas; Szoke, Szilard; Vinci, Walter; Aeppli, Gabriel; Warburton, Paul A.
2016-03-01
Optimisation problems typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this maximises the likelihood that the solution is correct. The maximum entropy solution on the other hand takes the form of a Boltzmann distribution over the ground and excited states of the cost function to correct for noise. Here we use a programmable annealer for the information decoding problem which we simulate as a random Ising model in a field. We show experimentally that finite temperature maximum entropy decoding can give slightly better bit-error-rates than the maximum likelihood approach, confirming that useful information can be extracted from the excited states of the annealer. Furthermore we introduce a bit-by-bit analytical method which is agnostic to the specific application and use it to show that the annealer samples from a highly Boltzmann-like distribution. Machines of this kind are therefore candidates for use in a variety of machine learning applications which exploit maximum entropy inference, including language processing and image recognition.
Dewar, R
2003-01-01
Jaynes' information theory formalism of statistical mechanics is applied to the stationary states of open, non-equilibrium systems. First, it is shown that the probability distribution p subGAMMA of the underlying microscopic phase space trajectories GAMMA over a time interval of length tau satisfies p subGAMMA propor to exp(tau sigma subGAMMA/2k sub B) where sigma subGAMMA is the time-averaged rate of entropy production of GAMMA. Three consequences of this result are then derived: (1) the fluctuation theorem, which describes the exponentially declining probability of deviations from the second law of thermodynamics as tau -> infinity; (2) the selection principle of maximum entropy production for non-equilibrium stationary states, empirical support for which has been found in studies of phenomena as diverse as the Earth's climate and crystal growth morphology; and (3) the emergence of self-organized criticality for flux-driven systems in the slowly-driven limit. The explanation of these results on general inf...
MAXIMUM-LIKELIHOOD-ESTIMATION OF THE ENTROPY OF AN ATTRACTOR
SCHOUTEN, JC; TAKENS, F; VANDENBLEEK, CM
In this paper, a maximum-likelihood estimate of the (Kolmogorov) entropy of an attractor is proposed that can be obtained directly from a time series. Also, the relative standard deviation of the entropy estimate is derived; it is dependent on the entropy and on the number of samples used in the
Mammographic image restoration using maximum entropy deconvolution
International Nuclear Information System (INIS)
Jannetta, A; Jackson, J C; Kotre, C J; Birch, I P; Robson, K J; Padgett, R
2004-01-01
An image restoration approach based on a Bayesian maximum entropy method (MEM) has been applied to a radiological image deconvolution problem, that of reduction of geometric blurring in magnification mammography. The aim of the work is to demonstrate an improvement in image spatial resolution in realistic noisy radiological images with no associated penalty in terms of reduction in the signal-to-noise ratio perceived by the observer. Images of the TORMAM mammographic image quality phantom were recorded using the standard magnification settings of 1.8 magnification/fine focus and also at 1.8 magnification/broad focus and 3.0 magnification/fine focus; the latter two arrangements would normally give rise to unacceptable geometric blurring. Measured point-spread functions were used in conjunction with the MEM image processing to de-blur these images. The results are presented as comparative images of phantom test features and as observer scores for the raw and processed images. Visualization of high resolution features and the total image scores for the test phantom were improved by the application of the MEM processing. It is argued that this successful demonstration of image de-blurring in noisy radiological images offers the possibility of weakening the link between focal spot size and geometric blurring in radiology, thus opening up new approaches to system optimization
Application of maximum entropy to neutron tunneling spectroscopy
International Nuclear Information System (INIS)
Mukhopadhyay, R.; Silver, R.N.
1990-01-01
We demonstrate the maximum entropy method for the deconvolution of high resolution tunneling data acquired with a quasielastic spectrometer. Given a precise characterization of the instrument resolution function, a maximum entropy analysis of lutidine data obtained with the IRIS spectrometer at ISIS results in an effective factor of three improvement in resolution. 7 refs., 4 figs
Maximum entropy principle and hydrodynamic models in statistical mechanics
International Nuclear Information System (INIS)
Trovato, M.; Reggiani, L.
2012-01-01
This review presents the state of the art of the maximum entropy principle (MEP) in its classical and quantum (QMEP) formulation. Within the classical MEP we overview a general theory able to provide, in a dynamical context, the macroscopic relevant variables for carrier transport in the presence of electric fields of arbitrary strength. For the macroscopic variables the linearized maximum entropy approach is developed including full-band effects within a total energy scheme. Under spatially homogeneous conditions, we construct a closed set of hydrodynamic equations for the small-signal (dynamic) response of the macroscopic variables. The coupling between the driving field and the energy dissipation is analyzed quantitatively by using an arbitrary number of moments of the distribution function. Analogously, the theoretical approach is applied to many one-dimensional n + nn + submicron Si structures by using different band structure models, different doping profiles, different applied biases and is validated by comparing numerical calculations with ensemble Monte Carlo simulations and with available experimental data. Within the quantum MEP we introduce a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is then asserted as fundamental principle of quantum statistical mechanics. Accordingly, we have developed a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theory is formulated both in thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of ħ 2 , being ħ the reduced Planck constant. In particular, by using an arbitrary number of moments, we prove that: i) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives both of the
Maximum entropy production: Can it be used to constrain conceptual hydrological models?
M.C. Westhoff; E. Zehe
2013-01-01
In recent years, optimality principles have been proposed to constrain hydrological models. The principle of maximum entropy production (MEP) is one of the proposed principles and is subject of this study. It states that a steady state system is organized in such a way that entropy production is maximized. Although successful applications have been reported in...
Jarzynski equality in the context of maximum path entropy
González, Diego; Davis, Sergio
2017-06-01
In the global framework of finding an axiomatic derivation of nonequilibrium Statistical Mechanics from fundamental principles, such as the maximum path entropy - also known as Maximum Caliber principle -, this work proposes an alternative derivation of the well-known Jarzynski equality, a nonequilibrium identity of great importance today due to its applications to irreversible processes: biological systems (protein folding), mechanical systems, among others. This equality relates the free energy differences between two equilibrium thermodynamic states with the work performed when going between those states, through an average over a path ensemble. In this work the analysis of Jarzynski's equality will be performed using the formalism of inference over path space. This derivation highlights the wide generality of Jarzynski's original result, which could even be used in non-thermodynamical settings such as social systems, financial and ecological systems.
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.
Combining Experiments and Simulations Using the Maximum Entropy Principle
DEFF Research Database (Denmark)
Boomsma, Wouter; Ferkinghoff-Borg, Jesper; Lindorff-Larsen, Kresten
2014-01-01
are not in quantitative agreement with experimental data. The principle of maximum entropy is a general procedure for constructing probability distributions in the light of new data, making it a natural tool in cases when an initial model provides results that are at odds with experiments. The number of maximum entropy...... in the context of a simple example, after which we proceed with a real-world application in the field of molecular simulations, where the maximum entropy procedure has recently provided new insight. Given the limited accuracy of force fields, macromolecular simulations sometimes produce results....... Three very recent papers have explored this problem using the maximum entropy approach, providing both new theoretical and practical insights to the problem. We highlight each of these contributions in turn and conclude with a discussion on remaining challenges....
Configurational entropy of glueball states
Energy Technology Data Exchange (ETDEWEB)
Bernardini, Alex E., E-mail: alexeb@ufscar.br [Departamento de Física, Universidade Federal de São Carlos, PO Box 676, 13565-905, São Carlos, SP (Brazil); Braga, Nelson R.F., E-mail: braga@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, RJ 21941-972 (Brazil); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [CMCC, Universidade Federal do ABC, UFABC, 09210-580, Santo André (Brazil)
2017-02-10
The configurational entropy of glueball states is calculated using a holographic description. Glueball states are represented by a supergravity dual picture, consisting of a 5-dimensional graviton–dilaton action of a dynamical holographic AdS/QCD model. The configurational entropy is studied as a function of the glueball spin and of the mass, providing information about the stability of the glueball states.
Power spectrum of the geomagnetic field by the maximum entropy method
International Nuclear Information System (INIS)
Kantor, I.J.; Trivedi, N.B.
1980-01-01
Monthly mean values of Vassouras (state of Rio de Janeiro) geomagnetic field are analyzed us the maximum entropy method. The method is described and compared with other methods of spectral analysis, and its advantages and disadvantages are presented. (Author) [pt
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
Hanel, Rudolf; Thurner, Stefan; Gell-Mann, Murray
2014-05-13
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there has been an ongoing controversy over whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon-Khinchin axioms, the (c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept for nonergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is to our knowledge the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process.
Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains
Cofré, Rodrigo; Maldonado, Cesar
2018-01-01
We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.
Maximum entropy models of ecosystem functioning
International Nuclear Information System (INIS)
Bertram, Jason
2014-01-01
Using organism-level traits to deduce community-level relationships is a fundamental problem in theoretical ecology. This problem parallels the physical one of using particle properties to deduce macroscopic thermodynamic laws, which was successfully achieved with the development of statistical physics. Drawing on this parallel, theoretical ecologists from Lotka onwards have attempted to construct statistical mechanistic theories of ecosystem functioning. Jaynes’ broader interpretation of statistical mechanics, which hinges on the entropy maximisation algorithm (MaxEnt), is of central importance here because the classical foundations of statistical physics do not have clear ecological analogues (e.g. phase space, dynamical invariants). However, models based on the information theoretic interpretation of MaxEnt are difficult to interpret ecologically. Here I give a broad discussion of statistical mechanical models of ecosystem functioning and the application of MaxEnt in these models. Emphasising the sample frequency interpretation of MaxEnt, I show that MaxEnt can be used to construct models of ecosystem functioning which are statistical mechanical in the traditional sense using a savanna plant ecology model as an example
Maximum entropy models of ecosystem functioning
Energy Technology Data Exchange (ETDEWEB)
Bertram, Jason, E-mail: jason.bertram@anu.edu.au [Research School of Biology, The Australian National University, Canberra ACT 0200 (Australia)
2014-12-05
Using organism-level traits to deduce community-level relationships is a fundamental problem in theoretical ecology. This problem parallels the physical one of using particle properties to deduce macroscopic thermodynamic laws, which was successfully achieved with the development of statistical physics. Drawing on this parallel, theoretical ecologists from Lotka onwards have attempted to construct statistical mechanistic theories of ecosystem functioning. Jaynes’ broader interpretation of statistical mechanics, which hinges on the entropy maximisation algorithm (MaxEnt), is of central importance here because the classical foundations of statistical physics do not have clear ecological analogues (e.g. phase space, dynamical invariants). However, models based on the information theoretic interpretation of MaxEnt are difficult to interpret ecologically. Here I give a broad discussion of statistical mechanical models of ecosystem functioning and the application of MaxEnt in these models. Emphasising the sample frequency interpretation of MaxEnt, I show that MaxEnt can be used to construct models of ecosystem functioning which are statistical mechanical in the traditional sense using a savanna plant ecology model as an example.
Tail Risk Constraints and Maximum Entropy
Directory of Open Access Journals (Sweden)
Donald Geman
2015-06-01
Full Text Available Portfolio selection in the financial literature has essentially been analyzed under two central assumptions: full knowledge of the joint probability distribution of the returns of the securities that will comprise the target portfolio; and investors’ preferences are expressed through a utility function. In the real world, operators build portfolios under risk constraints which are expressed both by their clients and regulators and which bear on the maximal loss that may be generated over a given time period at a given confidence level (the so-called Value at Risk of the position. Interestingly, in the finance literature, a serious discussion of how much or little is known from a probabilistic standpoint about the multi-dimensional density of the assets’ returns seems to be of limited relevance. Our approach in contrast is to highlight these issues and then adopt throughout a framework of entropy maximization to represent the real world ignorance of the “true” probability distributions, both univariate and multivariate, of traded securities’ returns. In this setting, we identify the optimal portfolio under a number of downside risk constraints. Two interesting results are exhibited: (i the left- tail constraints are sufficiently powerful to override all other considerations in the conventional theory; (ii the “barbell portfolio” (maximal certainty/ low risk in one set of holdings, maximal uncertainty in another, which is quite familiar to traders, naturally emerges in our construction.
The Maximum Entropy Principle and the Modern Portfolio Theory
Directory of Open Access Journals (Sweden)
Ailton Cassetari
2003-12-01
Full Text Available In this work, a capital allocation methodology base don the Principle of Maximum Entropy was developed. The Shannons entropy is used as a measure, concerning the Modern Portfolio Theory, are also discuted. Particularly, the methodology is tested making a systematic comparison to: 1 the mean-variance (Markovitz approach and 2 the mean VaR approach (capital allocations based on the Value at Risk concept. In principle, such confrontations show the plausibility and effectiveness of the developed method.
Maximum entropy deconvolution of low count nuclear medicine images
International Nuclear Information System (INIS)
McGrath, D.M.
1998-12-01
Maximum entropy is applied to the problem of deconvolving nuclear medicine images, with special consideration for very low count data. The physics of the formation of scintigraphic images is described, illustrating the phenomena which degrade planar estimates of the tracer distribution. Various techniques which are used to restore these images are reviewed, outlining the relative merits of each. The development and theoretical justification of maximum entropy as an image processing technique is discussed. Maximum entropy is then applied to the problem of planar deconvolution, highlighting the question of the choice of error parameters for low count data. A novel iterative version of the algorithm is suggested which allows the errors to be estimated from the predicted Poisson mean values. This method is shown to produce the exact results predicted by combining Poisson statistics and a Bayesian interpretation of the maximum entropy approach. A facility for total count preservation has also been incorporated, leading to improved quantification. In order to evaluate this iterative maximum entropy technique, two comparable methods, Wiener filtering and a novel Bayesian maximum likelihood expectation maximisation technique, were implemented. The comparison of results obtained indicated that this maximum entropy approach may produce equivalent or better measures of image quality than the compared methods, depending upon the accuracy of the system model used. The novel Bayesian maximum likelihood expectation maximisation technique was shown to be preferable over many existing maximum a posteriori methods due to its simplicity of implementation. A single parameter is required to define the Bayesian prior, which suppresses noise in the solution and may reduce the processing time substantially. Finally, maximum entropy deconvolution was applied as a pre-processing step in single photon emission computed tomography reconstruction of low count data. Higher contrast results were
DeVore, Matthew S.; Gull, Stephen F.; Johnson, Carey K.
2013-08-01
We analyzed single molecule FRET burst measurements using Bayesian nested sampling. The MultiNest algorithm produces accurate FRET efficiency distributions from single-molecule data. FRET efficiency distributions recovered by MultiNest and classic maximum entropy are compared for simulated data and for calmodulin labeled at residues 44 and 117. MultiNest compares favorably with maximum entropy analysis for simulated data, judged by the Bayesian evidence. FRET efficiency distributions recovered for calmodulin labeled with two different FRET dye pairs depended on the dye pair and changed upon Ca2+ binding. We also looked at the FRET efficiency distributions of calmodulin bound to the calcium/calmodulin dependent protein kinase II (CaMKII) binding domain. For both dye pairs, the FRET efficiency distribution collapsed to a single peak in the case of calmodulin bound to the CaMKII peptide. These measurements strongly suggest that consideration of dye-protein interactions is crucial in forming an accurate picture of protein conformations from FRET data.
Devore, Matthew S; Gull, Stephen F; Johnson, Carey K
2013-08-30
We analyze single molecule FRET burst measurements using Bayesian nested sampling. The MultiNest algorithm produces accurate FRET efficiency distributions from single-molecule data. FRET efficiency distributions recovered by MultiNest and classic maximum entropy are compared for simulated data and for calmodulin labeled at residues 44 and 117. MultiNest compares favorably with maximum entropy analysis for simulated data, judged by the Bayesian evidence. FRET efficiency distributions recovered for calmodulin labeled with two different FRET dye pairs depended on the dye pair and changed upon Ca 2+ binding. We also looked at the FRET efficiency distributions of calmodulin bound to the calcium/calmodulin dependent protein kinase II (CaMKII) binding domain. For both dye pairs, the FRET efficiency distribution collapsed to a single peak in the case of calmodulin bound to the CaMKII peptide. These measurements strongly suggest that consideration of dye-protein interactions is crucial in forming an accurate picture of protein conformations from FRET data.
Modeling multisite streamflow dependence with maximum entropy copula
Hao, Z.; Singh, V. P.
2013-10-01
Synthetic streamflows at different sites in a river basin are needed for planning, operation, and management of water resources projects. Modeling the temporal and spatial dependence structure of monthly streamflow at different sites is generally required. In this study, the maximum entropy copula method is proposed for multisite monthly streamflow simulation, in which the temporal and spatial dependence structure is imposed as constraints to derive the maximum entropy copula. The monthly streamflows at different sites are then generated by sampling from the conditional distribution. A case study for the generation of monthly streamflow at three sites in the Colorado River basin illustrates the application of the proposed method. Simulated streamflow from the maximum entropy copula is in satisfactory agreement with observed streamflow.
On an Objective Basis for the Maximum Entropy Principle
Directory of Open Access Journals (Sweden)
David J. Miller
2015-01-01
Full Text Available In this letter, we elaborate on some of the issues raised by a recent paper by Neapolitan and Jiang concerning the maximum entropy (ME principle and alternative principles for estimating probabilities consistent with known, measured constraint information. We argue that the ME solution for the “problematic” example introduced by Neapolitan and Jiang has stronger objective basis, rooted in results from information theory, than their alternative proposed solution. We also raise some technical concerns about the Bayesian analysis in their work, which was used to independently support their alternative to the ME solution. The letter concludes by noting some open problems involving maximum entropy statistical inference.
A Maximum Entropy Method for a Robust Portfolio Problem
Directory of Open Access Journals (Sweden)
Yingying Xu
2014-06-01
Full Text Available We propose a continuous maximum entropy method to investigate the robustoptimal portfolio selection problem for the market with transaction costs and dividends.This robust model aims to maximize the worst-case portfolio return in the case that allof asset returns lie within some prescribed intervals. A numerical optimal solution tothe problem is obtained by using a continuous maximum entropy method. Furthermore,some numerical experiments indicate that the robust model in this paper can result in betterportfolio performance than a classical mean-variance model.
Maximum entropy reconstruction of spin densities involving non uniform prior
International Nuclear Information System (INIS)
Schweizer, J.; Ressouche, E.; Papoular, R.J.; Zheludev, A.I.
1997-01-01
Diffraction experiments give microscopic information on structures in crystals. A method which uses the concept of maximum of entropy (MaxEnt), appears to be a formidable improvement in the treatment of diffraction data. This method is based on a bayesian approach: among all the maps compatible with the experimental data, it selects that one which has the highest prior (intrinsic) probability. Considering that all the points of the map are equally probable, this probability (flat prior) is expressed via the Boltzman entropy of the distribution. This method has been used for the reconstruction of charge densities from X-ray data, for maps of nuclear densities from unpolarized neutron data as well as for distributions of spin density. The density maps obtained by this method, as compared to those resulting from the usual inverse Fourier transformation, are tremendously improved. In particular, any substantial deviation from the background is really contained in the data, as it costs entropy compared to a map that would ignore such features. However, in most of the cases, before the measurements are performed, some knowledge exists about the distribution which is investigated. It can range from the simple information of the type of scattering electrons to an elaborate theoretical model. In these cases, the uniform prior which considers all the different pixels as equally likely, is too weak a requirement and has to be replaced. In a rigorous bayesian analysis, Skilling has shown that prior knowledge can be encoded into the Maximum Entropy formalism through a model m(rvec r), via a new definition for the entropy given in this paper. In the absence of any data, the maximum of the entropy functional is reached for ρ(rvec r) = m(rvec r). Any substantial departure from the model, observed in the final map, is really contained in the data as, with the new definition, it costs entropy. This paper presents illustrations of model testing
Rumor Identification with Maximum Entropy in MicroNet
Directory of Open Access Journals (Sweden)
Suisheng Yu
2017-01-01
Full Text Available The widely used applications of Microblog, WeChat, and other social networking platforms (that we call MicroNet shorten the period of information dissemination and expand the range of information dissemination, which allows rumors to cause greater harm and have more influence. A hot topic in the information dissemination field is how to identify and block rumors. Based on the maximum entropy model, this paper constructs the recognition mechanism of rumor information in the micronetwork environment. First, based on the information entropy theory, we obtained the characteristics of rumor information using the maximum entropy model. Next, we optimized the original classifier training set and the feature function to divide the information into rumors and nonrumors. Finally, the experimental simulation results show that the rumor identification results using this method are better than the original classifier and other related classification methods.
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 ...
Gamma-ray spectra deconvolution by maximum-entropy methods
International Nuclear Information System (INIS)
Los Arcos, J.M.
1996-01-01
A maximum-entropy method which includes the response of detectors and the statistical fluctuations of spectra is described and applied to the deconvolution of γ-ray spectra. Resolution enhancement of 25% can be reached for experimental peaks and up to 50% for simulated ones, while the intensities are conserved within 1-2%. (orig.)
The constraint rule of the maximum entropy principle
Uffink, J.
1995-01-01
The principle of maximum entropy is a method for assigning values to probability distributions on the basis of partial information. In usual formulations of this and related methods of inference one assumes that this partial information takes the form of a constraint on allowed probability
Applications of the Maximum Entropy Method in superspace
Czech Academy of Sciences Publication Activity Database
van Smaalen, S.; Palatinus, Lukáš
2004-01-01
Roč. 305, - (2004), s. 57-62 ISSN 0015-0193 Grant - others:DFG and FCI(DE) XX Institutional research plan: CEZ:AV0Z1010914 Keywords : Maximum Entropy Method * modulated structures * charge density Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.517, year: 2004
Maximum entropy estimation via Gauss-LP quadratures
Thély, Maxime; Sutter, Tobias; Mohajerin Esfahani, P.; Lygeros, John; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri
2017-01-01
We present an approximation method to a class of parametric integration problems that naturally appear when solving the dual of the maximum entropy estimation problem. Our method builds up on a recent generalization of Gauss quadratures via an infinite-dimensional linear program, and utilizes a
On the maximum entropy distributions of inherently positive nuclear data
Energy Technology Data Exchange (ETDEWEB)
Taavitsainen, A., E-mail: aapo.taavitsainen@gmail.com; Vanhanen, R.
2017-05-11
The multivariate log-normal distribution is used by many authors and statistical uncertainty propagation programs for inherently positive quantities. Sometimes it is claimed that the log-normal distribution results from the maximum entropy principle, if only means, covariances and inherent positiveness of quantities are known or assumed to be known. In this article we show that this is not true. Assuming a constant prior distribution, the maximum entropy distribution is in fact a truncated multivariate normal distribution – whenever it exists. However, its practical application to multidimensional cases is hindered by lack of a method to compute its location and scale parameters from means and covariances. Therefore, regardless of its theoretical disadvantage, use of other distributions seems to be a practical necessity. - Highlights: • Statistical uncertainty propagation requires a sampling distribution. • The objective distribution of inherently positive quantities is determined. • The objectivity is based on the maximum entropy principle. • The maximum entropy distribution is the truncated normal distribution. • Applicability of log-normal or normal distribution approximation is limited.
Current opinion about maximum entropy methods in Moessbauer spectroscopy
International Nuclear Information System (INIS)
Szymanski, K
2009-01-01
Current opinion about Maximum Entropy Methods in Moessbauer Spectroscopy is presented. The most important advantage offered by the method is the correct data processing under circumstances of incomplete information. Disadvantage is the sophisticated algorithm and its application to the specific problems.
Combining Experiments and Simulations Using the Maximum Entropy Principle
DEFF Research Database (Denmark)
Boomsma, Wouter; Ferkinghoff-Borg, Jesper; Lindorff-Larsen, Kresten
2014-01-01
in the context of a simple example, after which we proceed with a real-world application in the field of molecular simulations, where the maximum entropy procedure has recently provided new insight. Given the limited accuracy of force fields, macromolecular simulations sometimes produce results...
MAXIMUM PRINCIPLE FOR SUBSONIC FLOW WITH VARIABLE ENTROPY
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B. Sizykh Grigory
2017-01-01
Full Text Available Maximum principle for subsonic flow is fair for stationary irrotational subsonic gas flows. According to this prin- ciple, if the value of the velocity is not constant everywhere, then its maximum is achieved on the boundary and only on the boundary of the considered domain. This property is used when designing form of an aircraft with a maximum critical val- ue of the Mach number: it is believed that if the local Mach number is less than unit in the incoming flow and on the body surface, then the Mach number is less then unit in all points of flow. The known proof of maximum principle for subsonic flow is based on the assumption that in the whole considered area of the flow the pressure is a function of density. For the ideal and perfect gas (the role of diffusion is negligible, and the Mendeleev-Clapeyron law is fulfilled, the pressure is a function of density if entropy is constant in the entire considered area of the flow. Shows an example of a stationary sub- sonic irrotational flow, in which the entropy has different values on different stream lines, and the pressure is not a function of density. The application of the maximum principle for subsonic flow with respect to such a flow would be unreasonable. This example shows the relevance of the question about the place of the points of maximum value of the velocity, if the entropy is not a constant. To clarify the regularities of the location of these points, was performed the analysis of the com- plete Euler equations (without any simplifying assumptions in 3-D case. The new proof of the maximum principle for sub- sonic flow was proposed. This proof does not rely on the assumption that the pressure is a function of density. Thus, it is shown that the maximum principle for subsonic flow is true for stationary subsonic irrotational flows of ideal perfect gas with variable entropy.
The Kalman Filter Revisited Using Maximum Relative Entropy
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Adom Giffin
2014-02-01
Full Text Available In 1960, Rudolf E. Kalman created what is known as the Kalman filter, which is a way to estimate unknown variables from noisy measurements. The algorithm follows the logic that if the previous state of the system is known, it could be used as the best guess for the current state. This information is first applied a priori to any measurement by using it in the underlying dynamics of the system. Second, measurements of the unknown variables are taken. These two pieces of information are taken into account to determine the current state of the system. Bayesian inference is specifically designed to accommodate the problem of updating what we think of the world based on partial or uncertain information. In this paper, we present a derivation of the general Bayesian filter, then adapt it for Markov systems. A simple example is shown for pedagogical purposes. We also show that by using the Kalman assumptions or “constraints”, we can arrive at the Kalman filter using the method of maximum (relative entropy (MrE, which goes beyond Bayesian methods. Finally, we derive a generalized, nonlinear filter using MrE, where the original Kalman Filter is a special case. We further show that the variable relationship can be any function, and thus, approximations, such as the extended Kalman filter, the unscented Kalman filter and other Kalman variants are special cases as well.
Akita, Yasuyuki; Chen, Jiu-Chiuan; Serre, Marc L
2012-09-01
Geostatistical methods are widely used in estimating long-term exposures for epidemiological studies on air pollution, despite their limited capabilities to handle spatial non-stationarity over large geographic domains and the uncertainty associated with missing monitoring data. We developed a moving-window (MW) Bayesian maximum entropy (BME) method and applied this framework to estimate fine particulate matter (PM(2.5)) yearly average concentrations over the contiguous US. The MW approach accounts for the spatial non-stationarity, while the BME method rigorously processes the uncertainty associated with data missingness in the air-monitoring system. In the cross-validation analyses conducted on a set of randomly selected complete PM(2.5) data in 2003 and on simulated data with different degrees of missing data, we demonstrate that the MW approach alone leads to at least 17.8% reduction in mean square error (MSE) in estimating the yearly PM(2.5). Moreover, the MWBME method further reduces the MSE by 8.4-43.7%, with the proportion of incomplete data increased from 18.3% to 82.0%. The MWBME approach leads to significant reductions in estimation error and thus is recommended for epidemiological studies investigating the effect of long-term exposure to PM(2.5) across large geographical domains with expected spatial non-stationarity.
Akita, Yasuyuki; Chen, Jiu-Chiuan; Serre, Marc L.
2013-01-01
Geostatistical methods are widely used in estimating long-term exposures for air pollution epidemiological studies, despite their limited capabilities to handle spatial non-stationarity over large geographic domains and uncertainty associated with missing monitoring data. We developed a moving-window (MW) Bayesian Maximum Entropy (BME) method and applied this framework to estimate fine particulate matter (PM2.5) yearly average concentrations over the contiguous U.S. The MW approach accounts for the spatial non-stationarity, while the BME method rigorously processes the uncertainty associated with data missingnees in the air monitoring system. In the cross-validation analyses conducted on a set of randomly selected complete PM2.5 data in 2003 and on simulated data with different degrees of missing data, we demonstrate that the MW approach alone leads to at least 17.8% reduction in mean square error (MSE) in estimating the yearly PM2.5. Moreover, the MWBME method further reduces the MSE by 8.4% to 43.7% with the proportion of incomplete data increased from 18.3% to 82.0%. The MWBME approach leads to significant reductions in estimation error and thus is recommended for epidemiological studies investigating the effect of long-term exposure to PM2.5 across large geographical domains with expected spatial non-stationarity. PMID:22739679
Maximum Entropy Estimation of Transition Probabilities of Reversible Markov Chains
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Erik Van der Straeten
2009-11-01
Full Text Available In this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use one-dimensional classical spin systems to illustrate the theoretical ideas. The examples studied in this paper are: the Ising model, the Potts model and the Blume-Emery-Griffiths model.
Precise charge density studies by maximum entropy method
Takata, M
2003-01-01
For the production research and development of nanomaterials, their structural information is indispensable. Recently, a sophisticated analytical method, which is based on information theory, the Maximum Entropy Method (MEM) using synchrotron radiation powder data, has been successfully applied to determine precise charge densities of metallofullerenes and nanochannel microporous compounds. The results revealed various endohedral natures of metallofullerenes and one-dimensional array formation of adsorbed gas molecules in nanochannel microporous compounds. The concept of MEM analysis was also described briefly. (author)
PNNL: A Supervised Maximum Entropy Approach to Word Sense Disambiguation
Energy Technology Data Exchange (ETDEWEB)
Tratz, Stephen C.; Sanfilippo, Antonio P.; Gregory, Michelle L.; Chappell, Alan R.; Posse, Christian; Whitney, Paul D.
2007-06-23
In this paper, we described the PNNL Word Sense Disambiguation system as applied to the English All-Word task in Se-mEval 2007. We use a supervised learning approach, employing a large number of features and using Information Gain for dimension reduction. Our Maximum Entropy approach combined with a rich set of features produced results that are significantly better than baseline and are the highest F-score for the fined-grained English All-Words subtask.
The maximum entropy method of moments and Bayesian probability theory
Bretthorst, G. Larry
2013-08-01
The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) may be generated. In a given tissue type there is no single intensity that characterizes the tissue, rather there is a distribution of intensities. Often this distributions can be characterized by a Gaussian, but just as often it is much more complicated. Either way, estimating the distribution of intensities is an inference problem. In the case of a Gaussian distribution, one must estimate the mean and standard deviation. However, in the Non-Gaussian case the shape of the density function itself must be inferred. Three common techniques for estimating density functions are binned histograms [1, 2], kernel density estimation [3, 4], and the maximum entropy method of moments [5, 6]. In the introduction, the maximum entropy method of moments will be reviewed. Some of its problems and conditions under which it fails will be discussed. Then in later sections, the functional form of the maximum entropy method of moments probability distribution will be incorporated into Bayesian probability theory. It will be shown that Bayesian probability theory solves all of the problems with the maximum entropy method of moments. One gets posterior probabilities for the Lagrange multipliers, and, finally, one can put error bars on the resulting estimated density function.
Bayesian interpretation of Generalized empirical likelihood by maximum entropy
Rochet , Paul
2011-01-01
We study a parametric estimation problem related to moment condition models. As an alternative to the generalized empirical likelihood (GEL) and the generalized method of moments (GMM), a Bayesian approach to the problem can be adopted, extending the MEM procedure to parametric moment conditions. We show in particular that a large number of GEL estimators can be interpreted as a maximum entropy solution. Moreover, we provide a more general field of applications by proving the method to be rob...
ON A GENERALIZATION OF THE MAXIMUM ENTROPY THEOREM OF BURG
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JOSÉ MARCANO
2017-01-01
Full Text Available In this article we introduce some matrix manipulations that allow us to obtain a version of the original Christoffel-Darboux formula, which is of interest in many applications of linear algebra. Using these developments matrix and Jensen’s inequality, we obtain the main result of this proposal, which is the generalization of the maximum entropy theorem of Burg for multivariate processes.
Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains
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Rodrigo Cofré
2018-01-01
Full Text Available The spiking activity of neuronal networks follows laws that are not time-reversal symmetric; the notion of pre-synaptic and post-synaptic neurons, stimulus correlations and noise correlations have a clear time order. Therefore, a biologically realistic statistical model for the spiking activity should be able to capture some degree of time irreversibility. We use the thermodynamic formalism to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.
Application of the maximum entropy method to dynamical fermion simulations
Clowser, Jonathan
This thesis presents results for spectral functions extracted from imaginary-time correlation functions obtained from Monte Carlo simulations using the Maximum Entropy Method (MEM). The advantages this method are (i) no a priori assumptions or parametrisations of the spectral function are needed, (ii) a unique solution exists and (iii) the statistical significance of the resulting image can be quantitatively analysed. The Gross Neveu model in d = 3 spacetime dimensions (GNM3) is a particularly interesting model to study with the MEM because at T = 0 it has a broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are resonances. Results for the elementary fermion, the Goldstone boson (pion), the sigma, the massive pseudoscalar meson and the symmetric phase resonances are presented. UKQCD Nf = 2 dynamical QCD data is also studied with MEM. Results are compared to those found from the quenched approximation, where the effects of quark loops in the QCD vacuum are neglected, to search for sea-quark effects in the extracted spectral functions. Information has been extract from the difficult axial spatial and scalar as well as the pseudoscalar, vector and axial temporal channels. An estimate for the non-singlet scalar mass in the chiral limit is given which is in agreement with the experimental value of Mao = 985 MeV.
Maximum Entropy and Theory Construction: A Reply to Favretti
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John Harte
2018-04-01
Full Text Available In the maximum entropy theory of ecology (METE, the form of a function describing the distribution of abundances over species and metabolic rates over individuals in an ecosystem is inferred using the maximum entropy inference procedure. Favretti shows that an alternative maximum entropy model exists that assumes the same prior knowledge and makes predictions that differ from METE’s. He shows that both cannot be correct and asserts that his is the correct one because it can be derived from a classic microstate-counting calculation. I clarify here exactly what the core entities and definitions are for METE, and discuss the relevance of two critical issues raised by Favretti: the existence of a counting procedure for microstates and the choices of definition of the core elements of a theory. I emphasize that a theorist controls how the core entities of his or her theory are defined, and that nature is the final arbiter of the validity of a theory.
Hidden states and hidden entropy
International Nuclear Information System (INIS)
Betak, E.
1993-06-01
We study the properties of master equations of the pre-equilibrium exciton model. For the case when the emission is included, we have proved the entropy to be a nondecreasing function of time. The opposite statement in the recent paper of Pan et al. has been caused mainly by neglecting a part of the exciton states. (author). 17 refs
Energy Technology Data Exchange (ETDEWEB)
Papoular, R
1997-07-01
The Fourier Transform is of central importance to Crystallography since it allows the visualization in real space of tridimensional scattering densities pertaining to physical systems from diffraction data (powder or single-crystal diffraction, using x-rays, neutrons, electrons or else). In turn, this visualization makes it possible to model and parametrize these systems, the crystal structures of which are eventually refined by Least-Squares techniques (e.g., the Rietveld method in the case of Powder Diffraction). The Maximum Entropy Method (sometimes called MEM or MaxEnt) is a general imaging technique, related to solving ill-conditioned inverse problems. It is ideally suited for tackling undetermined systems of linear questions (for which the number of variables is much larger than the number of equations). It is already being applied successfully in Astronomy, Radioastronomy and Medical Imaging. The advantages of using MAXIMUM Entropy over conventional Fourier and `difference Fourier` syntheses stem from the following facts: MaxEnt takes the experimental error bars into account; MaxEnt incorporate Prior Knowledge (e.g., the positivity of the scattering density in some instances); MaxEnt allows density reconstructions from incompletely phased data, as well as from overlapping Bragg reflections; MaxEnt substantially reduces truncation errors to which conventional experimental Fourier reconstructions are usually prone. The principles of Maximum Entropy imaging as applied to Crystallography are first presented. The method is then illustrated by a detailed example specific to Neutron Diffraction: the search for proton in solids. (author). 17 refs.
A Maximum Entropy Approach to Loss Distribution Analysis
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Marco Bee
2013-03-01
Full Text Available In this paper we propose an approach to the estimation and simulation of loss distributions based on Maximum Entropy (ME, a non-parametric technique that maximizes the Shannon entropy of the data under moment constraints. Special cases of the ME density correspond to standard distributions; therefore, this methodology is very general as it nests most classical parametric approaches. Sampling the ME distribution is essential in many contexts, such as loss models constructed via compound distributions. Given the difficulties in carrying out exact simulation,we propose an innovative algorithm, obtained by means of an extension of Adaptive Importance Sampling (AIS, for the approximate simulation of the ME distribution. Several numerical experiments confirm that the AIS-based simulation technique works well, and an application to insurance data gives further insights in the usefulness of the method for modelling, estimating and simulating loss distributions.
Application of the maximum entropy production principle to electrical systems
International Nuclear Information System (INIS)
Christen, Thomas
2006-01-01
For a simple class of electrical systems, the principle of the maximum entropy production rate (MaxEP) is discussed. First, we compare the MaxEP principle and the principle of the minimum entropy production rate and illustrate the superiority of the MaxEP principle for the example of two parallel constant resistors. Secondly, we show that the Steenbeck principle for the electric arc as well as the ohmic contact behaviour of space-charge limited conductors follow from the MaxEP principle. In line with work by Dewar, the investigations seem to suggest that the MaxEP principle can also be applied to systems far from equilibrium, provided appropriate information is available that enters the constraints of the optimization problem. Finally, we apply the MaxEP principle to a mesoscopic system and show that the universal conductance quantum, e 2 /h, of a one-dimensional ballistic conductor can be estimated
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).
The mechanics of granitoid systems and maximum entropy production rates.
Hobbs, Bruce E; Ord, Alison
2010-01-13
A model for the formation of granitoid systems is developed involving melt production spatially below a rising isotherm that defines melt initiation. Production of the melt volumes necessary to form granitoid complexes within 10(4)-10(7) years demands control of the isotherm velocity by melt advection. This velocity is one control on the melt flux generated spatially just above the melt isotherm, which is the control valve for the behaviour of the complete granitoid system. Melt transport occurs in conduits initiated as sheets or tubes comprising melt inclusions arising from Gurson-Tvergaard constitutive behaviour. Such conduits appear as leucosomes parallel to lineations and foliations, and ductile and brittle dykes. The melt flux generated at the melt isotherm controls the position of the melt solidus isotherm and hence the physical height of the Transport/Emplacement Zone. A conduit width-selection process, driven by changes in melt viscosity and constitutive behaviour, operates within the Transport Zone to progressively increase the width of apertures upwards. Melt can also be driven horizontally by gradients in topography; these horizontal fluxes can be similar in magnitude to vertical fluxes. Fluxes induced by deformation can compete with both buoyancy and topographic-driven flow over all length scales and results locally in transient 'ponds' of melt. Pluton emplacement is controlled by the transition in constitutive behaviour of the melt/magma from elastic-viscous at high temperatures to elastic-plastic-viscous approaching the melt solidus enabling finite thickness plutons to develop. The system involves coupled feedback processes that grow at the expense of heat supplied to the system and compete with melt advection. The result is that limits are placed on the size and time scale of the system. Optimal characteristics of the system coincide with a state of maximum entropy production rate. This journal is © 2010 The Royal Society
Entanglement entropy of excited states
International Nuclear Information System (INIS)
Alba, Vincenzo; Fagotti, Maurizio; Calabrese, Pasquale
2009-01-01
We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spin chain. For the latter, we developed a numerical application of the algebraic Bethe ansatz. We find two main classes of states with logarithmic and extensive behavior in the dimension of the block, characterized by the properties of excitations of the state. This behavior can be related to the locality properties of the Hamiltonian having a given state as the ground state. We also provide several details of the finite size scaling
Twenty-five years of maximum-entropy principle
Kapur, J. N.
1983-04-01
The strengths and weaknesses of the maximum entropy principle (MEP) are examined and some challenging problems that remain outstanding at the end of the first quarter century of the principle are discussed. The original formalism of the MEP is presented and its relationship to statistical mechanics is set forth. The use of MEP for characterizing statistical distributions, in statistical inference, nonlinear spectral analysis, transportation models, population density models, models for brand-switching in marketing and vote-switching in elections is discussed. Its application to finance, insurance, image reconstruction, pattern recognition, operations research and engineering, biology and medicine, and nonparametric density estimation is considered.
Maximum entropy technique in the doublet structure analysis
International Nuclear Information System (INIS)
Belashev, B.Z.; Panebrattsev, Yu.A.; Shakhaliev, Eh.I.; Soroko, L.M.
1998-01-01
The Maximum Entropy Technique (MENT) for solution of the inverse problems is explained. The effective computer program for resolution of the nonlinear equations system encountered in the MENT has been developed and tested. The possibilities of the MENT have been demonstrated on the example of the MENT in the doublet structure analysis of noisy experimental data. The comparison of the MENT results with results of the Fourier algorithm technique without regularization is presented. The tolerant noise level is equal to 30% for MENT and only 0.1% for the Fourier algorithm
Energy Technology Data Exchange (ETDEWEB)
Kawaguchi, K; Egashira, Y; Watanabe, G [Mazda Motor Corp., Hiroshima (Japan)
1997-10-01
Vehicle and unit performance change according to not only external causes represented by the environment such as temperature or weather, but also internal causes which are dispersion of component characteristics and manufacturing processes or aged deteriorations. We developed the design method to estimate thus performance distributions with maximum entropy method and to calculate specifications with high performance robustness using Fuzzy theory. This paper describes the details of these methods and examples applied to power window system. 3 refs., 7 figs., 4 tabs.
Maximum Entropy Closure of Balance Equations for Miniband Semiconductor Superlattices
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Luis L. Bonilla
2016-07-01
Full Text Available Charge transport in nanosized electronic systems is described by semiclassical or quantum kinetic equations that are often costly to solve numerically and difficult to reduce systematically to macroscopic balance equations for densities, currents, temperatures and other moments of macroscopic variables. The maximum entropy principle can be used to close the system of equations for the moments but its accuracy or range of validity are not always clear. In this paper, we compare numerical solutions of balance equations for nonlinear electron transport in semiconductor superlattices. The equations have been obtained from Boltzmann–Poisson kinetic equations very far from equilibrium for strong fields, either by the maximum entropy principle or by a systematic Chapman–Enskog perturbation procedure. Both approaches produce the same current-voltage characteristic curve for uniform fields. When the superlattices are DC voltage biased in a region where there are stable time periodic solutions corresponding to recycling and motion of electric field pulses, the differences between the numerical solutions produced by numerically solving both types of balance equations are smaller than the expansion parameter used in the perturbation procedure. These results and possible new research venues are discussed.
Maximum entropy networks are more controllable than preferential attachment networks
International Nuclear Information System (INIS)
Hou, Lvlin; Small, Michael; Lao, Songyang
2014-01-01
A maximum entropy (ME) method to generate typical scale-free networks has been recently introduced. We investigate the controllability of ME networks and Barabási–Albert preferential attachment networks. Our experimental results show that ME networks are significantly more easily controlled than BA networks of the same size and the same degree distribution. Moreover, the control profiles are used to provide insight into control properties of both classes of network. We identify and classify the driver nodes and analyze the connectivity of their neighbors. We find that driver nodes in ME networks have fewer mutual neighbors and that their neighbors have lower average degree. We conclude that the properties of the neighbors of driver node sensitively affect the network controllability. Hence, subtle and important structural differences exist between BA networks and typical scale-free networks of the same degree distribution. - Highlights: • The controllability of maximum entropy (ME) and Barabási–Albert (BA) networks is investigated. • ME networks are significantly more easily controlled than BA networks of the same degree distribution. • The properties of the neighbors of driver node sensitively affect the network controllability. • Subtle and important structural differences exist between BA networks and typical scale-free networks
Stimulus-dependent maximum entropy models of neural population codes.
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Einat Granot-Atedgi
Full Text Available Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME model-a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population.
The Structure of the Class of Maximum Tsallis–Havrda–Chavát Entropy Copulas
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Jesús E. García
2016-07-01
Full Text Available A maximum entropy copula is the copula associated with the joint distribution, with prescribed marginal distributions on [ 0 , 1 ] , which maximizes the Tsallis–Havrda–Chavát entropy with q = 2 . We find necessary and sufficient conditions for each maximum entropy copula to be a copula in the class introduced in Rodríguez-Lallena and Úbeda-Flores (2004, and we also show that each copula in that class is a maximum entropy copula.
Applications of the maximum entropy principle in nuclear physics
International Nuclear Information System (INIS)
Froehner, F.H.
1990-01-01
Soon after the advent of information theory the principle of maximum entropy was recognized as furnishing the missing rationale for the familiar rules of classical thermodynamics. More recently it has also been applied successfully in nuclear physics. As an elementary example we derive a physically meaningful macroscopic description of the spectrum of neutrons emitted in nuclear fission, and compare the well known result with accurate data on 252 Cf. A second example, derivation of an expression for resonance-averaged cross sections for nuclear reactions like scattering or fission, is less trivial. Entropy maximization, constrained by given transmission coefficients, yields probability distributions for the R- and S-matrix elements, from which average cross sections can be calculated. If constrained only by the range of the spectrum of compound-nuclear levels it produces the Gaussian Orthogonal Ensemble (GOE) of Hamiltonian matrices that again yields expressions for average cross sections. Both avenues give practically the same numbers in spite of the quite different cross section formulae. These results were employed in a new model-aided evaluation of the 238 U neutron cross sections in the unresolved resonance region. (orig.) [de
LensEnt2: Maximum-entropy weak lens reconstruction
Marshall, P. J.; Hobson, M. P.; Gull, S. F.; Bridle, S. L.
2013-08-01
LensEnt2 is a maximum entropy reconstructor of weak lensing mass maps. The method takes each galaxy shape as an independent estimator of the reduced shear field and incorporates an intrinsic smoothness, determined by Bayesian methods, into the reconstruction. The uncertainties from both the intrinsic distribution of galaxy shapes and galaxy shape estimation are carried through to the final mass reconstruction, and the mass within arbitrarily shaped apertures are calculated with corresponding uncertainties. The input is a galaxy ellipticity catalog with each measured galaxy shape treated as a noisy tracer of the reduced shear field, which is inferred on a fine pixel grid assuming positivity, and smoothness on scales of w arcsec where w is an input parameter. The ICF width w can be chosen by computing the evidence for it.
Venus atmosphere profile from a maximum entropy principle
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L. N. Epele
2007-10-01
Full Text Available The variational method with constraints recently developed by Verkley and Gerkema to describe maximum-entropy atmospheric profiles is generalized to ideal gases but with temperature-dependent specific heats. In so doing, an extended and non standard potential temperature is introduced that is well suited for tackling the problem under consideration. This new formalism is successfully applied to the atmosphere of Venus. Three well defined regions emerge in this atmosphere up to a height of 100 km from the surface: the lowest one up to about 35 km is adiabatic, a transition layer located at the height of the cloud deck and finally a third region which is practically isothermal.
LIBOR troubles: Anomalous movements detection based on maximum entropy
Bariviera, Aurelio F.; Martín, María T.; Plastino, Angelo; Vampa, Victoria
2016-05-01
According to the definition of the London Interbank Offered Rate (LIBOR), contributing banks should give fair estimates of their own borrowing costs in the interbank market. Between 2007 and 2009, several banks made inappropriate submissions of LIBOR, sometimes motivated by profit-seeking from their trading positions. In 2012, several newspapers' articles began to cast doubt on LIBOR integrity, leading surveillance authorities to conduct investigations on banks' behavior. Such procedures resulted in severe fines imposed to involved banks, who recognized their financial inappropriate conduct. In this paper, we uncover such unfair behavior by using a forecasting method based on the Maximum Entropy principle. Our results are robust against changes in parameter settings and could be of great help for market surveillance.
Maximum Entropy and Probability Kinematics Constrained by Conditionals
Directory of Open Access Journals (Sweden)
Stefan Lukits
2015-03-01
Full Text Available Two open questions of inductive reasoning are solved: (1 does the principle of maximum entropy (PME give a solution to the obverse Majerník problem; and (2 isWagner correct when he claims that Jeffrey’s updating principle (JUP contradicts PME? Majerník shows that PME provides unique and plausible marginal probabilities, given conditional probabilities. The obverse problem posed here is whether PME also provides such conditional probabilities, given certain marginal probabilities. The theorem developed to solve the obverse Majerník problem demonstrates that in the special case introduced by Wagner PME does not contradict JUP, but elegantly generalizes it and offers a more integrated approach to probability updating.
A maximum entropy reconstruction technique for tomographic particle image velocimetry
International Nuclear Information System (INIS)
Bilsky, A V; Lozhkin, V A; Markovich, D M; Tokarev, M P
2013-01-01
This paper studies a novel approach for reducing tomographic PIV computational complexity. The proposed approach is an algebraic reconstruction technique, termed MENT (maximum entropy). This technique computes the three-dimensional light intensity distribution several times faster than SMART, using at least ten times less memory. Additionally, the reconstruction quality remains nearly the same as with SMART. This paper presents the theoretical computation performance comparison for MENT, SMART and MART, followed by validation using synthetic particle images. Both the theoretical assessment and validation of synthetic images demonstrate significant computational time reduction. The data processing accuracy of MENT was compared to that of SMART in a slot jet experiment. A comparison of the average velocity profiles shows a high level of agreement between the results obtained with MENT and those obtained with SMART. (paper)
Tsallis distribution as a standard maximum entropy solution with 'tail' constraint
International Nuclear Information System (INIS)
Bercher, J.-F.
2008-01-01
We show that Tsallis' distributions can be derived from the standard (Shannon) maximum entropy setting, by incorporating a constraint on the divergence between the distribution and another distribution imagined as its tail. In this setting, we find an underlying entropy which is the Renyi entropy. Furthermore, escort distributions and generalized means appear as a direct consequence of the construction. Finally, the 'maximum entropy tail distribution' is identified as a Generalized Pareto Distribution
Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings
Yan, Xiaoyong; Minnhagen, Petter
2015-01-01
The word-frequency distribution of a text written by an author is well accounted for by a maximum entropy distribution, the RGF (random group formation)-prediction. The RGF-distribution is completely determined by the a priori values of the total number of words in the text (M), the number of distinct words (N) and the number of repetitions of the most common word (kmax). It is here shown that this maximum entropy prediction also describes a text written in Chinese characters. In particular it is shown that although the same Chinese text written in words and Chinese characters have quite differently shaped distributions, they are nevertheless both well predicted by their respective three a priori characteristic values. It is pointed out that this is analogous to the change in the shape of the distribution when translating a given text to another language. Another consequence of the RGF-prediction is that taking a part of a long text will change the input parameters (M, N, kmax) and consequently also the shape of the frequency distribution. This is explicitly confirmed for texts written in Chinese characters. Since the RGF-prediction has no system-specific information beyond the three a priori values (M, N, kmax), any specific language characteristic has to be sought in systematic deviations from the RGF-prediction and the measured frequencies. One such systematic deviation is identified and, through a statistical information theoretical argument and an extended RGF-model, it is proposed that this deviation is caused by multiple meanings of Chinese characters. The effect is stronger for Chinese characters than for Chinese words. The relation between Zipf’s law, the Simon-model for texts and the present results are discussed. PMID:25955175
Kleidon, Axel
2009-06-01
The Earth system is maintained in a unique state far from thermodynamic equilibrium, as, for instance, reflected in the high concentration of reactive oxygen in the atmosphere. The myriad of processes that transform energy, that result in the motion of mass in the atmosphere, in oceans, and on land, processes that drive the global water, carbon, and other biogeochemical cycles, all have in common that they are irreversible in their nature. Entropy production is a general consequence of these processes and measures their degree of irreversibility. The proposed principle of maximum entropy production (MEP) states that systems are driven to steady states in which they produce entropy at the maximum possible rate given the prevailing constraints. In this review, the basics of nonequilibrium thermodynamics are described, as well as how these apply to Earth system processes. Applications of the MEP principle are discussed, ranging from the strength of the atmospheric circulation, the hydrological cycle, and biogeochemical cycles to the role that life plays in these processes. Nonequilibrium thermodynamics and the MEP principle have potentially wide-ranging implications for our understanding of Earth system functioning, how it has evolved in the past, and why it is habitable. Entropy production allows us to quantify an objective direction of Earth system change (closer to vs further away from thermodynamic equilibrium, or, equivalently, towards a state of MEP). When a maximum in entropy production is reached, MEP implies that the Earth system reacts to perturbations primarily with negative feedbacks. In conclusion, this nonequilibrium thermodynamic view of the Earth system shows great promise to establish a holistic description of the Earth as one system. This perspective is likely to allow us to better understand and predict its function as one entity, how it has evolved in the past, and how it is modified by human activities in the future.
Comparison Between Bayesian and Maximum Entropy Analyses of Flow Networks†
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Steven H. Waldrip
2017-02-01
Full Text Available We compare the application of Bayesian inference and the maximum entropy (MaxEnt method for the analysis of ﬂow networks, such as water, electrical and transport networks. The two methods have the advantage of allowing a probabilistic prediction of ﬂow rates and other variables, when there is insufﬁcient information to obtain a deterministic solution, and also allow the effects of uncertainty to be included. Both methods of inference update a prior to a posterior probability density function (pdf by the inclusion of new information, in the form of data or constraints. The MaxEnt method maximises an entropy function subject to constraints, using the method of Lagrange multipliers,to give the posterior, while the Bayesian method ﬁnds its posterior by multiplying the prior with likelihood functions incorporating the measured data. In this study, we examine MaxEnt using soft constraints, either included in the prior or as probabilistic constraints, in addition to standard moment constraints. We show that when the prior is Gaussian,both Bayesian inference and the MaxEnt method with soft prior constraints give the same posterior means, but their covariances are different. In the Bayesian method, the interactions between variables are applied through the likelihood function, using second or higher-order cross-terms within the posterior pdf. In contrast, the MaxEnt method incorporates interactions between variables using Lagrange multipliers, avoiding second-order correlation terms in the posterior covariance. The MaxEnt method with soft prior constraints, therefore, has a numerical advantage over Bayesian inference, in that the covariance terms are avoided in its integrations. The second MaxEnt method with soft probabilistic constraints is shown to give posterior means of similar, but not identical, structure to the other two methods, due to its different formulation.
A Hybrid Physical and Maximum-Entropy Landslide Susceptibility Model
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Jerry Davis
2015-06-01
Full Text Available The clear need for accurate landslide susceptibility mapping has led to multiple approaches. Physical models are easily interpreted and have high predictive capabilities but rely on spatially explicit and accurate parameterization, which is commonly not possible. Statistical methods can include other factors influencing slope stability such as distance to roads, but rely on good landslide inventories. The maximum entropy (MaxEnt model has been widely and successfully used in species distribution mapping, because data on absence are often uncertain. Similarly, knowledge about the absence of landslides is often limited due to mapping scale or methodology. In this paper a hybrid approach is described that combines the physically-based landslide susceptibility model “Stability INdex MAPping” (SINMAP with MaxEnt. This method is tested in a coastal watershed in Pacifica, CA, USA, with a well-documented landslide history including 3 inventories of 154 scars on 1941 imagery, 142 in 1975, and 253 in 1983. Results indicate that SINMAP alone overestimated susceptibility due to insufficient data on root cohesion. Models were compared using SINMAP stability index (SI or slope alone, and SI or slope in combination with other environmental factors: curvature, a 50-m trail buffer, vegetation, and geology. For 1941 and 1975, using slope alone was similar to using SI alone; however in 1983 SI alone creates an Areas Under the receiver operator Curve (AUC of 0.785, compared with 0.749 for slope alone. In maximum-entropy models created using all environmental factors, the stability index (SI from SINMAP represented the greatest contributions in all three years (1941: 48.1%; 1975: 35.3; and 1983: 48%, with AUC of 0.795, 0822, and 0.859, respectively; however; using slope instead of SI created similar overall AUC values, likely due to the combined effect with plan curvature indicating focused hydrologic inputs and vegetation identifying the effect of root cohesion
Application of Maximum Entropy Distribution to the Statistical Properties of Wave Groups
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFT filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins (1984) with the laboratory wind-wave data show that the former gives a better fit.
Application of the maximum entropy method to profile analysis
International Nuclear Information System (INIS)
Armstrong, N.; Kalceff, W.; Cline, J.P.
1999-01-01
Full text: A maximum entropy (MaxEnt) method for analysing crystallite size- and strain-induced x-ray profile broadening is presented. This method treats the problems of determining the specimen profile, crystallite size distribution, and strain distribution in a general way by considering them as inverse problems. A common difficulty faced by many experimenters is their inability to determine a well-conditioned solution of the integral equation, which preserves the positivity of the profile or distribution. We show that the MaxEnt method overcomes this problem, while also enabling a priori information, in the form of a model, to be introduced into it. Additionally, we demonstrate that the method is fully quantitative, in that uncertainties in the solution profile or solution distribution can be determined and used in subsequent calculations, including mean particle sizes and rms strain. An outline of the MaxEnt method is presented for the specific problems of determining the specimen profile and crystallite or strain distributions for the correspondingly broadened profiles. This approach offers an alternative to standard methods such as those of Williamson-Hall and Warren-Averbach. An application of the MaxEnt method is demonstrated in the analysis of alumina size-broadened diffraction data (from NIST, Gaithersburg). It is used to determine the specimen profile and column-length distribution of the scattering domains. Finally, these results are compared with the corresponding Williamson-Hall and Warren-Averbach analyses. Copyright (1999) Australian X-ray Analytical Association Inc
On the Five-Moment Hamburger Maximum Entropy Reconstruction
Summy, D. P.; Pullin, D. I.
2018-05-01
We consider the Maximum Entropy Reconstruction (MER) as a solution to the five-moment truncated Hamburger moment problem in one dimension. In the case of five monomial moment constraints, the probability density function (PDF) of the MER takes the form of the exponential of a quartic polynomial. This implies a possible bimodal structure in regions of moment space. An analytical model is developed for the MER PDF applicable near a known singular line in a centered, two-component, third- and fourth-order moment (μ _3 , μ _4 ) space, consistent with the general problem of five moments. The model consists of the superposition of a perturbed, centered Gaussian PDF and a small-amplitude packet of PDF-density, called the outlying moment packet (OMP), sitting far from the mean. Asymptotic solutions are obtained which predict the shape of the perturbed Gaussian and both the amplitude and position on the real line of the OMP. The asymptotic solutions show that the presence of the OMP gives rise to an MER solution that is singular along a line in (μ _3 , μ _4 ) space emanating from, but not including, the point representing a standard normal distribution, or thermodynamic equilibrium. We use this analysis of the OMP to develop a numerical regularization of the MER, creating a procedure we call the Hybrid MER (HMER). Compared with the MER, the HMER is a significant improvement in terms of robustness and efficiency while preserving accuracy in its prediction of other important distribution features, such as higher order moments.
Maximum entropy method approach to the θ term
International Nuclear Information System (INIS)
Imachi, Masahiro; Shinno, Yasuhiko; Yoneyama, Hiroshi
2004-01-01
In Monte Carlo simulations of lattice field theory with a θ term, one confronts the complex weight problem, or the sign problem. This is circumvented by performing the Fourier transform of the topological charge distribution P(Q). This procedure, however, causes flattening phenomenon of the free energy f(θ), which makes study of the phase structure unfeasible. In order to treat this problem, we apply the maximum entropy method (MEM) to a Gaussian form of P(Q), which serves as a good example to test whether the MEM can be applied effectively to the θ term. We study the case with flattering as well as that without flattening. In the latter case, the results of the MEM agree with those obtained from the direct application of the Fourier transform. For the former, the MEM gives a smoother f(θ) than that of the Fourier transform. Among various default models investigated, the images which yield the least error do not show flattening, although some others cannot be excluded given the uncertainly related to statistical error. (author)
Using Maximum Entropy to Find Patterns in Genomes
Liu, Sophia; Hockenberry, Adam; Lancichinetti, Andrea; Jewett, Michael; Amaral, Luis
The existence of over- and under-represented sequence motifs in genomes provides evidence of selective evolutionary pressures on biological mechanisms such as transcription, translation, ligand-substrate binding, and host immunity. To accurately identify motifs and other genome-scale patterns of interest, it is essential to be able to generate accurate null models that are appropriate for the sequences under study. There are currently no tools available that allow users to create random coding sequences with specified amino acid composition and GC content. Using the principle of maximum entropy, we developed a method that generates unbiased random sequences with pre-specified amino acid and GC content. Our method is the simplest way to obtain maximally unbiased random sequences that are subject to GC usage and primary amino acid sequence constraints. This approach can also be easily be expanded to create unbiased random sequences that incorporate more complicated constraints such as individual nucleotide usage or even di-nucleotide frequencies. The ability to generate correctly specified null models will allow researchers to accurately identify sequence motifs which will lead to a better understanding of biological processes. National Institute of General Medical Science, Northwestern University Presidential Fellowship, National Science Foundation, David and Lucile Packard Foundation, Camille Dreyfus Teacher Scholar Award.
On the maximum-entropy/autoregressive modeling of time series
Chao, B. F.
1984-01-01
The autoregressive (AR) model of a random process is interpreted in the light of the Prony's relation which relates a complex conjugate pair of poles of the AR process in the z-plane (or the z domain) on the one hand, to the complex frequency of one complex harmonic function in the time domain on the other. Thus the AR model of a time series is one that models the time series as a linear combination of complex harmonic functions, which include pure sinusoids and real exponentials as special cases. An AR model is completely determined by its z-domain pole configuration. The maximum-entropy/autogressive (ME/AR) spectrum, defined on the unit circle of the z-plane (or the frequency domain), is nothing but a convenient, but ambiguous visual representation. It is asserted that the position and shape of a spectral peak is determined by the corresponding complex frequency, and the height of the spectral peak contains little information about the complex amplitude of the complex harmonic functions.
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M. E. Haji Abadi
2013-09-01
Full Text Available In this paper, the continuous optimal control theory is used to model and solve the maximum entropy problem for a continuous random variable. The maximum entropy principle provides a method to obtain least-biased probability density function (Pdf estimation. In this paper, to find a closed form solution for the maximum entropy problem with any number of moment constraints, the entropy is considered as a functional measure and the moment constraints are considered as the state equations. Therefore, the Pdf estimation problem can be reformulated as the optimal control problem. Finally, the proposed method is applied to estimate the Pdf of the hourly electricity prices of New England and Ontario electricity markets. Obtained results show the efficiency of the proposed method.
Multifield stochastic particle production: beyond a maximum entropy ansatz
Energy Technology Data Exchange (ETDEWEB)
Amin, Mustafa A.; Garcia, Marcos A.G.; Xie, Hong-Yi; Wen, Osmond, E-mail: mustafa.a.amin@gmail.com, E-mail: marcos.garcia@rice.edu, E-mail: hxie39@wisc.edu, E-mail: ow4@rice.edu [Physics and Astronomy Department, Rice University, 6100 Main Street, Houston, TX 77005 (United States)
2017-09-01
We explore non-adiabatic particle production for N {sub f} coupled scalar fields in a time-dependent background with stochastically varying effective masses, cross-couplings and intervals between interactions. Under the assumption of weak scattering per interaction, we provide a framework for calculating the typical particle production rates after a large number of interactions. After setting up the framework, for analytic tractability, we consider interactions (effective masses and cross couplings) characterized by series of Dirac-delta functions in time with amplitudes and locations drawn from different distributions. Without assuming that the fields are statistically equivalent, we present closed form results (up to quadratures) for the asymptotic particle production rates for the N {sub f}=1 and N {sub f}=2 cases. We also present results for the general N {sub f} >2 case, but with more restrictive assumptions. We find agreement between our analytic results and direct numerical calculations of the total occupation number of the produced particles, with departures that can be explained in terms of violation of our assumptions. We elucidate the precise connection between the maximum entropy ansatz (MEA) used in Amin and Baumann (2015) and the underlying statistical distribution of the self and cross couplings. We provide and justify a simple to use (MEA-inspired) expression for the particle production rate, which agrees with our more detailed treatment when the parameters characterizing the effective mass and cross-couplings between fields are all comparable to each other. However, deviations are seen when some parameters differ significantly from others. We show that such deviations become negligible for a broad range of parameters when N {sub f}>> 1.
Principle of maximum entropy for reliability analysis in the design of machine components
Zhang, Yimin
2018-03-01
We studied the reliability of machine components with parameters that follow an arbitrary statistical distribution using the principle of maximum entropy (PME). We used PME to select the statistical distribution that best fits the available information. We also established a probability density function (PDF) and a failure probability model for the parameters of mechanical components using the concept of entropy and the PME. We obtained the first four moments of the state function for reliability analysis and design. Furthermore, we attained an estimate of the PDF with the fewest human bias factors using the PME. This function was used to calculate the reliability of the machine components, including a connecting rod, a vehicle half-shaft, a front axle, a rear axle housing, and a leaf spring, which have parameters that typically follow a non-normal distribution. Simulations were conducted for comparison. This study provides a design methodology for the reliability of mechanical components for practical engineering projects.
International Nuclear Information System (INIS)
Banach, Zbigniew; Larecki, Wieslaw
2013-01-01
The spectral formulation of the nine-moment radiation hydrodynamics resulting from using the Boltzmann entropy maximization procedure is considered. The analysis is restricted to the one-dimensional flows of a gas of massless fermions. The objective of the paper is to demonstrate that, for such flows, the spectral nine-moment maximum entropy hydrodynamics of fermionic radiation is not a purely formal theory. We first determine the domains of admissible values of the spectral moments and of the Lagrange multipliers corresponding to them. We then prove the existence of a solution to the constrained entropy optimization problem. Due to the strict concavity of the entropy functional defined on the space of distribution functions, there exists a one-to-one correspondence between the Lagrange multipliers and the moments. The maximum entropy closure of moment equations results in the symmetric conservative system of first-order partial differential equations for the Lagrange multipliers. However, this system can be transformed into the equivalent system of conservation equations for the moments. These two systems are consistent with the additional conservation equation interpreted as the balance of entropy. Exploiting the above facts, we arrive at the differential relations satisfied by the entropy function and the additional function required to close the system of moment equations. We refer to this additional function as the moment closure function. In general, the moment closure and entropy–entropy flux functions cannot be explicitly calculated in terms of the moments determining the state of a gas. Therefore, we develop a perturbation method of calculating these functions. Some additional analytical (and also numerical) results are obtained, assuming that the maximum entropy distribution function tends to the Maxwell–Boltzmann limit. (paper)
Exact Maximum-Entropy Estimation with Feynman Diagrams
Netser Zernik, Amitai; Schlank, Tomer M.; Tessler, Ran J.
2018-02-01
A longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using perturbative Feynman calculus. The explicit expression is given as a sum over weighted trees.
Network Inference and Maximum Entropy Estimation on Information Diagrams
Czech Academy of Sciences Publication Activity Database
Martin, E.A.; Hlinka, J.; Meinke, A.; Děchtěrenko, Filip; Tintěra, J.; Oliver, I.; Davidsen, J.
2017-01-01
Roč. 7, č. 1 (2017), s. 1-15, č. článku 7062. ISSN 2045-2322 R&D Projects: GA ČR GA13-23940S Institutional support: RVO:68081740 Keywords : complex networks * mutual information * entropy maximization * fMRI Subject RIV: AN - Psychology OBOR OECD: Cognitive sciences Impact factor: 4.259, year: 2016
Directory of Open Access Journals (Sweden)
Axel Kleidon
2010-03-01
Full Text Available The Maximum Entropy Production (MEP principle has been remarkably successful in producing accurate predictions for non-equilibrium states. We argue that this is because the MEP principle is an effective inference procedure that produces the best predictions from the available information. Since all Earth system processes are subject to the conservation of energy, mass and momentum, we argue that in practical terms the MEP principle should be applied to Earth system processes in terms of the already established framework of non-equilibrium thermodynamics, with the assumption of local thermodynamic equilibrium at the appropriate scales.
Quantum entropy and uncertainty for two-mode squeezed, coherent and intelligent spin states
Aragone, C.; Mundarain, D.
1993-01-01
We compute the quantum entropy for monomode and two-mode systems set in squeezed states. Thereafter, the quantum entropy is also calculated for angular momentum algebra when the system is either in a coherent or in an intelligent spin state. These values are compared with the corresponding values of the respective uncertainties. In general, quantum entropies and uncertainties have the same minimum and maximum points. However, for coherent and intelligent spin states, it is found that some minima for the quantum entropy turn out to be uncertainty maxima. We feel that the quantum entropy we use provides the right answer, since it is given in an essentially unique way.
Improvement of the detector resolution in X-ray spectrometry by using the maximum entropy method
International Nuclear Information System (INIS)
Fernández, Jorge E.; Scot, Viviana; Giulio, Eugenio Di; Sabbatucci, Lorenzo
2015-01-01
In every X-ray spectroscopy measurement the influence of the detection system causes loss of information. Different mechanisms contribute to form the so-called detector response function (DRF): the detector efficiency, the escape of photons as a consequence of photoelectric or scattering interactions, the spectrum smearing due to the energy resolution, and, in solid states detectors (SSD), the charge collection artifacts. To recover the original spectrum, it is necessary to remove the detector influence by solving the so-called inverse problem. The maximum entropy unfolding technique solves this problem by imposing a set of constraints, taking advantage of the known a priori information and preserving the positive-defined character of the X-ray spectrum. This method has been included in the tool UMESTRAT (Unfolding Maximum Entropy STRATegy), which adopts a semi-automatic strategy to solve the unfolding problem based on a suitable combination of the codes MAXED and GRAVEL, developed at PTB. In the past UMESTRAT proved the capability to resolve characteristic peaks which were revealed as overlapped by a Si SSD, giving good qualitative results. In order to obtain quantitative results, UMESTRAT has been modified to include the additional constraint of the total number of photons of the spectrum, which can be easily determined by inverting the diagonal efficiency matrix. The features of the improved code are illustrated with some examples of unfolding from three commonly used SSD like Si, Ge, and CdTe. The quantitative unfolding can be considered as a software improvement of the detector resolution. - Highlights: • Radiation detection introduces distortions in X- and Gamma-ray spectrum measurements. • UMESTRAT is a graphical tool to unfold X- and Gamma-ray spectra. • UMESTRAT uses the maximum entropy method. • UMESTRAT’s new version produces unfolded spectra with quantitative meaning. • UMESTRAT is a software tool to improve the detector resolution.
Xiao, Ning-Cong; Li, Yan-Feng; Wang, Zhonglai; Peng, Weiwen; Huang, Hong-Zhong
2013-01-01
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 cal...
Unification of field theory and maximum entropy methods for learning probability densities
Kinney, Justin B.
2014-01-01
The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy de...
Predicting the Outcome of NBA Playoffs Based on the Maximum Entropy Principle
Ge Cheng; Zhenyu Zhang; Moses Ntanda Kyebambe; Nasser Kimbugwe
2016-01-01
Predicting the outcome of National Basketball Association (NBA) matches poses a challenging problem of interest to the research community as well as the general public. In this article, we formalize the problem of predicting NBA game results as a classification problem and apply the principle of Maximum Entropy to construct an NBA Maximum Entropy (NBAME) model that fits to discrete statistics for NBA games, and then predict the outcomes of NBA playoffs using the model. Our results reveal that...
Network Inference and Maximum Entropy Estimation on Information Diagrams
Czech Academy of Sciences Publication Activity Database
Martin, E.A.; Hlinka, Jaroslav; Meinke, A.; Děchtěrenko, Filip; Tintěra, J.; Oliver, I.; Davidsen, J.
2017-01-01
Roč. 7, č. 1 (2017), č. článku 7062. ISSN 2045-2322 R&D Projects: GA ČR GA13-23940S; GA MZd(CZ) NV15-29835A Grant - others:GA MŠk(CZ) LO1611 Institutional support: RVO:67985807 Keywords : complex networks * mutual information * entropy maximization * fMRI Subject RIV: BD - Theory of Information OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 4.259, year: 2016
Directory of Open Access Journals (Sweden)
Zhuofei Xu
2017-01-01
Full Text Available Empirical mode decomposition (EMD is a self-adaptive analysis method for nonlinear and nonstationary signals. It has been widely applied to machinery fault diagnosis and structural damage detection. A novel feature, maximum symbolic entropy of intrinsic mode function based on EMD, is proposed to enhance the ability of recognition of EMD in this paper. First, a signal is decomposed into a collection of intrinsic mode functions (IMFs based on the local characteristic time scale of the signal, and then IMFs are transformed into a serious of symbolic sequence with different parameters. Second, it can be found that the entropies of symbolic IMFs are quite different. However, there is always a maximum value for a certain symbolic IMF. Third, take the maximum symbolic entropy as features to describe IMFs from a signal. Finally, the proposed features are applied to evaluate the effect of maximum symbolic entropy in fault diagnosis of rolling bearing, and then the maximum symbolic entropy is compared with other standard time analysis features in a contrast experiment. Although maximum symbolic entropy is only a time domain feature, it can reveal the signal characteristic information accurately. It can also be used in other fields related to EMD method.
Unification of field theory and maximum entropy methods for learning probability densities
Kinney, Justin B.
2015-09-01
The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.
Unification of field theory and maximum entropy methods for learning probability densities.
Kinney, Justin B
2015-09-01
The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.
Entropy Concept for Paramacrosystems with Complex States
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Yuri S. Popkov
2012-05-01
Full Text Available Consideration is given to macrosystems called paramacrosystems with states of finite capacity and distinguishable and undistinguishable elements with stochastic behavior. The paramacrosystems fill a gap between Fermi and Einstein macrosystems. Using the method of the generating functions, we have obtained expressions for probabilistic characteristics (distribution of the macrostate probabilities, physical and information entropies of the paramacrosystems. The cases with equal and unequal prior probabilities for elements to occupy the states with finite capacities are considered. The unequal prior probabilities influence the morphological properties of the entropy functions and the functions of the macrostate probabilities, transforming them in the multimodal functions. The examples of the paramacrosystems with two-modal functions of the entropy and distribution of the macrostate probabilities are presented. The variation principle does not work for such cases.
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S. Pascale
2012-01-01
Full Text Available The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m^{−2} K^{−1} of material entropy production is due to vertical heat transport and 5–7 mW m^{−2} K^{−1} to horizontal heat transport.
Non-equilibrium thermodynamics, maximum entropy production and Earth-system evolution.
Kleidon, Axel
2010-01-13
The present-day atmosphere is in a unique state far from thermodynamic equilibrium. This uniqueness is for instance reflected in the high concentration of molecular oxygen and the low relative humidity in the atmosphere. Given that the concentration of atmospheric oxygen has likely increased throughout Earth-system history, we can ask whether this trend can be generalized to a trend of Earth-system evolution that is directed away from thermodynamic equilibrium, why we would expect such a trend to take place and what it would imply for Earth-system evolution as a whole. The justification for such a trend could be found in the proposed general principle of maximum entropy production (MEP), which states that non-equilibrium thermodynamic systems maintain steady states at which entropy production is maximized. Here, I justify and demonstrate this application of MEP to the Earth at the planetary scale. I first describe the non-equilibrium thermodynamic nature of Earth-system processes and distinguish processes that drive the system's state away from equilibrium from those that are directed towards equilibrium. I formulate the interactions among these processes from a thermodynamic perspective and then connect them to a holistic view of the planetary thermodynamic state of the Earth system. In conclusion, non-equilibrium thermodynamics and MEP have the potential to provide a simple and holistic theory of Earth-system functioning. This theory can be used to derive overall evolutionary trends of the Earth's past, identify the role that life plays in driving thermodynamic states far from equilibrium, identify habitability in other planetary environments and evaluate human impacts on Earth-system functioning. This journal is © 2010 The Royal Society
Maximum Entropy Methods as the Bridge Between Microscopic and Macroscopic Theory
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.
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.
Maximum-entropy networks pattern detection, network reconstruction and graph combinatorics
Squartini, Tiziano
2017-01-01
This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties. After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem o...
A Bayes-Maximum Entropy method for multi-sensor data fusion
Energy Technology Data Exchange (ETDEWEB)
Beckerman, M.
1991-01-01
In this paper we introduce a Bayes-Maximum Entropy formalism for multi-sensor data fusion, and present an application of this methodology to the fusion of ultrasound and visual sensor data as acquired by a mobile robot. In our approach the principle of maximum entropy is applied to the construction of priors and likelihoods from the data. Distances between ultrasound and visual points of interest in a dual representation are used to define Gibbs likelihood distributions. Both one- and two-dimensional likelihoods are presented, and cast into a form which makes explicit their dependence upon the mean. The Bayesian posterior distributions are used to test a null hypothesis, and Maximum Entropy Maps used for navigation are updated using the resulting information from the dual representation. 14 refs., 9 figs.
On some problems of the maximum entropy ansatz
Indian Academy of Sciences (India)
Pilot calculations involving the ground quantum eigenenergy states of the quartic ... well-defined (finite) values for all its moments, e.g. a Lorentzian. Further, in practice, it is .... to test the degree of accuracy of p (m). Here μТ and μТ refer, ...
A Novel Maximum Entropy Markov Model for Human Facial Expression Recognition.
Directory of Open Access Journals (Sweden)
Muhammad Hameed Siddiqi
Full Text Available Research in video based FER systems has exploded in the past decade. However, most of the previous methods work well when they are trained and tested on the same dataset. Illumination settings, image resolution, camera angle, and physical characteristics of the people differ from one dataset to another. Considering a single dataset keeps the variance, which results from differences, to a minimum. Having a robust FER system, which can work across several datasets, is thus highly desirable. The aim of this work is to design, implement, and validate such a system using different datasets. In this regard, the major contribution is made at the recognition module which uses the maximum entropy Markov model (MEMM for expression recognition. In this model, the states of the human expressions are modeled as the states of an MEMM, by considering the video-sensor observations as the observations of MEMM. A modified Viterbi is utilized to generate the most probable expression state sequence based on such observations. Lastly, an algorithm is designed which predicts the expression state from the generated state sequence. Performance is compared against several existing state-of-the-art FER systems on six publicly available datasets. A weighted average accuracy of 97% is achieved across all datasets.
Maximum non-extensive entropy block bootstrap for non-stationary processes
Czech Academy of Sciences Publication Activity Database
Bergamelli, M.; Novotný, Jan; Urga, G.
2015-01-01
Roč. 91, 1/2 (2015), s. 115-139 ISSN 0001-771X R&D Projects: GA ČR(CZ) GA14-27047S Institutional support: RVO:67985998 Keywords : maximum entropy * bootstrap * Monte Carlo simulations Subject RIV: AH - Economics
Brus, D.J.; Bogaert, P.; Heuvelink, G.B.M.
2008-01-01
Bayesian Maximum Entropy was used to estimate the probabilities of occurrence of soil categories in the Netherlands, and to simulate realizations from the associated multi-point pdf. Besides the hard observations (H) of the categories at 8369 locations, the soil map of the Netherlands 1:50 000 was
Using maximum entropy modeling to identify and prioritize red spruce forest habitat in West Virginia
Nathan R. Beane; James S. Rentch; Thomas M. Schuler
2013-01-01
Red spruce forests in West Virginia are found in island-like distributions at high elevations and provide essential habitat for the endangered Cheat Mountain salamander and the recently delisted Virginia northern flying squirrel. Therefore, it is important to identify restoration priorities of red spruce forests. Maximum entropy modeling was used to identify areas of...
Critical Analysis of Non-Nuclear Electron-Density Maxima and the Maximum Entropy Method
de Vries, R.Y.; Briels, Willem J.; Feil, D.; Feil, D.
1996-01-01
Experimental evidence for the existence of non-nuclear maxima in charge densities is questioned. It is shown that the non-nuclear maxima reported for silicon are artifacts of the maximum entropy method that was used to analyze the x-ray diffraction data. This method can be improved by the use of
Deconvolution in the presence of noise using the Maximum Entropy Principle
International Nuclear Information System (INIS)
Steenstrup, S.
1984-01-01
The main problem in deconvolution in the presence of noise is the nonuniqueness. This problem is overcome by the application of the Maximum Entropy Principle. The way the noise enters in the formulation of the problem is examined in some detail and the final equations are derived such that the necessary assumptions becomes explicit. Examples using X-ray diffraction data are shown. (orig.)
Uncertainty estimation of the self-thinning process by Maximum-Entropy Principle
Shoufan Fang; George Z. Gertner
2000-01-01
When available information is scarce, the Maximum-Entropy Principle can estimate the distributions of parameters. In our case study, we estimated the distributions of the parameters of the forest self-thinning process based on literature information, and we derived the conditional distribution functions and estimated the 95 percent confidence interval (CI) of the self-...
Comparison of tomography reconstruction by maximum entropy and filtered retro projection
International Nuclear Information System (INIS)
Abdala, F.J.P.; Simpson, D.M.; Roberty, N.C.
1992-01-01
The tomographic reconstruction with few projections is studied, comparing the maximum entropy method with filtered retro projection. Simulations with and without the presence of noise and also with the presence of an object of high density inside of the skull are showed. (C.G.C.)
Czech Academy of Sciences Publication Activity Database
Palatinus, Lukáš; Amami, M.; van Smaalen, S.
2004-01-01
Roč. 60, - (2004), s. 127-137 ISSN 0108-7681 Grant - others:DFG(DE) XX Institutional research plan: CEZ:AV0Z1010914 Keywords : incommensurate modulation * superspace * maximum entropy method Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 5.418, year: 2004
Incommensurate modulations made visible by the Maximum Entropy Method in superspace
Czech Academy of Sciences Publication Activity Database
Palatinus, Lukáš; van Smaalen, S.
2004-01-01
Roč. 219, - (2004), s. 719-729 ISSN 0044-2968 Grant - others:DFG(DE) XX Institutional research plan: CEZ:AV0Z1010914 Keywords : Maximum Entropy Method * modulated structures * charge density Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.390, year: 2004
The prior-derived F constraints in the maximum-entropy method
Czech Academy of Sciences Publication Activity Database
Palatinus, Lukáš; van Smaalen, S.
2005-01-01
Roč. 61, - (2005), s. 363-372 ISSN 0108-7673 Institutional research plan: CEZ:AV0Z10100521 Keywords : charge density * maximum-entropy method * sodium nitrite Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.791, year: 2005
The generalized F constraint in the maximum-entropy method - a study on simulated data
Czech Academy of Sciences Publication Activity Database
Palatinus, Lukáš; van Smaalen, S.
2002-01-01
Roč. 58, - (2002), s. 559-567 ISSN 0108-7673 Grant - others:DFG(DE) XX Institutional research plan: CEZ:AV0Z1010914 Keywords : maximum-entropy method * electron density * oxalic acid Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.417, year: 2002
Can the maximum entropy principle be explained as a consistency requirement?
Uffink, J.
1997-01-01
The principle of maximum entropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in
Application of the Maximum Entropy Method to Risk Analysis of Mergers and Acquisitions
Xie, Jigang; Song, Wenyun
The maximum entropy (ME) method can be used to analyze the risk of mergers and acquisitions when only pre-acquisition information is available. A practical example of the risk analysis of China listed firms’ mergers and acquisitions is provided to testify the feasibility and practicality of the method.
Reinterpreting maximum entropy in ecology: a null hypothesis constrained by ecological mechanism.
O'Dwyer, James P; Rominger, Andrew; Xiao, Xiao
2017-07-01
Simplified mechanistic models in ecology have been criticised for the fact that a good fit to data does not imply the mechanism is true: pattern does not equal process. In parallel, the maximum entropy principle (MaxEnt) has been applied in ecology to make predictions constrained by just a handful of state variables, like total abundance or species richness. But an outstanding question remains: what principle tells us which state variables to constrain? Here we attempt to solve both problems simultaneously, by translating a given set of mechanisms into the state variables to be used in MaxEnt, and then using this MaxEnt theory as a null model against which to compare mechanistic predictions. In particular, we identify the sufficient statistics needed to parametrise a given mechanistic model from data and use them as MaxEnt constraints. Our approach isolates exactly what mechanism is telling us over and above the state variables alone. © 2017 John Wiley & Sons Ltd/CNRS.
Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics
Abe, Sumiyoshi
2014-11-01
The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach to systems governed by dynamics with largely separated time scales and is based on three key concepts: conjugate pairs of variables, dimensionless integration measures with coarse-graining factors and partial maximization of the joint entropy. The method enables one to calculate a prior purely from a likelihood in a simple way. It is shown, in particular, how it not only yields Jeffreys's rules but also reveals new structures hidden behind them.
Predicting the Outcome of NBA Playoffs Based on the Maximum Entropy Principle
Directory of Open Access Journals (Sweden)
Ge Cheng
2016-12-01
Full Text Available Predicting the outcome of National Basketball Association (NBA matches poses a challenging problem of interest to the research community as well as the general public. In this article, we formalize the problem of predicting NBA game results as a classification problem and apply the principle of Maximum Entropy to construct an NBA Maximum Entropy (NBAME model that fits to discrete statistics for NBA games, and then predict the outcomes of NBA playoffs using the model. Our results reveal that the model is able to predict the winning team with 74.4% accuracy, outperforming other classical machine learning algorithms that could only afford a maximum prediction accuracy of 70.6% in the experiments that we performed.
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.
International Nuclear Information System (INIS)
Chavanis, Pierre-Henri
2014-01-01
In the context of two-dimensional (2D) turbulence, we apply the maximum entropy production principle (MEPP) by enforcing a local conservation of energy. This leads to an equation for the vorticity distribution that conserves all the Casimirs, the energy, and that increases monotonically the mixing entropy (H-theorem). Furthermore, the equation for the coarse-grained vorticity dissipates monotonically all the generalized enstrophies. These equations may provide a parametrization of 2D turbulence. They do not generally relax towards the maximum entropy state. The vorticity current vanishes for any steady state of the 2D Euler equation. Interestingly, the equation for the coarse-grained vorticity obtained from the MEPP turns out to coincide, after some algebraic manipulations, with the one obtained with the anticipated vorticity method. This shows a connection between these two approaches when the conservation of energy is treated locally. Furthermore, the newly derived equation, which incorporates a diffusion term and a drift term, has a nice physical interpretation in terms of a selective decay principle. This sheds new light on both the MEPP and the anticipated vorticity method. (paper)
Relative entropy as a measure of entanglement for Gaussian states
Institute of Scientific and Technical Information of China (English)
Lu Huai-Xin; Zhao Bo
2006-01-01
In this paper, we derive an explicit analytic expression of the relative entropy between two general Gaussian states. In the restriction of the set for Gaussian states and with the help of relative entropy formula and Peres-Simon separability criterion, one can conveniently obtain the relative entropy entanglement for Gaussian states. As an example,the relative entanglement for a two-mode squeezed thermal state has been obtained.
Takahashi, Osamu; Nomura, Tetsuo; Tabayashi, Kiyohiko; Yamasaki, Katsuyoshi
2008-07-01
We performed spectral analysis by using the maximum entropy method instead of the traditional Fourier transform technique to investigate the short-time behavior in molecular systems, such as the energy transfer between vibrational modes and chemical reactions. This procedure was applied to direct ab initio molecular dynamics calculations for the decomposition of formic acid. More reactive trajectories of dehydrolation than those of decarboxylation were obtained for Z-formic acid, which was consistent with the prediction of previous theoretical and experimental studies. Short-time maximum entropy method analyses were performed for typical reactive and non-reactive trajectories. Spectrograms of a reactive trajectory were obtained; these clearly showed the reactant, transient, and product regions, especially for the dehydrolation path.
Directory of Open Access Journals (Sweden)
Nicholas Scott Cardell
2013-05-01
Full Text Available Maximum entropy methods of parameter estimation are appealing because they impose no additional structure on the data, other than that explicitly assumed by the analyst. In this paper we prove that the data constrained GME estimator of the general linear model is consistent and asymptotically normal. The approach we take in establishing the asymptotic properties concomitantly identifies a new computationally efficient method for calculating GME estimates. Formulae are developed to compute asymptotic variances and to perform Wald, likelihood ratio, and Lagrangian multiplier statistical tests on model parameters. Monte Carlo simulations are provided to assess the performance of the GME estimator in both large and small sample situations. Furthermore, we extend our results to maximum cross-entropy estimators and indicate a variant of the GME estimator that is unbiased. Finally, we discuss the relationship of GME estimators to Bayesian estimators, pointing out the conditions under which an unbiased GME estimator would be efficient.
Derivation of some new distributions in statistical mechanics using maximum entropy approach
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Ray Amritansu
2014-01-01
Full Text Available The maximum entropy principle has been earlier used to derive the Bose Einstein(B.E., Fermi Dirac(F.D. & Intermediate Statistics(I.S. distribution of statistical mechanics. The central idea of these distributions is to predict the distribution of the microstates, which are the particle of the system, on the basis of the knowledge of some macroscopic data. The latter information is specified in the form of some simple moment constraints. One distribution differs from the other in the way in which the constraints are specified. In the present paper, we have derived some new distributions similar to B.E., F.D. distributions of statistical mechanics by using maximum entropy principle. Some proofs of B.E. & F.D. distributions are shown, and at the end some new results are discussed.
Inferring Pairwise Interactions from Biological Data Using Maximum-Entropy Probability Models.
Directory of Open Access Journals (Sweden)
Richard R Stein
2015-07-01
Full Text Available Maximum entropy-based inference methods have been successfully used to infer direct interactions from biological datasets such as gene expression data or sequence ensembles. Here, we review undirected pairwise maximum-entropy probability models in two categories of data types, those with continuous and categorical random variables. As a concrete example, we present recently developed inference methods from the field of protein contact prediction and show that a basic set of assumptions leads to similar solution strategies for inferring the model parameters in both variable types. These parameters reflect interactive couplings between observables, which can be used to predict global properties of the biological system. Such methods are applicable to the important problems of protein 3-D structure prediction and association of gene-gene networks, and they enable potential applications to the analysis of gene alteration patterns and to protein design.
On the maximum-entropy method for kinetic equation of radiation, particle and gas
International Nuclear Information System (INIS)
El-Wakil, S.A.; Madkour, M.A.; Degheidy, A.R.; Machali, H.M.
1995-01-01
The maximum-entropy approach is used to calculate some problems in radiative transfer and reactor physics such as the escape probability, the emergent and transmitted intensities for a finite slab as well as the emergent intensity for a semi-infinite medium. Also, it is employed to solve problems involving spherical geometry, such as luminosity (the total energy emitted by a sphere), neutron capture probability and the albedo problem. The technique is also employed in the kinetic theory of gases to calculate the Poiseuille flow and thermal creep of a rarefied gas between two plates. Numerical calculations are achieved and compared with the published data. The comparisons demonstrate that the maximum-entropy results are good in agreement with the exact ones. (orig.)
Comments on a derivation and application of the 'maximum entropy production' principle
International Nuclear Information System (INIS)
Grinstein, G; Linsker, R
2007-01-01
We show that (1) an error invalidates the derivation (Dewar 2005 J. Phys. A: Math. Gen. 38 L371) of the maximum entropy production (MaxEP) principle for systems far from equilibrium, for which the constitutive relations are nonlinear; and (2) the claim (Dewar 2003 J. Phys. A: Math. Gen. 36 631) that the phenomenon of 'self-organized criticality' is a consequence of MaxEP for slowly driven systems is unjustified. (comment)
Hydrodynamic equations for electrons in graphene obtained from the maximum entropy principle
Energy Technology Data Exchange (ETDEWEB)
Barletti, Luigi, E-mail: luigi.barletti@unifi.it [Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze (Italy)
2014-08-15
The maximum entropy principle is applied to the formal derivation of isothermal, Euler-like equations for semiclassical fermions (electrons and holes) in graphene. After proving general mathematical properties of the equations so obtained, their asymptotic form corresponding to significant physical regimes is investigated. In particular, the diffusive regime, the Maxwell-Boltzmann regime (high temperature), the collimation regime and the degenerate gas limit (vanishing temperature) are considered.
Bistability, non-ergodicity, and inhibition in pairwise maximum-entropy models.
Rostami, Vahid; Porta Mana, PierGianLuca; Grün, Sonja; Helias, Moritz
2017-10-01
Pairwise maximum-entropy models have been used in neuroscience to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, would produce a bimodal distribution for the population-averaged activity, and for some population sizes the second mode would peak at high activities, that experimentally would be equivalent to 90% of the neuron population active within time-windows of few milliseconds. Several problems are connected with this bimodality: 1. The presence of the high-activity mode is unrealistic in view of observed neuronal activity and on neurobiological grounds. 2. Boltzmann learning becomes non-ergodic, hence the pairwise maximum-entropy distribution cannot be found: in fact, Boltzmann learning would produce an incorrect distribution; similarly, common variants of mean-field approximations also produce an incorrect distribution. 3. The Glauber dynamics associated with the model is unrealistically bistable and cannot be used to generate realistic surrogate data. This bimodality problem is first demonstrated for an experimental dataset from 159 neurons in the motor cortex of macaque monkey. Evidence is then provided that this problem affects typical neural recordings of population sizes of a couple of hundreds or more neurons. The cause of the bimodality problem is identified as the inability of standard maximum-entropy distributions with a uniform reference measure to model neuronal inhibition. To eliminate this problem a modified maximum-entropy model is presented, which reflects a basic effect of inhibition in the form of a simple but non-uniform reference measure. This model does not lead to unrealistic bimodalities, can be found with Boltzmann learning, and has an associated Glauber dynamics which incorporates a minimal asymmetric inhibition.
Reconstruction of the electron momentum density distribution by the maximum entropy method
International Nuclear Information System (INIS)
Dobrzynski, L.
1996-01-01
The application of the Maximum Entropy Algorithm to the analysis of the Compton profiles is discussed. It is shown that the reconstruction of electron momentum density may be reliably carried out. However, there are a number of technical problems which have to be overcome in order to produce trustworthy results. In particular one needs the experimental Compton profiles measured for many directions, and to have efficient computational resources. The use of various cross-checks is recommended. (orig.)
Use of the maximum entropy method in X-ray astronomy
International Nuclear Information System (INIS)
Willingale, R.
1981-01-01
An algorithm used to apply the maximum entropy method in X-ray astronomy is described. It is easy to programme on a digital computer and fast enough to allow processing of two-dimensional images. The method gives good noise suppression without loss of instrumental resolution and has been successfully applied to several data analysis problems in X-ray astronomy. The restoration of a high-resolution image from the Einstein Observatory demonstrates the use of the algorithm. (author)
International Nuclear Information System (INIS)
Bastiens, K.; Lemahieu, I.
1994-01-01
The application of a maximum entropy reconstruction algorithm to PET images requires a lot of computing resources. A parallel implementation could seriously reduce the execution time. However, programming a parallel application is still a non trivial task, needing specialized people. In this paper a programming environment based on a visual programming language is used for a parallel implementation of the reconstruction algorithm. This programming environment allows less experienced programmers to use the performance of multiprocessor systems. (authors)
Energy Technology Data Exchange (ETDEWEB)
Bastiens, K; Lemahieu, I [University of Ghent - ELIS Department, St. Pietersnieuwstraat 41, B-9000 Ghent (Belgium)
1994-12-31
The application of a maximum entropy reconstruction algorithm to PET images requires a lot of computing resources. A parallel implementation could seriously reduce the execution time. However, programming a parallel application is still a non trivial task, needing specialized people. In this paper a programming environment based on a visual programming language is used for a parallel implementation of the reconstruction algorithm. This programming environment allows less experienced programmers to use the performance of multiprocessor systems. (authors). 8 refs, 3 figs, 1 tab.
Maximum entropy restoration of laser fusion target x-ray photographs
International Nuclear Information System (INIS)
Brolley, J.E.; Lazarus, R.B.; Suydam, B.R.
1976-01-01
Maximum entropy principles were used to analyze the microdensitometer traces of a laser-fusion target photograph. The object is a glowing laser-fusion target microsphere 0.95 cm from a pinhole of radius 2 x 10 -4 cm, the image is 7.2 cm from the pinhole and the photon wavelength is likely to be 6.2 x 10 -8 cm. Some computational aspects of the problem are also considered
L. Jubair Ahmed; A. Ebenezer Jeyakumar
2013-01-01
Thresholding is one of the most important techniques for performing image segmentation. In this paper to compute optimum thresholds for Maximum Tsallis entropy thresholding (MTET) model, a new hybrid algorithm is proposed by integrating the Comprehensive Learning Particle Swarm Optimizer (CPSO) with the Powell’s Conjugate Gradient (PCG) method. Here the CPSO will act as the main optimizer for searching the near-optimal thresholds while the PCG method will be used to fine tune the best solutio...
Maximum Entropy Method in Moessbauer Spectroscopy - a Problem of Magnetic Texture
International Nuclear Information System (INIS)
Satula, D.; Szymanski, K.; Dobrzynski, L.
2011-01-01
A reconstruction of the three dimensional distribution of the hyperfine magnetic field, isomer shift and texture parameter z from the Moessbauer spectra by the maximum entropy method is presented. The method was tested on the simulated spectrum consisting of two Gaussian hyperfine field distributions with different values of the texture parameters. It is shown that proper prior has to be chosen in order to arrive at the physically meaningful results. (authors)
Lattice Field Theory with the Sign Problem and the Maximum Entropy Method
Directory of Open Access Journals (Sweden)
Masahiro Imachi
2007-02-01
Full Text Available Although numerical simulation in lattice field theory is one of the most effective tools to study non-perturbative properties of field theories, it faces serious obstacles coming from the sign problem in some theories such as finite density QCD and lattice field theory with the θ term. We reconsider this problem from the point of view of the maximum entropy method.
Kleidon, A.
2010-01-01
The Earth system is remarkably different from its planetary neighbours in that it shows pronounced, strong global cycling of matter. These global cycles result in the maintenance of a unique thermodynamic state of the Earth's atmosphere which is far from thermodynamic equilibrium (TE). Here, I provide a simple introduction of the thermodynamic basis to understand why Earth system processes operate so far away from TE. I use a simple toy model to illustrate the application of non-equilibrium thermodynamics and to classify applications of the proposed principle of maximum entropy production (MEP) to such processes into three different cases of contrasting flexibility in the boundary conditions. I then provide a brief overview of the different processes within the Earth system that produce entropy, review actual examples of MEP in environmental and ecological systems, and discuss the role of interactions among dissipative processes in making boundary conditions more flexible. I close with a brief summary and conclusion. PMID:20368248
Kleidon, A
2010-05-12
The Earth system is remarkably different from its planetary neighbours in that it shows pronounced, strong global cycling of matter. These global cycles result in the maintenance of a unique thermodynamic state of the Earth's atmosphere which is far from thermodynamic equilibrium (TE). Here, I provide a simple introduction of the thermodynamic basis to understand why Earth system processes operate so far away from TE. I use a simple toy model to illustrate the application of non-equilibrium thermodynamics and to classify applications of the proposed principle of maximum entropy production (MEP) to such processes into three different cases of contrasting flexibility in the boundary conditions. I then provide a brief overview of the different processes within the Earth system that produce entropy, review actual examples of MEP in environmental and ecological systems, and discuss the role of interactions among dissipative processes in making boundary conditions more flexible. I close with a brief summary and conclusion.
Using maximum entropy modeling for optimal selection of sampling sites for monitoring networks
Stohlgren, Thomas J.; Kumar, Sunil; Barnett, David T.; Evangelista, Paul H.
2011-01-01
Environmental monitoring programs must efficiently describe state shifts. We propose using maximum entropy modeling to select dissimilar sampling sites to capture environmental variability at low cost, and demonstrate a specific application: sample site selection for the Central Plains domain (453,490 km2) of the National Ecological Observatory Network (NEON). We relied on four environmental factors: mean annual temperature and precipitation, elevation, and vegetation type. A “sample site” was defined as a 20 km × 20 km area (equal to NEON’s airborne observation platform [AOP] footprint), within which each 1 km2 cell was evaluated for each environmental factor. After each model run, the most environmentally dissimilar site was selected from all potential sample sites. The iterative selection of eight sites captured approximately 80% of the environmental envelope of the domain, an improvement over stratified random sampling and simple random designs for sample site selection. This approach can be widely used for cost-efficient selection of survey and monitoring sites.
Liu, Jian; Miller, William H
2008-09-28
The maximum entropy analytic continuation (MEAC) method is used to extend the range of accuracy of the linearized semiclassical initial value representation (LSC-IVR)/classical Wigner approximation for real time correlation functions. LSC-IVR provides a very effective "prior" for the MEAC procedure since it is very good for short times, exact for all time and temperature for harmonic potentials (even for correlation functions of nonlinear operators), and becomes exact in the classical high temperature limit. This combined MEAC+LSC/IVR approach is applied here to two highly nonlinear dynamical systems, a pure quartic potential in one dimensional and liquid para-hydrogen at two thermal state points (25 and 14 K under nearly zero external pressure). The former example shows the MEAC procedure to be a very significant enhancement of the LSC-IVR for correlation functions of both linear and nonlinear operators, and especially at low temperature where semiclassical approximations are least accurate. For liquid para-hydrogen, the LSC-IVR is seen already to be excellent at T=25 K, but the MEAC procedure produces a significant correction at the lower temperature (T=14 K). Comparisons are also made as to how the MEAC procedure is able to provide corrections for other trajectory-based dynamical approximations when used as priors.
Roostaee, M.; Deng, Z.
2017-12-01
The states' environmental agencies are required by The Clean Water Act to assess all waterbodies and evaluate potential sources of impairments. Spatial and temporal distributions of water quality parameters are critical in identifying Critical Source Areas (CSAs). However, due to limitations in monetary resources and a large number of waterbodies, available monitoring stations are typically sparse with intermittent periods of data collection. Hence, scarcity of water quality data is a major obstacle in addressing sources of pollution through management strategies. In this study spatiotemporal Bayesian Maximum Entropy method (BME) is employed to model the inherent temporal and spatial variability of measured water quality indicators such as Dissolved Oxygen (DO) concentration for Turkey Creek Watershed. Turkey Creek is located in northern Louisiana and has been listed in 303(d) list for DO impairment since 2014 in Louisiana Water Quality Inventory Reports due to agricultural practices. BME method is proved to provide more accurate estimates than the methods of purely spatial analysis by incorporating space/time distribution and uncertainty in available measured soft and hard data. This model would be used to estimate DO concentration at unmonitored locations and times and subsequently identifying CSAs. The USDA's crop-specific land cover data layers of the watershed were then used to determine those practices/changes that led to low DO concentration in identified CSAs. Primary results revealed that cultivation of corn and soybean as well as urban runoff are main contributing sources in low dissolved oxygen in Turkey Creek Watershed.
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
Mixed memory, (non) Hurst effect, and maximum entropy of rainfall in the tropical Andes
Poveda, Germán
2011-02-01
Diverse linear and nonlinear statistical parameters of rainfall under aggregation in time and the kind of temporal memory are investigated. Data sets from the Andes of Colombia at different resolutions (15 min and 1-h), and record lengths (21 months and 8-40 years) are used. A mixture of two timescales is found in the autocorrelation and autoinformation functions, with short-term memory holding for time lags less than 15-30 min, and long-term memory onwards. Consistently, rainfall variance exhibits different temporal scaling regimes separated at 15-30 min and 24 h. Tests for the Hurst effect evidence the frailty of the R/ S approach in discerning the kind of memory in high resolution rainfall, whereas rigorous statistical tests for short-memory processes do reject the existence of the Hurst effect. Rainfall information entropy grows as a power law of aggregation time, S( T) ˜ Tβ with = 0.51, up to a timescale, TMaxEnt (70-202 h), at which entropy saturates, with β = 0 onwards. Maximum entropy is reached through a dynamic Generalized Pareto distribution, consistently with the maximum information-entropy principle for heavy-tailed random variables, and with its asymptotically infinitely divisible property. The dynamics towards the limit distribution is quantified. Tsallis q-entropies also exhibit power laws with T, such that Sq( T) ˜ Tβ( q) , with β( q) ⩽ 0 for q ⩽ 0, and β( q) ≃ 0.5 for q ⩾ 1. No clear patterns are found in the geographic distribution within and among the statistical parameters studied, confirming the strong variability of tropical Andean rainfall.
Spectrum unfolding in X-ray spectrometry using the maximum entropy method
International Nuclear Information System (INIS)
Fernandez, Jorge E.; Scot, Viviana; Di Giulio, Eugenio
2014-01-01
The solution of the unfolding problem is an ever-present issue in X-ray spectrometry. The maximum entropy technique solves this problem by taking advantage of some known a priori physical information and by ensuring an outcome with only positive values. This method is implemented in MAXED (MAXimum Entropy Deconvolution), a software code contained in the package UMG (Unfolding with MAXED and GRAVEL) developed at PTB and distributed by NEA Data Bank. This package contains also the code GRAVEL (used to estimate the precision of the solution). This article introduces the new code UMESTRAT (Unfolding Maximum Entropy STRATegy) which applies a semi-automatic strategy to solve the unfolding problem by using a suitable combination of MAXED and GRAVEL for applications in X-ray spectrometry. Some examples of the use of UMESTRAT are shown, demonstrating its capability to remove detector artifacts from the measured spectrum consistently with the model used for the detector response function (DRF). - Highlights: ► A new strategy to solve the unfolding problem in X-ray spectrometry is presented. ► The presented strategy uses a suitable combination of the codes MAXED and GRAVEL. ► The applied strategy provides additional information on the Detector Response Function. ► The code UMESTRAT is developed to apply this new strategy in a semi-automatic mode
International Nuclear Information System (INIS)
Trovato, M.; Reggiani, L.
2011-01-01
By introducing a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is asserted as fundamental principle of quantum statistical mechanics. Accordingly, we develop a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theoretical formalism is formulated in both thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of (ℎ/2π) 2 . In particular, by using an arbitrary number of moments, we prove that (1) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives, both of the numerical density n and of the effective temperature T; (2) the results available from the literature in the framework of both a quantum Boltzmann gas and a degenerate quantum Fermi gas are recovered as a particular case; (3) the statistics for the quantum Fermi and Bose gases at different levels of degeneracy are explicitly incorporated; (4) a set of relevant applications admitting exact analytical equations are explicitly given and discussed; (5) the quantum maximum entropy principle keeps full validity in the classical limit, when (ℎ/2π)→0.
Applications of the principle of maximum entropy: from physics to ecology.
Banavar, Jayanth R; Maritan, Amos; Volkov, Igor
2010-02-17
There are numerous situations in physics and other disciplines which can be described at different levels of detail in terms of probability distributions. Such descriptions arise either intrinsically as in quantum mechanics, or because of the vast amount of details necessary for a complete description as, for example, in Brownian motion and in many-body systems. We show that an application of the principle of maximum entropy for estimating the underlying probability distribution can depend on the variables used for describing the system. The choice of characterization of the system carries with it implicit assumptions about fundamental attributes such as whether the system is classical or quantum mechanical or equivalently whether the individuals are distinguishable or indistinguishable. We show that the correct procedure entails the maximization of the relative entropy subject to known constraints and, additionally, requires knowledge of the behavior of the system in the absence of these constraints. We present an application of the principle of maximum entropy to understanding species diversity in ecology and introduce a new statistical ensemble corresponding to the distribution of a variable population of individuals into a set of species not defined a priori.
Applications of the principle of maximum entropy: from physics to ecology
International Nuclear Information System (INIS)
Banavar, Jayanth R; Volkov, Igor; Maritan, Amos
2010-01-01
There are numerous situations in physics and other disciplines which can be described at different levels of detail in terms of probability distributions. Such descriptions arise either intrinsically as in quantum mechanics, or because of the vast amount of details necessary for a complete description as, for example, in Brownian motion and in many-body systems. We show that an application of the principle of maximum entropy for estimating the underlying probability distribution can depend on the variables used for describing the system. The choice of characterization of the system carries with it implicit assumptions about fundamental attributes such as whether the system is classical or quantum mechanical or equivalently whether the individuals are distinguishable or indistinguishable. We show that the correct procedure entails the maximization of the relative entropy subject to known constraints and, additionally, requires knowledge of the behavior of the system in the absence of these constraints. We present an application of the principle of maximum entropy to understanding species diversity in ecology and introduce a new statistical ensemble corresponding to the distribution of a variable population of individuals into a set of species not defined a priori. (topical review)
The simplest maximum entropy model for collective behavior in a neural network
International Nuclear Information System (INIS)
Tkačik, Gašper; Marre, Olivier; Mora, Thierry; Amodei, Dario; Bialek, William; Berry II, Michael J
2013-01-01
Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on capturing the measured correlations among pairs of neurons. Here we suggest an alternative, constructing models that are consistent with the distribution of global network activity, i.e. the probability that K out of N cells in the network generate action potentials in the same small time bin. The inverse problem that we need to solve in constructing the model is analytically tractable, and provides a natural ‘thermodynamics’ for the network in the limit of large N. We analyze the responses of neurons in a small patch of the retina to naturalistic stimuli, and find that the implied thermodynamics is very close to an unusual critical point, in which the entropy (in proper units) is exactly equal to the energy. (paper)
Maximum entropy approach to H-theory: Statistical mechanics of hierarchical systems.
Vasconcelos, Giovani L; Salazar, Domingos S P; Macêdo, A M S
2018-02-01
A formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small subsystem-representing the region where the measurements are made-in contact with a set of "nested heat reservoirs" corresponding to the hierarchical structure of the system, where the temperatures of the reservoirs are allowed to fluctuate owing to the complex interactions between degrees of freedom at different scales. The probability distribution function (pdf) of the temperature of the reservoir at a given scale, conditioned on the temperature of the reservoir at the next largest scale in the hierarchy, is determined from a maximum entropy principle subject to appropriate constraints that describe the thermal equilibrium properties of the system. The marginal temperature distribution of the innermost reservoir is obtained by integrating over the conditional distributions of all larger scales, and the resulting pdf is written in analytical form in terms of certain special transcendental functions, known as the Fox H functions. The distribution of states of the small subsystem is then computed by averaging the quasiequilibrium Boltzmann distribution over the temperature of the innermost reservoir. This distribution can also be written in terms of H functions. The general family of distributions reported here recovers, as particular cases, the stationary distributions recently obtained by Macêdo et al. [Phys. Rev. E 95, 032315 (2017)10.1103/PhysRevE.95.032315] from a stochastic dynamical approach to the problem.
Maximum Entropy Approach in Dynamic Contrast-Enhanced Magnetic Resonance Imaging.
Farsani, Zahra Amini; Schmid, Volker J
2017-01-01
In the estimation of physiological kinetic parameters from Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) data, the determination of the arterial input function (AIF) plays a key role. This paper proposes a Bayesian method to estimate the physiological parameters of DCE-MRI along with the AIF in situations, where no measurement of the AIF is available. In the proposed algorithm, the maximum entropy method (MEM) is combined with the maximum a posterior approach (MAP). To this end, MEM is used to specify a prior probability distribution of the unknown AIF. The ability of this method to estimate the AIF is validated using the Kullback-Leibler divergence. Subsequently, the kinetic parameters can be estimated with MAP. The proposed algorithm is evaluated with a data set from a breast cancer MRI study. The application shows that the AIF can reliably be determined from the DCE-MRI data using MEM. Kinetic parameters can be estimated subsequently. The maximum entropy method is a powerful tool to reconstructing images from many types of data. This method is useful for generating the probability distribution based on given information. The proposed method gives an alternative way to assess the input function from the existing data. The proposed method allows a good fit of the data and therefore a better estimation of the kinetic parameters. In the end, this allows for a more reliable use of DCE-MRI. Schattauer GmbH.
The entropy concept for non-equilibrium states.
Lieb, Elliott H; Yngvason, Jakob
2013-10-08
In earlier work, we presented a foundation for the second law of classical thermodynamics in terms of the entropy principle. More precisely, we provided an empirically accessible axiomatic derivation of an entropy function defined on all equilibrium states of all systems that has the appropriate additivity and scaling properties, and whose increase is a necessary and sufficient condition for an adiabatic process between two states to be possible. Here, after a brief review of this approach, we address the question of defining entropy for non-equilibrium states. Our conclusion is that it is generally not possible to find a unique entropy that has all relevant physical properties. We do show, however, that one can define two entropy functions, called S - and S + , which, taken together, delimit the range of adiabatic processes that can occur between non-equilibrium states. The concept of comparability of states with respect to adiabatic changes plays an important role in our reasoning.
de Beer, Alex G F; Samson, Jean-Sebastièn; Hua, Wei; Huang, Zishuai; Chen, Xiangke; Allen, Heather C; Roke, Sylvie
2011-12-14
We present a direct comparison of phase sensitive sum-frequency generation experiments with phase reconstruction obtained by the maximum entropy method. We show that both methods lead to the same complex spectrum. Furthermore, we discuss the strengths and weaknesses of each of these methods, analyzing possible sources of experimental and analytical errors. A simulation program for maximum entropy phase reconstruction is available at: http://lbp.epfl.ch/. © 2011 American Institute of Physics
Analysis of positron lifetime spectra using quantified maximum entropy and a general linear filter
International Nuclear Information System (INIS)
Shukla, A.; Peter, M.; Hoffmann, L.
1993-01-01
Two new approaches are used to analyze positron annihilation lifetime spectra. A general linear filter is designed to filter the noise from lifetime data. The quantified maximum entropy method is used to solve the inverse problem of finding the lifetimes and intensities present in data. We determine optimal values of parameters needed for fitting using Bayesian methods. Estimates of errors are provided. We present results on simulated and experimental data with extensive tests to show the utility of this method and compare it with other existing methods. (orig.)
International Nuclear Information System (INIS)
Fiebig, H. Rudolf
2002-01-01
We study various aspects of extracting spectral information from time correlation functions of lattice QCD by means of Bayesian inference with an entropic prior, the maximum entropy method (MEM). Correlator functions of a heavy-light meson-meson system serve as a repository for lattice data with diverse statistical quality. Attention is given to spectral mass density functions, inferred from the data, and their dependence on the parameters of the MEM. We propose to employ simulated annealing, or cooling, to solve the Bayesian inference problem, and discuss the practical issues of the approach
Nuclear Enhanced X-ray Maximum Entropy Method Used to Analyze Local Distortions in Simple Structures
DEFF Research Database (Denmark)
Christensen, Sebastian; Bindzus, Niels; Christensen, Mogens
We introduce a novel method for reconstructing pseudo nuclear density distributions (NDDs): Nuclear Enhanced X-ray Maximum Entropy Method (NEXMEM). NEXMEM offers an alternative route to experimental NDDs, exploiting the superior quality of synchrotron X-ray data compared to neutron data. The method...... proposed to result from anharmonic phonon scattering or from local fluctuating dipoles on the Pb site.[1,2] No macroscopic symmetry change are associated with these effects, rendering them invisible to conventional crystallographic techniques. For this reason PbX was until recently believed to adopt...
Chaos control of ferroresonance system based on RBF-maximum entropy clustering algorithm
International Nuclear Information System (INIS)
Liu Fan; Sun Caixin; Sima Wenxia; Liao Ruijin; Guo Fei
2006-01-01
With regards to the ferroresonance overvoltage of neutral grounded power system, a maximum-entropy learning algorithm based on radial basis function neural networks is used to control the chaotic system. The algorithm optimizes the object function to derive learning rule of central vectors, and uses the clustering function of network hidden layers. It improves the regression and learning ability of neural networks. The numerical experiment of ferroresonance system testifies the effectiveness and feasibility of using the algorithm to control chaos in neutral grounded system
Maximum-entropy data restoration using both real- and Fourier-space analysis
International Nuclear Information System (INIS)
Anderson, D.M.; Martin, D.C.; Thomas, E.L.
1989-01-01
An extension of the maximum-entropy (ME) data-restoration method is presented that is sensitive to periodic correlations in data. The method takes advantage of the higher signal-to-noise ratio for periodic information in Fourier space, thus enhancing statistically significant frequencies in a manner which avoids the user bias inherent in conventional Fourier filtering. This procedure incorporates concepts underlying new approaches in quantum mechanics that consider entropies in both position and momentum spaces, although the emphasis here is on data restoration rather than quantum physics. After a fast Fourier transform of the image, the phases are saved and the array of Fourier moduli are restored using the maximum-entropy criterion. A first-order continuation method is introduced that speeds convergence of the ME computation. The restored moduli together with the original phases are then Fourier inverted to yield a new image; traditional real-space ME restoration is applied to this new image completing one stage in the restoration process. In test cases improvement can be obtained from two to four stages of iteration. It is shown that in traditional Fourier filtering spurious features can be induced by selection or elimination of Fourier components without regard to their statistical significance. With the present approach there is no such freedom for the user to exert personal bias, so that features present in the final image and power spectrum are those which have survived the tests of statistical significance in both real and Fourier space. However, it is still possible for periodicities to 'bleed' across sharp boundaries. An 'uncertainty' relation is derived describing the inverse relationship between the resolution of these boundaries and the level of noise that can be eliminated. (orig./BHO)
Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation
Bergeron, Dominic; Tremblay, A.-M. S.
2016-08-01
Analytic continuation of numerical data obtained in imaginary time or frequency has become an essential part of many branches of quantum computational physics. It is, however, an ill-conditioned procedure and thus a hard numerical problem. The maximum-entropy approach, based on Bayesian inference, is the most widely used method to tackle that problem. Although the approach is well established and among the most reliable and efficient ones, useful developments of the method and of its implementation are still possible. In addition, while a few free software implementations are available, a well-documented, optimized, general purpose, and user-friendly software dedicated to that specific task is still lacking. Here we analyze all aspects of the implementation that are critical for accuracy and speed and present a highly optimized approach to maximum entropy. Original algorithmic and conceptual contributions include (1) numerical approximations that yield a computational complexity that is almost independent of temperature and spectrum shape (including sharp Drude peaks in broad background, for example) while ensuring quantitative accuracy of the result whenever precision of the data is sufficient, (2) a robust method of choosing the entropy weight α that follows from a simple consistency condition of the approach and the observation that information- and noise-fitting regimes can be identified clearly from the behavior of χ2 with respect to α , and (3) several diagnostics to assess the reliability of the result. Benchmarks with test spectral functions of different complexity and an example with an actual physical simulation are presented. Our implementation, which covers most typical cases for fermions, bosons, and response functions, is available as an open source, user-friendly software.
Directory of Open Access Journals (Sweden)
Michael J. Markham
2011-07-01
Full Text Available Some problems occurring in Expert Systems can be resolved by employing a causal (Bayesian network and methodologies exist for this purpose. These require data in a specific form and make assumptions about the independence relationships involved. Methodologies using Maximum Entropy (ME are free from these conditions and have the potential to be used in a wider context including systems consisting of given sets of linear and independence constraints, subject to consistency and convergence. ME can also be used to validate results from the causal network methodologies. Three ME methods for determining the prior probability distribution of causal network systems are considered. The first method is Sequential Maximum Entropy in which the computation of a progression of local distributions leads to the over-all distribution. This is followed by development of the Method of Tribus. The development takes the form of an algorithm that includes the handling of explicit independence constraints. These fall into two groups those relating parents of vertices, and those deduced from triangulation of the remaining graph. The third method involves a variation in the part of that algorithm which handles independence constraints. Evidence is presented that this adaptation only requires the linear constraints and the parental independence constraints to emulate the second method in a substantial class of examples.
Estimation of typhoon rainfall in GaoPing River: A Multivariate Maximum Entropy Method
Pei-Jui, Wu; Hwa-Lung, Yu
2016-04-01
The heavy rainfall from typhoons is the main factor of the natural disaster in Taiwan, which causes the significant loss of human lives and properties. Statistically average 3.5 typhoons invade Taiwan every year, and the serious typhoon, Morakot in 2009, impacted Taiwan in recorded history. Because the duration, path and intensity of typhoon, also affect the temporal and spatial rainfall type in specific region , finding the characteristics of the typhoon rainfall type is advantageous when we try to estimate the quantity of rainfall. This study developed a rainfall prediction model and can be divided three parts. First, using the EEOF(extended empirical orthogonal function) to classify the typhoon events, and decompose the standard rainfall type of all stations of each typhoon event into the EOF and PC(principal component). So we can classify the typhoon events which vary similarly in temporally and spatially as the similar typhoon types. Next, according to the classification above, we construct the PDF(probability density function) in different space and time by means of using the multivariate maximum entropy from the first to forth moment statistically. Therefore, we can get the probability of each stations of each time. Final we use the BME(Bayesian Maximum Entropy method) to construct the typhoon rainfall prediction model , and to estimate the rainfall for the case of GaoPing river which located in south of Taiwan.This study could be useful for typhoon rainfall predictions in future and suitable to government for the typhoon disaster prevention .
Estimation of Lithological Classification in Taipei Basin: A Bayesian Maximum Entropy Method
Wu, Meng-Ting; Lin, Yuan-Chien; Yu, Hwa-Lung
2015-04-01
In environmental or other scientific applications, we must have a certain understanding of geological lithological composition. Because of restrictions of real conditions, only limited amount of data can be acquired. To find out the lithological distribution in the study area, many spatial statistical methods used to estimate the lithological composition on unsampled points or grids. This study applied the Bayesian Maximum Entropy (BME method), which is an emerging method of the geological spatiotemporal statistics field. The BME method can identify the spatiotemporal correlation of the data, and combine not only the hard data but the soft data to improve estimation. The data of lithological classification is discrete categorical data. Therefore, this research applied Categorical BME to establish a complete three-dimensional Lithological estimation model. Apply the limited hard data from the cores and the soft data generated from the geological dating data and the virtual wells to estimate the three-dimensional lithological classification in Taipei Basin. Keywords: Categorical Bayesian Maximum Entropy method, Lithological Classification, Hydrogeological Setting
Maximum entropy methods for extracting the learned features of deep neural networks.
Finnegan, Alex; Song, Jun S
2017-10-01
New architectures of multilayer artificial neural networks and new methods for training them are rapidly revolutionizing the application of machine learning in diverse fields, including business, social science, physical sciences, and biology. Interpreting deep neural networks, however, currently remains elusive, and a critical challenge lies in understanding which meaningful features a network is actually learning. We present a general method for interpreting deep neural networks and extracting network-learned features from input data. We describe our algorithm in the context of biological sequence analysis. Our approach, based on ideas from statistical physics, samples from the maximum entropy distribution over possible sequences, anchored at an input sequence and subject to constraints implied by the empirical function learned by a network. Using our framework, we demonstrate that local transcription factor binding motifs can be identified from a network trained on ChIP-seq data and that nucleosome positioning signals are indeed learned by a network trained on chemical cleavage nucleosome maps. Imposing a further constraint on the maximum entropy distribution also allows us to probe whether a network is learning global sequence features, such as the high GC content in nucleosome-rich regions. This work thus provides valuable mathematical tools for interpreting and extracting learned features from feed-forward neural networks.
Maximum entropy estimation of a Benzene contaminated plume using ecotoxicological assays
International Nuclear Information System (INIS)
Wahyudi, Agung; Bartzke, Mariana; Küster, Eberhard; Bogaert, Patrick
2013-01-01
Ecotoxicological bioassays, e.g. based on Danio rerio teratogenicity (DarT) or the acute luminescence inhibition with Vibrio fischeri, could potentially lead to significant benefits for detecting on site contaminations on qualitative or semi-quantitative bases. The aim was to use the observed effects of two ecotoxicological assays for estimating the extent of a Benzene groundwater contamination plume. We used a Maximum Entropy (MaxEnt) method to rebuild a bivariate probability table that links the observed toxicity from the bioassays with Benzene concentrations. Compared with direct mapping of the contamination plume as obtained from groundwater samples, the MaxEnt concentration map exhibits on average slightly higher concentrations though the global pattern is close to it. This suggest MaxEnt is a valuable method to build a relationship between quantitative data, e.g. contaminant concentrations, and more qualitative or indirect measurements, in a spatial mapping framework, which is especially useful when clear quantitative relation is not at hand. - Highlights: ► Ecotoxicological shows significant benefits for detecting on site contaminations. ► MaxEnt to rebuild qualitative link on concentration and ecotoxicological assays. ► MaxEnt shows similar pattern when compared with concentrations map of groundwater. ► MaxEnt is a valuable method especially when quantitative relation is not at hand. - A Maximum Entropy method to rebuild qualitative relationships between Benzene groundwater concentrations and their ecotoxicological effect.
Principle of Entropy Maximization for Nonequilibrium Steady States
DEFF Research Database (Denmark)
Shapiro, Alexander; Stenby, Erling Halfdan
2002-01-01
The goal of this contribution is to find out to what extent the principle of entropy maximization, which serves as a basis for the equilibrium thermodynamics, may be generalized onto non-equilibrium steady states. We prove a theorem that, in the system of thermodynamic coordinates, where entropy...
Chen, Xiao; Li, Yaan; Yu, Jing; Li, Yuxing
2018-01-01
For fast and more effective implementation of tracking multiple targets in a cluttered environment, we propose a multiple targets tracking (MTT) algorithm called maximum entropy fuzzy c-means clustering joint probabilistic data association that combines fuzzy c-means clustering and the joint probabilistic data association (PDA) algorithm. The algorithm uses the membership value to express the probability of the target originating from measurement. The membership value is obtained through fuzzy c-means clustering objective function optimized by the maximum entropy principle. When considering the effect of the public measurement, we use a correction factor to adjust the association probability matrix to estimate the state of the target. As this algorithm avoids confirmation matrix splitting, it can solve the high computational load problem of the joint PDA algorithm. The results of simulations and analysis conducted for tracking neighbor parallel targets and cross targets in a different density cluttered environment show that the proposed algorithm can realize MTT quickly and efficiently in a cluttered environment. Further, the performance of the proposed algorithm remains constant with increasing process noise variance. The proposed algorithm has the advantages of efficiency and low computational load, which can ensure optimum performance when tracking multiple targets in a dense cluttered environment.
Information entropies in antikaon-nucleon scattering and optimal state analysis
International Nuclear Information System (INIS)
Ion, D.B.; Ion, M.L.; Petrascu, C.
1998-01-01
It is known that Jaynes interpreted the entropy as the expected self-information of a class of mutually exclusive and exhaustive events, while the probability is considered to be the rational degree of belief we assign to events based on available experimental evidence. The axiomatic derivation of Jaynes principle of maximum entropy as well as of the Kullback principle of minimum cross-entropy have been reported. Moreover, the optimal states in the Hilbert space of the scattering amplitude, which are analogous to the coherent states from the Hilbert space of the wave functions, were introduced and developed. The possibility that each optimal state possesses a specific minimum entropic uncertainty relation similar to that of the coherent states was recently conjectured. In fact, the (angle and angular momenta) information entropies, as well as the entropic angle-angular momentum uncertainty relations, in the hadron-hadron scattering, are introduced. The experimental information entropies for the pion-nucleon scattering are calculated by using the available phase shift analyses. These results are compared with the information entropies of the optimal states. Then, the optimal state dominance in the pion-nucleon scattering is systematically observed for all P LAB = 0.02 - 10 GeV/c. Also, it is shown that the angle-angular momentum entropic uncertainty relations are satisfied with high accuracy by all the experimental information entropies. In this paper the (angle and angular momentum) information entropies of hadron-hadron scattering are experimentally investigated by using the antikaon-nucleon phase shift analysis. Then, it is shown that the experimental entropies are in agreement with the informational entropies of optimal states. The results obtained in this paper can be explained not only by the presence of an optimal background which accompanied the production of the elementary resonances but also by the presence of the optimal resonances. On the other hand
Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions
Kraberger, Gernot J.; Triebl, Robert; Zingl, Manuel; Aichhorn, Markus
2017-10-01
We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO3, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.
Maximum entropy approach to statistical inference for an ocean acoustic waveguide.
Knobles, D P; Sagers, J D; Koch, R A
2012-02-01
A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations. © 2012 Acoustical Society of America
How fast can we learn maximum entropy models of neural populations?
Energy Technology Data Exchange (ETDEWEB)
Ganmor, Elad; Schneidman, Elad [Department of Neuroscience, Weizmann Institute of Science, Rehovot 76100 (Israel); Segev, Ronen, E-mail: elad.ganmor@weizmann.ac.i, E-mail: elad.schneidman@weizmann.ac.i [Department of Life Sciences and Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel)
2009-12-01
Most of our knowledge about how the brain encodes information comes from recordings of single neurons. However, computations in the brain are carried out by large groups of neurons. Modelling the joint activity of many interacting elements is computationally hard because of the large number of possible activity patterns and limited experimental data. Recently it was shown in several different neural systems that maximum entropy pairwise models, which rely only on firing rates and pairwise correlations of neurons, are excellent models for the distribution of activity patterns of neural populations, and in particular, their responses to natural stimuli. Using simultaneous recordings of large groups of neurons in the vertebrate retina responding to naturalistic stimuli, we show here that the relevant statistics required for finding the pairwise model can be accurately estimated within seconds. Furthermore, while higher order statistics may, in theory, improve model accuracy, they are, in practice, harmful for times of up to 20 minutes due to sampling noise. Finally, we demonstrate that trading accuracy for entropy may actually improve model performance when data is limited, and suggest an optimization method that automatically adjusts model constraints in order to achieve good performance.
How fast can we learn maximum entropy models of neural populations?
International Nuclear Information System (INIS)
Ganmor, Elad; Schneidman, Elad; Segev, Ronen
2009-01-01
Most of our knowledge about how the brain encodes information comes from recordings of single neurons. However, computations in the brain are carried out by large groups of neurons. Modelling the joint activity of many interacting elements is computationally hard because of the large number of possible activity patterns and limited experimental data. Recently it was shown in several different neural systems that maximum entropy pairwise models, which rely only on firing rates and pairwise correlations of neurons, are excellent models for the distribution of activity patterns of neural populations, and in particular, their responses to natural stimuli. Using simultaneous recordings of large groups of neurons in the vertebrate retina responding to naturalistic stimuli, we show here that the relevant statistics required for finding the pairwise model can be accurately estimated within seconds. Furthermore, while higher order statistics may, in theory, improve model accuracy, they are, in practice, harmful for times of up to 20 minutes due to sampling noise. Finally, we demonstrate that trading accuracy for entropy may actually improve model performance when data is limited, and suggest an optimization method that automatically adjusts model constraints in order to achieve good performance.
Imaging VLBI polarimetry data from Active Galactic Nuclei using the Maximum Entropy Method
Directory of Open Access Journals (Sweden)
Coughlan Colm P.
2013-12-01
Full Text Available Mapping the relativistic jets emanating from AGN requires the use of a deconvolution algorithm to account for the effects of missing baseline spacings. The CLEAN algorithm is the most commonly used algorithm in VLBI imaging today and is suitable for imaging polarisation data. The Maximum Entropy Method (MEM is presented as an alternative with some advantages over the CLEAN algorithm, including better spatial resolution and a more rigorous and unbiased approach to deconvolution. We have developed a MEM code suitable for deconvolving VLBI polarisation data. Monte Carlo simulations investigating the performance of CLEAN and the MEM code on a variety of source types are being carried out. Real polarisation (VLBA data taken at multiple wavelengths have also been deconvolved using MEM, and several of the resulting polarisation and Faraday rotation maps are presented and discussed.
Halo-independence with quantified maximum entropy at DAMA/LIBRA
Energy Technology Data Exchange (ETDEWEB)
Fowlie, Andrew, E-mail: andrew.j.fowlie@googlemail.com [ARC Centre of Excellence for Particle Physics at the Tera-scale, Monash University, Melbourne, Victoria 3800 (Australia)
2017-10-01
Using the DAMA/LIBRA anomaly as an example, we formalise the notion of halo-independence in the context of Bayesian statistics and quantified maximum entropy. We consider an infinite set of possible profiles, weighted by an entropic prior and constrained by a likelihood describing noisy measurements of modulated moments by DAMA/LIBRA. Assuming an isotropic dark matter (DM) profile in the galactic rest frame, we find the most plausible DM profiles and predictions for unmodulated signal rates at DAMA/LIBRA. The entropic prior contains an a priori unknown regularisation factor, β, that describes the strength of our conviction that the profile is approximately Maxwellian. By varying β, we smoothly interpolate between a halo-independent and a halo-dependent analysis, thus exploring the impact of prior information about the DM profile.
Reginatto, M; Neumann, S
2002-01-01
MAXED was developed to apply the maximum entropy principle to the unfolding of neutron spectrometric measurements. The approach followed in MAXED has several features that make it attractive: it permits inclusion of a priori information in a well-defined and mathematically consistent way, the algorithm used to derive the solution spectrum is not ad hoc (it can be justified on the basis of arguments that originate in information theory), and the solution spectrum is a non-negative function that can be written in closed form. This last feature permits the use of standard methods for the sensitivity analysis and propagation of uncertainties of MAXED solution spectra. We illustrate its use with unfoldings of NE 213 scintillation detector measurements of photon calibration spectra, and of multisphere neutron spectrometer measurements of cosmic-ray induced neutrons at high altitude (approx 20 km) in the atmosphere.
Maximum entropy based reconstruction of soft X ray emissivity profiles in W7-AS
International Nuclear Information System (INIS)
Ertl, K.; Linden, W. von der; Dose, V.; Weller, A.
1996-01-01
The reconstruction of 2-D emissivity profiles from soft X ray tomography measurements constitutes a highly underdetermined and ill-posed inversion problem, because of the restricted viewing access, the number of chords and the increased noise level in most plasma devices. An unbiased and consistent probabilistic approach within the framework of Bayesian inference is provided by the maximum entropy method, which is independent of model assumptions, but allows any prior knowledge available to be incorporated. The formalism is applied to the reconstruction of emissivity profiles in an NBI heated plasma discharge to determine the dependence of the Shafranov shift on β, the reduction of which was a particular objective in designing the advanced W7-AS stellarator. (author). 40 refs, 7 figs
International Nuclear Information System (INIS)
Sivia, D.S.; Hamilton, W.A.; Smith, G.S.
1991-01-01
The analysis of neutron reflectivity data to obtain nuclear scattering length density profiles is akin to the notorious phaseless Fourier problem, well known in many fields such as crystallography. Current methods of analysis culminate in the refinement of a few parameters of a functional model, and are often preceded by a long and laborious process of trial and error. We start by discussing the use of maximum entropy for obtained 'free-form' solutions of the density profile, as an alternative to the trial and error phase when a functional model is not available. Next we consider a Bayesian spectral analysis approach, which is appropriate for optimising the parameters of a simple (but adequate) type of model when the number of parameters is not known. Finally, we suggest a novel experimental procedure, the analogue of astronomical speckle holography, designed to alleviate the ambiguity problems inherent in traditional reflectivity measurements. (orig.)
Comparison of two views of maximum entropy in biodiversity: Frank (2011) and Pueyo et al. (2007).
Pueyo, Salvador
2012-05-01
An increasing number of authors agree in that the maximum entropy principle (MaxEnt) is essential for the understanding of macroecological patterns. However, there are subtle but crucial differences among the approaches by several of these authors. This poses a major obstacle for anyone interested in applying the methodology of MaxEnt in this context. In a recent publication, Frank (2011) gives some arguments why his own approach would represent an improvement as compared to the earlier paper by Pueyo et al. (2007) and also to the views by Edwin T. Jaynes, who first formulated MaxEnt in the context of statistical physics. Here I show that his criticisms are flawed and that there are fundamental reasons to prefer the original approach.
International Nuclear Information System (INIS)
Reginatto, Marcel; Zimbal, Andreas
2008-01-01
In applications of neutron spectrometry to fusion diagnostics, it is advantageous to use methods of data analysis which can extract information from the spectrum that is directly related to the parameters of interest that describe the plasma. We present here methods of data analysis which were developed with this goal in mind, and which were applied to spectrometric measurements made with an organic liquid scintillation detector (type NE213). In our approach, we combine Bayesian parameter estimation methods and unfolding methods based on the maximum entropy principle. This two-step method allows us to optimize the analysis of the data depending on the type of information that we want to extract from the measurements. To illustrate these methods, we analyze neutron measurements made at the PTB accelerator under controlled conditions, using accelerator-produced neutron beams. Although the methods have been chosen with a specific application in mind, they are general enough to be useful for many other types of measurements
Modelling streambank erosion potential using maximum entropy in a central Appalachian watershed
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J. Pitchford
2015-03-01
Full Text Available We used maximum entropy to model streambank erosion potential (SEP in a central Appalachian watershed to help prioritize sites for management. Model development included measuring erosion rates, application of a quantitative approach to locate Target Eroding Areas (TEAs, and creation of maps of boundary conditions. We successfully constructed a probability distribution of TEAs using the program Maxent. All model evaluation procedures indicated that the model was an excellent predictor, and that the major environmental variables controlling these processes were streambank slope, soil characteristics, bank position, and underlying geology. A classification scheme with low, moderate, and high levels of SEP derived from logistic model output was able to differentiate sites with low erosion potential from sites with moderate and high erosion potential. A major application of this type of modelling framework is to address uncertainty in stream restoration planning, ultimately helping to bridge the gap between restoration science and practice.
An understanding of human dynamics in urban subway traffic from the Maximum Entropy Principle
Yong, Nuo; Ni, Shunjiang; Shen, Shifei; Ji, Xuewei
2016-08-01
We studied the distribution of entry time interval in Beijing subway traffic by analyzing the smart card transaction data, and then deduced the probability distribution function of entry time interval based on the Maximum Entropy Principle. Both theoretical derivation and data statistics indicated that the entry time interval obeys power-law distribution with an exponential cutoff. In addition, we pointed out the constraint conditions for the distribution form and discussed how the constraints affect the distribution function. It is speculated that for bursts and heavy tails in human dynamics, when the fitted power exponent is less than 1.0, it cannot be a pure power-law distribution, but with an exponential cutoff, which may be ignored in the previous studies.
International Nuclear Information System (INIS)
Urniezius, Renaldas
2011-01-01
The principle of Maximum relative Entropy optimization was analyzed for dead reckoning localization of a rigid body when observation data of two attached accelerometers was collected. Model constraints were derived from the relationships between the sensors. The experiment's results confirmed that accelerometers each axis' noise can be successfully filtered utilizing dependency between channels and the dependency between time series data. Dependency between channels was used for a priori calculation, and a posteriori distribution was derived utilizing dependency between time series data. There was revisited data of autocalibration experiment by removing the initial assumption that instantaneous rotation axis of a rigid body was known. Performance results confirmed that such an approach could be used for online dead reckoning localization.
Bayesian Maximum Entropy Based Algorithm for Digital X-ray Mammogram Processing
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Radu Mutihac
2009-06-01
Full Text Available Basics of Bayesian statistics in inverse problems using the maximum entropy principle are summarized in connection with the restoration of positive, additive images from various types of data like X-ray digital mammograms. An efficient iterative algorithm for image restoration from large data sets based on the conjugate gradient method and Lagrange multipliers in nonlinear optimization of a specific potential function was developed. The point spread function of the imaging system was determined by numerical simulations of inhomogeneous breast-like tissue with microcalcification inclusions of various opacities. The processed digital and digitized mammograms resulted superior in comparison with their raw counterparts in terms of contrast, resolution, noise, and visibility of details.
Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle.
Shalymov, Dmitry S; Fradkov, Alexander L
2016-01-01
We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.
Shortening a loop can increase protein native state entropy.
Gavrilov, Yulian; Dagan, Shlomi; Levy, Yaakov
2015-12-01
Protein loops are essential structural elements that influence not only function but also protein stability and folding rates. It was recently reported that shortening a loop in the AcP protein may increase its native state conformational entropy. This effect on the entropy of the folded state can be much larger than the lower entropic penalty of ordering a shorter loop upon folding, and can therefore result in a more pronounced stabilization than predicted by polymer model for loop closure entropy. In this study, which aims at generalizing the effect of loop length shortening on native state dynamics, we use all-atom molecular dynamics simulations to study how gradual shortening a very long or solvent-exposed loop region in four different proteins can affect their stability. For two proteins, AcP and Ubc7, we show an increase in native state entropy in addition to the known effect of the loop length on the unfolded state entropy. However, for two permutants of SH3 domain, shortening a loop results only with the expected change in the entropy of the unfolded state, which nicely reproduces the observed experimental stabilization. Here, we show that an increase in the native state entropy following loop shortening is not unique to the AcP protein, yet nor is it a general rule that applies to all proteins following the truncation of any loop. This modification of the loop length on the folded state and on the unfolded state may result with a greater effect on protein stability. © 2015 Wiley Periodicals, Inc.
The Maximum Entropy Method for Optical Spectrum Analysis of Real-Time TDDFT
International Nuclear Information System (INIS)
Toogoshi, M; Kano, S S; Zempo, Y
2015-01-01
The maximum entropy method (MEM) is one of the key techniques for spectral analysis. The major feature is that spectra in the low frequency part can be described by the short time-series data. Thus, we applied MEM to analyse the spectrum from the time dependent dipole moment obtained from the time-dependent density functional theory (TDDFT) calculation in real time. It is intensively studied for computing optical properties. In the MEM analysis, however, the maximum lag of the autocorrelation is restricted by the total number of time-series data. We proposed that, as an improved MEM analysis, we use the concatenated data set made from the several-times repeated raw data. We have applied this technique to the spectral analysis of the TDDFT dipole moment of ethylene and oligo-fluorene with n = 8. As a result, the higher resolution can be obtained, which is closer to that of FT with practically time-evoluted data as the same total number of time steps. The efficiency and the characteristic feature of this technique are presented in this paper. (paper)
On the definition of entropy for quantum unstable states
International Nuclear Information System (INIS)
Civitarese, Osvaldo; Gadella, Manuel
2015-01-01
The concept of entropy is central to the formulation of the quantum statistical mechanics, and it is linked to the definition of the density operator and the associated probabilities of occupation of quantum states. The extension of this scheme to accommodate for quantum decaying states is conceptually difficult, because of the nature of these states. Here we present a way to treat quantum unstable states in the context of statistical mechanics. We focuss on the definition of the entropy and avoid the use of complex temperatures
Test the principle of maximum entropy in constant sum 2×2 game: Evidence in experimental economics
International Nuclear Information System (INIS)
Xu, Bin; Zhang, Hongen; Wang, Zhijian; Zhang, Jianbo
2012-01-01
By using laboratory experimental data, we test the uncertainty of strategy type in various competing environments with two-person constant sum 2×2 game in the social system. It firstly shows that, in these competing game environments, the outcome of human's decision-making obeys the principle of the maximum entropy. -- Highlights: ► Test the uncertainty in two-person constant sum games with experimental data. ► On game level, the constant sum game fits the principle of maximum entropy. ► On group level, all empirical entropy values are close to theoretical maxima. ► The results can be different for the games that are not constant sum game.
Test the principle of maximum entropy in constant sum 2×2 game: Evidence in experimental economics
Energy Technology Data Exchange (ETDEWEB)
Xu, Bin, E-mail: xubin211@zju.edu.cn [Experimental Social Science Laboratory, Zhejiang University, Hangzhou, 310058 (China); Public Administration College, Zhejiang Gongshang University, Hangzhou, 310018 (China); Zhang, Hongen, E-mail: hongen777@163.com [Department of Physics, Zhejiang University, Hangzhou, 310027 (China); Wang, Zhijian, E-mail: wangzj@zju.edu.cn [Experimental Social Science Laboratory, Zhejiang University, Hangzhou, 310058 (China); Zhang, Jianbo, E-mail: jbzhang08@zju.edu.cn [Department of Physics, Zhejiang University, Hangzhou, 310027 (China)
2012-03-19
By using laboratory experimental data, we test the uncertainty of strategy type in various competing environments with two-person constant sum 2×2 game in the social system. It firstly shows that, in these competing game environments, the outcome of human's decision-making obeys the principle of the maximum entropy. -- Highlights: ► Test the uncertainty in two-person constant sum games with experimental data. ► On game level, the constant sum game fits the principle of maximum entropy. ► On group level, all empirical entropy values are close to theoretical maxima. ► The results can be different for the games that are not constant sum game.
Cheung, Shao-Yong; Lee, Chieh-Han; Yu, Hwa-Lung
2017-04-01
Due to the limited hydrogeological observation data and high levels of uncertainty within, parameter estimation of the groundwater model has been an important issue. There are many methods of parameter estimation, for example, Kalman filter provides a real-time calibration of parameters through measurement of groundwater monitoring wells, related methods such as Extended Kalman Filter and Ensemble Kalman Filter are widely applied in groundwater research. However, Kalman Filter method is limited to linearity. This study propose a novel method, Bayesian Maximum Entropy Filtering, which provides a method that can considers the uncertainty of data in parameter estimation. With this two methods, we can estimate parameter by given hard data (certain) and soft data (uncertain) in the same time. In this study, we use Python and QGIS in groundwater model (MODFLOW) and development of Extended Kalman Filter and Bayesian Maximum Entropy Filtering in Python in parameter estimation. This method may provide a conventional filtering method and also consider the uncertainty of data. This study was conducted through numerical model experiment to explore, combine Bayesian maximum entropy filter and a hypothesis for the architecture of MODFLOW groundwater model numerical estimation. Through the virtual observation wells to simulate and observe the groundwater model periodically. The result showed that considering the uncertainty of data, the Bayesian maximum entropy filter will provide an ideal result of real-time parameters estimation.
International Nuclear Information System (INIS)
Kubo, S.; Narihara, K.; Tomita, Y.; Hasegawa, M.; Tsuzuki, T.; Mohri, A.
1988-01-01
A multichannel HCN laser interferometer system has been developed to investigate the plasma electron confinement properties in SPAC VII device. Maximum entropy method is applied to reconstruct the electron density profile from measured line integrated data. Particle diffusion coefficient in the peripheral region of the REB ring core spherator was obtained from the evolution of the density profile. (author)
de Nazelle, Audrey; Arunachalam, Saravanan; Serre, Marc L
2010-08-01
States in the USA are required to demonstrate future compliance of criteria air pollutant standards by using both air quality monitors and model outputs. In the case of ozone, the demonstration tests aim at relying heavily on measured values, due to their perceived objectivity and enforceable quality. Weight given to numerical models is diminished by integrating them in the calculations only in a relative sense. For unmonitored locations, the EPA has suggested the use of a spatial interpolation technique to assign current values. We demonstrate that this approach may lead to erroneous assignments of nonattainment and may make it difficult for States to establish future compliance. We propose a method that combines different sources of information to map air pollution, using the Bayesian Maximum Entropy (BME) Framework. The approach gives precedence to measured values and integrates modeled data as a function of model performance. We demonstrate this approach in North Carolina, using the State's ozone monitoring network in combination with outputs from the Multiscale Air Quality Simulation Platform (MAQSIP) modeling system. We show that the BME data integration approach, compared to a spatial interpolation of measured data, improves the accuracy and the precision of ozone estimations across the state.
Pedagogical introduction to the entropy of entanglement for Gaussian states
Demarie, Tommaso F.
2018-05-01
In quantum information theory, the entropy of entanglement is a standard measure of bipartite entanglement between two partitions of a composite system. For a particular class of continuous variable quantum states, the Gaussian states, the entropy of entanglement can be expressed elegantly in terms of symplectic eigenvalues, elements that characterise a Gaussian state and depend on the correlations of the canonical variables. We give a rigorous step-by-step derivation of this result and provide physical insights, together with an example that can be useful in practice for calculations.
Well posedness and maximum entropy approximation for the dynamics of quantitative traits
Boďová , Katarí na; Haskovec, Jan; Markowich, Peter A.
2017-01-01
We study the Fokker–Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker–Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain’s boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker–Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.
LQG and maximum entropy control design for the Hubble Space Telescope
Collins, Emmanuel G., Jr.; Richter, Stephen
Solar array vibrations are responsible for serious pointing control problems on the Hubble Space Telescope (HST). The original HST control law was not designed to attenuate these disturbances because they were not perceived to be a problem prior to launch. However, significant solar array vibrations do occur due to large changes in the thermal environment as the HST orbits the earth. Using classical techniques, Marshall Space Flight Center in conjunction with Lockheed Missiles and Space Company developed modified HST controllers that were able to suppress the influence of the vibrations of the solar arrays on the line-of-sight (LOS) performance. Substantial LOS improvement was observed when two of these controllers were implemented on orbit. This paper describes the development of modified HST controllers by using modern control techniques, particularly linear-quadratic-gaussian (LQG) design and Maximum Entropy robust control design, a generalization of LQG that incorporates robustness constraints with respect to modal errors. The fundamental issues are discussed candidly and controllers designed using these modern techniques are described.
Directory of Open Access Journals (Sweden)
E. Ridolfi
2011-07-01
Full Text Available Hydrological models are the basis of operational flood-forecasting systems. The accuracy of these models is strongly dependent on the quality and quantity of the input information represented by rainfall height. Finer space-time rainfall resolution results in more accurate hazard forecasting. In this framework, an optimum raingauge network is essential in predicting flood events.
This paper develops an entropy-based approach to evaluate the maximum information content achievable by a rainfall network for different sampling time intervals. The procedure is based on the determination of the coefficients of transferred and nontransferred information and on the relative isoinformation contours.
The nontransferred information value achieved by the whole network is strictly dependent on the sampling time intervals considered. An empirical curve is defined, to assess the objective of the research: the nontransferred information value is plotted versus the associated sampling time on a semi-log scale. The curve has a linear trend.
In this paper, the methodology is applied to the high-density raingauge network of the urban area of Rome.
Directory of Open Access Journals (Sweden)
George Kesidis
2008-06-01
Full Text Available In many ensemble classification paradigms, the function which combines local/base classifier decisions is learned in a supervised fashion. Such methods require common labeled training examples across the classifier ensemble. However, in some scenarios, where an ensemble solution is necessitated, common labeled data may not exist: (i legacy/proprietary classifiers, and (ii spatially distributed and/or multiple modality sensors. In such cases, it is standard to apply fixed (untrained decision aggregation such as voting, averaging, or naive Bayes rules. In recent work, an alternative transductive learning strategy was proposed. There, decisions on test samples were chosen aiming to satisfy constraints measured by each local classifier. This approach was shown to reliably correct for class prior mismatch and to robustly account for classifier dependencies. Significant gains in accuracy over fixed aggregation rules were demonstrated. There are two main limitations of that work. First, feasibility of the constraints was not guaranteed. Second, heuristic learning was applied. Here, we overcome these problems via a transductive extension of maximum entropy/improved iterative scaling for aggregation in distributed classification. This method is shown to achieve improved decision accuracy over the earlier transductive approach and fixed rules on a number of UC Irvine datasets.
Tang, Shaolei; Yang, Xiaofeng; Dong, Di; Li, Ziwei
2015-12-01
Sea surface temperature (SST) is an important variable for understanding interactions between the ocean and the atmosphere. SST fusion is crucial for acquiring SST products of high spatial resolution and coverage. This study introduces a Bayesian maximum entropy (BME) method for blending daily SSTs from multiple satellite sensors. A new spatiotemporal covariance model of an SST field is built to integrate not only single-day SSTs but also time-adjacent SSTs. In addition, AVHRR 30-year SST climatology data are introduced as soft data at the estimation points to improve the accuracy of blended results within the BME framework. The merged SSTs, with a spatial resolution of 4 km and a temporal resolution of 24 hours, are produced in the Western Pacific Ocean region to demonstrate and evaluate the proposed methodology. Comparisons with in situ drifting buoy observations show that the merged SSTs are accurate and the bias and root-mean-square errors for the comparison are 0.15°C and 0.72°C, respectively.
Hosseini, Marjan; Kerachian, Reza
2017-09-01
This paper presents a new methodology for analyzing the spatiotemporal variability of water table levels and redesigning a groundwater level monitoring network (GLMN) using the Bayesian Maximum Entropy (BME) technique and a multi-criteria decision-making approach based on ordered weighted averaging (OWA). The spatial sampling is determined using a hexagonal gridding pattern and a new method, which is proposed to assign a removal priority number to each pre-existing station. To design temporal sampling, a new approach is also applied to consider uncertainty caused by lack of information. In this approach, different time lag values are tested by regarding another source of information, which is simulation result of a numerical groundwater flow model. Furthermore, to incorporate the existing uncertainties in available monitoring data, the flexibility of the BME interpolation technique is taken into account in applying soft data and improving the accuracy of the calculations. To examine the methodology, it is applied to the Dehgolan plain in northwestern Iran. Based on the results, a configuration of 33 monitoring stations for a regular hexagonal grid of side length 3600 m is proposed, in which the time lag between samples is equal to 5 weeks. Since the variance estimation errors of the BME method are almost identical for redesigned and existing networks, the redesigned monitoring network is more cost-effective and efficient than the existing monitoring network with 52 stations and monthly sampling frequency.
Directory of Open Access Journals (Sweden)
Yi-Ming Kuo
2011-06-01
Full Text Available Fine airborne particulate matter (PM2.5 has adverse effects on human health. Assessing the long-term effects of PM2.5 exposure on human health and ecology is often limited by a lack of reliable PM2.5 measurements. In Taipei, PM2.5 levels were not systematically measured until August, 2005. Due to the popularity of geographic information systems (GIS, the landuse regression method has been widely used in the spatial estimation of PM concentrations. This method accounts for the potential contributing factors of the local environment, such as traffic volume. Geostatistical methods, on other hand, account for the spatiotemporal dependence among the observations of ambient pollutants. This study assesses the performance of the landuse regression model for the spatiotemporal estimation of PM2.5 in the Taipei area. Specifically, this study integrates the landuse regression model with the geostatistical approach within the framework of the Bayesian maximum entropy (BME method. The resulting epistemic framework can assimilate knowledge bases including: (a empirical-based spatial trends of PM concentration based on landuse regression, (b the spatio-temporal dependence among PM observation information, and (c site-specific PM observations. The proposed approach performs the spatiotemporal estimation of PM2.5 levels in the Taipei area (Taiwan from 2005–2007.
Yu, Hwa-Lung; Wang, Chih-Hsih; Liu, Ming-Che; Kuo, Yi-Ming
2011-06-01
Fine airborne particulate matter (PM2.5) has adverse effects on human health. Assessing the long-term effects of PM2.5 exposure on human health and ecology is often limited by a lack of reliable PM2.5 measurements. In Taipei, PM2.5 levels were not systematically measured until August, 2005. Due to the popularity of geographic information systems (GIS), the landuse regression method has been widely used in the spatial estimation of PM concentrations. This method accounts for the potential contributing factors of the local environment, such as traffic volume. Geostatistical methods, on other hand, account for the spatiotemporal dependence among the observations of ambient pollutants. This study assesses the performance of the landuse regression model for the spatiotemporal estimation of PM2.5 in the Taipei area. Specifically, this study integrates the landuse regression model with the geostatistical approach within the framework of the Bayesian maximum entropy (BME) method. The resulting epistemic framework can assimilate knowledge bases including: (a) empirical-based spatial trends of PM concentration based on landuse regression, (b) the spatio-temporal dependence among PM observation information, and (c) site-specific PM observations. The proposed approach performs the spatiotemporal estimation of PM2.5 levels in the Taipei area (Taiwan) from 2005-2007.
Jat, Prahlad; Serre, Marc L
2016-12-01
Widespread contamination of surface water chloride is an emerging environmental concern. Consequently accurate and cost-effective methods are needed to estimate chloride along all river miles of potentially contaminated watersheds. Here we introduce a Bayesian Maximum Entropy (BME) space/time geostatistical estimation framework that uses river distances, and we compare it with Euclidean BME to estimate surface water chloride from 2005 to 2014 in the Gunpowder-Patapsco, Severn, and Patuxent subbasins in Maryland. River BME improves the cross-validation R 2 by 23.67% over Euclidean BME, and river BME maps are significantly different than Euclidean BME maps, indicating that it is important to use river BME maps to assess water quality impairment. The river BME maps of chloride concentration show wide contamination throughout Baltimore and Columbia-Ellicott cities, the disappearance of a clean buffer separating these two large urban areas, and the emergence of multiple localized pockets of contamination in surrounding areas. The number of impaired river miles increased by 0.55% per year in 2005-2009 and by 1.23% per year in 2011-2014, corresponding to a marked acceleration of the rate of impairment. Our results support the need for control measures and increased monitoring of unassessed river miles. Copyright © 2016. Published by Elsevier Ltd.
Gustafsson, Mats G; Wallman, Mikael; Wickenberg Bolin, Ulrika; Göransson, Hanna; Fryknäs, M; Andersson, Claes R; Isaksson, Anders
2010-06-01
Successful use of classifiers that learn to make decisions from a set of patient examples require robust methods for performance estimation. Recently many promising approaches for determination of an upper bound for the error rate of a single classifier have been reported but the Bayesian credibility interval (CI) obtained from a conventional holdout test still delivers one of the tightest bounds. The conventional Bayesian CI becomes unacceptably large in real world applications where the test set sizes are less than a few hundred. The source of this problem is that fact that the CI is determined exclusively by the result on the test examples. In other words, there is no information at all provided by the uniform prior density distribution employed which reflects complete lack of prior knowledge about the unknown error rate. Therefore, the aim of the study reported here was to study a maximum entropy (ME) based approach to improved prior knowledge and Bayesian CIs, demonstrating its relevance for biomedical research and clinical practice. It is demonstrated how a refined non-uniform prior density distribution can be obtained by means of the ME principle using empirical results from a few designs and tests using non-overlapping sets of examples. Experimental results show that ME based priors improve the CIs when employed to four quite different simulated and two real world data sets. An empirically derived ME prior seems promising for improving the Bayesian CI for the unknown error rate of a designed classifier. Copyright 2010 Elsevier B.V. All rights reserved.
Chen, Yihang; Xiao, Chijie; Yang, Xiaoyi; Wang, Tianbo; Xu, Tianchao; Yu, Yi; Xu, Min; Wang, Long; Lin, Chen; Wang, Xiaogang
2017-10-01
The Laser-driven Ion beam trace probe (LITP) is a new diagnostic method for measuring poloidal magnetic field (Bp) and radial electric field (Er) in tokamaks. LITP injects a laser-driven ion beam into the tokamak, and Bp and Er profiles can be reconstructed using tomography methods. A reconstruction code has been developed to validate the LITP theory, and both 2D reconstruction of Bp and simultaneous reconstruction of Bp and Er have been attained. To reconstruct from experimental data with noise, Maximum Entropy and Gaussian-Bayesian tomography methods were applied and improved according to the characteristics of the LITP problem. With these improved methods, a reconstruction error level below 15% has been attained with a data noise level of 10%. These methods will be further tested and applied in the following LITP experiments. Supported by the ITER-CHINA program 2015GB120001, CHINA MOST under 2012YQ030142 and National Natural Science Foundation Abstract of China under 11575014 and 11375053.
A Maximum Entropy Approach to Assess Debonding in Honeycomb aluminum Plates
Directory of Open Access Journals (Sweden)
Viviana Meruane
2014-05-01
Full Text Available Honeycomb sandwich structures are used in a wide variety of applications. Nevertheless, due to manufacturing defects or impact loads, these structures can be subject to imperfect bonding or debonding between the skin and the honeycomb core. The presence of debonding reduces the bending stiffness of the composite panel, which causes detectable changes in its vibration characteristics. This article presents a new supervised learning algorithm to identify debonded regions in aluminum honeycomb panels. The algorithm uses a linear approximation method handled by a statistical inference model based on the maximum-entropy principle. The merits of this new approach are twofold: training is avoided and data is processed in a period of time that is comparable to the one of neural networks. The honeycomb panels are modeled with finite elements using a simplified three-layer shell model. The adhesive layer between the skin and core is modeled using linear springs, the rigidities of which are reduced in debonded sectors. The algorithm is validated using experimental data of an aluminum honeycomb panel under different damage scenarios.
Clements, Gopalasamy Reuben; Rayan, D Mark; Aziz, Sheema Abdul; Kawanishi, Kae; Traeholt, Carl; Magintan, David; Yazi, Muhammad Fadlli Abdul; Tingley, Reid
2012-12-01
In 2008, the IUCN threat status of the Asian tapir (Tapirus indicus) was reclassified from 'vulnerable' to 'endangered'. The latest distribution map from the IUCN Red List suggests that the tapirs' native range is becoming increasingly fragmented in Peninsular Malaysia, but distribution data collected by local researchers suggest a more extensive geographical range. Here, we compile a database of 1261 tapir occurrence records within Peninsular Malaysia, and demonstrate that this species, indeed, has a much broader geographical range than the IUCN range map suggests. However, extreme spatial and temporal bias in these records limits their utility for conservation planning. Therefore, we used maximum entropy (MaxEnt) modeling to elucidate the potential extent of the Asian tapir's occurrence in Peninsular Malaysia while accounting for bias in existing distribution data. Our MaxEnt model predicted that the Asian tapir has a wider geographic range than our fine-scale data and the IUCN range map both suggest. Approximately 37% of Peninsular Malaysia contains potentially suitable tapir habitats. Our results justify a revision to the Asian tapir's extent of occurrence in the IUCN Red List. Furthermore, our modeling demonstrated that selectively logged forests encompass 45% of potentially suitable tapir habitats, underscoring the importance of these habitats for the conservation of this species in Peninsular Malaysia. © 2012 Wiley Publishing Asia Pty Ltd, ISZS and IOZ/CAS.
Nazeri, Mona; Jusoff, Kamaruzaman; Madani, Nima; Mahmud, Ahmad Rodzi; Bahman, Abdul Rani; Kumar, Lalit
2012-01-01
One of the available tools for mapping the geographical distribution and potential suitable habitats is species distribution models. These techniques are very helpful for finding poorly known distributions of species in poorly sampled areas, such as the tropics. Maximum Entropy (MaxEnt) is a recently developed modeling method that can be successfully calibrated using a relatively small number of records. In this research, the MaxEnt model was applied to describe the distribution and identify the key factors shaping the potential distribution of the vulnerable Malayan Sun Bear (Helarctos malayanus) in one of the main remaining habitats in Peninsular Malaysia. MaxEnt results showed that even though Malaysian sun bear habitat is tied with tropical evergreen forests, it lives in a marginal threshold of bio-climatic variables. On the other hand, current protected area networks within Peninsular Malaysia do not cover most of the sun bears potential suitable habitats. Assuming that the predicted suitability map covers sun bears actual distribution, future climate change, forest degradation and illegal hunting could potentially severely affect the sun bear's population.
Directory of Open Access Journals (Sweden)
Mona Nazeri
Full Text Available One of the available tools for mapping the geographical distribution and potential suitable habitats is species distribution models. These techniques are very helpful for finding poorly known distributions of species in poorly sampled areas, such as the tropics. Maximum Entropy (MaxEnt is a recently developed modeling method that can be successfully calibrated using a relatively small number of records. In this research, the MaxEnt model was applied to describe the distribution and identify the key factors shaping the potential distribution of the vulnerable Malayan Sun Bear (Helarctos malayanus in one of the main remaining habitats in Peninsular Malaysia. MaxEnt results showed that even though Malaysian sun bear habitat is tied with tropical evergreen forests, it lives in a marginal threshold of bio-climatic variables. On the other hand, current protected area networks within Peninsular Malaysia do not cover most of the sun bears potential suitable habitats. Assuming that the predicted suitability map covers sun bears actual distribution, future climate change, forest degradation and illegal hunting could potentially severely affect the sun bear's population.
Stotts, Steven A; Koch, Robert A
2017-08-01
In this paper an approach is presented to estimate the constraint required to apply maximum entropy (ME) for statistical inference with underwater acoustic data from a single track segment. Previous algorithms for estimating the ME constraint require multiple source track segments to determine the constraint. The approach is relevant for addressing model mismatch effects, i.e., inaccuracies in parameter values determined from inversions because the propagation model does not account for all acoustic processes that contribute to the measured data. One effect of model mismatch is that the lowest cost inversion solution may be well outside a relatively well-known parameter value's uncertainty interval (prior), e.g., source speed from track reconstruction or towed source levels. The approach requires, for some particular parameter value, the ME constraint to produce an inferred uncertainty interval that encompasses the prior. Motivating this approach is the hypothesis that the proposed constraint determination procedure would produce a posterior probability density that accounts for the effect of model mismatch on inferred values of other inversion parameters for which the priors might be quite broad. Applications to both measured and simulated data are presented for model mismatch that produces minimum cost solutions either inside or outside some priors.
Gul, Sehrish; Zou, Xiang; Hassan, Che Hashim; Azam, Muhammad; Zaman, Khalid
2015-12-01
This study investigates the relationship between energy consumption and carbon dioxide emission in the causal framework, as the direction of causality remains has a significant policy implication for developed and developing countries. The study employed maximum entropy bootstrap (Meboot) approach to examine the causal nexus between energy consumption and carbon dioxide emission using bivariate as well as multivariate framework for Malaysia, over a period of 1975-2013. This is a unified approach without requiring the use of conventional techniques based on asymptotical theory such as testing for possible unit root and cointegration. In addition, it can be applied in the presence of non-stationary of any type including structural breaks without any type of data transformation to achieve stationary. Thus, it provides more reliable and robust inferences which are insensitive to time span as well as lag length used. The empirical results show that there is a unidirectional causality running from energy consumption to carbon emission both in the bivariate model and multivariate framework, while controlling for broad money supply and population density. The results indicate that Malaysia is an energy-dependent country and hence energy is stimulus to carbon emissions.
The Maximum Entropy Limit of Small-scale Magnetic Field Fluctuations in the Quiet Sun
Gorobets, A. Y.; Berdyugina, S. V.; Riethmüller, T. L.; Blanco Rodríguez, J.; Solanki, S. K.; Barthol, P.; Gandorfer, A.; Gizon, L.; Hirzberger, J.; van Noort, M.; Del Toro Iniesta, J. C.; Orozco Suárez, D.; Schmidt, W.; Martínez Pillet, V.; Knölker, M.
2017-11-01
The observed magnetic field on the solar surface is characterized by a very complex spatial and temporal behavior. Although feature-tracking algorithms have allowed us to deepen our understanding of this behavior, subjectivity plays an important role in the identification and tracking of such features. In this paper, we continue studies of the temporal stochasticity of the magnetic field on the solar surface without relying either on the concept of magnetic features or on subjective assumptions about their identification and interaction. We propose a data analysis method to quantify fluctuations of the line-of-sight magnetic field by means of reducing the temporal field’s evolution to the regular Markov process. We build a representative model of fluctuations converging to the unique stationary (equilibrium) distribution in the long time limit with maximum entropy. We obtained different rates of convergence to the equilibrium at fixed noise cutoff for two sets of data. This indicates a strong influence of the data spatial resolution and mixing-polarity fluctuations on the relaxation process. The analysis is applied to observations of magnetic fields of the relatively quiet areas around an active region carried out during the second flight of the Sunrise/IMaX and quiet Sun areas at the disk center from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory satellite.
Maximum-Entropy Models of Sequenced Immune Repertoires Predict Antigen-Antibody Affinity.
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Lorenzo Asti
2016-04-01
Full Text Available The immune system has developed a number of distinct complex mechanisms to shape and control the antibody repertoire. One of these mechanisms, the affinity maturation process, works in an evolutionary-like fashion: after binding to a foreign molecule, the antibody-producing B-cells exhibit a high-frequency mutation rate in the genome region that codes for the antibody active site. Eventually, cells that produce antibodies with higher affinity for their cognate antigen are selected and clonally expanded. Here, we propose a new statistical approach based on maximum entropy modeling in which a scoring function related to the binding affinity of antibodies against a specific antigen is inferred from a sample of sequences of the immune repertoire of an individual. We use our inference strategy to infer a statistical model on a data set obtained by sequencing a fairly large portion of the immune repertoire of an HIV-1 infected patient. The Pearson correlation coefficient between our scoring function and the IC50 neutralization titer measured on 30 different antibodies of known sequence is as high as 0.77 (p-value 10-6, outperforming other sequence- and structure-based models.
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Guo-Jheng Yang
2013-08-01
Full Text Available The fragile watermarking technique is used to protect intellectual property rights while also providing security and rigorous protection. In order to protect the copyright of the creators, it can be implanted in some representative text or totem. Because all of the media on the Internet are digital, protection has become a critical issue, and determining how to use digital watermarks to protect digital media is thus the topic of our research. This paper uses the Logistic map with parameter u = 4 to generate chaotic dynamic behavior with the maximum entropy 1. This approach increases the security and rigor of the protection. The main research target of information hiding is determining how to hide confidential data so that the naked eye cannot see the difference. Next, we introduce one method of information hiding. Generally speaking, if the image only goes through Arnold’s cat map and the Logistic map, it seems to lack sufficient security. Therefore, our emphasis is on controlling Arnold’s cat map and the initial value of the chaos system to undergo small changes and generate different chaos sequences. Thus, the current time is used to not only make encryption more stringent but also to enhance the security of the digital media.
Analysis of QCD sum rule based on the maximum entropy method
International Nuclear Information System (INIS)
Gubler, Philipp
2012-01-01
QCD sum rule was developed about thirty years ago and has been used up to the present to calculate various physical quantities like hadrons. It has been, however, needed to assume 'pole + continuum' for the spectral function in the conventional analyses. Application of this method therefore came across with difficulties when the above assumption is not satisfied. In order to avoid this difficulty, analysis to make use of the maximum entropy method (MEM) has been developed by the present author. It is reported here how far this new method can be successfully applied. In the first section, the general feature of the QCD sum rule is introduced. In section 2, it is discussed why the analysis by the QCD sum rule based on the MEM is so effective. In section 3, the MEM analysis process is described, and in the subsection 3.1 likelihood function and prior probability are considered then in subsection 3.2 numerical analyses are picked up. In section 4, some cases of applications are described starting with ρ mesons, then charmoniums in the finite temperature and finally recent developments. Some figures of the spectral functions are shown. In section 5, summing up of the present analysis method and future view are given. (S. Funahashi)
Zhang, Lin; Hou, Xuexia; Liu, Huixin; Liu, Wei; Wan, Kanglin; Hao, Qin
2016-01-01
To predict the potential geographic distribution of Lyme disease in Qinghai by using Maximum Entropy model (MaxEnt). The sero-diagnosis data of Lyme disease in 6 counties (Huzhu, Zeku, Tongde, Datong, Qilian and Xunhua) and the environmental and anthropogenic data including altitude, human footprint, normalized difference vegetation index (NDVI) and temperature in Qinghai province since 1990 were collected. By using the data of Huzhu Zeku and Tongde, the prediction of potential distribution of Lyme disease in Qinghai was conducted with MaxEnt. The prediction results were compared with the human sero-prevalence of Lyme disease in Datong, Qilian and Xunhua counties in Qinghai. Three hot spots of Lyme disease were predicted in Qinghai, which were all in the east forest areas. Furthermore, the NDVI showed the most important role in the model prediction, followed by human footprint. Datong, Qilian and Xunhua counties were all in eastern Qinghai. Xunhua was in hot spot areaⅡ, Datong was close to the north of hot spot area Ⅲ, while Qilian with lowest sero-prevalence of Lyme disease was not in the hot spot areas. The data were well modeled in MaxEnt (Area Under Curve=0.980). The actual distribution of Lyme disease in Qinghai was in consistent with the results of the model prediction. MaxEnt could be used in predicting the potential distribution patterns of Lyme disease. The distribution of vegetation and the range and intensity of human activity might be related with Lyme disease distribution.
Well posedness and maximum entropy approximation for the dynamics of quantitative traits
Boďová, Katarína
2017-11-06
We study the Fokker–Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker–Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain’s boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker–Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.
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Hea-Jung Kim
2016-05-01
Full Text Available This paper proposes a two-stage maximum entropy prior to elicit uncertainty regarding a multivariate interval constraint of the location parameter of a scale mixture of normal model. Using Shannon’s entropy, this study demonstrates how the prior, obtained by using two stages of a prior hierarchy, appropriately accounts for the information regarding the stochastic constraint and suggests an objective measure of the degree of belief in the stochastic constraint. The study also verifies that the proposed prior plays the role of bridging the gap between the canonical maximum entropy prior of the parameter with no interval constraint and that with a certain multivariate interval constraint. It is shown that the two-stage maximum entropy prior belongs to the family of rectangle screened normal distributions that is conjugate for samples from a normal distribution. Some properties of the prior density, useful for developing a Bayesian inference of the parameter with the stochastic constraint, are provided. We also propose a hierarchical constrained scale mixture of normal model (HCSMN, which uses the prior density to estimate the constrained location parameter of a scale mixture of normal model and demonstrates the scope of its applicability.
A subjective supply–demand model: the maximum Boltzmann/Shannon entropy solution
International Nuclear Information System (INIS)
Piotrowski, Edward W; Sładkowski, Jan
2009-01-01
The present authors have put forward a projective geometry model of rational trading. The expected (mean) value of the time that is necessary to strike a deal and the profit strongly depend on the strategies adopted. A frequent trader often prefers maximal profit intensity to the maximization of profit resulting from a separate transaction because the gross profit/income is the adopted/recommended benchmark. To investigate activities that have different periods of duration we define, following the queuing theory, the profit intensity as a measure of this economic category. The profit intensity in repeated trading has a unique property of attaining its maximum at a fixed point regardless of the shape of demand curves for a wide class of probability distributions of random reverse transactions (i.e. closing of the position). These conclusions remain valid for an analogous model based on supply analysis. This type of market game is often considered in research aiming at finding an algorithm that maximizes profit of a trader who negotiates prices with the Rest of the World (a collective opponent), possessing a definite and objective supply profile. Such idealization neglects the sometimes important influence of an individual trader on the demand/supply profile of the Rest of the World and in extreme cases questions the very idea of demand/supply profile. Therefore we put forward a trading model in which the demand/supply profile of the Rest of the World induces the (rational) trader to (subjectively) presume that he/she lacks (almost) all knowledge concerning the market but his/her average frequency of trade. This point of view introduces maximum entropy principles into the model and broadens the range of economic phenomena that can be perceived as a sort of thermodynamical system. As a consequence, the profit intensity has a fixed point with an astonishing connection with Fibonacci classical works and looking for the quickest algorithm for obtaining the extremum of a
A subjective supply-demand model: the maximum Boltzmann/Shannon entropy solution
Piotrowski, Edward W.; Sładkowski, Jan
2009-03-01
The present authors have put forward a projective geometry model of rational trading. The expected (mean) value of the time that is necessary to strike a deal and the profit strongly depend on the strategies adopted. A frequent trader often prefers maximal profit intensity to the maximization of profit resulting from a separate transaction because the gross profit/income is the adopted/recommended benchmark. To investigate activities that have different periods of duration we define, following the queuing theory, the profit intensity as a measure of this economic category. The profit intensity in repeated trading has a unique property of attaining its maximum at a fixed point regardless of the shape of demand curves for a wide class of probability distributions of random reverse transactions (i.e. closing of the position). These conclusions remain valid for an analogous model based on supply analysis. This type of market game is often considered in research aiming at finding an algorithm that maximizes profit of a trader who negotiates prices with the Rest of the World (a collective opponent), possessing a definite and objective supply profile. Such idealization neglects the sometimes important influence of an individual trader on the demand/supply profile of the Rest of the World and in extreme cases questions the very idea of demand/supply profile. Therefore we put forward a trading model in which the demand/supply profile of the Rest of the World induces the (rational) trader to (subjectively) presume that he/she lacks (almost) all knowledge concerning the market but his/her average frequency of trade. This point of view introduces maximum entropy principles into the model and broadens the range of economic phenomena that can be perceived as a sort of thermodynamical system. As a consequence, the profit intensity has a fixed point with an astonishing connection with Fibonacci classical works and looking for the quickest algorithm for obtaining the extremum of a
Quantumness of bipartite states in terms of conditional entropies
International Nuclear Information System (INIS)
Li, Nan; Luo, Shunlong; Zhang, Zhengmin
2007-01-01
Quantum discord, as defined by Olliver and Zurek (2002 Phys. Rev. Lett. 88 017901) as the difference of two natural quantum extensions of the classical mutual information, plays an interesting role in characterizing quantumness of correlations. Inspired by this idea, we will study quantumness of bipartite states arising from different quantum analogs of the classical conditional entropy. Our approach is intrinsic, in contrast to the Olliver-Zurek method that involves extrinsic local measurements. For this purpose, we introduce two alternative variants of quantum conditional entropies via conditional density operators, which in turn are intuitive quantum extensions of equivalent classical expressions for the conditional probability. The significance of these quantum conditional entropies in characterizing quantumness of bipartite states is illustrated through several examples
Entanglement entropy from tensor network states for stabilizer codes
He, Huan; Zheng, Yunqin; Bernevig, B. Andrei; Regnault, Nicolas
2018-03-01
In this paper, we present the construction of tensor network states (TNS) for some of the degenerate ground states of three-dimensional (3D) stabilizer codes. We then use the TNS formalism to obtain the entanglement spectrum and entropy of these ground states for some special cuts. In particular, we work out examples of the 3D toric code, the X-cube model, and the Haah code. The latter two models belong to the category of "fracton" models proposed recently, while the first one belongs to the conventional topological phases. We mention the cases for which the entanglement entropy and spectrum can be calculated exactly: For these, the constructed TNS is a singular value decomposition (SVD) of the ground states with respect to particular entanglement cuts. Apart from the area law, the entanglement entropies also have constant and linear corrections for the fracton models, while the entanglement entropies for the toric code models only have constant corrections. For the cuts we consider, the entanglement spectra of these three models are completely flat. We also conjecture that the negative linear correction to the area law is a signature of extensive ground-state degeneracy. Moreover, the transfer matrices of these TNSs can be constructed. We show that the transfer matrices are projectors whose eigenvalues are either 1 or 0. The number of nonzero eigenvalues is tightly related to the ground-state degeneracy.
Tang, Qingxin; Bo, Yanchen; Zhu, Yuxin
2016-04-01
Merging multisensor aerosol optical depth (AOD) products is an effective way to produce more spatiotemporally complete and accurate AOD products. A spatiotemporal statistical data fusion framework based on a Bayesian maximum entropy (BME) method was developed for merging satellite AOD products in East Asia. The advantages of the presented merging framework are that it not only utilizes the spatiotemporal autocorrelations but also explicitly incorporates the uncertainties of the AOD products being merged. The satellite AOD products used for merging are the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 5.1 Level-2 AOD products (MOD04_L2) and the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Deep Blue Level 2 AOD products (SWDB_L2). The results show that the average completeness of the merged AOD data is 95.2%,which is significantly superior to the completeness of MOD04_L2 (22.9%) and SWDB_L2 (20.2%). By comparing the merged AOD to the Aerosol Robotic Network AOD records, the results show that the correlation coefficient (0.75), root-mean-square error (0.29), and mean bias (0.068) of the merged AOD are close to those (the correlation coefficient (0.82), root-mean-square error (0.19), and mean bias (0.059)) of the MODIS AOD. In the regions where both MODIS and SeaWiFS have valid observations, the accuracy of the merged AOD is higher than those of MODIS and SeaWiFS AODs. Even in regions where both MODIS and SeaWiFS AODs are missing, the accuracy of the merged AOD is also close to the accuracy of the regions where both MODIS and SeaWiFS have valid observations.
Yu, Hwa-Lung; Wang, Chih-Hsin
2013-02-05
Understanding the daily changes in ambient air quality concentrations is important to the assessing human exposure and environmental health. However, the fine temporal scales (e.g., hourly) involved in this assessment often lead to high variability in air quality concentrations. This is because of the complex short-term physical and chemical mechanisms among the pollutants. Consequently, high heterogeneity is usually present in not only the averaged pollution levels, but also the intraday variance levels of the daily observations of ambient concentration across space and time. This characteristic decreases the estimation performance of common techniques. This study proposes a novel quantile-based Bayesian maximum entropy (QBME) method to account for the nonstationary and nonhomogeneous characteristics of ambient air pollution dynamics. The QBME method characterizes the spatiotemporal dependence among the ambient air quality levels based on their location-specific quantiles and accounts for spatiotemporal variations using a local weighted smoothing technique. The epistemic framework of the QBME method can allow researchers to further consider the uncertainty of space-time observations. This study presents the spatiotemporal modeling of daily CO and PM10 concentrations across Taiwan from 1998 to 2009 using the QBME method. Results show that the QBME method can effectively improve estimation accuracy in terms of lower mean absolute errors and standard deviations over space and time, especially for pollutants with strong nonhomogeneous variances across space. In addition, the epistemic framework can allow researchers to assimilate the site-specific secondary information where the observations are absent because of the common preferential sampling issues of environmental data. The proposed QBME method provides a practical and powerful framework for the spatiotemporal modeling of ambient pollutants.
Gutierrez-Jurado, H. A.; Guan, H.; Wang, J.; Wang, H.; Bras, R. L.; Simmons, C. T.
2015-12-01
Quantification of evapotranspiration (ET) and its partition over regions of heterogeneous topography and canopy poses a challenge using traditional approaches. In this study, we report the results of a novel field experiment design guided by the Maximum Entropy Production model of ET (MEP-ET), formulated for estimating evaporation and transpiration from homogeneous soil and canopy. A catchment with complex terrain and patchy vegetation in South Australia was instrumented to measure temperature, humidity and net radiation at soil and canopy surfaces. Performance of the MEP-ET model to quantify transpiration and soil evaporation was evaluated during wet and dry conditions with independently and directly measured transpiration from sapflow and soil evaporation using the Bowen Ratio Energy Balance (BREB). MEP-ET transpiration shows remarkable agreement with that obtained through sapflow measurements during wet conditions, but consistently overestimates the flux during dry periods. However, an additional term introduced to the original MEP-ET model accounting for higher stomatal regulation during dry spells, based on differences between leaf and air vapor pressure deficits and temperatures, significantly improves the model performance. On the other hand, MEP-ET soil evaporation is in good agreement with that from BREB regardless of moisture conditions. The experimental design allows a plot and tree scale quantification of evaporation and transpiration respectively. This study confirms for the first time that the MEP-ET originally developed for homogeneous open bare soil and closed canopy can be used for modeling ET over heterogeneous land surfaces. Furthermore, we show that with the addition of an empirical function simulating the plants ability to regulate transpiration, and based on the same measurements of temperature and humidity, the method can produce reliable estimates of ET during both wet and dry conditions without compromising its parsimony.
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Kai Yan
2015-01-01
Full Text Available A predictive model for droplet size and velocity distributions of a pressure swirl atomizer has been proposed based on the maximum entropy formalism (MEF. The constraint conditions of the MEF model include the conservation laws of mass, momentum, and energy. The effects of liquid swirling strength, Weber number, gas-to-liquid axial velocity ratio and gas-to-liquid density ratio on the droplet size and velocity distributions of a pressure swirl atomizer are investigated. Results show that model based on maximum entropy formalism works well to predict droplet size and velocity distributions under different spray conditions. Liquid swirling strength, Weber number, gas-to-liquid axial velocity ratio and gas-to-liquid density ratio have different effects on droplet size and velocity distributions of a pressure swirl atomizer.
International Nuclear Information System (INIS)
Nasser, Hassan; Cessac, Bruno; Marre, Olivier
2013-01-01
Understanding the dynamics of neural networks is a major challenge in experimental neuroscience. For that purpose, a modelling of the recorded activity that reproduces the main statistics of the data is required. In the first part, we present a review on recent results dealing with spike train statistics analysis using maximum entropy models (MaxEnt). Most of these studies have focused on modelling synchronous spike patterns, leaving aside the temporal dynamics of the neural activity. However, the maximum entropy principle can be generalized to the temporal case, leading to Markovian models where memory effects and time correlations in the dynamics are properly taken into account. In the second part, we present a new method based on Monte Carlo sampling which is suited for the fitting of large-scale spatio-temporal MaxEnt models. The formalism and the tools presented here will be essential to fit MaxEnt spatio-temporal models to large neural ensembles. (paper)
International Nuclear Information System (INIS)
Gutierrez, Rafael M.; Useche, Gina M.; Buitrago, Elias
2007-01-01
We present a procedure developed to detect stochastic and deterministic information contained in empirical time series, useful to characterize and make models of different aspects of complex phenomena represented by such data. This procedure is applied to a seismological time series to obtain new information to study and understand geological phenomena. We use concepts and methods from nonlinear dynamics and maximum entropy. The mentioned method allows an optimal analysis of the available information
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Lotfi Khribi
2017-12-01
Full Text Available In the Bayesian framework, the usual choice of prior in the prediction of homogeneous Poisson processes with random effects is the gamma one. Here, we propose the use of higher order maximum entropy priors. Their advantage is illustrated in a simulation study and the choice of the best order is established by two goodness-of-fit criteria: Kullback–Leibler divergence and a discrepancy measure. This procedure is illustrated on a warranty data set from the automobile industry.
International Nuclear Information System (INIS)
Reginatto, M.; Goldhagen, P.
1998-06-01
The problem of analyzing data from a multisphere neutron spectrometer to infer the energy spectrum of the incident neutrons is discussed. The main features of the code MAXED, a computer program developed to apply the maximum entropy principle to the deconvolution (unfolding) of multisphere neutron spectrometer data, are described, and the use of the code is illustrated with an example. A user's guide for the code MAXED is included in an appendix. The code is available from the authors upon request
International Nuclear Information System (INIS)
Bispo, Heleno; Silva, Nilton; Brito, Romildo; Manzi, João
2013-01-01
Highlights: • Minimum entropy generation (MEG) principle improved the reaction performance. • MEG rate and the maximum conversion equivalence have been analyzed. • Temperature and residence time are used to the domain establishment of MEG. • Satisfying the temperature and residence time relationship results a optimal performance. - Abstract: The analysis of the equivalence between the minimum entropy generation (MEG) rate and the maximum conversion rate for a reactive system is the main purpose of this paper. While being used as a strategy of optimization, the minimum entropy production was applied to the production of propylene glycol in a Continuous Stirred-Tank Reactor (CSTR) with a view to determining the best operating conditions, and under such conditions, a high conversion rate was found. The effects of the key variables and restrictions on the validity domain of MEG were investigated, which raises issues that are included within a broad discussion. The results from simulations indicate that from the chemical reaction standpoint a maximum conversion rate can be considered as equivalent to MEG. Such a result can be clearly explained by examining the classical Maxwell–Boltzmann distribution, where the molecules of the reactive system under the condition of the MEG rate present a distribution of energy with reduced dispersion resulting in a better quality of collision between molecules with a higher conversion rate
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Javier A. Dottori
2015-01-01
Full Text Available A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that there is a correlation with the velocity gradient during the flow development.
International Nuclear Information System (INIS)
Iwama, N.; Inoue, A.; Tsukishima, T.; Sato, M.; Kawahata, K.
1981-07-01
A new procedure for the maximum entropy spectral estimation is studied for the purpose of data processing in Fourier transform spectroscopy. The autoregressive model fitting is examined under a least squares criterion based on the Yule-Walker equations. An AIC-like criterion is suggested for selecting the model order. The principal advantage of the new procedure lies in the enhanced frequency resolution particularly for small values of the maximum optical path-difference of the interferogram. The usefulness of the procedure is ascertained by some numerical simulations and further by experiments with respect to a highly coherent submillimeter wave and the electron cyclotron emission from a stellarator plasma. (author)
Mishra, V.; Cruise, J. F.; Mecikalski, J. R.
2015-12-01
Developing accurate vertical soil moisture profiles with minimum input requirements is important to agricultural as well as land surface modeling. Earlier studies show that the principle of maximum entropy (POME) can be utilized to develop vertical soil moisture profiles with accuracy (MAE of about 1% for a monotonically dry profile; nearly 2% for monotonically wet profiles and 3.8% for mixed profiles) with minimum constraints (surface, mean and bottom soil moisture contents). In this study, the constraints for the vertical soil moisture profiles were obtained from remotely sensed data. Low resolution (25 km) MW soil moisture estimates (AMSR-E) were downscaled to 4 km using a soil evaporation efficiency index based disaggregation approach. The downscaled MW soil moisture estimates served as a surface boundary condition, while 4 km resolution TIR based Atmospheric Land Exchange Inverse (ALEXI) estimates provided the required mean root-zone soil moisture content. Bottom soil moisture content is assumed to be a soil dependent constant. Mulit-year (2002-2011) gridded profiles were developed for the southeastern United States using the POME method. The soil moisture profiles were compared to those generated in land surface models (Land Information System (LIS) and an agricultural model DSSAT) along with available NRCS SCAN sites in the study region. The end product, spatial soil moisture profiles, can be assimilated into agricultural and hydrologic models in lieu of precipitation for data scarce regions.Developing accurate vertical soil moisture profiles with minimum input requirements is important to agricultural as well as land surface modeling. Previous studies have shown that the principle of maximum entropy (POME) can be utilized with minimal constraints to develop vertical soil moisture profiles with accuracy (MAE = 1% for monotonically dry profiles; MAE = 2% for monotonically wet profiles and MAE = 3.8% for mixed profiles) when compared to laboratory and field
International Nuclear Information System (INIS)
Engel, Y.M.; Friedman, E.; Levine, R.D.
1982-01-01
Radial moments of the real part of the optical potential for elastic scattering of 104 MeV α particles are used as constraints, in determining the nuclear density of maximal entropy. The potential is related to the density by the folding model. (orig.)
Maximum nonlocality and minimum uncertainty using magic states
Howard, Mark
2015-04-01
We prove that magic states from the Clifford hierarchy give optimal solutions for tasks involving nonlocality and entropic uncertainty with respect to Pauli measurements. For both the nonlocality and uncertainty tasks, stabilizer states are the worst possible pure states, so our solutions have an operational interpretation as being highly nonstabilizer. The optimal strategy for a qudit version of the Clauser-Horne-Shimony-Holt game in prime dimensions is achieved by measuring maximally entangled states that are isomorphic to single-qudit magic states. These magic states have an appealingly simple form, and our proof shows that they are "balanced" with respect to all but one of the mutually unbiased stabilizer bases. Of all equatorial qudit states, magic states minimize the average entropic uncertainties for collision entropy and also, for small prime dimensions, min-entropy, a fact that may have implications for cryptography.
Can state or response entropy be used as a measure of sleep depth?
LENUS (Irish Health Repository)
Mahon, P
2012-02-03
SUMMARY: In this prospective observational study we examined the potential of the spectral entropy measures \\'state\\' and \\'response\\' entropy (Entropy monitor), as measures of sleep depth in 12 healthy adult subjects. Both median state and response entropy values varied significantly with sleep stage (p = 0.017 and p = 0.014 respectively; ANOVA). Median state or response entropy did not decrease significantly during the transition from awake to stage I sleep (p > 0.017). State entropy values decreased significantly between sleep stages I and II (p < 0.001). Both state and response entropy values were significantly less (40 and 45 arbitrary units respectively) in stage III (slow wave sleep) vs stage II sleep (p = 0.008). We conclude that state and response entropy values, when expressed as a function of time, may be a useful means of quantifying aspects of sleep.
International Nuclear Information System (INIS)
Johannessen, Eivind; Rosjorde, Audun
2007-01-01
We show that the theorem of equipartition of entropy production is important for the understanding of the state of minimum entropy production in diabatic distillation. The theorem is not valid in a strictly mathematical sense. We explain why, when and in what sense this theorem is a good approximation to the optimal state in diabatic distillation. In order to make these predictions, we use a hypothesis for the state of minimum entropy production of an optimally controlled system, which was formulated on the basis of results of entropy production minimisation in chemical reactors. The hypothesis says that the state of minimum entropy production is characterised by approximately constant local entropy production and thermodynamic forces, given that there is sufficient freedom in the system. We present numerical results which are in agreement with the predictions. The results show that a column with constant tray entropy production in the stripping section and in the rectifying section is a good approximation to the optimal column, except when the total heat transfer area is low. The agreement between the two columns becomes better and better as the total heat transfer area and the number of trays increase. The fact that the predictions and the numerical results agree very well gives support to the validity of the hypothesis
Maximum Kolmogorov-Sinai Entropy Versus Minimum Mixing Time in Markov Chains
Mihelich, M.; Dubrulle, B.; Paillard, D.; Kral, Q.; Faranda, D.
2018-01-01
We establish a link between the maximization of Kolmogorov Sinai entropy (KSE) and the minimization of the mixing time for general Markov chains. Since the maximisation of KSE is analytical and easier to compute in general than mixing time, this link provides a new faster method to approximate the minimum mixing time dynamics. It could be interesting in computer sciences and statistical physics, for computations that use random walks on graphs that can be represented as Markov chains.
Directory of Open Access Journals (Sweden)
Guoqing Li
2014-11-01
Full Text Available Black locust (Robinia pseudoacacia L. is a tree species of high economic and ecological value, but is also considered to be highly invasive. Understanding the global potential distribution and ecological characteristics of this species is a prerequisite for its practical exploitation as a resource. Here, a maximum entropy modeling (MaxEnt was used to simulate the potential distribution of this species around the world, and the dominant climatic factors affecting its distribution were selected by using a jackknife test and the regularized gain change during each iteration of the training algorithm. The results show that the MaxEnt model performs better than random, with an average test AUC value of 0.9165 (±0.0088. The coldness index, annual mean temperature and warmth index were the most important climatic factors affecting the species distribution, explaining 65.79% of the variability in the geographical distribution. Species response curves showed unimodal relationships with the annual mean temperature and warmth index, whereas there was a linear relationship with the coldness index. The dominant climatic conditions in the core of the black locust distribution are a coldness index of −9.8 °C–0 °C, an annual mean temperature of 5.8 °C–14.5 °C, a warmth index of 66 °C–168 °C and an annual precipitation of 508–1867 mm. The potential distribution of black locust is located mainly in the United States, the United Kingdom, Germany, France, the Netherlands, Belgium, Italy, Switzerland, Australia, New Zealand, China, Japan, South Korea, South Africa, Chile and Argentina. The predictive map of black locust, climatic thresholds and species response curves can provide globally applicable guidelines and valuable information for policymakers and planners involved in the introduction, planting and invasion control of this species around the world.
International Nuclear Information System (INIS)
Yin, Chukai; Su, Bingjing
2001-01-01
The Minerbo's maximum entropy Eddington factor (MEEF) method was proposed as a low-order approximation to transport theory, in which the first two moment equations are closed for the scalar flux f and the current F through a statistically derived nonlinear Eddington factor f. This closure has the ability to handle various degrees of anisotropy of angular flux and is well justified both numerically and theoretically. Thus, a lot of efforts have been made to use this approximation in transport computations, especially in the radiative transfer and astrophysics communities. However, the method suffers numerical instability and may lead to anomalous solutions if the equations are solved by certain commonly used (implicit) mesh schemes. Studies on numerical stability in one-dimensional cases show that the MEEF equations can be solved satisfactorily by an implicit scheme (of treating δΦ/δx) if the angular flux is not too anisotropic so that f 32 , the classic diffusion solution P 1 , the MEEF solution f M obtained by Riemann solvers, and the NFLD solution D M for the two problems, respectively. In Fig. 1, NFLD and MEEF quantitatively predict very close results. However, the NFLD solution is qualitatively better because it is continuous while MEEF predicts unphysical jumps near the middle of the slab. In Fig. 2, the NFLD and MEEF solutions are almost identical, except near the material interface. In summary, the flux-limited diffusion theory derived from the MEEF description is quantitatively as accurate as the MEEF method. However, it is more qualitatively correct and user-friendly than the MEEF method and can be applied efficiently to various steady-state problems. Numerical tests show that this method is widely valid and overall predicts better results than other low-order approximations for various kinds of problems, including eigenvalue problems. Thus, it is an appealing approximate solution technique that is fast computationally and yet is accurate enough for a
Entropy and density of states from isoenergetic nonequilibrium processes
Adib, Artur B.
2005-05-01
Two identities in statistical mechanics involving entropy differences (or ratios of densities of states) at constant energy are derived. The first provides a nontrivial extension of the Jarzynski equality to the microcanonical ensemble [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)], which can be seen as a “fast-switching” version of the adiabatic switching method for computing entropies [M. Watanabe and W. P. Reinhardt, Phys. Rev. Lett. 65, 3301 (1990)]. The second is a thermodynamic integration formula analogous to a well-known expression for free energies, and follows after taking the quasistatic limit of the first. Both identities can be conveniently used in conjunction with a scaling relation (herein derived) that allows one to extrapolate measurements taken at a single energy to a wide range of energy values. Practical aspects of these identities in the context of numerical simulations are discussed.
Lorenz, Ralph D
2010-05-12
The 'two-box model' of planetary climate is discussed. This model has been used to demonstrate consistency of the equator-pole temperature gradient on Earth, Mars and Titan with what would be predicted from a principle of maximum entropy production (MEP). While useful for exposition and for generating first-order estimates of planetary heat transports, it has too low a resolution to investigate climate systems with strong feedbacks. A two-box MEP model agrees well with the observed day : night temperature contrast observed on the extrasolar planet HD 189733b.
Ishimatsu, N; Takata, M; Nishibori, E; Sakata, M; Hayashi, J; Shirotani, I; Shimomura, O
2002-01-01
The physical properties relating to 4f electrons in cerium phosphide, especially the temperature dependence and the isomorphous transition that occurs at around 10 GPa, were studied by means of x-ray powder diffraction and charge density distribution maps derived by the maximum-entropy method. The compressibility of CeP was exactly determined using a helium pressure medium and the anomaly that indicated the isomorphous transition was observed in the compressibility. We also discuss the anisotropic charge density distribution of Ce ions and its temperature dependence.
Zero-contingent entropy of quantum states of a Hydrogen atom
International Nuclear Information System (INIS)
Charvot, R.; Majernik, V.
1996-01-01
We calculated the zero-contingent entropy for the position of electron in H-atom as a function of its quantum numbers and compared it with the corresponding value of the Shannon entropy. The values of zero-contingent entropy of quantum states of H-atom correlate well with the corresponding values of Shannon's entropy. This points out that, besides the Shannon entropy, the zero-contingent entropy represents an appropriate, and mathematically rather simple, measure of the spreading out of the wave functions in H-atom. (authors)
2017-08-21
number of neurons. Time is discretized and we assume any neuron can spike no more than once in a time bin. We have ν ≤ µ because ν is the probability of a...Comput. Appl. Math . 2000, 121, 331–354. 27. Shalizi, C.; Crutchfield, J. Computational mechanics: Pattern and prediction, structure and simplicity. J...Minimization of a Linearly Constrained Function by Partition of Feasible Domain. Math . Oper. Res. 1983, 8, 215–230. Entropy 2017, 19, 427 33 of 33 54. Candes, E
Maximum entropy algorithm and its implementation for the neutral beam profile measurement
Energy Technology Data Exchange (ETDEWEB)
Lee, Seung Wook; Cho, Gyu Seong [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of); Cho, Yong Sub [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1997-12-31
A tomography algorithm to maximize the entropy of image using Lagrangian multiplier technique and conjugate gradient method has been designed for the measurement of 2D spatial distribution of intense neutral beams of KSTAR NBI (Korea Superconducting Tokamak Advanced Research Neutral Beam Injector), which is now being designed. A possible detection system was assumed and a numerical simulation has been implemented to test the reconstruction quality of given beam profiles. This algorithm has the good applicability for sparse projection data and thus, can be used for the neutral beam tomography. 8 refs., 3 figs. (Author)
Maximum entropy algorithm and its implementation for the neutral beam profile measurement
Energy Technology Data Exchange (ETDEWEB)
Lee, Seung Wook; Cho, Gyu Seong [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of); Cho, Yong Sub [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
A tomography algorithm to maximize the entropy of image using Lagrangian multiplier technique and conjugate gradient method has been designed for the measurement of 2D spatial distribution of intense neutral beams of KSTAR NBI (Korea Superconducting Tokamak Advanced Research Neutral Beam Injector), which is now being designed. A possible detection system was assumed and a numerical simulation has been implemented to test the reconstruction quality of given beam profiles. This algorithm has the good applicability for sparse projection data and thus, can be used for the neutral beam tomography. 8 refs., 3 figs. (Author)
International Nuclear Information System (INIS)
Papoular, R.J.; Zheludev, A.; Ressouche, E.; Schweizer, J.
1995-01-01
When density distributions in crystals are reconstructed from 3D diffraction data, a problem sometimes occurs when the spatial resolution in one given direction is very small compared to that in perpendicular directions. In this case, a 2D projected density is usually reconstructed. For this task, the conventional Fourier inversion method only makes use of those structure factors measured in the projection plane. All the other structure factors contribute zero to the reconstruction of a projected density. On the contrary, the maximum-entropy method uses all the 3D data, to yield 3D-enhanced 2D projected density maps. It is even possible to reconstruct a projection in the extreme case when not one structure factor in the plane of projection is known. In the case of poor resolution along one given direction, a Fourier inversion reconstruction gives very low quality 3D densities 'smeared' in the third dimension. The application of the maximum-entropy procedure reduces the smearing significantly and reasonably well resolved projections along most directions can now be obtained from the MaxEnt 3D density. To illustrate these two ideas, particular examples based on real polarized neutron diffraction data sets are presented. (orig.)
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.)
Directory of Open Access Journals (Sweden)
S. H. Chiang
2016-06-01
Full Text Available Forest is a very important ecosystem and natural resource for living things. Based on forest inventories, government is able to make decisions to converse, improve and manage forests in a sustainable way. Field work for forestry investigation is difficult and time consuming, because it needs intensive physical labor and the costs are high, especially surveying in remote mountainous regions. A reliable forest inventory can give us a more accurate and timely information to develop new and efficient approaches of forest management. The remote sensing technology has been recently used for forest investigation at a large scale. To produce an informative forest inventory, forest attributes, including tree species are unavoidably required to be considered. In this study the aim is to classify forest tree species in Erdenebulgan County, Huwsgul province in Mongolia, using Maximum Entropy method. The study area is covered by a dense forest which is almost 70% of total territorial extension of Erdenebulgan County and is located in a high mountain region in northern Mongolia. For this study, Landsat satellite imagery and a Digital Elevation Model (DEM were acquired to perform tree species mapping. The forest tree species inventory map was collected from the Forest Division of the Mongolian Ministry of Nature and Environment as training data and also used as ground truth to perform the accuracy assessment of the tree species classification. Landsat images and DEM were processed for maximum entropy modeling, and this study applied the model with two experiments. The first one is to use Landsat surface reflectance for tree species classification; and the second experiment incorporates terrain variables in addition to the Landsat surface reflectance to perform the tree species classification. All experimental results were compared with the tree species inventory to assess the classification accuracy. Results show that the second one which uses Landsat surface
Hao Chiang, Shou; Valdez, Miguel; Chen, Chi-Farn
2016-06-01
Forest is a very important ecosystem and natural resource for living things. Based on forest inventories, government is able to make decisions to converse, improve and manage forests in a sustainable way. Field work for forestry investigation is difficult and time consuming, because it needs intensive physical labor and the costs are high, especially surveying in remote mountainous regions. A reliable forest inventory can give us a more accurate and timely information to develop new and efficient approaches of forest management. The remote sensing technology has been recently used for forest investigation at a large scale. To produce an informative forest inventory, forest attributes, including tree species are unavoidably required to be considered. In this study the aim is to classify forest tree species in Erdenebulgan County, Huwsgul province in Mongolia, using Maximum Entropy method. The study area is covered by a dense forest which is almost 70% of total territorial extension of Erdenebulgan County and is located in a high mountain region in northern Mongolia. For this study, Landsat satellite imagery and a Digital Elevation Model (DEM) were acquired to perform tree species mapping. The forest tree species inventory map was collected from the Forest Division of the Mongolian Ministry of Nature and Environment as training data and also used as ground truth to perform the accuracy assessment of the tree species classification. Landsat images and DEM were processed for maximum entropy modeling, and this study applied the model with two experiments. The first one is to use Landsat surface reflectance for tree species classification; and the second experiment incorporates terrain variables in addition to the Landsat surface reflectance to perform the tree species classification. All experimental results were compared with the tree species inventory to assess the classification accuracy. Results show that the second one which uses Landsat surface reflectance coupled
Chung-Wei, Li; Gwo-Hshiung, Tzeng
To deal with complex problems, structuring them through graphical representations and analyzing causal influences can aid in illuminating complex issues, systems, or concepts. The DEMATEL method is a methodology which can be used for researching and solving complicated and intertwined problem groups. The end product of the DEMATEL process is a visual representation—the impact-relations map—by which respondents organize their own actions in the world. The applicability of the DEMATEL method is widespread, ranging from analyzing world problematique decision making to industrial planning. The most important property of the DEMATEL method used in the multi-criteria decision making (MCDM) field is to construct interrelations between criteria. In order to obtain a suitable impact-relations map, an appropriate threshold value is needed to obtain adequate information for further analysis and decision-making. In this paper, we propose a method based on the entropy approach, the maximum mean de-entropy algorithm, to achieve this purpose. Using real cases to find the interrelationships between the criteria for evaluating effects in E-learning programs as an examples, we will compare the results obtained from the respondents and from our method, and discuss that the different impact-relations maps from these two methods.
Spectral shaping of a randomized PWM DC-DC converter using maximum entropy probability distributions
CSIR Research Space (South Africa)
Dove, Albert
2017-01-01
Full Text Available maintaining constraints in a DC-DC converter is investigated. A probability distribution whose aim is to ensure maximal harmonic spreading and yet mainaint constraints is presented. The PDFs are determined from a direct application of the method of Maximum...
Kakemoto, H; Makita, Y; Kino, Y; Tsukamoto, T; Shin, S; Wada, S; Tsurumi, T
2003-01-01
The electronic structure of beta-FeSi sub 2 was investigated by maximum entropy method (MEM) and photoemission spectroscopy. The electronic structure obtained by MEM using X-ray diffraction data at room temperature (RT) showed covalent bonds of Fe-Si and Si-Si electrons. The photoemission spectra of beta-FeSi sub 2 at RT were changed by incidence photon energies. For photon energies between 50 and 100 eV, resonant photoemission spectra caused by a super Coster-Kronig transition were observed. In order to reduce resonant effect about Fe(3d) for obtained photoemission spectra, difference spectrum between 53 and 57 eV was calculated, and it was compared with ab-initio band calculation and spectra function.
Xu, Jun; Dang, Chao; Kong, Fan
2017-10-01
This paper presents a new method for efficient structural reliability analysis. In this method, a rotational quasi-symmetric point method (RQ-SPM) is proposed for evaluating the fractional moments of the performance function. Then, the derivation of the performance function's probability density function (PDF) is carried out based on the maximum entropy method in which constraints are specified in terms of fractional moments. In this regard, the probability of failure can be obtained by a simple integral over the performance function's PDF. Six examples, including a finite element-based reliability analysis and a dynamic system with strong nonlinearity, are used to illustrate the efficacy of the proposed method. All the computed results are compared with those by Monte Carlo simulation (MCS). It is found that the proposed method can provide very accurate results with low computational effort.
Directory of Open Access Journals (Sweden)
Jorge Pereira
2015-12-01
Full Text Available Biological invasion by exotic organisms became a key issue, a concern associated to the deep impacts on several domains described as resultant from such processes. A better understanding of the processes, the identification of more susceptible areas, and the definition of preventive or mitigation measures are identified as critical for the purpose of reducing associated impacts. The use of species distribution modeling might help on the purpose of identifying areas that are more susceptible to invasion. This paper aims to present preliminary results on assessing the susceptibility to invasion by the exotic species Acacia dealbata Mill. in the Ceira river basin. The results are based on the maximum entropy modeling approach, considered one of the correlative modelling techniques with better predictive performance. Models which validation is based on independent data sets present better performance, an evaluation based on the AUC of ROC accuracy measure.
Gosseries, Olivia; Schnakers, Caroline; Ledoux, Didier; Vanhaudenhuyse, Audrey; Bruno, Marie-Aurélie; Demertzi, Athéna; Noirhomme, Quentin; Lehembre, Rémy; Damas, Pierre; Goldman, Serge; Peeters, Erika; Moonen, Gustave; Laureys, Steven
Summary Monitoring the level of consciousness in brain-injured patients with disorders of consciousness is crucial as it provides diagnostic and prognostic information. Behavioral assessment remains the gold standard for assessing consciousness but previous studies have shown a high rate of misdiagnosis. This study aimed to investigate the usefulness of electroencephalography (EEG) entropy measurements in differentiating unconscious (coma or vegetative) from minimally conscious patients. Left fronto-temporal EEG recordings (10-minute resting state epochs) were prospectively obtained in 56 patients and 16 age-matched healthy volunteers. Patients were assessed in the acute (≤1 month post-injury; n=29) or chronic (>1 month post-injury; n=27) stage. The etiology was traumatic in 23 patients. Automated online EEG entropy calculations (providing an arbitrary value ranging from 0 to 91) were compared with behavioral assessments (Coma Recovery Scale-Revised) and outcome. EEG entropy correlated with Coma Recovery Scale total scores (r=0.49). Mean EEG entropy values were higher in minimally conscious (73±19; mean and standard deviation) than in vegetative/unresponsive wakefulness syndrome patients (45±28). Receiver operating characteristic analysis revealed an entropy cut-off value of 52 differentiating acute unconscious from minimally conscious patients (sensitivity 89% and specificity 90%). In chronic patients, entropy measurements offered no reliable diagnostic information. EEG entropy measurements did not allow prediction of outcome. User-independent time-frequency balanced spectral EEG entropy measurements seem to constitute an interesting diagnostic – albeit not prognostic – tool for assessing neural network complexity in disorders of consciousness in the acute setting. Future studies are needed before using this tool in routine clinical practice, and these should seek to improve automated EEG quantification paradigms in order to reduce the remaining false
DeVore, Matthew S; Gull, Stephen F; Johnson, Carey K
2012-04-05
We describe a method for analysis of single-molecule Förster resonance energy transfer (FRET) burst measurements using classic maximum entropy. Classic maximum entropy determines the Bayesian inference for the joint probability describing the total fluorescence photons and the apparent FRET efficiency. The method was tested with simulated data and then with DNA labeled with fluorescent dyes. The most probable joint distribution can be marginalized to obtain both the overall distribution of fluorescence photons and the apparent FRET efficiency distribution. This method proves to be ideal for determining the distance distribution of FRET-labeled biomolecules, and it successfully predicts the shape of the recovered distributions.
Brain entropy and human intelligence: A resting-state fMRI study.
Saxe, Glenn N; Calderone, Daniel; Morales, Leah J
2018-01-01
Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns.
Brain entropy and human intelligence: A resting-state fMRI study
Calderone, Daniel; Morales, Leah J.
2018-01-01
Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns. PMID:29432427
Maximum entropy theory of recoil charge distributions in electron-capture collisions
International Nuclear Information System (INIS)
Aberg, T.; Blomberg, A.; Tulkki, J.; Goscinski, O.
1984-01-01
A generalized Fermi-Dirac distribution is derived and applied to charge-state distributions in single collisions between multiply charged ions and rare-gas atoms. It relates multiple electron loss in single-electron capture to multiple ionization in multiphoton absorption and discloses inner-shell vacancy formation in double- and triple-electron capture
Thermality and excited state Rényi entropy in two-dimensional CFT
Energy Technology Data Exchange (ETDEWEB)
Lin, Feng-Li [Department of Physics, National Taiwan Normal University,Taipei 11677, Taiwan (China); Wang, Huajia [Department of Physics, University of Illinois,Urbana-Champaign, IL 61801 (United States); Zhang, Jia-ju [Dipartimento di Fisica, Università degli Studi di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Theoretical Physics Division, Institute of High Energy Physics, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China); Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences,19B Yuquan Rd, Beijing 100049 (China)
2016-11-21
We evaluate one-interval Rényi entropy and entanglement entropy for the excited states of two-dimensional conformal field theory (CFT) on a cylinder, and examine their differences from the ones for the thermal state. We assume the interval to be short so that we can use operator product expansion (OPE) of twist operators to calculate Rényi entropy in terms of sum of one-point functions of OPE blocks. We find that the entanglement entropy for highly excited state and thermal state behave the same way after appropriate identification of the conformal weight of the state with the temperature. However, there exists no such universal identification for the Rényi entropy in the short-interval expansion. Therefore, the highly excited state does not look thermal when comparing its Rényi entropy to the thermal state one. As the Rényi entropy captures the higher moments of the reduced density matrix but the entanglement entropy only the average, our results imply that the emergence of thermality depends on how refined we look into the entanglement structure of the underlying pure excited state.
Entropy, energy and negativity in Fermi-resonance coupled states of substituted methanes
International Nuclear Information System (INIS)
Hou Xiwen; Wan Mingfang; Ma Zhongqi
2010-01-01
Several measures of entanglement have attracted considerable interest in the relationship of a measure of entanglement with other quantities. The dynamics of entropy, energy and negativity is studied for Fermi-resonance coupled vibrations in substituted methanes with three kinds of initial mixed states, which are the mixed density matrices of binomial states, thermal states and squeezed states on two vibrational modes, respectively. It is demonstrated that for mixed binomial states and mixed thermal states with small magnitudes the entropies of the stretch and the bend are anti-correlated in the same oscillatory frequency, so do the energies for each kind of state with small magnitudes, whereas the entropies exhibit positive correlations with the corresponding energies. Furthermore, for small magnitudes quantum mutual entropy is positively correlated with the interacting energy. Analytic forms of entropies and energies are provided with initial conditions in which they are stationary, and the agreement between analytic and numerical simulations is satisfactory. The dynamical entanglement measured by negativity is examined for those states and conditions. It is shown that negativity displays a sudden death for mixed binomial states and mixed thermal states with small magnitudes, and the time-averaged negativity has the minimal value under the conditions of stationary entropies and energies. Moreover, negativity is positively correlated with the mutual entropy and the interacting energy just for mixed squeezed states with small magnitudes. Those are useful for molecular quantum information processing and dynamical entanglement.
Directory of Open Access Journals (Sweden)
Wassim M. Haddad
2014-07-01
Full Text Available Advances in neuroscience have been closely linked to mathematical modeling beginning with the integrate-and-fire model of Lapicque and proceeding through the modeling of the action potential by Hodgkin and Huxley to the current era. The fundamental building block of the central nervous system, the neuron, may be thought of as a dynamic element that is “excitable”, and can generate a pulse or spike whenever the electrochemical potential across the cell membrane of the neuron exceeds a threshold. A key application of nonlinear dynamical systems theory to the neurosciences is to study phenomena of the central nervous system that exhibit nearly discontinuous transitions between macroscopic states. A very challenging and clinically important problem exhibiting this phenomenon is the induction of general anesthesia. In any specific patient, the transition from consciousness to unconsciousness as the concentration of anesthetic drugs increases is very sharp, resembling a thermodynamic phase transition. This paper focuses on multistability theory for continuous and discontinuous dynamical systems having a set of multiple isolated equilibria and/or a continuum of equilibria. Multistability is the property whereby the solutions of a dynamical system can alternate between two or more mutually exclusive Lyapunov stable and convergent equilibrium states under asymptotically slowly changing inputs or system parameters. In this paper, we extend the theory of multistability to continuous, discontinuous, and stochastic nonlinear dynamical systems. In particular, Lyapunov-based tests for multistability and synchronization of dynamical systems with continuously differentiable and absolutely continuous flows are established. The results are then applied to excitatory and inhibitory biological neuronal networks to explain the underlying mechanism of action for anesthesia and consciousness from a multistable dynamical system perspective, thereby providing a
Zaylaa, Amira; Oudjemia, Souad; Charara, Jamal; Girault, Jean-Marc
2015-09-01
This paper presents two new concepts for discrimination of signals of different complexity. The first focused initially on solving the problem of setting entropy descriptors by varying the pattern size instead of the tolerance. This led to the search for the optimal pattern size that maximized the similarity entropy. The second paradigm was based on the n-order similarity entropy that encompasses the 1-order similarity entropy. To improve the statistical stability, n-order fuzzy similarity entropy was proposed. Fractional Brownian motion was simulated to validate the different methods proposed, and fetal heart rate signals were used to discriminate normal from abnormal fetuses. In all cases, it was found that it was possible to discriminate time series of different complexity such as fractional Brownian motion and fetal heart rate signals. The best levels of performance in terms of sensitivity (90%) and specificity (90%) were obtained with the n-order fuzzy similarity entropy. However, it was shown that the optimal pattern size and the maximum similarity measurement were related to intrinsic features of the time series. Copyright © 2015 Elsevier Ltd. All rights reserved.
Yu, Hwa-Lung; Chiang, Chi-Ting; Lin, Shu-De; Chang, Tsun-Kuo
2010-02-01
Incidence rate of oral cancer in Changhua County is the highest among the 23 counties of Taiwan during 2001. However, in health data analysis, crude or adjusted incidence rates of a rare event (e.g., cancer) for small populations often exhibit high variances and are, thus, less reliable. We proposed a generalized Bayesian Maximum Entropy (GBME) analysis of spatiotemporal disease mapping under conditions of considerable data uncertainty. GBME was used to study the oral cancer population incidence in Changhua County (Taiwan). Methodologically, GBME is based on an epistematics principles framework and generates spatiotemporal estimates of oral cancer incidence rates. In a way, it accounts for the multi-sourced uncertainty of rates, including small population effects, and the composite space-time dependence of rare events in terms of an extended Poisson-based semivariogram. The results showed that GBME analysis alleviates the noises of oral cancer data from population size effect. Comparing to the raw incidence data, the maps of GBME-estimated results can identify high risk oral cancer regions in Changhua County, where the prevalence of betel quid chewing and cigarette smoking is relatively higher than the rest of the areas. GBME method is a valuable tool for spatiotemporal disease mapping under conditions of uncertainty. 2010 Elsevier Inc. All rights reserved.
Wang, Chaolin; Zhong, Shaobo; Zhang, Fushen; Huang, Quanyi
2016-11-01
Precipitation interpolation has been a hot area of research for many years. It had close relation to meteorological factors. In this paper, precipitation from 91 meteorological stations located in and around Yunnan, Guizhou and Guangxi Zhuang provinces (or autonomous region), Mainland China was taken into consideration for spatial interpolation. Multivariate Bayesian maximum entropy (BME) method with auxiliary variables, including mean relative humidity, water vapour pressure, mean temperature, mean wind speed and terrain elevation, was used to get more accurate regional distribution of annual precipitation. The means, standard deviations, skewness and kurtosis of meteorological factors were calculated. Variogram and cross- variogram were fitted between precipitation and auxiliary variables. The results showed that the multivariate BME method was precise with hard and soft data, probability density function. Annual mean precipitation was positively correlated with mean relative humidity, mean water vapour pressure, mean temperature and mean wind speed, negatively correlated with terrain elevation. The results are supposed to provide substantial reference for research of drought and waterlog in the region.
Directory of Open Access Journals (Sweden)
Chengquan Zhou
2018-02-01
Full Text Available To obtain an accurate count of wheat spikes, which is crucial for estimating yield, this paper proposes a new algorithm that uses computer vision to achieve this goal from an image. First, a home-built semi-autonomous multi-sensor field-based phenotype platform (FPP is used to obtain orthographic images of wheat plots at the filling stage. The data acquisition system of the FPP provides high-definition RGB images and multispectral images of the corresponding quadrats. Then, the high-definition panchromatic images are obtained by fusion of three channels of RGB. The Gram–Schmidt fusion algorithm is then used to fuse these multispectral and panchromatic images, thereby improving the color identification degree of the targets. Next, the maximum entropy segmentation method is used to do the coarse-segmentation. The threshold of this method is determined by a firefly algorithm based on chaos theory (FACT, and then a morphological filter is used to de-noise the coarse-segmentation results. Finally, morphological reconstruction theory is applied to segment the adhesive part of the de-noised image and realize the fine-segmentation of the image. The computer-generated counting results for the wheat plots, using independent regional statistical function in Matlab R2017b software, are then compared with field measurements which indicate that the proposed method provides a more accurate count of wheat spikes when compared with other traditional fusion and segmentation methods mentioned in this paper.
Hoffman, Steven J; Justicz, Victoria
2016-07-01
To develop and validate a method for automatically quantifying the scientific quality and sensationalism of individual news records. After retrieving 163,433 news records mentioning the Severe Acute Respiratory Syndrome (SARS) and H1N1 pandemics, a maximum entropy model for inductive machine learning was used to identify relationships among 500 randomly sampled news records that correlated with systematic human assessments of their scientific quality and sensationalism. These relationships were then computationally applied to automatically classify 10,000 additional randomly sampled news records. The model was validated by randomly sampling 200 records and comparing human assessments of them to the computer assessments. The computer model correctly assessed the relevance of 86% of news records, the quality of 65% of records, and the sensationalism of 73% of records, as compared to human assessments. Overall, the scientific quality of SARS and H1N1 news media coverage had potentially important shortcomings, but coverage was not too sensationalizing. Coverage slightly improved between the two pandemics. Automated methods can evaluate news records faster, cheaper, and possibly better than humans. The specific procedure implemented in this study can at the very least identify subsets of news records that are far more likely to have particular scientific and discursive qualities. Copyright © 2016 Elsevier Inc. All rights reserved.
Fu, Hui; Zhong, Jiayou; Yuan, Guixiang; Guo, Chunjing; Lou, Qian; Zhang, Wei; Xu, Jun; Ni, Leyi; Xie, Ping; Cao, Te
2015-01-01
Trait-based approaches have been widely applied to investigate how community dynamics respond to environmental gradients. In this study, we applied a series of maximum entropy (maxent) models incorporating functional traits to unravel the processes governing macrophyte community structure along water depth gradient in a freshwater lake. We sampled 42 plots and 1513 individual plants, and measured 16 functional traits and abundance of 17 macrophyte species. Study results showed that maxent model can be highly robust (99.8%) in predicting the species relative abundance of macrophytes with observed community-weighted mean (CWM) traits as the constraints, while relative low (about 30%) with CWM traits fitted from water depth gradient as the constraints. The measured traits showed notably distinct importance in predicting species abundances, with lowest for perennial growth form and highest for leaf dry mass content. For tuber and leaf nitrogen content, there were significant shifts in their effects on species relative abundance from positive in shallow water to negative in deep water. This result suggests that macrophyte species with tuber organ and greater leaf nitrogen content would become more abundant in shallow water, but would become less abundant in deep water. Our study highlights how functional traits distributed across gradients provide a robust path towards predictive community ecology. PMID:26167856
Directory of Open Access Journals (Sweden)
ChunPing Ren
2017-01-01
Full Text Available We propose a novel mathematical algorithm to offer a solution for the inverse random dynamic force identification in practical engineering. Dealing with the random dynamic force identification problem using the proposed algorithm, an improved maximum entropy (IME regularization technique is transformed into an unconstrained optimization problem, and a novel conjugate gradient (NCG method was applied to solve the objective function, which was abbreviated as IME-NCG algorithm. The result of IME-NCG algorithm is compared with that of ME, ME-CG, ME-NCG, and IME-CG algorithm; it is found that IME-NCG algorithm is available for identifying the random dynamic force due to smaller root mean-square-error (RMSE, lower restoration time, and fewer iterative steps. Example of engineering application shows that L-curve method is introduced which is better than Generalized Cross Validation (GCV method and is applied to select regularization parameter; thus the proposed algorithm can be helpful to alleviate the ill-conditioned problem in identification of dynamic force and to acquire an optimal solution of inverse problem in practical engineering.
DEFF Research Database (Denmark)
Escudero, Javier; Evrim, Acar Ataman; Fernández, Alberto
2015-01-01
dynamics. We consider the "refined composite multiscale entropy" (rcMSE), which computes entropy "profiles" showing levels of physiological complexity over temporal scales for individual signals. We compute the rcMSE of resting-state magnetoencephalogram (MEG) recordings from 36 patients with Alzheimer...
Lee, Chieh-Han; Yu, Hwa-Lung; Chien, Lung-Chang
2014-05-01
Dengue fever has been identified as one of the most widespread vector-borne diseases in tropical and sub-tropical. In the last decade, dengue is an emerging infectious disease epidemic in Taiwan especially in the southern area where have annually high incidences. For the purpose of disease prevention and control, an early warning system is urgently needed. Previous studies have showed significant relationships between climate variables, in particular, rainfall and temperature, and the temporal epidemic patterns of dengue cases. However, the transmission of the dengue fever is a complex interactive process that mostly understated the composite space-time effects of dengue fever. This study proposes developing a one-week ahead warning system of dengue fever epidemics in the southern Taiwan that considered nonlinear associations between weekly dengue cases and meteorological factors across space and time. The early warning system based on an integration of distributed lag nonlinear model (DLNM) and stochastic Bayesian Maximum Entropy (BME) analysis. The study identified the most significant meteorological measures including weekly minimum temperature and maximum 24-hour rainfall with continuous 15-week lagged time to dengue cases variation under condition of uncertainty. Subsequently, the combination of nonlinear lagged effects of climate variables and space-time dependence function is implemented via a Bayesian framework to predict dengue fever occurrences in the southern Taiwan during 2012. The result shows the early warning system is useful for providing potential outbreak spatio-temporal prediction of dengue fever distribution. In conclusion, the proposed approach can provide a practical disease control tool for environmental regulators seeking more effective strategies for dengue fever prevention.
Relative entropy of excited states in two dimensional conformal field theories
Energy Technology Data Exchange (ETDEWEB)
Sárosi, Gábor [Department of Theoretical Physics, Institute of Physics, Budapest University of Technology,Budapest, H-1521 (Hungary); Ugajin, Tomonori [Kavli Institute for Theoretical Physics, University of California,Santa Barbara,CA 93106 (United States)
2016-07-21
We study the relative entropy and the trace square distance, both of which measure the distance between reduced density matrices of two excited states in two dimensional conformal field theories. We find a general formula for the relative entropy between two primary states with the same conformal dimension in the limit of a single small interval and find that in this case the relative entropy is proportional to the trace square distance. We check our general formulae by calculating the relative entropy between two generalized free fields and the trace square distance between the spin and disorder operators of the critical Ising model. We also give the leading term of the relative entropy in the small interval expansion when the two operators have different conformal dimensions. This turns out to be universal when the CFT has no primaires lighter than the stress tensor. The result reproduces the previously known special cases.
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy
Directory of Open Access Journals (Sweden)
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.
Campbell, Cara; Hilderbrand, Robert H.
2017-01-01
Species distribution modelling can be useful for the conservation of rare and endangered species. Freshwater mussel declines have thinned species ranges producing spatially fragmented distributions across large areas. Spatial fragmentation in combination with a complex life history and heterogeneous environment makes predictive modelling difficult.A machine learning approach (maximum entropy) was used to model occurrences and suitable habitat for the federally endangered dwarf wedgemussel, Alasmidonta heterodon, in Maryland's Coastal Plain catchments. Landscape-scale predictors (e.g. land cover, land use, soil characteristics, geology, flow characteristics, and climate) were used to predict the suitability of individual stream segments for A. heterodon.The best model contained variables at three scales: minimum elevation (segment scale), percentage Tertiary deposits, low intensity development, and woody wetlands (sub-catchment), and percentage low intensity development, pasture/hay agriculture, and average depth to the water table (catchment). Despite a very small sample size owing to the rarity of A. heterodon, cross-validated prediction accuracy was 91%.Most predicted suitable segments occur in catchments not known to contain A. heterodon, which provides opportunities for new discoveries or population restoration. These model predictions can guide surveys toward the streams with the best chance of containing the species or, alternatively, away from those streams with little chance of containing A. heterodon.Developed reaches had low predicted suitability for A. heterodon in the Coastal Plain. Urban and exurban sprawl continues to modify stream ecosystems in the region, underscoring the need to preserve existing populations and to discover and protect new populations.
Directory of Open Access Journals (Sweden)
Junguo Hu
Full Text Available Soil respiration inherently shows strong spatial variability. It is difficult to obtain an accurate characterization of soil respiration with an insufficient number of monitoring points. However, it is expensive and cumbersome to deploy many sensors. To solve this problem, we proposed employing the Bayesian Maximum Entropy (BME algorithm, using soil temperature as auxiliary information, to study the spatial distribution of soil respiration. The BME algorithm used the soft data (auxiliary information effectively to improve the estimation accuracy of the spatiotemporal distribution of soil respiration. Based on the functional relationship between soil temperature and soil respiration, the BME algorithm satisfactorily integrated soil temperature data into said spatial distribution. As a means of comparison, we also applied the Ordinary Kriging (OK and Co-Kriging (Co-OK methods. The results indicated that the root mean squared errors (RMSEs and absolute values of bias for both Day 1 and Day 2 were the lowest for the BME method, thus demonstrating its higher estimation accuracy. Further, we compared the performance of the BME algorithm coupled with auxiliary information, namely soil temperature data, and the OK method without auxiliary information in the same study area for 9, 21, and 37 sampled points. The results showed that the RMSEs for the BME algorithm (0.972 and 1.193 were less than those for the OK method (1.146 and 1.539 when the number of sampled points was 9 and 37, respectively. This indicates that the former method using auxiliary information could reduce the required number of sampling points for studying spatial distribution of soil respiration. Thus, the BME algorithm, coupled with soil temperature data, can not only improve the accuracy of soil respiration spatial interpolation but can also reduce the number of sampling points.
Hu, Junguo; Zhou, Jian; Zhou, Guomo; Luo, Yiqi; Xu, Xiaojun; Li, Pingheng; Liang, Junyi
2016-01-01
Soil respiration inherently shows strong spatial variability. It is difficult to obtain an accurate characterization of soil respiration with an insufficient number of monitoring points. However, it is expensive and cumbersome to deploy many sensors. To solve this problem, we proposed employing the Bayesian Maximum Entropy (BME) algorithm, using soil temperature as auxiliary information, to study the spatial distribution of soil respiration. The BME algorithm used the soft data (auxiliary information) effectively to improve the estimation accuracy of the spatiotemporal distribution of soil respiration. Based on the functional relationship between soil temperature and soil respiration, the BME algorithm satisfactorily integrated soil temperature data into said spatial distribution. As a means of comparison, we also applied the Ordinary Kriging (OK) and Co-Kriging (Co-OK) methods. The results indicated that the root mean squared errors (RMSEs) and absolute values of bias for both Day 1 and Day 2 were the lowest for the BME method, thus demonstrating its higher estimation accuracy. Further, we compared the performance of the BME algorithm coupled with auxiliary information, namely soil temperature data, and the OK method without auxiliary information in the same study area for 9, 21, and 37 sampled points. The results showed that the RMSEs for the BME algorithm (0.972 and 1.193) were less than those for the OK method (1.146 and 1.539) when the number of sampled points was 9 and 37, respectively. This indicates that the former method using auxiliary information could reduce the required number of sampling points for studying spatial distribution of soil respiration. Thus, the BME algorithm, coupled with soil temperature data, can not only improve the accuracy of soil respiration spatial interpolation but can also reduce the number of sampling points.
Directory of Open Access Journals (Sweden)
Xiaokang Kou
2016-01-01
Full Text Available Land surface temperature (LST plays a major role in the study of surface energy balances. Remote sensing techniques provide ways to monitor LST at large scales. However, due to atmospheric influences, significant missing data exist in LST products retrieved from satellite thermal infrared (TIR remotely sensed data. Although passive microwaves (PMWs are able to overcome these atmospheric influences while estimating LST, the data are constrained by low spatial resolution. In this study, to obtain complete and high-quality LST data, the Bayesian Maximum Entropy (BME method was introduced to merge 0.01° and 0.25° LSTs inversed from MODIS and AMSR-E data, respectively. The result showed that the missing LSTs in cloudy pixels were filled completely, and the availability of merged LSTs reaches 100%. Because the depths of LST and soil temperature measurements are different, before validating the merged LST, the station measurements were calibrated with an empirical equation between MODIS LST and 0~5 cm soil temperatures. The results showed that the accuracy of merged LSTs increased with the increasing quantity of utilized data, and as the availability of utilized data increased from 25.2% to 91.4%, the RMSEs of the merged data decreased from 4.53 °C to 2.31 °C. In addition, compared with the filling gap method in which MODIS LST gaps were filled with AMSR-E LST directly, the merged LSTs from the BME method showed better spatial continuity. The different penetration depths of TIR and PMWs may influence fusion performance and still require further studies.
Ashford, Oliver S.; Davies, Andrew J.; Jones, Daniel O. B.
2014-12-01
Xenophyophores are a group of exclusively deep-sea agglutinating rhizarian protozoans, at least some of which are foraminifera. They are an important constituent of the deep-sea megafauna that are sometimes found in sufficient abundance to act as a significant source of habitat structure for meiofaunal and macrofaunal organisms. This study utilised maximum entropy modelling (Maxent) and a high-resolution environmental database to explore the environmental factors controlling the presence of Xenophyophorea and two frequently sampled xenophyophore species that are taxonomically stable: Syringammina fragilissima and Stannophyllum zonarium. These factors were also used to predict the global distribution of each taxon. Areas of high habitat suitability for xenophyophores were highlighted throughout the world's oceans, including in a large number of areas yet to be suitably sampled, but the Northeast and Southeast Atlantic Ocean, Gulf of Mexico and Caribbean Sea, the Red Sea and deep-water regions of the Malay Archipelago represented particular hotspots. The two species investigated showed more specific habitat requirements when compared to the model encompassing all xenophyophore records, perhaps in part due to the smaller number and relatively more clustered nature of the presence records available for modelling at present. The environmental variables depth, oxygen parameters, nitrate concentration, carbon-chemistry parameters and temperature were of greatest importance in determining xenophyophore distributions, but, somewhat surprisingly, hydrodynamic parameters were consistently shown to have low importance, possibly due to the paucity of well-resolved global hydrodynamic datasets. The results of this study (and others of a similar type) have the potential to guide further sample collection, environmental policy, and spatial planning of marine protected areas and industrial activities that impact the seafloor, particularly those that overlap with aggregations of
Almog, Assaf; Garlaschelli, Diego
2014-09-01
The dynamics of complex systems, from financial markets to the brain, can be monitored in terms of multiple time series of activity of the constituent units, such as stocks or neurons, respectively. While the main focus of time series analysis is on the magnitude of temporal increments, a significant piece of information is encoded into the binary projection (i.e. the sign) of such increments. In this paper we provide further evidence of this by showing strong nonlinear relations between binary and non-binary properties of financial time series. These relations are a novel quantification of the fact that extreme price increments occur more often when most stocks move in the same direction. We then introduce an information-theoretic approach to the analysis of the binary signature of single and multiple time series. Through the definition of maximum-entropy ensembles of binary matrices and their mapping to spin models in statistical physics, we quantify the information encoded into the simplest binary properties of real time series and identify the most informative property given a set of measurements. Our formalism is able to accurately replicate, and mathematically characterize, the observed binary/non-binary relations. We also obtain a phase diagram allowing us to identify, based only on the instantaneous aggregate return of a set of multiple time series, a regime where the so-called ‘market mode’ has an optimal interpretation in terms of collective (endogenous) effects, a regime where it is parsimoniously explained by pure noise, and a regime where it can be regarded as a combination of endogenous and exogenous factors. Our approach allows us to connect spin models, simple stochastic processes, and ensembles of time series inferred from partial information.
Directory of Open Access Journals (Sweden)
Hannah Slater
Full Text Available Modelling the spatial distributions of human parasite species is crucial to understanding the environmental determinants of infection as well as for guiding the planning of control programmes. Here, we use ecological niche modelling to map the current potential distribution of the macroparasitic disease, lymphatic filariasis (LF, in Africa, and to estimate how future changes in climate and population could affect its spread and burden across the continent. We used 508 community-specific infection presence data collated from the published literature in conjunction with five predictive environmental/climatic and demographic variables, and a maximum entropy niche modelling method to construct the first ecological niche maps describing potential distribution and burden of LF in Africa. We also ran the best-fit model against climate projections made by the HADCM3 and CCCMA models for 2050 under A2a and B2a scenarios to simulate the likely distribution of LF under future climate and population changes. We predict a broad geographic distribution of LF in Africa extending from the west to the east across the middle region of the continent, with high probabilities of occurrence in the Western Africa compared to large areas of medium probability interspersed with smaller areas of high probability in Central and Eastern Africa and in Madagascar. We uncovered complex relationships between predictor ecological niche variables and the probability of LF occurrence. We show for the first time that predicted climate change and population growth will expand both the range and risk of LF infection (and ultimately disease in an endemic region. We estimate that populations at risk to LF may range from 543 and 804 million currently, and that this could rise to between 1.65 to 1.86 billion in the future depending on the climate scenario used and thresholds applied to signify infection presence.
International Nuclear Information System (INIS)
Almog, Assaf; Garlaschelli, Diego
2014-01-01
The dynamics of complex systems, from financial markets to the brain, can be monitored in terms of multiple time series of activity of the constituent units, such as stocks or neurons, respectively. While the main focus of time series analysis is on the magnitude of temporal increments, a significant piece of information is encoded into the binary projection (i.e. the sign) of such increments. In this paper we provide further evidence of this by showing strong nonlinear relations between binary and non-binary properties of financial time series. These relations are a novel quantification of the fact that extreme price increments occur more often when most stocks move in the same direction. We then introduce an information-theoretic approach to the analysis of the binary signature of single and multiple time series. Through the definition of maximum-entropy ensembles of binary matrices and their mapping to spin models in statistical physics, we quantify the information encoded into the simplest binary properties of real time series and identify the most informative property given a set of measurements. Our formalism is able to accurately replicate, and mathematically characterize, the observed binary/non-binary relations. We also obtain a phase diagram allowing us to identify, based only on the instantaneous aggregate return of a set of multiple time series, a regime where the so-called ‘market mode’ has an optimal interpretation in terms of collective (endogenous) effects, a regime where it is parsimoniously explained by pure noise, and a regime where it can be regarded as a combination of endogenous and exogenous factors. Our approach allows us to connect spin models, simple stochastic processes, and ensembles of time series inferred from partial information. (paper)
THE LICK AGN MONITORING PROJECT: VELOCITY-DELAY MAPS FROM THE MAXIMUM-ENTROPY METHOD FOR Arp 151
International Nuclear Information System (INIS)
Bentz, Misty C.; Barth, Aaron J.; Walsh, Jonelle L.; Horne, Keith; Bennert, Vardha Nicola; Treu, Tommaso; Canalizo, Gabriela; Filippenko, Alexei V.; Gates, Elinor L.; Malkan, Matthew A.; Minezaki, Takeo; Woo, Jong-Hak
2010-01-01
We present velocity-delay maps for optical H I, He I, and He II recombination lines in Arp 151, recovered by fitting a reverberation model to spectrophotometric monitoring data using the maximum-entropy method. H I response is detected over the range 0-15 days, with the response confined within the virial envelope. The Balmer-line maps have similar morphologies but exhibit radial stratification, with progressively longer delays for Hγ to Hβ to Hα. The He I and He II response is confined within 1-2 days. There is a deficit of prompt response in the Balmer-line cores but strong prompt response in the red wings. Comparison with simple models identifies two classes that reproduce these features: free-falling gas and a half-illuminated disk with a hot spot at small radius on the receding lune. Symmetrically illuminated models with gas orbiting in an inclined disk or an isotropic distribution of randomly inclined circular orbits can reproduce the virial structure but not the observed asymmetry. Radial outflows are also largely ruled out by the observed asymmetry. A warped-disk geometry provides a physically plausible mechanism for the asymmetric illumination and hot spot features. Simple estimates show that a disk in the broad-line region of Arp 151 could be unstable to warping induced by radiation pressure. Our results demonstrate the potential power of detailed modeling combined with monitoring campaigns at higher cadence to characterize the gas kinematics and physical processes that give rise to the broad emission lines in active galactic nuclei.
Yusop, Syazwani Mohd; Mustapha, Muzzneena Ahmad
2018-04-01
The coupling of fishing locations for R. kanagurta obtained from SEAFDEC and multi-sensor satellite imageries of oceanographic variables; sea surface temperature (SST), sea surface height (SSH) and chl-a concentration (chl-a) were utilized to evaluate the performance of maximum entropy (MaxEnt) models for R. kanagurta fishing ground for prediction. Besides, this study was conducted to identify the relative percentage contribution of each environmental variable considered in order to describe the effects of the oceanographic factors on the species distribution in the study area. The potential fishing grounds during intermonsoon periods; April and October 2008-2009 were simulated separately and covered the near-coast of Kelantan, Terengganu, Pahang and Johor. The oceanographic conditions differed between regions by the inherent seasonal variability. The seasonal and spatial extents of potential fishing grounds were largely explained by chl-a concentration (0.21-0.99 mg/m3 in April and 0.28-1.00 mg/m3 in October), SSH (77.37-85.90 cm in April and 107.60-108.97 cm in October) and SST (30.43-33.70 °C in April and 30.48-30.97 °C in October). The constructed models were applicable and therefore they were suitable for predicting the potential fishing zones of R. kanagurta in EEZ. The results from this study revealed MaxEnt's potential for predicting the spatial distribution of R. kanagurta and highlighted the use of multispectral satellite images for describing the seasonal potential fishing grounds.
Maximum-confidence discrimination among symmetric qudit states
International Nuclear Information System (INIS)
Jimenez, O.; Solis-Prosser, M. A.; Delgado, A.; Neves, L.
2011-01-01
We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure (POVM) that maximizes our confidence in identifying each state in the set and minimizes the probability of obtaining inconclusive results. The physical realization of this POVM is completely determined and it is shown that after an inconclusive outcome, the input states may be mapped into a new set of equiprobable symmetric states, restricted, however, to a subspace of the original qudit Hilbert space. By applying the MC measurement again onto this new set, we can still gain some information about the input states, although with less confidence than before. This leads us to introduce the concept of sequential maximum-confidence (SMC) measurements, where the optimized MC strategy is iterated in as many stages as allowed by the input set, until no further information can be extracted from an inconclusive result. Within each stage of this measurement our confidence in identifying the input states is the highest possible, although it decreases from one stage to the next. In addition, the more stages we accomplish within the maximum allowed, the higher will be the probability of correct identification. We will discuss an explicit example of the optimal SMC measurement applied in the discrimination among four symmetric qutrit states and propose an optical network to implement it.
Säwén, Elin; Massad, Tariq; Landersjö, Clas; Damberg, Peter; Widmalm, Göran
2010-08-21
The conformational space available to the flexible molecule α-D-Manp-(1-->2)-α-D-Manp-OMe, a model for the α-(1-->2)-linked mannose disaccharide in N- or O-linked glycoproteins, is determined using experimental data and molecular simulation combined with a maximum entropy approach that leads to a converged population distribution utilizing different input information. A database survey of the Protein Data Bank where structures having the constituent disaccharide were retrieved resulted in an ensemble with >200 structures. Subsequent filtering removed erroneous structures and gave the database (DB) ensemble having three classes of mannose-containing compounds, viz., N- and O-linked structures, and ligands to proteins. A molecular dynamics (MD) simulation of the disaccharide revealed a two-state equilibrium with a major and a minor conformational state, i.e., the MD ensemble. These two different conformation ensembles of the disaccharide were compared to measured experimental spectroscopic data for the molecule in water solution. However, neither of the two populations were compatible with experimental data from optical rotation, NMR (1)H,(1)H cross-relaxation rates as well as homo- and heteronuclear (3)J couplings. The conformational distributions were subsequently used as background information to generate priors that were used in a maximum entropy analysis. The resulting posteriors, i.e., the population distributions after the application of the maximum entropy analysis, still showed notable deviations that were not anticipated based on the prior information. Therefore, reparameterization of homo- and heteronuclear Karplus relationships for the glycosidic torsion angles Φ and Ψ were carried out in which the importance of electronegative substituents on the coupling pathway was deemed essential resulting in four derived equations, two (3)J(COCC) and two (3)J(COCH) being different for the Φ and Ψ torsions, respectively. These Karplus relationships are denoted
Relative entropy of excited states in conformal field theories of arbitrary dimensions
Energy Technology Data Exchange (ETDEWEB)
Sárosi, Gábor [Theoretische Natuurkunde, Vrije Universiteit Brussels and International Solvay Institutes,Pleinlaan 2, Brussels, B-1050 (Belgium); David Rittenhouse Laboratory, University of Pennsylvania,Philadelphia, PA 19104 (United States); Ugajin, Tomonori [Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 (United States)
2017-02-10
Extending our previous work, we study the relative entropy between the reduced density matrices obtained from globally excited states in conformal field theories of arbitrary dimensions. We find a general formula in the small subsystem size limit. When one of the states is the vacuum of the CFT, our result matches with the holographic entanglement entropy computations in the corresponding bulk geometries, including AdS black branes. We also discuss the first asymmetric part of the relative entropy and comment on some implications of the results on the distinguishability of black hole microstates in AdS/CFT.
Entropy correlation and entanglement for mixed states in an algebraic model
International Nuclear Information System (INIS)
Hou Xiwen; Chen Jinghua; Wan Mingfang; Ma Zhongqi
2009-01-01
As an alternative with potential connections to actual experiments, other than the systems more usually used in the field of entanglement, the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well-established algebraic model, with parameters extracted from fitting to highly excited spectral experimental results for molecules H 2 O and SO 2 , is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode. For a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti-correlation. And the linear entropy of each mode is positively correlated with the negativities just for the mixed-squeezed states with small parameters in H 2 O while they do not display any correlation in other cases. For the mixed-squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy. The differences in the linear entropy and the negativities between H 2 O and SO 2 are discussed as well. Those are useful for molecular quantum computing and quantum information processing
Hsia, Wei-Shen
1986-01-01
In the Control Systems Division of the Systems Dynamics Laboratory of the NASA/MSFC, a Ground Facility (GF), in which the dynamics and control system concepts being considered for Large Space Structures (LSS) applications can be verified, was designed and built. One of the important aspects of the GF is to design an analytical model which will be as close to experimental data as possible so that a feasible control law can be generated. Using Hyland's Maximum Entropy/Optimal Projection Approach, a procedure was developed in which the maximum entropy principle is used for stochastic modeling and the optimal projection technique is used for a reduced-order dynamic compensator design for a high-order plant.
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
Institute of Scientific and Technical Information of China (English)
吴金平
1991-01-01
The relation between the excess entropy production criterion of thermodynamic stabilityfor nonequilibrium states and kinetic linear stability principle is discussed. It is shown thatthe condition required by the excess entropy production criterion generally is sufficient, butnot necessary to judge the system stability. The condition required by the excess entropyproduction criterion is stronger than that of the linear stability principle. Only when theproduct matrix between the linearized matrix of kinetic equations and matrix of quadraticform of second-order excess entropy is symmetric, is the condition required by the excessentropy production criterion that the steady steate is asymptotically stable (δ_xP>0) necessaryand sufficient. The counterexample given by Fox to prove that the excess entropy, (δ~2S)ss,is not a Liapunov function is incorrect. Contradictory to his conclusion, the counterexampleis just a positive one that proves that the excess entropy is a Liapunov function. Moreover,the excess entropy production criterion is not limited by symmetric conditions of the linear-ized matrix of kinetic equations. The excess entropy around nonequilibrium steady states,(δ~2S)ss, is a Liapunov function of thermodynamic system.
Field’s entropy in the atom–field interaction: Statistical mixture of coherent states
Energy Technology Data Exchange (ETDEWEB)
Zúñiga-Segundo, Arturo [Instituto Politécnico Nacional. ESFM Departamento de Física, Edificio 9 Unidad Profesional Adolfo López Mateos, CP 07738 CDMX (Mexico); Juárez-Amaro, Raúl [Universidad Tecnológica de la Mixteca, Apdo. Postal 71, Huajuapan de León, Oax., 69000 (Mexico); Aguilar-Loreto, Omar [Departamento de Ingenierías, CUCSur, Universidad de Guadalajara CP 48900, Autlán de Navarro, Jal. (Mexico); Moya-Cessa, Héctor M., E-mail: hmmc@inaoep.mx [Instituto Nacional de Astrofísica, Óptica y Electrónica, Calle Luis Enrique Erro No. 1, Sta. Ma. Tonantzintla, Pue. CP 72840 (Mexico)
2017-04-15
We study the atom–field interaction when the field is in a mixture of coherent states. We show that in this case it is possible to calculate analytically the field entropy for times of the order of twice the collapse time. Such analytical results are done with the help of numerical analysis. We also give an expression in terms of Chebyshev polynomials for power of density matrices. - Highlights: • We calculate the field entropy for times of the order of twice the collapse time. • We give a relation between powers of the density matrices of the subsystems. • Entropy operators for both subsystems are obtained.
Entropy production and thermodynamics of nonequilibrium stationary states: a point of view.
Gallavotti, Giovanni
2004-09-01
Entropy might be a not well defined concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called "caloric") in transformations that are not isochoric (i.e., which involve mechanical work): it could be just a quantity that can be transferred or created, like heat in equilibrium. The text first reviews the philosophy behind a recently proposed definition of entropy production in nonequilibrium stationary systems. A detailed technical attempt at defining the entropy of a stationary states via their variational properties follows: the unsatisfactory aspects of the results add arguments in favor of the nonexistence of a function of state to be identified with entropy; at the same time new aspects and properties of the phase space contraction emerge. Copyright 2004 American Institute of Physics
Directory of Open Access Journals (Sweden)
Bruce T. Milne
2017-05-01
Full Text Available Stream networks are branched structures wherein water and energy move between land and atmosphere, modulated by evapotranspiration and its interaction with the gravitational dissipation of potential energy as runoff. These actions vary among climates characterized by Budyko theory, yet have not been integrated with Horton scaling, the ubiquitous pattern of eco-hydrological variation among Strahler streams that populate river basins. From Budyko theory, we reveal optimum entropy coincident with high biodiversity. Basins on either side of optimum respond in opposite ways to precipitation, which we evaluated for the classic Hubbard Brook experiment in New Hampshire and for the Whitewater River basin in Kansas. We demonstrate that Horton ratios are equivalent to Lagrange multipliers used in the extremum function leading to Shannon information entropy being maximal, subject to constraints. Properties of stream networks vary with constraints and inter-annual variation in water balance that challenge vegetation to match expected resource supply throughout the network. The entropy-Horton framework informs questions of biodiversity, resilience to perturbations in water supply, changes in potential evapotranspiration, and land use changes that move ecosystems away from optimal entropy with concomitant loss of productivity and biodiversity.
International Nuclear Information System (INIS)
Peřinová, Vlasta; Lukš, Antonín
2015-01-01
The SU(2) group is used in two different fields of quantum optics, the quantum polarization and quantum interferometry. Quantum degrees of polarization may be based on distances of a polarization state from the set of unpolarized states. The maximum polarization is achieved in the case where the state is pure and then the distribution of the photon-number sums is optimized. In quantum interferometry, the SU(2) intelligent states have also the property that the Fisher measure of information is equal to the inverse minimum detectable phase shift on the usual simplifying condition. Previously, the optimization of the Fisher information under a constraint was studied. Now, in the framework of constraint optimization, states similar to the SU(2) intelligent states are treated. (paper)
Proof of an entropy conjecture for Bloch coherent spin states and its generalizations
DEFF Research Database (Denmark)
H. Lieb, Elliott; Solovej, Jan Philip
2014-01-01
Wehrl used Glauber coherent states to define a map from quantum density matrices to classical phase space densities and conjectured that for Glauber coherent states the mininimum classical entropy would occur for density matrices equal to projectors onto coherent states. This was proved by Lieb...
Entropy-power uncertainty relations: towards a tight inequality for all Gaussian pure states
International Nuclear Information System (INIS)
Hertz, Anaelle; Jabbour, Michael G; Cerf, Nicolas J
2017-01-01
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting entropy-power uncertainty relation is equivalent to the entropic formulation of the uncertainty relation due to Bialynicki-Birula and Mycielski, but can be further extended to rotated variables. Hence, based on a reasonable assumption, we give a partial proof of a tighter form of the entropy-power uncertainty relation taking correlations into account and provide extensive numerical evidence of its validity. Interestingly, it implies the generalized (rotation-invariant) Schrödinger–Robertson uncertainty relation exactly as the original entropy-power uncertainty relation implies Heisenberg relation. It is saturated for all Gaussian pure states, in contrast with hitherto known entropic formulations of the uncertainty principle. (paper)
Maximum Correntropy Unscented Kalman Filter for Spacecraft Relative State Estimation
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Xi Liu
2016-09-01
Full Text Available A new algorithm called maximum correntropy unscented Kalman filter (MCUKF is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC, the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm.
International Nuclear Information System (INIS)
Alvarez R, J.T.
1998-01-01
This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ( 4 He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator ρhut FP that is evaluated as Wigneris function through ρ CG obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D mn defined with a nonequilibrium coarse grained statistical operator ρhut CG , matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine ρhut CG by means of the local equilibrium statistical operator ρhut l -tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D mn but with aid of a quasi equilibrium statistical operator ρhut qe instead of the local equilibrium operator ρhut l -tilde. Matrix
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Chien-Hao Lin
2015-09-01
Full Text Available In the present work, we report an investigation on quantum entanglement in the doubly excited 2s2 1Se resonance state of the positronium negative ion by using highly correlated Hylleraas type wave functions, determined by calculation of the density of resonance states with the stabilization method. Once the resonance wave function is obtained, the spatial (electron-electron orbital entanglement entropies (von Neumann and linear can be quantified using the Schmidt decomposition method. Furthermore, Shannon entropy in position space, a measure for localization (or delocalization for such a doubly excited state, is also calculated.
Furbish, David; Schmeeckle, Mark; Schumer, Rina; Fathel, Siobhan
2016-01-01
We describe the most likely forms of the probability distributions of bed load particle velocities, accelerations, hop distances, and travel times, in a manner that formally appeals to inferential statistics while honoring mechanical and kinematic constraints imposed by equilibrium transport conditions. The analysis is based on E. Jaynes's elaboration of the implications of the similarity between the Gibbs entropy in statistical mechanics and the Shannon entropy in information theory. By maximizing the information entropy of a distribution subject to known constraints on its moments, our choice of the form of the distribution is unbiased. The analysis suggests that particle velocities and travel times are exponentially distributed and that particle accelerations follow a Laplace distribution with zero mean. Particle hop distances, viewed alone, ought to be distributed exponentially. However, the covariance between hop distances and travel times precludes this result. Instead, the covariance structure suggests that hop distances follow a Weibull distribution. These distributions are consistent with high-resolution measurements obtained from high-speed imaging of bed load particle motions. The analysis brings us closer to choosing distributions based on our mechanical insight.
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.
International Nuclear Information System (INIS)
Chen, Z.Q.; Wang, S.J.
1999-01-01
A newly developed maximum entropy method, which was realized by the computer program MELT introduced by Shukla et al., was used to analyze positron lifetime spectra measured in semiconductors. Several simulation studies were done to test the performance of this algorithm. Reliable reconstruction of positron lifetime distributions can be extracted at relatively lower counts, which shows the applicability and superiority of this method. Two positron lifetime spectra measured in ion-implanted p-InP(Zn) at 140 and 280 K, respectively were analyzed by this program. The lifetime distribution differed greatly for the two temperatures, giving direct evidence of the existence of shallow positron traps at low temperature
International Nuclear Information System (INIS)
Berrocal T, Mariella J.; Roberty, Nilson C.; Silva Neto, Antonio J.; Universidade Federal, Rio de Janeiro, RJ
2002-01-01
The solution of inverse problems in participating media where there is emission, absorption and dispersion of the radiation possesses several applications in engineering and medicine. The objective of this work is to estimative the coefficients of absorption and dispersion in two-dimensional heterogeneous participating media, using in independent form the Generalized Maximum Entropy and Levenberg Marquardt methods. Both methods are based on the solution of the direct problem that is modeled by the Boltzmann equation in cartesian geometry. Some cases testes are presented. (author)
International Nuclear Information System (INIS)
Ho, Yew Kam; Lin, Chien-Hao
2015-01-01
In this work, we study the quantum entanglement for doubly excited resonance states in two-electron atomic systems such as the H - and Ps - ions and the He atom by using highly correlated Hylleraas type functions The resonance states are determined by calculation of density of resonance states with the stabilization method. The spatial (electron-electron orbital) entanglement entropies (linear and von Neumann) for the low-lying doubly excited states are quantified using the Schmidt-Slater decomposition method. (paper)
Entanglement in random pure states: spectral density and average von Neumann entropy
Energy Technology Data Exchange (ETDEWEB)
Kumar, Santosh; Pandey, Akhilesh, E-mail: skumar.physics@gmail.com, E-mail: ap0700@mail.jnu.ac.in [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067 (India)
2011-11-04
Quantum entanglement plays a crucial role in quantum information, quantum teleportation and quantum computation. The information about the entanglement content between subsystems of the composite system is encoded in the Schmidt eigenvalues. We derive here closed expressions for the spectral density of Schmidt eigenvalues for all three invariant classes of random matrix ensembles. We also obtain exact results for average von Neumann entropy. We find that maximum average entanglement is achieved if the system belongs to the symplectic invariant class. (paper)
Liu, Yong; Qin, Zhimeng; Hu, Baodan; Feng, Shuai
2018-04-01
Stability analysis is of great significance to landslide hazard prevention, especially the dynamic stability. However, many existing stability analysis methods are difficult to analyse the continuous landslide stability and its changing regularities in a uniform criterion due to the unique landslide geological conditions. Based on the relationship between displacement monitoring data, deformation states and landslide stability, a state fusion entropy method is herein proposed to derive landslide instability through a comprehensive multi-attribute entropy analysis of deformation states, which are defined by a proposed joint clustering method combining K-means and a cloud model. Taking Xintan landslide as the detailed case study, cumulative state fusion entropy presents an obvious increasing trend after the landslide entered accelerative deformation stage and historical maxima match highly with landslide macroscopic deformation behaviours in key time nodes. Reasonable results are also obtained in its application to several other landslides in the Three Gorges Reservoir in China. Combined with field survey, state fusion entropy may serve for assessing landslide stability and judging landslide evolutionary stages.
Dispersion entropy for the analysis of resting-state MEG regularity in Alzheimer's disease.
Azami, Hamed; Rostaghi, Mostafa; Fernandez, Alberto; Escudero, Javier
2016-08-01
Alzheimer's disease (AD) is a progressive degenerative brain disorder affecting memory, thinking, behaviour and emotion. It is the most common form of dementia and a big social problem in western societies. The analysis of brain activity may help to diagnose this disease. Changes in entropy methods have been reported useful in research studies to characterize AD. We have recently proposed dispersion entropy (DisEn) as a very fast and powerful tool to quantify the irregularity of time series. The aim of this paper is to evaluate the ability of DisEn, in comparison with fuzzy entropy (FuzEn), sample entropy (SampEn), and permutation entropy (PerEn), to discriminate 36 AD patients from 26 elderly control subjects using resting-state magnetoencephalogram (MEG) signals. The results obtained by DisEn, FuzEn, and SampEn, unlike PerEn, show that the AD patients' signals are more regular than controls' time series. The p-values obtained by DisEn, FuzEn, SampEn, and PerEn based methods demonstrate the superiority of DisEn over PerEn, SampEn, and PerEn. Moreover, the computation time for the newly proposed DisEn-based method is noticeably less than for the FuzEn, SampEn, and PerEn based approaches.
Resting state fMRI entropy probes complexity of brain activity in adults with ADHD.
Sokunbi, Moses O; Fung, Wilson; Sawlani, Vijay; Choppin, Sabine; Linden, David E J; Thome, Johannes
2013-12-30
In patients with attention deficit hyperactivity disorder (ADHD), quantitative neuroimaging techniques have revealed abnormalities in various brain regions, including the frontal cortex, striatum, cerebellum, and occipital cortex. Nonlinear signal processing techniques such as sample entropy have been used to probe the regularity of brain magnetoencephalography signals in patients with ADHD. In the present study, we extend this technique to analyse the complex output patterns of the 4 dimensional resting state functional magnetic resonance imaging signals in adult patients with ADHD. After adjusting for the effect of age, we found whole brain entropy differences (P=0.002) between groups and negative correlation (r=-0.45) between symptom scores and mean whole brain entropy values, indicating lower complexity in patients. In the regional analysis, patients showed reduced entropy in frontal and occipital regions bilaterally and a significant negative correlation between the symptom scores and the entropy maps at a family-wise error corrected cluster level of Pentropy is a useful tool in revealing abnormalities in the brain dynamics of patients with psychiatric disorders. © 2013 Elsevier Ireland Ltd. All rights reserved.
An application of sample entropy to precipitation in Paraíba State, Brazil
Xavier, Sílvio Fernando Alves; da Silva Jale, Jader; Stosic, Tatijana; dos Santos, Carlos Antonio Costa; Singh, Vijay P.
2018-05-01
A climate system is characterized to be a complex non-linear system. In order to describe the complex characteristics of precipitation series in Paraíba State, Brazil, we aim the use of sample entropy, a kind of entropy-based algorithm, to evaluate the complexity of precipitation series. Sixty-nine meteorological stations are distributed over four macroregions: Zona da Mata, Agreste, Borborema, and Sertão. The results of the analysis show that intricacies of monthly average precipitation have differences in the macroregions. Sample entropy is able to reflect the dynamic change of precipitation series providing a new way to investigate complexity of hydrological series. The complexity exhibits areal variation of local water resource systems which can influence the basis for utilizing and developing resources in dry areas.
International Nuclear Information System (INIS)
Handel, P.H.
1998-01-01
The author's recent application of the new Quantum Information Theory Approach (QIT) to Infra Quantum Physics (IQP) explains for the first time the apparent lack of unitarity caused by the entropy increase in the Quantum 1/f Effect (Q1/fE). This allows for a better understanding of the quantum 1/f effect in this paper, showing no resultant entropy increase and therefore no violation of unitarity. This new interpretation involves the concept of von Neumann Quantum Entropy, including the new negative conditional entropy concept for quantum entangled states introduced by QIT. The Q1/fE was applied to many high-tech systems, in particular to ultra small electronic devices. The present paper explains how the additional entropy implied by the Q1/fE arises in spite of the entropy-conserving evolution of the system. On this basis, a general derivation of the conventional and coherent quantum 1/f effect is given. (author)
Li, Guanchen; von Spakovsky, Michael R.
2016-01-01
This paper presents a study of the nonequilibrium relaxation process of chemically reactive systems using steepest-entropy-ascent quantum thermodynamics (SEAQT). The trajectory of the chemical reaction, i.e., the accessible intermediate states, is predicted and discussed. The prediction is made using a thermodynamic-ensemble approach, which does not require detailed information about the particle mechanics involved (e.g., the collision of particles). Instead, modeling the kinetics and dynamics of the relaxation process is based on the principle of steepest-entropy ascent (SEA) or maximum-entropy production, which suggests a constrained gradient dynamics in state space. The SEAQT framework is based on general definitions for energy and entropy and at least theoretically enables the prediction of the nonequilibrium relaxation of system state at all temporal and spatial scales. However, to make this not just theoretically but computationally possible, the concept of density of states is introduced to simplify the application of the relaxation model, which in effect extends the application of the SEAQT framework even to infinite energy eigenlevel systems. The energy eigenstructure of the reactive system considered here consists of an extremely large number of such levels (on the order of 10130) and yields to the quasicontinuous assumption. The principle of SEA results in a unique trajectory of system thermodynamic state evolution in Hilbert space in the nonequilibrium realm, even far from equilibrium. To describe this trajectory, the concepts of subsystem hypoequilibrium state and temperature are introduced and used to characterize each system-level, nonequilibrium state. This definition of temperature is fundamental rather than phenomenological and is a generalization of the temperature defined at stable equilibrium. In addition, to deal with the large number of energy eigenlevels, the equation of motion is formulated on the basis of the density of states and a set of
Chen, Li; Gao, Shuang; Zhang, Hui; Sun, Yanling; Ma, Zhenxing; Vedal, Sverre; Mao, Jian; Bai, Zhipeng
2018-05-03
Concentrations of particulate matter with aerodynamic diameter Bayesian Maximum Entropy (BME) interpolation of the LUR space-time residuals were developed to estimate the PM 2.5 concentrations on a national scale in China. This hybrid model could potentially provide more valid predictions than a commonly-used LUR model. The LUR/BME model had good performance characteristics, with R 2 = 0.82 and root mean square error (RMSE) of 4.6 μg/m 3 . Prediction errors of the LUR/BME model were reduced by incorporating soft data accounting for data uncertainty, with the R 2 increasing by 6%. The performance of LUR/BME is better than OK/BME. The LUR/BME model is the most accurate fine spatial scale PM 2.5 model developed to date for China. Copyright © 2018. Published by Elsevier Ltd.
Directory of Open Access Journals (Sweden)
Rong Jiang
2014-09-01
Full Text Available As the early design decision-making structure, a software architecture plays a key role in the final software product quality and the whole project. In the software design and development process, an effective evaluation of the trustworthiness of a software architecture can help making scientific and reasonable decisions on the architecture, which are necessary for the construction of highly trustworthy software. In consideration of lacking the trustworthiness evaluation and measurement studies for software architecture, this paper provides one trustworthy attribute model of software architecture. Based on this model, the paper proposes to use the Principle of Maximum Entropy (POME and Grey Decision-making Method (GDMM as the trustworthiness evaluation method of a software architecture and proves the scientificity and rationality of this method, as well as verifies the feasibility through case analysis.
Entanglement entropy in quantum many-particle systems and their simulation via ansatz states
International Nuclear Information System (INIS)
Barthel, Thomas
2009-01-01
A main topic of this thesis is the development of efficient numerical methods for the simulation of strongly correlated quantum lattice models. For one-dimensional systems, the density-matrix renormalization-group (DMRG) is such a very successful method. The physical states of interest are approximated within a certain class of ansatz states. These ansatz states are designed in a way that the number of degrees of freedom are prevented from growing exponentially. They are the so-called matrix product states. The first part of the thesis, therefore, provides analytical and numerical analysis of the scaling of quantum nonlocality with the system size or time in different, physically relevant scenarios. For example, the scaling of Renyi entropies and their dependence on boundary conditions is derived within the 1+1-dimensional conformal field theory. Conjectures and analytical indications concerning the properties of entanglement entropy in critical fermionic and bosonic systems are confirmed numerically with high precision. For integrable models in the thermodynamic limit, general preconditions are derived under which subsystems converge to steady states. These steady states are non-thermal and retain information about the initial state. It is shown that the entanglement entropy in such steady states is extensive. For short times, the entanglement entropy grows typically linearly with time, causing an exponential increase in computation costs for the DMRG method. The second part of the thesis focuses on the development and improvement of the abovementioned numerical techniques. The time-dependent DMRG is complemented with an extrapolation technique for the evaluated observables. In this way, the problem of the entropy increase can be circumvented, allowing for a precise determination of spectral functions. The method is demonstrated using the example of the Heisenberg antiferromagnet and results are compared to Bethe-Ansatz data for T=0 and quantum Monte Carlo data
Entanglement entropy in quantum many-particle systems and their simulation via ansatz states
Energy Technology Data Exchange (ETDEWEB)
Barthel, Thomas
2009-12-10
A main topic of this thesis is the development of efficient numerical methods for the simulation of strongly correlated quantum lattice models. For one-dimensional systems, the density-matrix renormalization-group (DMRG) is such a very successful method. The physical states of interest are approximated within a certain class of ansatz states. These ansatz states are designed in a way that the number of degrees of freedom are prevented from growing exponentially. They are the so-called matrix product states. The first part of the thesis, therefore, provides analytical and numerical analysis of the scaling of quantum nonlocality with the system size or time in different, physically relevant scenarios. For example, the scaling of Renyi entropies and their dependence on boundary conditions is derived within the 1+1-dimensional conformal field theory. Conjectures and analytical indications concerning the properties of entanglement entropy in critical fermionic and bosonic systems are confirmed numerically with high precision. For integrable models in the thermodynamic limit, general preconditions are derived under which subsystems converge to steady states. These steady states are non-thermal and retain information about the initial state. It is shown that the entanglement entropy in such steady states is extensive. For short times, the entanglement entropy grows typically linearly with time, causing an exponential increase in computation costs for the DMRG method. The second part of the thesis focuses on the development and improvement of the abovementioned numerical techniques. The time-dependent DMRG is complemented with an extrapolation technique for the evaluated observables. In this way, the problem of the entropy increase can be circumvented, allowing for a precise determination of spectral functions. The method is demonstrated using the example of the Heisenberg antiferromagnet and results are compared to Bethe-Ansatz data for T=0 and quantum Monte Carlo data
Directory of Open Access Journals (Sweden)
Raji HeyrovskÃƒÂ¡
2004-03-01
Full Text Available Abstract: Recently, the author suggested a simple and composite equation of state by incorporating fundamental thermodynamic properties like heat capacities into her earlier concise equation of state for gases based on free volume and molecular association / dissociation. This work brings new results for aqueous solutions, based on the analogy of the equation of state for gases and solutions over wide ranges of pressures (for gases and concentrations (for solutions. The definitions of entropy and heat energy through the equation of state for gases, also holds for solutions.
Partition Function and Configurational Entropy in Non-Equilibrium States: A New Theoretical Model
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Akira Takada
2018-03-01
Full Text Available A new model of non-equilibrium thermodynamic states has been investigated on the basis of the fact that all thermodynamic variables can be derived from partition functions. We have thus attempted to define partition functions for non-equilibrium conditions by introducing the concept of pseudo-temperature distributions. These pseudo-temperatures are configurational in origin and distinct from kinetic (phonon temperatures because they refer to the particular fragments of the system with specific energies. This definition allows thermodynamic states to be described either for equilibrium or non-equilibrium conditions. In addition; a new formulation of an extended canonical partition function; internal energy and entropy are derived from this new temperature definition. With this new model; computational experiments are performed on simple non-interacting systems to investigate cooling and two distinct relaxational effects in terms of the time profiles of the partition function; internal energy and configurational entropy.
Low-Entropy States of Neutral Atoms in Polarization-Synthesized Optical Lattices.
Robens, Carsten; Zopes, Jonathan; Alt, Wolfgang; Brakhane, Stefan; Meschede, Dieter; Alberti, Andrea
2017-02-10
We create low-entropy states of neutral atoms by utilizing a conceptually new optical-lattice technique that relies on a high-precision, high-bandwidth synthesis of light polarization. Polarization-synthesized optical lattices provide two fully controllable optical lattice potentials, each of them confining only atoms in either one of the two long-lived hyperfine states. By employing one lattice as the storage register and the other one as the shift register, we provide a proof of concept using four atoms that selected regions of the periodic potential can be filled with one particle per site. We expect that our results can be scaled up to thousands of atoms by employing an atom-sorting algorithm with logarithmic complexity, which is enabled by polarization-synthesized optical lattices. Vibrational entropy is subsequently removed by sideband cooling methods. Our results pave the way for a bottom-up approach to creating ultralow-entropy states of a many-body system.
Wavelet Packet Entropy in Speaker-Independent Emotional State Detection from Speech Signal
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Mina Kadkhodaei Elyaderani
2015-01-01
Full Text Available In this paper, wavelet packet entropy is proposed for speaker-independent emotion detection from speech. After pre-processing, wavelet packet decomposition using wavelet type db3 at level 4 is calculated and Shannon entropy in its nodes is calculated to be used as feature. In addition, prosodic features such as first four formants, jitter or pitch deviation amplitude, and shimmer or energy variation amplitude besides MFCC features are applied to complete the feature vector. Then, Support Vector Machine (SVM is used to classify the vectors in multi-class (all emotions or two-class (each emotion versus normal state format. 46 different utterances of a single sentence from Berlin Emotional Speech Dataset are selected. These are uttered by 10 speakers in sadness, happiness, fear, boredom, anger, and normal emotional state. Experimental results show that proposed features can improve emotional state detection accuracy in multi-class situation. Furthermore, adding to other features wavelet entropy coefficients increase the accuracy of two-class detection for anger, fear, and happiness.
Nonthreshold D-brane bound states and black holes with nonzero entropy
International Nuclear Information System (INIS)
Costa, M.S.; Cvetic, M.
1997-01-01
We start with Bogomol close-quote nyi-Prasad-Sommerfield- (BPS) saturated configurations of two (orthogonally) intersecting M-branes and use the electromagnetic duality or dimensional reduction along a boost, in order to obtain new p-brane bound states. In the first case the resulting configurations are interpreted as BPS-saturated nonthreshold bound states of intersecting p-branes, and in the second case as p-branes intersecting at angles and their duals. As a by-product we deduce the enhancement of supersymmetry as the angle approaches zero. We also comment on the D-brane theory describing these new bound states, and a connection between the angle and the world-volume gauge fields of the D-brane system. We use these configurations to find new embeddings of the four- and five-dimensional black holes with nonzero entropy, whose entropy now also depends on the angle and world-volume gauge fields. The corresponding D-brane configuration sheds light on the microscopic entropy of such black holes. copyright 1997 The American Physical Society
Energy Technology Data Exchange (ETDEWEB)
Escalante Sandoval, Carlos A.; Dominguez Esquivel, Jose Y. [Universidad Nacional Autonoma de Mexico (Mexico)
2001-09-01
The principle of maximum entropy (POME) is used to derive an alternative method of parameter estimation for the bivariate Gumbel distribution. A simple algorithm for this parameter estimation technique is presented. This method is applied to analyze the precipitation in a region of Mexico. Design events are compered with those obtained by the maximum likelihood procedure. According to the results, the proposed technique is a suitable option to be considered when performing frequency analysis of precipitation with small samples. [Spanish] El principio de maxima entropia, conocido como POME, es utilizado para derivar un procedimiento alternativo de estimacion de parametros de la distribucion bivariada de valores extremos con marginales Gumbel. El modelo se aplica al analisis de la precipitacion maxima en 24 horas en una region de Mexico y los eventos de diseno obtenidos son comparados con los proporcionados por la tecnica de maxima verosimilitud. De acuerdo con los resultados obtenidos, se concluye que la tecnica propuesta representa una buena opcion, sobre todo para el caso de muestras pequenas.
Role of entropy in the ground state formation of frustrated systems
Sereni, Julian G.
2018-05-01
The absence of magnetic order in Rare Earth-based frustrated compounds allows to recognize the action of the third law of thermodynamics in the low temperature behavior of those systems. One of the most relevant findings is the appearance of a coincident specific heat Cm / T|T→0 ≈ 7 J /molK2 'plateau' in six Yb systems. This characteristic feature occurs after a systematic modification of the thermal trajectory of their entropies Sm (T) in the range of a few hundred milikelvin degrees. Such behavior is explained by the formation of an entropy-bottleneck imposed by the third law constraint (Sm|T→0 ≥ 0), that drives the system into alternative ground states. Based in these finding, three possible approaches to the Sm|T→0 limit observed in real systems are analyzed in terms of the ∂2Sm / ∂T2 dependencies.
Pilge, Stefanie; Kreuzer, Matthias; Karatchiviev, Veliko; Kochs, Eberhard F; Malcharek, Michael; Schneider, Gerhard
2015-05-01
It is claimed that bispectral index (BIS) and state entropy reflect an identical clinical spectrum, the hypnotic component of anaesthesia. So far, it is not known to what extent different devices display similar index values while processing identical electroencephalogram (EEG) signals. To compare BIS and state entropy during analysis of identical EEG data. Inspection of raw EEG input to detect potential causes of erroneous index calculation. Offline re-analysis of EEG data from a randomised, single-centre controlled trial using the Entropy Module and an Aspect A-2000 monitor. Klinikum rechts der Isar, Technische Universität München, Munich. Forty adult patients undergoing elective surgery under general anaesthesia. Blocked randomisation of 20 patients per anaesthetic group (sevoflurane/remifentanil or propofol/remifentanil). Isolated forearm technique for differentiation between consciousness and unconsciousness. Prediction probability (PK) of state entropy to discriminate consciousness from unconsciousness. Correlation and agreement between state entropy and BIS from deep to light hypnosis. Analysis of raw EEG compared with index values that are in conflict with clinical examination, with frequency measures (frequency bands/Spectral Edge Frequency 95) and visual inspection for physiological EEG patterns (e.g. beta or delta arousal), pathophysiological features such as high-frequency signals (electromyogram/high-frequency EEG or eye fluttering/saccades), different types of electro-oculogram or epileptiform EEG and technical artefacts. PK of state entropy was 0.80 and of BIS 0.84; correlation coefficient of state entropy with BIS 0.78. Nine percent BIS and 14% state entropy values disagreed with clinical examination. Highest incidence of disagreement occurred after state transitions, in particular for state entropy after loss of consciousness during sevoflurane anaesthesia. EEG sequences which led to false 'conscious' index values often showed high
Behavior of the maximum likelihood in quantum state tomography
Scholten, Travis L.; Blume-Kohout, Robin
2018-02-01
Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model selection methods typically rely on a test statistic and a null theory that describes its behavior when two models are equally good. Here, we consider the loglikelihood ratio. Because of the positivity constraint ρ ≥ 0, quantum state space does not generally satisfy local asymptotic normality (LAN), meaning the classical null theory for the loglikelihood ratio (the Wilks theorem) should not be used. Thus, understanding and quantifying how positivity affects the null behavior of this test statistic is necessary for its use in model selection for state tomography. We define a new generalization of LAN, metric-projected LAN, show that quantum state space satisfies it, and derive a replacement for the Wilks theorem. In addition to enabling reliable model selection, our results shed more light on the qualitative effects of the positivity constraint on state tomography.
Behavior of the maximum likelihood in quantum state tomography
Energy Technology Data Exchange (ETDEWEB)
Blume-Kohout, Robin J [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States); Scholten, Travis L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)
2018-02-22
Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model selection methods typically rely on a test statistic and a null theory that describes its behavior when two models are equally good. Here, we consider the loglikelihood ratio. Because of the positivity constraint ρ ≥ 0, quantum state space does not generally satisfy local asymptotic normality (LAN), meaning the classical null theory for the loglikelihood ratio (the Wilks theorem) should not be used. Thus, understanding and quantifying how positivity affects the null behavior of this test statistic is necessary for its use in model selection for state tomography. We define a new generalization of LAN, metric-projected LAN, show that quantum state space satisfies it, and derive a replacement for the Wilks theorem. In addition to enabling reliable model selection, our results shed more light on the qualitative effects of the positivity constraint on state tomography.
Goldstein, Sheldon; Tumulka, Roderich; Zanghı, Nino
2016-07-01
According to statistical mechanics, microstates of an isolated physical system (say, a gas in a box) at time t0 in a given macrostate of less-than-maximal entropy typically evolve in such a way that the entropy at time t increases with |t -t0| in both time directions. In order to account for the observed entropy increase in only one time direction, the thermodynamic arrow of time, one usually appeals to the hypothesis that the initial state of the Universe was one of very low entropy. In certain recent models of cosmology, however, no hypothesis about the initial state of the Universe is invoked. We discuss how the emergence of a thermodynamic arrow of time in such models can nevertheless be compatible with the above-mentioned consequence of statistical mechanics, appearances to the contrary notwithstanding.
Ferrari, Ulisse
2016-08-01
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case of large but finite datasets. We first show how the steepest descent dynamics is not optimal as it is slowed down by the inhomogeneous curvature of the model parameters' space. We then provide a way for rectifying this space which relies only on dataset properties and does not require large computational efforts. We conclude by solving the long-time limit of the parameters' dynamics including the randomness generated by the systematic use of Gibbs sampling. In this stochastic framework, rather than converging to a fixed point, the dynamics reaches a stationary distribution, which for the rectified dynamics reproduces the posterior distribution of the parameters. We sum up all these insights in a "rectified" data-driven algorithm that is fast and by sampling from the parameters' posterior avoids both under- and overfitting along all the directions of the parameters' space. Through the learning of pairwise Ising models from the recording of a large population of retina neurons, we show how our algorithm outperforms the steepest descent method.
Directory of Open Access Journals (Sweden)
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!
Indian Academy of Sciences (India)
problem is important from an experimental point of view, because absorption is always present. ... equal-a-priori probabilities is expressed mathematically by the invariant measure on the matrix space ... the interval between zero and one.
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.
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.
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
Entropy concentration and the empirical coding game
Grünwald, P.D.
2008-01-01
We give a characterization of maximum entropy/minimum relative entropy inference by providing two 'strong entropy concentration' theorems. These theorems unify and generalize Jaynes''concentration phenomenon' and Van Campenhout and Cover's 'conditional limit theorem'. The theorems characterize
Jennings, Robert C; Zucchelli, Giuseppe
2014-01-01
We examine ergodicity and configurational entropy for a dilute pigment solution and for a suspension of plant photosystem particles in which both ground and excited state pigments are present. It is concluded that the pigment solution, due to the extreme brevity of the excited state lifetime, is non-ergodic and the configurational entropy approaches zero. Conversely, due to the rapid energy transfer among pigments, each photosystem is ergodic and the configurational entropy is positive. This decreases the free energy of the single photosystem pigment array by a small amount. On the other hand, the suspension of photosystems is non-ergodic and the configurational entropy approaches zero. The overall configurational entropy which, in principle, includes contributions from both the single excited photosystems and the suspension which contains excited photosystems, also approaches zero. Thus the configurational entropy upon photon absorption by either a pigment solution or a suspension of photosystem particles is approximately zero. Copyright © 2014 Elsevier B.V. All rights reserved.
Bounds on the entanglement entropy of droplet states in the XXZ spin chain
Beaud, V.; Warzel, S.
2018-01-01
We consider a class of one-dimensional quantum spin systems on the finite lattice Λ ⊂Z , related to the XXZ spin chain in its Ising phase. It includes in particular the so-called droplet Hamiltonian. The entanglement entropy of energetically low-lying states over a bipartition Λ = B ∪ Bc is investigated and proven to satisfy a logarithmic bound in terms of min{n, |B|, |Bc|}, where n denotes the maximal number of down spins in the considered state. Upon addition of any (positive) random potential, the bound becomes uniformly constant on average, thereby establishing an area law. The proof is based on spectral methods: a deterministic bound on the local (many-body integrated) density of states is derived from an energetically motivated Combes-Thomas estimate.
Institute of Scientific and Technical Information of China (English)
S.Abdel-Khalek; M.M.A.Ahmed; A-S F.Obada
2011-01-01
We present an effective two-level system in interaction through two-photon processes with a single mode quantized electromagnetic field,initially prepared in a coherent state.Field entropy squeezing as an indicator of the entanglement in a mixed state system is suggested.The temporal evolution of the negativity,Wehrl entropy,Wehrl phase distribution and field entropy squeezing are investigated.The results highlight the important roles played by both the Stark shift parameters and the mixed state setting in the dynamics of the Wehrl entropy,Wehrl phase distribution and field entropy squeezing.%We present an effective two-level system in interaction through two-photon processes with a single mode quantized electromagnetic Reid, initially prepared in a coherent state. Field entropy squeezing as an indicator of the entanglement in a mixed state system is suggested. The temporal evolution of the negativity, Wehrl entropy, Wehrl phase distribution and field entropy squeezing are investigated. The results highlight the important roles played by both the Stark shift parameters and the mixed state setting in the dynamics of the Wehrl entropy, Wehrl phase distribution and field entropy squeezing.
Solutions to the Cosmic Initial Entropy Problem without Equilibrium Initial Conditions
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Vihan M. Patel
2017-08-01
Full Text Available The entropy of the observable universe is increasing. Thus, at earlier times the entropy was lower. However, the cosmic microwave background radiation reveals an apparently high entropy universe close to thermal and chemical equilibrium. A two-part solution to this cosmic initial entropy problem is proposed. Following Penrose, we argue that the evenly distributed matter of the early universe is equivalent to low gravitational entropy. There are two competing explanations for how this initial low gravitational entropy comes about. (1 Inflation and baryogenesis produce a virtually homogeneous distribution of matter with a low gravitational entropy. (2 Dissatisfied with explaining a low gravitational entropy as the product of a ‘special’ scalar field, some theorists argue (following Boltzmann for a “more natural” initial condition in which the entire universe is in an initial equilibrium state of maximum entropy. In this equilibrium model, our observable universe is an unusual low entropy fluctuation embedded in a high entropy universe. The anthropic principle and the fluctuation theorem suggest that this low entropy region should be as small as possible and have as large an entropy as possible, consistent with our existence. However, our low entropy universe is much larger than needed to produce observers, and we see no evidence for an embedding in a higher entropy background. The initial conditions of inflationary models are as natural as the equilibrium background favored by many theorists.
Lombardo, Luigi; Bachofer, F.; Cama, M.; Mä rker, M.; Rotigliano, E.
2016-01-01
This study aims at evaluating the performance of the Maximum Entropy method in assessing landslide susceptibility, exploiting topographic and multispectral remote sensing predictors. We selected the catchment of the Giampilieri stream, which is located in the north-eastern sector of Sicily (southern Italy), as test site. On 1/10/2009, a storm rainfall triggered in this area hundreds of debris flow/avalanche phenomena causing extensive economical damage and loss of life. Within this area a presence-only-based statistical method was applied to obtain susceptibility models capable of distinguish future activation sites of debris flow and debris slide, which where the main source failure mechanisms for flow or avalanche type propagation. The set of predictors used in this experiment comprised primary and secondary topographic attributes, derived by processing a high resolution digital elevation model, CORINE land cover data and a set of vegetation and mineral indices obtained by processing multispectral ASTER images. All the selected data sources are dated before the disaster. A spatially random partition technique was adopted for validation, generating fifty replicates for each of the two considered movement typologies in order to assess accuracy, precision and reliability of the models. The debris slide and debris flow susceptibility models produced high performances with the first type being the best fitted. The evaluation of the probability estimates around the mean value for each mapped pixel shows an inverted relation, with the most robust models corresponding to the debris flows. With respect to the role of each predictor within the modelling phase, debris flows appeared to be primarily controlled by topographic attributes whilst the debris slides were better explained by remotely sensed derived indices, particularly by the occurrence of previous wildfires across the slope. The overall excellent performances of the two models suggest promising perspectives for
Messier, K. P.; Serre, M. L.
2015-12-01
Radon (222Rn) is a naturally occurring chemically inert, colorless, and odorless radioactive gas produced from the decay of uranium (238U), which is ubiquitous in rocks and soils worldwide. Exposure to 222Rn is likely the second leading cause of lung cancer after cigarette smoking via inhalation; however, exposure through untreated groundwater is also a contributing factor to both inhalation and ingestion routes. A land use regression (LUR) model for groundwater 222Rn with anisotropic geological and 238U based explanatory variables is developed, which helps elucidate the factors contributing to elevated 222Rn across North Carolina. Geological and uranium based variables are constructed in elliptical buffers surrounding each observation such that they capture the lateral geometric anisotropy present in groundwater 222Rn. Moreover, geological features are defined at three different geological spatial scales to allow the model to distinguish between large area and small area effects of geology on groundwater 222Rn. The LUR is also integrated into the Bayesian Maximum Entropy (BME) geostatistical framework to increase accuracy and produce a point-level LUR-BME model of groundwater 222Rn across North Carolina including prediction uncertainty. The LUR-BME model of groundwater 222Rn results in a leave-one out cross-validation of 0.46 (Pearson correlation coefficient= 0.68), effectively predicting within the spatial covariance range. Modeled results of 222Rn concentrations show variability among Intrusive Felsic geological formations likely due to average bedrock 238U defined on the basis of overlying stream-sediment 238U concentrations that is a widely distributed consistently analyzed point-source data.
Adam-Poupart, Ariane; Brand, Allan; Fournier, Michel; Jerrett, Michael; Smargiassi, Audrey
2014-09-01
Ambient air ozone (O3) is a pulmonary irritant that has been associated with respiratory health effects including increased lung inflammation and permeability, airway hyperreactivity, respiratory symptoms, and decreased lung function. Estimation of O3 exposure is a complex task because the pollutant exhibits complex spatiotemporal patterns. To refine the quality of exposure estimation, various spatiotemporal methods have been developed worldwide. We sought to compare the accuracy of three spatiotemporal models to predict summer ground-level O3 in Quebec, Canada. We developed a land-use mixed-effects regression (LUR) model based on readily available data (air quality and meteorological monitoring data, road networks information, latitude), a Bayesian maximum entropy (BME) model incorporating both O3 monitoring station data and the land-use mixed model outputs (BME-LUR), and a kriging method model based only on available O3 monitoring station data (BME kriging). We performed leave-one-station-out cross-validation and visually assessed the predictive capability of each model by examining the mean temporal and spatial distributions of the average estimated errors. The BME-LUR was the best predictive model (R2 = 0.653) with the lowest root mean-square error (RMSE ;7.06 ppb), followed by the LUR model (R2 = 0.466, RMSE = 8.747) and the BME kriging model (R2 = 0.414, RMSE = 9.164). Our findings suggest that errors of estimation in the interpolation of O3 concentrations with BME can be greatly reduced by incorporating outputs from a LUR model developed with readily available data.
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Matthew W Breece
Full Text Available Atlantic sturgeon (Acipenser oxyrinchus oxyrinchus experienced severe declines due to habitat destruction and overfishing beginning in the late 19(th century. Subsequent to the boom and bust period of exploitation, there has been minimal fishing pressure and improving habitats. However, lack of recovery led to the 2012 listing of Atlantic sturgeon under the Endangered Species Act. Although habitats may be improving, the availability of high quality spawning habitat, essential for the survival and development of eggs and larvae may still be a limiting factor in the recovery of Atlantic sturgeon. To estimate adult Atlantic sturgeon spatial distributions during riverine occupancy in the Delaware River, we utilized a maximum entropy (MaxEnt approach along with passive biotelemetry during the likely spawning season. We found that substrate composition and distance from the salt front significantly influenced the locations of adult Atlantic sturgeon in the Delaware River. To broaden the scope of this study we projected our model onto four scenarios depicting varying locations of the salt front in the Delaware River: the contemporary location of the salt front during the likely spawning season, the location of the salt front during the historic fishery in the late 19(th century, an estimated shift in the salt front by the year 2100 due to climate change, and an extreme drought scenario, similar to that which occurred in the 1960's. The movement of the salt front upstream as a result of dredging and climate change likely eliminated historic spawning habitats and currently threatens areas where Atlantic sturgeon spawning may be taking place. Identifying where suitable spawning substrate and water chemistry intersect with the likely occurrence of adult Atlantic sturgeon in the Delaware River highlights essential spawning habitats, enhancing recovery prospects for this imperiled species.
Lombardo, Luigi
2016-07-18
This study aims at evaluating the performance of the Maximum Entropy method in assessing landslide susceptibility, exploiting topographic and multispectral remote sensing predictors. We selected the catchment of the Giampilieri stream, which is located in the north-eastern sector of Sicily (southern Italy), as test site. On 1/10/2009, a storm rainfall triggered in this area hundreds of debris flow/avalanche phenomena causing extensive economical damage and loss of life. Within this area a presence-only-based statistical method was applied to obtain susceptibility models capable of distinguish future activation sites of debris flow and debris slide, which where the main source failure mechanisms for flow or avalanche type propagation. The set of predictors used in this experiment comprised primary and secondary topographic attributes, derived by processing a high resolution digital elevation model, CORINE land cover data and a set of vegetation and mineral indices obtained by processing multispectral ASTER images. All the selected data sources are dated before the disaster. A spatially random partition technique was adopted for validation, generating fifty replicates for each of the two considered movement typologies in order to assess accuracy, precision and reliability of the models. The debris slide and debris flow susceptibility models produced high performances with the first type being the best fitted. The evaluation of the probability estimates around the mean value for each mapped pixel shows an inverted relation, with the most robust models corresponding to the debris flows. With respect to the role of each predictor within the modelling phase, debris flows appeared to be primarily controlled by topographic attributes whilst the debris slides were better explained by remotely sensed derived indices, particularly by the occurrence of previous wildfires across the slope. The overall excellent performances of the two models suggest promising perspectives for
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.
Energy Technology Data Exchange (ETDEWEB)
Praveen, E., E-mail: svmstaya@gmail.com; Satyanarayana, S. V. M., E-mail: svmstaya@gmail.com [Department of Physics, Pondicherry University, Puducherry-605014 (India)
2014-04-24
Traditional definition of phase transition involves an infinitely large system in thermodynamic limit. Finite systems such as biological proteins exhibit cooperative behavior similar to phase transitions. We employ recently discovered analysis of inflection points of microcanonical entropy to estimate the transition temperature of the phase transition in q state Potts model on a finite two dimensional square lattice for q=3 (second order) and q=8 (first order). The difference of energy density of states (DOS) Δ ln g(E) = ln g(E+ ΔE) −ln g(E) exhibits a point of inflexion at a value corresponding to inverse transition temperature. This feature is common to systems exhibiting both first as well as second order transitions. While the difference of DOS registers a monotonic variation around the point of inflexion for systems exhibiting second order transition, it has an S-shape with a minimum and maximum around the point of inflexion for the case of first order transition.
International Nuclear Information System (INIS)
Praveen, E.; Satyanarayana, S. V. M.
2014-01-01
Traditional definition of phase transition involves an infinitely large system in thermodynamic limit. Finite systems such as biological proteins exhibit cooperative behavior similar to phase transitions. We employ recently discovered analysis of inflection points of microcanonical entropy to estimate the transition temperature of the phase transition in q state Potts model on a finite two dimensional square lattice for q=3 (second order) and q=8 (first order). The difference of energy density of states (DOS) Δ ln g(E) = ln g(E+ ΔE) −ln g(E) exhibits a point of inflexion at a value corresponding to inverse transition temperature. This feature is common to systems exhibiting both first as well as second order transitions. While the difference of DOS registers a monotonic variation around the point of inflexion for systems exhibiting second order transition, it has an S-shape with a minimum and maximum around the point of inflexion for the case of first order transition
Entropy Constraints in the Ground State Formation of Magnetically Frustrated Systems
Sereni, Julian G.
2018-01-01
A systematic modification of the entropy trajectory (S_m(T)) is observed at very low temperature in magnetically frustrated systems as a consequence of the constraint (S_mg 0) imposed by the Nernst postulate. The lack of magnetic order allows to explore and compare new thermodynamic properties by tracing the specific heat (C_m) behavior down to the sub-Kelvin range. Some of the most relevant findings are: (i) a common C_m/T|_{T→ 0} ≈ 7 J/mol K^2 `plateau' in at least five Yb-based very-heavy-fermions (VHF) compounds; (ii) quantitative and qualitative differences between VHF and standard non-Fermi-liquids; (iii) entropy bottlenecks governing the change of S_m(T) trajectories in a continuous transition into alternative ground states. A comparative analysis of S_m(T→ 0) dependencies is performed in compounds suitable for adiabatic demagnetization processes according to their partial ^2 S_m/partial T^2 derivatives.
International Nuclear Information System (INIS)
Das, S; Amaral, J S; Amaral, V S
2010-01-01
We present an approach to extract a realistic magnetic entropy value from non-equilibrium magnetization data near the transition temperature of a typical first-order system with a mixed-phase state, influenced by the phase transformation, which is responsible for large values reported, even higher than the theoretical limit. The effect of the mixed-phase state is modelled in the magnetization and its non-physical contribution is removed to obtain the magnetic entropy in accordance with calorimetric experiment and theoretical simulation. This approach gives a reliable estimation of the magnetic entropy value incorporating experimental non-equilibrium magnetization data and correcting the use of Maxwell's relation. (fast track communication)
Entropy of entangled states and SU(1,1) and SU(2) symmetries
International Nuclear Information System (INIS)
Santana, A.E.; Khanna, F.C.; Revzen, M.
2002-01-01
Based on a recent definition of a measure for entanglement [Plenio and Vedral, Contemp. Phys. 39, 431 (1998)], examples of maximum entangled states are presented. The construction of such states, which have symmetry SU(1,1) and SU(2), follows the guidance of thermofield dynamics formalism
Decreased Complexity in Alzheimer's Disease: Resting-State fMRI Evidence of Brain Entropy Mapping
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Bin Wang
2017-11-01
Full Text Available Alzheimer's disease (AD is a frequently observed, irreversible brain function disorder among elderly individuals. Resting-state functional magnetic resonance imaging (rs-fMRI has been introduced as an alternative approach to assessing brain functional abnormalities in AD patients. However, alterations in the brain rs-fMRI signal complexities in mild cognitive impairment (MCI and AD patients remain unclear. Here, we described the novel application of permutation entropy (PE to investigate the abnormal complexity of rs-fMRI signals in MCI and AD patients. The rs-fMRI signals of 30 normal controls (NCs, 33 early MCI (EMCI, 32 late MCI (LMCI, and 29 AD patients were obtained from the Alzheimer's disease Neuroimaging Initiative (ADNI database. After preprocessing, whole-brain entropy maps of the four groups were extracted and subjected to Gaussian smoothing. We performed a one-way analysis of variance (ANOVA on the brain entropy maps of the four groups. The results after adjusting for age and sex differences together revealed that the patients with AD exhibited lower complexity than did the MCI and NC controls. We found five clusters that exhibited significant differences and were distributed primarily in the occipital, frontal, and temporal lobes. The average PE of the five clusters exhibited a decreasing trend from MCI to AD. The AD group exhibited the least complexity. Additionally, the average PE of the five clusters was significantly positively correlated with the Mini-Mental State Examination (MMSE scores and significantly negatively correlated with Functional Assessment Questionnaire (FAQ scores and global Clinical Dementia Rating (CDR scores in the patient groups. Significant correlations were also found between the PE and regional homogeneity (ReHo in the patient groups. These results indicated that declines in PE might be related to changes in regional functional homogeneity in AD. These findings suggested that complexity analyses using PE
Entropy and equilibrium via games of complexity
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.
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Evgeni B. Starikov
2018-02-01
Full Text Available This work has shown the way to put the formal statistical-mechanical basement under the hotly debated notion of enthalpy-entropy compensation. The possibility of writing down the universal equation of state based upon the statistical mechanics is discussed here.
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R. Vlijm, I. S. Eliëns, J. -S. Caux
2016-10-01
Full Text Available Pumping a finite energy density into a quantum system typically leads to `melted' states characterized by exponentially-decaying correlations, as is the case for finite-temperature equilibrium situations. An important exception to this rule are states which, while being at high energy, maintain a low entropy. Such states can interestingly still display features of quantum criticality, especially in one dimension. Here, we consider high-energy states in anisotropic Heisenberg quantum spin chains obtained by splitting the ground state's magnon Fermi sea into separate pieces. Using methods based on integrability, we provide a detailed study of static and dynamical spin-spin correlations. These carry distinctive signatures of the Fermi sea splittings, which would be observable in eventual experimental realizations. Going further, we employ a multi-component Tomonaga-Luttinger model in order to predict the asymptotics of static correlations. For this effective field theory, we fix all universal exponents from energetics, and all non-universal correlation prefactors using finite-size scaling of matrix elements. The correlations obtained directly from integrability and those emerging from the Luttinger field theory description are shown to be in extremely good correspondence, as expected, for the large distance asymptotics, but surprisingly also for the short distance behavior. Finally, we discuss the description of dynamical correlations from a mobile impurity model, and clarify the relation of the effective field theory parameters to the Bethe Ansatz solution.
Ground state entropy of the Potts antiferromagnet on triangular lattice strips
International Nuclear Information System (INIS)
Chang Shuchiuan; Shrock, Robert
2001-01-01
We present exact calculations of the zero-temperature partition function (chromatic polynomial) P for the q-state Potts antiferromagnet on triangular lattice strips of arbitrarily great length L x vertices and of width L y vertices and, in the L x →∞ limit, the exponent of the ground state entropy, W=e S 0 /k B . The strips considered, with their boundary conditions (BC), are (a) (FBC y , PBC x ) = cyclic for L y =3, 4, (b) (FBC y , TPBC x ) = Moebius, L y =3, (c) (PBC y , PBC x ) = toroidal, L y =3, (d) (PBC y , TPBC x ) = Klein bottle, L y =3, (e) (PBC y , FBC x ) = cylindrical, L y =5, 6, and (f) (FBC y , FBC x ) = free, L y =5, where F, P, and TP denote free, periodic, and twisted periodic. Several interesting features are found, including the presence of terms in P proportional to cos(2πL x /3) for case (c). The continuous locus of points B where W is nonanalytic in the q plane is discussed for each case and a comparative discussion is given of the respective loci B for families with different boundary conditions. Numerical values of W are given for infinite-length strips of various widths and are shown to approach values for the 2D lattice rapidly. A remark is also made concerning a zero-free region for chromatic zeros. Some results are given for strips of other lattices
RNA Thermodynamic Structural Entropy.
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
RNA Thermodynamic Structural Entropy.
Directory of Open Access Journals (Sweden)
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
Energy Technology Data Exchange (ETDEWEB)
Boyaval, S.
2000-06-15
This PhD presents a study on a series of high pressure swirl atomizers dedicated to Gasoline Direct Injection (GDI). Measurements are performed in stationary and pulsed working conditions. A great aspect of this thesis is the development of an original experimental set-up to correct multiple light scattering that biases the drop size distributions measurements obtained with a laser diffraction technique (Malvern 2600D). This technique allows to perform a study of drop size characteristics near the injector tip. Correction factors on drop size characteristics and on the diffracted intensities are defined from the developed procedure. Another point consists in applying the Maximum Entropy Formalism (MEF) to calculate drop size distributions. Comparisons between experimental distributions corrected with the correction factors and the calculated distributions show good agreement. This work points out that the mean diameter D{sub 43}, which is also the mean of the volume drop size distribution, and the relative volume span factor {delta}{sub v} are important characteristics of volume drop size distributions. The end of the thesis proposes to determine local drop size characteristics from a new development of deconvolution technique for line-of-sight scattering measurements. The first results show reliable behaviours of radial evolution of local characteristics. In GDI application, we notice that the critical point is the opening stage of the injection. This study shows clearly the effects of injection pressure and nozzle internal geometry on the working characteristics of these injectors, in particular, the influence of the pre-spray. This work points out important behaviours that the improvement of GDI principle ought to consider. (author)
Wavelet Packet Entropy in Speaker-Independent Emotional State Detection from Speech Signal
Mina Kadkhodaei Elyaderani; Seyed Hamid Mahmoodian; Ghazaal Sheikhi
2015-01-01
In this paper, wavelet packet entropy is proposed for speaker-independent emotion detection from speech. After pre-processing, wavelet packet decomposition using wavelet type db3 at level 4 is calculated and Shannon entropy in its nodes is calculated to be used as feature. In addition, prosodic features such as first four formants, jitter or pitch deviation amplitude, and shimmer or energy variation amplitude besides MFCC features are applied to complete the feature vector. Then, Support Vect...
Novel methods for estimating lithium-ion battery state of energy and maximum available energy
International Nuclear Information System (INIS)
Zheng, Linfeng; Zhu, Jianguo; Wang, Guoxiu; He, Tingting; Wei, Yiying
2016-01-01
Highlights: • Study on temperature, current, aging dependencies of maximum available energy. • Study on the various factors dependencies of relationships between SOE and SOC. • A quantitative relationship between SOE and SOC is proposed for SOE estimation. • Estimate maximum available energy by means of moving-window energy-integral. • The robustness and feasibility of the proposed approaches are systematic evaluated. - Abstract: The battery state of energy (SOE) allows a direct determination of the ratio between the remaining and maximum available energy of a battery, which is critical for energy optimization and management in energy storage systems. In this paper, the ambient temperature, battery discharge/charge current rate and cell aging level dependencies of battery maximum available energy and SOE are comprehensively analyzed. An explicit quantitative relationship between SOE and state of charge (SOC) for LiMn_2O_4 battery cells is proposed for SOE estimation, and a moving-window energy-integral technique is incorporated to estimate battery maximum available energy. Experimental results show that the proposed approaches can estimate battery maximum available energy and SOE with high precision. The robustness of the proposed approaches against various operation conditions and cell aging levels is systematically evaluated.
EEG entropy measures in anesthesia
Directory of Open Access Journals (Sweden)
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.
Adjoint entropy vs topological entropy
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...
Entropy Inequality Violations from Ultraspinning Black Holes.
Hennigar, Robie A; Mann, Robert B; Kubizňák, David
2015-07-17
We construct a new class of rotating anti-de Sitter (AdS) black hole solutions with noncompact event horizons of finite area in any dimension and study their thermodynamics. In four dimensions these black holes are solutions to gauged supergravity. We find that their entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality, which states that for a given thermodynamic volume, the black hole entropy is maximized for Schwarzschild-AdS space. We use this result to suggest more stringent conditions under which this conjecture may hold.
Applications of Entropy in Finance: A Review
Directory of Open Access Journals (Sweden)
Guanqun Tong
2013-11-01
Full Text Available Although the concept of entropy is originated from thermodynamics, its concepts and relevant principles, especially the principles of maximum entropy and minimum cross-entropy, have been extensively applied in finance. In this paper, we review the concepts and principles of entropy, as well as their applications in the field of finance, especially in portfolio selection and asset pricing. Furthermore, we review the effects of the applications of entropy and compare them with other traditional and new methods.
Entropy and transverse section reconstruction
International Nuclear Information System (INIS)
Gullberg, G.T.
1976-01-01
A new approach to the reconstruction of a transverse section using projection data from multiple views incorporates the concept of maximum entropy. The principle of maximizing information entropy embodies the assurance of minimizing bias or prejudice in the reconstruction. Using maximum entropy is a necessary condition for the reconstructed image. This entropy criterion is most appropriate for 3-D reconstruction of objects from projections where the system is underdetermined or the data are limited statistically. This is the case in nuclear medicine time limitations in patient studies do not yield sufficient projections
The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems
International Nuclear Information System (INIS)
Kościk, Przemysław
2015-01-01
We study one-dimensional systems of N particles in a one-dimensional harmonic trap with an inverse power law interaction ∼|x| −d . Within the framework of the harmonic approximation we derive, in the strong interaction limit, the Schmidt decomposition of the one-particle reduced density matrix and investigate the nature of the degeneracy appearing in its spectrum. Furthermore, the ground-state asymptotic occupancies and their natural orbitals are derived in closed analytic form, which enables their easy determination for a wide range of values of N. A closed form asymptotic expression for the von Neumann entanglement entropy is also provided and its dependence on N is discussed for the systems with d=1 (charged particles) and with d=3 (dipolar particles). - Highlights: • We study confined systems of N particles with an inverse power law interaction. • We apply the harmonic approximation to the systems. • We derive closed form expressions for the asymptotic von Neumann entropy. • The asymptotic von Neumann entropy grows monotonically as N increases
EEG entropy measures in anesthesia
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
Maximum principle for a stochastic delayed system involving terminal state constraints.
Wen, Jiaqiang; Shi, Yufeng
2017-01-01
We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.
PURE STATE ENTANGLEMENT ENTROPY IN NONCOMMUTATIVE 2D DE SITTER SPACE TIME
Directory of Open Access Journals (Sweden)
M.F Ghiti
2014-12-01
Full Text Available Using the general modified field equation, a general noncommutative Klein-Gordon equation up to the second order of the noncommutativity parameter is derived in the context of noncommutative 2D De Sitter space-time. Using Bogoliubov coefficients and a special technics called conformal time; the boson-antiboson pair creation density is determined. The Von Neumann boson-antiboson pair creation quantum entanglement entropy is presented to compute the entanglement between the modes created presented.
Entropy of international trades
Oh, Chang-Young; Lee, D.-S.
2017-05-01
The organization of international trades is highly complex under the collective efforts towards economic profits of participating countries given inhomogeneous resources for production. Considering the trade flux as the probability of exporting a product from a country to another, we evaluate the entropy of the world trades in the period 1950-2000. The trade entropy has increased with time, and we show that it is mainly due to the extension of trade partnership. For a given number of trade partners, the mean trade entropy is about 60% of the maximum possible entropy, independent of time, which can be regarded as a characteristic of the trade fluxes' heterogeneity and is shown to be derived from the scaling and functional behaviors of the universal trade-flux distribution. The correlation and time evolution of the individual countries' gross-domestic products and the number of trade partners show that most countries achieved their economic growth partly by extending their trade relationship.
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.
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.
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)
Smolin, John A; Gambetta, Jay M; Smith, Graeme
2012-02-17
We provide an efficient method for computing the maximum-likelihood mixed quantum state (with density matrix ρ) given a set of measurement outcomes in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix μ which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst O(d(4)) for the basis change plus O(d(3)) for finding ρ where d is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only O(d(3)) as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one.
Giant onsite electronic entropy enhances the performance of ceria for water splitting.
Naghavi, S Shahab; Emery, Antoine A; Hansen, Heine A; Zhou, Fei; Ozolins, Vidvuds; Wolverton, Chris
2017-08-18
Previous studies have shown that a large solid-state entropy of reduction increases the thermodynamic efficiency of metal oxides, such as ceria, for two-step thermochemical water splitting cycles. In this context, the configurational entropy arising from oxygen off-stoichiometry in the oxide, has been the focus of most previous work. Here we report a different source of entropy, the onsite electronic configurational entropy, arising from coupling between orbital and spin angular momenta in lanthanide f orbitals. We find that onsite electronic configurational entropy is sizable in all lanthanides, and reaches a maximum value of ≈4.7 k B per oxygen vacancy for Ce 4+ /Ce 3+ reduction. This unique and large positive entropy source in ceria explains its excellent performance for high-temperature catalytic redox reactions such as water splitting. Our calculations also show that terbium dioxide has a high electronic entropy and thus could also be a potential candidate for solar thermochemical reactions.Solid-state entropy of reduction increases the thermodynamic efficiency of ceria for two-step thermochemical water splitting. Here, the authors report a large and different source of entropy, the onsite electronic configurational entropy arising from coupling between orbital and spin angular momenta in f orbitals.
Particle-filtering-based estimation of maximum available power state in Lithium-Ion batteries
International Nuclear Information System (INIS)
Burgos-Mellado, Claudio; Orchard, Marcos E.; Kazerani, Mehrdad; Cárdenas, Roberto; Sáez, Doris
2016-01-01
Highlights: • Approach to estimate the state of maximum power available in Lithium-Ion battery. • Optimisation problem is formulated on the basis of a non-linear dynamic model. • Solutions of the optimisation problem are functions of state of charge estimates. • State of charge estimates computed using particle filter algorithms. - Abstract: Battery Energy Storage Systems (BESS) are important for applications related to both microgrids and electric vehicles. If BESS are used as the main energy source, then it is required to include adequate procedures for the estimation of critical variables such as the State of Charge (SoC) and the State of Health (SoH) in the design of Battery Management Systems (BMS). Furthermore, in applications where batteries are exposed to high charge and discharge rates it is also desirable to estimate the State of Maximum Power Available (SoMPA). In this regard, this paper presents a novel approach to the estimation of SoMPA in Lithium-Ion batteries. This method formulates an optimisation problem for the battery power based on a non-linear dynamic model, where the resulting solutions are functions of the SoC. In the battery model, the polarisation resistance is modelled using fuzzy rules that are function of both SoC and the discharge (charge) current. Particle filtering algorithms are used as an online estimation technique, mainly because these algorithms allow approximating the probability density functions of the SoC and SoMPA even in the case of non-Gaussian sources of uncertainty. The proposed method for SoMPA estimation is validated using the experimental data obtained from an experimental setup designed for charging and discharging the Lithium-Ion batteries.
Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET
Energy Technology Data Exchange (ETDEWEB)
Gopich, Irina V. [Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892 (United States)
2015-01-21
Photon sequences from single-molecule Förster resonance energy transfer (FRET) experiments can be analyzed using a maximum likelihood method. Parameters of the underlying kinetic model (FRET efficiencies of the states and transition rates between conformational states) are obtained by maximizing the appropriate likelihood function. In addition, the errors (uncertainties) of the extracted parameters can be obtained from the curvature of the likelihood function at the maximum. We study the standard deviations of the parameters of a two-state model obtained from photon sequences with recorded colors and arrival times. The standard deviations can be obtained analytically in a special case when the FRET efficiencies of the states are 0 and 1 and in the limiting cases of fast and slow conformational dynamics. These results are compared with the results of numerical simulations. The accuracy and, therefore, the ability to predict model parameters depend on how fast the transition rates are compared to the photon count rate. In the limit of slow transitions, the key parameters that determine the accuracy are the number of transitions between the states and the number of independent photon sequences. In the fast transition limit, the accuracy is determined by the small fraction of photons that are correlated with their neighbors. The relative standard deviation of the relaxation rate has a “chevron” shape as a function of the transition rate in the log-log scale. The location of the minimum of this function dramatically depends on how well the FRET efficiencies of the states are separated.
Vacuum state of the Dirac field in de Sitter space and entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Kanno, Sugumi [Department of Theoretical Physics and History of Science,University of the Basque Country,48080 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science,Maria Diaz de Haro 3, 48013, Bilbao (Spain); Sasaki, Misao [Center for Gravitational Physics,Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); Tanaka, Takahiro [Department of Physics, Kyoto University,Kyoto 606-8502 (Japan); Center for Gravitational Physics,Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan)
2017-03-13
We compute the entanglement entropy of a free massive Dirac field between two causally disconnected open charts in de Sitter space. We first derive the Bunch-Davies vacuum mode functions of the Dirac field. We find there exists no supercurvature mode for the Dirac field. We then give the Bogoliubov transformation between the Bunch-Davies vacuum and the open chart vacua that makes the reduced density matrix diagonal. We find that the Dirac field becomes more entangled than a scalar field as m{sup 2}/H{sup 2} becomes small, and the difference is maximal in the massless limit.
Directory of Open Access Journals (Sweden)
Renata Gebara Sampaio Dória
2015-12-01
Full Text Available ABSTRACT. Dória R.G.S., Freitas S.H., Laskoski L.M., Carvalho M.B., Monteiro A.O.N., Camplesi A.C. & Valadão C.A.A. [Clinical evaluation and evolution of colic cases associated with Panicum maximum in Mato Grosso State, Brazil.] Avaliação clínica e da evolução dos casos de cólica associados a Panicum maximum no Estado de Mato Grosso, Brasil. Revista Brasileira de Medicina Veterinária, 37(4:303-308, 2015. Departamento de Medicina Veterinária, Curso de Medicina Veterinária, Faculdade de Zootecnia e Engenharia de Alimentos, Universidade de São Paulo, Av. Duque de Caxias Norte, 225, Centro, Pirassununga, SP 13635-900, Brasil. E-mail: redoria@usp.br An acute disease characterized by colic and timpanism was reported in Pará and Rondônia after horses fed with Panicum maximum cultivars Momba- ça, Tanzânia and Massai pasture grazing. In this study an acute abdomen case was experimentally reproduced after the ingestion of Panicum maximum var Massai pasture based on twenty two clinic and surgical cases of acute timpanic colic cases reported in a farm in the city of Cuiabá – MT, fed with Panicum maximum var Massai pasture, confirming the etiology and accompanying the clinical evolution of the disease. A horse kept in a stall fed only with Massai pasture was daily evaluated and it was verified that the animal presented as result a clinic perfil of pain, high cardiac frequency, respiratory difficulty, intestinal motility absence and exaggerated distention of the stomach and bowels by gas, seeing during the necropsy the stomach and bowels fully distended by gas with liquefied content except by small colon where the feces presented dry and with mucus characterizing the intestinal atony. The necessity of studies that search the identification of the agent responsible for the intestinal atony and gas accumulation in horses fed with Panicum maximum is exposed.
Goolsby, Eric W
2017-04-01
Ancestral state reconstruction is a method used to study the evolutionary trajectories of quantitative characters on phylogenies. Although efficient methods for univariate ancestral state reconstruction under a Brownian motion model have been described for at least 25 years, to date no generalization has been described to allow more complex evolutionary models, such as multivariate trait evolution, non-Brownian models, missing data, and within-species variation. Furthermore, even for simple univariate Brownian motion models, most phylogenetic comparative R packages compute ancestral states via inefficient tree rerooting and full tree traversals at each tree node, making ancestral state reconstruction extremely time-consuming for large phylogenies. Here, a computationally efficient method for fast maximum likelihood ancestral state reconstruction of continuous characters is described. The algorithm has linear complexity relative to the number of species and outperforms the fastest existing R implementations by several orders of magnitude. The described algorithm is capable of performing ancestral state reconstruction on a 1,000,000-species phylogeny in fewer than 2 s using a standard laptop, whereas the next fastest R implementation would take several days to complete. The method is generalizable to more complex evolutionary models, such as phylogenetic regression, within-species variation, non-Brownian evolutionary models, and multivariate trait evolution. Because this method enables fast repeated computations on phylogenies of virtually any size, implementation of the described algorithm can drastically alleviate the computational burden of many otherwise prohibitively time-consuming tasks requiring reconstruction of ancestral states, such as phylogenetic imputation of missing data, bootstrapping procedures, Expectation-Maximization algorithms, and Bayesian estimation. The described ancestral state reconstruction algorithm is implemented in the Rphylopars
'Legalized' forms of corruption in Serbia: Anomical state of social entropy
Directory of Open Access Journals (Sweden)
Zindović Ilija B.
2012-01-01
Full Text Available The subject of this research will be phenomena of 'legalized' form of corruption. The name we gave to all those forms of social behavior that anomical escape incrimination, are not defined precisely by laws, a cause of increasing social anomie, and ultimately lead to destruction, entropy and disintegration of society. The study will include a spatial framework of the Republic of Serbia, during the time interval since 2000. onwards, with a look in the 90's of the last century, and follows a period of transition from socialism, and post-socialism, to this wild and unrestrained form of capitalism. Methods that are used in the study were: a sociological method (observation, comparative method, Legal (dogmatic-normative, method of the target interpretation and the logical method of generalization and concretization. The study aims to highlight the manifestations of corruption that have for various reasons are not criminalized, and thus indicate the harmfulness social-anomical conditions that are directly related to the entropy of society in which we live. After that follows the proposal of measures to remove these harmful emergent phenomena in the border area of sociology and law.
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.
Quantum key distribution with finite resources: Smooth Min entropy vs. Smooth Renyi entropy
Energy Technology Data Exchange (ETDEWEB)
Mertz, Markus; Abruzzo, Silvestre; Bratzik, Sylvia; Kampermann, Hermann; Bruss, Dagmar [Institut fuer Theoretische Physik III, Duesseldorf (Germany)
2010-07-01
We consider different entropy measures that play an important role in the analysis of the security of QKD with finite resources. The smooth min entropy leads to an optimal bound for the length of a secure key. Another bound on the secure key length was derived by using Renyi entropies. Unfortunately, it is very hard or even impossible to calculate these entropies for realistic QKD scenarios. To estimate the security rate it becomes important to find computable bounds on these entropies. Here, we compare a lower bound for the smooth min entropy with a bound using Renyi entropies. We compare these entropies for the six-state protocol with symmetric attacks.
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.
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.
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
Dynamical reconstruction of the global ocean state during the Last Glacial Maximum
Kurahashi-Nakamura, Takasumi; Paul, André; Losch, Martin
2017-04-01
The global ocean state for the modern age and for the Last Glacial Maximum (LGM) was dynamically reconstructed with a sophisticated data assimilation technique. A substantial amount of data including global seawater temperature, salinity (only for the modern estimate), and the isotopic composition of oxygen and carbon (only in the Atlantic for the LGM) were integrated into an ocean general circulation model with the help of the adjoint method, thereby the model was optimized to reconstruct plausible continuous fields of tracers, overturning circulation and water mass distribution. The adjoint-based LGM state estimation of this study represents the state of the art in terms of the length of forward model runs, the number of observations assimilated, and the model domain. Compared to the modern state, the reconstructed continuous sea-surface temperature field for the LGM shows a global-mean cooling of 2.2 K, and the reconstructed LGM ocean has a more vigorous Atlantic meridional overturning circulation, shallower North Atlantic Deep Water (NADW) equivalent, stronger stratification, and more saline deep water.
Change-Point and Trend Analysis on Annual Maximum Discharge in Continental United States
Serinaldi, F.; Villarini, G.; Smith, J. A.; Krajewski, W. F.
2008-12-01
Annual maximum discharge records from 36 stations representing different hydro-climatic regimes in the continental United States with at least 100 years of records are used to investigate the presence of temporal trends and abrupt changes in mean and variance. Change point analysis is performed by means of two non- parametric (Pettitt and CUSUM), one semi-parametric (Guan), and two parametric (Rodionov and Bayesian Change Point) tests. Two non-parametric (Mann-Kendall and Spearman) and one parametric (Pearson) tests are applied to detect the presence of temporal trends. Generalized Additive Model for Location Scale and Shape (GAMLSS) models are also used to parametrically model the streamflow data exploiting their flexibility to account for changes and temporal trends in the parameters of distribution functions. Additionally, serial correlation is assessed in advance by computing the autocorrelation function (ACF), and the Hurst parameter is estimated using two estimators (aggregated variance and differenced variance methods) to investigate the presence of long range dependence. The results of this study indicate lack of long range dependence in the maximum streamflow series. At some stations the authors found a statistically significant change point in the mean and/or variance, while in general they detected no statistically significant temporal trends.
Quantum Rényi relative entropies affirm universality of thermodynamics.
Misra, Avijit; Singh, Uttam; Bera, Manabendra Nath; Rajagopal, A K
2015-10-01
We formulate a complete theory of quantum thermodynamics in the Rényi entropic formalism exploiting the Rényi relative entropies, starting from the maximum entropy principle. In establishing the first and second laws of quantum thermodynamics, we have correctly identified accessible work and heat exchange in both equilibrium and nonequilibrium cases. The free energy (internal energy minus temperature times entropy) remains unaltered, when all the entities entering this relation are suitably defined. Exploiting Rényi relative entropies we have shown that this "form invariance" holds even beyond equilibrium and has profound operational significance in isothermal process. These results reduce to the Gibbs-von Neumann results when the Rényi entropic parameter α approaches 1. Moreover, it is shown that the universality of the Carnot statement of the second law is the consequence of the form invariance of the free energy, which is in turn the consequence of maximum entropy principle. Further, the Clausius inequality, which is the precursor to the Carnot statement, is also shown to hold based on the data processing inequalities for the traditional and sandwiched Rényi relative entropies. Thus, we find that the thermodynamics of nonequilibrium state and its deviation from equilibrium together determine the thermodynamic laws. This is another important manifestation of the concepts of information theory in thermodynamics when they are extended to the quantum realm. Our work is a substantial step towards formulating a complete theory of quantum thermodynamics and corresponding resource theory.
Role of entropy and structural parameters in the spin-state transition of LaCoO3
Chakrabarti, Bismayan; Birol, Turan; Haule, Kristjan
2017-11-01
The spin-state transition in LaCoO3 has eluded description for decades despite concerted theoretical and experimental effort. In this study, we approach this problem using fully charge self-consistent density functional theory + embedded dynamical mean field theory (DFT+DMFT). We show from first principles that LaCoO3 cannot be described by a single, pure spin state at any temperature. Instead, we observe a gradual change in the population of higher-spin multiplets with increasing temperature, with the high-spin multiplets being excited at the onset of the spin-state transition followed by the intermediate-spin multiplets being excited at the metal-insulator-transition temperature. We explicitly elucidate the critical role of lattice expansion and oxygen octahedral rotations in the spin-state transition. We also reproduce, from first principles, that the spin-state transition and the metal-insulator transition in LaCoO3 occur at different temperature scales. In addition, our results shed light on the importance of electronic entropy in driving the spin-state transition, which has so far been ignored in all first-principles studies of this material.
A comparison of maximum entropy and maximum likelihood estimation
Oude Lansink, A.G.J.M.
1999-01-01
Gegevens betreffende het ondernemerschap op Nederlandse akkerbouwbedrijven zijn in 2 benaderingsmethodes verwerkt, welke onderling op voorspellende nauwkeurigheid en op prijs-elasticiteit zijn vergeleken
The Wehrl entropy has Gaussian optimizers
DEFF Research Database (Denmark)
De Palma, Giacomo
2018-01-01
We determine the minimum Wehrl entropy among the quantum states with a given von Neumann entropy and prove that it is achieved by thermal Gaussian states. This result determines the relation between the von Neumann and the Wehrl entropies. The key idea is proving that the quantum-classical channel...
On thermodynamic limits of entropy densities
Moriya, H; Van Enter, A
We give some sufficient conditions which guarantee that the entropy density in the thermodynamic limit is equal to the thermodynamic limit of the entropy densities of finite-volume (local) Gibbs states.
Multicollinearity and maximum entropy leuven estimator
Sudhanshu Mishra
2004-01-01
Multicollinearity is a serious problem in applied regression analysis. Q. Paris (2001) introduced the MEL estimator to resolve the multicollinearity problem. This paper improves the MEL estimator to the Modular MEL (MMEL) estimator and shows by Monte Carlo experiments that MMEL estimator performs significantly better than OLS as well as MEL estimators.
Maximum entropy analysis of cosmic ray composition
Czech Academy of Sciences Publication Activity Database
Nosek, D.; Ebr, Jan; Vícha, Jakub; Trávníček, Petr; Nosková, J.
2016-01-01
Roč. 76, Mar (2016), s. 9-18 ISSN 0927-6505 R&D Projects: GA ČR(CZ) GA14-17501S Institutional support: RVO:68378271 Keywords : ultra-high energy cosmic rays * extensive air showers * cosmic ray composition Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 3.257, year: 2016
Spatial data modelling and maximum entropy theory
Czech Academy of Sciences Publication Activity Database
Klimešová, Dana; Ocelíková, E.
2005-01-01
Roč. 51, č. 2 (2005), s. 80-83 ISSN 0139-570X Institutional research plan: CEZ:AV0Z10750506 Keywords : spatial data classification * distribution function * error distribution Subject RIV: BD - Theory of Information
Indian Academy of Sciences (India)
Abstract. It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf f that satisfy. ∫ fhi dμ = λi for i = 1, 2,...,...k the maximizer of entropy is an f0 that is pro- portional to exp(. ∑ ci hi ) for some choice of ci . An extension of this to a continuum of.
Indian Academy of Sciences (India)
It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf that satisfy ∫ f h i d = i for i = 1 , 2 , … , … k the maximizer of entropy is an f 0 that is proportional to exp ( ∑ c i h i ) for some choice of c i . An extension of this to a continuum of ...
International Nuclear Information System (INIS)
Wang, Tianyi; Yu, Song; Zhang, Yi-Chen; Gu, Wanyi; Guo, Hong
2014-01-01
By employing a nondeterministic noiseless linear amplifier, we propose to increase the maximum transmission distance of continuous-variable quantum key distribution with noisy coherent states. With the covariance matrix transformation, the expression of secret key rate under reverse reconciliation is derived against collective entangling cloner attacks. We show that the noiseless linear amplifier can compensate the detrimental effect of the preparation noise with an enhancement of the maximum transmission distance and the noise resistance. - Highlights: • Noiseless amplifier is applied in noisy coherent state quantum key distribution. • Negative effect of preparation noise is compensated by noiseless amplification. • Maximum transmission distance and noise resistance are both enhanced
Indian Academy of Sciences (India)
Consider the integral. taken over a reversible transformation. We shall call this function the entropy of state A.” 'Thermodynamics' by Enrico Fermi. “Let Γ be the volume of the region of motion of the states, and. This is the basic assumption of ...
Use of mutual information to decrease entropy: Implications for the second law of thermodynamics
International Nuclear Information System (INIS)
Lloyd, S.
1989-01-01
Several theorems on the mechanics of gathering information are proved, and the possibility of violating the second law of thermodynamics by obtaining information is discussed in light of these theorems. Maxwell's demon can lower the entropy of his surroundings by an amount equal to the difference between the maximum entropy of his recording device and its initial entropy, without generating a compensating entropy increase. A demon with human-scale recording devices can reduce the entropy of a gas by a negligible amount only, but the proof of the demon's impracticability leaves open the possibility that systems highly correlated with their environment can reduce the environment's entropy by a substantial amount without increasing entropy elsewhere. In the event that a boundary condition for the universe requires it to be in a state of low entropy when small, the correlations induced between different particle modes during the expansion phase allow the modes to behave like Maxwell's demons during the contracting phase, reducing the entropy of the universe to a low value
Optimized Kernel Entropy Components.
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.
Phase transitions and quantum entropy
International Nuclear Information System (INIS)
Arrachea, L.; Canosa, N.; Plastino, A.; Portesi, M.; Rossignoli, R.
1990-01-01
An examination is made of the possibility to predict phase transitions of the fundamental state of finite quantum system, knowing the quantum entropy of these states, defined on the basis of the information theory. (Author). 7 refs., 3 figs
Definition and measurement of entropy in high energy heavy ion collisions
International Nuclear Information System (INIS)
Remler, E.A.
1986-01-01
This talk has two parts: the first on the definition and the second on the measurement of entropy. The connection to nuclear thermodynamics can be retained without the local equilibrium assumption via two steps. The first is relatively simple and goes as follows. The authors make the certainly reasonable assumption that in central collisions, at the moment of maximum compression, the state is similar to one or more fireballs and that the total entropy of each fireball approximates that of an equilibrated system at the same total energy and average density. This entropy, if measurable, would determine much of the thermodynamic properties of nuclear matter. The second step therefore concerns measurement of this entropy. This paper develops a method by which entropy may be measured using a minimum amount of theory. In particular, it is not based on any assumption local equilibrium
Wavelet entropy characterization of elevated intracranial pressure.
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.
On S-mixing entropy of quantum channels
Mukhamedov, Farrukh; Watanabe, Noboru
2018-06-01
In this paper, an S-mixing entropy of quantum channels is introduced as a generalization of Ohya's S-mixing entropy. We investigate several properties of the introduced entropy. Moreover, certain relations between the S-mixing entropy and the existing map and output entropies of quantum channels are investigated as well. These relations allowed us to find certain connections between separable states and the introduced entropy. Hence, there is a sufficient condition to detect entangled states. Moreover, several properties of the introduced entropy are investigated. Besides, entropies of qubit and phase-damping channels are calculated.
38 CFR 59.40 - Maximum number of nursing home care and domiciliary care beds for veterans by State.
2010-07-01
... home care and domiciliary care beds for veterans by State. 59.40 Section 59.40 Pensions, Bonuses, and... ACQUISITION OF STATE HOMES § 59.40 Maximum number of nursing home care and domiciliary care beds for veterans... projection of demand for nursing home and domiciliary care by veterans who at such time are 65 years of age...
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.
Entropy-based implied volatility and its information content
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
Entropy dynamics in cone production of longleaf pine forests in the southeastern United States
Xiongwen Chen; Dale G. Brockway; Qinfeng Guo
2016-01-01
Sporadic temporal patterns of seed production are a challenge for the regeneration and restoration of longleaf pine, which is a keystone component of an endangered ecosystem in the southeastern United States. In this study, long-term data for longleaf pine cone production, collected at six sites across the southeastern region, was examined from the perspective of...
Directory of Open Access Journals (Sweden)
Luca Faes
2017-01-01
Full Text Available The most common approach to assess the dynamical complexity of a time series across multiple temporal scales makes use of the multiscale entropy (MSE and refined MSE (RMSE measures. In spite of their popularity, MSE and RMSE lack an analytical framework allowing their calculation for known dynamic processes and cannot be reliably computed over short time series. To overcome these limitations, we propose a method to assess RMSE for autoregressive (AR stochastic processes. The method makes use of linear state-space (SS models to provide the multiscale parametric representation of an AR process observed at different time scales and exploits the SS parameters to quantify analytically the complexity of the process. The resulting linear MSE (LMSE measure is first tested in simulations, both theoretically to relate the multiscale complexity of AR processes to their dynamical properties and over short process realizations to assess its computational reliability in comparison with RMSE. Then, it is applied to the time series of heart period, arterial pressure, and respiration measured for healthy subjects monitored in resting conditions and during physiological stress. This application to short-term cardiovascular variability documents that LMSE can describe better than RMSE the activity of physiological mechanisms producing biological oscillations at different temporal scales.
Nonadditive entropy maximization is inconsistent with Bayesian updating
Pressé, Steve
2014-11-01
The maximum entropy method—used to infer probabilistic models from data—is a special case of Bayes's model inference prescription which, in turn, is grounded in basic propositional logic. By contrast to the maximum entropy method, the compatibility of nonadditive entropy maximization with Bayes's model inference prescription has never been established. Here we demonstrate that nonadditive entropy maximization is incompatible with Bayesian updating and discuss the immediate implications of this finding. We focus our attention on special cases as illustrations.
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
Controlling the Shannon Entropy of Quantum Systems
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.
Energy conservation and maximal entropy production in enzyme reactions.
Dobovišek, Andrej; Vitas, Marko; Brumen, Milan; Fajmut, Aleš
2017-08-01
A procedure for maximization of the density of entropy production in a single stationary two-step enzyme reaction is developed. Under the constraints of mass conservation, fixed equilibrium constant of a reaction and fixed products of forward and backward enzyme rate constants the existence of maximum in the density of entropy production is demonstrated. In the state with maximal density of entropy production the optimal enzyme rate constants, the stationary concentrations of the substrate and the product, the stationary product yield as well as the stationary reaction flux are calculated. The test, whether these calculated values of the reaction parameters are consistent with their corresponding measured values, is performed for the enzyme Glucose Isomerase. It is found that calculated and measured rate constants agree within an order of magnitude, whereas the calculated reaction flux and the product yield differ from their corresponding measured values for less than 20 % and 5 %, respectively. This indicates that the enzyme Glucose Isomerase, considered in a non-equilibrium stationary state, as found in experiments using the continuous stirred tank reactors, possibly operates close to the state with the maximum in the density of entropy production. Copyright © 2017 Elsevier B.V. All rights reserved.
Entropy jump across an inviscid shock wave
Salas, Manuel D.; Iollo, Angelo
1995-01-01
The shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure are shown to be the same, however density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy, propagation equation cannot be used as a conservation law.
Caticha, Ariel
2007-11-01
What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds. This problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), which is designed for updating from arbitrary priors given information in the form of arbitrary constraints, includes as special cases both MaxEnt (which allows arbitrary constraints) and Bayes' rule (which allows arbitrary priors). Thus, ME unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme that allows us to handle problems that lie beyond the reach of either of the two methods separately. I conclude with a couple of simple illustrative examples.
Bergboer, N.H.; Verdult, V.; Verhaegen, M.H.G.
2002-01-01
We present a numerically efficient implementation of the nonlinear least squares and maximum likelihood identification of multivariable linear time-invariant (LTI) state-space models. This implementation is based on a local parameterization of the system and a gradient search in the resulting
Entropy inequalities from reflection positivity
International Nuclear Information System (INIS)
Casini, H
2010-01-01
We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for the correlators are mapped into inequalities for the entropies. We write them using a real-time version of reflection positivity, which can be generalized to general quantum systems. Using this generalization we can prove an infinite sequence of inequalities which are obeyed by the Renyi entropies of integer index. There is one independent inequality involving any number of different subsystems. In quantum field theory the inequalities acquire a simple geometrical form and are consistent with the integer index Renyi entropies being given by vacuum expectation values of twisting operators in the Euclidean formulation. Several possible generalizations and specific examples are analyzed
Fuzzy tracking algorithm with feedback based on maximum entropy principle%带反馈多传感器模糊最大熵单目标跟踪算法
Institute of Scientific and Technical Information of China (English)
刘智; 陈丰; 黄继平
2012-01-01
针对矩阵加权融合算法计算量大、传感器数量不易扩充的特点,提出了一种带反馈的模糊最大熵融合算法.该算法采用模糊C-均值算法和最大熵原理计算状态向量中每一分量的权值,不但从整体考虑各分量对融合估计的影响,而且减少了复杂的矩阵运算过程,实时性较好.与矩阵加权算法相比,该融合算法还具有容易扩充的特点,能够直接应用于传感器数量大于2时的融合计算.实验仿真结果表明,融合估计的准确性与矩阵加权融合算法基本一致,算法的有效性得到了验证.%Aiming at the disadvantages of high computation overhead and bad extensibility in matrix weighted fusion methods, this paper proposed a multisensor fusion algorithm with feedback based on fuzzy C-means( FCM) clustering and tnaximun en-tropy principle( MEP). This algorithm combined FCM and MEP to calculate fusion matrix weight of state vector considering ev-ery components integratedly. What' s more, this algoritm had a good real-time performance due to less matrix computation and good extensibility which showed it could directly be applied into tracking system comprising more than two sensors. Experi-ments and results reveal that the tracking accuracy of fusion estimate is consistent with that of matrix weighted fusion methods.
Minimal length, Friedmann equations and maximum density
Energy Technology Data Exchange (ETDEWEB)
Awad, Adel [Center for Theoretical Physics, British University of Egypt,Sherouk City 11837, P.O. Box 43 (Egypt); Department of Physics, Faculty of Science, Ain Shams University,Cairo, 11566 (Egypt); Ali, Ahmed Farag [Centre for Fundamental Physics, Zewail City of Science and Technology,Sheikh Zayed, 12588, Giza (Egypt); Department of Physics, Faculty of Science, Benha University,Benha, 13518 (Egypt)
2014-06-16
Inspired by Jacobson’s thermodynamic approach, Cai et al. have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation http://dx.doi.org/10.1103/PhysRevD.75.084003 of Friedmann equations to accommodate a general entropy-area law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ,a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p=ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.
Quantum Entropy of Black Hole with Internal Global Monopole
Institute of Scientific and Technical Information of China (English)
HAN Yi-Wen; YANG Shu-Zheng; LIU Wen-Biao
2005-01-01
Using the generalized uncertainty relation, the new equation of state density is obtained, and then the entropy of black hole with an internal global monopole is discussed. The divergence that appears in black hole entropy calculation through original brick-wall model is overcome. The result of the direct proportion between black hole entropy and its event horizon area is drawn and given. The result shows that the black hole entropy must be the entropy of quantum state near the event horizon.
On unified-entropy characterization of quantum channels
International Nuclear Information System (INIS)
Rastegin, A E
2012-01-01
We consider properties of quantum channels with the use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map (q, s)-entropy is naturally defined as the unified (q, s)-entropy of a rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. The known inequality of Lindblad with the entropy exchange is generalized to many of the unified entropies. For the tensor product of a pair of quantum channels, we derive a two-sided estimate on the output entropy of a maximally entangled input state. (paper)
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 Â© 2016 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Chen, Yong; Ge, Hao; Xiong, Jie; Xu, Lihu
2016-01-01
Fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades. There exist very few results for steady-state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes due to the technical difficulties. Here we give a proof for the steady-state fluctuation theorem of a diffusion process in magnetic fields, with explicit expressions of the free energy function and rate function. The proof is based on the Karhunen-Loève expansion of complex-valued Ornstein-Uhlenbeck process.
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)
Campbell, D A; Chkrebtii, O
2013-12-01
Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories. Crown Copyright © 2013. Published by Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Bernard S. Kay
2015-12-01
Full Text Available We give a review, in the style of an essay, of the author’s 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state—entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author’s recent arguments based on this alternative description which suggest that the Anti de Sitter space (AdS/conformal field theory (CFT correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory.
Tsallis Entropy and the Transition to Scaling in Fragmentation
Sotolongo-Costa, Oscar; Rodriguez, Arezky H.; Rodgers, G. J.
2000-12-01
By using the maximum entropy principle with Tsallis entropy we obtain a fragment size distribution function which undergoes a transition to scaling. This distribution function reduces to those obtained by other authors using Shannon entropy. The treatment is easily generalisable to any process of fractioning with suitable constraints.
Kou, Jisheng; Sun, Shuyu
2018-01-01
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager's reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.
Kou, Jisheng
2018-02-25
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager\\'s reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.
All Inequalities for the Relative Entropy
Ibinson, Ben; Linden, Noah; Winter, Andreas
2007-01-01
The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party states to a smaller number m of parties is always less than or equal to the relative entropy of the two original n-party states. This is the monotonicity of relative entropy. Using techniques from convex geometry, we prove that monotonicity under restrictions is the only general inequality satisfied by quantum relative entropies. In doing so we make a connection to secret sharing schemes with general access structures: indeed, it turns out that the extremal rays of the cone defined by monotonicity are populated by classical secret sharing schemes. A surprising outcome is that the structure of allowed relative entropy values of subsets of multiparty states is much simpler than the structure of allowed entropy values. And the structure of allowed relative entropy values (unlike that of entropies) is the same for classical probability distributions and quantum states.
Energy Technology Data Exchange (ETDEWEB)
Alvarez R, J.T
1998-10-01
This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ({sup 4} He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator {rho}hut{sub FP} that is evaluated as Wigneris function through {rho}{sub CG} obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D{sub mn} defined with a nonequilibrium coarse grained statistical operator {rho}hut{sub CG}, matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine {rho}hut{sub CG} by means of the local equilibrium statistical operator {rho}hut{sub l}-tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D{sub mn} but with aid of a quasi equilibrium statistical operator {rho}hut{sub qe} instead
Study on spectral entropy of two-phase flow density wave instability
International Nuclear Information System (INIS)
Zhang Zuoyi
1992-05-01
By using mathematic proof, spectral entropy calculations for simple examples and a practical two-phase flow system, it has been proved that under the same stochastic input, the output spectral entropy of a stable linear system is in maximum, while for an unstable linear system, its entropy is in relative lower level. Because the spectral entropy describes the output uncertainty of a system and the second law of thermodynamics rules the direction of natural tendency, the spontaneous process can develop only toward the direction of uncertainty increasing, and the opposite is impossible. It seems that the physical mechanism of the stability of a system can be explained as following: Any deviation from its original state of a stable system will reduce the spectral entropy and violate the natural tendency so that the system will return to original state. On the contrary, the deviation from its original state of an unstable system will increase the spectral entropy that will enhance the deviation and the system will be further away from its original state
Reliability of buildings in service limit state for maximum horizontal displacements
Directory of Open Access Journals (Sweden)
A. G. B. Corelhano
Full Text Available Brazilian design code ABNT NBR6118:2003 - Design of Concrete Structures - Procedures - [1] proposes the use of simplified models for the consideration of non-linear material behavior in the evaluation of horizontal displacements in buildings. These models penalize stiffness of columns and beams, representing the effects of concrete cracking and avoiding costly physical non-linear analyses. The objectives of the present paper are to investigate the accuracy and uncertainty of these simplified models, as well as to evaluate the reliabilities of structures designed following ABNT NBR6118:2003[1&] in the service limit state for horizontal displacements. Model error statistics are obtained from 42 representative plane frames. The reliabilities of three typical (4, 8 and 12 floor buildings are evaluated, using the simplified models and a rigorous, physical and geometrical non-linear analysis. Results show that the 70/70 (column/beam stiffness reduction model is more accurate and less conservative than the 80/40 model. Results also show that ABNT NBR6118:2003 [1] design criteria for horizontal displacement limit states (masonry damage according to ACI 435.3R-68(1984 [10] are conservative, and result in reliability indexes which are larger than those recommended in EUROCODE [2] for irreversible service limit states.
Entropy Generation Across Earth's Bow Shock
Parks, George K.; McCarthy, Michael; Fu, Suiyan; Lee E. s; Cao, Jinbin; Goldstein, Melvyn L.; Canu, Patrick; Dandouras, Iannis S.; Reme, Henri; Fazakerley, Andrew;
2011-01-01
Earth's bow shock is a transition layer that causes an irreversible change in the state of plasma that is stationary in time. Theories predict entropy increases across the bow shock but entropy has never been directly measured. Cluster and Double Star plasma experiments measure 3D plasma distributions upstream and downstream of the bow shock that allow calculation of Boltzmann's entropy function H and his famous H-theorem, dH/dt O. We present the first direct measurements of entropy density changes across Earth's bow shock. We will show that this entropy generation may be part of the processes that produce the non-thermal plasma distributions is consistent with a kinetic entropy flux model derived from the collisionless Boltzmann equation, giving strong support that solar wind's total entropy across the bow shock remains unchanged. As far as we know, our results are not explained by any existing shock models and should be of interests to theorists.
An Adaptively Accelerated Bayesian Deblurring Method with Entropy Prior
Directory of Open Access Journals (Sweden)
Yong-Hoon Kim
2008-05-01
Full Text Available The development of an efficient adaptively accelerated iterative deblurring algorithm based on Bayesian statistical concept has been reported. Entropy of an image has been used as a Ã¢Â€ÂœpriorÃ¢Â€Â distribution and instead of additive form, used in conventional acceleration methods an exponent form of relaxation constant has been used for acceleration. Thus the proposed method is called hereafter as adaptively accelerated maximum a posteriori with entropy prior (AAMAPE. Based on empirical observations in different experiments, the exponent is computed adaptively using first-order derivatives of the deblurred image from previous two iterations. This exponent improves speed of the AAMAPE method in early stages and ensures stability at later stages of iteration. In AAMAPE method, we also consider the constraint of the nonnegativity and flux conservation. The paper discusses the fundamental idea of the Bayesian image deblurring with the use of entropy as prior, and the analytical analysis of superresolution and the noise amplification characteristics of the proposed method. The experimental results show that the proposed AAMAPE method gives lower RMSE and higher SNR in 44% lesser iterations as compared to nonaccelerated maximum a posteriori with entropy prior (MAPE method. Moreover, AAMAPE followed by wavelet wiener filtering gives better result than the state-of-the-art methods.
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
Excess Entropy and Diffusivity
Indian Academy of Sciences (India)
First page Back Continue Last page Graphics. Excess Entropy and Diffusivity. Excess entropy scaling of diffusivity (Rosenfeld,1977). Analogous relationships also exist for viscosity and thermal conductivity.
Quantum statistical entropy for Kerr-de Sitter black hole
Institute of Scientific and Technical Information of China (English)
Zhang Li-Chun; Wu Yue-Qin; Zhao Ren
2004-01-01
Improving the membrane model by which the entropy of the black hole is studied, we study the entropy of the black hole in the non-thermal equilibrium state. To give the problem stated here widespread meaning, we discuss the (n+2)-dimensional de Sitter spacetime. Through discussion, we obtain that the black hole's entropy which contains two horizons (a black hole's horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black hole's horizon and the entropy corresponding to the cosmological horizon. Furthermore, the entropy of the black hole is a natural property of the black hole. The entropy is irrelevant to the radiation field out of the horizon. This deepens the understanding of the relationship between black hole's entropy and horizon's area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.
International Nuclear Information System (INIS)
Monthus, Cécile
2011-01-01
Filyokov and Karpov (1967 Inzh.-Fiz. Zh. 13 624) have proposed a theory of non-equilibrium steady states in direct analogy with the theory of equilibrium states: the principle is to maximize the Shannon entropy associated with the probability distribution of dynamical trajectories in the presence of constraints, including the macroscopic current of interest, via the method of Lagrange multipliers. This maximization leads directly to the generalized Gibbs distribution for the probability distribution of dynamical trajectories, and to some fluctuation relation of the integrated current. The simplest stochastic dynamics where these ideas can be applied are discrete-time Markov chains, defined by transition probabilities W i→j between configurations i and j: instead of choosing the dynamical rules W i→j a priori, one determines the transition probabilities and the associate stationary state that maximize the entropy of dynamical trajectories with the other physical constraints that one wishes to impose. We give a self-contained and unified presentation of this type of approach, both for discrete-time Markov chains and for continuous-time master equations. The obtained results are in full agreement with the Bayesian approach introduced by Evans (2004 Phys. Rev. Lett. 92 150601) under the name 'Non-equilibrium Counterpart to detailed balance', and with the 'invariant quantities' derived by Baule and Evans (2008 Phys. Rev. Lett. 101 240601), but provide a slightly different perspective via the formulation in terms of an eigenvalue problem
Algorithmic randomness and physical entropy
International Nuclear Information System (INIS)
Zurek, W.H.
1989-01-01
Algorithmic randomness provides a rigorous, entropylike measure of disorder of an individual, microscopic, definite state of a physical system. It is defined by the size (in binary digits) of the shortest message specifying the microstate uniquely up to the assumed resolution. Equivalently, algorithmic randomness can be expressed as the number of bits in the smallest program for a universal computer that can reproduce the state in question (for instance, by plotting it with the assumed accuracy). In contrast to the traditional definitions of entropy, algorithmic randomness can be used to measure disorder without any recourse to probabilities. Algorithmic randomness is typically very difficult to calculate exactly but relatively easy to estimate. In large systems, probabilistic ensemble definitions of entropy (e.g., coarse-grained entropy of Gibbs and Boltzmann's entropy H=lnW, as well as Shannon's information-theoretic entropy) provide accurate estimates of the algorithmic entropy of an individual system or its average value for an ensemble. One is thus able to rederive much of thermodynamics and statistical mechanics in a setting very different from the usual. Physical entropy, I suggest, is a sum of (i) the missing information measured by Shannon's formula and (ii) of the algorithmic information content---algorithmic randomness---present in the available data about the system. This definition of entropy is essential in describing the operation of thermodynamic engines from the viewpoint of information gathering and using systems. These Maxwell demon-type entities are capable of acquiring and processing information and therefore can ''decide'' on the basis of the results of their measurements and computations the best strategy for extracting energy from their surroundings. From their internal point of view the outcome of each measurement is definite
Equipartition of entropy production
International Nuclear Information System (INIS)
Tondeur, D.
1990-01-01
This paper deals with the optimal design or operation of heat and mass transfer processes and develops the following conjecture: for a given duty, the best configuration of the process is that in which the entropy production rate is most uniformly distributed. This principle is first analyzed in detail on the simple example of tubular heat exchangers, and within the framework of linear irreversible thermodynamics. A main result is established, which states that the total entropy production is minimal when the local production is uniformly distributed (equipartition). Corollaries then result, which relate the entropy production and the variance of its distribution to economic factors such as the duty, the exchange area, the fluid flow-rates, and the temperature changes. The equipartition principle is then extended to multiple independent variables (time and space), multicomponent transfer, and non-linear but concave flux vs force relationship. Chemical Engineering examples are discussed, where the equipartition property has been applied implicitly or explicitly: design of distillation plates, cyclic distillation, optimal state of feed, and flow-sheets in chromatographic separations. Finally, a generalization of the equipartition principle is proposed, for systems with a distributed design variable (such as the size of the various elements of a system). The optimal distribution of investment is such that the investment in each element (properly amortized) is equal to the cost of irreversible energy degradation in this element. This is equivalent to saying that the ratio of these two quantities is uniformly distributed over the system, and reduces to equipartition of entropy production when the cost factors are constant over the whole system
Energy Technology Data Exchange (ETDEWEB)
Berrocal T, Mariella J. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]|[Universidad Nacional de Ingenieria, Lima (Peru); Roberty, Nilson C. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear; Silva Neto, Antonio J. [Universidade do Estado, Nova Friburgo, RJ (Brazil). Instituto Politecnico. Dept. de Engenharia Mecanica e Energia]|[Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear
2002-07-01
The solution of inverse problems in participating media where there is emission, absorption and dispersion of the radiation possesses several applications in engineering and medicine. The objective of this work is to estimative the coefficients of absorption and dispersion in two-dimensional heterogeneous participating media, using in independent form the Generalized Maximum Entropy and Levenberg Marquardt methods. Both methods are based on the solution of the direct problem that is modeled by the Boltzmann equation in cartesian geometry. Some cases testes are presented. (author)
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)
Relative entropy and the RG flow
Energy Technology Data Exchange (ETDEWEB)
Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Río Negro, R8402AGP (Argentina)
2017-03-16
We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d=2 space-time dimensions and, for d>2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.
What is the entropy of the universe?
International Nuclear Information System (INIS)
Frampton, Paul H; Hsu, Stephen D H; Reeb, David; Kephart, Thomas W
2009-01-01
Standard calculations suggest that the entropy of our universe is dominated by black holes, whose entropy is of order their area in Planck units, although they comprise only a tiny fraction of its total energy. Statistical entropy is the logarithm of the number of microstates consistent with the observed macroscopic properties of a system, hence a measure of uncertainty about its precise state. Therefore, assuming unitarity in black hole evaporation, the standard results suggest that the largest uncertainty in the future quantum state of the universe is due to the Hawking radiation from evaporating black holes. However, the entropy of the matter precursors to astrophysical black holes is enormously less than that given by area entropy. If unitarity relates the future radiation states to the black hole precursor states, then the standard results are highly misleading, at least for an observer that can differentiate the individual states of the Hawking radiation.
What is the entropy of the universe?
Energy Technology Data Exchange (ETDEWEB)
Frampton, Paul H [Department of Physics and Astronomy, UNC-Chapel Hill, NC 27599 (United States); Hsu, Stephen D H; Reeb, David [Institute of Theoretical Science, University of Oregon, Eugene, OR 97403 (United States); Kephart, Thomas W, E-mail: frampton@physics.unc.ed, E-mail: hsu@uoregon.ed, E-mail: tom.kephart@gmail.co, E-mail: dreeb@uoregon.ed [Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 (United States)
2009-07-21
Standard calculations suggest that the entropy of our universe is dominated by black holes, whose entropy is of order their area in Planck units, although they comprise only a tiny fraction of its total energy. Statistical entropy is the logarithm of the number of microstates consistent with the observed macroscopic properties of a system, hence a measure of uncertainty about its precise state. Therefore, assuming unitarity in black hole evaporation, the standard results suggest that the largest uncertainty in the future quantum state of the universe is due to the Hawking radiation from evaporating black holes. However, the entropy of the matter precursors to astrophysical black holes is enormously less than that given by area entropy. If unitarity relates the future radiation states to the black hole precursor states, then the standard results are highly misleading, at least for an observer that can differentiate the individual states of the Hawking radiation.
Directory of Open Access Journals (Sweden)
Roriz Luciano Machado
2010-01-01
Full Text Available Knowledge of maximum daily rain and its return period in a region is an important tool to soil conservation, hydraulic engineering and preservation of road projects. The objective of this work was to evaluate the spatial variability of maximum annual daily rain considering different return periods, at the Rio de Janeiro State. The data set was composed by historical series of 119 rain gauges, for 36 years of observation. The return periods, estimated by Gumbel distribution, were 2, 5, 10, 25, 50 and 100 years. The spatial variability of the return periods was evaluated by semivariograms. All the return periods presented spatial dependence, with exponential and spherical model fitted to the experimental semivariograms. The parameters of the fitted semivariogram model were very similar; however, it was observed the presence of higher nugget effects for semivariograms of longer return periods. The values of maximum annual daily average rain in all the return periods increased from north to south and from countryside to the coast. In the region between the Serra do Mar range and the coast, besides increasing in magnitude, an increase in the spatial variability of the studied values with increasing return periods was also noticed. This behavior is probably caused by the orographic effect. The interpolated maps were more erratic for higher return periods and at the North, Northeast and Coastal Plain regions, in which the installation of new pluviometric stations are recommended.
Gálisová, Lucia
2018-05-01
Ground-state properties of a hybrid double-tetrahedral chain, in which the localized Ising spins regularly alternate with triangular plaquettes occupied by a variable number of mobile electrons, are exactly investigated. We demonstrate that the zero-temperature phase diagram of the model involves several non-degenerate, two-fold degenerate and macroscopically degenerate chiral phases. Low-temperature dependencies of the entropy and specific heat are also examined in order to gain a deeper insight into the degeneracy of individual ground-state phases and phase transitions. It is shown that a diversity of the ground-state degeneracy manifests itself in multiple-peak structures of both thermodynamic quantities. A remarkable temperature dependencies of the specific heat with two and three Schottky-type maxima are discussed in detail.
Frusawa, Hiroshi
2014-05-01
A coarse-grained system of one-dimensional (1D) hard spheres (HSs) is created using the Delaunay tessellation, which enables one to define the quasi-0D state. It is found from comparing the quasi-0D and 1D free energy densities that a frozen state due to the emergence of quasi-0D HSs is thermodynamically more favorable than fluidity with a large-scale heterogeneity above crossover volume fraction of ϕc=e/(1+e)=0.731⋯ , at which the total entropy of the 1D state vanishes. The Delaunay-based lattice mapping further provides a similarity between the dense HS system above ϕc and the jamming limit in the car parking problem.
International Nuclear Information System (INIS)
Frusawa, Hiroshi
2014-01-01
A coarse-grained system of one-dimensional (1D) hard spheres (HSs) is created using the Delaunay tessellation, which enables one to define the quasi-0D state. It is found from comparing the quasi-0D and 1D free energy densities that a frozen state due to the emergence of quasi-0D HSs is thermodynamically more favorable than fluidity with a large-scale heterogeneity above crossover volume fraction of ϕ c =e/(1+e)=0.731⋯ , at which the total entropy of the 1D state vanishes. The Delaunay-based lattice mapping further provides a similarity between the dense HS system above ϕ c and the jamming limit in the car parking problem.
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.