Stochastic modeling and control system designs of the NASA/MSFC Ground Facility for large space structures: The maximum entropy/optimal projection approach

NASA Technical Reports Server (NTRS)

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.

Exploration of the Maximum Entropy/Optimal Projection Approach to Control Design Synthesis for Large Space Structures.

DTIC Science & Technology

1985-02-01

Energy Analysis , a branch of dynamic modal analysis developed for analyzing acoustic vibration problems, its present stage of development embodies a...Maximum Entropy Stochastic Modelling and Reduced-Order Design Synthesis is a rigorous new approach to this class of problems. Inspired by Statistical

Maximum Relative Entropy of Coherence: An Operational Coherence Measure.

PubMed

Bu, Kaifeng; Singh, Uttam; Fei, Shao-Ming; Pati, Arun Kumar; Wu, Junde

2017-10-13

The operational characterization of quantum coherence is the cornerstone in the development of the resource theory of coherence. We introduce a new coherence quantifier based on maximum relative entropy. We prove that the maximum relative entropy of coherence is directly related to the maximum overlap with maximally coherent states under a particular class of operations, which provides an operational interpretation of the maximum relative entropy of coherence. Moreover, we show that, for any coherent state, there are examples of subchannel discrimination problems such that this coherent state allows for a higher probability of successfully discriminating subchannels than that of all incoherent states. This advantage of coherent states in subchannel discrimination can be exactly characterized by the maximum relative entropy of coherence. By introducing a suitable smooth maximum relative entropy of coherence, we prove that the smooth maximum relative entropy of coherence provides a lower bound of one-shot coherence cost, and the maximum relative entropy of coherence is equivalent to the relative entropy of coherence in the asymptotic limit. Similar to the maximum relative entropy of coherence, the minimum relative entropy of coherence has also been investigated. We show that the minimum relative entropy of coherence provides an upper bound of one-shot coherence distillation, and in the asymptotic limit the minimum relative entropy of coherence is equivalent to the relative entropy of coherence.

[Maximum entropy model versus remote sensing-based methods for extracting Oncomelania hupensis snail habitats].

PubMed

Cong-Cong, Xia; Cheng-Fang, Lu; Si, Li; Tie-Jun, Zhang; Sui-Heng, Lin; Yi, Hu; Ying, Liu; Zhi-Jie, Zhang

2016-12-02

To explore the technique of maximum entropy model for extracting Oncomelania hupensis snail habitats in Poyang Lake zone. The information of snail habitats and related environment factors collected in Poyang Lake zone were integrated to set up the maximum entropy based species model and generate snail habitats distribution map. Two Landsat 7 ETM+ remote sensing images of both wet and drought seasons in Poyang Lake zone were obtained, where the two indices of modified normalized difference water index (MNDWI) and normalized difference vegetation index (NDVI) were applied to extract snail habitats. The ROC curve, sensitivities and specificities were applied to assess their results. Furthermore, the importance of the variables for snail habitats was analyzed by using Jackknife approach. The evaluation results showed that the area under receiver operating characteristic curve (AUC) of testing data by the remote sensing-based method was only 0.56, and the sensitivity and specificity were 0.23 and 0.89 respectively. Nevertheless, those indices above-mentioned of maximum entropy model were 0.876, 0.89 and 0.74 respectively. The main concentration of snail habitats in Poyang Lake zone covered the northeast part of Yongxiu County, northwest of Yugan County, southwest of Poyang County and middle of Xinjian County, and the elevation was the most important environment variable affecting the distribution of snails, and the next was land surface temperature (LST). The maximum entropy model is more reliable and accurate than the remote sensing-based method for the sake of extracting snail habitats, which has certain guiding significance for the relevant departments to carry out measures to prevent and control high-risk snail habitats.

Using the Maximum Entropy Principle as a Unifying Theory Characterization and Sampling of Multi-Scaling Processes in Hydrometeorology

DTIC Science & Technology

2015-08-20

evapotranspiration (ET) over oceans may be significantly lower than previously thought. The MEP model parameterized turbulent transfer coefficients...fluxes, ocean freshwater fluxes, regional crop yield among others. An on-going study suggests that the global annual evapotranspiration (ET) over...Bras, Jingfeng Wang. A model of evapotranspiration based on the theory of maximum entropy production, Water Resources Research, (03 2011): 0. doi

Combining Experiments and Simulations Using the Maximum Entropy Principle

PubMed Central

Boomsma, Wouter; Ferkinghoff-Borg, Jesper; Lindorff-Larsen, Kresten

2014-01-01

A key component of computational biology is to compare the results of computer modelling with experimental measurements. Despite substantial progress in the models and algorithms used in many areas of computational biology, such comparisons sometimes reveal that the computations 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 applications in our field has grown steadily in recent years, in areas as diverse as sequence analysis, structural modelling, and neurobiology. In this Perspectives article, we give a broad introduction to the method, in an attempt to encourage its further adoption. The general procedure is explained 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 that are at not in complete and quantitative accordance with experiments. A common solution to this problem is to explicitly ensure agreement between the two by perturbing the potential energy function towards the experimental data. So far, a general consensus for how such perturbations should be implemented has been lacking. 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. PMID:24586124

Entropy maximization under the constraints on the generalized Gini index and its application in modeling income distributions

NASA Astrophysics Data System (ADS)

Khosravi Tanak, A.; Mohtashami Borzadaran, G. R.; Ahmadi, J.

2015-11-01

In economics and social sciences, the inequality measures such as Gini index, Pietra index etc., are commonly used to measure the statistical dispersion. There is a generalization of Gini index which includes it as special case. In this paper, we use principle of maximum entropy to approximate the model of income distribution with a given mean and generalized Gini index. Many distributions have been used as descriptive models for the distribution of income. The most widely known of these models are the generalized beta of second kind and its subclass distributions. The obtained maximum entropy distributions are fitted to the US family total money income in 2009, 2011 and 2013 and their relative performances with respect to generalized beta of second kind family are compared.

Maximum-Entropy Inference with a Programmable Annealer

PubMed Central

Chancellor, Nicholas; Szoke, Szilard; Vinci, Walter; Aeppli, Gabriel; Warburton, Paul A.

2016-01-01

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. PMID:26936311

The two-box model of climate: limitations and applications to planetary habitability and maximum entropy production studies.

PubMed

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.

From Maximum Entropy Models to Non-Stationarity and Irreversibility

NASA Astrophysics Data System (ADS)

Cofre, Rodrigo; Cessac, Bruno; Maldonado, Cesar

The maximum entropy distribution can be obtained from a variational principle. This is important as a matter of principle and for the purpose of finding approximate solutions. One can exploit this fact to obtain relevant information about the underlying stochastic process. We report here in recent progress in three aspects to this approach.1- Biological systems are expected to show some degree of irreversibility in time. Based on the transfer matrix technique to find the spatio-temporal maximum entropy distribution, we build a framework to quantify the degree of irreversibility of any maximum entropy distribution.2- The maximum entropy solution is characterized by a functional called Gibbs free energy (solution of the variational principle). The Legendre transformation of this functional is the rate function, which controls the speed of convergence of empirical averages to their ergodic mean. We show how the correct description of this functional is determinant for a more rigorous characterization of first and higher order phase transitions.3- We assess the impact of a weak time-dependent external stimulus on the collective statistics of spiking neuronal networks. We show how to evaluate this impact on any higher order spatio-temporal correlation. RC supported by ERC advanced Grant ``Bridges'', BC: KEOPS ANR-CONICYT, Renvision and CM: CONICYT-FONDECYT No. 3140572.

Fast and Efficient Stochastic Optimization for Analytic Continuation

DOE PAGES

Bao, Feng; Zhang, Guannan; Webster, Clayton G; ...

2016-09-28

In this analytic continuation of imaginary-time quantum Monte Carlo data to extract real-frequency spectra remains a key problem in connecting theory with experiment. Here we present a fast and efficient stochastic optimization method (FESOM) as a more accessible variant of the stochastic optimization method introduced by Mishchenko et al. [Phys. Rev. B 62, 6317 (2000)], and we benchmark the resulting spectra with those obtained by the standard maximum entropy method for three representative test cases, including data taken from studies of the two-dimensional Hubbard model. Genearally, we find that our FESOM approach yields spectra similar to the maximum entropy results.more » In particular, while the maximum entropy method yields superior results when the quality of the data is strong, we find that FESOM is able to resolve fine structure with more detail when the quality of the data is poor. In addition, because of its stochastic nature, the method provides detailed information on the frequency-dependent uncertainty of the resulting spectra, while the maximum entropy method does so only for the spectral weight integrated over a finite frequency region. Therefore, we believe that this variant of the stochastic optimization approach provides a viable alternative to the routinely used maximum entropy method, especially for data of poor quality.« less

A Maximum Entropy Method for Particle Filtering

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.; Kim, Sangil

2006-06-01

Standard ensemble or particle filtering schemes do not properly represent states of low priori probability when the number of available samples is too small, as is often the case in practical applications. We introduce here a set of parametric resampling methods to solve this problem. Motivated by a general H-theorem for relative entropy, we construct parametric models for the filter distributions as maximum-entropy/minimum-information models consistent with moments of the particle ensemble. When the prior distributions are modeled as mixtures of Gaussians, our method naturally generalizes the ensemble Kalman filter to systems with highly non-Gaussian statistics. We apply the new particle filters presented here to two simple test cases: a one-dimensional diffusion process in a double-well potential and the three-dimensional chaotic dynamical system of Lorenz.

Interatomic potentials in condensed matter via the maximum-entropy principle

NASA Astrophysics Data System (ADS)

Carlsson, A. E.

1987-09-01

A general method is described for the calculation of interatomic potentials in condensed-matter systems by use of a maximum-entropy Ansatz for the interatomic correlation functions. The interatomic potentials are given explicitly in terms of statistical correlation functions involving the potential energy and the structure factor of a ``reference medium.'' Illustrations are given for Al-Cu alloys and a model transition metal.

Maximum Entropy for the International Division of Labor.

PubMed

Lei, Hongmei; Chen, Ying; Li, Ruiqi; He, Deli; Zhang, Jiang

2015-01-01

As a result of the international division of labor, the trade value distribution on different products substantiated by international trade flows can be regarded as one country's strategy for competition. According to the empirical data of trade flows, countries may spend a large fraction of export values on ubiquitous and competitive products. Meanwhile, countries may also diversify their exports share on different types of products to reduce the risk. In this paper, we report that the export share distribution curves can be derived by maximizing the entropy of shares on different products under the product's complexity constraint once the international market structure (the country-product bipartite network) is given. Therefore, a maximum entropy model provides a good fit to empirical data. The empirical data is consistent with maximum entropy subject to a constraint on the expected value of the product complexity for each country. One country's strategy is mainly determined by the types of products this country can export. In addition, our model is able to fit the empirical export share distribution curves of nearly every country very well by tuning only one parameter.

Maximum Entropy for the International Division of Labor

PubMed Central

Lei, Hongmei; Chen, Ying; Li, Ruiqi; He, Deli; Zhang, Jiang

2015-01-01

As a result of the international division of labor, the trade value distribution on different products substantiated by international trade flows can be regarded as one country’s strategy for competition. According to the empirical data of trade flows, countries may spend a large fraction of export values on ubiquitous and competitive products. Meanwhile, countries may also diversify their exports share on different types of products to reduce the risk. In this paper, we report that the export share distribution curves can be derived by maximizing the entropy of shares on different products under the product’s complexity constraint once the international market structure (the country-product bipartite network) is given. Therefore, a maximum entropy model provides a good fit to empirical data. The empirical data is consistent with maximum entropy subject to a constraint on the expected value of the product complexity for each country. One country’s strategy is mainly determined by the types of products this country can export. In addition, our model is able to fit the empirical export share distribution curves of nearly every country very well by tuning only one parameter. PMID:26172052

Holographic equipartition and the maximization of entropy

NASA Astrophysics Data System (ADS)

Krishna, P. B.; Mathew, Titus K.

2017-09-01

The accelerated expansion of the Universe can be interpreted as a tendency to satisfy holographic equipartition. It can be expressed by a simple law, Δ V =Δ t (Nsurf-ɛ Nbulk) , where V is the Hubble volume in Planck units, t is the cosmic time in Planck units, and Nsurf /bulk is the number of degrees of freedom on the horizon/bulk of the Universe. We show that this holographic equipartition law effectively implies the maximization of entropy. In the cosmological context, a system that obeys the holographic equipartition law behaves as an ordinary macroscopic system that proceeds to an equilibrium state of maximum entropy. We consider the standard Λ CDM model of the Universe and show that it is consistent with the holographic equipartition law. Analyzing the entropy evolution, we find that it also proceeds to an equilibrium state of maximum entropy.

Maximum entropy PDF projection: A review

NASA Astrophysics Data System (ADS)

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.

Derivation of Hunt equation for suspension distribution using Shannon entropy theory

NASA Astrophysics Data System (ADS)

Kundu, Snehasis

2017-12-01

In this study, the Hunt equation for computing suspension concentration in sediment-laden flows is derived using Shannon entropy theory. Considering the inverse of the void ratio as a random variable and using principle of maximum entropy, probability density function and cumulative distribution function of suspension concentration is derived. A new and more general cumulative distribution function for the flow domain is proposed which includes several specific other models of CDF reported in literature. This general form of cumulative distribution function also helps to derive the Rouse equation. The entropy based approach helps to estimate model parameters using suspension data of sediment concentration which shows the advantage of using entropy theory. Finally model parameters in the entropy based model are also expressed as functions of the Rouse number to establish a link between the parameters of the deterministic and probabilistic approaches.

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

NASA Astrophysics Data System (ADS)

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.

Stimulus-dependent Maximum Entropy Models of Neural Population Codes

PubMed Central

Segev, Ronen; Schneidman, Elad

2013-01-01

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. PMID:23516339

Maximum Entropy/Optimal Projection (MEOP) control design synthesis: Optimal quantification of the major design tradeoffs

NASA Technical Reports Server (NTRS)

Hyland, D. C.; Bernstein, D. S.

1987-01-01

The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated.

The two-box model of climate: limitations and applications to planetary habitability and maximum entropy production studies

PubMed Central

Lorenz, Ralph D.

2010-01-01

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. PMID:20368253

Twenty-five years of maximum-entropy principle

NASA Astrophysics Data System (ADS)

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.

Competition between Homophily and Information Entropy Maximization in Social Networks

PubMed Central

Zhao, Jichang; Liang, Xiao; Xu, Ke

2015-01-01

In social networks, it is conventionally thought that two individuals with more overlapped friends tend to establish a new friendship, which could be stated as homophily breeding new connections. While the recent hypothesis of maximum information entropy is presented as the possible origin of effective navigation in small-world networks. We find there exists a competition between information entropy maximization and homophily in local structure through both theoretical and experimental analysis. This competition suggests that a newly built relationship between two individuals with more common friends would lead to less information entropy gain for them. We demonstrate that in the evolution of the social network, both of the two assumptions coexist. The rule of maximum information entropy produces weak ties in the network, while the law of homophily makes the network highly clustered locally and the individuals would obtain strong and trust ties. A toy model is also presented to demonstrate the competition and evaluate the roles of different rules in the evolution of real networks. Our findings could shed light on the social network modeling from a new perspective. PMID:26334994

Formulating the shear stress distribution in circular open channels based on the Renyi entropy

NASA Astrophysics Data System (ADS)

Khozani, Zohreh Sheikh; Bonakdari, Hossein

2018-01-01

The principle of maximum entropy is employed to derive the shear stress distribution by maximizing the Renyi entropy subject to some constraints and by assuming that dimensionless shear stress is a random variable. A Renyi entropy-based equation can be used to model the shear stress distribution along the entire wetted perimeter of circular channels and circular channels with flat beds and deposited sediments. A wide range of experimental results for 12 hydraulic conditions with different Froude numbers (0.375 to 1.71) and flow depths (20.3 to 201.5 mm) were used to validate the derived shear stress distribution. For circular channels, model performance enhanced with increasing flow depth (mean relative error (RE) of 0.0414) and only deteriorated slightly at the greatest flow depth (RE of 0.0573). For circular channels with flat beds, the Renyi entropy model predicted the shear stress distribution well at lower sediment depth. The Renyi entropy model results were also compared with Shannon entropy model results. Both models performed well for circular channels, but for circular channels with flat beds the Renyi entropy model displayed superior performance in estimating the shear stress distribution. The Renyi entropy model was highly precise and predicted the shear stress distribution in a circular channel with RE of 0.0480 and in a circular channel with a flat bed with RE of 0.0488.

In Vivo potassium-39 NMR spectra by the burg maximum-entropy method

NASA Astrophysics Data System (ADS)

Uchiyama, Takanori; Minamitani, Haruyuki

The Burg maximum-entropy method was applied to estimate 39K NMR spectra of mung bean root tips. The maximum-entropy spectra have as good a linearity between peak areas and potassium concentrations as those obtained by fast Fourier transform and give a better estimation of intracellular potassium concentrations. Therefore potassium uptake and loss processes of mung bean root tips are shown to be more clearly traced by the maximum-entropy method.

Beyond maximum entropy: Fractal pixon-based image reconstruction

NASA Technical Reports Server (NTRS)

Puetter, R. C.; Pina, R. K.

1994-01-01

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other methods, including Goodness-of-Fit (e.g. Least-Squares and Lucy-Richardson) and Maximum Entropy (ME). Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME.

Unification of field theory and maximum entropy methods for learning probability densities

NASA Astrophysics Data System (ADS)

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.

PubMed

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.

Modelling the spreading rate of controlled communicable epidemics through an entropy-based thermodynamic model

NASA Astrophysics Data System (ADS)

Wang, WenBin; Wu, ZiNiu; Wang, ChunFeng; Hu, RuiFeng

2013-11-01

A model based on a thermodynamic approach is proposed for predicting the dynamics of communicable epidemics assumed to be governed by controlling efforts of multiple scales so that an entropy is associated with the system. All the epidemic details are factored into a single and time-dependent coefficient, the functional form of this coefficient is found through four constraints, including notably the existence of an inflexion point and a maximum. The model is solved to give a log-normal distribution for the spread rate, for which a Shannon entropy can be defined. The only parameter, that characterizes the width of the distribution function, is uniquely determined through maximizing the rate of entropy production. This entropy-based thermodynamic (EBT) model predicts the number of hospitalized cases with a reasonable accuracy for SARS in the year 2003. This EBT model can be of use for potential epidemics such as avian influenza and H7N9 in China.

Steepest entropy ascent quantum thermodynamic model of electron and phonon transport

NASA Astrophysics Data System (ADS)

Li, Guanchen; von Spakovsky, Michael R.; Hin, Celine

2018-01-01

An advanced nonequilibrium thermodynamic model for electron and phonon transport is formulated based on the steepest-entropy-ascent quantum thermodynamics framework. This framework, based on the principle of steepest entropy ascent (or the equivalent maximum entropy production principle), inherently satisfies the laws of thermodynamics and mechanics and is applicable at all temporal and spatial scales even in the far-from-equilibrium realm. Specifically, the model is proven to recover the Boltzmann transport equations in the near-equilibrium limit and the two-temperature model of electron-phonon coupling when no dispersion is assumed. The heat and mass transport at a temperature discontinuity across a homogeneous interface where the dispersion and coupling of electron and phonon transport are both considered are then modeled. Local nonequilibrium system evolution and nonquasiequilibrium interactions are predicted and the results discussed.

Cosmic equilibration: A holographic no-hair theorem from the generalized second law

NASA Astrophysics Data System (ADS)

Carroll, Sean M.; Chatwin-Davies, Aidan

2018-02-01

In a wide class of cosmological models, a positive cosmological constant drives cosmological evolution toward an asymptotically de Sitter phase. Here we connect this behavior to the increase of entropy over time, based on the idea that de Sitter spacetime is a maximum-entropy state. We prove a cosmic no-hair theorem for Robertson-Walker and Bianchi I spacetimes that admit a Q-screen ("quantum" holographic screen) with certain entropic properties: If generalized entropy, in the sense of the cosmological version of the generalized second law conjectured by Bousso and Engelhardt, increases up to a finite maximum value along the screen, then the spacetime is asymptotically de Sitter in the future. Moreover, the limiting value of generalized entropy coincides with the de Sitter horizon entropy. We do not use the Einstein field equations in our proof, nor do we assume the existence of a positive cosmological constant. As such, asymptotic relaxation to a de Sitter phase can, in a precise sense, be thought of as cosmological equilibration.

Entropy and equilibrium via games of complexity

NASA Astrophysics Data System (ADS)

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.

Maximum entropy production in environmental and ecological systems.

PubMed

Kleidon, Axel; Malhi, Yadvinder; Cox, Peter M

2010-05-12

The coupled biosphere-atmosphere system entails a vast range of processes at different scales, from ecosystem exchange fluxes of energy, water and carbon to the processes that drive global biogeochemical cycles, atmospheric composition and, ultimately, the planetary energy balance. These processes are generally complex with numerous interactions and feedbacks, and they are irreversible in their nature, thereby producing entropy. The proposed principle of maximum entropy production (MEP), based on statistical mechanics and information theory, states that thermodynamic processes far from thermodynamic equilibrium will adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate. This issue focuses on the latest development of applications of MEP to the biosphere-atmosphere system including aspects of the atmospheric circulation, the role of clouds, hydrology, vegetation effects, ecosystem exchange of energy and mass, biogeochemical interactions and the Gaia hypothesis. The examples shown in this special issue demonstrate the potential of MEP to contribute to improved understanding and modelling of the biosphere and the wider Earth system, and also explore limitations and constraints to the application of the MEP principle.

Bayesian Image Segmentations by Potts Prior and Loopy Belief Propagation

NASA Astrophysics Data System (ADS)

Tanaka, Kazuyuki; Kataoka, Shun; Yasuda, Muneki; Waizumi, Yuji; Hsu, Chiou-Ting

2014-12-01

This paper presents a Bayesian image segmentation model based on Potts prior and loopy belief propagation. The proposed Bayesian model involves several terms, including the pairwise interactions of Potts models, and the average vectors and covariant matrices of Gauss distributions in color image modeling. These terms are often referred to as hyperparameters in statistical machine learning theory. In order to determine these hyperparameters, we propose a new scheme for hyperparameter estimation based on conditional maximization of entropy in the Potts prior. The algorithm is given based on loopy belief propagation. In addition, we compare our conditional maximum entropy framework with the conventional maximum likelihood framework, and also clarify how the first order phase transitions in loopy belief propagations for Potts models influence our hyperparameter estimation procedures.

Maximum Entropy Production As a Framework for Understanding How Living Systems Evolve, Organize and Function

NASA Astrophysics Data System (ADS)

Vallino, J. J.; Algar, C. K.; Huber, J. A.; Fernandez-Gonzalez, N.

2014-12-01

The maximum entropy production (MEP) principle holds that non equilibrium systems with sufficient degrees of freedom will likely be found in a state that maximizes entropy production or, analogously, maximizes potential energy destruction rate. The theory does not distinguish between abiotic or biotic systems; however, we will show that systems that can coordinate function over time and/or space can potentially dissipate more free energy than purely Markovian processes (such as fire or a rock rolling down a hill) that only maximize instantaneous entropy production. Biological systems have the ability to store useful information acquired via evolution and curated by natural selection in genomic sequences that allow them to execute temporal strategies and coordinate function over space. For example, circadian rhythms allow phototrophs to "predict" that sun light will return and can orchestrate metabolic machinery appropriately before sunrise, which not only gives them a competitive advantage, but also increases the total entropy production rate compared to systems that lack such anticipatory control. Similarly, coordination over space, such a quorum sensing in microbial biofilms, can increase acquisition of spatially distributed resources and free energy and thereby enhance entropy production. In this talk we will develop a modeling framework to describe microbial biogeochemistry based on the MEP conjecture constrained by information and resource availability. Results from model simulations will be compared to laboratory experiments to demonstrate the usefulness of the MEP approach.

Prediction of pKa Values for Neutral and Basic Drugs based on Hybrid Artificial Intelligence Methods.

PubMed

Li, Mengshan; Zhang, Huaijing; Chen, Bingsheng; Wu, Yan; Guan, Lixin

2018-03-05

The pKa value of drugs is an important parameter in drug design and pharmacology. In this paper, an improved particle swarm optimization (PSO) algorithm was proposed based on the population entropy diversity. In the improved algorithm, when the population entropy was higher than the set maximum threshold, the convergence strategy was adopted; when the population entropy was lower than the set minimum threshold the divergence strategy was adopted; when the population entropy was between the maximum and minimum threshold, the self-adaptive adjustment strategy was maintained. The improved PSO algorithm was applied in the training of radial basis function artificial neural network (RBF ANN) model and the selection of molecular descriptors. A quantitative structure-activity relationship model based on RBF ANN trained by the improved PSO algorithm was proposed to predict the pKa values of 74 kinds of neutral and basic drugs and then validated by another database containing 20 molecules. The validation results showed that the model had a good prediction performance. The absolute average relative error, root mean square error, and squared correlation coefficient were 0.3105, 0.0411, and 0.9685, respectively. The model can be used as a reference for exploring other quantitative structure-activity relationships.

Multi-Group Maximum Entropy Model for Translational Non-Equilibrium

NASA Technical Reports Server (NTRS)

Jayaraman, Vegnesh; Liu, Yen; Panesi, Marco

2017-01-01

The aim of the current work is to describe a new model for flows in translational non- equilibrium. Starting from the statistical description of a gas proposed by Boltzmann, the model relies on a domain decomposition technique in velocity space. Using the maximum entropy principle, the logarithm of the distribution function in each velocity sub-domain (group) is expressed with a power series in molecular velocity. New governing equations are obtained using the method of weighted residuals by taking the velocity moments of the Boltzmann equation. The model is applied to a spatially homogeneous Boltzmann equation with a Bhatnagar-Gross-Krook1(BGK) model collision operator and the relaxation of an initial non-equilibrium distribution to a Maxwellian is studied using the model. In addition, numerical results obtained using the model for a 1D shock tube problem are also reported.

Moisture sorption isotherms and thermodynamic properties of bovine leather

NASA Astrophysics Data System (ADS)

Fakhfakh, Rihab; Mihoubi, Daoued; Kechaou, Nabil

2018-04-01

This study was aimed at the determination of bovine leather moisture sorption characteristics using a static gravimetric method at 30, 40, 50, 60 and 70 °C. The curves exhibit type II behaviour according to the BET classification. The sorption isotherms fitting by seven equations shows that GAB model is able to reproduce the equilibrium moisture content evolution with water activity for moisture range varying from 0.02 to 0.83 kg/kg d.b (0.9898 < R2 < 0.999). The sorption isotherms exhibit hysteresis effect. Additionally, sorption isotherms data were used to determine the thermodynamic properties such as isosteric heat of sorption, sorption entropy, spreading pressure, net integral enthalpy and entropy. Net isosteric heat of sorption and differential entropy were evaluated through direct use of moisture isotherms by applying the Clausius-Clapeyron equation and used to investigate the enthalpy-entropy compensation theory. Both sorption enthalpy and entropy for desorption increase to a maximum with increasing moisture content, and then decrease sharply with rising moisture content. Adsorption enthalpy decreases with increasing moisture content. Whereas, adsorption entropy increases smoothly with increasing moisture content to a maximum of 6.29 J/K.mol. Spreading pressure increases with rising water activity. The net integral enthalpy seemed to decrease and then increase to become asymptotic. The net integral entropy decreased with moisture content increase.

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

NASA Astrophysics Data System (ADS)

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.

Entropic criterion for model selection

NASA Astrophysics Data System (ADS)

Tseng, Chih-Yuan

2006-10-01

Model or variable selection is usually achieved through ranking models according to the increasing order of preference. One of methods is applying Kullback-Leibler distance or relative entropy as a selection criterion. Yet that will raise two questions, why use this criterion and are there any other criteria. Besides, conventional approaches require a reference prior, which is usually difficult to get. Following the logic of inductive inference proposed by Caticha [Relative entropy and inductive inference, in: G. Erickson, Y. Zhai (Eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings, vol. 707, 2004 (available from arXiv.org/abs/physics/0311093)], we show relative entropy to be a unique criterion, which requires no prior information and can be applied to different fields. We examine this criterion by considering a physical problem, simple fluids, and results are promising.

A probability space for quantum models

NASA Astrophysics Data System (ADS)

Lemmens, L. F.

2017-06-01

A probability space contains a set of outcomes, a collection of events formed by subsets of the set of outcomes and probabilities defined for all events. A reformulation in terms of propositions allows to use the maximum entropy method to assign the probabilities taking some constraints into account. The construction of a probability space for quantum models is determined by the choice of propositions, choosing the constraints and making the probability assignment by the maximum entropy method. This approach shows, how typical quantum distributions such as Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein are partly related with well-known classical distributions. The relation between the conditional probability density, given some averages as constraints and the appropriate ensemble is elucidated.

Maximum entropy perception-action space: a Bayesian model of eye movement selection

NASA Astrophysics Data System (ADS)

Colas, Francis; Bessière, Pierre; Girard, Benoît

2011-03-01

In this article, we investigate the issue of the selection of eye movements in a free-eye Multiple Object Tracking task. We propose a Bayesian model of retinotopic maps with a complex logarithmic mapping. This model is structured in two parts: a representation of the visual scene, and a decision model based on the representation. We compare different decision models based on different features of the representation and we show that taking into account uncertainty helps predict the eye movements of subjects recorded in a psychophysics experiment. Finally, based on experimental data, we postulate that the complex logarithmic mapping has a functional relevance, as the density of objects in this space in more uniform than expected. This may indicate that the representation space and control strategies are such that the object density is of maximum entropy.

Predicting protein β-sheet contacts using a maximum entropy-based correlated mutation measure.

PubMed

Burkoff, Nikolas S; Várnai, Csilla; Wild, David L

2013-03-01

The problem of ab initio protein folding is one of the most difficult in modern computational biology. The prediction of residue contacts within a protein provides a more tractable immediate step. Recently introduced maximum entropy-based correlated mutation measures (CMMs), such as direct information, have been successful in predicting residue contacts. However, most correlated mutation studies focus on proteins that have large good-quality multiple sequence alignments (MSA) because the power of correlated mutation analysis falls as the size of the MSA decreases. However, even with small autogenerated MSAs, maximum entropy-based CMMs contain information. To make use of this information, in this article, we focus not on general residue contacts but contacts between residues in β-sheets. The strong constraints and prior knowledge associated with β-contacts are ideally suited for prediction using a method that incorporates an often noisy CMM. Using contrastive divergence, a statistical machine learning technique, we have calculated a maximum entropy-based CMM. We have integrated this measure with a new probabilistic model for β-contact prediction, which is used to predict both residue- and strand-level contacts. Using our model on a standard non-redundant dataset, we significantly outperform a 2D recurrent neural network architecture, achieving a 5% improvement in true positives at the 5% false-positive rate at the residue level. At the strand level, our approach is competitive with the state-of-the-art single methods achieving precision of 61.0% and recall of 55.4%, while not requiring residue solvent accessibility as an input. http://www2.warwick.ac.uk/fac/sci/systemsbiology/research/software/

Shock heating of the solar wind plasma

NASA Technical Reports Server (NTRS)

Whang, Y. C.; Liu, Shaoliang; Burlaga, L. F.

1990-01-01

The role played by shocks in heating solar-wind plasma is investigated using data on 413 shocks which were identified from the plasma and magnetic-field data collected between 1973 and 1982 by Pioneer and Voyager spacecraft. It is found that the average shock strength increased with the heliocentric distance outside 1 AU, reaching a maximum near 5 AU, after which the shock strength decreased with the distance; the entropy of the solar wind protons also reached a maximum at 5 AU. An MHD simulation model in which shock heating is the only heating mechanism available was used to calculate the entropy changes for the November 1977 event. The calculated entropy agreed well with the value calculated from observational data, suggesting that shocks are chiefly responsible for heating solar wind plasma between 1 and 15 AU.

An implementation of the maximum-caliber principle by replica-averaged time-resolved restrained simulations

NASA Astrophysics Data System (ADS)

Capelli, Riccardo; Tiana, Guido; Camilloni, Carlo

2018-05-01

Inferential methods can be used to integrate experimental informations and molecular simulations. The maximum entropy principle provides a framework for using equilibrium experimental data, and it has been shown that replica-averaged simulations, restrained using a static potential, are a practical and powerful implementation of such a principle. Here we show that replica-averaged simulations restrained using a time-dependent potential are equivalent to the principle of maximum caliber, the dynamic version of the principle of maximum entropy, and thus may allow us to integrate time-resolved data in molecular dynamics simulations. We provide an analytical proof of the equivalence as well as a computational validation making use of simple models and synthetic data. Some limitations and possible solutions are also discussed.

An implementation of the maximum-caliber principle by replica-averaged time-resolved restrained simulations.

PubMed

Capelli, Riccardo; Tiana, Guido; Camilloni, Carlo

2018-05-14

Inferential methods can be used to integrate experimental informations and molecular simulations. The maximum entropy principle provides a framework for using equilibrium experimental data, and it has been shown that replica-averaged simulations, restrained using a static potential, are a practical and powerful implementation of such a principle. Here we show that replica-averaged simulations restrained using a time-dependent potential are equivalent to the principle of maximum caliber, the dynamic version of the principle of maximum entropy, and thus may allow us to integrate time-resolved data in molecular dynamics simulations. We provide an analytical proof of the equivalence as well as a computational validation making use of simple models and synthetic data. Some limitations and possible solutions are also discussed.

Maximum-entropy probability distributions under Lp-norm constraints

NASA Technical Reports Server (NTRS)

Dolinar, S.

1991-01-01

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

The maximum entropy production principle: two basic questions.

PubMed

Martyushev, Leonid M

2010-05-12

The overwhelming majority of maximum entropy production applications to ecological and environmental systems are based on thermodynamics and statistical physics. Here, we discuss briefly maximum entropy production principle and raises two questions: (i) can this principle be used as the basis for non-equilibrium thermodynamics and statistical mechanics and (ii) is it possible to 'prove' the principle? We adduce one more proof which is most concise today.

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

NASA Astrophysics Data System (ADS)

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.

Perspective: Maximum caliber is a general variational principle for dynamical systems

NASA Astrophysics Data System (ADS)

Dixit, Purushottam D.; Wagoner, Jason; Weistuch, Corey; Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A.

2018-01-01

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics—such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production—are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Estimation of Lithological Classification in Taipei Basin: A Bayesian Maximum Entropy Method

NASA Astrophysics Data System (ADS)

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

Perspective: Maximum caliber is a general variational principle for dynamical systems.

PubMed

Dixit, Purushottam D; Wagoner, Jason; Weistuch, Corey; Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A

2018-01-07

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics-such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production-are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Monitoring of Time-Dependent System Profiles by Multiplex Gas Chromatography with Maximum Entropy Demodulation

NASA Technical Reports Server (NTRS)

Becker, Joseph F.; Valentin, Jose

1996-01-01

The maximum entropy technique was successfully applied to the deconvolution of overlapped chromatographic peaks. An algorithm was written in which the chromatogram was represented as a vector of sample concentrations multiplied by a peak shape matrix. Simulation results demonstrated that there is a trade off between the detector noise and peak resolution in the sense that an increase of the noise level reduced the peak separation that could be recovered by the maximum entropy method. Real data originated from a sample storage column was also deconvoluted using maximum entropy. Deconvolution is useful in this type of system because the conservation of time dependent profiles depends on the band spreading processes in the chromatographic column, which might smooth out the finer details in the concentration profile. The method was also applied to the deconvolution of previously interpretted Pioneer Venus chromatograms. It was found in this case that the correct choice of peak shape function was critical to the sensitivity of maximum entropy in the reconstruction of these chromatograms.

Statistical mechanics of letters in words

PubMed Central

Stephens, Greg J.; Bialek, William

2013-01-01

We consider words as a network of interacting letters, and approximate the probability distribution of states taken on by this network. Despite the intuition that the rules of English spelling are highly combinatorial and arbitrary, we find that maximum entropy models consistent with pairwise correlations among letters provide a surprisingly good approximation to the full statistics of words, capturing ~92% of the multi-information in four-letter words and even “discovering” words that were not represented in the data. These maximum entropy models incorporate letter interactions through a set of pairwise potentials and thus define an energy landscape on the space of possible words. Guided by the large letter redundancy we seek a lower-dimensional encoding of the letter distribution and show that distinctions between local minima in the landscape account for ~68% of the four-letter entropy. We suggest that these states provide an effective vocabulary which is matched to the frequency of word use and much smaller than the full lexicon. PMID:20866490

Convex Accelerated Maximum Entropy Reconstruction

PubMed Central

Worley, Bradley

2016-01-01

Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm – called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm – is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra. PMID:26894476

The existence of negative absolute temperatures in Axelrod’s social influence model

NASA Astrophysics Data System (ADS)

Villegas-Febres, J. C.; Olivares-Rivas, W.

2008-06-01

We introduce the concept of temperature as an order parameter in the standard Axelrod’s social influence model. It is defined as the relation between suitably defined entropy and energy functions, T=(. We show that at the critical point, where the order/disorder transition occurs, this absolute temperature changes in sign. At this point, which corresponds to the transition homogeneous/heterogeneous culture, the entropy of the system shows a maximum. We discuss the relationship between the temperature and other properties of the model in terms of cultural traits.

Entropy-based goodness-of-fit test: Application to the Pareto distribution

NASA Astrophysics Data System (ADS)

Lequesne, Justine

2013-08-01

Goodness-of-fit tests based on entropy have been introduced in [13] for testing normality. The maximum entropy distribution in a class of probability distributions defined by linear constraints induces a Pythagorean equality between the Kullback-Leibler information and an entropy difference. This allows one to propose a goodness-of-fit test for maximum entropy parametric distributions which is based on the Kullback-Leibler information. We will focus on the application of the method to the Pareto distribution. The power of the proposed test is computed through Monte Carlo simulation.

How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems.

PubMed

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.

Maximum entropy method applied to deblurring images on a MasPar MP-1 computer

NASA Technical Reports Server (NTRS)

Bonavito, N. L.; Dorband, John; Busse, Tim

1991-01-01

A statistical inference method based on the principle of maximum entropy is developed for the purpose of enhancing and restoring satellite images. The proposed maximum entropy image restoration method is shown to overcome the difficulties associated with image restoration and provide the smoothest and most appropriate solution consistent with the measured data. An implementation of the method on the MP-1 computer is described, and results of tests on simulated data are presented.

A measure of uncertainty regarding the interval constraint of normal mean elicited by two stages of a prior hierarchy.

PubMed

Kim, Hea-Jung

2014-01-01

This paper considers a hierarchical screened Gaussian model (HSGM) for Bayesian inference of normal models when an interval constraint in the mean parameter space needs to be incorporated in the modeling but when such a restriction is uncertain. An objective measure of the uncertainty, regarding the interval constraint, accounted for by using the HSGM is proposed for the Bayesian inference. For this purpose, we drive a maximum entropy prior of the normal mean, eliciting the uncertainty regarding the interval constraint, and then obtain the uncertainty measure by considering the relationship between the maximum entropy prior and the marginal prior of the normal mean in HSGM. Bayesian estimation procedure of HSGM is developed and two numerical illustrations pertaining to the properties of the uncertainty measure are provided.

Ab initio-informed maximum entropy modeling of rovibrational relaxation and state-specific dissociation with application to the O2 + O system

NASA Astrophysics Data System (ADS)

Kulakhmetov, Marat; Gallis, Michael; Alexeenko, Alina

2016-05-01

Quasi-classical trajectory (QCT) calculations are used to study state-specific ro-vibrational energy exchange and dissociation in the O2 + O system. Atom-diatom collisions with energy between 0.1 and 20 eV are calculated with a double many body expansion potential energy surface by Varandas and Pais [Mol. Phys. 65, 843 (1988)]. Inelastic collisions favor mono-quantum vibrational transitions at translational energies above 1.3 eV although multi-quantum transitions are also important. Post-collision vibrational favoring decreases first exponentially and then linearly as Δv increases. Vibrationally elastic collisions (Δv = 0) favor small ΔJ transitions while vibrationally inelastic collisions have equilibrium post-collision rotational distributions. Dissociation exhibits both vibrational and rotational favoring. New vibrational-translational (VT), vibrational-rotational-translational (VRT) energy exchange, and dissociation models are developed based on QCT observations and maximum entropy considerations. Full set of parameters for state-to-state modeling of oxygen is presented. The VT energy exchange model describes 22 000 state-to-state vibrational cross sections using 11 parameters and reproduces vibrational relaxation rates within 30% in the 2500-20 000 K temperature range. The VRT model captures 80 × 106 state-to-state ro-vibrational cross sections using 19 parameters and reproduces vibrational relaxation rates within 60% in the 5000-15 000 K temperature range. The developed dissociation model reproduces state-specific and equilibrium dissociation rates within 25% using just 48 parameters. The maximum entropy framework makes it feasible to upscale ab initio simulation to full nonequilibrium flow calculations.

Direct comparison of phase-sensitive vibrational sum frequency generation with maximum entropy method: case study of water.

PubMed

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

Energy transports by ocean and atmosphere based on an entropy extremum principle. I - Zonal averaged transports

NASA Technical Reports Server (NTRS)

Sohn, Byung-Ju; Smith, Eric A.

1993-01-01

The maximum entropy production principle suggested by Paltridge (1975) is applied to separating the satellite-determined required total transports into atmospheric and oceanic components. Instead of using the excessively restrictive equal energy dissipation hypothesis as a deterministic tool for separating transports between the atmosphere and ocean fluids, the satellite-inferred required 2D energy transports are imposed on Paltridge's energy balance model, which is then solved as a variational problem using the equal energy dissipation hypothesis only to provide an initial guess field. It is suggested that Southern Ocean transports are weaker than previously reported. It is argued that a maximum entropy production principle can serve as a governing rule on macroscale global climate, and, in conjunction with conventional satellite measurements of the net radiation balance, provides a means to decompose atmosphere and ocean transports from the total transport field.

A graphic approach to include dissipative-like effects in reversible thermal cycles

NASA Astrophysics Data System (ADS)

Gonzalez-Ayala, Julian; Arias-Hernandez, Luis Antonio; Angulo-Brown, Fernando

2017-05-01

Since the decade of 1980's, a connection between a family of maximum-work reversible thermal cycles and maximum-power finite-time endoreversible cycles has been established. The endoreversible cycles produce entropy at their couplings with the external heat baths. Thus, this kind of cycles can be optimized under criteria of merit that involve entropy production terms. Meanwhile the relation between the concept of work and power is quite direct, apparently, the finite-time objective functions involving entropy production have not reversible counterparts. In the present paper we show that it is also possible to establish a connection between irreversible cycle models and reversible ones by means of the concept of "geometric dissipation", which has to do with the equivalent role of a deficit of areas between some reversible cycles and the Carnot cycle and actual dissipative terms in a Curzon-Ahlborn engine.

Online Robot Dead Reckoning Localization Using Maximum Relative Entropy Optimization With Model Constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Urniezius, Renaldas

2011-03-14

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 rigidmore » body was known. Performance results confirmed that such an approach could be used for online dead reckoning localization.« less

On the sufficiency of pairwise interactions in maximum entropy models of networks

NASA Astrophysics Data System (ADS)

Nemenman, Ilya; Merchan, Lina

Biological information processing networks consist of many components, which are coupled by an even larger number of complex multivariate interactions. However, analyses of data sets from fields as diverse as neuroscience, molecular biology, and behavior have reported that observed statistics of states of some biological networks can be approximated well by maximum entropy models with only pairwise interactions among the components. Based on simulations of random Ising spin networks with p-spin (p > 2) interactions, here we argue that this reduction in complexity can be thought of as a natural property of some densely interacting networks in certain regimes, and not necessarily as a special property of living systems. This work was supported in part by James S. McDonnell Foundation Grant No. 220020321.

Maximum entropy models as a tool for building precise neural controls.

PubMed

Savin, Cristina; Tkačik, Gašper

2017-10-01

Neural responses are highly structured, with population activity restricted to a small subset of the astronomical range of possible activity patterns. Characterizing these statistical regularities is important for understanding circuit computation, but challenging in practice. Here we review recent approaches based on the maximum entropy principle used for quantifying collective behavior in neural activity. We highlight recent models that capture population-level statistics of neural data, yielding insights into the organization of the neural code and its biological substrate. Furthermore, the MaxEnt framework provides a general recipe for constructing surrogate ensembles that preserve aspects of the data, but are otherwise maximally unstructured. This idea can be used to generate a hierarchy of controls against which rigorous statistical tests are possible. Copyright © 2017 Elsevier Ltd. All rights reserved.

A maximum entropy model for chromatin structure

NASA Astrophysics Data System (ADS)

Farre, Pau; Emberly, Eldon; Emberly Group Team

The DNA inside the nucleus of eukaryotic cells shows a variety of conserved structures at different length scales These structures are formed by interactions between protein complexes that bind to the DNA and regulate gene activity. Recent high throughput sequencing techniques allow for the measurement both of the genome wide contact map of the folded DNA within a cell (HiC) and where various proteins are bound to the DNA (ChIP-seq). In this talk I will present a maximum-entropy method capable of both predicting HiC contact maps from binding data, and binding data from HiC contact maps. This method results in an intuitive Ising-type model that is able to predict how altering the presence of binding factors can modify chromosome conformation, without the need of polymer simulations.

Consistent maximum entropy representations of pipe flow networks

NASA Astrophysics Data System (ADS)

Waldrip, Steven H.; Niven, Robert K.; Abel, Markus; Schlegel, Michael

2017-06-01

The maximum entropy method is used to predict flows on water distribution networks. This analysis extends the water distribution network formulation of Waldrip et al. (2016) Journal of Hydraulic Engineering (ASCE), by the use of a continuous relative entropy defined on a reduced parameter set. This reduction in the parameters that the entropy is defined over ensures consistency between different representations of the same network. The performance of the proposed reduced parameter method is demonstrated with a one-loop network case study.

1/ f noise from the laws of thermodynamics for finite-size fluctuations.

PubMed

Chamberlin, Ralph V; Nasir, Derek M

2014-07-01

Computer simulations of the Ising model exhibit white noise if thermal fluctuations are governed by Boltzmann's factor alone; whereas we find that the same model exhibits 1/f noise if Boltzmann's factor is extended to include local alignment entropy to all orders. We show that this nonlinear correction maintains maximum entropy during equilibrium fluctuations. Indeed, as with the usual way to resolve Gibbs' paradox that avoids entropy reduction during reversible processes, the correction yields the statistics of indistinguishable particles. The correction also ensures conservation of energy if an instantaneous contribution from local entropy is included. Thus, a common mechanism for 1/f noise comes from assuming that finite-size fluctuations strictly obey the laws of thermodynamics, even in small parts of a large system. Empirical evidence for the model comes from its ability to match the measured temperature dependence of the spectral-density exponents in several metals and to show non-Gaussian fluctuations characteristic of nanoscale systems.

Understanding Peripheral Bat Populations Using Maximum-Entropy Suitability Modeling

PubMed Central

Barnhart, Paul R.; Gillam, Erin H.

2016-01-01

Individuals along the periphery of a species distribution regularly encounter more challenging environmental and climatic conditions than conspecifics near the center of the distribution. Due to these potential constraints, individuals in peripheral margins are expected to change their habitat and behavioral characteristics. Managers typically rely on species distribution maps when developing adequate management practices. However, these range maps are often too simplistic and do not provide adequate information as to what fine-scale biotic and abiotic factors are driving a species occurrence. In the last decade, habitat suitability modelling has become widely used as a substitute for simplistic distribution mapping which allows regional managers the ability to fine-tune management resources. The objectives of this study were to use maximum-entropy modeling to produce habitat suitability models for seven species that have a peripheral margin intersecting the state of North Dakota, according to current IUCN distributions, and determine the vegetative and climatic characteristics driving these models. Mistnetting resulted in the documentation of five species outside the IUCN distribution in North Dakota, indicating that current range maps for North Dakota, and potentially the northern Great Plains, are in need of update. Maximum-entropy modeling showed that temperature and not precipitation were the variables most important for model production. This fine-scale result highlights the importance of habitat suitability modelling as this information cannot be extracted from distribution maps. Our results provide baseline information needed for future research about how and why individuals residing in the peripheral margins of a species’ distribution may show marked differences in habitat use as a result of urban expansion, habitat loss, and climate change compared to more centralized populations. PMID:27935936

Convex foundations for generalized MaxEnt models

NASA Astrophysics Data System (ADS)

Frongillo, Rafael; Reid, Mark D.

2014-12-01

We present an approach to maximum entropy models that highlights the convex geometry and duality of generalized exponential families (GEFs) and their connection to Bregman divergences. Using our framework, we are able to resolve a puzzling aspect of the bijection of Banerjee and coauthors between classical exponential families and what they call regular Bregman divergences. Their regularity condition rules out all but Bregman divergences generated from log-convex generators. We recover their bijection and show that a much broader class of divergences correspond to GEFs via two key observations: 1) Like classical exponential families, GEFs have a "cumulant" C whose subdifferential contains the mean: Eo˜pθ[φ(o)]∈∂C(θ) ; 2) Generalized relative entropy is a C-Bregman divergence between parameters: DF(pθ,pθ')= D C(θ,θ') , where DF becomes the KL divergence for F = -H. We also show that every incomplete market with cost function C can be expressed as a complete market, where the prices are constrained to be a GEF with cumulant C. This provides an entirely new interpretation of prediction markets, relating their design back to the principle of maximum entropy.

On the maximum-entropy/autoregressive modeling of time series

NASA Technical Reports Server (NTRS)

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.

Maximum entropy production allows a simple representation of heterogeneity in semiarid ecosystems.

PubMed

Schymanski, Stanislaus J; Kleidon, Axel; Stieglitz, Marc; Narula, Jatin

2010-05-12

Feedbacks between water use, biomass and infiltration capacity in semiarid ecosystems have been shown to lead to the spontaneous formation of vegetation patterns in a simple model. The formation of patterns permits the maintenance of larger overall biomass at low rainfall rates compared with homogeneous vegetation. This results in a bias of models run at larger scales neglecting subgrid-scale variability. In the present study, we investigate the question whether subgrid-scale heterogeneity can be parameterized as the outcome of optimal partitioning between bare soil and vegetated area. We find that a two-box model reproduces the time-averaged biomass of the patterns emerging in a 100 x 100 grid model if the vegetated fraction is optimized for maximum entropy production (MEP). This suggests that the proposed optimality-based representation of subgrid-scale heterogeneity may be generally applicable to different systems and at different scales. The implications for our understanding of self-organized behaviour and its modelling are discussed.

Moisture sorption isotherms and thermodynamic properties of mexican mennonite-style cheese.

PubMed

Martinez-Monteagudo, Sergio I; Salais-Fierro, Fabiola

2014-10-01

Moisture adsorption isotherms of fresh and ripened Mexican Mennonite-style cheese were investigated using the static gravimetric method at 4, 8, and 12 °C in a water activity range (aw) of 0.08-0.96. These isotherms were modeled using GAB, BET, Oswin and Halsey equations through weighed non-linear regression. All isotherms were sigmoid in shape, showing a type II BET isotherm, and the data were best described by GAB model. GAB model coefficients revealed that water adsorption by cheese matrix is a multilayer process characterized by molecules that are strongly bound in the monolayer and molecules that are slightly structured in a multilayer. Using the GAB model, it was possible to estimate thermodynamic functions (net isosteric heat, differential entropy, integral enthalpy and entropy, and enthalpy-entropy compensation) as function of moisture content. For both samples, the isosteric heat and differential entropy decreased with moisture content in exponential fashion. The integral enthalpy gradually decreased with increasing moisture content after reached a maximum value, while the integral entropy decreased with increasing moisture content after reached a minimum value. A linear compensation was found between integral enthalpy and entropy suggesting enthalpy controlled adsorption. Determination of moisture content and aw relationship yields to important information of controlling the ripening, drying and storage operations as well as understanding of the water state within a cheese matrix.

Bayesian Maximum Entropy Integration of Ozone Observations and Model Predictions: A National Application.

PubMed

Xu, Yadong; Serre, Marc L; Reyes, Jeanette; Vizuete, William

2016-04-19

To improve ozone exposure estimates for ambient concentrations at a national scale, we introduce our novel Regionalized Air Quality Model Performance (RAMP) approach to integrate chemical transport model (CTM) predictions with the available ozone observations using the Bayesian Maximum Entropy (BME) framework. The framework models the nonlinear and nonhomoscedastic relation between air pollution observations and CTM predictions and for the first time accounts for variability in CTM model performance. A validation analysis using only noncollocated data outside of a validation radius rv was performed and the R(2) between observations and re-estimated values for two daily metrics, the daily maximum 8-h average (DM8A) and the daily 24-h average (D24A) ozone concentrations, were obtained with the OBS scenario using ozone observations only in contrast with the RAMP and a Constant Air Quality Model Performance (CAMP) scenarios. We show that, by accounting for the spatial and temporal variability in model performance, our novel RAMP approach is able to extract more information in terms of R(2) increase percentage, with over 12 times for the DM8A and over 3.5 times for the D24A ozone concentrations, from CTM predictions than the CAMP approach assuming that model performance does not change across space and time.

Non-life insurance pricing: multi-agent model

NASA Astrophysics Data System (ADS)

Darooneh, A. H.

2004-11-01

We use the maximum entropy principle for the pricing of non-life insurance and recover the Bühlmann results for the economic premium principle. The concept of economic equilibrium is revised in this respect.

Maximum and minimum entropy states yielding local continuity bounds

NASA Astrophysics Data System (ADS)

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.

Ab initio-informed maximum entropy modeling of rovibrational relaxation and state-specific dissociation with application to the O{sub 2} + O system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kulakhmetov, Marat, E-mail: mkulakhm@purdue.edu; Alexeenko, Alina, E-mail: alexeenk@purdue.edu; Gallis, Michael, E-mail: magalli@sandia.gov

Quasi-classical trajectory (QCT) calculations are used to study state-specific ro-vibrational energy exchange and dissociation in the O{sub 2} + O system. Atom-diatom collisions with energy between 0.1 and 20 eV are calculated with a double many body expansion potential energy surface by Varandas and Pais [Mol. Phys. 65, 843 (1988)]. Inelastic collisions favor mono-quantum vibrational transitions at translational energies above 1.3 eV although multi-quantum transitions are also important. Post-collision vibrational favoring decreases first exponentially and then linearly as Δv increases. Vibrationally elastic collisions (Δv = 0) favor small ΔJ transitions while vibrationally inelastic collisions have equilibrium post-collision rotational distributions. Dissociationmore » exhibits both vibrational and rotational favoring. New vibrational-translational (VT), vibrational-rotational-translational (VRT) energy exchange, and dissociation models are developed based on QCT observations and maximum entropy considerations. Full set of parameters for state-to-state modeling of oxygen is presented. The VT energy exchange model describes 22 000 state-to-state vibrational cross sections using 11 parameters and reproduces vibrational relaxation rates within 30% in the 2500–20 000 K temperature range. The VRT model captures 80 × 10{sup 6} state-to-state ro-vibrational cross sections using 19 parameters and reproduces vibrational relaxation rates within 60% in the 5000–15 000 K temperature range. The developed dissociation model reproduces state-specific and equilibrium dissociation rates within 25% using just 48 parameters. The maximum entropy framework makes it feasible to upscale ab initio simulation to full nonequilibrium flow calculations.« less

Optimality and inference in hydrology from entropy production considerations: synthetic hillslope numerical experiments

NASA Astrophysics Data System (ADS)

Kollet, S. J.

2015-05-01

In this study, entropy production optimization and inference principles are applied to a synthetic semi-arid hillslope in high-resolution, physics-based simulations. The results suggest that entropy or power is indeed maximized, because of the strong nonlinearity of variably saturated flow and competing processes related to soil moisture fluxes, the depletion of gradients, and the movement of a free water table. Thus, it appears that the maximum entropy production (MEP) principle may indeed be applicable to hydrologic systems. In the application to hydrologic system, the free water table constitutes an important degree of freedom in the optimization of entropy production and may also relate the theory to actual observations. In an ensuing analysis, an attempt is made to transfer the complex, "microscopic" hillslope model into a macroscopic model of reduced complexity using the MEP principle as an interference tool to obtain effective conductance coefficients and forces/gradients. The results demonstrate a new approach for the application of MEP to hydrologic systems and may form the basis for fruitful discussions and research in future.

Quantitative LC-MS of polymers: determining accurate molecular weight distributions by combined size exclusion chromatography and electrospray mass spectrometry with maximum entropy data processing.

PubMed

Gruendling, Till; Guilhaus, Michael; Barner-Kowollik, Christopher

2008-09-15

We report on the successful application of size exclusion chromatography (SEC) combined with electrospray ionization mass spectrometry (ESI-MS) and refractive index (RI) detection for the determination of accurate molecular weight distributions of synthetic polymers, corrected for chromatographic band broadening. The presented method makes use of the ability of ESI-MS to accurately depict the peak profiles and retention volumes of individual oligomers eluting from the SEC column, whereas quantitative information on the absolute concentration of oligomers is obtained from the RI-detector only. A sophisticated computational algorithm based on the maximum entropy principle is used to process the data gained by both detectors, yielding an accurate molecular weight distribution, corrected for chromatographic band broadening. Poly(methyl methacrylate) standards with molecular weights up to 10 kDa serve as model compounds. Molecular weight distributions (MWDs) obtained by the maximum entropy procedure are compared to MWDs, which were calculated by a conventional calibration of the SEC-retention time axis with peak retention data obtained from the mass spectrometer. Comparison showed that for the employed chromatographic system, distributions below 7 kDa were only weakly influenced by chromatographic band broadening. However, the maximum entropy algorithm could successfully correct the MWD of a 10 kDa standard for band broadening effects. Molecular weight averages were between 5 and 14% lower than the manufacturer stated data obtained by classical means of calibration. The presented method demonstrates a consistent approach for analyzing data obtained by coupling mass spectrometric detectors and concentration sensitive detectors to polymer liquid chromatography.

Research of MPPT for photovoltaic generation based on two-dimensional cloud model

NASA Astrophysics Data System (ADS)

Liu, Shuping; Fan, Wei

2013-03-01

The cloud model is a mathematical representation to fuzziness and randomness in linguistic concepts. It represents a qualitative concept with expected value Ex, entropy En and hyper entropy He, and integrates the fuzziness and randomness of a linguistic concept in a unified way. This model is a new method for transformation between qualitative and quantitative in the knowledge. This paper is introduced MPPT (maximum power point tracking, MPPT) controller based two- dimensional cloud model through analysis of auto-optimization MPPT control of photovoltaic power system and combining theory of cloud model. Simulation result shows that the cloud controller is simple and easy, directly perceived through the senses, and has strong robustness, better control performance.

Multiple Diffusion Mechanisms Due to Nanostructuring in Crowded Environments

PubMed Central

Sanabria, Hugo; Kubota, Yoshihisa; Waxham, M. Neal

2007-01-01

One of the key questions regarding intracellular diffusion is how the environment affects molecular mobility. Mostly, intracellular diffusion has been described as hindered, and the physical reasons for this behavior are: immobile barriers, molecular crowding, and binding interactions with immobile or mobile molecules. Using results from multi-photon fluorescence correlation spectroscopy, we describe how immobile barriers and crowding agents affect translational mobility. To study the hindrance produced by immobile barriers, we used sol-gels (silica nanostructures) that consist of a continuous solid phase and aqueous phase in which fluorescently tagged molecules diffuse. In the case of molecular crowding, translational mobility was assessed in increasing concentrations of 500 kDa dextran solutions. Diffusion of fluorescent tracers in both sol-gels and dextran solutions shows clear evidence of anomalous subdiffusion. In addition, data from the autocorrelation function were analyzed using the maximum entropy method as adapted to fluorescence correlation spectroscopy data and compared with the standard model that incorporates anomalous diffusion. The maximum entropy method revealed evidence of different diffusion mechanisms that had not been revealed using the anomalous diffusion model. These mechanisms likely correspond to nanostructuring in crowded environments and to the relative dimensions of the crowding agent with respect to the tracer molecule. Analysis with the maximum entropy method also revealed information about the degree of heterogeneity in the environment as reported by the behavior of diffusive molecules. PMID:17040979

Possible dynamical explanations for Paltridge's principle of maximum entropy production

DOE Office of Scientific and Technical Information (OSTI.GOV)

Virgo, Nathaniel, E-mail: nathanielvirgo@gmail.com; Ikegami, Takashi, E-mail: nathanielvirgo@gmail.com

2014-12-05

Throughout the history of non-equilibrium thermodynamics a number of theories have been proposed in which complex, far from equilibrium flow systems are hypothesised to reach a steady state that maximises some quantity. Perhaps the most celebrated is Paltridge's principle of maximum entropy production for the horizontal heat flux in Earth's atmosphere, for which there is some empirical support. There have been a number of attempts to derive such a principle from maximum entropy considerations. However, we currently lack a more mechanistic explanation of how any particular system might self-organise into a state that maximises some quantity. This is in contrastmore » to equilibrium thermodynamics, in which models such as the Ising model have been a great help in understanding the relationship between the predictions of MaxEnt and the dynamics of physical systems. In this paper we show that, unlike in the equilibrium case, Paltridge-type maximisation in non-equilibrium systems cannot be achieved by a simple dynamical feedback mechanism. Nevertheless, we propose several possible mechanisms by which maximisation could occur. Showing that these occur in any real system is a task for future work. The possibilities presented here may not be the only ones. We hope that by presenting them we can provoke further discussion about the possible dynamical mechanisms behind extremum principles for non-equilibrium systems, and their relationship to predictions obtained through MaxEnt.« less

Cluster-size entropy in the Axelrod model of social influence: Small-world networks and mass media

NASA Astrophysics Data System (ADS)

Gandica, Y.; Charmell, A.; Villegas-Febres, J.; Bonalde, I.

2011-10-01

We study the Axelrod's cultural adaptation model using the concept of cluster-size entropy Sc, which gives information on the variability of the cultural cluster size present in the system. Using networks of different topologies, from regular to random, we find that the critical point of the well-known nonequilibrium monocultural-multicultural (order-disorder) transition of the Axelrod model is given by the maximum of the Sc(q) distributions. The width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first or second order. By scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait qc and the number F of cultural features in two-dimensional regular networks. We also analyze the effect of the mass media (external field) on social systems within the Axelrod model in a square network. We find a partially ordered phase whose largest cultural cluster is not aligned with the external field, in contrast with a recent suggestion that this type of phase cannot be formed in regular networks. We draw a q-B phase diagram for the Axelrod model in regular networks.

Cluster-size entropy in the Axelrod model of social influence: small-world networks and mass media.

PubMed

Gandica, Y; Charmell, A; Villegas-Febres, J; Bonalde, I

2011-10-01

We study the Axelrod's cultural adaptation model using the concept of cluster-size entropy S(c), which gives information on the variability of the cultural cluster size present in the system. Using networks of different topologies, from regular to random, we find that the critical point of the well-known nonequilibrium monocultural-multicultural (order-disorder) transition of the Axelrod model is given by the maximum of the S(c)(q) distributions. The width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first or second order. By scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait q(c) and the number F of cultural features in two-dimensional regular networks. We also analyze the effect of the mass media (external field) on social systems within the Axelrod model in a square network. We find a partially ordered phase whose largest cultural cluster is not aligned with the external field, in contrast with a recent suggestion that this type of phase cannot be formed in regular networks. We draw a q-B phase diagram for the Axelrod model in regular networks.

Statistical theory on the analytical form of cloud particle size distributions

NASA Astrophysics Data System (ADS)

Wu, Wei; McFarquhar, Greg

2017-11-01

Several analytical forms of cloud particle size distributions (PSDs) have been used in numerical modeling and remote sensing retrieval studies of clouds and precipitation, including exponential, gamma, lognormal, and Weibull distributions. However, there is no satisfying physical explanation as to why certain distribution forms preferentially occur instead of others. Theoretically, the analytical form of a PSD can be derived by directly solving the general dynamic equation, but no analytical solutions have been found yet. Instead of using a process level approach, the use of the principle of maximum entropy (MaxEnt) for determining the analytical form of PSDs from the perspective of system is examined here. Here, the issue of variability under coordinate transformations that arises using the Gibbs/Shannon definition of entropy is identified, and the use of the concept of relative entropy to avoid these problems is discussed. Focusing on cloud physics, the four-parameter generalized gamma distribution is proposed as the analytical form of a PSD using the principle of maximum (relative) entropy with assumptions on power law relations between state variables, scale invariance and a further constraint on the expectation of one state variable (e.g. bulk water mass). DOE ASR.

A maximum (non-extensive) entropy approach to equity options bid-ask spread

NASA Astrophysics Data System (ADS)

Tapiero, Oren J.

2013-07-01

The cross-section of options bid-ask spreads with their strikes are modelled by maximising the Kaniadakis entropy. A theoretical model results with the bid-ask spread depending explicitly on the implied volatility; the probability of expiring at-the-money and an asymmetric information parameter (κ). Considering AIG as a test case for the period between January 2006 and October 2008, we find that information flows uniquely from the trading activity in the underlying asset to its derivatives. Suggesting that κ is possibly an option implied measure of the current state of trading liquidity in the underlying asset.

A basic introduction to the thermodynamics of the Earth system far from equilibrium and maximum entropy production

PubMed Central

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

A basic introduction to the thermodynamics of the Earth system far from equilibrium and maximum entropy production.

PubMed

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.

An entropy-based method for determining the flow depth distribution in natural channels

NASA Astrophysics Data System (ADS)

Moramarco, Tommaso; Corato, Giovanni; Melone, Florisa; Singh, Vijay P.

2013-08-01

A methodology for determining the bathymetry of river cross-sections during floods by the sampling of surface flow velocity and existing low flow hydraulic data is developed . Similar to Chiu (1988) who proposed an entropy-based velocity distribution, the flow depth distribution in a cross-section of a natural channel is derived by entropy maximization. The depth distribution depends on one parameter, whose estimate is straightforward, and on the maximum flow depth. Applying to a velocity data set of five river gage sites, the method modeled the flow area observed during flow measurements and accurately assessed the corresponding discharge by coupling the flow depth distribution and the entropic relation between mean velocity and maximum velocity. The methodology unfolds a new perspective for flow monitoring by remote sensing, considering that the two main quantities on which the methodology is based, i.e., surface flow velocity and flow depth, might be potentially sensed by new sensors operating aboard an aircraft or satellite.

Principle of maximum entropy for reliability analysis in the design of machine components

NASA Astrophysics Data System (ADS)

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.

Forest Tree Species Distribution Mapping Using Landsat Satellite Imagery and Topographic Variables with the Maximum Entropy Method in Mongolia

NASA Astrophysics Data System (ADS)

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 with terrain variables produced better result, with the higher overall accuracy and kappa coefficient than first experiment. The results indicate that the Maximum Entropy method is an applicable, and to classify tree species using satellite imagery data coupled with terrain information can improve the classification of tree species in the study area.

Ecosystem functioning and maximum entropy production: a quantitative test of hypotheses.

PubMed

Meysman, Filip J R; Bruers, Stijn

2010-05-12

The idea that entropy production puts a constraint on ecosystem functioning is quite popular in ecological thermodynamics. Yet, until now, such claims have received little quantitative verification. Here, we examine three 'entropy production' hypotheses that have been forwarded in the past. The first states that increased entropy production serves as a fingerprint of living systems. The other two hypotheses invoke stronger constraints. The state selection hypothesis states that when a system can attain multiple steady states, the stable state will show the highest entropy production rate. The gradient response principle requires that when the thermodynamic gradient increases, the system's new stable state should always be accompanied by a higher entropy production rate. We test these three hypotheses by applying them to a set of conventional food web models. Each time, we calculate the entropy production rate associated with the stable state of the ecosystem. This analysis shows that the first hypothesis holds for all the food webs tested: the living state shows always an increased entropy production over the abiotic state. In contrast, the state selection and gradient response hypotheses break down when the food web incorporates more than one trophic level, indicating that they are not generally valid.

Entropy of adsorption of mixed surfactants from solutions onto the air/water interface

USGS Publications Warehouse

Chen, L.-W.; Chen, J.-H.; Zhou, N.-F.

1995-01-01

The partial molar entropy change for mixed surfactant molecules adsorbed from solution at the air/water interface has been investigated by surface thermodynamics based upon the experimental surface tension isotherms at various temperatures. Results for different surfactant mixtures of sodium dodecyl sulfate and sodium tetradecyl sulfate, decylpyridinium chloride and sodium alkylsulfonates have shown that the partial molar entropy changes for adsorption of the mixed surfactants were generally negative and decreased with increasing adsorption to a minimum near the maximum adsorption and then increased abruptly. The entropy decrease can be explained by the adsorption-orientation of surfactant molecules in the adsorbed monolayer and the abrupt entropy increase at the maximum adsorption is possible due to the strong repulsion between the adsorbed molecules.

Numerical optimization using flow equations.

PubMed

Punk, Matthias

2014-12-01

We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.

Numerical optimization using flow equations

NASA Astrophysics Data System (ADS)

Punk, Matthias

2014-12-01

We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.

Maximum entropy modeling of metabolic networks by constraining growth-rate moments predicts coexistence of phenotypes

NASA Astrophysics Data System (ADS)

De Martino, Daniele

2017-12-01

In this work maximum entropy distributions in the space of steady states of metabolic networks are considered upon constraining the first and second moments of the growth rate. Coexistence of fast and slow phenotypes, with bimodal flux distributions, emerges upon considering control on the average growth (optimization) and its fluctuations (heterogeneity). This is applied to the carbon catabolic core of Escherichia coli where it quantifies the metabolic activity of slow growing phenotypes and it provides a quantitative map with metabolic fluxes, opening the possibility to detect coexistence from flux data. A preliminary analysis on data for E. coli cultures in standard conditions shows degeneracy for the inferred parameters that extend in the coexistence region.

Tsallis Entropy and the Transition to Scaling in Fragmentation

NASA Astrophysics Data System (ADS)

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.

Weak scale from the maximum entropy principle

NASA Astrophysics Data System (ADS)

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.

Infrared image segmentation method based on spatial coherence histogram and maximum entropy

NASA Astrophysics Data System (ADS)

Liu, Songtao; Shen, Tongsheng; Dai, Yao

2014-11-01

In order to segment the target well and suppress background noises effectively, an infrared image segmentation method based on spatial coherence histogram and maximum entropy is proposed. First, spatial coherence histogram is presented by weighting the importance of the different position of these pixels with the same gray-level, which is obtained by computing their local density. Then, after enhancing the image by spatial coherence histogram, 1D maximum entropy method is used to segment the image. The novel method can not only get better segmentation results, but also have a faster computation time than traditional 2D histogram-based segmentation methods.

Stationary properties of maximum-entropy random walks.

PubMed

Dixit, Purushottam D

2015-10-01

Maximum-entropy (ME) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic systems, how state space topology and path-dependent constraints affect ME-inferred state probabilities remains unknown. To that end, we derive the transition probabilities and the stationary distribution of a maximum path entropy Markov process subject to state- and path-dependent constraints. A main finding is that the stationary distribution over states differs significantly from the Boltzmann distribution and reflects a competition between path multiplicity and imposed constraints. We illustrate our results with particle diffusion on a two-dimensional landscape. Connections with the path integral approach to diffusion are discussed.

Correlation between magnetocaloric and electrical properties based on phenomenological models in La0.47Pr0.2Pb0.33MnO3 perovskite

NASA Astrophysics Data System (ADS)

Mechi, Nesrine; Alzahrani, Bandar; Hcini, Sobhi; Bouazizi, Mohamed Lamjed; Dhahri, Abdessalem

2018-06-01

We have investigated the correlation between magnetocaloric and electrical properties of La0.47Pr0.2Pb0.33MnO3 perovskite prepared using the sol-gel method. Rietveld analysis of X-ray diffraction (XRD) pattern shows pure crystalline phase with rhombohedral ? structure. Magnetic entropy change, relative cooling power (RCP) and specific heat were predicted from M(T, μ0H) data at different magnetic fields with the help of the phenomenological model. The magnetic entropy change reaches a maximum value ? of about 3.96 J kg-1 K-1 for μ0H = 5 T corresponding to RCP of 183 J kg-1. These values are relatively higher, making our sample a promising candidate for the magnetic refrigeration. Electrical-resistivity measurements were well fitted with the phenomenological percolation model, which is based on the phase segregation of ferromagnetic-metallic clusters and paramagnetic-semiconductor regions. The temperature and magnetic field dependences of resistivity data, ρ(T, μ0H), allowed us to determine the magnetic entropy change ?. Results show that the as-obtained magnetic entropy change values are similar to those determined from the phenomenological model.

Reinterpreting maximum entropy in ecology: a null hypothesis constrained by ecological mechanism.

PubMed

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.

Using maximum entropy modeling for optimal selection of sampling sites for monitoring networks

USGS Publications Warehouse

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.

Steepest entropy ascent model for far-nonequilibrium thermodynamics: Unified implementation of the maximum entropy production principle

NASA Astrophysics Data System (ADS)

Beretta, Gian Paolo

2014-10-01

By suitable reformulations, we cast the mathematical frameworks of several well-known different approaches to the description of nonequilibrium dynamics into a unified formulation valid in all these contexts, which extends to such frameworks the concept of steepest entropy ascent (SEA) dynamics introduced by the present author in previous works on quantum thermodynamics. Actually, the present formulation constitutes a generalization also for the quantum thermodynamics framework. The analysis emphasizes that in the SEA modeling principle a key role is played by the geometrical metric with respect to which to measure the length of a trajectory in state space. In the near-thermodynamic-equilibrium limit, the metric tensor is directly related to the Onsager's generalized resistivity tensor. Therefore, through the identification of a suitable metric field which generalizes the Onsager generalized resistance to the arbitrarily far-nonequilibrium domain, most of the existing theories of nonequilibrium thermodynamics can be cast in such a way that the state exhibits the spontaneous tendency to evolve in state space along the path of SEA compatible with the conservation constraints and the boundary conditions. The resulting unified family of SEA dynamical models is intrinsically and strongly consistent with the second law of thermodynamics. The non-negativity of the entropy production is a general and readily proved feature of SEA dynamics. In several of the different approaches to nonequilibrium description we consider here, the SEA concept has not been investigated before. We believe it defines the precise meaning and the domain of general validity of the so-called maximum entropy production principle. Therefore, it is hoped that the present unifying approach may prove useful in providing a fresh basis for effective, thermodynamically consistent, numerical models and theoretical treatments of irreversible conservative relaxation towards equilibrium from far nonequilibrium states. The mathematical frameworks we consider are the following: (A) statistical or information-theoretic models of relaxation; (B) small-scale and rarefied gas dynamics (i.e., kinetic models for the Boltzmann equation); (C) rational extended thermodynamics, macroscopic nonequilibrium thermodynamics, and chemical kinetics; (D) mesoscopic nonequilibrium thermodynamics, continuum mechanics with fluctuations; and (E) quantum statistical mechanics, quantum thermodynamics, mesoscopic nonequilibrium quantum thermodynamics, and intrinsic quantum thermodynamics.

Revisiting the global surface energy budgets with maximum-entropy-production model of surface heat fluxes

NASA Astrophysics Data System (ADS)

Huang, Shih-Yu; Deng, Yi; Wang, Jingfeng

2017-09-01

The maximum-entropy-production (MEP) model of surface heat fluxes, based on contemporary non-equilibrium thermodynamics, information theory, and atmospheric turbulence theory, is used to re-estimate the global surface heat fluxes. The MEP model predicted surface fluxes automatically balance the surface energy budgets at all time and space scales without the explicit use of near-surface temperature and moisture gradient, wind speed and surface roughness data. The new MEP-based global annual mean fluxes over the land surface, using input data of surface radiation, temperature data from National Aeronautics and Space Administration-Clouds and the Earth's Radiant Energy System (NASA CERES) supplemented by surface specific humidity data from the Modern-Era Retrospective Analysis for Research and Applications (MERRA), agree closely with previous estimates. The new estimate of ocean evaporation, not using the MERRA reanalysis data as model inputs, is lower than previous estimates, while the new estimate of ocean sensible heat flux is higher than previously reported. The MEP model also produces the first global map of ocean surface heat flux that is not available from existing global reanalysis products.

Entropy generation in biophysical systems

NASA Astrophysics Data System (ADS)

Lucia, U.; Maino, G.

2013-03-01

Recently, in theoretical biology and in biophysical engineering the entropy production has been verified to approach asymptotically its maximum rate, by using the probability of individual elementary modes distributed in accordance with the Boltzmann distribution. The basis of this approach is the hypothesis that the entropy production rate is maximum at the stationary state. In the present work, this hypothesis is explained and motivated, starting from the entropy generation analysis. This latter quantity is obtained from the entropy balance for open systems considering the lifetime of the natural real process. The Lagrangian formalism is introduced in order to develop an analytical approach to the thermodynamic analysis of the open irreversible systems. The stationary conditions of the open systems are thus obtained in relation to the entropy generation and the least action principle. Consequently, the considered hypothesis is analytically proved and it represents an original basic approach in theoretical and mathematical biology and also in biophysical engineering. It is worth remarking that the present results show that entropy generation not only increases but increases as fast as possible.

Determining Dynamical Path Distributions usingMaximum Relative Entropy

DTIC Science & Technology

2015-05-31

entropy to a one-dimensional continuum labeled by a parameter η. The resulting η-entropies are equivalent to those proposed by Renyi [12] or by Tsallis [13...1995). [12] A. Renyi , “On measures of entropy and information,”Proc. 4th Berkeley Simposium on Mathematical Statistics and Probability, Vol 1, p. 547-461

Entropy of spatial network ensembles

NASA Astrophysics Data System (ADS)

Coon, Justin P.; Dettmann, Carl P.; Georgiou, Orestis

2018-04-01

We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly in space and links formed independently between pairs of nodes with probability given by a specified function (the "pair connection function") of their mutual distance. We consider the general case where randomness arises in node positions as well as pairwise connections (i.e., for a given pair distance, the corresponding edge state is a random variable). Classical random geometric graph and exponential graph models can be recovered in certain limits. We derive a simple bound for the entropy of a spatial network ensemble and calculate the conditional entropy of an ensemble given the node location distribution for hard and soft (probabilistic) pair connection functions. Under this formalism, we derive the connection function that yields maximum entropy under general constraints. Finally, we apply our analytical framework to study two practical examples: ad hoc wireless networks and the US flight network. Through the study of these examples, we illustrate that both exhibit properties that are indicative of nearly maximally entropic ensembles.

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

NASA Astrophysics Data System (ADS)

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).

Elements of the cognitive universe

NASA Astrophysics Data System (ADS)

Topsøe, Flemming

2017-06-01

"The least biased inference, taking available information into account, is the one with maximum entropy". So we are taught by Jaynes. The many followers from a broad spectrum of the natural and social sciences point to the wisdom of this principle, the maximum entropy principle, MaxEnt. But "entropy" need not be tied only to classical entropy and thus to probabilistic thinking. In fact, the arguments found in Jaynes' writings and elsewhere can, as we shall attempt to demonstrate, profitably be revisited, elaborated and transformed to apply in a much more general abstract setting. The approach is based on game theoretical thinking. Philosophical considerations dealing with notions of cognition - basically truth and belief - lie behind. Quantitative elements are introduced via a concept of description effort. An interpretation of Tsallis Entropy is indicated.

Exploiting the Maximum Entropy Principle to Increase Retrieval Effectiveness.

ERIC Educational Resources Information Center

Cooper, William S.

1983-01-01

Presents information retrieval design approach in which queries of computer-based system consist of sets of terms, either unweighted or weighted with subjective term precision estimates, and retrieval outputs ranked by probability of usefulness estimated by "maximum entropy principle." Boolean and weighted request systems are discussed.…

A model for Entropy Production, Entropy Decrease and Action Minimization in Self-Organization

NASA Astrophysics Data System (ADS)

Georgiev, Georgi; Chatterjee, Atanu; Vu, Thanh; Iannacchione, Germano

In self-organization energy gradients across complex systems lead to change in the structure of systems, decreasing their internal entropy to ensure the most efficient energy transport and therefore maximum entropy production in the surroundings. This approach stems from fundamental variational principles in physics, such as the principle of least action. It is coupled to the total energy flowing through a system, which leads to increase the action efficiency. We compare energy transport through a fluid cell which has random motion of its molecules, and a cell which can form convection cells. We examine the signs of change of entropy, and the action needed for the motion inside those systems. The system in which convective motion occurs, reduces the time for energy transmission, compared to random motion. For more complex systems, those convection cells form a network of transport channels, for the purpose of obeying the equations of motion in this geometry. Those transport networks are an essential feature of complex systems in biology, ecology, economy and society.

Estimation of typhoon rainfall in GaoPing River: A Multivariate Maximum Entropy Method

NASA Astrophysics Data System (ADS)

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 .

Trends in entropy production during ecosystem development in the Amazon Basin.

PubMed

Holdaway, Robert J; Sparrow, Ashley D; Coomes, David A

2010-05-12

Understanding successional trends in energy and matter exchange across the ecosystem-atmosphere boundary layer is an essential focus in ecological research; however, a general theory describing the observed pattern remains elusive. This paper examines whether the principle of maximum entropy production could provide the solution. A general framework is developed for calculating entropy production using data from terrestrial eddy covariance and micrometeorological studies. We apply this framework to data from eight tropical forest and pasture flux sites in the Amazon Basin and show that forest sites had consistently higher entropy production rates than pasture sites (0.461 versus 0.422 W m(-2) K(-1), respectively). It is suggested that during development, changes in canopy structure minimize surface albedo, and development of deeper root systems optimizes access to soil water and thus potential transpiration, resulting in lower surface temperatures and increased entropy production. We discuss our results in the context of a theoretical model of entropy production versus ecosystem developmental stage. We conclude that, although further work is required, entropy production could potentially provide a much-needed theoretical basis for understanding the effects of deforestation and land-use change on the land-surface energy balance.

Exact results of 1D traffic cellular automata: The low-density behavior of the Fukui-Ishibashi model

NASA Astrophysics Data System (ADS)

Salcido, Alejandro; Hernández-Zapata, Ernesto; Carreón-Sierra, Susana

2018-03-01

The maximum entropy states of the cellular automata models for traffic flow in a single-lane with no anticipation are presented and discussed. The exact analytical solutions for the low-density behavior of the stochastic Fukui-Ishibashi traffic model were obtained and compared with computer simulations of the model. An excellent agreement was found.

Spatiotemporal modeling of PM2.5 concentrations at the national scale combining land use regression and Bayesian maximum entropy in China.

PubMed

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 <2.5 μm (PM 2.5 ) are relatively high in China. Estimation of PM 2.5 exposure is complex because PM 2.5 exhibits complex spatiotemporal patterns. To improve the validity of exposure predictions, several methods have been developed and applied worldwide. A hybrid approach combining a land use regression (LUR) model and 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.

Inverting ion images without Abel inversion: maximum entropy reconstruction of velocity maps.

PubMed

Dick, Bernhard

2014-01-14

A new method for the reconstruction of velocity maps from ion images is presented, which is based on the maximum entropy concept. In contrast to other methods used for Abel inversion the new method never applies an inversion or smoothing to the data. Instead, it iteratively finds the map which is the most likely cause for the observed data, using the correct likelihood criterion for data sampled from a Poissonian distribution. The entropy criterion minimizes the information content in this map, which hence contains no information for which there is no evidence in the data. Two implementations are proposed, and their performance is demonstrated with simulated and experimental data: Maximum Entropy Velocity Image Reconstruction (MEVIR) obtains a two-dimensional slice through the velocity distribution and can be compared directly to Abel inversion. Maximum Entropy Velocity Legendre Reconstruction (MEVELER) finds one-dimensional distribution functions Q(l)(v) in an expansion of the velocity distribution in Legendre polynomials P((cos θ) for the angular dependence. Both MEVIR and MEVELER can be used for the analysis of ion images with intensities as low as 0.01 counts per pixel, with MEVELER performing significantly better than MEVIR for images with low intensity. Both methods perform better than pBASEX, in particular for images with less than one average count per pixel.

Chapman Enskog-maximum entropy method on time-dependent neutron transport equation

NASA Astrophysics Data System (ADS)

Abdou, M. A.

2006-09-01

The time-dependent neutron transport equation in semi and infinite medium with linear anisotropic and Rayleigh scattering is proposed. The problem is solved by means of the flux-limited, Chapman Enskog-maximum entropy for obtaining the solution of the time-dependent neutron transport. The solution gives the neutron distribution density function which is used to compute numerically the radiant energy density E(x,t), net flux F(x,t) and reflectivity Rf. The behaviour of the approximate flux-limited maximum entropy neutron density function are compared with those found by other theories. Numerical calculations for the radiant energy, net flux and reflectivity of the proposed medium are calculated at different time and space.

Classic maximum entropy recovery of the average joint distribution of apparent FRET efficiency and fluorescence photons for single-molecule burst measurements.

PubMed

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.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle.

PubMed

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.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle

PubMed Central

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. PMID:26997886

Parabolic replicator dynamics and the principle of minimum Tsallis information gain

PubMed Central

2013-01-01

Background Non-linear, parabolic (sub-exponential) and hyperbolic (super-exponential) models of prebiological evolution of molecular replicators have been proposed and extensively studied. The parabolic models appear to be the most realistic approximations of real-life replicator systems due primarily to product inhibition. Unlike the more traditional exponential models, the distribution of individual frequencies in an evolving parabolic population is not described by the Maximum Entropy (MaxEnt) Principle in its traditional form, whereby the distribution with the maximum Shannon entropy is chosen among all the distributions that are possible under the given constraints. We sought to identify a more general form of the MaxEnt principle that would be applicable to parabolic growth. Results We consider a model of a population that reproduces according to the parabolic growth law and show that the frequencies of individuals in the population minimize the Tsallis relative entropy (non-additive information gain) at each time moment. Next, we consider a model of a parabolically growing population that maintains a constant total size and provide an “implicit” solution for this system. We show that in this case, the frequencies of the individuals in the population also minimize the Tsallis information gain at each moment of the ‘internal time” of the population. Conclusions The results of this analysis show that the general MaxEnt principle is the underlying law for the evolution of a broad class of replicator systems including not only exponential but also parabolic and hyperbolic systems. The choice of the appropriate entropy (information) function depends on the growth dynamics of a particular class of systems. The Tsallis entropy is non-additive for independent subsystems, i.e. the information on the subsystems is insufficient to describe the system as a whole. In the context of prebiotic evolution, this “non-reductionist” nature of parabolic replicator systems might reflect the importance of group selection and competition between ensembles of cooperating replicators. Reviewers This article was reviewed by Viswanadham Sridhara (nominated by Claus Wilke), Puushottam Dixit (nominated by Sergei Maslov), and Nick Grishin. For the complete reviews, see the Reviewers’ Reports section. PMID:23937956

Predictive modeling and mapping of Malayan Sun Bear (Helarctos malayanus) distribution using maximum entropy.

PubMed

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.

Predictive Modeling and Mapping of Malayan Sun Bear (Helarctos malayanus) Distribution Using Maximum Entropy

PubMed Central

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. PMID:23110182

Application of the Maximum Entropy Method to Risk Analysis of Mergers and Acquisitions

NASA Astrophysics Data System (ADS)

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.

Entropy, Ergodicity, and Stem Cell Multipotency

NASA Astrophysics Data System (ADS)

Ridden, Sonya J.; Chang, Hannah H.; Zygalakis, Konstantinos C.; MacArthur, Ben D.

2015-11-01

Populations of mammalian stem cells commonly exhibit considerable cell-cell variability. However, the functional role of this diversity is unclear. Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and find that the observed dynamics naturally lie close to a critical state, thereby producing a diverse population that is able to respond rapidly to environmental changes. We propose an information-theoretic interpretation of these results that views cellular multipotency as an instance of maximum entropy statistical inference.

Predicting the potential environmental suitability for Theileria orientalis transmission in New Zealand cattle using maximum entropy niche modelling.

PubMed

Lawrence, K E; Summers, S R; Heath, A C G; McFadden, A M J; Pulford, D J; Pomroy, W E

2016-07-15

The tick-borne haemoparasite Theileria orientalis is the most important infectious cause of anaemia in New Zealand cattle. Since 2012 a previously unrecorded type, T. orientalis type 2 (Ikeda), has been associated with disease outbreaks of anaemia, lethargy, jaundice and deaths on over 1000 New Zealand cattle farms, with most of the affected farms found in the upper North Island. The aim of this study was to model the relative environmental suitability for T. orientalis transmission throughout New Zealand, to predict the proportion of cattle farms potentially suitable for active T. orientalis infection by region, island and the whole of New Zealand and to estimate the average relative environmental suitability per farm by region, island and the whole of New Zealand. The relative environmental suitability for T. orientalis transmission was estimated using the Maxent (maximum entropy) modelling program. The Maxent model predicted that 99% of North Island cattle farms (n=36,257), 64% South Island cattle farms (n=15,542) and 89% of New Zealand cattle farms overall (n=51,799) could potentially be suitable for T. orientalis transmission. The average relative environmental suitability of T. orientalis transmission at the farm level was 0.34 in the North Island, 0.02 in the South Island and 0.24 overall. The study showed that the potential spatial distribution of T. orientalis environmental suitability was much greater than presumed in the early part of the Theileria associated bovine anaemia (TABA) epidemic. Maximum entropy offers a computer efficient method of modelling the probability of habitat suitability for an arthropod vectored disease. This model could help estimate the boundaries of the endemically stable and endemically unstable areas for T. orientalis transmission within New Zealand and be of considerable value in informing practitioner and farmer biosecurity decisions in these respective areas. Copyright © 2016 Elsevier B.V. All rights reserved.

Maximum entropy approach to statistical inference for an ocean acoustic waveguide.

PubMed

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

Entropic Inference

NASA Astrophysics Data System (ADS)

Caticha, Ariel

2011-03-01

In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The 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), includes as special cases both MaxEnt and Bayes' rule, and therefore unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme.

Prediction of Metabolite Concentrations, Rate Constants and Post-Translational Regulation Using Maximum Entropy-Based Simulations with Application to Central Metabolism of Neurospora crassa

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cannon, William; Zucker, Jeremy; Baxter, Douglas

We report the application of a recently proposed approach for modeling biological systems using a maximum entropy production rate principle in lieu of having in vivo rate constants. The method is applied in four steps: (1) a new ODE-based optimization approach based on Marcelin’s 1910 mass action equation is used to obtain the maximum entropy distribution, (2) the predicted metabolite concentrations are compared to those generally expected from experiment using a loss function from which post-translational regulation of enzymes is inferred, (3) the system is re-optimized with the inferred regulation from which rate constants are determined from the metabolite concentrationsmore » and reaction fluxes, and finally (4) a full ODE-based, mass action simulation with rate parameters and allosteric regulation is obtained. From the last step, the power characteristics and resistance of each reaction can be determined. The method is applied to the central metabolism of Neurospora crassa and the flow of material through the three competing pathways of upper glycolysis, the non-oxidative pentose phosphate pathway, and the oxidative pentose phosphate pathway are evaluated as a function of the NADP/NADPH ratio. It is predicted that regulation of phosphofructokinase (PFK) and flow through the pentose phosphate pathway are essential for preventing an extreme level of fructose 1, 6-bisphophate accumulation. Such an extreme level of fructose 1,6-bisphophate would otherwise result in a glassy cytoplasm with limited diffusion, dramatically decreasing the entropy and energy production rate and, consequently, biological competitiveness.« less

Uncertainty estimation of the self-thinning process by Maximum-Entropy Principle

Treesearch

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-...

Classic Maximum Entropy Recovery of the Average Joint Distribution of Apparent FRET Efficiency and Fluorescence Photons for Single-molecule Burst Measurements

PubMed Central

DeVore, Matthew S.; Gull, Stephen F.; Johnson, Carey K.

2012-01-01

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. PMID:22338694

A unified approach to computational drug discovery.

PubMed

Tseng, Chih-Yuan; Tuszynski, Jack

2015-11-01

It has been reported that a slowdown in the development of new medical therapies is affecting clinical outcomes. The FDA has thus initiated the Critical Path Initiative project investigating better approaches. We review the current strategies in drug discovery and focus on the advantages of the maximum entropy method being introduced in this area. The maximum entropy principle is derived from statistical thermodynamics and has been demonstrated to be an inductive inference tool. We propose a unified method to drug discovery that hinges on robust information processing using entropic inductive inference. Increasingly, applications of maximum entropy in drug discovery employ this unified approach and demonstrate the usefulness of the concept in the area of pharmaceutical sciences. Copyright © 2015. Published by Elsevier Ltd.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Maximum entropy modeling of invasive plants in the forests of Cumberland Plateau and Mountain Region

Treesearch

Dawn Lemke; Philip Hulme; Jennifer Brown; Wubishet. Tadesse

2011-01-01

As anthropogenic influences on the landscape change the composition of 'natural' areas, it is important that we apply spatial technology in active management to mitigate human impact. This research explores the integration of geographic information systems (GIS) and remote sensing with statistical analysis to assist in modeling the distribution of invasive...

Adaptive Statistical Language Modeling; A Maximum Entropy Approach

DTIC Science & Technology

1994-04-19

models exploit the immediate past only. To extract information from further back in the document’s history , I use trigger pairs as the basic information...9 2.2 Context-Free Estimation (Unigram) ...... .................... 12 2.3 Short-Term History (Conventional N-gram...12 2.4 Short-term Class History (Class-Based N-gram) ................... 14 2.5 Intermediate Distance ........ ........................... 16

Bivariate Rainfall and Runoff Analysis Using Shannon Entropy Theory

NASA Astrophysics Data System (ADS)

Rahimi, A.; Zhang, L.

2012-12-01

Rainfall-Runoff analysis is the key component for many hydrological and hydraulic designs in which the dependence of rainfall and runoff needs to be studied. It is known that the convenient bivariate distribution are often unable to model the rainfall-runoff variables due to that they either have constraints on the range of the dependence or fixed form for the marginal distributions. Thus, this paper presents an approach to derive the entropy-based joint rainfall-runoff distribution using Shannon entropy theory. The distribution derived can model the full range of dependence and allow different specified marginals. The modeling and estimation can be proceeded as: (i) univariate analysis of marginal distributions which includes two steps, (a) using the nonparametric statistics approach to detect modes and underlying probability density, and (b) fitting the appropriate parametric probability density functions; (ii) define the constraints based on the univariate analysis and the dependence structure; (iii) derive and validate the entropy-based joint distribution. As to validate the method, the rainfall-runoff data are collected from the small agricultural experimental watersheds located in semi-arid region near Riesel (Waco), Texas, maintained by the USDA. The results of unviariate analysis show that the rainfall variables follow the gamma distribution, whereas the runoff variables have mixed structure and follow the mixed-gamma distribution. With this information, the entropy-based joint distribution is derived using the first moments, the first moments of logarithm transformed rainfall and runoff, and the covariance between rainfall and runoff. The results of entropy-based joint distribution indicate: (1) the joint distribution derived successfully preserves the dependence between rainfall and runoff, and (2) the K-S goodness of fit statistical tests confirm the marginal distributions re-derived reveal the underlying univariate probability densities which further assure that the entropy-based joint rainfall-runoff distribution are satisfactorily derived. Overall, the study shows the Shannon entropy theory can be satisfactorily applied to model the dependence between rainfall and runoff. The study also shows that the entropy-based joint distribution is an appropriate approach to capture the dependence structure that cannot be captured by the convenient bivariate joint distributions. Joint Rainfall-Runoff Entropy Based PDF, and Corresponding Marginal PDF and Histogram for W12 Watershed The K-S Test Result and RMSE on Univariate Distributions Derived from the Maximum Entropy Based Joint Probability Distribution;

Diffusivity anomaly in modified Stillinger-Weber liquids

NASA Astrophysics Data System (ADS)

Sengupta, Shiladitya; Vasisht, Vishwas V.; Sastry, Srikanth

2014-01-01

By modifying the tetrahedrality (the strength of the three body interactions) in the well-known Stillinger-Weber model for silicon, we study the diffusivity of a series of model liquids as a function of tetrahedrality and temperature at fixed pressure. Previous work has shown that at constant temperature, the diffusivity exhibits a maximum as a function of tetrahedrality, which we refer to as the diffusivity anomaly, in analogy with the well-known anomaly in water upon variation of pressure at constant temperature. We explore to what extent the structural and thermodynamic changes accompanying changes in the interaction potential can help rationalize the diffusivity anomaly, by employing the Rosenfeld relation between diffusivity and the excess entropy (over the ideal gas reference value), and the pair correlation entropy, which provides an approximation to the excess entropy in terms of the pair correlation function. We find that in the modified Stillinger-Weber liquids, the Rosenfeld relation works well above the melting temperatures but exhibits deviations below, with the deviations becoming smaller for smaller tetrahedrality. Further we find that both the excess entropy and the pair correlation entropy at constant temperature go through maxima as a function of the tetrahedrality, thus demonstrating the close relationship between structural, thermodynamic, and dynamical anomalies in the modified Stillinger-Weber liquids.

Computing the Energy Cost of the Information Transmitted by Model Biological Neurons

NASA Astrophysics Data System (ADS)

Torrealdea, F. J.; Sarasola, C.; d'Anjou, A.; Moujahid, A.

2009-08-01

We assign an energy function to a Hindmarsh-Rose model of a neuron and use it to compute values of average energy consumption during its signalling activity. We also compute values of information entropy of an isolated neuron and of mutual information between two electrically coupled neurons. We find that for the isolated neuron the chaotic signaling regime is the one with the biggest ratio of information entropy to energy consumption. We also find that in the case of electrically coupled neurons there are values of the coupling strength at which the mutual information to energy consumption ratio is maximum, that is, that transmitting at that coupling conditions is energetically less expensive.

Economics and Maximum Entropy Production

NASA Astrophysics Data System (ADS)

Lorenz, R. D.

2003-04-01

Price differentials, sales volume and profit can be seen as analogues of temperature difference, heat flow and work or entropy production in the climate system. One aspect in which economic systems exhibit more clarity than the climate is that the empirical and/or statistical mechanical tendency for systems to seek a maximum in production is very evident in economics, in that the profit motive is very clear. Noting the common link between 1/f noise, power laws and Self-Organized Criticality with Maximum Entropy Production, the power law fluctuations in security and commodity prices is not inconsistent with the analogy. There is an additional thermodynamic analogy, in that scarcity is valued. A commodity concentrated among a few traders is valued highly by the many who do not have it. The market therefore encourages via prices the spreading of those goods among a wider group, just as heat tends to diffuse, increasing entropy. I explore some empirical price-volume relationships of metals and meteorites in this context.

Bayesian Probability Theory

NASA Astrophysics Data System (ADS)

von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo

2014-06-01

Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.

LANDMARK-BASED SPEECH RECOGNITION: REPORT OF THE 2004 JOHNS HOPKINS SUMMER WORKSHOP.

PubMed

Hasegawa-Johnson, Mark; Baker, James; Borys, Sarah; Chen, Ken; Coogan, Emily; Greenberg, Steven; Juneja, Amit; Kirchhoff, Katrin; Livescu, Karen; Mohan, Srividya; Muller, Jennifer; Sonmez, Kemal; Wang, Tianyu

2005-01-01

Three research prototype speech recognition systems are described, all of which use recently developed methods from artificial intelligence (specifically support vector machines, dynamic Bayesian networks, and maximum entropy classification) in order to implement, in the form of an automatic speech recognizer, current theories of human speech perception and phonology (specifically landmark-based speech perception, nonlinear phonology, and articulatory phonology). All three systems begin with a high-dimensional multiframe acoustic-to-distinctive feature transformation, implemented using support vector machines trained to detect and classify acoustic phonetic landmarks. Distinctive feature probabilities estimated by the support vector machines are then integrated using one of three pronunciation models: a dynamic programming algorithm that assumes canonical pronunciation of each word, a dynamic Bayesian network implementation of articulatory phonology, or a discriminative pronunciation model trained using the methods of maximum entropy classification. Log probability scores computed by these models are then combined, using log-linear combination, with other word scores available in the lattice output of a first-pass recognizer, and the resulting combination score is used to compute a second-pass speech recognition output.

Metabolic networks evolve towards states of maximum entropy production.

PubMed

Unrean, Pornkamol; Srienc, Friedrich

2011-11-01

A metabolic network can be described by a set of elementary modes or pathways representing discrete metabolic states that support cell function. We have recently shown that in the most likely metabolic state the usage probability of individual elementary modes is distributed according to the Boltzmann distribution law while complying with the principle of maximum entropy production. To demonstrate that a metabolic network evolves towards such state we have carried out adaptive evolution experiments with Thermoanaerobacterium saccharolyticum operating with a reduced metabolic functionality based on a reduced set of elementary modes. In such reduced metabolic network metabolic fluxes can be conveniently computed from the measured metabolite secretion pattern. Over a time span of 300 generations the specific growth rate of the strain continuously increased together with a continuous increase in the rate of entropy production. We show that the rate of entropy production asymptotically approaches the maximum entropy production rate predicted from the state when the usage probability of individual elementary modes is distributed according to the Boltzmann distribution. Therefore, the outcome of evolution of a complex biological system can be predicted in highly quantitative terms using basic statistical mechanical principles. Copyright © 2011 Elsevier Inc. All rights reserved.

The maximum entropy method of moments and Bayesian probability theory

NASA Astrophysics Data System (ADS)

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.

Time dependence of Hawking radiation entropy

NASA Astrophysics Data System (ADS)

Page, Don N.

2013-09-01

If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4πM02, or about 7.509M02 ≈ 6.268 × 1076(M0/Msolar)2, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018M02 ≈ 1.254 × 1077(M0/Msolar)2, and then decreases back down to 4πM02 = 1.049 × 1077(M0/Msolar)2.

Habitat suitability of patch types: A case study of the Yosemite toad

Treesearch

Christina T. Liang; Thomas J. Stohlgren

2011-01-01

Understanding patch variability is crucial in understanding the spatial population structure of wildlife species, especially for rare or threatened species.We used a well-tested maximum entropy species distribution model (Maxent) to map the Yosemite toad (Anaxyrus (= Bufo) canorus) in the Sierra Nevada...

n-Order and maximum fuzzy similarity entropy for discrimination of signals of different complexity: Application to fetal heart rate signals.

PubMed

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.

Speech parts as Poisson processes.

PubMed

Badalamenti, A F

2001-09-01

This paper presents evidence that six of the seven parts of speech occur in written text as Poisson processes, simple or recurring. The six major parts are nouns, verbs, adjectives, adverbs, prepositions, and conjunctions, with the interjection occurring too infrequently to support a model. The data consist of more than the first 5000 words of works by four major authors coded to label the parts of speech, as well as periods (sentence terminators). Sentence length is measured via the period and found to be normally distributed with no stochastic model identified for its occurrence. The models for all six speech parts but the noun significantly distinguish some pairs of authors and likewise for the joint use of all words types. Any one author is significantly distinguished from any other by at least one word type and sentence length very significantly distinguishes each from all others. The variety of word type use, measured by Shannon entropy, builds to about 90% of its maximum possible value. The rate constants for nouns are close to the fractions of maximum entropy achieved. This finding together with the stochastic models and the relations among them suggest that the noun may be a primitive organizer of written text.

Computational design of hepatitis C vaccines using maximum entropy models and population dynamics

NASA Astrophysics Data System (ADS)

Hart, Gregory; Ferguson, Andrew

Hepatitis C virus (HCV) afflicts 170 million people and kills 350,000 annually. Vaccination offers the most realistic and cost effective hope of controlling this epidemic. Despite 20 years of research, no vaccine is available. A major obstacle is the virus' extreme genetic variability and rapid mutational escape from immune pressure. Improvements in the vaccine design process are urgently needed. Coupling data mining with spin glass models and maximum entropy inference, we have developed a computational approach to translate sequence databases into empirical fitness landscapes. These landscapes explicitly connect viral genotype to phenotypic fitness and reveal vulnerable targets that can be exploited to rationally design immunogens. Viewing these landscapes as the mutational ''playing field'' over which the virus is constrained to evolve, we have integrated them with agent-based models of the viral mutational and host immune response dynamics, establishing a data-driven immune simulator of HCV infection. We have employed this simulator to perform in silico screening of HCV immunogens. By systematically identifying a small number of promising vaccine candidates, these models can accelerate the search for a vaccine by massively reducing the experimental search space.

Coupling diffusion and maximum entropy models to estimate thermal inertia

USDA-ARS?s Scientific Manuscript database

Thermal inertia is a physical property of soil at the land surface related to water content. We have developed a method for estimating soil thermal inertia using two daily measurements of surface temperature, to capture the diurnal range, and diurnal time series of net radiation and specific humidi...

Minimum and Maximum Entropy Distributions for Binary Systems with Known Means and Pairwise Correlations

DTIC Science & Technology

2017-08-21

distributions, and we discuss some applications for engineered and biological information transmission systems. Keywords: information theory; minimum...of its interpretation as a measure of the amount of information communicable by a neural system to groups of downstream neurons. Previous authors...of the maximum entropy approach. Our results also have relevance for engineered information transmission systems. We show that empirically measured

Stochastic characteristics of different duration annual maximum rainfall and its spatial difference in China based on information entropy

NASA Astrophysics Data System (ADS)

Li, X.; Sang, Y. F.

2017-12-01

Mountain torrents, urban floods and other disasters caused by extreme precipitation bring great losses to the ecological environment, social and economic development, people's lives and property security. So there is of great significance to floods prevention and control by the study of its spatial distribution. Based on the annual maximum rainfall data of 60min, 6h and 24h, the paper generate long sequences following Pearson-III distribution, and then use the information entropy index to study the spatial distribution and difference of different duration. The results show that the information entropy value of annual maximum rainfall in the south region is greater than that in the north region, indicating more obvious stochastic characteristics of annual maximum rainfall in the latter. However, the spatial distribution of stochastic characteristics is different in different duration. For example, stochastic characteristics of 60min annual maximum rainfall in the Eastern Tibet is smaller than surrounding, but 6h and 24h annual maximum rainfall is larger than surrounding area. In the Haihe River Basin and the Huaihe River Basin, the stochastic characteristics of the 60min annual maximum rainfall was not significantly different from that in the surrounding area, and stochastic characteristics of 6h and 24h was smaller than that in the surrounding area. We conclude that the spatial distribution of information entropy values of annual maximum rainfall in different duration can reflect the spatial distribution of its stochastic characteristics, thus the results can be an importantly scientific basis for the flood prevention and control, agriculture, economic-social developments and urban flood control and waterlogging.

Quantum and Ecosystem Entropies

NASA Astrophysics Data System (ADS)

Kirwan, A. D.

2008-06-01

Ecosystems and quantum gases share a number of superficial similarities including enormous numbers of interacting elements and the fundamental role of energy in such interactions. A theory for the synthesis of data and prediction of new phenomena is well established in quantum statistical mechanics. The premise of this paper is that the reason a comparable unifying theory has not emerged in ecology is that a proper role for entropy has yet to be assigned. To this end, a phase space entropy model of ecosystems is developed. Specification of an ecosystem phase space cell size based on microbial mass, length, and time scales gives an ecosystem uncertainty parameter only about three orders of magnitude larger than Planck’s constant. Ecosystem equilibria is specified by conservation of biomass and total metabolic energy, along with the principle of maximum entropy at equilibria. Both Bose - Einstein and Fermi - Dirac equilibrium conditions arise in ecosystems applications. The paper concludes with a discussion of some broader aspects of an ecosystem phase space.

Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: a basis for q-exponential distributions.

PubMed

Abe, Sumiyoshi

2002-10-01

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Rényi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingly, mere fittings of observed data by the q-exponential distributions do not lead to identification of the correct physical entropy. Here, stabilities of these entropies, i.e., their behaviors under arbitrary small deformation of a distribution, are examined. It is shown that, among the three, the Tsallis entropy is stable and can provide an entropic basis for the q-exponential distributions, whereas the others are unstable and cannot represent any experimentally observable quantities.

Time dependence of Hawking radiation entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Page, Don N., E-mail: profdonpage@gmail.com

2013-09-01

If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its originalmore » Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4πM{sub 0}{sup 2}, or about 7.509M{sub 0}{sup 2} ≈ 6.268 × 10{sup 76}(M{sub 0}/M{sub s}un){sup 2}, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018M{sub 0}{sup 2} ≈ 1.254 × 10{sup 77}(M{sub 0}/M{sub s}un){sup 2}, and then decreases back down to 4πM{sub 0}{sup 2} = 1.049 × 10{sup 77}(M{sub 0}/M{sub s}un){sup 2}.« less

Quantifying the entropic cost of cellular growth control

NASA Astrophysics Data System (ADS)

De Martino, Daniele; Capuani, Fabrizio; De Martino, Andrea

2017-07-01

Viewing the ways a living cell can organize its metabolism as the phase space of a physical system, regulation can be seen as the ability to reduce the entropy of that space by selecting specific cellular configurations that are, in some sense, optimal. Here we quantify the amount of regulation required to control a cell's growth rate by a maximum-entropy approach to the space of underlying metabolic phenotypes, where a configuration corresponds to a metabolic flux pattern as described by genome-scale models. We link the mean growth rate achieved by a population of cells to the minimal amount of metabolic regulation needed to achieve it through a phase diagram that highlights how growth suppression can be as costly (in regulatory terms) as growth enhancement. Moreover, we provide an interpretation of the inverse temperature β controlling maximum-entropy distributions based on the underlying growth dynamics. Specifically, we show that the asymptotic value of β for a cell population can be expected to depend on (i) the carrying capacity of the environment, (ii) the initial size of the colony, and (iii) the probability distribution from which the inoculum was sampled. Results obtained for E. coli and human cells are found to be remarkably consistent with empirical evidence.

Bayesian maximum entropy integration of ozone observations and model predictions: an application for attainment demonstration in North Carolina.

PubMed

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.

Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics

NASA Astrophysics Data System (ADS)

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.

Pareto versus lognormal: A maximum entropy test

NASA Astrophysics Data System (ADS)

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.

Entropy generation minimization for the sloshing phenomenon in half-full elliptical storage tanks

NASA Astrophysics Data System (ADS)

Saghi, Hassan

2018-02-01

In this paper, the entropy generation in the sloshing phenomenon was obtained in elliptical storage tanks and the optimum geometry of tank was suggested. To do this, a numerical model was developed to simulate the sloshing phenomenon by using coupled Reynolds-Averaged Navier-Stokes (RANS) solver and the Volume-of-Fluid (VOF) method. The RANS equations were discretized and solved using the staggered grid finite difference and SMAC methods, and the available data were used for the model validation. Some parameters consisting of maximum free surface displacement (MFSD), maximum horizontal force exerted on the tank perimeter (MHF), tank perimeter (TP), and total entropy generation (Sgen) were introduced as design criteria for elliptical storage tanks. The entropy generation distribution provides designers with useful information about the causes of the energy loss. In this step, horizontal periodic sway motions as X =amsin(ωt) were applied to elliptical storage tanks with different aspect ratios namely ratios of large diameter to small diameter of elliptical storage tank (AR). Then, the effect of am and ω was studied on the results. The results show that the relation between MFSD and MHF is almost linear relative to the sway motion amplitude. Moreover, the results show that an increase in the AR causes a decrease in the MFSD and MHF. The results, also, show that the relation between MFSD and MHF is nonlinear relative to the sway motion angular frequency. Furthermore, the results show that an increase in the AR causes that the relation between MFSD and MHF becomes linear relative to the sway motion angular frequency. In addition, MFSD and MHF were minimized in a sway motion with a 7 rad/s angular frequency. Finally, the results show that the elliptical storage tank with AR =1.2-1.4 is the optimum section.

Propane spectral resolution enhancement by the maximum entropy method

NASA Technical Reports Server (NTRS)

Bonavito, N. L.; Stewart, K. P.; Hurley, E. J.; Yeh, K. C.; Inguva, R.

1990-01-01

The Burg algorithm for maximum entropy power spectral density estimation is applied to a time series of data obtained from a Michelson interferometer and compared with a standard FFT estimate for resolution capability. The propane transmittance spectrum was estimated by use of the FFT with a 2 to the 18th data sample interferogram, giving a maximum unapodized resolution of 0.06/cm. This estimate was then interpolated by zero filling an additional 2 to the 18th points, and the final resolution was taken to be 0.06/cm. Comparison of the maximum entropy method (MEM) estimate with the FFT was made over a 45/cm region of the spectrum for several increasing record lengths of interferogram data beginning at 2 to the 10th. It is found that over this region the MEM estimate with 2 to the 16th data samples is in close agreement with the FFT estimate using 2 to the 18th samples.

Evidence of the big fix

NASA Astrophysics Data System (ADS)

Hamada, Yuta; Kawai, Hikaru; Kawana, Kiyoharu

2014-06-01

We give an evidence of the Big Fix. The theory of wormholes and multiverse suggests that the parameters of the Standard Model are fixed in such a way that the total entropy at the late stage of the universe is maximized, which we call the maximum entropy principle. In this paper, we discuss how it can be confirmed by the experimental data, and we show that it is indeed true for the Higgs vacuum expectation value vh. We assume that the baryon number is produced by the sphaleron process, and that the current quark masses, the gauge couplings and the Higgs self-coupling are fixed when we vary vh. It turns out that the existence of the atomic nuclei plays a crucial role to maximize the entropy. This is reminiscent of the anthropic principle, however it is required by the fundamental law in our case.

Thermodynamic resource theories, non-commutativity and maximum entropy principles

NASA Astrophysics Data System (ADS)

Lostaglio, Matteo; Jennings, David; Rudolph, Terry

2017-04-01

We discuss some features of thermodynamics in the presence of multiple conserved quantities. We prove a generalisation of Landauer principle illustrating tradeoffs between the erasure costs paid in different ‘currencies’. We then show how the maximum entropy and complete passivity approaches give different answers in the presence of multiple observables. We discuss how this seems to prevent current resource theories from fully capturing thermodynamic aspects of non-commutativity.

Hydrodynamic equations for electrons in graphene obtained from the maximum entropy principle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barletti, Luigi, E-mail: luigi.barletti@unifi.it

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.

Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings

PubMed Central

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

Sample entropy analysis of cervical neoplasia gene-expression signatures

PubMed Central

Botting, Shaleen K; Trzeciakowski, Jerome P; Benoit, Michelle F; Salama, Salama A; Diaz-Arrastia, Concepcion R

2009-01-01

Background We introduce Approximate Entropy as a mathematical method of analysis for microarray data. Approximate entropy is applied here as a method to classify the complex gene expression patterns resultant of a clinical sample set. Since Entropy is a measure of disorder in a system, we believe that by choosing genes which display minimum entropy in normal controls and maximum entropy in the cancerous sample set we will be able to distinguish those genes which display the greatest variability in the cancerous set. Here we describe a method of utilizing Approximate Sample Entropy (ApSE) analysis to identify genes of interest with the highest probability of producing an accurate, predictive, classification model from our data set. Results In the development of a diagnostic gene-expression profile for cervical intraepithelial neoplasia (CIN) and squamous cell carcinoma of the cervix, we identified 208 genes which are unchanging in all normal tissue samples, yet exhibit a random pattern indicative of the genetic instability and heterogeneity of malignant cells. This may be measured in terms of the ApSE when compared to normal tissue. We have validated 10 of these genes on 10 Normal and 20 cancer and CIN3 samples. We report that the predictive value of the sample entropy calculation for these 10 genes of interest is promising (75% sensitivity, 80% specificity for prediction of cervical cancer over CIN3). Conclusion The success of the Approximate Sample Entropy approach in discerning alterations in complexity from biological system with such relatively small sample set, and extracting biologically relevant genes of interest hold great promise. PMID:19232110

Quantifying and minimizing entropy generation in AMTEC cells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hendricks, T.J.; Huang, C.

1997-12-31

Entropy generation in an AMTEC cell represents inherent power loss to the AMTEC cell. Minimizing cell entropy generation directly maximizes cell power generation and efficiency. An internal project is on-going at AMPS to identify, quantify and minimize entropy generation mechanisms within an AMTEC cell, with the goal of determining cost-effective design approaches for maximizing AMTEC cell power generation. Various entropy generation mechanisms have been identified and quantified. The project has investigated several cell design techniques in a solar-driven AMTEC system to minimize cell entropy generation and produce maximum power cell designs. In many cases, various sources of entropy generation aremore » interrelated such that minimizing entropy generation requires cell and system design optimization. Some of the tradeoffs between various entropy generation mechanisms are quantified and explained and their implications on cell design are discussed. The relationship between AMTEC cell power and efficiency and entropy generation is presented and discussed.« less

Biological evolution of replicator systems: towards a quantitative approach.

PubMed

Martin, Osmel; Horvath, J E

2013-04-01

The aim of this work is to study the features of a simple replicator chemical model of the relation between kinetic stability and entropy production under the action of external perturbations. We quantitatively explore the different paths leading to evolution in a toy model where two independent replicators compete for the same substrate. To do that, the same scenario described originally by Pross (J Phys Org Chem 17:312-316, 2004) is revised and new criteria to define the kinetic stability are proposed. Our results suggest that fast replicator populations are continually favored by the effects of strong stochastic environmental fluctuations capable to determine the global population, the former assumed to be the only acting evolution force. We demonstrate that the process is continually driven by strong perturbations only, and that population crashes may be useful proxies for these catastrophic environmental fluctuations. As expected, such behavior is particularly enhanced under very large scale perturbations, suggesting a likely dynamical footprint in the recovery patterns of new species after mass extinction events in the Earth's geological past. Furthermore, the hypothesis that natural selection always favors the faster processes may give theoretical support to different studies that claim the applicability of maximum principles like the Maximum Metabolic Flux (MMF) or Maximum Entropy Productions Principle (MEPP), seen as the main goal of biological evolution.

Biological Evolution of Replicator Systems: Towards a Quantitative Approach

NASA Astrophysics Data System (ADS)

Martin, Osmel; Horvath, J. E.

2013-04-01

The aim of this work is to study the features of a simple replicator chemical model of the relation between kinetic stability and entropy production under the action of external perturbations. We quantitatively explore the different paths leading to evolution in a toy model where two independent replicators compete for the same substrate. To do that, the same scenario described originally by Pross (J Phys Org Chem 17:312-316, 2004) is revised and new criteria to define the kinetic stability are proposed. Our results suggest that fast replicator populations are continually favored by the effects of strong stochastic environmental fluctuations capable to determine the global population, the former assumed to be the only acting evolution force. We demonstrate that the process is continually driven by strong perturbations only, and that population crashes may be useful proxies for these catastrophic environmental fluctuations. As expected, such behavior is particularly enhanced under very large scale perturbations, suggesting a likely dynamical footprint in the recovery patterns of new species after mass extinction events in the Earth's geological past. Furthermore, the hypothesis that natural selection always favors the faster processes may give theoretical support to different studies that claim the applicability of maximum principles like the Maximum Metabolic Flux (MMF) or Maximum Entropy Productions Principle (MEPP), seen as the main goal of biological evolution.

Application of maximum entropy to statistical inference for inversion of data from a single track segment.

PubMed

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.

Grammars Leak: Modeling How Phonotactic Generalizations Interact within the Grammar

ERIC Educational Resources Information Center

Martin, Andrew

2011-01-01

I present evidence from Navajo and English that weaker, gradient versions of morpheme-internal phonotactic constraints, such as the ban on geminate consonants in English, hold even across prosodic word boundaries. I argue that these lexical biases are the result of a MAXIMUM ENTROPY phonotactic learning algorithm that maximizes the probability of…

Bayesian energy landscape tilting: towards concordant models of molecular ensembles.

PubMed

Beauchamp, Kyle A; Pande, Vijay S; Das, Rhiju

2014-03-18

Predicting biological structure has remained challenging for systems such as disordered proteins that take on myriad conformations. Hybrid simulation/experiment strategies have been undermined by difficulties in evaluating errors from computational model inaccuracies and data uncertainties. Building on recent proposals from maximum entropy theory and nonequilibrium thermodynamics, we address these issues through a Bayesian energy landscape tilting (BELT) scheme for computing Bayesian hyperensembles over conformational ensembles. BELT uses Markov chain Monte Carlo to directly sample maximum-entropy conformational ensembles consistent with a set of input experimental observables. To test this framework, we apply BELT to model trialanine, starting from disagreeing simulations with the force fields ff96, ff99, ff99sbnmr-ildn, CHARMM27, and OPLS-AA. BELT incorporation of limited chemical shift and (3)J measurements gives convergent values of the peptide's α, β, and PPII conformational populations in all cases. As a test of predictive power, all five BELT hyperensembles recover set-aside measurements not used in the fitting and report accurate errors, even when starting from highly inaccurate simulations. BELT's principled framework thus enables practical predictions for complex biomolecular systems from discordant simulations and sparse data. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Entropy jump across an inviscid shock wave

NASA Technical Reports Server (NTRS)

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.

Maximum caliber inference of nonequilibrium processes

NASA Astrophysics Data System (ADS)

Otten, Moritz; Stock, Gerhard

2010-07-01

Thirty years ago, Jaynes suggested a general theoretical approach to nonequilibrium statistical mechanics, called maximum caliber (MaxCal) [Annu. Rev. Phys. Chem. 31, 579 (1980)]. MaxCal is a variational principle for dynamics in the same spirit that maximum entropy is a variational principle for equilibrium statistical mechanics. Motivated by the success of maximum entropy inference methods for equilibrium problems, in this work the MaxCal formulation is applied to the inference of nonequilibrium processes. That is, given some time-dependent observables of a dynamical process, one constructs a model that reproduces these input data and moreover, predicts the underlying dynamics of the system. For example, the observables could be some time-resolved measurements of the folding of a protein, which are described by a few-state model of the free energy landscape of the system. MaxCal then calculates the probabilities of an ensemble of trajectories such that on average the data are reproduced. From this probability distribution, any dynamical quantity of the system can be calculated, including population probabilities, fluxes, or waiting time distributions. After briefly reviewing the formalism, the practical numerical implementation of MaxCal in the case of an inference problem is discussed. Adopting various few-state models of increasing complexity, it is demonstrated that the MaxCal principle indeed works as a practical method of inference: The scheme is fairly robust and yields correct results as long as the input data are sufficient. As the method is unbiased and general, it can deal with any kind of time dependency such as oscillatory transients and multitime decays.

An improved wavelet neural network medical image segmentation algorithm with combined maximum entropy

NASA Astrophysics Data System (ADS)

Hu, Xiaoqian; Tao, Jinxu; Ye, Zhongfu; Qiu, Bensheng; Xu, Jinzhang

2018-05-01

In order to solve the problem of medical image segmentation, a wavelet neural network medical image segmentation algorithm based on combined maximum entropy criterion is proposed. Firstly, we use bee colony algorithm to optimize the network parameters of wavelet neural network, get the parameters of network structure, initial weights and threshold values, and so on, we can quickly converge to higher precision when training, and avoid to falling into relative extremum; then the optimal number of iterations is obtained by calculating the maximum entropy of the segmented image, so as to achieve the automatic and accurate segmentation effect. Medical image segmentation experiments show that the proposed algorithm can reduce sample training time effectively and improve convergence precision, and segmentation effect is more accurate and effective than traditional BP neural network (back propagation neural network : a multilayer feed forward neural network which trained according to the error backward propagation algorithm.

Maximum entropy deconvolution of the optical jet of 3C 273

NASA Technical Reports Server (NTRS)

Evans, I. N.; Ford, H. C.; Hui, X.

1989-01-01

The technique of maximum entropy image restoration is applied to the problem of deconvolving the point spread function from a deep, high-quality V band image of the optical jet of 3C 273. The resulting maximum entropy image has an approximate spatial resolution of 0.6 arcsec and has been used to study the morphology of the optical jet. Four regularly-spaced optical knots are clearly evident in the data, together with an optical 'extension' at each end of the optical jet. The jet oscillates around its center of gravity, and the spatial scale of the oscillations is very similar to the spacing between the optical knots. The jet is marginally resolved in the transverse direction and has an asymmetric profile perpendicular to the jet axis. The distribution of V band flux along the length of the jet, and accurate astrometry of the optical knot positions are presented.

Quantum entropy and uncertainty for two-mode squeezed, coherent and intelligent spin states

NASA Technical Reports Server (NTRS)

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.

Entropy and climate. I - ERBE observations of the entropy production of the earth

NASA Technical Reports Server (NTRS)

Stephens, G. L.; O'Brien, D. M.

1993-01-01

An approximate method for estimating the global distributions of the entropy fluxes flowing through the upper boundary of the climate system is introduced, and an estimate of the entropy exchange between the earth and space and the entropy production of the planet is provided. Entropy fluxes calculated from the Earth Radiation Budget Experiment measurements show how the long-wave entropy flux densities dominate the total entropy fluxes at all latitudes compared with the entropy flux densities associated with reflected sunlight, although the short-wave flux densities are important in the context of clear sky-cloudy sky net entropy flux differences. It is suggested that the entropy production of the planet is both constant for the 36 months of data considered and very near its maximum possible value. The mean value of this production is 0.68 x 10 exp 15 W/K, and the amplitude of the annual cycle is approximately 1 to 2 percent of this value.

Mixed memory, (non) Hurst effect, and maximum entropy of rainfall in the tropical Andes

NASA Astrophysics Data System (ADS)

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 < β> = 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.

Structural Evolutions of STOCK Markets Controlled by Generalized Entropy Principles of Complex Systems

NASA Astrophysics Data System (ADS)

Wang, Yi Jiao; Feng, Qing Yi; Chai, Li He

As one of the most important financial markets and one of the main parts of economic system, the stock market has become the research focus in economics. The stock market is a typical complex open system far from equilibrium. Many available models that make huge contribution to researches on market are strong in describing the market however, ignoring strong nonlinear interactions among active agents and weak in reveal underlying dynamic mechanisms of structural evolutions of market. From econophysical perspectives, this paper analyzes the complex interactions among agents and defines the generalized entropy in stock markets. Nonlinear evolutionary dynamic equation for the stock markets is then derived from Maximum Generalized Entropy Principle. Simulations are accordingly conducted for a typical case with the given data, by which the structural evolution of the stock market system is demonstrated. Some discussions and implications are finally provided.

Estimation of Groundwater Radon in North Carolina Using Land Use Regression and Bayesian Maximum Entropy.

PubMed

Messier, Kyle P; Campbell, Ted; Bradley, Philip J; Serre, Marc L

2015-08-18

Radon ((222)Rn) is a naturally occurring chemically inert, colorless, and odorless radioactive gas produced from the decay of uranium ((238)U), which is ubiquitous in rocks and soils worldwide. Exposure to (222)Rn 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 (222)Rn with anisotropic geological and (238)U based explanatory variables is developed, which helps elucidate the factors contributing to elevated (222)Rn across North Carolina. 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 (222)Rn across North Carolina including prediction uncertainty. The LUR-BME model of groundwater (222)Rn results in a leave-one out cross-validation r(2) of 0.46 (Pearson correlation coefficient = 0.68), effectively predicting within the spatial covariance range. Modeled results of (222)Rn concentrations show variability among intrusive felsic geological formations likely due to average bedrock (238)U defined on the basis of overlying stream-sediment (238)U concentrations that is a widely distributed consistently analyzed point-source data.

Learning maximum entropy models from finite-size data sets: A fast data-driven algorithm allows sampling from the posterior distribution.

PubMed

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.

Nonequilibrium thermodynamics and maximum entropy production in the Earth system: applications and implications.

PubMed

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.

Applications of the principle of maximum entropy: from physics to ecology.

PubMed

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.

Entropy Methods For Univariate Distributions in Decision Analysis

NASA Astrophysics Data System (ADS)

Abbas, Ali E.

2003-03-01

One of the most important steps in decision analysis practice is the elicitation of the decision-maker's belief about an uncertainty of interest in the form of a representative probability distribution. However, the probability elicitation process is a task that involves many cognitive and motivational biases. Alternatively, the decision-maker may provide other information about the distribution of interest, such as its moments, and the maximum entropy method can be used to obtain a full distribution subject to the given moment constraints. In practice however, decision makers cannot readily provide moments for the distribution, and are much more comfortable providing information about the fractiles of the distribution of interest or bounds on its cumulative probabilities. In this paper we present a graphical method to determine the maximum entropy distribution between upper and lower probability bounds and provide an interpretation for the shape of the maximum entropy distribution subject to fractile constraints, (FMED). We also discuss the problems with the FMED in that it is discontinuous and flat over each fractile interval. We present a heuristic approximation to a distribution if in addition to its fractiles, we also know it is continuous and work through full examples to illustrate the approach.

Estimation of the magnetic entropy change by means of Landau theory and phenomenological model in La0.6Ca0.2 Sr0.2MnO3/Sb2O3 ceramic composites

NASA Astrophysics Data System (ADS)

Nasri, M.; Dhahri, E.; Hlil, E. K.

2018-06-01

In this paper, magnetocaloric properties of La0.6Ca0.2Sr0.2MnO3/Sb2O3 oxides have been investigated. The composite samples were prepared using the conventional solid-state reaction method. The second-order phase transition can be testified with the positive slope in Arrott plots. An excellent agreement has been found between the -ΔSM values estimated by Landau theory and those obtained using the classical Maxwell relation. The field dependence of the magnetic entropy change analysis shows a power law dependence,|ΔSM|≈Hn , with n(TC) = 0.65. Moreover, the scaling analysis of magnetic entropy change exhibits that ΔSM(T) curves collapse into a single universal curve, indicating that the observed paramagnetic to ferromagnetic phase transition is an authentic second-order phase transition. The maximum value of magnetic entropy change of composites is found to decrease slightly with the further increasing of Sb2O3 concentration. A phenomenological model was used to predict magnetocaloric properties of La0.6Ca0.2Sr0.2MnO3/Sb2O3 composites. The theoretical calculations are compared with the available experimental data.

Soft context clustering for F0 modeling in HMM-based speech synthesis

NASA Astrophysics Data System (ADS)

Khorram, Soheil; Sameti, Hossein; King, Simon

2015-12-01

This paper proposes the use of a new binary decision tree, which we call a soft decision tree, to improve generalization performance compared to the conventional `hard' decision tree method that is used to cluster context-dependent model parameters in statistical parametric speech synthesis. We apply the method to improve the modeling of fundamental frequency, which is an important factor in synthesizing natural-sounding high-quality speech. Conventionally, hard decision tree-clustered hidden Markov models (HMMs) are used, in which each model parameter is assigned to a single leaf node. However, this `divide-and-conquer' approach leads to data sparsity, with the consequence that it suffers from poor generalization, meaning that it is unable to accurately predict parameters for models of unseen contexts: the hard decision tree is a weak function approximator. To alleviate this, we propose the soft decision tree, which is a binary decision tree with soft decisions at the internal nodes. In this soft clustering method, internal nodes select both their children with certain membership degrees; therefore, each node can be viewed as a fuzzy set with a context-dependent membership function. The soft decision tree improves model generalization and provides a superior function approximator because it is able to assign each context to several overlapped leaves. In order to use such a soft decision tree to predict the parameters of the HMM output probability distribution, we derive the smoothest (maximum entropy) distribution which captures all partial first-order moments and a global second-order moment of the training samples. Employing such a soft decision tree architecture with maximum entropy distributions, a novel speech synthesis system is trained using maximum likelihood (ML) parameter re-estimation and synthesis is achieved via maximum output probability parameter generation. In addition, a soft decision tree construction algorithm optimizing a log-likelihood measure is developed. Both subjective and objective evaluations were conducted and indicate a considerable improvement over the conventional method.

Genetic algorithm dynamics on a rugged landscape

NASA Astrophysics Data System (ADS)

Bornholdt, Stefan

1998-04-01

The genetic algorithm is an optimization procedure motivated by biological evolution and is successfully applied to optimization problems in different areas. A statistical mechanics model for its dynamics is proposed based on the parent-child fitness correlation of the genetic operators, making it applicable to general fitness landscapes. It is compared to a recent model based on a maximum entropy ansatz. Finally it is applied to modeling the dynamics of a genetic algorithm on the rugged fitness landscape of the NK model.

Sorption isotherms, thermodynamic properties and glass transition temperature of mucilage extracted from chia seeds (Salvia hispanica L.).

PubMed

Velázquez-Gutiérrez, Sandra Karina; Figueira, Ana Cristina; Rodríguez-Huezo, María Eva; Román-Guerrero, Angélica; Carrillo-Navas, Hector; Pérez-Alonso, César

2015-05-05

Freeze-dried chia mucilage adsorption isotherms were determined at 25, 35 and 40°C and fitted with the Guggenheim-Anderson-de Boer model. The integral thermodynamic properties (enthalpy and entropy) were estimated with the Clausius-Clapeyron equation. Pore radius of the mucilage, calculated with the Kelvin equation, varied from 0.87 to 6.44 nm in the temperature range studied. The point of maximum stability (minimum integral entropy) ranged between 7.56 and 7.63kg H2O per 100 kg of dry solids (d.s.) (water activity of 0.34-0.53). Enthalpy-entropy compensation for the mucilage showed two isokinetic temperatures: (i) one occurring at low moisture contents (0-7.56 kg H2O per 100 kg d.s.), controlled by changes in water entropy; and (ii) another happening in the moisture interval of 7.56-24 kg H2O per 100 kg d.s. and was enthalpy driven. The glass transition temperature Tg of the mucilage fluctuated between 42.93 and 57.93°C. Copyright © 2015 Elsevier Ltd. All rights reserved.

Implications of climate change for bird conservation in the southwestern U.S

Treesearch

Megan M. Friggens; Deborah M. Finch

2015-01-01

Future expected changes in climate and human activity threaten many riparian habitats, particularly in the southwestern U.S. Using Maximum Entropy (MaxEnt3.3.3) modeling, we characterized habitat relationships and generated spatial predictions of habitat suitability for the Lucy’s warbler (Oreothlypis luciae), the Southwestern willow flycatcher (Empidonax...

Entity Relation Detection with Factorial Hidden Markov Models and Maximum Entropy Discriminant Latent Dirichlet Allocations

ERIC Educational Resources Information Center

Li, Dingcheng

2011-01-01

Coreference resolution (CR) and entity relation detection (ERD) aim at finding predefined relations between pairs of entities in text. CR focuses on resolving identity relations while ERD focuses on detecting non-identity relations. Both CR and ERD are important as they can potentially improve other natural language processing (NLP) related tasks…

Time-specific ecologic niche models forecast the risk of hemorrhagic fever with renal syndrome in Dongting Lake district, China, 2005-2010.

PubMed

Liu, Hai-Ning; Gao, Li-Dong; Chowell, Gerardo; Hu, Shi-Xiong; Lin, Xiao-Ling; Li, Xiu-Jun; Ma, Gui-Hua; Huang, Ru; Yang, Hui-Suo; Tian, Huaiyu; Xiao, Hong

2014-01-01

Hemorrhagic fever with renal syndrome (HFRS), a rodent-borne infectious disease, is one of the most serious public health threats in China. Increasing our understanding of the spatial and temporal patterns of HFRS infections could guide local prevention and control strategies. We employed statistical models to analyze HFRS case data together with environmental data from the Dongting Lake district during 2005-2010. Specifically, time-specific ecologic niche models (ENMs) were used to quantify and identify risk factors associated with HFRS transmission as well as forecast seasonal variation in risk across geographic areas. Results showed that the Maximum Entropy model provided the best predictive ability (AUC = 0.755). Time-specific Maximum Entropy models showed that the potential risk areas of HFRS significantly varied across seasons. High-risk areas were mainly found in the southeastern and southwestern areas of the Dongting Lake district. Our findings based on models focused on the spring and winter seasons showed particularly good performance. The potential risk areas were smaller in March, May and August compared with those identified for June, July and October to December. Both normalized difference vegetation index (NDVI) and land use types were found to be the dominant risk factors. Our findings indicate that time-specific ENMs provide a useful tool to forecast the spatial and temporal risk of HFRS.

Clauser-Horne-Shimony-Holt violation and the entropy-concurrence plane

DOE Office of Scientific and Technical Information (OSTI.GOV)

Derkacz, Lukasz; Jakobczyk, Lech

2005-10-15

We characterize violation of Clauser-Horne-Shimony-Holt (CHSH) inequalities for mixed two-qubit states by their mixedness and entanglement. The class of states that have maximum degree of CHSH violation for a given linear entropy is also constructed.

Maximum entropy, fluctuations and priors

NASA Astrophysics Data System (ADS)

Caticha, A.

2001-05-01

The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are distributions with lower entropy supposed to be ruled out. Two applications are given. The first is to the theory of thermodynamic fluctuations. The formulation is exact, covariant under changes of coordinates, and allows fluctuations of both the extensive and the conjugate intensive variables. The second application is to the construction of an objective prior for Bayesian inference. The prior obtained by following the ME method to its inevitable conclusion turns out to be a special case (α=1) of what are currently known under the name of entropic priors. .

Numerical and Statistical Analysis of Fractures in Mechanically Dissimilar Rocks of Limestone Interbedded with Shale from Nash Point in Bristol Channel, South Wales, UK.

NASA Astrophysics Data System (ADS)

Adeoye-Akinde, K.; Gudmundsson, A.

2017-12-01

Heterogeneity and anisotropy, especially with layered strata within the same reservoir, makes the geometry and permeability of an in-situ fracture network challenging to forecast. This study looks at outcrops analogous to reservoir rocks for a better understanding of in-situ fracture networks and permeability, especially fracture formation, propagation, and arrest/deflection. Here, fracture geometry (e.g. length and aperture) from interbedded limestone and shale is combined with statistical and numerical modelling (using the Finite Element Method) to better forecast fracture network properties and permeability. The main aim is to bridge the gap between fracture data obtained at the core level (cm-scale) and at the seismic level (km-scale). Analysis has been made of geometric properties of over 250 fractures from the blue Lias in Nash Point, UK. As fractures propagate, energy is required to keep them going, and according to the laws of thermodynamics, this energy can be linked to entropy. As fractures grow, entropy increases, therefore, the result shows a strong linear correlation between entropy and the scaling exponent of fracture length and aperture-size distributions. Modelling is used to numerically simulate the stress/fracture behaviour in mechanically dissimilar rocks. Results show that the maximum principal compressive stress orientation changes in the host rock as the fracture-induced stress tip moves towards a more compliant (shale) layer. This behaviour can be related to the three mechanisms of fracture arrest/deflection at an interface, namely: elastic mismatch, stress barrier and Cook-Gordon debonding. Tensile stress concentrates at the contact between the stratigraphic layers, ahead of and around the propagating fracture. However, as shale stiffens with time, the stresses concentrated at the contact start to dissipate into it. This can happen in nature through diagenesis, and with greater depth of burial. This study also investigates how induced fractures propagate and interact with existing discontinuities in layered rocks using analogue modelling. Further work will introduce the Maximum Entropy Method for more accurate statistical modelling. This method is mainly useful to forecast likely fracture-size probability distributions from incomplete subsurface information.

Universal and measurable entanglement entropy in the spin-boson model.

PubMed

Kopp, Angela; Le Hur, Karyn

2007-06-01

We study the entanglement between a qubit and its environment from the spin-boson model with Ohmic dissipation. Through a mapping to the anisotropic Kondo model, we derive the entropy of entanglement of the spin E(alpha,Delta,h), where alpha is the dissipation strength, Delta is the tunneling amplitude between qubit states, and h is the level asymmetry. For 1-alpha>Delta/omegac and (Delta,h)TK, E vanishes as (TK/h)2-2alpha, up to a logarithmic correction. For a given h, the maximum entanglement occurs at a value of alpha which lies in the crossover regime h approximately TK. We emphasize the possibility of measuring this entanglement using charge qubits subject to electromagnetic noise.

REMARKS ON THE MAXIMUM ENTROPY METHOD APPLIED TO FINITE TEMPERATURE LATTICE QCD.

DOE Office of Scientific and Technical Information (OSTI.GOV)

UMEDA, T.; MATSUFURU, H.

2005-07-25

We make remarks on the Maximum Entropy Method (MEM) for studies of the spectral function of hadronic correlators in finite temperature lattice QCD. We discuss the virtues and subtlety of MEM in the cases that one does not have enough number of data points such as at finite temperature. Taking these points into account, we suggest several tests which one should examine to keep the reliability for the results, and also apply them using mock and lattice QCD data.

Merging daily sea surface temperature data from multiple satellites using a Bayesian maximum entropy method

NASA Astrophysics Data System (ADS)

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.

It is not the entropy you produce, rather, how you produce it

PubMed Central

Volk, Tyler; Pauluis, Olivier

2010-01-01

The principle of maximum entropy production (MEP) seeks to better understand a large variety of the Earth's environmental and ecological systems by postulating that processes far from thermodynamic equilibrium will ‘adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate’. Our aim in this ‘outside view’, invited by Axel Kleidon, is to focus on what we think is an outstanding challenge for MEP and for irreversible thermodynamics in general: making specific predictions about the relative contribution of individual processes to entropy production. Using studies that compared entropy production in the atmosphere of a dry versus humid Earth, we show that two systems might have the same entropy production rate but very different internal dynamics of dissipation. Using the results of several of the papers in this special issue and a thought experiment, we show that components of life-containing systems can evolve to either lower or raise the entropy production rate. Our analysis makes explicit fundamental questions for MEP that should be brought into focus: can MEP predict not just the overall state of entropy production of a system but also the details of the sub-systems of dissipaters within the system? Which fluxes of the system are those that are most likely to be maximized? How it is possible for MEP theory to be so domain-neutral that it can claim to apply equally to both purely physical–chemical systems and also systems governed by the ‘laws’ of biological evolution? We conclude that the principle of MEP needs to take on the issue of exactly how entropy is produced. PMID:20368249

On the Black-Scholes European Option Pricing Model Robustness and Generality

NASA Astrophysics Data System (ADS)

Takada, Hellinton Hatsuo; de Oliveira Siqueira, José

2008-11-01

The common presentation of the widely known and accepted Black-Scholes European option pricing model explicitly imposes some restrictions such as the geometric Brownian motion assumption for the underlying stock price. In this paper, these usual restrictions are relaxed using maximum entropy principle of information theory, Pearson's distribution system, market frictionless and risk-neutrality theories to the calculation of a unique risk-neutral probability measure calibrated with market parameters.

Developing Soil Moisture Profiles Utilizing Remotely Sensed MW and TIR Based SM Estimates Through Principle of Maximum Entropy

NASA Astrophysics Data System (ADS)

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 data. In this study, vertical soil moisture profiles were developed using the POME model to evaluate an irrigation schedule over a maze field in north central Alabama (USA). The model was validated using both field data and a physically based mathematical model. The results demonstrate that a simple two-constraint entropy model under the assumption of a uniform initial soil moisture distribution can simulate most soil moisture profiles within the field area for 6 different soil types. The results of the irrigation simulation demonstrated that the POME model produced a very efficient irrigation strategy with loss of about 1.9% of the total applied irrigation water. However, areas of fine-textured soil (i.e. silty clay) resulted in plant stress of nearly 30% of the available moisture content due to insufficient water supply on the last day of the drying phase of the irrigation cycle. Overall, the POME approach showed promise as a general strategy to guide irrigation in humid environments, with minimum input requirements.

Stochastic model of the NASA/MSFC ground facility for large space structures with uncertain parameters: The maximum entropy approach, part 2

NASA Technical Reports Server (NTRS)

Hsia, Wei Shen

1989-01-01

A validated technology data base is being developed in the areas of control/structures interaction, deployment dynamics, and system performance for Large Space Structures (LSS). A Ground Facility (GF), in which the dynamics and control systems being considered for LSS applications can be verified, was designed and built. One of the important aspects of the GF is to verify the analytical model for the control system design. The procedure is to describe the control system mathematically as well as possible, then to perform tests on the control system, and finally to factor those results into the mathematical model. The reduction of the order of a higher order control plant was addressed. The computer program was improved for the maximum entropy principle adopted in Hyland's MEOP method. The program was tested against the testing problem. It resulted in a very close match. Two methods of model reduction were examined: Wilson's model reduction method and Hyland's optimal projection (OP) method. Design of a computer program for Hyland's OP method was attempted. Due to the difficulty encountered at the stage where a special matrix factorization technique is needed in order to obtain the required projection matrix, the program was successful up to the finding of the Linear Quadratic Gaussian solution but not beyond. Numerical results along with computer programs which employed ORACLS are presented.

Reconstruction of calmodulin single-molecule FRET states, dye interactions, and CaMKII peptide binding by MultiNest and classic maximum entropy

NASA Astrophysics Data System (ADS)

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.

Reconstruction of Calmodulin Single-Molecule FRET States, Dye-Interactions, and CaMKII Peptide Binding by MultiNest and Classic Maximum Entropy

PubMed Central

DeVore, Matthew S.; Gull, Stephen F.; Johnson, Carey K.

2013-01-01

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 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. PMID:24223465

Reconstruction of Calmodulin Single-Molecule FRET States, Dye-Interactions, and CaMKII Peptide Binding by MultiNest and Classic Maximum Entropy.

PubMed

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.

Information and Entropy

NASA Astrophysics Data System (ADS)

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.

Predicting Changes in Macrophyte Community Structure from Functional Traits in a Freshwater Lake: A Test of Maximum Entropy Model

PubMed Central

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

Development and application of the maximum entropy method and other spectral estimation techniques

NASA Astrophysics Data System (ADS)

King, W. R.

1980-09-01

This summary report is a collection of four separate progress reports prepared under three contracts, which are all sponsored by the Office of Naval Research in Arlington, Virginia. This report contains the results of investigations into the application of the maximum entropy method (MEM), a high resolution, frequency and wavenumber estimation technique. The report also contains a description of two, new, stable, high resolution spectral estimation techniques that is provided in the final report section. Many examples of wavenumber spectral patterns for all investigated techniques are included throughout the report. The maximum entropy method is also known as the maximum entropy spectral analysis (MESA) technique, and both names are used in the report. Many MEM wavenumber spectral patterns are demonstrated using both simulated and measured radar signal and noise data. Methods for obtaining stable MEM wavenumber spectra are discussed, broadband signal detection using the MEM prediction error transform (PET) is discussed, and Doppler radar narrowband signal detection is demonstrated using the MEM technique. It is also shown that MEM cannot be applied to randomly sampled data. The two new, stable, high resolution, spectral estimation techniques discussed in the final report section, are named the Wiener-King and the Fourier spectral estimation techniques. The two new techniques have a similar derivation based upon the Wiener prediction filter, but the two techniques are otherwise quite different. Further development of the techniques and measurement of the technique spectral characteristics is recommended for subsequent investigation.

Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arima, Takashi, E-mail: tks@stat.nitech.ac.jp; Mentrelli, Andrea, E-mail: andrea.mentrelli@unibo.it; Ruggeri, Tommaso, E-mail: tommaso.ruggeri@unibo.it

Molecular extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a molecule is taken into account. On the basis of physical relevance the truncation orders of the two hierarchies are proven to be not independent on each other, and the closure procedures based on the maximum entropy principle (MEP) and on the entropy principle (EP) are proven to be equivalent. The characteristic velocities of the emerging hyperbolic system of differential equations are compared to those obtained for monatomic gases and themore » lower bound estimate for the maximum equilibrium characteristic velocity established for monatomic gases (characterized by only one hierarchy for moments with truncation order of moments N) by Boillat and Ruggeri (1997) (λ{sub (N)}{sup E,max})/(c{sub 0}) ⩾√(6/5 (N−1/2 )),(c{sub 0}=√(5/3 k/m T)) is proven to hold also for rarefied polyatomic gases independently from the degrees of freedom of a molecule. -- Highlights: •Molecular extended thermodynamics of rarefied polyatomic gases is studied. •The relation between two hierarchies of equations for moments is derived. •The equivalence of maximum entropy principle and entropy principle is proven. •The characteristic velocities are compared to those of monatomic gases. •The lower bound of the maximum characteristic velocity is estimated.« less

Using Maximum Entropy to Find Patterns in Genomes

NASA Astrophysics Data System (ADS)

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.

Quantum Rényi relative entropies affirm universality of thermodynamics.

PubMed

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.

Low Streamflow Forcasting using Minimum Relative Entropy

NASA Astrophysics Data System (ADS)

Cui, H.; Singh, V. P.

2013-12-01

Minimum relative entropy spectral analysis is derived in this study, and applied to forecast streamflow time series. Proposed method extends the autocorrelation in the manner that the relative entropy of underlying process is minimized so that time series data can be forecasted. Different prior estimation, such as uniform, exponential and Gaussian assumption, is taken to estimate the spectral density depending on the autocorrelation structure. Seasonal and nonseasonal low streamflow series obtained from Colorado River (Texas) under draught condition is successfully forecasted using proposed method. Minimum relative entropy determines spectral of low streamflow series with higher resolution than conventional method. Forecasted streamflow is compared to the prediction using Burg's maximum entropy spectral analysis (MESA) and Configurational entropy. The advantage and disadvantage of each method in forecasting low streamflow is discussed.

Energy conservation and maximal entropy production in enzyme reactions.

PubMed

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.

Maximum entropy and equations of state for random cellular structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rivier, N.

Random, space-filling cellular structures (biological tissues, metallurgical grain aggregates, foams, etc.) are investigated. Maximum entropy inference under a few constraints yields structural equations of state, relating the size of cells to their topological shape. These relations are known empirically as Lewis's law in Botany, or Desch's relation in Metallurgy. Here, the functional form of the constraints is now known as a priori, and one takes advantage of this arbitrariness to increase the entropy further. The resulting structural equations of state are independent of priors, they are measurable experimentally and constitute therefore a direct test for the applicability of MaxEnt inferencemore » (given that the structure is in statistical equilibrium, a fact which can be tested by another simple relation (Aboav's law)). 23 refs., 2 figs., 1 tab.« less

Use of mutual information to decrease entropy: Implications for the second law of thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lloyd, S.

1989-05-15

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 environmentmore » 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.« less

Exact Maximum-Entropy Estimation with Feynman Diagrams

NASA Astrophysics Data System (ADS)

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.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Naghavi, S. Shahab; Emery, Antoine A.; Hansen, Heine A.

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 Cemore » 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.« less

Nonequilibrium Entropy in a Shock

DOE PAGES

Margolin, Len G.

2017-07-19

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies themore » Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.« less

Nonequilibrium Entropy in a Shock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, Len G.

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies themore » Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khosla, D.; Singh, M.

The estimation of three-dimensional dipole current sources on the cortical surface from the measured magnetoencephalogram (MEG) is a highly under determined inverse problem as there are many {open_quotes}feasible{close_quotes} images which are consistent with the MEG data. Previous approaches to this problem have concentrated on the use of weighted minimum norm inverse methods. While these methods ensure a unique solution, they often produce overly smoothed solutions and exhibit severe sensitivity to noise. In this paper we explore the maximum entropy approach to obtain better solutions to the problem. This estimation technique selects that image from the possible set of feasible imagesmore » which has the maximum entropy permitted by the information available to us. In order to account for the presence of noise in the data, we have also incorporated a noise rejection or likelihood term into our maximum entropy method. This makes our approach mirror a Bayesian maximum a posteriori (MAP) formulation. Additional information from other functional techniques like functional magnetic resonance imaging (fMRI) can be incorporated in the proposed method in the form of a prior bias function to improve solutions. We demonstrate the method with experimental phantom data from a clinical 122 channel MEG system.« less

Role of adjacency-matrix degeneracy in maximum-entropy-weighted network models

NASA Astrophysics Data System (ADS)

Sagarra, O.; Pérez Vicente, C. J.; Díaz-Guilera, A.

2015-11-01

Complex network null models based on entropy maximization are becoming a powerful tool to characterize and analyze data from real systems. However, it is not easy to extract good and unbiased information from these models: A proper understanding of the nature of the underlying events represented in them is crucial. In this paper we emphasize this fact stressing how an accurate counting of configurations compatible with given constraints is fundamental to build good null models for the case of networks with integer-valued adjacency matrices constructed from an aggregation of one or multiple layers. We show how different assumptions about the elements from which the networks are built give rise to distinctively different statistics, even when considering the same observables to match those of real data. We illustrate our findings by applying the formalism to three data sets using an open-source software package accompanying the present work and demonstrate how such differences are clearly seen when measuring network observables.

Respiration-Averaged CT for Attenuation Correction of PET Images – Impact on PET Texture Features in Non-Small Cell Lung Cancer Patients

PubMed Central

Cheng, Nai-Ming; Fang, Yu-Hua Dean; Tsan, Din-Li

2016-01-01

Purpose We compared attenuation correction of PET images with helical CT (PET/HCT) and respiration-averaged CT (PET/ACT) in patients with non-small-cell lung cancer (NSCLC) with the goal of investigating the impact of respiration-averaged CT on 18F FDG PET texture parameters. Materials and Methods A total of 56 patients were enrolled. Tumors were segmented on pretreatment PET images using the adaptive threshold. Twelve different texture parameters were computed: standard uptake value (SUV) entropy, uniformity, entropy, dissimilarity, homogeneity, coarseness, busyness, contrast, complexity, grey-level nonuniformity, zone-size nonuniformity, and high grey-level large zone emphasis. Comparisons of PET/HCT and PET/ACT were performed using Wilcoxon signed-rank tests, intraclass correlation coefficients, and Bland-Altman analysis. Receiver operating characteristic (ROC) curves as well as univariate and multivariate Cox regression analyses were used to identify the parameters significantly associated with disease-specific survival (DSS). A fixed threshold at 45% of the maximum SUV (T45) was used for validation. Results SUV maximum and total lesion glycolysis (TLG) were significantly higher in PET/ACT. However, texture parameters obtained with PET/ACT and PET/HCT showed a high degree of agreement. The lowest levels of variation between the two modalities were observed for SUV entropy (9.7%) and entropy (9.8%). SUV entropy, entropy, and coarseness from both PET/ACT and PET/HCT were significantly associated with DSS. Validation analyses using T45 confirmed the usefulness of SUV entropy and entropy in both PET/HCT and PET/ACT for the prediction of DSS, but only coarseness from PET/ACT achieved the statistical significance threshold. Conclusions Our results indicate that 1) texture parameters from PET/ACT are clinically useful in the prediction of survival in NSCLC patients and 2) SUV entropy and entropy are robust to attenuation correction methods. PMID:26930211

Estimation of temperature in micromaser-type systems

NASA Astrophysics Data System (ADS)

Farajollahi, B.; Jafarzadeh, M.; Rangani Jahromi, H.; Amniat-Talab, M.

2018-06-01

We address the estimation of the number of photons and temperature in a micromaser-type system with Fock state and thermal fields. We analyze the behavior of the quantum Fisher information (QFI) for both fields. In particular, we show that in the Fock state field model, the QFI for non-entangled initial state of the atoms increases monotonously with time, while for entangled initial state of the atoms, it shows oscillatory behavior, leading to non-Markovian dynamics. Moreover, it is observed that the QFI, entropy of entanglement and fidelity have collapse and revival behavior. Focusing on each period that the collapses and revivals occur, we see that the optimal points of the QFI and entanglement coincide. In addition, when one of the subsystems evolved state fidelity becomes maximum, the QFI also achieves its maximum. We also address the evolved fidelity versus the initial state as a good witness of non-Markovianity. Moreover, we interestingly find that the entropy of the composite system can be used as a witness of non-Markovian evolution of the subsystems. For the thermal field model, we similarly investigate the relation among the QFI associated with the temperature, von Neumann entropy, and fidelity. In particular, it is found that at the instants when the maximum values of the QFI are achieved, the entanglement between the two-qubit system and the environment is maximized while the entanglement between the probe and its environment is minimized. Moreover, we show that the thermometry may lead to optimal estimation of practical temperatures. Besides, extending our computation to the two-qubit system, we find that using a two-qubit probe generally leads to more effective estimation than the one-qubit scenario. Finally, we show that initial state entanglement plays a key role in the advent of non-Markovianity and determination of its strength in the composite system and its subsystems.

Predicting the distribution of the Asian tapir in Peninsular Malaysia using maximum entropy modeling.

PubMed

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.

Potential distribution of Mexican primates: modeling the ecological niche with the maximum entropy algorithm.

PubMed

Vidal-García, Francisca; Serio-Silva, Juan Carlos

2011-07-01

We developed a potential distribution model for the tropical rain forest species of primates of southern Mexico: the black howler monkey (Alouatta pigra), the mantled howler monkey (Alouatta palliata), and the spider monkey (Ateles geoffroyi). To do so, we applied the maximum entropy algorithm from the ecological niche modeling program MaxEnt. For each species, we used occurrence records from scientific collections, and published and unpublished sources, and we also used the 19 environmental coverage variables related to precipitation and temperature from WorldClim to develop the models. The predicted distribution of A. pigra was strongly associated with the mean temperature of the warmest quarter (23.6%), whereas the potential distributions of A. palliata and A. geoffroyi were strongly associated with precipitation during the coldest quarter (52.2 and 34.3% respectively). The potential distribution of A. geoffroyi is broader than that of the Alouatta spp. The areas with the greatest probability of presence of A. pigra and A. palliata are strongly associated with riparian vegetation, whereas the presence of A. geoffroyi is more strongly associated with the presence of rain forest. Our most significant contribution is the identification of areas with a high probability of the presence of these primate species, which is information that can be applied to planning future studies and then establishing criteria for the creation of areas to primate conservation in Mexico.

Automatically quantifying the scientific quality and sensationalism of news records mentioning pandemics: validating a maximum entropy machine-learning model.

PubMed

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.

Spatiotemporal modeling of ozone levels in Quebec (Canada): a comparison of kriging, land-use regression (LUR), and combined Bayesian maximum entropy-LUR approaches.

PubMed

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.

Giant onsite electronic entropy enhances the performance of ceria for water splitting

DOE PAGES

Naghavi, S. Shahab; Emery, Antoine A.; Hansen, Heine A.; ...

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 Cemore » 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.« less

Bounding species distribution models

USGS Publications Warehouse

Stohlgren, T.J.; Jarnevich, C.S.; Esaias, W.E.; Morisette, J.T.

2011-01-01

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

Bounding Species Distribution Models

NASA Technical Reports Server (NTRS)

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

2011-01-01

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

Time-Specific Ecologic Niche Models Forecast the Risk of Hemorrhagic Fever with Renal Syndrome in Dongting Lake District, China, 2005–2010

PubMed Central

Lin, Xiao-Ling; Li, Xiu-Jun; Ma, Gui-Hua; Huang, Ru; Yang, Hui-Suo; Tian, Huaiyu; Xiao, Hong

2014-01-01

Background Hemorrhagic fever with renal syndrome (HFRS), a rodent-borne infectious disease, is one of the most serious public health threats in China. Increasing our understanding of the spatial and temporal patterns of HFRS infections could guide local prevention and control strategies. Methodology/Principal Findings We employed statistical models to analyze HFRS case data together with environmental data from the Dongting Lake district during 2005–2010. Specifically, time-specific ecologic niche models (ENMs) were used to quantify and identify risk factors associated with HFRS transmission as well as forecast seasonal variation in risk across geographic areas. Results showed that the Maximum Entropy model provided the best predictive ability (AUC = 0.755). Time-specific Maximum Entropy models showed that the potential risk areas of HFRS significantly varied across seasons. High-risk areas were mainly found in the southeastern and southwestern areas of the Dongting Lake district. Our findings based on models focused on the spring and winter seasons showed particularly good performance. The potential risk areas were smaller in March, May and August compared with those identified for June, July and October to December. Both normalized difference vegetation index (NDVI) and land use types were found to be the dominant risk factors. Conclusions/Significance Our findings indicate that time-specific ENMs provide a useful tool to forecast the spatial and temporal risk of HFRS. PMID:25184252

Maximum Entropy Principle for Transportation

NASA Astrophysics Data System (ADS)

Bilich, F.; DaSilva, R.

2008-11-01

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.

The non-equilibrium statistical mechanics of a simple geophysical fluid dynamics model

NASA Astrophysics Data System (ADS)

Verkley, Wim; Severijns, Camiel

2014-05-01

Lorenz [1] has devised a dynamical system that has proved to be very useful as a benchmark system in geophysical fluid dynamics. The system in its simplest form consists of a periodic array of variables that can be associated with an atmospheric field on a latitude circle. The system is driven by a constant forcing, is damped by linear friction and has a simple advection term that causes the model to behave chaotically if the forcing is large enough. Our aim is to predict the statistics of Lorenz' model on the basis of a given average value of its total energy - obtained from a numerical integration - and the assumption of statistical stationarity. Our method is the principle of maximum entropy [2] which in this case reads: the information entropy of the system's probability density function shall be maximal under the constraints of normalization, a given value of the average total energy and statistical stationarity. Statistical stationarity is incorporated approximately by using `stationarity constraints', i.e., by requiring that the average first and possibly higher-order time-derivatives of the energy are zero in the maximization of entropy. The analysis [3] reveals that, if the first stationarity constraint is used, the resulting probability density function rather accurately reproduces the statistics of the individual variables. If the second stationarity constraint is used as well, the correlations between the variables are also reproduced quite adequately. The method can be generalized straightforwardly and holds the promise of a viable non-equilibrium statistical mechanics of the forced-dissipative systems of geophysical fluid dynamics. [1] E.N. Lorenz, 1996: Predictability - A problem partly solved, in Proc. Seminar on Predictability (ECMWF, Reading, Berkshire, UK), Vol. 1, pp. 1-18. [2] E.T. Jaynes, 2003: Probability Theory - The Logic of Science (Cambridge University Press, Cambridge). [3] W.T.M. Verkley and C.A. Severijns, 2014: The maximum entropy principle applied to a dynamical system proposed by Lorenz, Eur. Phys. J. B, 87:7, http://dx.doi.org/10.1140/epjb/e2013-40681-2 (open access).

Giant onsite electronic entropy enhances the performance of ceria for water splitting.

PubMed

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.

Information entropy of humpback whale songs.

PubMed

Suzuki, Ryuji; Buck, John R; Tyack, Peter L

2006-03-01

The structure of humpback whale (Megaptera novaeangliae) songs was examined using information theory techniques. The song is an ordered sequence of individual sound elements separated by gaps of silence. Song samples were converted into sequences of discrete symbols by both human and automated classifiers. This paper analyzes the song structure in these symbol sequences using information entropy estimators and autocorrelation estimators. Both parametric and nonparametric entropy estimators are applied to the symbol sequences representing the songs. The results provide quantitative evidence consistent with the hierarchical structure proposed for these songs by Payne and McVay [Science 173, 587-597 (1971)]. Specifically, this analysis demonstrates that: (1) There is a strong structural constraint, or syntax, in the generation of the songs, and (2) the structural constraints exhibit periodicities with periods of 6-8 and 180-400 units. This implies that no empirical Markov model is capable of representing the songs' structure. The results are robust to the choice of either human or automated song-to-symbol classifiers. In addition, the entropy estimates indicate that the maximum amount of information that could be communicated by the sequence of sounds made is less than 1 bit per second.

Temporal polyethism, life expectancy, and entropy of workers of the ant Ectatomma vizottoi Almeida, 1987 (Formicidae: Ectatomminae).

PubMed

Santana Vieira, Alexsandro; Desidério Fernandes, Wedson; Fernando Antonialli-Junior, William

2010-05-01

We investigated the changes in the behavioral repertoire over the course of life and determined the life expectancy and entropy of workers of the ant Ectatomma vizottoi. Newly emerged ants were individually marked with model airplane paint for observation of behaviors and determination of the age and life expectancy. Ants were divided into two groups: young and old workers. The 36 behaviors observed were divided into eight categories. Workers exhibit a clear division of tasks throughout their lives, with young workers performing more tasks inside the colony and old workers, outside, unlike species that have small colonies. This species also exhibits an intermediate life expectancy compared to workers of other species that are also intermediary in size. This supports the hypothesis of a relationship between size and maximum life expectancy, but it also suggests that other factors may also be acting in concert. Entropy value shows a high mortality rate during the first life intervals.

The limit behavior of the evolution of the Tsallis entropy in self-gravitating systems

NASA Astrophysics Data System (ADS)

Zheng, Yahui; Du, Jiulin; Liang, Faku

2017-06-01

In this letter, we study the limit behavior of the evolution of the Tsallis entropy in self-gravitating systems. The study is carried out under two different situations, drawing the same conclusion. No matter in the energy transfer process or in the mass transfer process inside the system, when the nonextensive parameter q is more than unity, the total entropy is bounded; on the contrary, when this parameter is less than unity, the total entropy is unbounded. There are proofs in both theory and observation that the q is always more than unity. So the Tsallis entropy in self-gravitating systems generally exhibits a bounded property. This indicates the existence of a global maximum of the Tsallis entropy. It is possible for self-gravitating systems to evolve to thermodynamically stable states.

Use of Anecdotal Occurrence Data in Species Distribution Models: An Example Based on the White-Nosed Coati (Nasua narica) in the American Southwest

PubMed Central

Frey, Jennifer K.; Lewis, Jeremy C.; Guy, Rachel K.; Stuart, James N.

2013-01-01

Simple Summary We evaluated the influence of occurrence records with different reliability on predicted distribution of a unique, rare mammal in the American Southwest, the white-nosed coati (Nasua narica). We concluded that occurrence datasets that include anecdotal records can be used to infer species distributions, providing such data are used only for easily-identifiable species and based on robust modeling methods such as maximum entropy. Use of a reliability rating system is critical for using anecdotal data. Abstract Species distributions are usually inferred from occurrence records. However, these records are prone to errors in spatial precision and reliability. Although influence of spatial errors has been fairly well studied, there is little information on impacts of poor reliability. Reliability of an occurrence record can be influenced by characteristics of the species, conditions during the observation, and observer’s knowledge. Some studies have advocated use of anecdotal data, while others have advocated more stringent evidentiary standards such as only accepting records verified by physical evidence, at least for rare or elusive species. Our goal was to evaluate the influence of occurrence records with different reliability on species distribution models (SDMs) of a unique mammal, the white-nosed coati (Nasua narica) in the American Southwest. We compared SDMs developed using maximum entropy analysis of combined bioclimatic and biophysical variables and based on seven subsets of occurrence records that varied in reliability and spatial precision. We found that the predicted distribution of the coati based on datasets that included anecdotal occurrence records were similar to those based on datasets that only included physical evidence. Coati distribution in the American Southwest was predicted to occur in southwestern New Mexico and southeastern Arizona and was defined primarily by evenness of climate and Madrean woodland and chaparral land-cover types. Coati distribution patterns in this region suggest a good model for understanding the biogeographic structure of range margins. We concluded that occurrence datasets that include anecdotal records can be used to infer species distributions, providing such data are used only for easily-identifiable species and based on robust modeling methods such as maximum entropy. Use of a reliability rating system is critical for using anecdotal data. PMID:26487405

Novel sonar signal processing tool using Shannon entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Quazi, A.H.

1996-06-01

Traditionally, conventional signal processing extracts information from sonar signals using amplitude, signal energy or frequency domain quantities obtained using spectral analysis techniques. The object is to investigate an alternate approach which is entirely different than that of traditional signal processing. This alternate approach is to utilize the Shannon entropy as a tool for the processing of sonar signals with emphasis on detection, classification, and localization leading to superior sonar system performance. Traditionally, sonar signals are processed coherently, semi-coherently, and incoherently, depending upon the a priori knowledge of the signals and noise. Here, the detection, classification, and localization technique will bemore » based on the concept of the entropy of the random process. Under a constant energy constraint, the entropy of a received process bearing finite number of sample points is maximum when hypothesis H{sub 0} (that the received process consists of noise alone) is true and decreases when correlated signal is present (H{sub 1}). Therefore, the strategy used for detection is: (I) Calculate the entropy of the received data; then, (II) compare the entropy with the maximum value; and, finally, (III) make decision: H{sub 1} is assumed if the difference is large compared to pre-assigned threshold and H{sub 0} is otherwise assumed. The test statistics will be different between entropies under H{sub 0} and H{sub 1}. Here, we shall show the simulated results for detecting stationary and non-stationary signals in noise, and results on detection of defects in a Plexiglas bar using an ultrasonic experiment conducted by Hughes. {copyright} {ital 1996 American Institute of Physics.}« less

Maximum entropy models of ecosystem functioning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bertram, Jason, E-mail: jason.bertram@anu.edu.au

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 themore » 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.« less

Nonequilibrium Thermodynamics in Biological Systems

NASA Astrophysics Data System (ADS)

Aoki, I.

2005-12-01

1. Respiration Oxygen-uptake by respiration in organisms decomposes macromolecules such as carbohydrate, protein and lipid and liberates chemical energy of high quality, which is then used to chemical reactions and motions of matter in organisms to support lively order in structure and function in organisms. Finally, this chemical energy becomes heat energy of low quality and is discarded to the outside (dissipation function). Accompanying this heat energy, entropy production which inevitably occurs by irreversibility also is discarded to the outside. Dissipation function and entropy production are estimated from data of respiration. 2. Human body From the observed data of respiration (oxygen absorption), the entropy production in human body can be estimated. Entropy production from 0 to 75 years old human has been obtained, and extrapolated to fertilized egg (beginning of human life) and to 120 years old (maximum period of human life). Entropy production show characteristic behavior in human life span : early rapid increase in short growing phase and later slow decrease in long aging phase. It is proposed that this tendency is ubiquitous and constitutes a Principle of Organization in complex biotic systems. 3. Ecological communities From the data of respiration of eighteen aquatic communities, specific (i.e. per biomass) entropy productions are obtained. They show two phase character with respect to trophic diversity : early increase and later decrease with the increase of trophic diversity. The trophic diversity in these aquatic ecosystems is shown to be positively correlated with the degree of eutrophication, and the degree of eutrophication is an "arrow of time" in the hierarchy of aquatic ecosystems. Hence specific entropy production has the two phase: early increase and later decrease with time. 4. Entropy principle for living systems The Second Law of Thermodynamics has been expressed as follows. 1) In isolated systems, entropy increases with time and approaches to a maximum value. This is well-known classical Clausius principle. 2) In open systems near equilibrium entropy production always decreases with time approaching a minimum stationary level. This is the minimum entropy production principle by Prigogine. These two principle are established ones. However, living systems are not isolated and not near to equilibrium. Hence, these two principles can not be applied to living systems. What is entropy principle for living systems? Answer: Entropy production in living systems consists of multi-stages with time: early increasing, later decreasing and/or intermediate stages. This tendency is supported by various living systems.

Beyond maximum entropy: Fractal Pixon-based image reconstruction

NASA Technical Reports Server (NTRS)

Puetter, Richard C.; Pina, R. K.

1994-01-01

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other competing methods, including Goodness-of-Fit methods such as Least-Squares fitting and Lucy-Richardson reconstruction, as well as Maximum Entropy (ME) methods such as those embodied in the MEMSYS algorithms. Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME. Our past work has shown how uniform information content pixons can be used to develop a 'Super-ME' method in which entropy is maximized exactly. Recently, however, we have developed a superior pixon basis for the image, the Fractal Pixon Basis (FPB). Unlike the Uniform Pixon Basis (UPB) of our 'Super-ME' method, the FPB basis is selected by employing fractal dimensional concepts to assess the inherent structure in the image. The Fractal Pixon Basis results in the best image reconstructions to date, superior to both UPB and the best ME reconstructions. In this paper, we review the theory of the UPB and FPB pixon and apply our methodology to the reconstruction of far-infrared imaging of the galaxy M51. The results of our reconstruction are compared to published reconstructions of the same data using the Lucy-Richardson algorithm, the Maximum Correlation Method developed at IPAC, and the MEMSYS ME algorithms. The results show that our reconstructed image has a spatial resolution a factor of two better than best previous methods (and a factor of 20 finer than the width of the point response function), and detects sources two orders of magnitude fainter than other methods.

Geotechnical parameter spatial distribution stochastic analysis based on multi-precision information assimilation

NASA Astrophysics Data System (ADS)

Wang, C.; Rubin, Y.

2014-12-01

Spatial distribution of important geotechnical parameter named compression modulus Es contributes considerably to the understanding of the underlying geological processes and the adequate assessment of the Es mechanics effects for differential settlement of large continuous structure foundation. These analyses should be derived using an assimilating approach that combines in-situ static cone penetration test (CPT) with borehole experiments. To achieve such a task, the Es distribution of stratum of silty clay in region A of China Expo Center (Shanghai) is studied using the Bayesian-maximum entropy method. This method integrates rigorously and efficiently multi-precision of different geotechnical investigations and sources of uncertainty. Single CPT samplings were modeled as a rational probability density curve by maximum entropy theory. Spatial prior multivariate probability density function (PDF) and likelihood PDF of the CPT positions were built by borehole experiments and the potential value of the prediction point, then, preceding numerical integration on the CPT probability density curves, the posterior probability density curve of the prediction point would be calculated by the Bayesian reverse interpolation framework. The results were compared between Gaussian Sequential Stochastic Simulation and Bayesian methods. The differences were also discussed between single CPT samplings of normal distribution and simulated probability density curve based on maximum entropy theory. It is shown that the study of Es spatial distributions can be improved by properly incorporating CPT sampling variation into interpolation process, whereas more informative estimations are generated by considering CPT Uncertainty for the estimation points. Calculation illustrates the significance of stochastic Es characterization in a stratum, and identifies limitations associated with inadequate geostatistical interpolation techniques. This characterization results will provide a multi-precision information assimilation method of other geotechnical parameters.

[Prediction of potential geographic distribution of Lyme disease in Qinghai province with Maximum Entropy model].

PubMed

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.

Human vision is determined based on information theory.

PubMed

Delgado-Bonal, Alfonso; Martín-Torres, Javier

2016-11-03

It is commonly accepted that the evolution of the human eye has been driven by the maximum intensity of the radiation emitted by the Sun. However, the interpretation of the surrounding environment is constrained not only by the amount of energy received but also by the information content of the radiation. Information is related to entropy rather than energy. The human brain follows Bayesian statistical inference for the interpretation of visual space. The maximization of information occurs in the process of maximizing the entropy. Here, we show that the photopic and scotopic vision absorption peaks in humans are determined not only by the intensity but also by the entropy of radiation. We suggest that through the course of evolution, the human eye has not adapted only to the maximum intensity or to the maximum information but to the optimal wavelength for obtaining information. On Earth, the optimal wavelengths for photopic and scotopic vision are 555 nm and 508 nm, respectively, as inferred experimentally. These optimal wavelengths are determined by the temperature of the star (in this case, the Sun) and by the atmospheric composition.

Human vision is determined based on information theory

NASA Astrophysics Data System (ADS)

Delgado-Bonal, Alfonso; Martín-Torres, Javier

2016-11-01

It is commonly accepted that the evolution of the human eye has been driven by the maximum intensity of the radiation emitted by the Sun. However, the interpretation of the surrounding environment is constrained not only by the amount of energy received but also by the information content of the radiation. Information is related to entropy rather than energy. The human brain follows Bayesian statistical inference for the interpretation of visual space. The maximization of information occurs in the process of maximizing the entropy. Here, we show that the photopic and scotopic vision absorption peaks in humans are determined not only by the intensity but also by the entropy of radiation. We suggest that through the course of evolution, the human eye has not adapted only to the maximum intensity or to the maximum information but to the optimal wavelength for obtaining information. On Earth, the optimal wavelengths for photopic and scotopic vision are 555 nm and 508 nm, respectively, as inferred experimentally. These optimal wavelengths are determined by the temperature of the star (in this case, the Sun) and by the atmospheric composition.

Quantifying Extrinsic Noise in Gene Expression Using the Maximum Entropy Framework

PubMed Central

Dixit, Purushottam D.

2013-01-01

We present a maximum entropy framework to separate intrinsic and extrinsic contributions to noisy gene expression solely from the profile of expression. We express the experimentally accessible probability distribution of the copy number of the gene product (mRNA or protein) by accounting for possible variations in extrinsic factors. The distribution of extrinsic factors is estimated using the maximum entropy principle. Our results show that extrinsic factors qualitatively and quantitatively affect the probability distribution of the gene product. We work out, in detail, the transcription of mRNA from a constitutively expressed promoter in Escherichia coli. We suggest that the variation in extrinsic factors may account for the observed wider-than-Poisson distribution of mRNA copy numbers. We successfully test our framework on a numerical simulation of a simple gene expression scheme that accounts for the variation in extrinsic factors. We also make falsifiable predictions, some of which are tested on previous experiments in E. coli whereas others need verification. Application of the presented framework to more complex situations is also discussed. PMID:23790383

Quantifying extrinsic noise in gene expression using the maximum entropy framework.

PubMed

Dixit, Purushottam D

2013-06-18

We present a maximum entropy framework to separate intrinsic and extrinsic contributions to noisy gene expression solely from the profile of expression. We express the experimentally accessible probability distribution of the copy number of the gene product (mRNA or protein) by accounting for possible variations in extrinsic factors. The distribution of extrinsic factors is estimated using the maximum entropy principle. Our results show that extrinsic factors qualitatively and quantitatively affect the probability distribution of the gene product. We work out, in detail, the transcription of mRNA from a constitutively expressed promoter in Escherichia coli. We suggest that the variation in extrinsic factors may account for the observed wider-than-Poisson distribution of mRNA copy numbers. We successfully test our framework on a numerical simulation of a simple gene expression scheme that accounts for the variation in extrinsic factors. We also make falsifiable predictions, some of which are tested on previous experiments in E. coli whereas others need verification. Application of the presented framework to more complex situations is also discussed. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Human vision is determined based on information theory

PubMed Central

Delgado-Bonal, Alfonso; Martín-Torres, Javier

2016-01-01

It is commonly accepted that the evolution of the human eye has been driven by the maximum intensity of the radiation emitted by the Sun. However, the interpretation of the surrounding environment is constrained not only by the amount of energy received but also by the information content of the radiation. Information is related to entropy rather than energy. The human brain follows Bayesian statistical inference for the interpretation of visual space. The maximization of information occurs in the process of maximizing the entropy. Here, we show that the photopic and scotopic vision absorption peaks in humans are determined not only by the intensity but also by the entropy of radiation. We suggest that through the course of evolution, the human eye has not adapted only to the maximum intensity or to the maximum information but to the optimal wavelength for obtaining information. On Earth, the optimal wavelengths for photopic and scotopic vision are 555 nm and 508 nm, respectively, as inferred experimentally. These optimal wavelengths are determined by the temperature of the star (in this case, the Sun) and by the atmospheric composition. PMID:27808236

Thermodynamics of photon-enhanced thermionic emission solar cells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reck, Kasper, E-mail: kasper.reck@nanotech.dtu.dk; Hansen, Ole, E-mail: ole.hansen@nanotech.dtu.dk; CINF Center for Individual Nanoparticle Functionality, Technical University of Denmark, Kgs. Lyngby 2800

2014-01-13

Photon-enhanced thermionic emission (PETE) cells in which direct photon energy as well as thermal energy can be harvested have recently been suggested as a new candidate for high efficiency solar cells. Here, we present an analytic thermodynamical model for evaluation of the efficiency of PETE solar cells including an analysis of the entropy production due to thermionic emission of general validity. The model is applied to find the maximum efficiency of a PETE cell for given cathode and anode work functions and temperatures.

Classification of pulmonary pathology from breath sounds using the wavelet packet transform and an extreme learning machine.

PubMed

Palaniappan, Rajkumar; Sundaraj, Kenneth; Sundaraj, Sebastian; Huliraj, N; Revadi, S S

2017-06-08

Auscultation is a medical procedure used for the initial diagnosis and assessment of lung and heart diseases. From this perspective, we propose assessing the performance of the extreme learning machine (ELM) classifiers for the diagnosis of pulmonary pathology using breath sounds. Energy and entropy features were extracted from the breath sound using the wavelet packet transform. The statistical significance of the extracted features was evaluated by one-way analysis of variance (ANOVA). The extracted features were inputted into the ELM classifier. The maximum classification accuracies obtained for the conventional validation (CV) of the energy and entropy features were 97.36% and 98.37%, respectively, whereas the accuracies obtained for the cross validation (CRV) of the energy and entropy features were 96.80% and 97.91%, respectively. In addition, maximum classification accuracies of 98.25% and 99.25% were obtained for the CV and CRV of the ensemble features, respectively. The results indicate that the classification accuracy obtained with the ensemble features was higher than those obtained with the energy and entropy features.

Origin and characteristics of high Shannon entropy at the pivot of locally stable rotors: insights from computational simulation.

PubMed

Ganesan, Anand N; Kuklik, Pawel; Gharaviri, Ali; Brooks, Anthony; Chapman, Darius; Lau, Dennis H; Roberts-Thomson, Kurt C; Sanders, Prashanthan

2014-01-01

Rotors are postulated to maintain cardiac fibrillation. Despite the importance of bipolar electrograms in clinical electrophysiology, few data exist on the properties of bipolar electrograms at rotor sites. The pivot of a spiral wave is characterized by relative uncertainty of wavefront propagation direction compared to the periphery. The bipolar electrograms used in electrophysiology recording encode information on both direction and timing of approaching wavefronts. To test the hypothesis that bipolar electrograms from the pivot of rotors have higher Shannon entropy (ShEn) than electrograms recorded at the periphery due to the spatial dynamics of spiral waves. We studied spiral wave propagation in 2-dimensional sheets constructed using a simple cell automaton (FitzHugh-Nagumo), atrial (Courtemanche-Ramirez-Nattel) and ventricular (Luo-Rudy) myocyte cell models and in a geometric model spiral wave. In each system, bipolar electrogram recordings were simulated, and Shannon entropy maps constructed as a measure of electrogram information content. ShEn was consistently highest in the pivoting region associated with the phase singularity of the spiral wave. This property was consistently preserved across; (i) variation of model system (ii) alterations in bipolar electrode spacing, (iii) alternative bipolar electrode orientation (iv) bipolar electrogram filtering and (v) in the presence of rotor meander. Directional activation plots demonstrated that the origin of high ShEn at the pivot was the directional diversity of wavefront propagation observed in this location. The pivot of the rotor is consistently associated with high Shannon entropy of bipolar electrograms despite differences in action potential model, bipolar electrode spacing, signal filtering and rotor meander. Maximum ShEn is co-located with the pivot for rotors observed in the bipolar electrogram recording mode, and may be an intrinsic property of spiral wave dynamic behaviour.

Applications of quantum entropy to statistics

NASA Astrophysics Data System (ADS)

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

This paper develops two generalizations of the maximum entropy (ME) principle. First, Shannon classical entropy is replaced by von Neumann quantum entropy to yield a broader class of information divergences (or penalty functions) for statistics applications. Negative relative quantum entropy enforces convexity, positivity, non-local extensivity and prior correlations such as smoothness. This enables the extension of ME methods from their traditional domain of ill-posed in-verse problems to new applications such as non-parametric density estimation. Second, given a choice of information divergence, a combination of ME and Bayes rule is used to assign both prior and posterior probabilities. Hyperparameters are interpreted as Lagrange multipliers enforcing constraints. Conservation principles are proposed to act statistical regularization and other hyperparameters, such as conservation of information and smoothness. ME provides an alternative to hierarchical Bayes methods.

Optimal behavior of viscoelastic flow at resonant frequencies.

PubMed

Lambert, A A; Ibáñez, G; Cuevas, S; del Río, J A

2004-11-01

The global entropy generation rate in the zero-mean oscillatory flow of a Maxwell fluid in a pipe is analyzed with the aim of determining its behavior at resonant flow conditions. This quantity is calculated explicitly using the analytic expression for the velocity field and assuming isothermal conditions. The global entropy generation rate shows well-defined peaks at the resonant frequencies where the flow displays maximum velocities. It was found that resonant frequencies can be considered optimal in the sense that they maximize the power transmitted to the pulsating flow at the expense of maximum dissipation.

Statistical mechanical theory for steady state systems. VI. Variational principles

NASA Astrophysics Data System (ADS)

Attard, Phil

2006-12-01

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed.

Direct measurement of the electrocaloric effect in poly(vinylidene fluoride-trifluoroethylene-chlorotrifluoroethylene) terpolymer films

NASA Astrophysics Data System (ADS)

Basso, Vittorio; Russo, Florence; Gerard, Jean-François; Pruvost, Sébastien

2013-11-01

We investigated the entropy change in poly(vinylidene fluoride-trifluoroethylene-chlorotrifluoroethylene) (P(VDF-TrFE-CTFE)) films in the temperature range between -5 ∘C and 60 ∘C by direct heat flux calorimetry using Peltier cell heat flux sensors. At the electric field E = 50 MVm-1 the isothermal entropy change attains a maximum of |Δs|=4.2 Jkg-1K-1 at 31∘C with an adiabatic temperature change ΔTad=1.1 K. At temperatures below the maximum, in the range from 25 ∘C to -5 ∘C, the entropy change |Δs | rapidly decreases and the unipolar P vs E relationship becomes hysteretic. This phenomenon is interpreted as the fact that the fluctuations of the polar segments of the polymer chain, responsible for the electrocaloric effect ECE in the polymer, becomes progressively frozen below the relaxor transition.

Maximum Renyi entropy principle for systems with power-law Hamiltonians.

PubMed

Bashkirov, A G

2004-09-24

The Renyi distribution ensuring the maximum of Renyi entropy is investigated for a particular case of a power-law Hamiltonian. Both Lagrange parameters alpha and beta can be eliminated. It is found that beta does not depend on a Renyi parameter q and can be expressed in terms of an exponent kappa of the power-law Hamiltonian and an average energy U. The Renyi entropy for the resulting Renyi distribution reaches its maximal value at q=1/(1+kappa) that can be considered as the most probable value of q when we have no additional information on the behavior of the stochastic process. The Renyi distribution for such q becomes a power-law distribution with the exponent -(kappa+1). When q=1/(1+kappa)+epsilon (0

Maximum one-shot dissipated work from Rényi divergences

NASA Astrophysics Data System (ADS)

Yunger Halpern, Nicole; Garner, Andrew J. P.; Dahlsten, Oscar C. O.; Vedral, Vlatko

2018-05-01

Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, to a relative entropy between quantum states, and to a relative entropy between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity Rényi divergence is proportional to the maximum possible dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics.

Maximum one-shot dissipated work from Rényi divergences.

PubMed

Yunger Halpern, Nicole; Garner, Andrew J P; Dahlsten, Oscar C O; Vedral, Vlatko

2018-05-01

Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, to a relative entropy between quantum states, and to a relative entropy between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity Rényi divergence is proportional to the maximum possible dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics.

Assessing Resilience in Power Grids as a Particular Case of Supply Chain Management

DTIC Science & Technology

2010-03-01

system , the budget needs, or the subject in question, would point to a differentiated approach. Table 1. Protection and Resilience Relationship...coast. Likewise, the US National Oceanic and Atmospheric Administration (NOAA) publishes 19 statistics about severe weather. Climatological models...toward maximum entropy . However, living systems are “open” in the sense that they continually draw upon external sources of energy and maintain a

Estimation of Fine Particulate Matter in Taipei Using Landuse Regression and Bayesian Maximum Entropy Methods

PubMed Central

Yu, Hwa-Lung; Wang, Chih-Hsih; Liu, Ming-Che; Kuo, Yi-Ming

2011-01-01

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. PMID:21776223

Estimation of fine particulate matter in Taipei using landuse regression and bayesian maximum entropy methods.

PubMed

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.

A subjective supply-demand model: the maximum Boltzmann/Shannon entropy solution

NASA Astrophysics Data System (ADS)

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 convex function: the profit intensity reaches its maximum when the probability of transaction is given by the golden ratio rule (\\sqrt {5}-1)/{2} . This condition sets a sharp criterion of validity of the model and can be tested with real market data.

Informational Entropy and Bridge Scour Estimation under Complex Hydraulic Scenarios

NASA Astrophysics Data System (ADS)

Pizarro, Alonso; Link, Oscar; Fiorentino, Mauro; Samela, Caterina; Manfreda, Salvatore

2017-04-01

Bridges are important for society because they allow social, cultural and economic connectivity. Flood events can compromise the safety of bridge piers up to the complete collapse. The Bridge Scour phenomena has been described by empirical formulae deduced from hydraulic laboratory experiments. The range of applicability of such models is restricted by the specific hydraulic conditions or flume geometry used for their derivation (e.g., water depth, mean flow velocity, pier diameter and sediment properties). We seek to identify a general formulation able to capture the main dynamic of the process in order to cover a wide range of hydraulic and geometric configuration, allowing to extend our analysis in different contexts. Therefore, exploiting the Principle of Maximum Entropy (POME) and applying it on the recently proposed dimensionless Effective flow work, W*, we derived a simple model characterized by only one parameter. The proposed Bridge Scour Entropic (BRISENT) model shows good performances under complex hydraulic conditions as well as under steady-state flow. Moreover, the model was able to capture the evolution of scour in several hydraulic configurations even if the model contains only one parameter. Furthermore, results show that the model parameter is controlled by the geometric configurations of the experiment. This offers a possible strategy to obtain a priori model parameter calibration. The BRISENT model represents a good candidate for estimating the time-dependent scour depth under complex hydraulic scenarios. The authors are keen to apply this idea for describing the scour behavior during a real flood event. Keywords: Informational entropy, Sediment transport, Bridge pier scour, Effective flow work.

Steepest entropy ascent for two-state systems with slowly varying Hamiltonians

NASA Astrophysics Data System (ADS)

Militello, Benedetto

2018-05-01

The steepest entropy ascent approach is considered and applied to two-state systems. When the Hamiltonian of the system is time-dependent, the principle of maximum entropy production can still be exploited; arguments to support this fact are given. In the limit of slowly varying Hamiltonians, which allows for the adiabatic approximation for the unitary part of the dynamics, the system exhibits significant robustness to the thermalization process. Specific examples such as a spin in a rotating field and a generic two-state system undergoing an avoided crossing are considered.

Entropy Inequality Violations from Ultraspinning Black Holes.

PubMed

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.

Maximum entropy principal for transportation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bilich, F.; Da Silva, R.

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 utilitymore » 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.« less

a Maximum Entropy Model of the Bearded Capuchin Monkey Habitat Incorporating Topography and Spectral Unmixing Analysis

NASA Astrophysics Data System (ADS)

Howard, A. M.; Bernardes, S.; Nibbelink, N.; Biondi, L.; Presotto, A.; Fragaszy, D. M.; Madden, M.

2012-07-01

Movement patterns of bearded capuchin monkeys (Cebus (Sapajus) libidinosus) in northeastern Brazil are likely impacted by environmental features such as elevation, vegetation density, or vegetation type. Habitat preferences of these monkeys provide insights regarding the impact of environmental features on species ecology and the degree to which they incorporate these features in movement decisions. In order to evaluate environmental features influencing movement patterns and predict areas suitable for movement, we employed a maximum entropy modelling approach, using observation points along capuchin monkey daily routes as species presence points. We combined these presence points with spatial data on important environmental features from remotely sensed data on land cover and topography. A spectral mixing analysis procedure was used to generate fraction images that represent green vegetation, shade and soil of the study area. A Landsat Thematic Mapper scene of the area of study was geometrically and atmospherically corrected and used as input in a Minimum Noise Fraction (MNF) procedure and a linear spectral unmixing approach was used to generate the fraction images. These fraction images and elevation were the environmental layer inputs for our logistic MaxEnt model of capuchin movement. Our models' predictive power (test AUC) was 0.775. Areas of high elevation (>450 m) showed low probabilities of presence, and percent green vegetation was the greatest overall contributor to model AUC. This work has implications for predicting daily movement patterns of capuchins in our field site, as suitability values from our model may relate to habitat preference and facility of movement.

Seasonal Variation in the Spatial Distribution of Basking Sharks (Cetorhinus maximus) in the Lower Bay of Fundy, Canada

PubMed Central

Siders, Zachary A.; Westgate, Andrew J.; Johnston, David W.; Murison, Laurie D.; Koopman, Heather N.

2013-01-01

The local distribution of basking sharks in the Bay of Fundy (BoF) is unknown despite frequent occurrences in the area from May to November. Defining this species’ spatial habitat use is critical for accurately assessing its Special Concern conservation status in Atlantic Canada. We developed maximum entropy distribution models for the lower BoF and the northeast Gulf of Maine (GoM) to describe spatiotemporal variation in habitat use of basking sharks. Under the Maxent framework, we assessed model responses and distribution shifts in relation to known migratory behavior and local prey dynamics. We used 10 years (2002-2011) of basking shark surface sightings from July-October acquired during boat-based surveys in relation to chlorophyll-a concentration, sea surface temperature, bathymetric features, and distance to seafloor contours to assess habitat suitability. Maximum entropy estimations were selected based on AICc criterion and used to predict habitat utilizing three model-fitting routines as well as converted to binary suitable/non-suitable habitat using the maximum sensitivity and specificity threshold. All models predicted habitat better than random (AUC values >0.796). From July-September, a majority of habitat was in the BoF, in waters >100 m deep, and in the Grand Manan Basin. In October, a majority of the habitat shifted southward into the GoM and to areas >200 m deep. Model responses suggest that suitable habitat from July - October is dependent on a mix of distance to the 0, 100, 150, and 200 m contours but in some models on sea surface temperature (July) and chlorophyll-a (August and September). Our results reveal temporally dynamic habitat use of basking sharks within the BoF and GoM. The relative importance of predictor variables suggests that prey dynamics constrained the species distribution in the BoF. Also, suitable habitat shifted minimally from July-September providing opportunities to conserve the species during peak abundance in the region. PMID:24324747

Potential effects of climate change on the distribution range of the main silicate sinker of the Southern Ocean.

PubMed

Pinkernell, Stefan; Beszteri, Bánk

2014-08-01

Fragilariopsis kerguelensis, a dominant diatom species throughout the Antarctic Circumpolar Current, is coined to be one of the main drivers of the biological silicate pump. Here, we study the distribution of this important species and expected consequences of climate change upon it, using correlative species distribution modeling and publicly available presence-only data. As experience with SDM is scarce for marine phytoplankton, this also serves as a pilot study for this organism group. We used the maximum entropy method to calculate distribution models for the diatom F. kerguelensis based on yearly and monthly environmental data (sea surface temperature, salinity, nitrate and silicate concentrations). Observation data were harvested from GBIF and the Global Diatom Database, and for further analyses also from the Hustedt Diatom Collection (BRM). The models were projected on current yearly and seasonal environmental data to study current distribution and its seasonality. Furthermore, we projected the seasonal model on future environmental data obtained from climate models for the year 2100. Projected on current yearly averaged environmental data, all models showed similar distribution patterns for F. kerguelensis. The monthly model showed seasonality, for example, a shift of the southern distribution boundary toward the north in the winter. Projections on future scenarios resulted in a moderately to negligibly shrinking distribution area and a change in seasonality. We found a substantial bias in the publicly available observation datasets, which could be reduced by additional observation records we obtained from the Hustedt Diatom Collection. Present-day distribution patterns inferred from the models coincided well with background knowledge and previous reports about F. kerguelensis distribution, showing that maximum entropy-based distribution models are suitable to map distribution patterns for oceanic planktonic organisms. Our scenario projections indicate moderate effects of climate change upon the biogeography of F. kerguelensis.

Validating predictions from climate envelope models

USGS Publications Warehouse

Watling, J.; Bucklin, D.; Speroterra, C.; Brandt, L.; Cabal, C.; Romañach, Stephanie S.; Mazzotti, Frank J.

2013-01-01

Climate envelope models are a potentially important conservation tool, but their ability to accurately forecast species’ distributional shifts using independent survey data has not been fully evaluated. We created climate envelope models for 12 species of North American breeding birds previously shown to have experienced poleward range shifts. For each species, we evaluated three different approaches to climate envelope modeling that differed in the way they treated climate-induced range expansion and contraction, using random forests and maximum entropy modeling algorithms. All models were calibrated using occurrence data from 1967–1971 (t1) and evaluated using occurrence data from 1998–2002 (t2). Model sensitivity (the ability to correctly classify species presences) was greater using the maximum entropy algorithm than the random forest algorithm. Although sensitivity did not differ significantly among approaches, for many species, sensitivity was maximized using a hybrid approach that assumed range expansion, but not contraction, in t2. Species for which the hybrid approach resulted in the greatest improvement in sensitivity have been reported from more land cover types than species for which there was little difference in sensitivity between hybrid and dynamic approaches, suggesting that habitat generalists may be buffered somewhat against climate-induced range contractions. Specificity (the ability to correctly classify species absences) was maximized using the random forest algorithm and was lowest using the hybrid approach. Overall, our results suggest cautious optimism for the use of climate envelope models to forecast range shifts, but also underscore the importance of considering non-climate drivers of species range limits. The use of alternative climate envelope models that make different assumptions about range expansion and contraction is a new and potentially useful way to help inform our understanding of climate change effects on species.

Characterizing Protease Specificity: How Many Substrates Do We Need?

PubMed Central

Schauperl, Michael; Fuchs, Julian E.; Waldner, Birgit J.; Huber, Roland G.; Kramer, Christian; Liedl, Klaus R.

2015-01-01

Calculation of cleavage entropies allows to quantify, map and compare protease substrate specificity by an information entropy based approach. The metric intrinsically depends on the number of experimentally determined substrates (data points). Thus a statistical analysis of its numerical stability is crucial to estimate the systematic error made by estimating specificity based on a limited number of substrates. In this contribution, we show the mathematical basis for estimating the uncertainty in cleavage entropies. Sets of cleavage entropies are calculated using experimental cleavage data and modeled extreme cases. By analyzing the underlying mathematics and applying statistical tools, a linear dependence of the metric in respect to 1/n was found. This allows us to extrapolate the values to an infinite number of samples and to estimate the errors. Analyzing the errors, a minimum number of 30 substrates was found to be necessary to characterize substrate specificity, in terms of amino acid variability, for a protease (S4-S4’) with an uncertainty of 5 percent. Therefore, we encourage experimental researchers in the protease field to record specificity profiles of novel proteases aiming to identify at least 30 peptide substrates of maximum sequence diversity. We expect a full characterization of protease specificity helpful to rationalize biological functions of proteases and to assist rational drug design. PMID:26559682

Effect of total and pair configurational entropy in determining dynamics of supercooled liquids over a range of densities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, Atreyee; Nandi, Manoj Kumar; Bhattacharyya, Sarika Maitra, E-mail: mb.sarika@ncl.res.in

2016-07-21

In this paper, we present a study of supercooled liquids interacting with the Lennard Jones potential and the corresponding purely repulsive (Weeks-Chandler-Andersen) potential, over a range of densities and temperatures, in order to understand the origin of their different dynamics in spite of their structures being similar. Using the configurational entropy as the thermodynamic marker via the Adam Gibbs relation, we show that the difference in the dynamics of these two systems at low temperatures can be explained from thermodynamics. At higher densities both the thermodynamical and dynamical difference between these model systems decrease, which is quantitatively demonstrated in thismore » paper by calculating different parameters. The study also reveals the origin of the difference in pair entropy despite the similarity in the structure. Although the maximum difference in structure is obtained in the partial radial distribution function of the B type of particles, the rdf of AA pairs and AB pairs gives rise to the differences in the entropy and dynamics. This work supports the observation made in an earlier study [A. Banerjee et al., Phys. Rev. Lett. 113, 225701 (2014)] and shows that they are generic in nature, independent of density.« less

Spatial analysis techniques applied to uranium prospecting in Chihuahua State, Mexico

NASA Astrophysics Data System (ADS)

Hinojosa de la Garza, Octavio R.; Montero Cabrera, María Elena; Sanín, Luz H.; Reyes Cortés, Manuel; Martínez Meyer, Enrique

2014-07-01

To estimate the distribution of uranium minerals in Chihuahua, the advanced statistical model "Maximun Entropy Method" (MaxEnt) was applied. A distinguishing feature of this method is that it can fit more complex models in case of small datasets (x and y data), as is the location of uranium ores in the State of Chihuahua. For georeferencing uranium ores, a database from the United States Geological Survey and workgroup of experts in Mexico was used. The main contribution of this paper is the proposal of maximum entropy techniques to obtain the mineral's potential distribution. For this model were used 24 environmental layers like topography, gravimetry, climate (worldclim), soil properties and others that were useful to project the uranium's distribution across the study area. For the validation of the places predicted by the model, comparisons were done with other research of the Mexican Service of Geological Survey, with direct exploration of specific areas and by talks with former exploration workers of the enterprise "Uranio de Mexico". Results. New uranium areas predicted by the model were validated, finding some relationship between the model predictions and geological faults. Conclusions. Modeling by spatial analysis provides additional information to the energy and mineral resources sectors.

Toward the Application of the Maximum Entropy Production Principle to a Broader Range of Far From Equilibrium Dissipative Systems

NASA Astrophysics Data System (ADS)

Lineweaver, C. H.

2005-12-01

The principle of Maximum Entropy Production (MEP) is being usefully applied to a wide range of non-equilibrium processes including flows in planetary atmospheres and the bioenergetics of photosynthesis. Our goal of applying the principle of maximum entropy production to an even wider range of Far From Equilibrium Dissipative Systems (FFEDS) depends on the reproducibility of the evolution of the system from macro-state A to macro-state B. In an attempt to apply the principle of MEP to astronomical and cosmological structures, we investigate the problematic relationship between gravity and entropy. In the context of open and non-equilibrium systems, we use a generalization of the Gibbs free energy to include the sources of free energy extracted by non-living FFEDS such as hurricanes and convection cells. Redox potential gradients and thermal and pressure gradients provide the free energy for a broad range of FFEDS, both living and non-living. However, these gradients have to be within certain ranges. If the gradients are too weak, FFEDS do not appear. If the gradients are too strong FFEDS disappear. Living and non-living FFEDS often have different source gradients (redox potential gradients vs thermal and pressure gradients) and when they share the same gradient, they exploit different ranges of the gradient. In a preliminary attempt to distinguish living from non-living FFEDS, we investigate the parameter space of: type of gradient and steepness of gradient.

Learning Probabilities From Random Observables in High Dimensions: The Maximum Entropy Distribution and Others

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Cocco, Simona; Monasson, Rémi

2015-11-01

We consider the problem of learning a target probability distribution over a set of N binary variables from the knowledge of the expectation values (with this target distribution) of M observables, drawn uniformly at random. The space of all probability distributions compatible with these M expectation values within some fixed accuracy, called version space, is studied. We introduce a biased measure over the version space, which gives a boost increasing exponentially with the entropy of the distributions and with an arbitrary inverse `temperature' Γ . The choice of Γ allows us to interpolate smoothly between the unbiased measure over all distributions in the version space (Γ =0) and the pointwise measure concentrated at the maximum entropy distribution (Γ → ∞ ). Using the replica method we compute the volume of the version space and other quantities of interest, such as the distance R between the target distribution and the center-of-mass distribution over the version space, as functions of α =(log M)/N and Γ for large N. Phase transitions at critical values of α are found, corresponding to qualitative improvements in the learning of the target distribution and to the decrease of the distance R. However, for fixed α the distance R does not vary with Γ which means that the maximum entropy distribution is not closer to the target distribution than any other distribution compatible with the observable values. Our results are confirmed by Monte Carlo sampling of the version space for small system sizes (N≤ 10).

Optimized Kernel Entropy Components.

PubMed

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.

The magnetic phase transition in Mn{sub 1.1}Fe{sub 0.9}P{sub 1−x}Ge{sub x} magnetocaloric alloys

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, X.; Ramanujan, R. V., E-mail: ramanujan@ntu.edu.sg

Mn-Fe-P-Ge alloys are promising, low cost, high performance candidates for magnetic cooling applications based on the magnetocaloric effect. These alloys undergo a magnetic phase transition which induces a large entropy change (ΔS). Experimental and modeling studies were conducted to study this transition for varying Ge content. Landau theory and the Bean-Rodbell model were applied to Mn{sub 1.1}Fe{sub 0.9}P{sub 1−x}Ge{sub x} (x = 0.26, 0.3, and 0.32) melt spun ribbons to model the phase transition and the associated entropy change. The critical behavior of these alloys was studied. The critical composition range at which the cross over from first order to second ordermore » magnetic transition occurs was determined. The calculated thermodynamic values and critical temperatures were in good agreement with our experimental results. A high maximum entropy change (ΔS) of ∼44.9 J kg{sup −1} K{sup −1} was observed in Mn{sub 1.1}Fe{sub 0.9}P{sub 0.74}Ge{sub 0.26} in a 5 T applied magnetic field. The results suggest that Mn-Fe-P-Ge alloys are very attractive materials for near room temperature magnetic cooling.« less

Spectral Entropies as Information-Theoretic Tools for Complex Network Comparison

NASA Astrophysics Data System (ADS)

De Domenico, Manlio; Biamonte, Jacob

2016-10-01

Any physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we use techniques inspired by quantum statistical mechanics to define an entropy measure for complex networks and to develop a set of information-theoretic tools, based on network spectral properties, such as Rényi q entropy, generalized Kullback-Leibler and Jensen-Shannon divergences, the latter allowing us to define a natural distance measure between complex networks. First, we show that by minimizing the Kullback-Leibler divergence between an observed network and a parametric network model, inference of model parameter(s) by means of maximum-likelihood estimation can be achieved and model selection can be performed with appropriate information criteria. Second, we show that the information-theoretic metric quantifies the distance between pairs of networks and we can use it, for instance, to cluster the layers of a multilayer system. By applying this framework to networks corresponding to sites of the human microbiome, we perform hierarchical cluster analysis and recover with high accuracy existing community-based associations. Our results imply that spectral-based statistical inference in complex networks results in demonstrably superior performance as well as a conceptual backbone, filling a gap towards a network information theory.

Hyperbolic heat conduction, effective temperature, and third law for nonequilibrium systems with heat flux

NASA Astrophysics Data System (ADS)

Sobolev, S. L.

2018-02-01

Some analogies between different nonequilibrium heat conduction models, particularly random walk, the discrete variable model, and the Boltzmann transport equation with the single relaxation time approximation, have been discussed. We show that, under an assumption of a finite value of the heat carrier velocity, these models lead to the hyperbolic heat conduction equation and the modified Fourier law with relaxation term. Corresponding effective temperature and entropy have been introduced and analyzed. It has been demonstrated that the effective temperature, defined as a geometric mean of the kinetic temperatures of the heat carriers moving in opposite directions, acts as a criterion for thermalization and is a nonlinear function of the kinetic temperature and heat flux. It is shown that, under highly nonequilibrium conditions when the heat flux tends to its maximum possible value, the effective temperature, heat capacity, and local entropy go to zero even at a nonzero equilibrium temperature. This provides a possible generalization of the third law to nonequilibrium situations. Analogies and differences between the proposed effective temperature and some other definitions of a temperature in nonequilibrium state, particularly for active systems, disordered semiconductors under electric field, and adiabatic gas flow, have been shown and discussed. Illustrative examples of the behavior of the effective temperature and entropy during nonequilibrium heat conduction in a monatomic gas and a strong shockwave have been analyzed.

An Entropy-Based Measure for Assessing Fuzziness in Logistic Regression

PubMed Central

Weiss, Brandi A.; Dardick, William

2015-01-01

This article introduces an entropy-based measure of data–model fit that can be used to assess the quality of logistic regression models. Entropy has previously been used in mixture-modeling to quantify how well individuals are classified into latent classes. The current study proposes the use of entropy for logistic regression models to quantify the quality of classification and separation of group membership. Entropy complements preexisting measures of data–model fit and provides unique information not contained in other measures. Hypothetical data scenarios, an applied example, and Monte Carlo simulation results are used to demonstrate the application of entropy in logistic regression. Entropy should be used in conjunction with other measures of data–model fit to assess how well logistic regression models classify cases into observed categories. PMID:29795897

An Entropy-Based Measure for Assessing Fuzziness in Logistic Regression.

PubMed

Weiss, Brandi A; Dardick, William

2016-12-01

This article introduces an entropy-based measure of data-model fit that can be used to assess the quality of logistic regression models. Entropy has previously been used in mixture-modeling to quantify how well individuals are classified into latent classes. The current study proposes the use of entropy for logistic regression models to quantify the quality of classification and separation of group membership. Entropy complements preexisting measures of data-model fit and provides unique information not contained in other measures. Hypothetical data scenarios, an applied example, and Monte Carlo simulation results are used to demonstrate the application of entropy in logistic regression. Entropy should be used in conjunction with other measures of data-model fit to assess how well logistic regression models classify cases into observed categories.

Sensitivity of Tropical Cyclone Spinup Time to the Initial Entropy Deficit

NASA Astrophysics Data System (ADS)

Tang, B.; Corbosiero, K. L.; Rios-Berrios, R.; Alland, J.; Berman, J.

2014-12-01

The development timescale of a tropical cyclone from genesis to the start of rapid intensification in an axisymmetric model is hypothesized to be a function of the initial entropy deficit. We run a set of idealized simulations in which the initial entropy deficit between the boundary layer and free troposphere varies from 0 to 100 J kg-1 K-1. The development timescale is measured by changes in the integrated kinetic energy of the low-level vortex. This timescale is inversely related to the mean mass flux during the tropical cyclone gestation period. The mean mass flux, in turn, is a function of the statistics of convective updrafts and downdrafts. Contour frequency by altitude diagrams show that entrainment of dry air into updrafts is predominately responsible for differences in the mass flux between the experiments, while downdrafts play a secondary role. Analyses of the potential and kinetic energy budgets indicate less efficient conversion of available potential energy to kinetic energy in the experiments with higher entropy deficits. Entrainment leads to the loss of buoyancy and the destruction of available potential energy. In the presence of strong downdrafts, there can even be a reversal of the conversion term. Weaker and more radially confined radial inflow results in less convergence of angular momentum in the experiments with higher entropy deficits. The result is a slower vortex spinup and a reduction in steady-state vortex size, despite similar steady-state maximum intensities among the experiments.

Analysis of rapid eye movement periodicity in narcoleptics based on maximum entropy method.

PubMed

Honma, H; Ohtomo, N; Kohsaka, M; Fukuda, N; Kobayashi, R; Sakakibara, S; Nakamura, F; Koyama, T

1999-04-01

We examined REM sleep periodicity in typical narcoleptics and patients who had shown signs of a narcoleptic tetrad without HLA-DRB1*1501/DQB1*0602 or DR2 antigens, using spectral analysis based on the maximum entropy method. The REM sleep period of typical narcoleptics showed two peaks, one at 70-90 min and one at 110-130 min at night, and a single peak at around 70-90 min during the daytime. The nocturnal REM sleep period of typical narcoleptics may be composed of several different periods, one of which corresponds to that of their daytime REM sleep.

A homotopy algorithm for synthesizing robust controllers for flexible structures via the maximum entropy design equations

NASA Technical Reports Server (NTRS)

Collins, Emmanuel G., Jr.; Richter, Stephen

1990-01-01

One well known deficiency of LQG compensators is that they do not guarantee any measure of robustness. This deficiency is especially highlighted when considering control design for complex systems such as flexible structures. There has thus been a need to generalize LQG theory to incorporate robustness constraints. Here we describe the maximum entropy approach to robust control design for flexible structures, a generalization of LQG theory, pioneered by Hyland, which has proved useful in practice. The design equations consist of a set of coupled Riccati and Lyapunov equations. A homotopy algorithm that is used to solve these design equations is presented.

16QAM Blind Equalization via Maximum Entropy Density Approximation Technique and Nonlinear Lagrange Multipliers

PubMed Central

Mauda, R.; Pinchas, M.

2014-01-01

Recently a new blind equalization method was proposed for the 16QAM constellation input inspired by the maximum entropy density approximation technique with improved equalization performance compared to the maximum entropy approach, Godard's algorithm, and others. In addition, an approximated expression for the minimum mean square error (MSE) was obtained. The idea was to find those Lagrange multipliers that bring the approximated MSE to minimum. Since the derivation of the obtained MSE with respect to the Lagrange multipliers leads to a nonlinear equation for the Lagrange multipliers, the part in the MSE expression that caused the nonlinearity in the equation for the Lagrange multipliers was ignored. Thus, the obtained Lagrange multipliers were not those Lagrange multipliers that bring the approximated MSE to minimum. In this paper, we derive a new set of Lagrange multipliers based on the nonlinear expression for the Lagrange multipliers obtained from minimizing the approximated MSE with respect to the Lagrange multipliers. Simulation results indicate that for the high signal to noise ratio (SNR) case, a faster convergence rate is obtained for a channel causing a high initial intersymbol interference (ISI) while the same equalization performance is obtained for an easy channel (initial ISI low). PMID:24723813

Using maximum entropy to predict suitable habitat for the endangered dwarf wedgemussel in the Maryland Coastal Plain

USGS Publications Warehouse

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.

Entropy in self-similar shock profiles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, Len G.; Reisner, Jon Michael; Jordan, Pedro M.

In this paper, we study the structure of a gaseous shock, and in particular the distribution of entropy within, in both a thermodynamics and a statistical mechanics context. The problem of shock structure has a long and distinguished history that we review. We employ the Navier–Stokes equations to construct a self–similar version of Becker’s solution for a shock assuming a particular (physically plausible) Prandtl number; that solution reproduces the well–known result of Morduchow & Libby that features a maximum of the equilibrium entropy inside the shock profile. We then construct an entropy profile, based on gas kinetic theory, that ismore » smooth and monotonically increasing. The extension of equilibrium thermodynamics to irreversible processes is based in part on the assumption of local thermodynamic equilibrium. We show that this assumption is not valid except for the weakest shocks. Finally, we conclude by hypothesizing a thermodynamic nonequilibrium entropy and demonstrating that it closely estimates the gas kinetic nonequilibrium entropy within a shock.« less

Entropy in self-similar shock profiles

DOE PAGES

Margolin, Len G.; Reisner, Jon Michael; Jordan, Pedro M.

2017-07-16

In this paper, we study the structure of a gaseous shock, and in particular the distribution of entropy within, in both a thermodynamics and a statistical mechanics context. The problem of shock structure has a long and distinguished history that we review. We employ the Navier–Stokes equations to construct a self–similar version of Becker’s solution for a shock assuming a particular (physically plausible) Prandtl number; that solution reproduces the well–known result of Morduchow & Libby that features a maximum of the equilibrium entropy inside the shock profile. We then construct an entropy profile, based on gas kinetic theory, that ismore » smooth and monotonically increasing. The extension of equilibrium thermodynamics to irreversible processes is based in part on the assumption of local thermodynamic equilibrium. We show that this assumption is not valid except for the weakest shocks. Finally, we conclude by hypothesizing a thermodynamic nonequilibrium entropy and demonstrating that it closely estimates the gas kinetic nonequilibrium entropy within a shock.« less

Data free inference with processed data products

DOE PAGES

Chowdhary, K.; Najm, H. N.

2014-07-12

Here, we consider the context of probabilistic inference of model parameters given error bars or confidence intervals on model output values, when the data is unavailable. We introduce a class of algorithms in a Bayesian framework, relying on maximum entropy arguments and approximate Bayesian computation methods, to generate consistent data with the given summary statistics. Once we obtain consistent data sets, we pool the respective posteriors, to arrive at a single, averaged density on the parameters. This approach allows us to perform accurate forward uncertainty propagation consistent with the reported statistics.

Rapidity distributions of hadrons in proton-nucleus collisions

NASA Astrophysics Data System (ADS)

Pirner, H. J.; Kopeliovich, B. Z.

2018-05-01

We study proton-lead collisions with a new model for the Fock states of the incoming proton. The number of collisions that the proton experiences selects the appropriate Fock state of the proton, which generates a multiple of p p -like rapidity distributions. We take as input the p p maximum entropy distributions, shifting the respective center-of-mass rapidities and reducing the available energies. A comparison with existing data at 5 TeV is made, and results for 8 TeV are presented. We also explore the high multiplicity data in this model.

Finding the quantum thermoelectric with maximal efficiency and minimal entropy production at given power output

NASA Astrophysics Data System (ADS)

Whitney, Robert S.

2015-03-01

We investigate the nonlinear scattering theory for quantum systems with strong Seebeck and Peltier effects, and consider their use as heat engines and refrigerators with finite power outputs. This paper gives detailed derivations of the results summarized in a previous paper [R. S. Whitney, Phys. Rev. Lett. 112, 130601 (2014), 10.1103/PhysRevLett.112.130601]. It shows how to use the scattering theory to find (i) the quantum thermoelectric with maximum possible power output, and (ii) the quantum thermoelectric with maximum efficiency at given power output. The latter corresponds to a minimal entropy production at that power output. These quantities are of quantum origin since they depend on system size over electronic wavelength, and so have no analog in classical thermodynamics. The maximal efficiency coincides with Carnot efficiency at zero power output, but decreases with increasing power output. This gives a fundamental lower bound on entropy production, which means that reversibility (in the thermodynamic sense) is impossible for finite power output. The suppression of efficiency by (nonlinear) phonon and photon effects is addressed in detail; when these effects are strong, maximum efficiency coincides with maximum power. Finally, we show in particular limits (typically without magnetic fields) that relaxation within the quantum system does not allow the system to exceed the bounds derived for relaxation-free systems, however, a general proof of this remains elusive.

Maximum Entropy Approach in Dynamic Contrast-Enhanced Magnetic Resonance Imaging.

PubMed

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.

Application of a multiscale maximum entropy image restoration algorithm to HXMT observations

NASA Astrophysics Data System (ADS)

Guan, Ju; Song, Li-Ming; Huo, Zhuo-Xi

2016-08-01

This paper introduces a multiscale maximum entropy (MSME) algorithm for image restoration of the Hard X-ray Modulation Telescope (HXMT), which is a collimated scan X-ray satellite mainly devoted to a sensitive all-sky survey and pointed observations in the 1-250 keV range. The novelty of the MSME method is to use wavelet decomposition and multiresolution support to control noise amplification at different scales. Our work is focused on the application and modification of this method to restore diffuse sources detected by HXMT scanning observations. An improved method, the ensemble multiscale maximum entropy (EMSME) algorithm, is proposed to alleviate the problem of mode mixing exiting in MSME. Simulations have been performed on the detection of the diffuse source Cen A by HXMT in all-sky survey mode. The results show that the MSME method is adapted to the deconvolution task of HXMT for diffuse source detection and the improved method could suppress noise and improve the correlation and signal-to-noise ratio, thus proving itself a better algorithm for image restoration. Through one all-sky survey, HXMT could reach a capacity of detecting a diffuse source with maximum differential flux of 0.5 mCrab. Supported by Strategic Priority Research Program on Space Science, Chinese Academy of Sciences (XDA04010300) and National Natural Science Foundation of China (11403014)

Uncertainty vs. Information (Invited)

NASA Astrophysics Data System (ADS)

Nearing, Grey

2017-04-01

Information theory is the branch of logic that describes how rational epistemic states evolve in the presence of empirical data (Knuth, 2005), and any logic of science is incomplete without such a theory. Developing a formal philosophy of science that recognizes this fact results in essentially trivial solutions to several longstanding problems are generally considered intractable, including: • Alleviating the need for any likelihood function or error model. • Derivation of purely logical falsification criteria for hypothesis testing. • Specification of a general quantitative method for process-level model diagnostics. More generally, I make the following arguments: 1. Model evaluation should not proceed by quantifying and/or reducing error or uncertainty, and instead should be approached as a problem of ensuring that our models contain as much information as our experimental data. I propose that the latter is the only question a scientist actually has the ability to ask. 2. Instead of building geophysical models as solutions to differential equations that represent conservation laws, we should build models as maximum entropy distributions constrained by conservation symmetries. This will allow us to derive predictive probabilities directly from first principles. Knuth, K. H. (2005) 'Lattice duality: The origin of probability and entropy', Neurocomputing, 67, pp. 245-274.

Towards operational interpretations of generalized entropies

NASA Astrophysics Data System (ADS)

Topsøe, Flemming

2010-12-01

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

Gypsophila bermejoi G. López: A possible case of speciation repressed by bioclimatic factors.

PubMed

de Luis, Miguel; Bartolomé, Carmen; García Cardo, Óscar; Álvarez-Jiménez, Julio

2018-01-01

Gypsophila bermejoi G. López is an allopolyploid species derived from the parental G. struthium L. subsp. struthium and G. tomentosa L. All these plants are gypsophytes endemic to the Iberian Peninsula of particular ecological, evolutionary and biochemical interest. In this study, we present evidence of a possible repression on the process of G. bermejoi speciation by climatic factors. We modelled the ecological niches of the three taxa considered here using a maximum entropy approach and employing a series of bioclimatic variables. Subsequently, we projected these models onto the geographical space of the Iberian Peninsula in the present age and at two past ages: the Last Glacial Maximum and the mid-Holocene period. Furthermore, we compared these niches using the statistical method devised by Warren to calculate their degree of overlap. We also evaluated the evolution of the bioclimatic habitat suitability at those sites were the soil favors the growth of these species. Both the maximum entropy model and the degree of overlap indicated that the ecological behavior of the hybrid differs notably from that of the parental species. During the Last Glacial Maximum, the two parental species appear to take refuge in the western coastal strip of the Peninsula, a region in which there are virtually no sites where G. bermejoi could potentially be found. However, in the mid-Holocene period the suitability of G. bermejoi to sites with favorable soils shifts from almost null to a strong adaptation, a clear change in this tendency. These results suggest that the ecological niches of hybrid allopolyploids can be considerably different to those of their parental species, which may have evolutionary and ecologically relevant consequences. The data obtained indicate that certain bioclimatic variables may possibly repress the processes by which new species are formed. The difference in the ecological niche of G. bermejoi with respect to its parental species prevented it from prospering during the Last Glacial Maximum. However, the climatic change in the mid-Holocene period released this block and as such, it permitted the new species to establish itself. Accordingly, we favor a recent origin of the current populations of G. bermejoi.

Gypsophila bermejoi G. López: A possible case of speciation repressed by bioclimatic factors

PubMed Central

de Luis, Miguel; García Cardo, Óscar; Álvarez-Jiménez, Julio

2018-01-01

Gypsophila bermejoi G. López is an allopolyploid species derived from the parental G. struthium L. subsp. struthium and G. tomentosa L. All these plants are gypsophytes endemic to the Iberian Peninsula of particular ecological, evolutionary and biochemical interest. In this study, we present evidence of a possible repression on the process of G. bermejoi speciation by climatic factors. We modelled the ecological niches of the three taxa considered here using a maximum entropy approach and employing a series of bioclimatic variables. Subsequently, we projected these models onto the geographical space of the Iberian Peninsula in the present age and at two past ages: the Last Glacial Maximum and the mid-Holocene period. Furthermore, we compared these niches using the statistical method devised by Warren to calculate their degree of overlap. We also evaluated the evolution of the bioclimatic habitat suitability at those sites were the soil favors the growth of these species. Both the maximum entropy model and the degree of overlap indicated that the ecological behavior of the hybrid differs notably from that of the parental species. During the Last Glacial Maximum, the two parental species appear to take refuge in the western coastal strip of the Peninsula, a region in which there are virtually no sites where G. bermejoi could potentially be found. However, in the mid-Holocene period the suitability of G. bermejoi to sites with favorable soils shifts from almost null to a strong adaptation, a clear change in this tendency. These results suggest that the ecological niches of hybrid allopolyploids can be considerably different to those of their parental species, which may have evolutionary and ecologically relevant consequences. The data obtained indicate that certain bioclimatic variables may possibly repress the processes by which new species are formed. The difference in the ecological niche of G. bermejoi with respect to its parental species prevented it from prospering during the Last Glacial Maximum. However, the climatic change in the mid-Holocene period released this block and as such, it permitted the new species to establish itself. Accordingly, we favor a recent origin of the current populations of G. bermejoi. PMID:29338010

Communication: Introducing prescribed biases in out-of-equilibrium Markov models

NASA Astrophysics Data System (ADS)

Dixit, Purushottam D.

2018-03-01

Markov models are often used in modeling complex out-of-equilibrium chemical and biochemical systems. However, many times their predictions do not agree with experiments. We need a systematic framework to update existing Markov models to make them consistent with constraints that are derived from experiments. Here, we present a framework based on the principle of maximum relative path entropy (minimum Kullback-Leibler divergence) to update Markov models using stationary state and dynamical trajectory-based constraints. We illustrate the framework using a biochemical model network of growth factor-based signaling. We also show how to find the closest detailed balanced Markov model to a given Markov model. Further applications and generalizations are discussed.

Entropy of international trades

NASA Astrophysics Data System (ADS)

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.

Jarzynski equality in the context of maximum path entropy

NASA Astrophysics Data System (ADS)

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.

High resolution schemes and the entropy condition

NASA Technical Reports Server (NTRS)

Osher, S.; Chakravarthy, S.

1983-01-01

A systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five point band width, approximations to scalar conservation laws, is presented. These schemes are constructed to also satisfy a single discrete entropy inequality. Thus, in the convex flux case, convergence is proven to be the unique physically correct solution. For hyperbolic systems of conservation laws, this construction is used formally to extend the first author's first order accurate scheme, and show (under some minor technical hypotheses) that limit solutions satisfy an entropy inequality. Results concerning discrete shocks, a maximum principle, and maximal order of accuracy are obtained. Numerical applications are also presented.

Multivariate quadrature for representing cloud condensation nuclei activity of aerosol populations

DOE PAGES

Fierce, Laura; McGraw, Robert L.

2017-07-26

Here, sparse representations of atmospheric aerosols are needed for efficient regional- and global-scale chemical transport models. Here we introduce a new framework for representing aerosol distributions, based on the quadrature method of moments. Given a set of moment constraints, we show how linear programming, combined with an entropy-inspired cost function, can be used to construct optimized quadrature representations of aerosol distributions. The sparse representations derived from this approach accurately reproduce cloud condensation nuclei (CCN) activity for realistically complex distributions simulated by a particleresolved model. Additionally, the linear programming techniques described in this study can be used to bound key aerosolmore » properties, such as the number concentration of CCN. Unlike the commonly used sparse representations, such as modal and sectional schemes, the maximum-entropy approach described here is not constrained to pre-determined size bins or assumed distribution shapes. This study is a first step toward a particle-based aerosol scheme that will track multivariate aerosol distributions with sufficient computational efficiency for large-scale simulations.« less

Multivariate quadrature for representing cloud condensation nuclei activity of aerosol populations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fierce, Laura; McGraw, Robert L.

Here, sparse representations of atmospheric aerosols are needed for efficient regional- and global-scale chemical transport models. Here we introduce a new framework for representing aerosol distributions, based on the quadrature method of moments. Given a set of moment constraints, we show how linear programming, combined with an entropy-inspired cost function, can be used to construct optimized quadrature representations of aerosol distributions. The sparse representations derived from this approach accurately reproduce cloud condensation nuclei (CCN) activity for realistically complex distributions simulated by a particleresolved model. Additionally, the linear programming techniques described in this study can be used to bound key aerosolmore » properties, such as the number concentration of CCN. Unlike the commonly used sparse representations, such as modal and sectional schemes, the maximum-entropy approach described here is not constrained to pre-determined size bins or assumed distribution shapes. This study is a first step toward a particle-based aerosol scheme that will track multivariate aerosol distributions with sufficient computational efficiency for large-scale simulations.« less

Excess entropy and crystallization in Stillinger-Weber and Lennard-Jones fluids

NASA Astrophysics Data System (ADS)

Dhabal, Debdas; Nguyen, Andrew Huy; Singh, Murari; Khatua, Prabir; Molinero, Valeria; Bandyopadhyay, Sanjoy; Chakravarty, Charusita

2015-10-01

Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW16). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW20), silicon (SW21), and water (SW23.15 or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. The tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by Strip, is also studied. Strip is a good entropy estimator for liquids where pair and triplet correlations are important such as Ge and Si, but loses accuracy for purely pair-dominated liquids, like LJ fluid, or near the crystallization temperature (Tthr). Since local tetrahedral order is compatible with both liquid and crystalline states, the reorganisation of tetrahedral liquids is accompanied by a clear rise in the pair, triplet, and thermodynamic contributions to the heat capacity, resulting in the heat capacity anomaly. In contrast, the pair-dominated liquids show increasing dominance of triplet correlations on approaching crystallization but no sharp rise in either the pair or thermodynamic heat capacities.

Optimal information networks: Application for data-driven integrated health in populations

PubMed Central

Servadio, Joseph L.; Convertino, Matteo

2018-01-01

Development of composite indicators for integrated health in populations typically relies on a priori assumptions rather than model-free, data-driven evidence. Traditional variable selection processes tend not to consider relatedness and redundancy among variables, instead considering only individual correlations. In addition, a unified method for assessing integrated health statuses of populations is lacking, making systematic comparison among populations impossible. We propose the use of maximum entropy networks (MENets) that use transfer entropy to assess interrelatedness among selected variables considered for inclusion in a composite indicator. We also define optimal information networks (OINs) that are scale-invariant MENets, which use the information in constructed networks for optimal decision-making. Health outcome data from multiple cities in the United States are applied to this method to create a systemic health indicator, representing integrated health in a city. PMID:29423440

Predicting the potential distribution of main malaria vectors Anopheles stephensi, An. culicifacies s.l. and An. fluviatilis s.l. in Iran based on maximum entropy model.

PubMed

Pakdad, Kamran; Hanafi-Bojd, Ahmad Ali; Vatandoost, Hassan; Sedaghat, Mohammad Mehdi; Raeisi, Ahmad; Moghaddam, Abdolreza Salahi; Foroushani, Abbas Rahimi

2017-05-01

Malaria is considered as a major public health problem in southern areas of Iran. The goal of this study was to predict best ecological niches of three main malaria vectors of Iran: Anopheles stephensi, Anopheles culicifacies s.l. and Anopheles fluviatilis s.l. A databank was created which included all published data about Anopheles species of Iran from 1961 to 2015. The suitable environmental niches for the three above mentioned Anopheles species were predicted using maximum entropy model (MaxEnt). AUC (area under Roc curve) values were 0.943, 0.974 and 0.956 for An. stephensi, An. culicifacies s.l. and An. fluviatilis s.l respectively, which are considered as high potential power of model in the prediction of species niches. The biggest bioclimatic contributor for An. stephensi and An. fluviatilis s.l. was bio 15 (precipitation seasonality), 25.5% and 36.1% respectively, followed by bio 1 (annual mean temperature), 20.8% for An. stephensi and bio 4 (temperature seasonality) with 49.4% contribution for An. culicifacies s.l. This is the first step in the mapping of the country's malaria vectors. Hence, future weather situation can change the dispersal maps of Anopheles. Iran is under elimination phase of malaria, so that such spatio-temporal studies are essential and could provide guideline for decision makers for IVM strategies in problematic areas. Copyright © 2017 Elsevier B.V. All rights reserved.

Droplet size and velocity distributions for spray modelling

NASA Astrophysics Data System (ADS)

Jones, D. P.; Watkins, A. P.

2012-01-01

Methods for constructing droplet size distributions and droplet velocity profiles are examined as a basis for the Eulerian spray model proposed in Beck and Watkins (2002,2003) [5,6]. Within the spray model, both distributions must be calculated at every control volume at every time-step where the spray is present and valid distributions must be guaranteed. Results show that the Maximum Entropy formalism combined with the Gamma distribution satisfy these conditions for the droplet size distributions. Approximating the droplet velocity profile is shown to be considerably more difficult due to the fact that it does not have compact support. An exponential model with a constrained exponent offers plausible profiles.

From points to forecasts: Predicting invasive species habitat suitability in the near term

USGS Publications Warehouse

Holcombe, Tracy R.; Stohlgren, Thomas J.; Jarnevich, Catherine S.

2010-01-01

We used near-term climate scenarios for the continental United States, to model 12 invasive plants species. We created three potential habitat suitability models for each species using maximum entropy modeling: (1) current; (2) 2020; and (3) 2035. Area under the curve values for the models ranged from 0.92 to 0.70, with 10 of the 12 being above 0.83 suggesting strong and predictable species-environment matching. Change in area between the current potential habitat and 2035 ranged from a potential habitat loss of about 217,000 km2, to a potential habitat gain of about 133,000 km2.

Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions

NASA Astrophysics Data System (ADS)

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.

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

NASA Astrophysics Data System (ADS)

Burnier, Yannis; Rothkopf, Alexander

2013-11-01

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33TC.

Bayesian approach to spectral function reconstruction for Euclidean quantum field theories.

PubMed

Burnier, Yannis; Rothkopf, Alexander

2013-11-01

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33T(C).

A secure image encryption method based on dynamic harmony search (DHS) combined with chaotic map

NASA Astrophysics Data System (ADS)

Mirzaei Talarposhti, Khadijeh; Khaki Jamei, Mehrzad

2016-06-01

In recent years, there has been increasing interest in the security of digital images. This study focuses on the gray scale image encryption using dynamic harmony search (DHS). In this research, first, a chaotic map is used to create cipher images, and then the maximum entropy and minimum correlation coefficient is obtained by applying a harmony search algorithm on them. This process is divided into two steps. In the first step, the diffusion of a plain image using DHS to maximize the entropy as a fitness function will be performed. However, in the second step, a horizontal and vertical permutation will be applied on the best cipher image, which is obtained in the previous step. Additionally, DHS has been used to minimize the correlation coefficient as a fitness function in the second step. The simulation results have shown that by using the proposed method, the maximum entropy and the minimum correlation coefficient, which are approximately 7.9998 and 0.0001, respectively, have been obtained.

A maximum entropy thermodynamics of small systems.

PubMed

Dixit, Purushottam D

2013-05-14

We present a maximum entropy approach to analyze the state space of a small system in contact with a large bath, e.g., a solvated macromolecular system. For the solute, the fluctuations around the mean values of observables are not negligible and the probability distribution P(r) of the state space depends on the intricate details of the interaction of the solute with the solvent. Here, we employ a superstatistical approach: P(r) is expressed as a marginal distribution summed over the variation in β, the inverse temperature of the solute. The joint distribution P(β, r) is estimated by maximizing its entropy. We also calculate the first order system-size corrections to the canonical ensemble description of the state space. We test the development on a simple harmonic oscillator interacting with two baths with very different chemical identities, viz., (a) Lennard-Jones particles and (b) water molecules. In both cases, our method captures the state space of the oscillator sufficiently well. Future directions and connections with traditional statistical mechanics are discussed.

Cyclic multiverses

NASA Astrophysics Data System (ADS)

Marosek, Konrad; Dąbrowski, Mariusz P.; Balcerzak, Adam

2016-09-01

Using the idea of regularization of singularities due to the variability of the fundamental constants in cosmology we study the cyclic universe models. We find two models of oscillating and non-singular mass density and pressure (`non-singular' bounce) regularized by varying gravitational constant G despite the scale factor evolution is oscillating and having sharp turning points (`singular' bounce). Both violating (big-bang) and non-violating (phantom) null energy condition models appear. Then, we extend this idea on to the multiverse containing cyclic individual universes with either growing or decreasing entropy though leaving the net entropy constant. In order to get an insight into the key idea, we consider the doubleverse with the same geometrical evolution of the two `parallel' universes with their physical evolution [physical coupling constants c(t) and G(t)] being different. An interesting point is that there is a possibility to exchange the universes at the point of maximum expansion - the fact which was already noticed in quantum cosmology. Similar scenario is also possible within the framework of Brans-Dicke theory where varying G(t) is replaced by the dynamical Brans-Dicke field φ(t) though these theories are slightly different.

An information entropy model on clinical assessment of patients based on the holographic field of meridian

NASA Astrophysics Data System (ADS)

Wu, Jingjing; Wu, Xinming; Li, Pengfei; Li, Nan; Mao, Xiaomei; Chai, Lihe

2017-04-01

Meridian system is not only the basis of traditional Chinese medicine (TCM) method (e.g. acupuncture, massage), but also the core of TCM's basic theory. This paper has introduced a new informational perspective to understand the reality and the holographic field of meridian. Based on maximum information entropy principle (MIEP), a dynamic equation for the holographic field has been deduced, which reflects the evolutionary characteristics of meridian. By using self-organizing artificial neural network as algorithm, the evolutionary dynamic equation of the holographic field can be resolved to assess properties of meridians and clinically diagnose the health characteristics of patients. Finally, through some cases from clinical patients (e.g. a 30-year-old male patient, an apoplectic patient, an epilepsy patient), we use this model to assess the evolutionary properties of meridians. It is proved that this model not only has significant implications in revealing the essence of meridian in TCM, but also may play a guiding role in clinical assessment of patients based on the holographic field of meridians.

Causal nexus between energy consumption and carbon dioxide emission for Malaysia using maximum entropy bootstrap approach.

PubMed

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.

Spectral and correlation analysis with applications to middle-atmosphere radars

NASA Technical Reports Server (NTRS)

Rastogi, Prabhat K.

1989-01-01

The correlation and spectral analysis methods for uniformly sampled stationary random signals, estimation of their spectral moments, and problems arising due to nonstationary are reviewed. Some of these methods are already in routine use in atmospheric radar experiments. Other methods based on the maximum entropy principle and time series models have been used in analyzing data, but are just beginning to receive attention in the analysis of radar signals. These methods are also briefly discussed.

Two-Dimensional Signal Processing and Storage and Theory and Applications of Electromagnetic Measurements.

DTIC Science & Technology

1987-01-01

the results of that problem to be applied to deblurring . Four procedures for finding the maximum entropy solution have been developed and have becn...distortion operator h, converges quadratically to an impulse and, as a result, the restoration x, converges quadratically to x. Therefore, when the standard...is concerned with the modeling of a * signal as the sum of sinusoids in white noise where the sinusoidal frequencies are varying as a function of time

Transfer entropy analysis of maternal and fetal heart rate coupling.

PubMed

Marzbanrad, Faezeh; Kimura, Yoshitaka; Endo, Miyuki; Palaniswami, Marimuthu; Khandoker, Ahsan H

2015-01-01

Although evidence of the short term relationship between maternal and fetal heart rates has been found in previous model-based studies, knowledge about the mechanism and patterns of the coupling during gestation is still limited. In this study, a model-free method based on Transfer Entropy (TE) was applied to quantify the maternal-fetal heart rate couplings in both directions. Furthermore, analysis of the lag at which TE was maximum and its changes throughout gestation, provided more information about the mechanism of coupling and its latency. Experimental results based on fetal electrocardiograms (fECGs) and maternal ECG showed the evidence of coupling for 62 out of 65 healthy mothers and fetuses in each direction, by statistically validating against the surrogate pairs. The fetuses were divided into three gestational age groups: early (16-25 weeks), mid (26-31 weeks) and late (32-41 weeks) gestation. The maximum TE from maternal to fetal heart rate significantly increased from early to mid gestation, while the coupling delay on both directions decreased significantly from mid to late gestation. These changes occur concomitant with the maturation of the fetal sensory and autonomic nervous systems with advancing gestational age. In conclusion, the application of TE with delays revealed detailed information about the changes in fetal-maternal heart rate coupling strength and latency throughout gestation, which could provide novel clinical markers of fetal development and well-being.

Phonological Concept Learning.

PubMed

Moreton, Elliott; Pater, Joe; Pertsova, Katya

2017-01-01

Linguistic and non-linguistic pattern learning have been studied separately, but we argue for a comparative approach. Analogous inductive problems arise in phonological and visual pattern learning. Evidence from three experiments shows that human learners can solve them in analogous ways, and that human performance in both cases can be captured by the same models. We test GMECCS (Gradual Maximum Entropy with a Conjunctive Constraint Schema), an implementation of the Configural Cue Model (Gluck & Bower, ) in a Maximum Entropy phonotactic-learning framework (Goldwater & Johnson, ; Hayes & Wilson, ) with a single free parameter, against the alternative hypothesis that learners seek featurally simple algebraic rules ("rule-seeking"). We study the full typology of patterns introduced by Shepard, Hovland, and Jenkins () ("SHJ"), instantiated as both phonotactic patterns and visual analogs, using unsupervised training. Unlike SHJ, Experiments 1 and 2 found that both phonotactic and visual patterns that depended on fewer features could be more difficult than those that depended on more features, as predicted by GMECCS but not by rule-seeking. GMECCS also correctly predicted performance differences between stimulus subclasses within each pattern. A third experiment tried supervised training (which can facilitate rule-seeking in visual learning) to elicit simple rule-seeking phonotactic learning, but cue-based behavior persisted. We conclude that similar cue-based cognitive processes are available for phonological and visual concept learning, and hence that studying either kind of learning can lead to significant insights about the other. Copyright © 2015 Cognitive Science Society, Inc.

Maximum Entropy Production Modeling of Evapotranspiration Partitioning on Heterogeneous Terrain and Canopy Cover: advantages and limitations.

NASA Astrophysics Data System (ADS)

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.

Development of an Anisotropic Geological-Based Land Use Regression and Bayesian Maximum Entropy Model for Estimating Groundwater Radon across Northing Carolina

NASA Astrophysics Data System (ADS)

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.

Modeling Loop Entropy

PubMed Central

Chirikjian, Gregory S.

2011-01-01

Proteins fold from a highly disordered state into a highly ordered one. Traditionally, the folding problem has been stated as one of predicting ‘the’ tertiary structure from sequential information. However, new evidence suggests that the ensemble of unfolded forms may not be as disordered as once believed, and that the native form of many proteins may not be described by a single conformation, but rather an ensemble of its own. Quantifying the relative disorder in the folded and unfolded ensembles as an entropy difference may therefore shed light on the folding process. One issue that clouds discussions of ‘entropy’ is that many different kinds of entropy can be defined: entropy associated with overall translational and rotational Brownian motion, configurational entropy, vibrational entropy, conformational entropy computed in internal or Cartesian coordinates (which can even be different from each other), conformational entropy computed on a lattice; each of the above with different solvation and solvent models; thermodynamic entropy measured experimentally, etc. The focus of this work is the conformational entropy of coil/loop regions in proteins. New mathematical modeling tools for the approximation of changes in conformational entropy during transition from unfolded to folded ensembles are introduced. In particular, models for computing lower and upper bounds on entropy for polymer models of polypeptide coils both with and without end constraints are presented. The methods reviewed here include kinematics (the mathematics of rigid-body motions), classical statistical mechanics and information theory. PMID:21187223

Autonomous entropy-based intelligent experimental design

NASA Astrophysics Data System (ADS)

Malakar, Nabin Kumar

2011-07-01

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

An Entropy-Based Measure for Assessing Fuzziness in Logistic Regression

ERIC Educational Resources Information Center

Weiss, Brandi A.; Dardick, William

2016-01-01

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

Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gubler, Philipp, E-mail: pgubler@riken.jp; RIKEN Nishina Center, Wako, Saitama 351-0198; Yamamoto, Naoki

2015-05-15

Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.

Learning probability distributions from smooth observables and the maximum entropy principle: some remarks

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Monasson, Rémi

2015-09-01

The maximum entropy principle (MEP) is a very useful working hypothesis in a wide variety of inference problems, ranging from biological to engineering tasks. To better understand the reasons of the success of MEP, we propose a statistical-mechanical formulation to treat the space of probability distributions constrained by the measures of (experimental) observables. In this paper we first review the results of a detailed analysis of the simplest case of randomly chosen observables. In addition, we investigate by numerical and analytical means the case of smooth observables, which is of practical relevance. Our preliminary results are presented and discussed with respect to the efficiency of the MEP.

The calculation of transport properties in quantum liquids using the maximum entropy numerical analytic continuation method: Application to liquid para-hydrogen

PubMed Central

Rabani, Eran; Reichman, David R.; Krilov, Goran; Berne, Bruce J.

2002-01-01

We present a method based on augmenting an exact relation between a frequency-dependent diffusion constant and the imaginary time velocity autocorrelation function, combined with the maximum entropy numerical analytic continuation approach to study transport properties in quantum liquids. The method is applied to the case of liquid para-hydrogen at two thermodynamic state points: a liquid near the triple point and a high-temperature liquid. Good agreement for the self-diffusion constant and for the real-time velocity autocorrelation function is obtained in comparison to experimental measurements and other theoretical predictions. Improvement of the methodology and future applications are discussed. PMID:11830656

Maximum entropy production, carbon assimilation, and the spatial organization of vegetation in river basins

PubMed Central

del Jesus, Manuel; Foti, Romano; Rinaldo, Andrea; Rodriguez-Iturbe, Ignacio

2012-01-01

The spatial organization of functional vegetation types in river basins is a major determinant of their runoff production, biodiversity, and ecosystem services. The optimization of different objective functions has been suggested to control the adaptive behavior of plants and ecosystems, often without a compelling justification. Maximum entropy production (MEP), rooted in thermodynamics principles, provides a tool to justify the choice of the objective function controlling vegetation organization. The application of MEP at the ecosystem scale results in maximum productivity (i.e., maximum canopy photosynthesis) as the thermodynamic limit toward which the organization of vegetation appears to evolve. Maximum productivity, which incorporates complex hydrologic feedbacks, allows us to reproduce the spatial macroscopic organization of functional types of vegetation in a thoroughly monitored river basin, without the need for a reductionist description of the underlying microscopic dynamics. The methodology incorporates the stochastic characteristics of precipitation and the associated soil moisture on a spatially disaggregated framework. Our results suggest that the spatial organization of functional vegetation types in river basins naturally evolves toward configurations corresponding to dynamically accessible local maxima of the maximum productivity of the ecosystem. PMID:23213227

Identifying topological-band insulator transitions in silicene and other 2D gapped Dirac materials by means of Rényi-Wehrl entropy

NASA Astrophysics Data System (ADS)

Calixto, M.; Romera, E.

2015-02-01

We propose a new method to identify transitions from a topological insulator to a band insulator in silicene (the silicon equivalent of graphene) in the presence of perpendicular magnetic and electric fields, by using the Rényi-Wehrl entropy of the quantum state in phase space. Electron-hole entropies display an inversion/crossing behavior at the charge neutrality point for any Landau level, and the combined entropy of particles plus holes turns out to be maximum at this critical point. The result is interpreted in terms of delocalization of the quantum state in phase space. The entropic description presented in this work will be valid in general 2D gapped Dirac materials, with a strong intrinsic spin-orbit interaction, isostructural with silicene.

Estimating the melting point, entropy of fusion, and enthalpy of ...

EPA Pesticide Factsheets

The entropies of fusion, enthalies of fusion, and melting points of organic compounds can be estimated through three models developed using the SPARC (SPARC Performs Automated Reasoning in Chemistry) platform. The entropy of fusion is modeled through a combination of interaction terms and physical descriptors. The enthalpy of fusion is modeled as a function of the entropy of fusion, boiling point, and fexibility of the molecule. The melting point model is the enthlapy of fusion divided by the entropy of fusion. These models were developed in part to improve SPARC's vapor pressure and solubility models. These models have been tested on 904 unique compounds. The entropy model has a RMS of 12.5 J mol-1K-1. The enthalpy model has a RMS of 4.87 kJ mol-1. The melting point model has a RMS of 54.4°C. Published in the journal, SAR and QSAR in Environmental Research

Estimating the melting point, entropy of fusion, and enthalpy of fusion of organic compounds via SPARC.

PubMed

Whiteside, T S; Hilal, S H; Brenner, A; Carreira, L A

2016-08-01

The entropy of fusion, enthalpy of fusion, and melting point of organic compounds can be estimated through three models developed using the SPARC (SPARC Performs Automated Reasoning in Chemistry) platform. The entropy of fusion is modelled through a combination of interaction terms and physical descriptors. The enthalpy of fusion is modelled as a function of the entropy of fusion, boiling point, and flexibility of the molecule. The melting point model is the enthalpy of fusion divided by the entropy of fusion. These models were developed in part to improve SPARC's vapour pressure and solubility models. These models have been tested on 904 unique compounds. The entropy model has a RMS of 12.5 J mol(-1) K(-1). The enthalpy model has a RMS of 4.87 kJ mol(-1). The melting point model has a RMS of 54.4°C.

Dual-threshold segmentation using Arimoto entropy based on chaotic bee colony optimization

NASA Astrophysics Data System (ADS)

Li, Li

2018-03-01

In order to extract target from complex background more quickly and accurately, and to further improve the detection effect of defects, a method of dual-threshold segmentation using Arimoto entropy based on chaotic bee colony optimization was proposed. Firstly, the method of single-threshold selection based on Arimoto entropy was extended to dual-threshold selection in order to separate the target from the background more accurately. Then intermediate variables in formulae of Arimoto entropy dual-threshold selection was calculated by recursion to eliminate redundant computation effectively and to reduce the amount of calculation. Finally, the local search phase of artificial bee colony algorithm was improved by chaotic sequence based on tent mapping. The fast search for two optimal thresholds was achieved using the improved bee colony optimization algorithm, thus the search could be accelerated obviously. A large number of experimental results show that, compared with the existing segmentation methods such as multi-threshold segmentation method using maximum Shannon entropy, two-dimensional Shannon entropy segmentation method, two-dimensional Tsallis gray entropy segmentation method and multi-threshold segmentation method using reciprocal gray entropy, the proposed method can segment target more quickly and accurately with superior segmentation effect. It proves to be an instant and effective method for image segmentation.

On the morphological instability of a bubble during inertia-controlled growth

NASA Astrophysics Data System (ADS)

Martyushev, L. M.; Birzina, A. I.; Soboleva, A. S.

2018-06-01

The morphological stability of a spherical bubble growing under inertia control is analyzed. Based on the comparison of entropy productions for a distorted and undistorted surface and using the maximum entropy production principle, the morphological instability of the bubble under arbitrary amplitude distortions is shown. This result allows explaining a number of experiments where the surface roughness of bubbles was observed during their explosive-type growth.

Entropy Production in Collisionless Systems. II. Arbitrary Phase-space Occupation Numbers

NASA Astrophysics Data System (ADS)

Barnes, Eric I.; Williams, Liliya L. R.

2012-04-01

We present an analysis of two thermodynamic techniques for determining equilibria of self-gravitating systems. One is the Lynden-Bell (LB) entropy maximization analysis that introduced violent relaxation. Since we do not use the Stirling approximation, which is invalid at small occupation numbers, our systems have finite mass, unlike LB's isothermal spheres. (Instead of Stirling, we utilize a very accurate smooth approximation for ln x!.) The second analysis extends entropy production extremization to self-gravitating systems, also without the use of the Stirling approximation. In addition to the LB statistical family characterized by the exclusion principle in phase space, and designed to treat collisionless systems, we also apply the two approaches to the Maxwell-Boltzmann (MB) families, which have no exclusion principle and hence represent collisional systems. We implicitly assume that all of the phase space is equally accessible. We derive entropy production expressions for both families and give the extremum conditions for entropy production. Surprisingly, our analysis indicates that extremizing entropy production rate results in systems that have maximum entropy, in both LB and MB statistics. In other words, both thermodynamic approaches lead to the same equilibrium structures.

On the pH Dependence of the Potential of Maximum Entropy of Ir(111) Electrodes.

PubMed

Ganassin, Alberto; Sebastián, Paula; Climent, Víctor; Schuhmann, Wolfgang; Bandarenka, Aliaksandr S; Feliu, Juan

2017-04-28

Studies over the entropy of components forming the electrode/electrolyte interface can give fundamental insights into the properties of electrified interphases. In particular, the potential where the entropy of formation of the double layer is maximal (potential of maximum entropy, PME) is an important parameter for the characterization of electrochemical systems. Indeed, this parameter determines the majority of electrode processes. In this work, we determine PMEs for Ir(111) electrodes. The latter currently play an important role to understand electrocatalysis for energy provision; and at the same time, iridium is one of the most stable metals against corrosion. For the experiments, we used a combination of the laser induced potential transient to determine the PME, and CO charge-displacement to determine the potentials of zero total charge, (E PZTC ). Both PME and E PZTC were assessed for perchlorate solutions in the pH range from 1 to 4. Surprisingly, we found that those are located in the potential region where the adsorption of hydrogen and hydroxyl species takes place, respectively. The PMEs demonstrated a shift by ~30 mV per a pH unit (in the RHE scale). Connections between the PME and electrocatalytic properties of the electrode surface are discussed.

Origin and Characteristics of High Shannon Entropy at the Pivot of Locally Stable Rotors: Insights from Computational Simulation

PubMed Central

Gharaviri, Ali; Brooks, Anthony; Chapman, Darius; Lau, Dennis H.; Roberts-Thomson, Kurt C.; Sanders, Prashanthan

2014-01-01

Background Rotors are postulated to maintain cardiac fibrillation. Despite the importance of bipolar electrograms in clinical electrophysiology, few data exist on the properties of bipolar electrograms at rotor sites. The pivot of a spiral wave is characterized by relative uncertainty of wavefront propagation direction compared to the periphery. The bipolar electrograms used in electrophysiology recording encode information on both direction and timing of approaching wavefronts. Objective To test the hypothesis that bipolar electrograms from the pivot of rotors have higher Shannon entropy (ShEn) than electrograms recorded at the periphery due to the spatial dynamics of spiral waves. Methods and Results We studied spiral wave propagation in 2-dimensional sheets constructed using a simple cell automaton (FitzHugh-Nagumo), atrial (Courtemanche-Ramirez-Nattel) and ventricular (Luo-Rudy) myocyte cell models and in a geometric model spiral wave. In each system, bipolar electrogram recordings were simulated, and Shannon entropy maps constructed as a measure of electrogram information content. ShEn was consistently highest in the pivoting region associated with the phase singularity of the spiral wave. This property was consistently preserved across; (i) variation of model system (ii) alterations in bipolar electrode spacing, (iii) alternative bipolar electrode orientation (iv) bipolar electrogram filtering and (v) in the presence of rotor meander. Directional activation plots demonstrated that the origin of high ShEn at the pivot was the directional diversity of wavefront propagation observed in this location. Conclusions The pivot of the rotor is consistently associated with high Shannon entropy of bipolar electrograms despite differences in action potential model, bipolar electrode spacing, signal filtering and rotor meander. Maximum ShEn is co-located with the pivot for rotors observed in the bipolar electrogram recording mode, and may be an intrinsic property of spiral wave dynamic behaviour. PMID:25401331

Developing the fuzzy c-means clustering algorithm based on maximum entropy for multitarget tracking in a cluttered environment

NASA Astrophysics Data System (ADS)

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.

Maximum entropy methods for extracting the learned features of deep neural networks.

PubMed

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.

Assimilation of Remotely Sensed Soil Moisture Profiles into a Crop Modeling Framework for Reliable Yield Estimations

NASA Astrophysics Data System (ADS)

Mishra, V.; Cruise, J.; Mecikalski, J. R.

2017-12-01

Much effort has been expended recently on the assimilation of remotely sensed soil moisture into operational land surface models (LSM). These efforts have normally been focused on the use of data derived from the microwave bands and results have often shown that improvements to model simulations have been limited due to the fact that microwave signals only penetrate the top 2-5 cm of the soil surface. It is possible that model simulations could be further improved through the introduction of geostationary satellite thermal infrared (TIR) based root zone soil moisture in addition to the microwave deduced surface estimates. In this study, root zone soil moisture estimates from the TIR based Atmospheric Land Exchange Inverse (ALEXI) model were merged with NASA Soil Moisture Active Passive (SMAP) based surface estimates through the application of informational entropy. Entropy can be used to characterize the movement of moisture within the vadose zone and accounts for both advection and diffusion processes. The Principle of Maximum Entropy (POME) can be used to derive complete soil moisture profiles and, fortuitously, only requires a surface boundary condition as well as the overall mean moisture content of the soil column. A lower boundary can be considered a soil parameter or obtained from the LSM itself. In this study, SMAP provided the surface boundary while ALEXI supplied the mean and the entropy integral was used to tie the two together and produce the vertical profile. However, prior to the merging, the coarse resolution (9 km) SMAP data were downscaled to the finer resolution (4.7 km) ALEXI grid. The disaggregation scheme followed the Soil Evaporative Efficiency approach and again, all necessary inputs were available from the TIR model. The profiles were then assimilated into a standard agricultural crop model (Decision Support System for Agrotechnology, DSSAT) via the ensemble Kalman Filter. The study was conducted over the Southeastern United States for the growing seasons from 2015-2017. Soil moisture profiles compared favorably to in situ data and simulated crop yields compared well with observed yields.

A mechanism producing power law etc. distributions

NASA Astrophysics Data System (ADS)

Li, Heling; Shen, Hongjun; Yang, Bin

2017-07-01

Power law distribution is playing an increasingly important role in the complex system study. Based on the insolvability of complex systems, the idea of incomplete statistics is utilized and expanded, three different exponential factors are introduced in equations about the normalization condition, statistical average and Shannon entropy, with probability distribution function deduced about exponential function, power function and the product form between power function and exponential function derived from Shannon entropy and maximal entropy principle. So it is shown that maximum entropy principle can totally replace equal probability hypothesis. Owing to the fact that power and probability distribution in the product form between power function and exponential function, which cannot be derived via equal probability hypothesis, can be derived by the aid of maximal entropy principle, it also can be concluded that maximal entropy principle is a basic principle which embodies concepts more extensively and reveals basic principles on motion laws of objects more fundamentally. At the same time, this principle also reveals the intrinsic link between Nature and different objects in human society and principles complied by all.

Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes

NASA Astrophysics Data System (ADS)

Neri, Izaak; Roldán, Édgar; Jülicher, Frank

2017-01-01

We study the statistics of infima, stopping times, and passage probabilities of entropy production in nonequilibrium steady states, and we show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches a given state for the first time. Our main results are as follows: (i) The distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann's constant; (ii) we find exact expressions for the passage probabilities of entropy production; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production; for example, we derive a relation between the maximal excursion of a molecular motor against the direction of an external force and the infimum of the corresponding entropy-production fluctuations. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follow from our universal results for entropy-production infima.

Searching for collective behavior in a large network of sensory neurons.

PubMed

Tkačik, Gašper; Marre, Olivier; Amodei, Dario; Schneidman, Elad; Bialek, William; Berry, Michael J

2014-01-01

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such "K-pairwise" models--being systematic extensions of the previously used pairwise Ising models--provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.

Deep-sea benthic megafaunal habitat suitability modelling: A global-scale maximum entropy model for xenophyophores

NASA Astrophysics Data System (ADS)

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 these conspicuously large single-celled eukaryotes.

An Equation for Moist Entropy in a Precipitating and Icy Atmosphere

NASA Technical Reports Server (NTRS)

Tao, Wei-Kuo; Simpson, Joanne; Zeng, Xiping

2003-01-01

Moist entropy is nearly conserved in adiabatic motion. It is redistributed rather than created by moist convection. Thus moist entropy and its equation, as a healthy direction, can be used to construct analytical and numerical models for the interaction between tropical convective clouds and large-scale circulations. Hence, an accurate equation of moist entropy is needed for the analysis and modeling of atmospheric convective clouds. On the basis of the consistency between the energy and the entropy equations, a complete equation of moist entropy is derived from the energy equation. The equation expresses explicitly the internal and external sources of moist entropy, including those in relation to the microphysics of clouds and precipitation. In addition, an accurate formula for the surface flux of moist entropy from the underlying surface into the air above is derived. Because moist entropy deals "easily" with the transition among three water phases, it will be used as a prognostic variable in the next generation of cloud-resolving models (e. g. a global cloud-resolving model) for low computational noise. Its equation that is derived in this paper is accurate and complete, providing a theoretical basis for using moist entropy as a prognostic variable in the long-term modeling of clouds and large-scale circulations.

Calibration of short rate term structure models from bid-ask coupon bond prices

NASA Astrophysics Data System (ADS)

Gomes-Gonçalves, Erika; Gzyl, Henryk; Mayoral, Silvia

2018-02-01

In this work we use the method of maximum entropy in the mean to provide a model free, non-parametric methodology that uses only market data to provide the prices of the zero coupon bonds, and then, a term structure of the short rates. The data used consists of the prices of the bid-ask ranges of a few coupon bonds quoted in the market. The prices of the zero coupon bonds obtained in the first stage, are then used as input to solve a recursive set of equations to determine a binomial recombinant model of the short term structure of the interest rates.

A spatiotemporal dengue fever early warning model accounting for nonlinear associations with meteorological factors: a Bayesian maximum entropy approach

NASA Astrophysics Data System (ADS)

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.

The More the Merrier?. Entropy and Statistics of Asexual Reproduction in Freshwater Planarians

NASA Astrophysics Data System (ADS)

Quinodoz, Sofia; Thomas, Michael A.; Dunkel, Jörn; Schötz, Eva-Maria

2011-04-01

The trade-off between traits in life-history strategies has been widely studied for sexual and parthenogenetic organisms, but relatively little is known about the reproduction strategies of asexual animals. Here, we investigate clonal reproduction in the freshwater planarian Schmidtea mediterranea, an important model organism for regeneration and stem cell research. We find that these flatworms adopt a randomized reproduction strategy that comprises both asymmetric binary fission and fragmentation (generation of multiple offspring during a reproduction cycle). Fragmentation in planarians has primarily been regarded as an abnormal behavior in the past; using a large-scale experimental approach, we now show that about one third of the reproduction events in S. mediterranea are fragmentations, implying that fragmentation is part of their normal reproductive behavior. Our analysis further suggests that certain characteristic aspects of the reproduction statistics can be explained in terms of a maximum relative entropy principle.

A Bayesian Interpretation of First-Order Phase Transitions

NASA Astrophysics Data System (ADS)

Davis, Sergio; Peralta, Joaquín; Navarrete, Yasmín; González, Diego; Gutiérrez, Gonzalo

2016-03-01

In this work we review the formalism used in describing the thermodynamics of first-order phase transitions from the point of view of maximum entropy inference. We present the concepts of transition temperature, latent heat and entropy difference between phases as emergent from the more fundamental concept of internal energy, after a statistical inference analysis. We explicitly demonstrate this point of view by making inferences on a simple game, resulting in the same formalism as in thermodynamical phase transitions. We show that analogous quantities will inevitably arise in any problem of inferring the result of a yes/no question, given two different states of knowledge and information in the form of expectation values. This exposition may help to clarify the role of these thermodynamical quantities in the context of different first-order phase transitions such as the case of magnetic Hamiltonians (e.g. the Potts model).

Approximation of the ruin probability using the scaled Laplace transform inversion

PubMed Central

Mnatsakanov, Robert M.; Sarkisian, Khachatur; Hakobyan, Artak

2015-01-01

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen–Weideman–Schmelzer and maximum entropy methods are presented via a simulation study. PMID:26752796

Divvy Economies Based On (An Abstract) Temperature

NASA Astrophysics Data System (ADS)

Collins, Dennis G.

2004-04-01

The Leontief Input-Output economic system can provide a model for a one-parameter family of economic systems based on an abstract temperature T. In particular, given a normalized input-output matrix R and taking R= R(1), a family of economic systems R(1/T)=R(α) is developed that represents heating (T>1) and cooling (T<1) of the economy relative to T=1. .The economy for a given value of T represents the solution of a constrained maximum entropy problem.

Molecular classification of pesticides including persistent organic pollutants, phenylurea and sulphonylurea herbicides.

PubMed

Torrens, Francisco; Castellano, Gloria

2014-06-05

Pesticide residues in wine were analyzed by liquid chromatography-tandem mass spectrometry. Retentions are modelled by structure-property relationships. Bioplastic evolution is an evolutionary perspective conjugating effect of acquired characters and evolutionary indeterminacy-morphological determination-natural selection principles; its application to design co-ordination index barely improves correlations. Fractal dimensions and partition coefficient differentiate pesticides. Classification algorithms are based on information entropy and its production. Pesticides allow a structural classification by nonplanarity, and number of O, S, N and Cl atoms and cycles; different behaviours depend on number of cycles. The novelty of the approach is that the structural parameters are related to retentions. Classification algorithms are based on information entropy. When applying procedures to moderate-sized sets, excessive results appear compatible with data suffering a combinatorial explosion. However, equipartition conjecture selects criterion resulting from classification between hierarchical trees. Information entropy permits classifying compounds agreeing with principal component analyses. Periodic classification shows that pesticides in the same group present similar properties; those also in equal period, maximum resemblance. The advantage of the classification is to predict the retentions for molecules not included in the categorization. Classification extends to phenyl/sulphonylureas and the application will be to predict their retentions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dhabal, Debdas; Chakravarty, Charusita, E-mail: charus@chemistry.iitd.ac.in; Nguyen, Andrew Huy

Molecular dynamics simulations are used to contrast the supercooling and crystallization behaviour of monatomic liquids that exemplify the transition from simple to anomalous, tetrahedral liquids. As examples of simple fluids, we use the Lennard-Jones (LJ) liquid and a pair-dominated Stillinger-Weber liquid (SW{sub 16}). As examples of tetrahedral, water-like fluids, we use the Stillinger-Weber model with variable tetrahedrality parameterized for germanium (SW{sub 20}), silicon (SW{sub 21}), and water (SW{sub 23.15} or mW model). The thermodynamic response functions show clear qualitative differences between simple and water-like liquids. For simple liquids, the compressibility and the heat capacity remain small on isobaric cooling. Themore » tetrahedral liquids in contrast show a very sharp rise in these two response functions as the lower limit of liquid-phase stability is reached. While the thermal expansivity decreases with temperature but never crosses zero in simple liquids, in all three tetrahedral liquids at the studied pressure, there is a temperature of maximum density below which thermal expansivity is negative. In contrast to the thermodynamic response functions, the excess entropy on isobaric cooling does not show qualitatively different features for simple and water-like liquids; however, the slope and curvature of the entropy-temperature plots reflect the heat capacity trends. Two trajectory-based computational estimation methods for the entropy and the heat capacity are compared for possible structural insights into supercooling, with the entropy obtained from thermodynamic integration. The two-phase thermodynamic estimator for the excess entropy proves to be fairly accurate in comparison to the excess entropy values obtained by thermodynamic integration, for all five Lennard-Jones and Stillinger-Weber liquids. The entropy estimator based on the multiparticle correlation expansion that accounts for both pair and triplet correlations, denoted by S{sub trip}, is also studied. S{sub trip} is a good entropy estimator for liquids where pair and triplet correlations are important such as Ge and Si, but loses accuracy for purely pair-dominated liquids, like LJ fluid, or near the crystallization temperature (T{sub thr}). Since local tetrahedral order is compatible with both liquid and crystalline states, the reorganisation of tetrahedral liquids is accompanied by a clear rise in the pair, triplet, and thermodynamic contributions to the heat capacity, resulting in the heat capacity anomaly. In contrast, the pair-dominated liquids show increasing dominance of triplet correlations on approaching crystallization but no sharp rise in either the pair or thermodynamic heat capacities.« less

Use and validity of principles of extremum of entropy production in the study of complex systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heitor Reis, A., E-mail: ahr@uevora.pt

2014-07-15

It is shown how both the principles of extremum of entropy production, which are often used in the study of complex systems, follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. A brief discussion on the validity of the application of the mEP and MEP principles in several cases, and in particular to themore » Earth’s climate is also presented. -- Highlights: •The principles of extremum of entropy production are not first principles. •They result from the maximization of conductivities under appropriate constraints. •The conditions of their validity are set explicitly. •Some long-standing controversies are discussed and clarified.« less

Simultaneous Multi-Scale Diffusion Estimation and Tractography Guided by Entropy Spectrum Pathways

PubMed Central

Galinsky, Vitaly L.; Frank, Lawrence R.

2015-01-01

We have developed a method for the simultaneous estimation of local diffusion and the global fiber tracts based upon the information entropy flow that computes the maximum entropy trajectories between locations and depends upon the global structure of the multi-dimensional and multi-modal diffusion field. Computation of the entropy spectrum pathways requires only solving a simple eigenvector problem for the probability distribution for which efficient numerical routines exist, and a straight forward integration of the probability conservation through ray tracing of the convective modes guided by a global structure of the entropy spectrum coupled with a small scale local diffusion. The intervoxel diffusion is sampled by multi b-shell multi q-angle DWI data expanded in spherical waves. This novel approach to fiber tracking incorporates global information about multiple fiber crossings in every individual voxel and ranks it in the most scientifically rigorous way. This method has potential significance for a wide range of applications, including studies of brain connectivity. PMID:25532167

On entropy, financial markets and minority games

NASA Astrophysics Data System (ADS)

Zapart, Christopher A.

2009-04-01

The paper builds upon an earlier statistical analysis of financial time series with Shannon information entropy, published in [L. Molgedey, W. Ebeling, Local order, entropy and predictability of financial time series, European Physical Journal B-Condensed Matter and Complex Systems 15/4 (2000) 733-737]. A novel generic procedure is proposed for making multistep-ahead predictions of time series by building a statistical model of entropy. The approach is first demonstrated on the chaotic Mackey-Glass time series and later applied to Japanese Yen/US dollar intraday currency data. The paper also reinterprets Minority Games [E. Moro, The minority game: An introductory guide, Advances in Condensed Matter and Statistical Physics (2004)] within the context of physical entropy, and uses models derived from minority game theory as a tool for measuring the entropy of a model in response to time series. This entropy conditional upon a model is subsequently used in place of information-theoretic entropy in the proposed multistep prediction algorithm.

Conserved actions, maximum entropy and dark matter haloes

NASA Astrophysics Data System (ADS)

Pontzen, Andrew; Governato, Fabio

2013-03-01

We use maximum entropy arguments to derive the phase-space distribution of a virialized dark matter halo. Our distribution function gives an improved representation of the end product of violent relaxation. This is achieved by incorporating physically motivated dynamical constraints (specifically on orbital actions) which prevent arbitrary redistribution of energy. We compare the predictions with three high-resolution dark matter simulations of widely varying mass. The numerical distribution function is accurately predicted by our argument, producing an excellent match for the vast majority of particles. The remaining particles constitute the central cusp of the halo (≲4 per cent of the dark matter). They can be accounted for within the presented framework once the short dynamical time-scales of the centre are taken into account.

Optimal protocol for maximum work extraction in a feedback process with a time-varying potential

NASA Astrophysics Data System (ADS)

Kwon, Chulan

2017-12-01

The nonequilibrium nature of information thermodynamics is characterized by the inequality or non-negativity of the total entropy change of the system, memory, and reservoir. Mutual information change plays a crucial role in the inequality, in particular if work is extracted and the paradox of Maxwell's demon is raised. We consider the Brownian information engine where the protocol set of the harmonic potential is initially chosen by the measurement and varies in time. We confirm the inequality of the total entropy change by calculating, in detail, the entropic terms including the mutual information change. We rigorously find the optimal values of the time-dependent protocol for maximum extraction of work both for the finite-time and the quasi-static process.

LIBOR troubles: Anomalous movements detection based on maximum entropy

NASA Astrophysics Data System (ADS)

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.

An understanding of human dynamics in urban subway traffic from the Maximum Entropy Principle

NASA Astrophysics Data System (ADS)

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.

A general methodology for population analysis

NASA Astrophysics Data System (ADS)

Lazov, Petar; Lazov, Igor

2014-12-01

For a given population with N - current and M - maximum number of entities, modeled by a Birth-Death Process (BDP) with size M+1, we introduce utilization parameter ρ, ratio of the primary birth and death rates in that BDP, which, physically, determines (equilibrium) macrostates of the population, and information parameter ν, which has an interpretation as population information stiffness. The BDP, modeling the population, is in the state n, n=0,1,…,M, if N=n. In presence of these two key metrics, applying continuity law, equilibrium balance equations concerning the probability distribution pn, n=0,1,…,M, of the quantity N, pn=Prob{N=n}, in equilibrium, and conservation law, and relying on the fundamental concepts population information and population entropy, we develop a general methodology for population analysis; thereto, by definition, population entropy is uncertainty, related to the population. In this approach, what is its essential contribution, the population information consists of three basic parts: elastic (Hooke's) or absorption/emission part, synchronization or inelastic part and null part; the first two parts, which determine uniquely the null part (the null part connects them), are the two basic components of the Information Spectrum of the population. Population entropy, as mean value of population information, follows this division of the information. A given population can function in information elastic, antielastic and inelastic regime. In an information linear population, the synchronization part of the information and entropy is absent. The population size, M+1, is the third key metric in this methodology. Namely, right supposing a population with infinite size, the most of the key quantities and results for populations with finite size, emerged in this methodology, vanish.

The performance evaluation model of mining project founded on the weight optimization entropy value method

NASA Astrophysics Data System (ADS)

Mao, Chao; Chen, Shou

2017-01-01

According to the traditional entropy value method still have low evaluation accuracy when evaluating the performance of mining projects, a performance evaluation model of mineral project founded on improved entropy is proposed. First establish a new weight assignment model founded on compatible matrix analysis of analytic hierarchy process (AHP) and entropy value method, when the compatibility matrix analysis to achieve consistency requirements, if it has differences between subjective weights and objective weights, moderately adjust both proportions, then on this basis, the fuzzy evaluation matrix for performance evaluation. The simulation experiments show that, compared with traditional entropy and compatible matrix analysis method, the proposed performance evaluation model of mining project based on improved entropy value method has higher accuracy assessment.

Probabilistic analysis for fatigue strength degradation of materials

NASA Technical Reports Server (NTRS)

Royce, Lola

1989-01-01

This report presents the results of the first year of a research program conducted for NASA-LeRC by the University of Texas at San Antonio. The research included development of methodology that provides a probabilistic treatment of lifetime prediction of structural components of aerospace propulsion systems subjected to fatigue. Material strength degradation models, based on primitive variables, include both a fatigue strength reduction model and a fatigue crack growth model. Linear elastic fracture mechanics is utilized in the latter model. Probabilistic analysis is based on simulation, and both maximum entropy and maximum penalized likelihood methods are used for the generation of probability density functions. The resulting constitutive relationships are included in several computer programs, RANDOM2, RANDOM3, and RANDOM4. These programs determine the random lifetime of an engine component, in mechanical load cycles, to reach a critical fatigue strength or crack size. The material considered was a cast nickel base superalloy, one typical of those used in the Space Shuttle Main Engine.

Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation.

PubMed

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 χ^{2} 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.

Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation

NASA Astrophysics Data System (ADS)

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.

Mapping distribution of Rastrelliger kanagurta in the exclusive economic zone (EEZ) of Malaysia using maximum entropy modeling approach

NASA Astrophysics Data System (ADS)

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.

Analysis of interacting entropy-corrected holographic and new agegraphic dark energies

NASA Astrophysics Data System (ADS)

Ranjit, Chayan; Debnath, Ujjal

In the present work, we assume the flat FRW model of the universe is filled with dark matter and dark energy where they are interacting. For dark energy model, we consider the entropy-corrected HDE (ECHDE) model and the entropy-corrected NADE (ECNADE). For entropy-corrected models, we assume logarithmic correction and power law correction. For ECHDE model, length scale L is assumed to be Hubble horizon and future event horizon. The ωde-ωde‧ analysis for our different horizons are discussed.

Comparison of image deconvolution algorithms on simulated and laboratory infrared images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Proctor, D.

1994-11-15

We compare Maximum Likelihood, Maximum Entropy, Accelerated Lucy-Richardson, Weighted Goodness of Fit, and Pixon reconstructions of simple scenes as a function of signal-to-noise ratio for simulated images with randomly generated noise. Reconstruction results of infrared images taken with the TAISIR (Temperature and Imaging System InfraRed) are also discussed.

[Quantitative assessment of urban ecosystem services flow based on entropy theory: A case study of Beijing, China].

PubMed

Li, Jing Xin; Yang, Li; Yang, Lei; Zhang, Chao; Huo, Zhao Min; Chen, Min Hao; Luan, Xiao Feng

2018-03-01

Quantitative evaluation of ecosystem service is a primary premise for rational resources exploitation and sustainable development. Examining ecosystem services flow provides a scientific method to quantity ecosystem services. We built an assessment indicator system based on land cover/land use under the framework of four types of ecosystem services. The types of ecosystem services flow were reclassified. Using entropy theory, disorder degree and developing trend of indicators and urban ecosystem were quantitatively assessed. Beijing was chosen as the study area, and twenty-four indicators were selected for evaluation. The results showed that the entropy value of Beijing urban ecosystem during 2004 to 2015 was 0.794 and the entropy flow was -0.024, suggesting a large disordered degree and near verge of non-health. The system got maximum values for three times, while the mean annual variation of the system entropy value increased gradually in three periods, indicating that human activities had negative effects on urban ecosystem. Entropy flow reached minimum value in 2007, implying the environmental quality was the best in 2007. The determination coefficient for the fitting function of total permanent population in Beijing and urban ecosystem entropy flow was 0.921, indicating that urban ecosystem health was highly correlated with total permanent population.

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

PubMed

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

2016-01-01

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

Entropy, complexity, and Markov diagrams for random walk cancer models.

PubMed

Newton, Paul K; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

2014-12-19

The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

Entropy, complexity, and Markov diagrams for random walk cancer models

NASA Astrophysics Data System (ADS)

Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

2014-12-01

The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

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

NASA Astrophysics Data System (ADS)

Zhao, Hui; Qu, Weilu; Qiu, Weiting

2018-03-01

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

Measuring Questions: Relevance and its Relation to Entropy

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.

2004-01-01

The Boolean lattice of logical statements induces the free distributive lattice of questions. Inclusion on this lattice is based on whether one question answers another. Generalizing the zeta function of the question lattice leads to a valuation called relevance or bearing, which is a measure of the degree to which one question answers another. Richard Cox conjectured that this degree can be expressed as a generalized entropy. With the assistance of yet another important result from Janos Acz6l, I show that this is indeed the case; and that the resulting inquiry calculus is a natural generalization of information theory. This approach provides a new perspective of the Principle of Maximum Entropy.

Information dynamics in living systems: prokaryotes, eukaryotes, and cancer.

PubMed

Frieden, B Roy; Gatenby, Robert A

2011-01-01

Living systems use information and energy to maintain stable entropy while far from thermodynamic equilibrium. The underlying first principles have not been established. We propose that stable entropy in living systems, in the absence of thermodynamic equilibrium, requires an information extremum (maximum or minimum), which is invariant to first order perturbations. Proliferation and death represent key feedback mechanisms that promote stability even in a non-equilibrium state. A system moves to low or high information depending on its energy status, as the benefit of information in maintaining and increasing order is balanced against its energy cost. Prokaryotes, which lack specialized energy-producing organelles (mitochondria), are energy-limited and constrained to an information minimum. Acquisition of mitochondria is viewed as a critical evolutionary step that, by allowing eukaryotes to achieve a sufficiently high energy state, permitted a phase transition to an information maximum. This state, in contrast to the prokaryote minima, allowed evolution of complex, multicellular organisms. A special case is a malignant cell, which is modeled as a phase transition from a maximum to minimum information state. The minimum leads to a predicted power-law governing the in situ growth that is confirmed by studies measuring growth of small breast cancers. We find living systems achieve a stable entropic state by maintaining an extreme level of information. The evolutionary divergence of prokaryotes and eukaryotes resulted from acquisition of specialized energy organelles that allowed transition from information minima to maxima, respectively. Carcinogenesis represents a reverse transition: of an information maximum to minimum. The progressive information loss is evident in accumulating mutations, disordered morphology, and functional decline characteristics of human cancers. The findings suggest energy restriction is a critical first step that triggers the genetic mutations that drive somatic evolution of the malignant phenotype.

Comparison of cosmology and seabed acoustics measurements using statistical inference from maximum entropy

NASA Astrophysics Data System (ADS)

Knobles, David; Stotts, Steven; Sagers, Jason

2012-03-01

Why can one obtain from similar measurements a greater amount of information about cosmological parameters than seabed parameters in ocean waveguides? The cosmological measurements are in the form of a power spectrum constructed from spatial correlations of temperature fluctuations within the microwave background radiation. The seabed acoustic measurements are in the form of spatial correlations along the length of a spatial aperture. This study explores the above question from the perspective of posterior probability distributions obtained from maximizing a relative entropy functional. An answer is in part that the seabed in shallow ocean environments generally has large temporal and spatial inhomogeneities, whereas the early universe was a nearly homogeneous cosmological soup with small but important fluctuations. Acoustic propagation models used in shallow water acoustics generally do not capture spatial and temporal variability sufficiently well, which leads to model error dominating the statistical inference problem. This is not the case in cosmology. Further, the physics of the acoustic modes in cosmology is that of a standing wave with simple initial conditions, whereas for underwater acoustics it is a traveling wave in a strongly inhomogeneous bounded medium.

Simulations of dissociation constants in low pressure supercritical water

NASA Astrophysics Data System (ADS)

Halstead, S. J.; An, P.; Zhang, S.

2014-09-01

This article reports molecular dynamics simulations of the dissociation of hydrochloric acid and sodium hydroxide in water from ambient to supercritical temperatures at a fixed pressure of 250 atm. Corrosion of reaction vessels is known to be a serious problem of supercritical water, and acid/base dissociation can be a significant contributing factor to this. The SPC/e model was used in conjunction with solute models determined from density functional calculations and OPLSAA Lennard-Jones parameters. Radial distribution functions were calculated, and these show a significant increase in solute-solvent ordering upon forming the product ions at all temperatures. For both dissociations, rapidly decreasing entropy of reaction was found to be the controlling thermodynamic factor, and this is thought to arise due to the ions produced from dissociation maintaining a relatively high density and ordered solvation shell compared to the reactants. The change in entropy of reaction reaches a minimum at the critical temperature. The values of pKa and pKb were calculated and both increased with temperature, in qualitative agreement with other work, until a maximum value at 748 K, after which there was a slight decrease.

Non-linear dielectric signatures of entropy changes in liquids subject to time dependent electric fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richert, Ranko

2016-03-21

A model of non-linear dielectric polarization is studied in which the field induced entropy change is the source of polarization dependent retardation time constants. Numerical solutions for the susceptibilities of the system are obtained for parameters that represent the dynamic and thermodynamic behavior of glycerol. The calculations for high amplitude sinusoidal fields show a significant enhancement of the steady state loss for frequencies below that of the low field loss peak. Also at relatively low frequencies, the third harmonic susceptibility spectrum shows a “hump,” i.e., a maximum, with an amplitude that increases with decreasing temperature. Both of these non-linear effectsmore » are consistent with experimental evidence. While such features have been used to conclude on a temperature dependent number of dynamically correlated particles, N{sub corr}, the present result demonstrates that the third harmonic susceptibility display a peak with an amplitude that tracks the variation of the activation energy in a model that does not involve dynamical correlations or spatial scales.« less

Identification of Watershed-scale Critical Source Areas Using Bayesian Maximum Entropy Spatiotemporal Analysis

NASA Astrophysics Data System (ADS)

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.

On the Five-Moment Hamburger Maximum Entropy Reconstruction

NASA Astrophysics Data System (ADS)

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.

Donor impurity incorporation during layer growth of Zn II-VI semiconductors

NASA Astrophysics Data System (ADS)

Barlow, D. A.

2017-12-01

The maximum halogen donor concentration in Zn II-VI semiconductors during layer growth is studied using a standard model from statistical mechanics. Here the driving force for incorporation is an increase in entropy upon mixing of the donor impurity into the available anion lattice sites in the host binary. A formation energy opposes this increase and thus equilibrium is attained at some maximum concentration. Considering the halogen donor impurities within the Zn II-VI binary semiconductors ZnO, ZnS, ZnSe and ZnTe, a heat of reaction obtained from reported diatomic bond strengths is shown to be directly proportional to the log of maximum donor concentration. The formation energy can then be estimated and an expression for maximum donor concentration derived. Values for the maximum donor concentration with each of the halogen impurities, within the Zn II-VI compounds, are computed. This model predicts that the halogens will serve as electron donors in these compounds in order of increasing effectiveness as: F, Br, I, Cl. Finally, this result is taken to be equivalent to an alternative model where donor concentration depends upon impurity diffusion and the conduction band energy shift due to a depletion region at the growing crystal's surface. From this, we are able to estimate the diffusion activation energy for each of the impurities mentioned above. Comparisons are made with reported values and relevant conclusions presented.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Maximum entropy production principle for geostrophic turbulence

NASA Astrophysics Data System (ADS)

Sommeria, J.; Bouchet, F.; Chavanis, P. H.

2003-04-01

In 2D turbulence, complex stirring leads to the formation of steady organized states, once fine scale fluctuations have been filtered out. This self-organization can be explained in terms of statistical equilibrium for vorticity, as the most likely outcome of vorticity parcel rearrangements with the constraints of the conservation laws. A mixing entropy describing the vorticity rearrangements is introduced. Extension to the shallow water system has been proposed by Chavanis P.H. and Sommeria J. (2002), Phys. Rev. E. Generalization to multi-layer geostrophic flows is formally straightforward. Outside equilibrium, eddy fluxes should drive the system toward equilibrium, in the spirit of non equilibrium linear thermodynamics. This can been formalized in terms of a principle of maximum entropy production (MEP), as shown by Robert and Sommeria (1991), Phys. Rev. Lett. 69. Then a parameterization of eddy fluxes is obtained, involving an eddy diffusivity plus a drift term acting at larger scale. These two terms balance each other at equilibrium, resulting in a non trivial steady flow, which is the mean state of the statistical equilibrium. Applications of this eddy parametrization will be presented, in the context of oceanic circulation and Jupiter's Great Red Spot. Quantitative tests will be discussed, obtained by comparisons with direct numerical simulations. Kinetic models, inspired from plasma physics, provide a more precise description of the relaxation toward equilibrium, as shown by Chavanis P.H. 2000 ``Quasilinear theory of the 2D Euler equation'', Phys. Rev. Lett. 84. This approach provides relaxation equations with a form similar to the MEP, but not identical. In conclusion, the MEP provides the right trends of the system but its precise justification remains elusive.

Uncertainties have a meaning: Information entropy as a quality measure for 3-D geological models

NASA Astrophysics Data System (ADS)

Wellmann, J. Florian; Regenauer-Lieb, Klaus

2012-03-01

Analyzing, visualizing and communicating uncertainties are important issues as geological models can never be fully determined. To date, there exists no general approach to quantify uncertainties in geological modeling. We propose here to use information entropy as an objective measure to compare and evaluate model and observational results. Information entropy was introduced in the 50s and defines a scalar value at every location in the model for predictability. We show that this method not only provides a quantitative insight into model uncertainties but, due to the underlying concept of information entropy, can be related to questions of data integration (i.e. how is the model quality interconnected with the used input data) and model evolution (i.e. does new data - or a changed geological hypothesis - optimize the model). In other words information entropy is a powerful measure to be used for data assimilation and inversion. As a first test of feasibility, we present the application of the new method to the visualization of uncertainties in geological models, here understood as structural representations of the subsurface. Applying the concept of information entropy on a suite of simulated models, we can clearly identify (a) uncertain regions within the model, even for complex geometries; (b) the overall uncertainty of a geological unit, which is, for example, of great relevance in any type of resource estimation; (c) a mean entropy for the whole model, important to track model changes with one overall measure. These results cannot easily be obtained with existing standard methods. The results suggest that information entropy is a powerful method to visualize uncertainties in geological models, and to classify the indefiniteness of single units and the mean entropy of a model quantitatively. Due to the relationship of this measure to the missing information, we expect the method to have a great potential in many types of geoscientific data assimilation problems — beyond pure visualization.

Estimation of depth to magnetic source using maximum entropy power spectra, with application to the Peru-Chile Trench

USGS Publications Warehouse

Blakely, Richard J.

1981-01-01

Estimations of the depth to magnetic sources using the power spectrum of magnetic anomalies generally require long magnetic profiles. The method developed here uses the maximum entropy power spectrum (MEPS) to calculate depth to source on short windows of magnetic data; resolution is thereby improved. The method operates by dividing a profile into overlapping windows, calculating a maximum entropy power spectrum for each window, linearizing the spectra, and calculating with least squares the various depth estimates. The assumptions of the method are that the source is two dimensional and that the intensity of magnetization includes random noise; knowledge of the direction of magnetization is not required. The method is applied to synthetic data and to observed marine anomalies over the Peru-Chile Trench. The analyses indicate a continuous magnetic basement extending from the eastern margin of the Nazca plate and into the subduction zone. The computed basement depths agree with acoustic basement seaward of the trench axis, but deepen as the plate approaches the inner trench wall. This apparent increase in the computed depths may result from the deterioration of magnetization in the upper part of the ocean crust, possibly caused by compressional disruption of the basaltic layer. Landward of the trench axis, the depth estimates indicate possible thrusting of the oceanic material into the lower slope of the continental margin.

Fitting and Modeling in the ASC Data Analysis Environment

NASA Astrophysics Data System (ADS)

Doe, S.; Siemiginowska, A.; Joye, W.; McDowell, J.

As part of the AXAF Science Center (ASC) Data Analysis Environment, we will provide to the astronomical community a Fitting Application. We present a design of the application in this paper. Our design goal is to give the user the flexibility to use a variety of optimization techniques (Levenberg-Marquardt, maximum entropy, Monte Carlo, Powell, downhill simplex, CERN-Minuit, and simulated annealing) and fit statistics (chi (2) , Cash, variance, and maximum likelihood); our modular design allows the user easily to add their own optimization techniques and/or fit statistics. We also present a comparison of the optimization techniques to be provided by the Application. The high spatial and spectral resolutions that will be obtained with AXAF instruments require a sophisticated data modeling capability. We will provide not only a suite of astronomical spatial and spectral source models, but also the capability of combining these models into source models of up to four data dimensions (i.e., into source functions f(E,x,y,t)). We will also provide tools to create instrument response models appropriate for each observation.

Foraminifera Models to Interrogate Ostensible Proxy-Model Discrepancies During Late Pliocene

NASA Astrophysics Data System (ADS)

Jacobs, P.; Dowsett, H. J.; de Mutsert, K.

2017-12-01

Planktic foraminifera faunal assemblages have been used in the reconstruction of past oceanic states (e.g. the Last Glacial Maximum, the mid-Piacenzian Warm Period). However these reconstruction efforts have typically relied on inverse modeling using transfer functions or the modern analog technique, which by design seek to translate foraminifera into one or two target oceanic variables, primarily sea surface temperature (SST). These reconstructed SST data have then been used to test the performance of climate models, and discrepancies have been attributed to shortcomings in climate model processes and/or boundary conditions. More recently forward proxy models or proxy system models have been used to leverage the multivariate nature of proxy relationships to their environment, and to "bring models into proxy space". Here we construct ecological models of key planktic foraminifera taxa, calibrated and validated with World Ocean Atlas (WO13) oceanographic data. Multiple modeling methods (e.g. multilayer perceptron neural networks, Mahalanobis distance, logistic regression, and maximum entropy) are investigated to ensure robust results. The resulting models are then driven by a Late Pliocene climate model simulation with biogeochemical as well as temperature variables. Similarities and differences with previous model-proxy comparisons (e.g. PlioMIP) are discussed.

A maximum entropy reconstruction technique for tomographic particle image velocimetry

NASA Astrophysics Data System (ADS)

Bilsky, A. V.; Lozhkin, V. A.; Markovich, D. M.; Tokarev, M. P.

2013-04-01

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.

LensEnt2: Maximum-entropy weak lens reconstruction

NASA Astrophysics Data System (ADS)

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.

Halo-independence with quantified maximum entropy at DAMA/LIBRA

NASA Astrophysics Data System (ADS)

Fowlie, Andrew

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.

Comparison of two views of maximum entropy in biodiversity: Frank (2011) and Pueyo et al. (2007).

PubMed

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.

Comparison of two views of maximum entropy in biodiversity: Frank (2011) and Pueyo et al. (2007)

PubMed Central

Pueyo, Salvador

2012-01-01

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. PMID:22837843

MaxEnt-Based Ecological Theory: A Template for Integrated Catchment Theory

NASA Astrophysics Data System (ADS)

Harte, J.

2017-12-01

The maximum information entropy procedure (MaxEnt) is both a powerful tool for inferring least-biased probability distributions from limited data and a framework for the construction of complex systems theory. The maximum entropy theory of ecology (METE) describes remarkably well widely observed patterns in the distribution, abundance and energetics of individuals and taxa in relatively static ecosystems. An extension to ecosystems undergoing change in response to disturbance or natural succession (DynaMETE) is in progress. I describe the structure of both the static and the dynamic theory and show a range of comparisons with census data. I then propose a generalization of the MaxEnt approach that could provide a framework for a predictive theory of both static and dynamic, fully-coupled, eco-socio-hydrological catchment systems.

A non-uniformly sampled 4D HCC(CO)NH-TOCSY experiment processed using maximum entropy for rapid protein sidechain assignment

PubMed Central

Mobli, Mehdi; Stern, Alan S.; Bermel, Wolfgang; King, Glenn F.; Hoch, Jeffrey C.

2010-01-01

One of the stiffest challenges in structural studies of proteins using NMR is the assignment of sidechain resonances. Typically, a panel of lengthy 3D experiments are acquired in order to establish connectivities and resolve ambiguities due to overlap. We demonstrate that these experiments can be replaced by a single 4D experiment that is time-efficient, yields excellent resolution, and captures unique carbon-proton connectivity information. The approach is made practical by the use of non-uniform sampling in the three indirect time dimensions and maximum entropy reconstruction of the corresponding 3D frequency spectrum. This 4D method will facilitate automated resonance assignment procedures and it should be particularly beneficial for increasing throughput in NMR-based structural genomics initiatives. PMID:20299257

Feasibility study of direct spectra measurements for Thomson scattered signals for KSTAR fusion-grade plasmas

NASA Astrophysics Data System (ADS)

Park, K.-R.; Kim, K.-h.; Kwak, S.; Svensson, J.; Lee, J.; Ghim, Y.-c.

2017-11-01

Feasibility study of direct spectra measurements of Thomson scattered photons for fusion-grade plasmas is performed based on a forward model of the KSTAR Thomson scattering system. Expected spectra in the forward model are calculated based on Selden function including the relativistic polarization correction. Noise in the signal is modeled with photon noise and Gaussian electrical noise. Electron temperature and density are inferred using Bayesian probability theory. Based on bias error, full width at half maximum and entropy of posterior distributions, spectral measurements are found to be feasible. Comparisons between spectrometer-based and polychromator-based Thomson scattering systems are performed with varying quantum efficiency and electrical noise levels.

DECONV-TOOL: An IDL based deconvolution software package

NASA Technical Reports Server (NTRS)

Varosi, F.; Landsman, W. B.

1992-01-01

There are a variety of algorithms for deconvolution of blurred images, each having its own criteria or statistic to be optimized in order to estimate the original image data. Using the Interactive Data Language (IDL), we have implemented the Maximum Likelihood, Maximum Entropy, Maximum Residual Likelihood, and sigma-CLEAN algorithms in a unified environment called DeConv_Tool. Most of the algorithms have as their goal the optimization of statistics such as standard deviation and mean of residuals. Shannon entropy, log-likelihood, and chi-square of the residual auto-correlation are computed by DeConv_Tool for the purpose of determining the performance and convergence of any particular method and comparisons between methods. DeConv_Tool allows interactive monitoring of the statistics and the deconvolved image during computation. The final results, and optionally, the intermediate results, are stored in a structure convenient for comparison between methods and review of the deconvolution computation. The routines comprising DeConv_Tool are available via anonymous FTP through the IDL Astronomy User's Library.

Entropy, complexity, and Markov diagrams for random walk cancer models

PubMed Central

Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

2014-01-01

The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential. PMID:25523357

New approach in the quantum statistical parton distribution

NASA Astrophysics Data System (ADS)

Sohaily, Sozha; Vaziri (Khamedi), Mohammad

2017-12-01

An attempt to find simple parton distribution functions (PDFs) based on quantum statistical approach is presented. The PDFs described by the statistical model have very interesting physical properties which help to understand the structure of partons. The longitudinal portion of distribution functions are given by applying the maximum entropy principle. An interesting and simple approach to determine the statistical variables exactly without fitting and fixing parameters is surveyed. Analytic expressions of the x-dependent PDFs are obtained in the whole x region [0, 1], and the computed distributions are consistent with the experimental observations. The agreement with experimental data, gives a robust confirm of our simple presented statistical model.

Using entropy measures to characterize human locomotion.

PubMed

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

2014-12-01

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

Value Focused Thinking Applications to Supervised Pattern Classification With Extensions to Hyperspectral Anomaly Detection Algorithms

DTIC Science & Technology

2015-03-26

performing. All reasonable permutations of factors will be used to develop a multitude of unique combinations. These combinations are considered different...are seen below (Duda et al., 2001). Entropy impurity: () = −�P�ωj�log2P(ωj) j (9) Gini impurity: () =�()�� = 1 2 ∗ [1...proportion of one class to another approaches 0.5, the impurity measure reaches its maximum, which for Entropy is 1.0, while it is 0.5 for Gini and

Regularization of Grad’s 13 -Moment-Equations in Kinetic Gas Theory

DTIC Science & Technology

2011-01-01

variant of the moment method has been proposed by Eu (1980) and is used, e.g., in Myong (2001). Recently, a maximum- entropy 10-moment system has been used...small amplitude linear waves, the R13 system is linearly stable in time for all modes and wave lengths. The instability of the Burnett system indicates...Boltzmann equation. Related to the problem of global hyperbolicity is the questions of the existence of an entropy law for the R13 system . In the linear

Maximum Kolmogorov-Sinai Entropy Versus Minimum Mixing Time in Markov Chains

NASA Astrophysics Data System (ADS)

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.

The Adiabatic Piston and the Second Law of Thermodynamics

NASA Astrophysics Data System (ADS)

Crosignani, Bruno; Di Porto, Paolo; Conti, Claudio

2002-11-01

A detailed analysis of the adiabatic-piston problem reveals peculiar dynamical features that challenge the general belief that isolated systems necessarily reach a static equilibrium state. In particular, the fact that the piston behaves like a perpetuum mobile, i.e., it never stops but keeps wandering, undergoing sizable oscillations, around the position corresponding to maximum entropy, has remarkable implications on the entropy variations of the system and on the validity of the second law when dealing with systems of mesoscopic dimensions.

Maximum Entropy Calculations on a Discrete Probability Space

DTIC Science & Technology

1986-01-01

constraints acting besides normalization. Statement 3: " The aim of this paper is to show that the die experiment just spoken of has solutions by classical ...analysis. Statement 4: We snall solve this problem in a purely classical way, without the need for recourse to any exotic estimator, such as ME." Note... The I’iximoun Entropy Principle lin i rejirk.ible -series ofT papers beginning in 1957, E. T. J.ayiieti (1957) be~gan a revuluuion in inductive

A Novel Multivoxel-Based Quantitation of Metabolites and Lipids Noninvasively Combined with Diffusion-Weighted Imaging in Breast Cancer

DTIC Science & Technology

2013-10-01

cancer for improving the overall specificity.  Our recent work has focused on testing retrospective Maximum Entropy and Compressed Sensing of the 4D...terparts and increases the entropy or sparsity of the reconstructed spectrum by narrowing the peak linewidths and de -noising smaller features. This, in...tightened’ beyond the standard de - viation of the noise in an effort to reduce the RMSE and reconstruc- tion non-linearity, but this prevents the

Dissipated energy and entropy production for an unconventional heat engine: the stepwise `circular cycle'

NASA Astrophysics Data System (ADS)

di Liberto, Francesco; Pastore, Raffaele; Peruggi, Fulvio

2011-05-01

When some entropy is transferred, by means of a reversible engine, from a hot heat source to a colder one, the maximum efficiency occurs, i.e. the maximum available work is obtained. Similarly, a reversible heat pumps transfer entropy from a cold heat source to a hotter one with the minimum expense of energy. In contrast, if we are faced with non-reversible devices, there is some lost work for heat engines, and some extra work for heat pumps. These quantities are both related to entropy production. The lost work, i.e. ? , is also called 'degraded energy' or 'energy unavailable to do work'. The extra work, i.e. ? , is the excess of work performed on the system in the irreversible process with respect to the reversible one (or the excess of heat given to the hotter source in the irreversible process). Both quantities are analysed in detail and are evaluated for a complex process, i.e. the stepwise circular cycle, which is similar to the stepwise Carnot cycle. The stepwise circular cycle is a cycle performed by means of N small weights, dw, which are first added and then removed from the piston of the vessel containing the gas or vice versa. The work performed by the gas can be found as the increase of the potential energy of the dw's. Each single dw is identified and its increase, i.e. its increase in potential energy, evaluated. In such a way it is found how the energy output of the cycle is distributed among the dw's. The size of the dw's affects entropy production and therefore the lost and extra work. The distribution of increases depends on the chosen removal process.

GABAergic excitation of spider mechanoreceptors increases information capacity by increasing entropy rather than decreasing jitter.

PubMed

Pfeiffer, Keram; French, Andrew S

2009-09-02

Neurotransmitter chemicals excite or inhibit a range of sensory afferents and sensory pathways. These changes in firing rate or static sensitivity can also be associated with changes in dynamic sensitivity or membrane noise and thus action potential timing. We measured action potential firing produced by random mechanical stimulation of spider mechanoreceptor neurons during long-duration excitation by the GABAA agonist muscimol. Information capacity was estimated from signal-to-noise ratio by averaging responses to repeated identical stimulation sequences. Information capacity was also estimated from the coherence function between input and output signals. Entropy rate was estimated by a data compression algorithm and maximum entropy rate from the firing rate. Action potential timing variability, or jitter, was measured as normalized interspike interval distance. Muscimol increased firing rate, information capacity, and entropy rate, but jitter was unchanged. We compared these data with the effects of increasing firing rate by current injection. Our results indicate that the major increase in information capacity by neurotransmitter action arose from the increased entropy rate produced by increased firing rate, not from reduction in membrane noise and action potential jitter.

An improved method for predicting the evolution of the characteristic parameters of an information system

NASA Astrophysics Data System (ADS)

Dushkin, A. V.; Kasatkina, T. I.; Novoseltsev, V. I.; Ivanov, S. V.

2018-03-01

The article proposes a forecasting method that allows, based on the given values of entropy and error level of the first and second kind, to determine the allowable time for forecasting the development of the characteristic parameters of a complex information system. The main feature of the method under consideration is the determination of changes in the characteristic parameters of the development of the information system in the form of the magnitude of the increment in the ratios of its entropy. When a predetermined value of the prediction error ratio is reached, that is, the entropy of the system, the characteristic parameters of the system and the depth of the prediction in time are estimated. The resulting values of the characteristics and will be optimal, since at that moment the system possessed the best ratio of entropy as a measure of the degree of organization and orderliness of the structure of the system. To construct a method for estimating the depth of prediction, it is expedient to use the maximum principle of the value of entropy.

Force-Time Entropy of Isometric Impulse.

PubMed

Hsieh, Tsung-Yu; Newell, Karl M

2016-01-01

The relation between force and temporal variability in discrete impulse production has been viewed as independent (R. A. Schmidt, H. Zelaznik, B. Hawkins, J. S. Frank, & J. T. Quinn, 1979 ) or dependent on the rate of force (L. G. Carlton & K. M. Newell, 1993 ). Two experiments in an isometric single finger force task investigated the joint force-time entropy with (a) fixed time to peak force and different percentages of force level and (b) fixed percentage of force level and different times to peak force. The results showed that the peak force variability increased either with the increment of force level or through a shorter time to peak force that also reduced timing error variability. The peak force entropy and entropy of time to peak force increased on the respective dimension as the parameter conditions approached either maximum force or a minimum rate of force production. The findings show that force error and timing error are dependent but complementary when considered in the same framework with the joint force-time entropy at a minimum in the middle parameter range of discrete impulse.

Prediction of Spatiotemporal Patterns of Neural Activity from Pairwise Correlations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marre, O.; El Boustani, S.; Fregnac, Y.

We designed a model-based analysis to predict the occurrence of population patterns in distributed spiking activity. Using a maximum entropy principle with a Markovian assumption, we obtain a model that accounts for both spatial and temporal pairwise correlations among neurons. This model is tested on data generated with a Glauber spin-glass system and is shown to correctly predict the occurrence probabilities of spatiotemporal patterns significantly better than Ising models only based on spatial correlations. This increase of predictability was also observed on experimental data recorded in parietal cortex during slow-wave sleep. This approach can also be used to generate surrogatesmore » that reproduce the spatial and temporal correlations of a given data set.« less

Probabilistic Modeling of Aircraft Trajectories for Dynamic Separation Volumes

NASA Technical Reports Server (NTRS)

Lewis, Timothy A.

2016-01-01

With a proliferation of new and unconventional vehicles and operations expected in the future, the ab initio airspace design will require new approaches to trajectory prediction for separation assurance and other air traffic management functions. This paper presents an approach to probabilistic modeling of the trajectory of an aircraft when its intent is unknown. The approach uses a set of feature functions to constrain a maximum entropy probability distribution based on a set of observed aircraft trajectories. This model can be used to sample new aircraft trajectories to form an ensemble reflecting the variability in an aircraft's intent. The model learning process ensures that the variability in this ensemble reflects the behavior observed in the original data set. Computational examples are presented.

Lévy-like diffusion in eye movements during spoken-language comprehension.

PubMed

Stephen, Damian G; Mirman, Daniel; Magnuson, James S; Dixon, James A

2009-05-01

This study explores the diffusive properties of human eye movements during a language comprehension task. In this task, adults are given auditory instructions to locate named objects on a computer screen. Although it has been convention to model visual search as standard Brownian diffusion, we find evidence that eye movements are hyperdiffusive. Specifically, we use comparisons of maximum-likelihood fit as well as standard deviation analysis and diffusion entropy analysis to show that visual search during language comprehension exhibits Lévy-like rather than Gaussian diffusion.

Lévy-like diffusion in eye movements during spoken-language comprehension

NASA Astrophysics Data System (ADS)

Stephen, Damian G.; Mirman, Daniel; Magnuson, James S.; Dixon, James A.

2009-05-01

This study explores the diffusive properties of human eye movements during a language comprehension task. In this task, adults are given auditory instructions to locate named objects on a computer screen. Although it has been convention to model visual search as standard Brownian diffusion, we find evidence that eye movements are hyperdiffusive. Specifically, we use comparisons of maximum-likelihood fit as well as standard deviation analysis and diffusion entropy analysis to show that visual search during language comprehension exhibits Lévy-like rather than Gaussian diffusion.

Comparison of liquid-state anomalies in Stillinger-Weber models of water, silicon, and germanium

NASA Astrophysics Data System (ADS)

Dhabal, Debdas; Chakravarty, Charusita; Molinero, Valeria; Kashyap, Hemant K.

2016-12-01

We use molecular dynamics simulations to compare and contrast the liquid-state anomalies in the Stillinger-Weber models of monatomic water (mW), silicon (Si), and germanium (Ge) over a fairly wide range of temperatures and densities. The relationships between structure, entropy, and mobility, as well as the extent of the regions of anomalous behavior, are discussed as a function of the degree of tetrahedrality. We map out the cascade of density, structural, pair entropy, excess entropy, viscosity, and diffusivity anomalies for these three liquids. Among the three liquids studied here, only mW displays anomalies in the thermal conductivity, and this anomaly is evident only at very low temperatures. Diffusivity and viscosity, on the other hand, show pronounced anomalous regions for the three liquids. The temperature of maximum density of the three liquids shows re-entrant behavior consistent with either singularity-free or liquid-liquid critical point scenarios proposed to explain thermodynamic anomalies. The order-map, which shows the evolution of translational versus tetrahedral order in liquids, is different for Ge than for Si and mW. We find that although the monatomic water reproduces several thermodynamic and dynamic properties of rigid-body water models (e.g., SPC/E, TIP4P/2005), its sequence of anomalies follows, the same as Si and Ge, the silica-like hierarchy: the region of dynamic (diffusivity and viscosity) anomalies encloses the region of structural anomalies, which in turn encloses the region of density anomaly. The hierarchy of the anomalies based on excess entropy and Rosenfeld scaling, on the other hand, reverses the order of the structural and dynamic anomalies, i.e., predicts that the three Stillinger-Weber liquids follow a water-like hierarchy of anomalies. We investigate the scaling of diffusivity, viscosity, and thermal conductivity with the excess entropy of the liquid and find that for dynamical properties that present anomalies there is no universal scaling of the reduced property with excess entropy for the whole range of temperatures and densities. Instead, Rosenfeld's scaling holds for all the three liquids at high densities and high temperatures, although deviations from simple exponential dependence are observed for diffusivity and viscosity at lower temperatures and intermediate densities. The slope of the scaling of transport properties obtained for Ge is comparable to that obtained for simple liquids, suggesting that this low tetrahedrality liquid, although it stabilizes a diamond crystal, is already close to simple liquid behavior for certain properties.

Comparison of liquid-state anomalies in Stillinger-Weber models of water, silicon, and germanium.

PubMed

Dhabal, Debdas; Chakravarty, Charusita; Molinero, Valeria; Kashyap, Hemant K

2016-12-07

We use molecular dynamics simulations to compare and contrast the liquid-state anomalies in the Stillinger-Weber models of monatomic water (mW), silicon (Si), and germanium (Ge) over a fairly wide range of temperatures and densities. The relationships between structure, entropy, and mobility, as well as the extent of the regions of anomalous behavior, are discussed as a function of the degree of tetrahedrality. We map out the cascade of density, structural, pair entropy, excess entropy, viscosity, and diffusivity anomalies for these three liquids. Among the three liquids studied here, only mW displays anomalies in the thermal conductivity, and this anomaly is evident only at very low temperatures. Diffusivity and viscosity, on the other hand, show pronounced anomalous regions for the three liquids. The temperature of maximum density of the three liquids shows re-entrant behavior consistent with either singularity-free or liquid-liquid critical point scenarios proposed to explain thermodynamic anomalies. The order-map, which shows the evolution of translational versus tetrahedral order in liquids, is different for Ge than for Si and mW. We find that although the monatomic water reproduces several thermodynamic and dynamic properties of rigid-body water models (e.g., SPC/E, TIP4P/2005), its sequence of anomalies follows, the same as Si and Ge, the silica-like hierarchy: the region of dynamic (diffusivity and viscosity) anomalies encloses the region of structural anomalies, which in turn encloses the region of density anomaly. The hierarchy of the anomalies based on excess entropy and Rosenfeld scaling, on the other hand, reverses the order of the structural and dynamic anomalies, i.e., predicts that the three Stillinger-Weber liquids follow a water-like hierarchy of anomalies. We investigate the scaling of diffusivity, viscosity, and thermal conductivity with the excess entropy of the liquid and find that for dynamical properties that present anomalies there is no universal scaling of the reduced property with excess entropy for the whole range of temperatures and densities. Instead, Rosenfeld's scaling holds for all the three liquids at high densities and high temperatures, although deviations from simple exponential dependence are observed for diffusivity and viscosity at lower temperatures and intermediate densities. The slope of the scaling of transport properties obtained for Ge is comparable to that obtained for simple liquids, suggesting that this low tetrahedrality liquid, although it stabilizes a diamond crystal, is already close to simple liquid behavior for certain properties.

Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2017-09-01

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

A new assessment method for urbanization environmental impact: urban environment entropy model and its application.

PubMed

Ouyang, Tingping; Fu, Shuqing; Zhu, Zhaoyu; Kuang, Yaoqiu; Huang, Ningsheng; Wu, Zhifeng

2008-11-01

The thermodynamic law is one of the most widely used scientific principles. The comparability between the environmental impact of urbanization and the thermodynamic entropy was systematically analyzed. Consequently, the concept "Urban Environment Entropy" was brought forward and the "Urban Environment Entropy" model was established for urbanization environmental impact assessment in this study. The model was then utilized in a case study for the assessment of river water quality in the Pearl River Delta Economic Zone. The results indicated that the assessing results of the model are consistent to that of the equalized synthetic pollution index method. Therefore, it can be concluded that the Urban Environment Entropy model has high reliability and can be applied widely in urbanization environmental assessment research using many different environmental parameters.

Two aspects of black hole entropy in Lanczos-Lovelock models of gravity

NASA Astrophysics Data System (ADS)

Kolekar, Sanved; Kothawala, Dawood; Padmanabhan, T.

2012-03-01

We consider two specific approaches to evaluate the black hole entropy which are known to produce correct results in the case of Einstein’s theory and generalize them to Lanczos-Lovelock models. In the first approach (which could be called extrinsic), we use a procedure motivated by earlier work by Pretorius, Vollick, and Israel, and by Oppenheim, and evaluate the entropy of a configuration of densely packed gravitating shells on the verge of forming a black hole in Lanczos-Lovelock theories of gravity. We find that this matter entropy is not equal to (it is less than) Wald entropy, except in the case of Einstein theory, where they are equal. The matter entropy is proportional to the Wald entropy if we consider a specific mth-order Lanczos-Lovelock model, with the proportionality constant depending on the spacetime dimensions D and the order m of the Lanczos-Lovelock theory as (D-2m)/(D-2). Since the proportionality constant depends on m, the proportionality between matter entropy and Wald entropy breaks down when we consider a sum of Lanczos-Lovelock actions involving different m. In the second approach (which could be called intrinsic), we generalize a procedure, previously introduced by Padmanabhan in the context of general relativity, to study off-shell entropy of a class of metrics with horizon using a path integral method. We consider the Euclidean action of Lanczos-Lovelock models for a class of metrics off shell and interpret it as a partition function. We show that in the case of spherically symmetric metrics, one can interpret the Euclidean action as the free energy and read off both the entropy and energy of a black hole spacetime. Surprisingly enough, this leads to exactly the Wald entropy and the energy of the spacetime in Lanczos-Lovelock models obtained by other methods. We comment on possible implications of the result.

Subgrid-scale Condensation Modeling for Entropy-based Large Eddy Simulations of Clouds

NASA Astrophysics Data System (ADS)

Kaul, C. M.; Schneider, T.; Pressel, K. G.; Tan, Z.

2015-12-01

An entropy- and total water-based formulation of LES thermodynamics, such as that used by the recently developed code PyCLES, is advantageous from physical and numerical perspectives. However, existing closures for subgrid-scale thermodynamic fluctuations assume more traditional choices for prognostic thermodynamic variables, such as liquid potential temperature, and are not directly applicable to entropy-based modeling. Since entropy and total water are generally nonlinearly related to diagnosed quantities like temperature and condensate amounts, neglecting their small-scale variability can lead to bias in simulation results. Here we present the development of a subgrid-scale condensation model suitable for use with entropy-based thermodynamic formulations.

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

PubMed Central

2016-01-01

Characterizing how people move through space has been an important component of many disciplines. With the advent of automated data collection through GPS and other location sensing systems, researchers have the opportunity to examine human mobility at spatio-temporal resolution heretofore impossible. However, the copious and complex data collected through these logging systems can be difficult for humans to fully exploit, leading many researchers to propose novel metrics for encapsulating movement patterns in succinct and useful ways. A particularly salient proposed metric is the mobility entropy rate of the string representing the sequence of locations visited by an individual. However, mobility entropy rate is not scale invariant: entropy rate calculations based on measurements of the same trajectory at varying spatial or temporal granularity do not yield the same value, limiting the utility of mobility entropy rate as a metric by confounding inter-experimental comparisons. In this paper, we derive a scaling relationship for mobility entropy rate of non-repeating straight line paths from the definition of Lempel-Ziv compression. We show that the resulting formulation predicts the scaling behavior of simulated mobility traces, and provides an upper bound on mobility entropy rate under certain assumptions. We further show that this formulation has a maximum value for a particular sampling rate, implying that optimal sampling rates for particular movement patterns exist. PMID:27571423

Modeling Information Content Via Dirichlet-Multinomial Regression Analysis.

PubMed

Ferrari, Alberto

2017-01-01

Shannon entropy is being increasingly used in biomedical research as an index of complexity and information content in sequences of symbols, e.g. languages, amino acid sequences, DNA methylation patterns and animal vocalizations. Yet, distributional properties of information entropy as a random variable have seldom been the object of study, leading to researchers mainly using linear models or simulation-based analytical approach to assess differences in information content, when entropy is measured repeatedly in different experimental conditions. Here a method to perform inference on entropy in such conditions is proposed. Building on results coming from studies in the field of Bayesian entropy estimation, a symmetric Dirichlet-multinomial regression model, able to deal efficiently with the issue of mean entropy estimation, is formulated. Through a simulation study the model is shown to outperform linear modeling in a vast range of scenarios and to have promising statistical properties. As a practical example, the method is applied to a data set coming from a real experiment on animal communication.

Parameter Estimation as a Problem in Statistical Thermodynamics.

PubMed

Earle, Keith A; Schneider, David J

2011-03-14

In this work, we explore the connections between parameter fitting and statistical thermodynamics using the maxent principle of Jaynes as a starting point. In particular, we show how signal averaging may be described by a suitable one particle partition function, modified for the case of a variable number of particles. These modifications lead to an entropy that is extensive in the number of measurements in the average. Systematic error may be interpreted as a departure from ideal gas behavior. In addition, we show how to combine measurements from different experiments in an unbiased way in order to maximize the entropy of simultaneous parameter fitting. We suggest that fit parameters may be interpreted as generalized coordinates and the forces conjugate to them may be derived from the system partition function. From this perspective, the parameter fitting problem may be interpreted as a process where the system (spectrum) does work against internal stresses (non-optimum model parameters) to achieve a state of minimum free energy/maximum entropy. Finally, we show how the distribution function allows us to define a geometry on parameter space, building on previous work[1, 2]. This geometry has implications for error estimation and we outline a program for incorporating these geometrical insights into an automated parameter fitting algorithm.

Evaluation of cluster expansions and correlated one-body properties of nuclei

NASA Astrophysics Data System (ADS)

Moustakidis, Ch. C.; Massen, S. E.; Panos, C. P.; Grypeos, M. E.; Antonov, A. N.

2001-07-01

Three different cluster expansions for the evaluation of correlated one-body properties of s-p and s-d shell nuclei are compared. Harmonic oscillator wave functions and Jastrow-type correlations are used, while analytical expressions are obtained for the charge form factor, density distribution, and momentum distribution by truncating the expansions and using a standard Jastrow correlation function f. The harmonic oscillator parameter b and the correlation parameter β have been determined by a least-squares fit to the experimental charge form factors in each case. The information entropy of nuclei in position space (Sr) and momentum space (Sk) according to the three methods are also calculated. It is found that the larger the entropy sum, S=Sr+Sk (the net information content of the system), the smaller the values of χ2. This indicates that maximal S is a criterion of the quality of a given nuclear model, according to the maximum entropy principle. Only two exceptions to this rule, out of many cases examined, were found. Finally an analytic expression for the so-called ``healing'' or ``wound'' integrals is derived with the function f considered, for any state of the relative two-nucleon motion, and their values in certain cases are computed and compared.

An Improved Evidential-IOWA Sensor Data Fusion Approach in Fault Diagnosis

PubMed Central

Zhou, Deyun; Zhuang, Miaoyan; Fang, Xueyi; Xie, Chunhe

2017-01-01

As an important tool of information fusion, Dempster–Shafer evidence theory is widely applied in handling the uncertain information in fault diagnosis. However, an incorrect result may be obtained if the combined evidence is highly conflicting, which may leads to failure in locating the fault. To deal with the problem, an improved evidential-Induced Ordered Weighted Averaging (IOWA) sensor data fusion approach is proposed in the frame of Dempster–Shafer evidence theory. In the new method, the IOWA operator is used to determine the weight of different sensor data source, while determining the parameter of the IOWA, both the distance of evidence and the belief entropy are taken into consideration. First, based on the global distance of evidence and the global belief entropy, the α value of IOWA is obtained. Simultaneously, a weight vector is given based on the maximum entropy method model. Then, according to IOWA operator, the evidence are modified before applying the Dempster’s combination rule. The proposed method has a better performance in conflict management and fault diagnosis due to the fact that the information volume of each evidence is taken into consideration. A numerical example and a case study in fault diagnosis are presented to show the rationality and efficiency of the proposed method. PMID:28927017

Equivalence of MAXENT and Poisson point process models for species distribution modeling in ecology.

PubMed

Renner, Ian W; Warton, David I

2013-03-01

Modeling the spatial distribution of a species is a fundamental problem in ecology. A number of modeling methods have been developed, an extremely popular one being MAXENT, a maximum entropy modeling approach. In this article, we show that MAXENT is equivalent to a Poisson regression model and hence is related to a Poisson point process model, differing only in the intercept term, which is scale-dependent in MAXENT. We illustrate a number of improvements to MAXENT that follow from these relations. In particular, a point process model approach facilitates methods for choosing the appropriate spatial resolution, assessing model adequacy, and choosing the LASSO penalty parameter, all currently unavailable to MAXENT. The equivalence result represents a significant step in the unification of the species distribution modeling literature. Copyright © 2013, The International Biometric Society.

Statistical Neurodynamics.

NASA Astrophysics Data System (ADS)

Paine, Gregory Harold

1982-03-01

The primary objective of the thesis is to explore the dynamical properties of small nerve networks by means of the methods of statistical mechanics. To this end, a general formalism is developed and applied to elementary groupings of model neurons which are driven by either constant (steady state) or nonconstant (nonsteady state) forces. Neuronal models described by a system of coupled, nonlinear, first-order, ordinary differential equations are considered. A linearized form of the neuronal equations is studied in detail. A Lagrange function corresponding to the linear neural network is constructed which, through a Legendre transformation, provides a constant of motion. By invoking the Maximum-Entropy Principle with the single integral of motion as a constraint, a probability distribution function for the network in a steady state can be obtained. The formalism is implemented for some simple networks driven by a constant force; accordingly, the analysis focuses on a study of fluctuations about the steady state. In particular, a network composed of N noninteracting neurons, termed Free Thinkers, is considered in detail, with a view to interpretation and numerical estimation of the Lagrange multiplier corresponding to the constant of motion. As an archetypical example of a net of interacting neurons, the classical neural oscillator, consisting of two mutually inhibitory neurons, is investigated. It is further shown that in the case of a network driven by a nonconstant force, the Maximum-Entropy Principle can be applied to determine a probability distribution functional describing the network in a nonsteady state. The above examples are reconsidered with nonconstant driving forces which produce small deviations from the steady state. Numerical studies are performed on simplified models of two physical systems: the starfish central nervous system and the mammalian olfactory bulb. Discussions are given as to how statistical neurodynamics can be used to gain a better understanding of the behavior of these systems.

Quantile-based Bayesian maximum entropy approach for spatiotemporal modeling of ambient air quality levels.

PubMed

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.

Binary versus non-binary information in real time series: empirical results and maximum-entropy matrix models

NASA Astrophysics Data System (ADS)

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.

A comparative study on the mechanical energy of the normal, ACL, osteoarthritis, and Parkinson subjects.

PubMed

Bahreinizad, Hossein; Salimi Bani, Milad; Hasani, Mojtaba; Karimi, Mohammad Taghi; Sharifmoradi, Keyvan; Karimi, Alireza

2017-08-09

The influence of various musculoskeletal disorders has been evaluated using different kinetic and kinematic parameters. But the efficiency of walking can be evaluated by measuring the effort of the subject, or by other words the energy that is required to walk. The aim of this study was to identify mechanical energy differences between the normal and pathological groups. Four groups of 15 healthy subjects, 13 Parkinson subjects, 4 osteoarthritis subjects, and 4 ACL reconstructed subjects have participated in this study. The motions of foot, shank and thigh were recorded using a three dimensional motion analysis system. The kinetic, potential and total mechanical energy of each segment was calculated using 3D markers positions and anthropometric measurements. Maximum value and sample entropy of energies was compared between the normal and abnormal subjects. Maximum value of potential energy of OA subjects was lower than the normal subjects. Furthermore, sample entropy of mechanical energy for Parkinson subjects was low in comparison to the normal subjects while sample entropy of mechanical energy for the ACL subjects was higher than that of the normal subjects. Findings of this study suggested that the subjects with different abilities show different mechanical energy during walking.

Multi-GPU maximum entropy image synthesis for radio astronomy

NASA Astrophysics Data System (ADS)

Cárcamo, M.; Román, P. E.; Casassus, S.; Moral, V.; Rannou, F. R.

2018-01-01

The maximum entropy method (MEM) is a well known deconvolution technique in radio-interferometry. This method solves a non-linear optimization problem with an entropy regularization term. Other heuristics such as CLEAN are faster but highly user dependent. Nevertheless, MEM has the following advantages: it is unsupervised, it has a statistical basis, it has a better resolution and better image quality under certain conditions. This work presents a high performance GPU version of non-gridding MEM, which is tested using real and simulated data. We propose a single-GPU and a multi-GPU implementation for single and multi-spectral data, respectively. We also make use of the Peer-to-Peer and Unified Virtual Addressing features of newer GPUs which allows to exploit transparently and efficiently multiple GPUs. Several ALMA data sets are used to demonstrate the effectiveness in imaging and to evaluate GPU performance. The results show that a speedup from 1000 to 5000 times faster than a sequential version can be achieved, depending on data and image size. This allows to reconstruct the HD142527 CO(6-5) short baseline data set in 2.1 min, instead of 2.5 days that takes a sequential version on CPU.

A maximum entropy fracture model for low and high strain-rate fracture in TinSilverCopper alloys

NASA Astrophysics Data System (ADS)

Chan, Dennis K.

SnAgCu solder alloys exhibit significant rate-dependent constitutive behavior. Solder joints made of these alloys exhibit failure modes that are also rate-dependent. Solder joints are an integral part of microelectronic packages and are subjected to a wide variety of loading conditions which range from thermo-mechanical fatigue to impact loading. Consequently, there is a need for non-empirical rate-dependent failure theory that is able to accurately predict fracture in these solder joints. In the present thesis, various failure models are first reviewed. But, these models are typically empirical or are not valid for solder joints due to limiting assumptions such as elastic behavior. Here, the development and validation of a maximum entropy fracture model (MEFM) valid for low strain-rate fracture in SnAgCu solders is presented. To this end, work on characterizing SnAgCu solder behavior at low strain-rates using a specially designed tester to estimate parameters for constitutive models is presented. Next, the maximum entropy fracture model is reviewed. This failure model uses a single damage accumulation parameter and relates the risk of fracture to accumulated inelastic dissipation. A methodology is presented to extract this model parameter through a custom-built microscale mechanical tester for Sn3.8Ag0.7Cu solder. This single parameter is used to numerically simulate fracture in two solder joints with entirely different geometries. The simulations are compared to experimentally observed fracture in these same packages. Following the simulations of fracture at low strain rate, the constitutive behavior of solder alloys across nine decades of strain rates through MTS compression tests and split-Hopkinson bar are presented. Preliminary work on using orthogonal machining as novel technique of material characterization at high strain rates is also presented. The resultant data from the MTS compression and split-Hopkinson bar tester is used to demonstrate the localization of stress to the interface of solder joints at high strain rates. The MEFM is further extended to predict failure in brittle materials. Such an extension allows for fracture prediction within intermetallic compounds (IMCs) in solder joints. It has been experimentally observed that the failure mode shifts from bulk solder to the IMC layer with increasing loading rates. The extension of the MEFM would allow for prediction of the fracture mode within the solder joint under different loading conditions. A fracture model capable of predicting failure modes at higher strain rates is necessary, as mobile electronics are becoming ubiquitous. Mobile devices are prone to being dropped which can induce loading rates within solder joints that are much larger than experienced under thermo-mechanical fatigue. A range of possible damage accumulation parameters for Cu6Sn 5 is determined for the MEFM. A value within the aforementioned range is used to demonstrate the increasing likelihood of IMC fracture in solder joints with larger loading rates. The thesis is concluded with remarks about ongoing work that include determining a more accurate damage accumulation parameter for Cu6Sn 5 IMC, and on using machining as a technique for extracting failure parameters for the MEFM.

Maximum entropy principle for stationary states underpinned by stochastic thermodynamics.

PubMed

Ford, Ian J

2015-11-01

The selection of an equilibrium state by maximizing the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of incomplete information. But such a framework can be more compelling if it is underpinned by dynamical arguments, and we show how this can be provided by stochastic thermodynamics, where an explicit link is made between the production of entropy and the stochastic dynamics of a system coupled to an environment. The separation of entropy production into three components allows us to select a stationary state by maximizing the change, averaged over all realizations of the motion, in the principal relaxational or nonadiabatic component, equivalent to requiring that this contribution to the entropy production should become time independent for all realizations. We show that this recovers the usual equilibrium probability density function (pdf) for a conservative system in an isothermal environment, as well as the stationary nonequilibrium pdf for a particle confined to a potential under nonisothermal conditions, and a particle subject to a constant nonconservative force under isothermal conditions. The two remaining components of entropy production account for a recently discussed thermodynamic anomaly between over- and underdamped treatments of the dynamics in the nonisothermal stationary state.

Origin of generalized entropies and generalized statistical mechanics for superstatistical multifractal systems

NASA Astrophysics Data System (ADS)

Gadjiev, Bahruz; Progulova, Tatiana

2015-01-01

We consider a multifractal structure as a mixture of fractal substructures and introduce a distribution function f (α), where α is a fractal dimension. Then we can introduce g(p)˜ ∫- ln p μe-yf(y)dy and show that the distribution functions f (α) in the form of f(α) = δ(α-1), f(α) = δ(α-θ) , f(α) = 1/α-1 , f(y)= y α-1 lead to the Boltzmann - Gibbs, Shafee, Tsallis and Anteneodo - Plastino entropies conformably. Here δ(x) is the Dirac delta function. Therefore the Shafee entropy corresponds to a fractal structure, the Tsallis entropy describes a multifractal structure with a homogeneous distribution of fractal substructures and the Anteneodo - Plastino entropy appears in case of a power law distribution f (y). We consider the Fokker - Planck equation for a fractal substructure and determine its stationary solution. To determine the distribution function of a multifractal structure we solve the two-dimensional Fokker - Planck equation and obtain its stationary solution. Then applying the Bayes theorem we obtain a distribution function for the entire system in the form of q-exponential function. We compare the results of the distribution functions obtained due to the superstatistical approach with the ones obtained according to the maximum entropy principle.

Halo-independence with quantified maximum entropy at DAMA/LIBRA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fowlie, Andrew, E-mail: andrew.j.fowlie@googlemail.com

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.more » 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.« less

How the Second Law of Thermodynamics Has Informed Ecosystem Ecology through Its History

NASA Astrophysics Data System (ADS)

Chapman, E. J.; Childers, D. L.; Vallino, J. J.

2014-12-01

Throughout the history of ecosystem ecology many attempts have been made to develop a general principle governing how systems develop and organize. We reviewed the historical developments that led to conceptualization of several goal-oriented principles in ecosystem ecology and the relationships among them. We focused our review on two prominent principles—the Maximum Power Principle and the Maximum Entropy Production Principle—and the literature that applies to both. While these principles have considerable conceptual overlap and both use concepts in physics (power and entropy), we found considerable differences in their historical development, the disciplines that apply these principles, and their adoption in the literature. We reviewed the literature using Web of Science keyword searches for the MPP, the MEPP, as well as for papers that cited pioneers in the MPP and the MEPP development. From the 6000 papers that our keyword searches returned, we limited our further meta-analysis to 32 papers by focusing on studies with a foundation in ecosystems research. Despite these seemingly disparate pasts, we concluded that the conceptual approaches of these two principles were more similar than dissimilar and that maximization of power in ecosystems occurs with maximum entropy production. We also found that these two principles have great potential to explain how systems develop, organize, and function, but there are no widely agreed upon theoretical derivations for the MEPP or the MPP, possibly hindering their broader use in ecological research. We end with recommendations for how ecosystems-level studies may better use these principles.

Predictive Computational Modeling of Chromatin Folding

NASA Astrophysics Data System (ADS)

di Pierro, Miichele; Zhang, Bin; Wolynes, Peter J.; Onuchic, Jose N.

In vivo, the human genome folds into well-determined and conserved three-dimensional structures. The mechanism driving the folding process remains unknown. We report a theoretical model (MiChroM) for chromatin derived by using the maximum entropy principle. The proposed model allows Molecular Dynamics simulations of the genome using as input the classification of loci into chromatin types and the presence of binding sites of loop forming protein CTCF. The model was trained to reproduce the Hi-C map of chromosome 10 of human lymphoblastoid cells. With no additional tuning the model was able to predict accurately the Hi-C maps of chromosomes 1-22 for the same cell line. Simulations show unknotted chromosomes, phase separation of chromatin types and a preference of chromatin of type A to sit at the periphery of the chromosomes.

Entanglement entropy production in gravitational collapse: covariant regularization and solvable models

NASA Astrophysics Data System (ADS)

Bianchi, Eugenio; De Lorenzo, Tommaso; Smerlak, Matteo

2015-06-01

We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the "black hole fireworks" model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that ( i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, ( ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the "purifying" phase, ( iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.

Steepest-entropy-ascent quantum thermodynamic modeling of the relaxation process of isolated chemically reactive systems using density of states and the concept of hypoequilibrium state

NASA Astrophysics Data System (ADS)

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 associated degeneracies. Their significance for the nonequilibrium evolution of system state is discussed. For the application presented, the numerical method used is described and is based on the density of states, which is specifically developed to solve the SEAQT equation of motion. Results for different kinds of initial nonequilibrium conditions, i.e., those for gamma and Maxwellian distributions, are studied. The advantage of the concept of hypoequilibrium state in studying nonequilibrium trajectories is discussed.

Entropy-based financial asset pricing.

PubMed

Ormos, Mihály; Zibriczky, Dávid

2014-01-01

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

Entropy-Based Financial Asset Pricing

PubMed Central

Ormos, Mihály; Zibriczky, Dávid

2014-01-01

We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return – entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy. PMID:25545668

Entropy Generation Across Earth's Bow Shock

NASA Technical Reports Server (NTRS)

Parks, George K.; McCarthy, Michael; Fu, Suiyan; Lee E. s; Cao, Jinbin; Goldstein, Melvyn L.; Canu, Patrick; Dandouras, Iannis S.; Reme, Henri; Fazakerley, Andrew;

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model.

PubMed

Chao, Anne; Jost, Lou; Hsieh, T C; Ma, K H; Sherwin, William B; Rollins, Lee Ann

2015-01-01

Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information ("Shannon differentiation") between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.

Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

PubMed Central

Ito, Sosuke

2016-01-01

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics. PMID:27833120

Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

NASA Astrophysics Data System (ADS)

Ito, Sosuke

2016-11-01

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics.

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

NASA Astrophysics Data System (ADS)

Shi, Yan; Lu, Zhenzhou; Zhou, Yicheng

2018-06-01

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

Generalized entropy formalism and a new holographic dark energy model

NASA Astrophysics Data System (ADS)

Sayahian Jahromi, A.; Moosavi, S. A.; Moradpour, H.; Morais Graça, J. P.; Lobo, I. P.; Salako, I. G.; Jawad, A.

2018-05-01

Recently, the Rényi and Tsallis generalized entropies have extensively been used in order to study various cosmological and gravitational setups. Here, using a special type of generalized entropy, a generalization of both the Rényi and Tsallis entropy, together with holographic principle, we build a new model for holographic dark energy. Thereinafter, considering a flat FRW universe, filled by a pressureless component and the new obtained dark energy model, the evolution of cosmos has been investigated showing satisfactory results and behavior. In our model, the Hubble horizon plays the role of IR cutoff, and there is no mutual interaction between the cosmos components. Our results indicate that the generalized entropy formalism may open a new window to become more familiar with the nature of spacetime and its properties.

[Evaluation of a simplified index (spectral entropy) about sleep state of electrocardiogram recorded by a simplified polygraph, MemCalc-Makin2].

PubMed

Ohisa, Noriko; Ogawa, Hiromasa; Murayama, Nobuki; Yoshida, Katsumi

2010-02-01

Polysomnography (PSG) is the gold standard for the diagnosis of sleep apnea hypopnea syndrome (SAHS), but it takes time to analyze the PSG and PSG cannot be performed repeatedly because of efforts and costs. Therefore, simplified sleep respiratory disorder indices in which are reflected the PSG results are needed. The Memcalc method, which is a combination of the maximum entropy method for spectral analysis and the non-linear least squares method for fitting analysis (Makin2, Suwa Trust, Tokyo, Japan) has recently been developed. Spectral entropy which is derived by the Memcalc method might be useful to expressing the trend of time-series behavior. Spectral entropy of ECG which is calculated with the Memcalc method was evaluated by comparing to the PSG results. Obstructive SAS patients (n = 79) and control volanteer (n = 7) ECG was recorded using MemCalc-Makin2 (GMS) with PSG recording using Alice IV (Respironics) from 20:00 to 6:00. Spectral entropy of ECG, which was calculated every 2 seconds using the Memcalc method, was compared to sleep stages which were analyzed manually from PSG recordings. Spectral entropy value (-0.473 vs. -0.418, p < 0.05) were significantly increased in the OSAHS compared to the control. For the entropy cutoff level of -0.423, sensitivity and specificity for OSAHS were 86.1% and 71.4%, respectively, resulting in a receiver operating characteristic with an area under the curve of 0.837. The absolute value of entropy had inverse correlation with stage 3. Spectral entropy, which was calculated with Memcalc method, might be a possible index evaluating the quality of sleep.

Methodes entropiques appliquees au probleme inverse en magnetoencephalographie

NASA Astrophysics Data System (ADS)

Lapalme, Ervig

2005-07-01

This thesis is devoted to biomagnetic source localization using magnetoencephalography. This problem is known to have an infinite number of solutions. So methods are required to take into account anatomical and functional information on the solution. The work presented in this thesis uses the maximum entropy on the mean method to constrain the solution. This method originates from statistical mechanics and information theory. This thesis is divided into two main parts containing three chapters each. The first part reviews the magnetoencephalographic inverse problem: the theory needed to understand its context and the hypotheses for simplifying the problem. In the last chapter of this first part, the maximum entropy on the mean method is presented: its origins are explained and also how it is applied to our problem. The second part is the original work of this thesis presenting three articles; one of them already published and two others submitted for publication. In the first article, a biomagnetic source model is developed and applied in a theoretical con text but still demonstrating the efficiency of the method. In the second article, we go one step further towards a realistic modelization of the cerebral activation. The main priors are estimated using the magnetoencephalographic data. This method proved to be very efficient in realistic simulations. In the third article, the previous method is extended to deal with time signals thus exploiting the excellent time resolution offered by magnetoencephalography. Compared with our previous work, the temporal method is applied to real magnetoencephalographic data coming from a somatotopy experience and results agree with previous physiological knowledge about this kind of cognitive process.

Core surface magnetic field evolution 2000-2010

NASA Astrophysics Data System (ADS)

Finlay, C. C.; Jackson, A.; Gillet, N.; Olsen, N.

2012-05-01

We present new dedicated core surface field models spanning the decade from 2000.0 to 2010.0. These models, called gufm-sat, are based on CHAMP, Ørsted and SAC-C satellite observations along with annual differences of processed observatory monthly means. A spatial parametrization of spherical harmonics up to degree and order 24 and a temporal parametrization of sixth-order B-splines with 0.25 yr knot spacing is employed. Models were constructed by minimizing an absolute deviation measure of misfit along with measures of spatial and temporal complexity at the core surface. We investigate traditional quadratic or maximum entropy regularization in space, and second or third time derivative regularization in time. Entropy regularization allows the construction of models with approximately constant spectral slope at the core surface, avoiding both the divergence characteristic of the crustal field and the unrealistic rapid decay typical of quadratic regularization at degrees above 12. We describe in detail aspects of the models that are relevant to core dynamics. Secular variation and secular acceleration are found to be of lower amplitude under the Pacific hemisphere where the core field is weaker. Rapid field evolution is observed under the eastern Indian Ocean associated with the growth and drift of an intense low latitude flux patch. We also find that the present axial dipole decay arises from a combination of subtle changes in the southern hemisphere field morphology.

Scaling of the entropy budget with surface temperature in radiative-convective equilibrium

NASA Astrophysics Data System (ADS)

Singh, Martin S.; O'Gorman, Paul A.

2016-09-01

The entropy budget of the atmosphere is examined in simulations of radiative-convective equilibrium with a cloud-system resolving model over a wide range of surface temperatures from 281 to 311 K. Irreversible phase changes and the diffusion of water vapor account for more than half of the irreversible entropy production within the atmosphere, even in the coldest simulation. As the surface temperature is increased, the atmospheric radiative cooling rate increases, driving a greater entropy sink that must be matched by greater irreversible entropy production. The entropy production resulting from irreversible moist processes increases at a similar fractional rate as the entropy sink and at a lower rate than that implied by Clausius-Clapeyron scaling. This allows the entropy production from frictional drag on hydrometeors and on the atmospheric flow to also increase with warming, in contrast to recent results for simulations with global climate models in which the work output decreases with warming. A set of approximate scaling relations is introduced for the terms in the entropy budget as the surface temperature is varied, and many of the terms are found to scale with the mean surface precipitation rate. The entropy budget provides some insight into changes in frictional dissipation in response to warming or changes in model resolution, but it is argued that frictional dissipation is not closely linked to other measures of convective vigor.

Magnetocaloric effect in potassium doped lanthanum manganite perovskites prepared by a pyrophoric method

NASA Astrophysics Data System (ADS)

Das, Soma; Dey, T. K.

2006-08-01

The magnetocaloric effect (MCE) in fine grained perovskite manganites of the type La1-xKxMnO3 (0

Dynamical entropy via entropy of non-random matrices: application to stability and complexity in modelling ecosystems.

PubMed

Chakrabarti, C G; Ghosh, Koyel

2013-10-01

In the present paper we have first introduced a measure of dynamical entropy of an ecosystem on the basis of the dynamical model of the system. The dynamical entropy which depends on the eigenvalues of the community matrix of the system leads to a consistent measure of complexity of the ecosystem to characterize the dynamical behaviours such as the stability, instability and periodicity around the stationary states of the system. We have illustrated the theory with some model ecosystems. Copyright © 2013 Elsevier Inc. All rights reserved.

Entropy in an expanding universe.

PubMed

Frautschi, S

1982-08-13

The question of how the observed evolution of organized structures from initial chaos in the expanding universe can be reconciled with the laws of statistical mechanics is studied, with emphasis on effects of the expansion and gravity. Some major sources of entropy increase are listed. An expanding "causal" region is defined in which the entropy, though increasing, tends to fall further and further behind its maximum possible value, thus allowing for the development of order. The related questions of whether entropy will continue increasing without limit in the future, and whether such increase in the form of Hawking radiation or radiation from positronium might enable life to maintain itself permanently, are considered. Attempts to find a scheme for preserving life based on solid structures fail because events such as quantum tunneling recurrently disorganize matter on a very long but fixed time scale, whereas all energy sources slow down progressively in an expanding universe. However, there remains hope that other modes of life capable of maintaining themselves permanently can be found.

Model-based reinforcement learning with dimension reduction.

PubMed

Tangkaratt, Voot; Morimoto, Jun; Sugiyama, Masashi

2016-12-01

The goal of reinforcement learning is to learn an optimal policy which controls an agent to acquire the maximum cumulative reward. The model-based reinforcement learning approach learns a transition model of the environment from data, and then derives the optimal policy using the transition model. However, learning an accurate transition model in high-dimensional environments requires a large amount of data which is difficult to obtain. To overcome this difficulty, in this paper, we propose to combine model-based reinforcement learning with the recently developed least-squares conditional entropy (LSCE) method, which simultaneously performs transition model estimation and dimension reduction. We also further extend the proposed method to imitation learning scenarios. The experimental results show that policy search combined with LSCE performs well for high-dimensional control tasks including real humanoid robot control. Copyright © 2016 Elsevier Ltd. All rights reserved.

Entropy Based Genetic Association Tests and Gene-Gene Interaction Tests

PubMed Central

de Andrade, Mariza; Wang, Xin

2011-01-01

In the past few years, several entropy-based tests have been proposed for testing either single SNP association or gene-gene interaction. These tests are mainly based on Shannon entropy and have higher statistical power when compared to standard χ2 tests. In this paper, we extend some of these tests using a more generalized entropy definition, Rényi entropy, where Shannon entropy is a special case of order 1. The order λ (>0) of Rényi entropy weights the events (genotype/haplotype) according to their probabilities (frequencies). Higher λ places more emphasis on higher probability events while smaller λ (close to 0) tends to assign weights more equally. Thus, by properly choosing the λ, one can potentially increase the power of the tests or the p-value level of significance. We conducted simulation as well as real data analyses to assess the impact of the order λ and the performance of these generalized tests. The results showed that for dominant model the order 2 test was more powerful and for multiplicative model the order 1 or 2 had similar power. The analyses indicate that the choice of λ depends on the underlying genetic model and Shannon entropy is not necessarily the most powerful entropy measure for constructing genetic association or interaction tests. PMID:23089811

Application of digital image processing techniques to astronomical imagery 1980

NASA Technical Reports Server (NTRS)

Lorre, J. J.

1981-01-01

Topics include: (1) polar coordinate transformations (M83); (2) multispectral ratios (M82); (3) maximum entropy restoration (M87); (4) automated computation of stellar magnitudes in nebulosity; (5) color and polarization; (6) aliasing.

Nonextensivity in a Dark Maximum Entropy Landscape

NASA Astrophysics Data System (ADS)

Leubner, M. P.

2011-03-01

Nonextensive statistics along with network science, an emerging branch of graph theory, are increasingly recognized as potential interdisciplinary frameworks whenever systems are subject to long-range interactions and memory. Such settings are characterized by non-local interactions evolving in a non-Euclidean fractal/multi-fractal space-time making their behavior nonextensive. After summarizing the theoretical foundations from first principles, along with a discussion of entropy bifurcation and duality in nonextensive systems, we focus on selected significant astrophysical consequences. Those include the gravitational equilibria of dark matter (DM) and hot gas in clustered structures, the dark energy(DE) negative pressure landscape governed by the highest degree of mutual correlations and the hierarchy of discrete cosmic structure scales, available upon extremizing the generalized nonextensive link entropy in a homogeneous growing network.

Using the principle of entropy maximization to infer genetic interaction networks from gene expression patterns.

PubMed

Lezon, Timothy R; Banavar, Jayanth R; Cieplak, Marek; Maritan, Amos; Fedoroff, Nina V

2006-12-12

We describe a method based on the principle of entropy maximization to identify the gene interaction network with the highest probability of giving rise to experimentally observed transcript profiles. In its simplest form, the method yields the pairwise gene interaction network, but it can also be extended to deduce higher-order interactions. Analysis of microarray data from genes in Saccharomyces cerevisiae chemostat cultures exhibiting energy metabolic oscillations identifies a gene interaction network that reflects the intracellular communication pathways that adjust cellular metabolic activity and cell division to the limiting nutrient conditions that trigger metabolic oscillations. The success of the present approach in extracting meaningful genetic connections suggests that the maximum entropy principle is a useful concept for understanding living systems, as it is for other complex, nonequilibrium systems.

New classes of Lorenz curves by maximizing Tsallis entropy under mean and Gini equality and inequality constraints

NASA Astrophysics Data System (ADS)

Preda, Vasile; Dedu, Silvia; Gheorghe, Carmen

2015-10-01

In this paper, by using the entropy maximization principle with Tsallis entropy, new distribution families for modeling the income distribution are derived. Also, new classes of Lorenz curves are obtained by applying the entropy maximization principle with Tsallis entropy, under mean and Gini index equality and inequality constraints.

The Maximum Entropy Limit of Small-scale Magnetic Field Fluctuations in the Quiet Sun

NASA Astrophysics Data System (ADS)

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.

Kinetic analysis of hyperpolarized data with minimum a priori knowledge: Hybrid maximum entropy and nonlinear least squares method (MEM/NLS).

PubMed

Mariotti, Erika; Veronese, Mattia; Dunn, Joel T; Southworth, Richard; Eykyn, Thomas R

2015-06-01

To assess the feasibility of using a hybrid Maximum-Entropy/Nonlinear Least Squares (MEM/NLS) method for analyzing the kinetics of hyperpolarized dynamic data with minimum a priori knowledge. A continuous distribution of rates obtained through the Laplace inversion of the data is used as a constraint on the NLS fitting to derive a discrete spectrum of rates. Performance of the MEM/NLS algorithm was assessed through Monte Carlo simulations and validated by fitting the longitudinal relaxation time curves of hyperpolarized [1-(13) C] pyruvate acquired at 9.4 Tesla and at three different flip angles. The method was further used to assess the kinetics of hyperpolarized pyruvate-lactate exchange acquired in vitro in whole blood and to re-analyze the previously published in vitro reaction of hyperpolarized (15) N choline with choline kinase. The MEM/NLS method was found to be adequate for the kinetic characterization of hyperpolarized in vitro time-series. Additional insights were obtained from experimental data in blood as well as from previously published (15) N choline experimental data. The proposed method informs on the compartmental model that best approximate the biological system observed using hyperpolarized (13) C MR especially when the metabolic pathway assessed is complex or a new hyperpolarized probe is used. © 2014 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc.

Nonequilibrium-thermodynamics approach to open quantum systems

NASA Astrophysics Data System (ADS)

Semin, Vitalii; Petruccione, Francesco

2014-11-01

Open quantum systems are studied from the thermodynamical point of view unifying the principle of maximum informational entropy and the hypothesis of relaxation times hierarchy. The result of the unification is a non-Markovian and local-in-time master equation that provides a direct connection for dynamical and thermodynamical properties of open quantum systems. The power of the approach is illustrated by the application to the damped harmonic oscillator and the damped driven two-level system, resulting in analytical expressions for the non-Markovian and nonequilibrium entropy and inverse temperature.

Third law of thermodynamics in the presence of a heat flux

DOE Office of Scientific and Technical Information (OSTI.GOV)

Camacho, J.

1995-01-01

Following a maximum entropy formalism, we study a one-dimensional crystal under a heat flux. We obtain the phonon distribution function and evaluate the nonequilibrium temperature, the specific heat, and the entropy as functions of the internal energy and the heat flux, in both the quantum and the classical limits. Some analogies between the behavior of equilibrium systems at low absolute temperature and nonequilibrium steady states under high values of the heat flux are shown, which point to a possible generalization of the third law in nonequilibrium situations.

Entanglement entropy and entanglement spectrum of the Kitaev model.

PubMed

Yao, Hong; Qi, Xiao-Liang

2010-08-20

In this letter, we obtain an exact formula for the entanglement entropy of the ground state and all excited states of the Kitaev model. Remarkably, the entanglement entropy can be expressed in a simple separable form S = SG+SF, with SF the entanglement entropy of a free Majorana fermion system and SG that of a Z2 gauge field. The Z2 gauge field part contributes to the universal "topological entanglement entropy" of the ground state while the fermion part is responsible for the nonlocal entanglement carried by the Z2 vortices (visons) in the non-Abelian phase. Our result also enables the calculation of the entire entanglement spectrum and the more general Renyi entropy of the Kitaev model. Based on our results we propose a new quantity to characterize topologically ordered states--the capacity of entanglement, which can distinguish the st ates with and without topologically protected gapless entanglement spectrum.

Two-phase thermodynamic model for computing entropies of liquids reanalyzed

NASA Astrophysics Data System (ADS)

Sun, Tao; Xian, Jiawei; Zhang, Huai; Zhang, Zhigang; Zhang, Yigang

2017-11-01

The two-phase thermodynamic (2PT) model [S.-T. Lin et al., J. Chem. Phys. 119, 11792-11805 (2003)] provides a promising paradigm to efficiently determine the ionic entropies of liquids from molecular dynamics. In this model, the vibrational density of states (VDoS) of a liquid is decomposed into a diffusive gas-like component and a vibrational solid-like component. By treating the diffusive component as hard sphere (HS) gas and the vibrational component as harmonic oscillators, the ionic entropy of the liquid is determined. Here we examine three issues crucial for practical implementations of the 2PT model: (i) the mismatch between the VDoS of the liquid system and that of the HS gas; (ii) the excess entropy of the HS gas; (iii) the partition of the gas-like and solid-like components. Some of these issues have not been addressed before, yet they profoundly change the entropy predicted from the model. Based on these findings, a revised 2PT formalism is proposed and successfully tested in systems with Lennard-Jones potentials as well as many-atom potentials of liquid metals. Aside from being capable of performing quick entropy estimations for a wide range of systems, the formalism also supports fine-tuning to accurately determine entropies at specific thermal states.

Finite entanglement entropy and spectral dimension in quantum gravity

NASA Astrophysics Data System (ADS)

Arzano, Michele; Calcagni, Gianluca

2017-12-01

What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

NASA Astrophysics Data System (ADS)

Xu, Kaixuan; Wang, Jun

2017-02-01

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model.

Predicting anthropogenic soils across the Amazonia

NASA Astrophysics Data System (ADS)

Mcmichael, C.; Palace, M. W.; Bush, M. B.; Braswell, B. H.; Hagen, S. C.; Silman, M.; Neves, E.; Czarnecki, C.

2012-12-01

Hidden under the forest canopy in lowland Amazonia are nutrient-enriched soils, called terra pretas (or Amazonian black earths), which were formed by prehistoric indigenous populations. These anthrosols are in stark contrast to typical nutrient-poor Amazonian soils, and have retained increased nutrient levels for hundreds of years. Because of their long-term nutrient retaining ability, terra pretas may be crucial for developing sustainable agricultural practices in Amazonia, especially given the deforestation necessary for traditional slash-and-burn systems. However, the frequency and distribution of terra preta soils across the landscape remains debatable, and archaeologists have estimated that terra pretas cover anywhere from 0.1% to 10% of the lowland Amazonian forests. The highest concentration of terra preta soils has been found along the central and eastern portions of the Amazon River and its major tributaries, but whether this is a true pattern or simply reflects sampling bias remains unknown. A possible explanation is that specific environmental or biotic conditions were preferred for human settlement and terra preta formation. Here, we use environmental parameters to predict the probabilities of terra preta soils across lowland Amazonian forests. We compiled a database of 2708 sites across Amazonia, including locations that contain terra pretas (n = 917), and those that are known to be terra preta-free (n = 1791). More than 20 environmental variables, including precipitation, elevation, slope, soil fertility, and distance to river were converted into 90-m resolution raster images across Amazonia and used to model the probability of terra preta occurrence. The relationship between the predictor variables and the occurrence of terra preta was examined using three modeling techniques: logistic regression, auto-logistic regression, and maximum entropy estimations. All three techniques provided similar predictions for terra preta distributions and the amount of area covered by terra preta. Distance to river, locations of bluffs, elevation, and soil fertility were important factors in determining distributions of terra preta, while other environmental variables had less effect. Terra pretas were most likely to be found in central and eastern Amazonia near the confluences of the Amazon River and its major tributaries. Within this general area of higher probability, terra pretas are most likely found atop the bluffs overlooking the rivers as opposed to lying on the floodplain. Interestingly, terra pretas are more probable in areas with less-fertile and more highly weathered soils. Although all three modeling techniques provided similar predictions of terra preta across Amazonia, we suggest that maximum entropy modeling is the best technique to predict anthropogenic soils across the vast Amazonian landscape. The auto-logistic regression corrects for spatial autocorrelation inherent to archaeological surveys, but still requires absence data, which was collected at different times and on different spatial scales than the presence data. The maximum entropy model requires presence only data, accounts for spatial autocorrelation, and is not affected by the differential soil sampling techniques.

Quantifying chaos for ecological stoichiometry.

PubMed

Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep

2010-09-01

The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing δ1. However, for higher values of δ1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ζ) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.

Searching for Collective Behavior in a Large Network of Sensory Neurons

PubMed Central

Tkačik, Gašper; Marre, Olivier; Amodei, Dario; Schneidman, Elad; Bialek, William; Berry, Michael J.

2014-01-01

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such “K-pairwise” models—being systematic extensions of the previously used pairwise Ising models—provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction. PMID:24391485

Universal Features of Left-Right Entanglement Entropy.

PubMed

Das, Diptarka; Datta, Shouvik

2015-09-25

We show the presence of universal features in the entanglement entropy of regularized boundary states for (1+1)D conformal field theories on a circle when the reduced density matrix is obtained by tracing over right- or left-moving modes. We derive a general formula for the left-right entanglement entropy in terms of the central charge and the modular S matrix of the theory. When the state is chosen to be an Ishibashi state, this measure of entanglement is shown to precisely reproduce the spatial entanglement entropy of a (2+1)D topological quantum field theory. We explicitly evaluate the left-right entanglement entropies for the Ising model, the tricritical Ising model and the su[over ^](2)_{k} Wess-Zumino-Witten model as examples.

The Primordial Entropy of Jupiter

NASA Astrophysics Data System (ADS)

Cumming, Andrew; Helled, Ravit; Venturini, Julia

2018-04-01

The formation history of giant planets determines their primordial structure and consequent evolution. We simulate various formation paths of Jupiter to determine its primordial entropy, and find that a common outcome is for proto-Jupiter to have non-convective regions in its interior. We use planet formation models to calculate how the entropy and post-formation luminosity depend on model properties such as the solid accretion rate and opacity, and show that the gas accretion rate and its time evolution play a key role in determining the entropy profile. The predicted luminosity of Jupiter shortly after formation varies by a factor of 2-3 for different choices of model parameters. We find that entropy gradients inside Jupiter persist for ˜10 Myr after formation. We suggest that these gradients should be considered together with heavy-element composition gradients when modeling Jupiter's evolution and internal structure.

The primordial entropy of Jupiter

NASA Astrophysics Data System (ADS)

Cumming, Andrew; Helled, Ravit; Venturini, Julia

2018-07-01

The formation history of giant planets determines their primordial structure and consequent evolution. We simulate various formation paths of Jupiter to determine its primordial entropy, and find that a common outcome is for proto-Jupiter to have non-convective regions in its interior. We use planet formation models to calculate how the entropy and post-formation luminosity depend on model properties such as the solid accretion rate and opacity, and show that the gas accretion rate and its time evolution play a key role in determining the entropy profile. The predicted luminosity of Jupiter shortly after formation varies by a factor of 2-3 for different choices of model parameters. We find that entropy gradients inside Jupiter persist for ˜10 Myr after formation. We suggest that these gradients should be considered together with heavy-element composition gradients when modelling Jupiter's evolution and internal structure.

Hole pairing and thermodynamic properties of the two dimensional frustrated t-J model

NASA Astrophysics Data System (ADS)

Roy, K.; Pal, P.; Nath, S.; Ghosh, N. K.

2018-04-01

The frustrated t-J model is investigated by using the exact-diagonalization (ED) method on an 8-site cluster. The effect on next-nearest-neighbor (NNN) exchange interaction J' (frustration) on the hole pairing and the thermodynamic properties of the system is considered. Two holes initially remain unbound at smaller value of J'/t, but tend to bind at larger value. The maximum possibility of pair formation has been observed to be at NNN sites. Entropy calculation shows that the system goes to more disordered state with J'. The specific heat curves show a single peak structure. A decrease in effective exchange energy is observed due to the frustration.

Truncated Gaussians as tolerance sets

NASA Technical Reports Server (NTRS)

Cozman, Fabio; Krotkov, Eric

1994-01-01

This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.

Wavelet entropy of BOLD time series: An application to Rolandic epilepsy.

PubMed

Gupta, Lalit; Jansen, Jacobus F A; Hofman, Paul A M; Besseling, René M H; de Louw, Anton J A; Aldenkamp, Albert P; Backes, Walter H

2017-12-01

To assess the wavelet entropy for the characterization of intrinsic aberrant temporal irregularities in the time series of resting-state blood-oxygen-level-dependent (BOLD) signal fluctuations. Further, to evaluate the temporal irregularities (disorder/order) on a voxel-by-voxel basis in the brains of children with Rolandic epilepsy. The BOLD time series was decomposed using the discrete wavelet transform and the wavelet entropy was calculated. Using a model time series consisting of multiple harmonics and nonstationary components, the wavelet entropy was compared with Shannon and spectral (Fourier-based) entropy. As an application, the wavelet entropy in 22 children with Rolandic epilepsy was compared to 22 age-matched healthy controls. The images were obtained by performing resting-state functional magnetic resonance imaging (fMRI) using a 3T system, an 8-element receive-only head coil, and an echo planar imaging pulse sequence ( T2*-weighted). The wavelet entropy was also compared to spectral entropy, regional homogeneity, and Shannon entropy. Wavelet entropy was found to identify the nonstationary components of the model time series. In Rolandic epilepsy patients, a significantly elevated wavelet entropy was observed relative to controls for the whole cerebrum (P = 0.03). Spectral entropy (P = 0.41), regional homogeneity (P = 0.52), and Shannon entropy (P = 0.32) did not reveal significant differences. The wavelet entropy measure appeared more sensitive to detect abnormalities in cerebral fluctuations represented by nonstationary effects in the BOLD time series than more conventional measures. This effect was observed in the model time series as well as in Rolandic epilepsy. These observations suggest that the brains of children with Rolandic epilepsy exhibit stronger nonstationary temporal signal fluctuations than controls. 2 Technical Efficacy: Stage 3 J. Magn. Reson. Imaging 2017;46:1728-1737. © 2017 International Society for Magnetic Resonance in Medicine.