Maximum entropy and Bayesian methods
International Nuclear Information System (INIS)
Smith, C.R.; Erickson, G.J.; Neudorfer, P.O.
1992-01-01
Bayesian probability theory and Maximum Entropy methods are at the core of a new view of scientific inference. These 'new' ideas, along with the revolution in computational methods afforded by modern computers allow astronomers, electrical engineers, image processors of any type, NMR chemists and physicists, and anyone at all who has to deal with incomplete and noisy data, to take advantage of methods that, in the past, have been applied only in some areas of theoretical physics. The title workshops have been the focus of a group of researchers from many different fields, and this diversity is evident in this book. There are tutorial and theoretical papers, and applications in a very wide variety of fields. Almost any instance of dealing with incomplete and noisy data can be usefully treated by these methods, and many areas of theoretical research are being enhanced by the thoughtful application of Bayes' theorem. Contributions contained in this volume present a state-of-the-art overview that will be influential and useful for many years to come
Topics in Bayesian statistics and maximum entropy
International Nuclear Information System (INIS)
Mutihac, R.; Cicuttin, A.; Cerdeira, A.; Stanciulescu, C.
1998-12-01
Notions of Bayesian decision theory and maximum entropy methods are reviewed with particular emphasis on probabilistic inference and Bayesian modeling. The axiomatic approach is considered as the best justification of Bayesian analysis and maximum entropy principle applied in natural sciences. Particular emphasis is put on solving the inverse problem in digital image restoration and Bayesian modeling of neural networks. Further topics addressed briefly include language modeling, neutron scattering, multiuser detection and channel equalization in digital communications, genetic information, and Bayesian court decision-making. (author)
Comparison Between Bayesian and Maximum Entropy Analyses of Flow Networks†
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Steven H. Waldrip
2017-02-01
Full Text Available We compare the application of Bayesian inference and the maximum entropy (MaxEnt method for the analysis of ﬂow networks, such as water, electrical and transport networks. The two methods have the advantage of allowing a probabilistic prediction of ﬂow rates and other variables, when there is insufﬁcient information to obtain a deterministic solution, and also allow the effects of uncertainty to be included. Both methods of inference update a prior to a posterior probability density function (pdf by the inclusion of new information, in the form of data or constraints. The MaxEnt method maximises an entropy function subject to constraints, using the method of Lagrange multipliers,to give the posterior, while the Bayesian method ﬁnds its posterior by multiplying the prior with likelihood functions incorporating the measured data. In this study, we examine MaxEnt using soft constraints, either included in the prior or as probabilistic constraints, in addition to standard moment constraints. We show that when the prior is Gaussian,both Bayesian inference and the MaxEnt method with soft prior constraints give the same posterior means, but their covariances are different. In the Bayesian method, the interactions between variables are applied through the likelihood function, using second or higher-order cross-terms within the posterior pdf. In contrast, the MaxEnt method incorporates interactions between variables using Lagrange multipliers, avoiding second-order correlation terms in the posterior covariance. The MaxEnt method with soft prior constraints, therefore, has a numerical advantage over Bayesian inference, in that the covariance terms are avoided in its integrations. The second MaxEnt method with soft probabilistic constraints is shown to give posterior means of similar, but not identical, structure to the other two methods, due to its different formulation.
Estimation of Lithological Classification in Taipei Basin: A Bayesian Maximum Entropy Method
Wu, Meng-Ting; Lin, Yuan-Chien; Yu, Hwa-Lung
2015-04-01
In environmental or other scientific applications, we must have a certain understanding of geological lithological composition. Because of restrictions of real conditions, only limited amount of data can be acquired. To find out the lithological distribution in the study area, many spatial statistical methods used to estimate the lithological composition on unsampled points or grids. This study applied the Bayesian Maximum Entropy (BME method), which is an emerging method of the geological spatiotemporal statistics field. The BME method can identify the spatiotemporal correlation of the data, and combine not only the hard data but the soft data to improve estimation. The data of lithological classification is discrete categorical data. Therefore, this research applied Categorical BME to establish a complete three-dimensional Lithological estimation model. Apply the limited hard data from the cores and the soft data generated from the geological dating data and the virtual wells to estimate the three-dimensional lithological classification in Taipei Basin. Keywords: Categorical Bayesian Maximum Entropy method, Lithological Classification, Hydrogeological Setting
Bayesian Maximum Entropy Based Algorithm for Digital X-ray Mammogram Processing
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Radu Mutihac
2009-06-01
Full Text Available Basics of Bayesian statistics in inverse problems using the maximum entropy principle are summarized in connection with the restoration of positive, additive images from various types of data like X-ray digital mammograms. An efficient iterative algorithm for image restoration from large data sets based on the conjugate gradient method and Lagrange multipliers in nonlinear optimization of a specific potential function was developed. The point spread function of the imaging system was determined by numerical simulations of inhomogeneous breast-like tissue with microcalcification inclusions of various opacities. The processed digital and digitized mammograms resulted superior in comparison with their raw counterparts in terms of contrast, resolution, noise, and visibility of details.
International Nuclear Information System (INIS)
Reginatto, Marcel; Zimbal, Andreas
2008-01-01
In applications of neutron spectrometry to fusion diagnostics, it is advantageous to use methods of data analysis which can extract information from the spectrum that is directly related to the parameters of interest that describe the plasma. We present here methods of data analysis which were developed with this goal in mind, and which were applied to spectrometric measurements made with an organic liquid scintillation detector (type NE213). In our approach, we combine Bayesian parameter estimation methods and unfolding methods based on the maximum entropy principle. This two-step method allows us to optimize the analysis of the data depending on the type of information that we want to extract from the measurements. To illustrate these methods, we analyze neutron measurements made at the PTB accelerator under controlled conditions, using accelerator-produced neutron beams. Although the methods have been chosen with a specific application in mind, they are general enough to be useful for many other types of measurements
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.
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.
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.
The determination of nuclear charge distributions using a Bayesian maximum entropy method
International Nuclear Information System (INIS)
Macaulay, V.A.; Buck, B.
1995-01-01
We treat the inference of nuclear charge densities from measurements of elastic electron scattering cross sections. In order to get the most reliable information from expensively acquired, incomplete and noisy measurements, we use Bayesian probability theory. Very little prior information about the charge densities is assumed. We derive a prior probability distribution which is a generalization of a form used widely in image restoration based on the entropy of a physical density. From the posterior distribution of possible densities, we select the most probable one, and show how error bars can be evaluated. These have very reasonable properties, such as increasing without bound as hypotheses about finer scale structures are included in the hypothesis space. The methods are demonstrated by using data on the nuclei 4 He and 12 C. (orig.)
Nonsymmetric entropy and maximum nonsymmetric entropy principle
International Nuclear Information System (INIS)
Liu Chengshi
2009-01-01
Under the frame of a statistical model, the concept of nonsymmetric entropy which generalizes the concepts of Boltzmann's entropy and Shannon's entropy, is defined. Maximum nonsymmetric entropy principle is proved. Some important distribution laws such as power law, can be derived from this principle naturally. Especially, nonsymmetric entropy is more convenient than other entropy such as Tsallis's entropy in deriving power laws.
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.
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.
International Nuclear Information System (INIS)
Ponman, T.J.
1984-01-01
For some years now two different expressions have been in use for maximum entropy image restoration and there has been some controversy over which one is appropriate for a given problem. Here two further entropies are presented and it is argued that there is no single correct algorithm. The properties of the four different methods are compared using simple 1D simulations with a view to showing how they can be used together to gain as much information as possible about the original object. (orig.)
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Xiaokang Kou
2016-01-01
Full Text Available Land surface temperature (LST plays a major role in the study of surface energy balances. Remote sensing techniques provide ways to monitor LST at large scales. However, due to atmospheric influences, significant missing data exist in LST products retrieved from satellite thermal infrared (TIR remotely sensed data. Although passive microwaves (PMWs are able to overcome these atmospheric influences while estimating LST, the data are constrained by low spatial resolution. In this study, to obtain complete and high-quality LST data, the Bayesian Maximum Entropy (BME method was introduced to merge 0.01° and 0.25° LSTs inversed from MODIS and AMSR-E data, respectively. The result showed that the missing LSTs in cloudy pixels were filled completely, and the availability of merged LSTs reaches 100%. Because the depths of LST and soil temperature measurements are different, before validating the merged LST, the station measurements were calibrated with an empirical equation between MODIS LST and 0~5 cm soil temperatures. The results showed that the accuracy of merged LSTs increased with the increasing quantity of utilized data, and as the availability of utilized data increased from 25.2% to 91.4%, the RMSEs of the merged data decreased from 4.53 °C to 2.31 °C. In addition, compared with the filling gap method in which MODIS LST gaps were filled with AMSR-E LST directly, the merged LSTs from the BME method showed better spatial continuity. The different penetration depths of TIR and PMWs may influence fusion performance and still require further studies.
Hu, Junguo; Zhou, Jian; Zhou, Guomo; Luo, Yiqi; Xu, Xiaojun; Li, Pingheng; Liang, Junyi
2016-01-01
Soil respiration inherently shows strong spatial variability. It is difficult to obtain an accurate characterization of soil respiration with an insufficient number of monitoring points. However, it is expensive and cumbersome to deploy many sensors. To solve this problem, we proposed employing the Bayesian Maximum Entropy (BME) algorithm, using soil temperature as auxiliary information, to study the spatial distribution of soil respiration. The BME algorithm used the soft data (auxiliary information) effectively to improve the estimation accuracy of the spatiotemporal distribution of soil respiration. Based on the functional relationship between soil temperature and soil respiration, the BME algorithm satisfactorily integrated soil temperature data into said spatial distribution. As a means of comparison, we also applied the Ordinary Kriging (OK) and Co-Kriging (Co-OK) methods. The results indicated that the root mean squared errors (RMSEs) and absolute values of bias for both Day 1 and Day 2 were the lowest for the BME method, thus demonstrating its higher estimation accuracy. Further, we compared the performance of the BME algorithm coupled with auxiliary information, namely soil temperature data, and the OK method without auxiliary information in the same study area for 9, 21, and 37 sampled points. The results showed that the RMSEs for the BME algorithm (0.972 and 1.193) were less than those for the OK method (1.146 and 1.539) when the number of sampled points was 9 and 37, respectively. This indicates that the former method using auxiliary information could reduce the required number of sampling points for studying spatial distribution of soil respiration. Thus, the BME algorithm, coupled with soil temperature data, can not only improve the accuracy of soil respiration spatial interpolation but can also reduce the number of sampling points.
Density estimation by maximum quantum entropy
Energy Technology Data Exchange (ETDEWEB)
Silver, R.N.; Wallstrom, T.; Martz, H.F.
1993-11-01
A new Bayesian method for non-parametric density estimation is proposed, based on a mathematical analogy to quantum statistical physics. The mathematical procedure is related to maximum entropy methods for inverse problems and image reconstruction. The information divergence enforces global smoothing toward default models, convexity, positivity, extensivity and normalization. The novel feature is the replacement of classical entropy by quantum entropy, so that local smoothing is enforced by constraints on differential operators. The linear response of the estimate is proportional to the covariance. The hyperparameters are estimated by type-II maximum likelihood (evidence). The method is demonstrated on textbook data sets.
Maximum entropy tokamak configurations
International Nuclear Information System (INIS)
Minardi, E.
1989-01-01
The new entropy concept for the collective magnetic equilibria is applied to the description of the states of a tokamak subject to ohmic and auxiliary heating. The condition for the existence of steady state plasma states with vanishing entropy production implies, on one hand, the resilience of specific current density profiles and, on the other, severe restrictions on the scaling of the confinement time with power and current. These restrictions are consistent with Goldston scaling and with the existence of a heat pinch. (author)
Maximum entropy beam diagnostic tomography
International Nuclear Information System (INIS)
Mottershead, C.T.
1985-01-01
This paper reviews the formalism of maximum entropy beam diagnostic tomography as applied to the Fusion Materials Irradiation Test (FMIT) prototype accelerator. The same formalism has also been used with streak camera data to produce an ultrahigh speed movie of the beam profile of the Experimental Test Accelerator (ETA) at Livermore. 11 refs., 4 figs
From Maximum Entropy to Maximum Entropy Production: A New Approach
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Nathaniel Virgo
2010-01-01
Full Text Available Evidence from climate science suggests that a principle of maximum thermodynamic entropy production can be used to make predictions about some physical systems. I discuss the general form of this principle and an inherent problem with it, currently unsolved by theoretical approaches: how to determine which system it should be applied to. I suggest a new way to derive the principle from statistical mechanics, and present a tentative solution to the system boundary problem. I discuss the need for experimental validation of the principle, and its impact on the way we see the relationship between thermodynamics and kinetics.
Maximum entropy deconvolution of low count nuclear medicine images
International Nuclear Information System (INIS)
McGrath, D.M.
1998-12-01
Maximum entropy is applied to the problem of deconvolving nuclear medicine images, with special consideration for very low count data. The physics of the formation of scintigraphic images is described, illustrating the phenomena which degrade planar estimates of the tracer distribution. Various techniques which are used to restore these images are reviewed, outlining the relative merits of each. The development and theoretical justification of maximum entropy as an image processing technique is discussed. Maximum entropy is then applied to the problem of planar deconvolution, highlighting the question of the choice of error parameters for low count data. A novel iterative version of the algorithm is suggested which allows the errors to be estimated from the predicted Poisson mean values. This method is shown to produce the exact results predicted by combining Poisson statistics and a Bayesian interpretation of the maximum entropy approach. A facility for total count preservation has also been incorporated, leading to improved quantification. In order to evaluate this iterative maximum entropy technique, two comparable methods, Wiener filtering and a novel Bayesian maximum likelihood expectation maximisation technique, were implemented. The comparison of results obtained indicated that this maximum entropy approach may produce equivalent or better measures of image quality than the compared methods, depending upon the accuracy of the system model used. The novel Bayesian maximum likelihood expectation maximisation technique was shown to be preferable over many existing maximum a posteriori methods due to its simplicity of implementation. A single parameter is required to define the Bayesian prior, which suppresses noise in the solution and may reduce the processing time substantially. Finally, maximum entropy deconvolution was applied as a pre-processing step in single photon emission computed tomography reconstruction of low count data. Higher contrast results were
Two-dimensional maximum entropy image restoration
International Nuclear Information System (INIS)
Brolley, J.E.; Lazarus, R.B.; Suydam, B.R.; Trussell, H.J.
1977-07-01
An optical check problem was constructed to test P LOG P maximum entropy restoration of an extremely distorted image. Useful recovery of the original image was obtained. Comparison with maximum a posteriori restoration is made. 7 figures
A dual method for maximum entropy restoration
Smith, C. B.
1979-01-01
A simple iterative dual algorithm for maximum entropy image restoration is presented. The dual algorithm involves fewer parameters than conventional minimization in the image space. Minicomputer test results for Fourier synthesis with inadequate phantom data are given.
The maximum entropy technique. System's statistical description
International Nuclear Information System (INIS)
Belashev, B.Z.; Sulejmanov, M.K.
2002-01-01
The maximum entropy technique (MENT) is applied for searching the distribution functions of physical values. MENT takes into consideration the demand of maximum entropy, the characteristics of the system and the connection conditions, naturally. It is allowed to apply MENT for statistical description of closed and open systems. The examples in which MENT had been used for the description of the equilibrium and nonequilibrium states and the states far from the thermodynamical equilibrium are considered
Maximum Entropy Approaches to Living Neural Networks
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John M. Beggs
2010-01-01
Full Text Available Understanding how ensembles of neurons collectively interact will be a key step in developing a mechanistic theory of cognitive processes. Recent progress in multineuron recording and analysis techniques has generated tremendous excitement over the physiology of living neural networks. One of the key developments driving this interest is a new class of models based on the principle of maximum entropy. Maximum entropy models have been reported to account for spatial correlation structure in ensembles of neurons recorded from several different types of data. Importantly, these models require only information about the firing rates of individual neurons and their pairwise correlations. If this approach is generally applicable, it would drastically simplify the problem of understanding how neural networks behave. Given the interest in this method, several groups now have worked to extend maximum entropy models to account for temporal correlations. Here, we review how maximum entropy models have been applied to neuronal ensemble data to account for spatial and temporal correlations. We also discuss criticisms of the maximum entropy approach that argue that it is not generally applicable to larger ensembles of neurons. We conclude that future maximum entropy models will need to address three issues: temporal correlations, higher-order correlations, and larger ensemble sizes. Finally, we provide a brief list of topics for future research.
Zipf's law, power laws and maximum entropy
International Nuclear Information System (INIS)
Visser, Matt
2013-01-01
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines—from astronomy to demographics to software structure to economics to linguistics to zoology, and even warfare. A recent model of random group formation (RGF) attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present paper I argue that the specific cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified. (paper)
Zipf's law, power laws and maximum entropy
Visser, Matt
2013-04-01
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines—from astronomy to demographics to software structure to economics to linguistics to zoology, and even warfare. A recent model of random group formation (RGF) attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present paper I argue that the specific cost function used in the RGF model is in fact unnecessarily complicated, and that power laws can be obtained in a much simpler way by applying maximum entropy ideas directly to the Shannon entropy subject only to a single constraint: that the average of the logarithm of the observable quantity is specified.
The maximum-entropy method in superspace
Czech Academy of Sciences Publication Activity Database
van Smaalen, S.; Palatinus, Lukáš; Schneider, M.
2003-01-01
Roč. 59, - (2003), s. 459-469 ISSN 0108-7673 Grant - others:DFG(DE) XX Institutional research plan: CEZ:AV0Z1010914 Keywords : maximum-entropy method, * aperiodic crystals * electron density Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.558, year: 2003
Vibrational mode analysis using maximum likelihood and maximum entropy
International Nuclear Information System (INIS)
Redondo, A.; Sinha, D.N.
1993-01-01
A simple algorithm is presented that uses the maximum likelihood and maximum entropy approaches to determine the vibrational modes of elastic bodies. This method assumes that the vibrational frequencies have been previously determined, but the modes to which they correspond are unknown. Although the method is illustrated through the analysis of simulated vibrational modes for a flat rectangular plate, it has broad applicability to any experimental technique in which spectral frequencies can be associated to specific modes by means of a mathematical model
The maximum entropy production and maximum Shannon information entropy in enzyme kinetics
Dobovišek, Andrej; Markovič, Rene; Brumen, Milan; Fajmut, Aleš
2018-04-01
We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.
Pareto versus lognormal: a maximum entropy test.
Bee, Marco; Riccaboni, Massimo; Schiavo, Stefano
2011-08-01
It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units.
Maximum entropy analysis of EGRET data
DEFF Research Database (Denmark)
Pohl, M.; Strong, A.W.
1997-01-01
EGRET data are usually analysed on the basis of the Maximum-Likelihood method \\cite{ma96} in a search for point sources in excess to a model for the background radiation (e.g. \\cite{hu97}). This method depends strongly on the quality of the background model, and thus may have high systematic unce...... uncertainties in region of strong and uncertain background like the Galactic Center region. Here we show images of such regions obtained by the quantified Maximum-Entropy method. We also discuss a possible further use of MEM in the analysis of problematic regions of the sky....
Unification of field theory and maximum entropy methods for learning probability densities.
Kinney, Justin B
2015-09-01
The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.
Superstatistical distributions from a maximum entropy principle.
Van der Straeten, Erik; Beck, Christian
2008-11-01
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter beta of a superstatistical system, given certain constraints on the complex system under consideration. We apply the theory to three examples: the superstatistical quantum-mechanical harmonic oscillator, the superstatistical classical ideal gas, and velocity time series as measured in a turbulent Taylor-Couette flow.
Dynamical maximum entropy approach to flocking.
Cavagna, Andrea; Giardina, Irene; Ginelli, Francesco; Mora, Thierry; Piovani, Duccio; Tavarone, Raffaele; Walczak, Aleksandra M
2014-04-01
We derive a new method to infer from data the out-of-equilibrium alignment dynamics of collectively moving animal groups, by considering the maximum entropy model distribution consistent with temporal and spatial correlations of flight direction. When bird neighborhoods evolve rapidly, this dynamical inference correctly learns the parameters of the model, while a static one relying only on the spatial correlations fails. When neighbors change slowly and the detailed balance is satisfied, we recover the static procedure. We demonstrate the validity of the method on simulated data. The approach is applicable to other systems of active matter.
On the maximum entropy principle in non-extensive thermostatistics
Naudts, Jan
2004-01-01
It is possible to derive the maximum entropy principle from thermodynamic stability requirements. Using as a starting point the equilibrium probability distribution, currently used in non-extensive thermostatistics, it turns out that the relevant entropy function is Renyi's alpha-entropy, and not Tsallis' entropy.
Principle of maximum entropy and irreversible processes
International Nuclear Information System (INIS)
Grandy, W.T. Jr.
1980-01-01
More than twenty years have passed since E.T. Jaynes pioneered the information-theoretic approach to the foundations of statistical mechanics. In the intervening period numerous applications have been worked out and new insights developed into traditional problems. Although the natural extension of these ideas to nonequilibrium statistical mechanics and irreversible processes has also been formulated, and both theory and applications have been considerably developed, much of this work has not appeared in the open literature. Yet the basic ideas and consequent theory seem to have an extraordinary unifying and illumination effect on the foundations of the many-body problem, as well as providing a transparent conceptual basis from which to view various groups of problems not previously formulated in a particularly sharp way. The aim of this review is to summarize these developements in the context of the principle of maximum entropy. (orig.)
MAXIMUM-LIKELIHOOD-ESTIMATION OF THE ENTROPY OF AN ATTRACTOR
SCHOUTEN, JC; TAKENS, F; VANDENBLEEK, CM
In this paper, a maximum-likelihood estimate of the (Kolmogorov) entropy of an attractor is proposed that can be obtained directly from a time series. Also, the relative standard deviation of the entropy estimate is derived; it is dependent on the entropy and on the number of samples used in the
An approximate method for Bayesian entropy estimation for a discrete random variable.
Yokota, Yasunari
2004-01-01
This article proposes an approximated Bayesian entropy estimator for a discrete random variable. An entropy estimator that achieves least square error is obtained through Bayesian estimation of the occurrence probabilities of each value taken by the discrete random variable. This Bayesian entropy estimator requires large amount of calculation cost if the random variable takes numerous sorts of values. Therefore, the present article proposes a practical method for calculating an Bayesian entropy estimate; the proposed method utilizes approximation of the entropy function by a truncated Taylor series. Numerical experiments demonstrate that the proposed entropy estimation method improves estimation precision of entropy remarkably in comparison to the conventional entropy estimation method.
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)=-∑_{i}p_{i}logp_{i}. 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 S_{EXT} for extensive entropy, S_{IT} for the source information rate in information theory, and S_{MEP} 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.
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.
A Bayes-Maximum Entropy method for multi-sensor data fusion
Energy Technology Data Exchange (ETDEWEB)
Beckerman, M.
1991-01-01
In this paper we introduce a Bayes-Maximum Entropy formalism for multi-sensor data fusion, and present an application of this methodology to the fusion of ultrasound and visual sensor data as acquired by a mobile robot. In our approach the principle of maximum entropy is applied to the construction of priors and likelihoods from the data. Distances between ultrasound and visual points of interest in a dual representation are used to define Gibbs likelihood distributions. Both one- and two-dimensional likelihoods are presented, and cast into a form which makes explicit their dependence upon the mean. The Bayesian posterior distributions are used to test a null hypothesis, and Maximum Entropy Maps used for navigation are updated using the resulting information from the dual representation. 14 refs., 9 figs.
Combining Experiments and Simulations Using the Maximum Entropy Principle
DEFF Research Database (Denmark)
Boomsma, Wouter; Ferkinghoff-Borg, Jesper; Lindorff-Larsen, Kresten
2014-01-01
are not in quantitative agreement with experimental data. The principle of maximum entropy is a general procedure for constructing probability distributions in the light of new data, making it a natural tool in cases when an initial model provides results that are at odds with experiments. The number of maximum entropy...... in the context of a simple example, after which we proceed with a real-world application in the field of molecular simulations, where the maximum entropy procedure has recently provided new insight. Given the limited accuracy of force fields, macromolecular simulations sometimes produce results....... Three very recent papers have explored this problem using the maximum entropy approach, providing both new theoretical and practical insights to the problem. We highlight each of these contributions in turn and conclude with a discussion on remaining challenges....
Directory of Open Access Journals (Sweden)
F. S. Zhang
2016-01-01
Full Text Available The spatial mapping of losses attributable to such disasters is now well established as a means of describing the spatial patterns of disaster risk, and it has been shown to be suitable for many types of major meteorological disasters. However, few studies have been carried out by developing a regression model to estimate the effects of the spatial distribution of meteorological factors on losses associated with meteorological disasters. In this study, the proposed approach is capable of the following: (a estimating the spatial distributions of seven meteorological factors using Bayesian maximum entropy, (b identifying the four mapping methods used in this research with the best performance based on the cross validation, and (c establishing a fitted model between the PLS components and disaster losses information using partial least squares regression within a specific research area. The results showed the following: (a best mapping results were produced by multivariate Bayesian maximum entropy with probabilistic soft data; (b the regression model using three PLS components, extracted from seven meteorological factors by PLS method, was the most predictive by means of PRESS/SS test; (c northern Hunan Province sustains the most damage, and southeastern Gansu Province and western Guizhou Province sustained the least.
Czech Academy of Sciences Publication Activity Database
Sečkárová, Vladimíra
2013-01-01
Roč. 22, č. 1 (2013), s. 159-168 ISSN 0204-9805 R&D Projects: GA ČR GA13-13502S Grant - others:GA MŠk(CZ) SVV-265315 Institutional support: RVO:67985556 Keywords : Kerridge inaccuracy * maximum entropy principle * parameter estimation Subject RIV: BD - Theory of Information http://library.utia.cas.cz/separaty/2013/AS/seckarova-on supra-bayesian weighted combination of available data determined by kerridge inaccuracy ane entropy.pdf
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.
Tail Risk Constraints and Maximum Entropy
Directory of Open Access Journals (Sweden)
Donald Geman
2015-06-01
Full Text Available Portfolio selection in the financial literature has essentially been analyzed under two central assumptions: full knowledge of the joint probability distribution of the returns of the securities that will comprise the target portfolio; and investors’ preferences are expressed through a utility function. In the real world, operators build portfolios under risk constraints which are expressed both by their clients and regulators and which bear on the maximal loss that may be generated over a given time period at a given confidence level (the so-called Value at Risk of the position. Interestingly, in the finance literature, a serious discussion of how much or little is known from a probabilistic standpoint about the multi-dimensional density of the assets’ returns seems to be of limited relevance. Our approach in contrast is to highlight these issues and then adopt throughout a framework of entropy maximization to represent the real world ignorance of the “true” probability distributions, both univariate and multivariate, of traded securities’ returns. In this setting, we identify the optimal portfolio under a number of downside risk constraints. Two interesting results are exhibited: (i the left- tail constraints are sufficiently powerful to override all other considerations in the conventional theory; (ii the “barbell portfolio” (maximal certainty/ low risk in one set of holdings, maximal uncertainty in another, which is quite familiar to traders, naturally emerges in our construction.
Two-dimensional maximum entropy reconstruction of radio brightness
International Nuclear Information System (INIS)
Wernecke, S.J.
1977-01-01
A procedure is described for maximum entropy reconstruction of two-dimensional radio brightness maps from noisy interferometer measurements. The method defines a map that obeys the nonnegativity constraint and is, in a sense, the smoothest of all brightness distributions that agree with the visibility measurements within the errors of observation. This approach acknowledges the fact that signal-to-noise considerations have a strong influence on useful resolution; fine structure appears only to the extent justified by measurement accuracy. Iterative computing is needed to find the maximum entropy image. It is shown that the primary computational burden of maximum entropy reconstruction involves calculations that are efficiently performed by fast Fourier transform techniques. Different techniques are used depending on whether visibility data are irregularly distributed in the u,ν plane or interpolated onto a rectangular lattice prior to reconstruction. The efficiency of the fast Fourier transform provides a tremendous computational advantage with the result that maximum entropy reconstruction on a moderately large grid (64 x 64) is practicable at reasonable cost. Several comparative examples are shown, and some of the limitations of the present theory of maximum entropy imaging are identified
Modeling multisite streamflow dependence with maximum entropy copula
Hao, Z.; Singh, V. P.
2013-10-01
Synthetic streamflows at different sites in a river basin are needed for planning, operation, and management of water resources projects. Modeling the temporal and spatial dependence structure of monthly streamflow at different sites is generally required. In this study, the maximum entropy copula method is proposed for multisite monthly streamflow simulation, in which the temporal and spatial dependence structure is imposed as constraints to derive the maximum entropy copula. The monthly streamflows at different sites are then generated by sampling from the conditional distribution. A case study for the generation of monthly streamflow at three sites in the Colorado River basin illustrates the application of the proposed method. Simulated streamflow from the maximum entropy copula is in satisfactory agreement with observed streamflow.
A Maximum Entropy Method for a Robust Portfolio Problem
Directory of Open Access Journals (Sweden)
Yingying Xu
2014-06-01
Full Text Available We propose a continuous maximum entropy method to investigate the robustoptimal portfolio selection problem for the market with transaction costs and dividends.This robust model aims to maximize the worst-case portfolio return in the case that allof asset returns lie within some prescribed intervals. A numerical optimal solution tothe problem is obtained by using a continuous maximum entropy method. Furthermore,some numerical experiments indicate that the robust model in this paper can result in betterportfolio performance than a classical mean-variance model.
Discontinuity of maximum entropy inference and quantum phase transitions
International Nuclear Information System (INIS)
Chen, Jianxin; Ji, Zhengfeng; Yu, Nengkun; Zeng, Bei; Li, Chi-Kwong; Poon, Yiu-Tung; Shen, Yi; Zhou, Duanlu
2015-01-01
In this paper, we discuss the connection between two genuinely quantum phenomena—the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit. (paper)
Influence of Pareto optimality on the maximum entropy methods
Peddavarapu, Sreehari; Sunil, Gujjalapudi Venkata Sai; Raghuraman, S.
2017-07-01
Galerkin meshfree schemes are emerging as a viable substitute to finite element method to solve partial differential equations for the large deformations as well as crack propagation problems. However, the introduction of Shanon-Jayne's entropy principle in to the scattered data approximation has deviated from the trend of defining the approximation functions, resulting in maximum entropy approximants. Further in addition to this, an objective functional which controls the degree of locality resulted in Local maximum entropy approximants. These are based on information-theoretical Pareto optimality between entropy and degree of locality that are defining the basis functions to the scattered nodes. The degree of locality in turn relies on the choice of locality parameter and prior (weight) function. The proper choices of both plays vital role in attain the desired accuracy. Present work is focused on the choice of locality parameter which defines the degree of locality and priors: Gaussian, Cubic spline and quartic spline functions on the behavior of local maximum entropy approximants.
Training Concept, Evolution Time, and the Maximum Entropy Production Principle
Directory of Open Access Journals (Sweden)
Alexey Bezryadin
2016-04-01
Full Text Available The maximum entropy production principle (MEPP is a type of entropy optimization which demands that complex non-equilibrium systems should organize such that the rate of the entropy production is maximized. Our take on this principle is that to prove or disprove the validity of the MEPP and to test the scope of its applicability, it is necessary to conduct experiments in which the entropy produced per unit time is measured with a high precision. Thus we study electric-field-induced self-assembly in suspensions of carbon nanotubes and realize precise measurements of the entropy production rate (EPR. As a strong voltage is applied the suspended nanotubes merge together into a conducting cloud which produces Joule heat and, correspondingly, produces entropy. We introduce two types of EPR, which have qualitatively different significance: global EPR (g-EPR and the entropy production rate of the dissipative cloud itself (DC-EPR. The following results are obtained: (1 As the system reaches the maximum of the DC-EPR, it becomes stable because the applied voltage acts as a stabilizing thermodynamic potential; (2 We discover metastable states characterized by high, near-maximum values of the DC-EPR. Under certain conditions, such efficient entropy-producing regimes can only be achieved if the system is allowed to initially evolve under mildly non-equilibrium conditions, namely at a reduced voltage; (3 Without such a “training” period the system typically is not able to reach the allowed maximum of the DC-EPR if the bias is high; (4 We observe that the DC-EPR maximum is achieved within a time, Te, the evolution time, which scales as a power-law function of the applied voltage; (5 Finally, we present a clear example in which the g-EPR theoretical maximum can never be achieved. Yet, under a wide range of conditions, the system can self-organize and achieve a dissipative regime in which the DC-EPR equals its theoretical maximum.
Rumor Identification with Maximum Entropy in MicroNet
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Suisheng Yu
2017-01-01
Full Text Available The widely used applications of Microblog, WeChat, and other social networking platforms (that we call MicroNet shorten the period of information dissemination and expand the range of information dissemination, which allows rumors to cause greater harm and have more influence. A hot topic in the information dissemination field is how to identify and block rumors. Based on the maximum entropy model, this paper constructs the recognition mechanism of rumor information in the micronetwork environment. First, based on the information entropy theory, we obtained the characteristics of rumor information using the maximum entropy model. Next, we optimized the original classifier training set and the feature function to divide the information into rumors and nonrumors. Finally, the experimental simulation results show that the rumor identification results using this method are better than the original classifier and other related classification methods.
Determining Dynamical Path Distributions usingMaximum Relative Entropy
2015-05-31
θ). The selected joint posterior Pnew(x, θ) is that which maximizes the entropy1 , S[P, Pold ] = − ∫ P (x, θ) log P (x, θ) Pold (x, θ) dxdθ , (15) 1...to the appropriate constraints (parameters can be discrete as well). Pold (x, θ) contains our prior information which we call the joint prior. To be...explicit, Pold (x, θ) = Pold (x) Pold (θ|x) , (16) where Pold (x) is the traditional Bayesian prior and Pold (θ|x) is the likelihood. It is important to
Maximum entropy estimation via Gauss-LP quadratures
Thély, Maxime; Sutter, Tobias; Mohajerin Esfahani, P.; Lygeros, John; Dochain, Denis; Henrion, Didier; Peaucelle, Dimitri
2017-01-01
We present an approximation method to a class of parametric integration problems that naturally appear when solving the dual of the maximum entropy estimation problem. Our method builds up on a recent generalization of Gauss quadratures via an infinite-dimensional linear program, and utilizes a
On some problems of the maximum entropy ansatz
Indian Academy of Sciences (India)
aforesaid problems are put forward. Pilot calculations involving the ground quantum eigenenergy states of the quartic oscillator, the particle-in-a-box model, and the classical Maxwellian speed and energy distributions lend credence to our approach. Keywords. Maximum entropy ansatz; Padй-type approximants; boundary ...
Image coding based on maximum entropy partitioning for identifying ...
Indian Academy of Sciences (India)
A new coding scheme based on maximum entropy partitioning is proposed in our work, particularly to identify the improbable intensities related to different emotions. The improbable intensities when used as a mask decode the facial expression correctly, providing an effectiveplatform for future emotion categorization ...
Applications of the Maximum Entropy Method in superspace
Czech Academy of Sciences Publication Activity Database
van Smaalen, S.; Palatinus, Lukáš
2004-01-01
Roč. 305, - (2004), s. 57-62 ISSN 0015-0193 Grant - others:DFG and FCI(DE) XX Institutional research plan: CEZ:AV0Z1010914 Keywords : Maximum Entropy Method * modulated structures * charge density Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.517, year: 2004
MAXIMUM PRINCIPLE FOR SUBSONIC FLOW WITH VARIABLE ENTROPY
Directory of Open Access Journals (Sweden)
B. Sizykh Grigory
2017-01-01
Full Text Available Maximum principle for subsonic flow is fair for stationary irrotational subsonic gas flows. According to this prin- ciple, if the value of the velocity is not constant everywhere, then its maximum is achieved on the boundary and only on the boundary of the considered domain. This property is used when designing form of an aircraft with a maximum critical val- ue of the Mach number: it is believed that if the local Mach number is less than unit in the incoming flow and on the body surface, then the Mach number is less then unit in all points of flow. The known proof of maximum principle for subsonic flow is based on the assumption that in the whole considered area of the flow the pressure is a function of density. For the ideal and perfect gas (the role of diffusion is negligible, and the Mendeleev-Clapeyron law is fulfilled, the pressure is a function of density if entropy is constant in the entire considered area of the flow. Shows an example of a stationary sub- sonic irrotational flow, in which the entropy has different values on different stream lines, and the pressure is not a function of density. The application of the maximum principle for subsonic flow with respect to such a flow would be unreasonable. This example shows the relevance of the question about the place of the points of maximum value of the velocity, if the entropy is not a constant. To clarify the regularities of the location of these points, was performed the analysis of the com- plete Euler equations (without any simplifying assumptions in 3-D case. The new proof of the maximum principle for sub- sonic flow was proposed. This proof does not rely on the assumption that the pressure is a function of density. Thus, it is shown that the maximum principle for subsonic flow is true for stationary subsonic irrotational flows of ideal perfect gas with variable entropy.
Maximum entropy principle and partial probability weighted moments
Deng, Jian; Pandey, M. D.; Xie, W. C.
2012-05-01
Maximum entropy principle (MaxEnt) is usually used for estimating the probability density function under specified moment constraints. The density function is then integrated to obtain the cumulative distribution function, which needs to be inverted to obtain a quantile corresponding to some specified probability. In such analysis, consideration of higher ordermoments is important for accurate modelling of the distribution tail. There are three drawbacks for this conventional methodology: (1) Estimates of higher order (>2) moments from a small sample of data tend to be highly biased; (2) It can merely cope with problems with complete or noncensored samples; (3) Only probability weighted moments of integer orders have been utilized. These difficulties inevitably induce bias and inaccuracy of the resultant quantile estimates and therefore have been the main impediments to the application of the MaxEnt Principle in extreme quantile estimation. This paper attempts to overcome these problems and presents a distribution free method for estimating the quantile function of a non-negative randomvariable using the principle of maximum partial entropy subject to constraints of the partial probability weighted moments estimated from censored sample. The main contributions include: (1) New concepts, i.e., partial entropy, fractional partial probability weighted moments, and partial Kullback-Leibler measure are elegantly defined; (2) Maximum entropy principle is re-formulated to be constrained by fractional partial probability weighted moments; (3) New distribution free quantile functions are derived. Numerical analyses are performed to assess the accuracy of extreme value estimates computed from censored samples.
Directory of Open Access Journals (Sweden)
Ali Mohammad-Djafari
2015-06-01
Full Text Available The main content of this review article is first to review the main inference tools using Bayes rule, the maximum entropy principle (MEP, information theory, relative entropy and the Kullback–Leibler (KL divergence, Fisher information and its corresponding geometries. For each of these tools, the precise context of their use is described. The second part of the paper is focused on the ways these tools have been used in data, signal and image processing and in the inverse problems, which arise in different physical sciences and engineering applications. A few examples of the applications are described: entropy in independent components analysis (ICA and in blind source separation, Fisher information in data model selection, different maximum entropy-based methods in time series spectral estimation and in linear inverse problems and, finally, the Bayesian inference for general inverse problems. Some original materials concerning the approximate Bayesian computation (ABC and, in particular, the variational Bayesian approximation (VBA methods are also presented. VBA is used for proposing an alternative Bayesian computational tool to the classical Markov chain Monte Carlo (MCMC methods. We will also see that VBA englobes joint maximum a posteriori (MAP, as well as the different expectation-maximization (EM algorithms as particular cases.
Maximum-Entropy Inference with a Programmable Annealer
Chancellor, Nicholas; Szoke, Szilard; Vinci, Walter; Aeppli, Gabriel; Warburton, Paul A.
2016-03-01
Optimisation problems typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this maximises the likelihood that the solution is correct. The maximum entropy solution on the other hand takes the form of a Boltzmann distribution over the ground and excited states of the cost function to correct for noise. Here we use a programmable annealer for the information decoding problem which we simulate as a random Ising model in a field. We show experimentally that finite temperature maximum entropy decoding can give slightly better bit-error-rates than the maximum likelihood approach, confirming that useful information can be extracted from the excited states of the annealer. Furthermore we introduce a bit-by-bit analytical method which is agnostic to the specific application and use it to show that the annealer samples from a highly Boltzmann-like distribution. Machines of this kind are therefore candidates for use in a variety of machine learning applications which exploit maximum entropy inference, including language processing and image recognition.
Triadic conceptual structure of the maximum entropy approach to evolution.
Herrmann-Pillath, Carsten; Salthe, Stanley N
2011-03-01
Many problems in evolutionary theory are cast in dyadic terms, such as the polar oppositions of organism and environment. We argue that a triadic conceptual structure offers an alternative perspective under which the information generating role of evolution as a physical process can be analyzed, and propose a new diagrammatic approach. Peirce's natural philosophy was deeply influenced by his reception of both Darwin's theory and thermodynamics. Thus, we elaborate on a new synthesis which puts together his theory of signs and modern Maximum Entropy approaches to evolution in a process discourse. Following recent contributions to the naturalization of Peircean semiosis, pointing towards 'physiosemiosis' or 'pansemiosis', we show that triadic structures involve the conjunction of three different kinds of causality, efficient, formal and final. In this, we accommodate the state-centered thermodynamic framework to a process approach. We apply this on Ulanowicz's analysis of autocatalytic cycles as primordial patterns of life. This paves the way for a semiotic view of thermodynamics which is built on the idea that Peircean interpretants are systems of physical inference devices evolving under natural selection. In this view, the principles of Maximum Entropy, Maximum Power, and Maximum Entropy Production work together to drive the emergence of information carrying structures, which at the same time maximize information capacity as well as the gradients of energy flows, such that ultimately, contrary to Schrödinger's seminal contribution, the evolutionary process is seen to be a physical expression of the Second Law. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.
Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains
Directory of Open Access Journals (Sweden)
Rodrigo Cofré
2018-01-01
Full Text Available The spiking activity of neuronal networks follows laws that are not time-reversal symmetric; the notion of pre-synaptic and post-synaptic neurons, stimulus correlations and noise correlations have a clear time order. Therefore, a biologically realistic statistical model for the spiking activity should be able to capture some degree of time irreversibility. We use the thermodynamic formalism to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.
Maximum information entropy: a foundation for ecological theory.
Harte, John; Newman, Erica A
2014-07-01
The maximum information entropy (MaxEnt) principle is a successful method of statistical inference that has recently been applied to ecology. Here, we show how MaxEnt can accurately predict patterns such as species-area relationships (SARs) and abundance distributions in macroecology and be a foundation for ecological theory. We discuss the conceptual foundation of the principle, why it often produces accurate predictions of probability distributions in science despite not incorporating explicit mechanisms, and how mismatches between predictions and data can shed light on driving mechanisms in ecology. We also review possible future extensions of the maximum entropy theory of ecology (METE), a potentially important foundation for future developments in ecological theory. Copyright © 2014 Elsevier Ltd. All rights reserved.
Collective behaviours in the stock market -- A maximum entropy approach
Bury, Thomas
2014-01-01
Scale invariance, collective behaviours and structural reorganization are crucial for portfolio management (portfolio composition, hedging, alternative definition of risk, etc.). This lack of any characteristic scale and such elaborated behaviours find their origin in the theory of complex systems. There are several mechanisms which generate scale invariance but maximum entropy models are able to explain both scale invariance and collective behaviours.The study of the structure and collective...
ON A GENERALIZATION OF THE MAXIMUM ENTROPY THEOREM OF BURG
Directory of Open Access Journals (Sweden)
JOSÉ MARCANO
2017-01-01
Full Text Available In this article we introduce some matrix manipulations that allow us to obtain a version of the original Christoffel-Darboux formula, which is of interest in many applications of linear algebra. Using these developments matrix and Jensen’s inequality, we obtain the main result of this proposal, which is the generalization of the maximum entropy theorem of Burg for multivariate processes.
Chebyshev recursion methods: Kernel polynomials and maximum entropy
Energy Technology Data Exchange (ETDEWEB)
Silver, R.N.; Roeder, H.; Voter, A.F.; Kress, J.D. [Los Alamos National Lab., NM (United States). Theoretical Div.
1995-10-01
The authors describe two Chebyshev recursion methods for calculations with very large sparse Hamiltonians, the kernel polynomial method (KPM) and the maximum entropy method (MEM). They are especially applicable to physical properties involving large numbers of eigenstates, which include densities of states, spectral functions, thermodynamics, total energies, as well as forces for molecular dynamics and Monte Carlo simulations. The authors apply Chebyshev methods to the electronic structure of Si, the thermodynamics of Heisenberg antiferromagnets, and a polaron problem.
Maximum Entropy Estimation of Transition Probabilities of Reversible Markov Chains
Directory of Open Access Journals (Sweden)
Erik Van der Straeten
2009-11-01
Full Text Available In this paper, we develop a general theory for the estimation of the transition probabilities of reversible Markov chains using the maximum entropy principle. A broad range of physical models can be studied within this approach. We use one-dimensional classical spin systems to illustrate the theoretical ideas. The examples studied in this paper are: the Ising model, the Potts model and the Blume-Emery-Griffiths model.
PNNL: A Supervised Maximum Entropy Approach to Word Sense Disambiguation
Energy Technology Data Exchange (ETDEWEB)
Tratz, Stephen C.; Sanfilippo, Antonio P.; Gregory, Michelle L.; Chappell, Alan R.; Posse, Christian; Whitney, Paul D.
2007-06-23
In this paper, we described the PNNL Word Sense Disambiguation system as applied to the English All-Word task in Se-mEval 2007. We use a supervised learning approach, employing a large number of features and using Information Gain for dimension reduction. Our Maximum Entropy approach combined with a rich set of features produced results that are significantly better than baseline and are the highest F-score for the fined-grained English All-Words subtask.
Maximum Entropy and Theory Construction: A Reply to Favretti
Directory of Open Access Journals (Sweden)
John Harte
2018-04-01
Full Text Available In the maximum entropy theory of ecology (METE, the form of a function describing the distribution of abundances over species and metabolic rates over individuals in an ecosystem is inferred using the maximum entropy inference procedure. Favretti shows that an alternative maximum entropy model exists that assumes the same prior knowledge and makes predictions that differ from METE’s. He shows that both cannot be correct and asserts that his is the correct one because it can be derived from a classic microstate-counting calculation. I clarify here exactly what the core entities and definitions are for METE, and discuss the relevance of two critical issues raised by Favretti: the existence of a counting procedure for microstates and the choices of definition of the core elements of a theory. I emphasize that a theorist controls how the core entities of his or her theory are defined, and that nature is the final arbiter of the validity of a theory.
Robust Discriminant Analysis Based on Nonparametric Maximum Entropy
He, Ran; Hu, Bao-Gang; Yuan, Xiao-Tong
In this paper, we propose a Robust Discriminant Analysis based on maximum entropy (MaxEnt) criterion (MaxEnt-RDA), which is derived from a nonparametric estimate of Renyi’s quadratic entropy. MaxEnt-RDA uses entropy as both objective and constraints; thus the structural information of classes is preserved while information loss is minimized. It is a natural extension of LDA from Gaussian assumption to any distribution assumption. Like LDA, the optimal solution of MaxEnt-RDA can also be solved by an eigen-decomposition method, where feature extraction is achieved by designing two Parzen probability matrices that characterize the within-class variation and the between-class variation respectively. Furthermore, MaxEnt-RDA makes use of high order statistics (entropy) to estimate the probability matrix so that it is robust to outliers. Experiments on toy problem , UCI datasets and face datasets demonstrate the effectiveness of the proposed method with comparison to other state-of-the-art methods.
Energy Technology Data Exchange (ETDEWEB)
Papoular, R
1997-07-01
The Fourier Transform is of central importance to Crystallography since it allows the visualization in real space of tridimensional scattering densities pertaining to physical systems from diffraction data (powder or single-crystal diffraction, using x-rays, neutrons, electrons or else). In turn, this visualization makes it possible to model and parametrize these systems, the crystal structures of which are eventually refined by Least-Squares techniques (e.g., the Rietveld method in the case of Powder Diffraction). The Maximum Entropy Method (sometimes called MEM or MaxEnt) is a general imaging technique, related to solving ill-conditioned inverse problems. It is ideally suited for tackling undetermined systems of linear questions (for which the number of variables is much larger than the number of equations). It is already being applied successfully in Astronomy, Radioastronomy and Medical Imaging. The advantages of using MAXIMUM Entropy over conventional Fourier and `difference Fourier` syntheses stem from the following facts: MaxEnt takes the experimental error bars into account; MaxEnt incorporate Prior Knowledge (e.g., the positivity of the scattering density in some instances); MaxEnt allows density reconstructions from incompletely phased data, as well as from overlapping Bragg reflections; MaxEnt substantially reduces truncation errors to which conventional experimental Fourier reconstructions are usually prone. The principles of Maximum Entropy imaging as applied to Crystallography are first presented. The method is then illustrated by a detailed example specific to Neutron Diffraction: the search for proton in solids. (author). 17 refs.
Network Inference and Maximum Entropy Estimation on Information Diagrams.
Martin, Elliot A; Hlinka, Jaroslav; Meinke, Alexander; Děchtěrenko, Filip; Tintěra, Jaroslav; Oliver, Isaura; Davidsen, Jörn
2017-08-01
Maximum entropy estimation is of broad interest for inferring properties of systems across many disciplines. Using a recently introduced technique for estimating the maximum entropy of a set of random discrete variables when conditioning on bivariate mutual informations and univariate entropies, we show how this can be used to estimate the direct network connectivity between interacting units from observed activity. As a generic example, we consider phase oscillators and show that our approach is typically superior to simply using the mutual information. In addition, we propose a nonparametric formulation of connected informations, used to test the explanatory power of a network description in general. We give an illustrative example showing how this agrees with the existing parametric formulation, and demonstrate its applicability and advantages for resting-state human brain networks, for which we also discuss its direct effective connectivity. Finally, we generalize to continuous random variables and vastly expand the types of information-theoretic quantities one can condition on. This allows us to establish significant advantages of this approach over existing ones. Not only does our method perform favorably in the undersampled regime, where existing methods fail, but it also can be dramatically less computationally expensive as the cardinality of the variables increases.
Maximum entropy principle and hydrodynamic models in statistical mechanics
International Nuclear Information System (INIS)
Trovato, M.; Reggiani, L.
2012-01-01
This review presents the state of the art of the maximum entropy principle (MEP) in its classical and quantum (QMEP) formulation. Within the classical MEP we overview a general theory able to provide, in a dynamical context, the macroscopic relevant variables for carrier transport in the presence of electric fields of arbitrary strength. For the macroscopic variables the linearized maximum entropy approach is developed including full-band effects within a total energy scheme. Under spatially homogeneous conditions, we construct a closed set of hydrodynamic equations for the small-signal (dynamic) response of the macroscopic variables. The coupling between the driving field and the energy dissipation is analyzed quantitatively by using an arbitrary number of moments of the distribution function. Analogously, the theoretical approach is applied to many one-dimensional n + nn + submicron Si structures by using different band structure models, different doping profiles, different applied biases and is validated by comparing numerical calculations with ensemble Monte Carlo simulations and with available experimental data. Within the quantum MEP we introduce a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is then asserted as fundamental principle of quantum statistical mechanics. Accordingly, we have developed a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theory is formulated both in thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of ħ 2 , being ħ the reduced Planck constant. In particular, by using an arbitrary number of moments, we prove that: i) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives both of the
A Maximum Entropy Approach to Loss Distribution Analysis
Directory of Open Access Journals (Sweden)
Marco Bee
2013-03-01
Full Text Available In this paper we propose an approach to the estimation and simulation of loss distributions based on Maximum Entropy (ME, a non-parametric technique that maximizes the Shannon entropy of the data under moment constraints. Special cases of the ME density correspond to standard distributions; therefore, this methodology is very general as it nests most classical parametric approaches. Sampling the ME distribution is essential in many contexts, such as loss models constructed via compound distributions. Given the difficulties in carrying out exact simulation,we propose an innovative algorithm, obtained by means of an extension of Adaptive Importance Sampling (AIS, for the approximate simulation of the ME distribution. Several numerical experiments confirm that the AIS-based simulation technique works well, and an application to insurance data gives further insights in the usefulness of the method for modelling, estimating and simulating loss distributions.
Application of the maximum entropy production principle to electrical systems
International Nuclear Information System (INIS)
Christen, Thomas
2006-01-01
For a simple class of electrical systems, the principle of the maximum entropy production rate (MaxEP) is discussed. First, we compare the MaxEP principle and the principle of the minimum entropy production rate and illustrate the superiority of the MaxEP principle for the example of two parallel constant resistors. Secondly, we show that the Steenbeck principle for the electric arc as well as the ohmic contact behaviour of space-charge limited conductors follow from the MaxEP principle. In line with work by Dewar, the investigations seem to suggest that the MaxEP principle can also be applied to systems far from equilibrium, provided appropriate information is available that enters the constraints of the optimization problem. Finally, we apply the MaxEP principle to a mesoscopic system and show that the universal conductance quantum, e 2 /h, of a one-dimensional ballistic conductor can be estimated
International Nuclear Information System (INIS)
Maeda, Shigetaka; Iguchi, Tetsuo
2013-01-01
We present a new spectrum unfolding code, the Maximum Entropy and Maximum Likelihood Unfolding Code (MEALU), based on the maximum likelihood method combined with the maximum entropy method, which can determine a neutron spectrum without requiring an initial guess spectrum. The Normal or Poisson distributions can be used for the statistical distribution. MEALU can treat full covariance data for a measured detector response and response function. The algorithm was verified through an analysis of mock-up data and its performance was checked by applying it to measured data. The results for measured data from the Joyo experimental fast reactor were also compared with those obtained by the conventional J-log method for neutron spectrum adjustment. It was found that MEALU has potential advantages over conventional methods with regard to preparation of a priori information and uncertainty estimation. (author)
Maximum entropy technique in the doublet structure analysis
International Nuclear Information System (INIS)
Belashev, B.Z.; Panebrattsev, Yu.A.; Shakhaliev, Eh.I.; Soroko, L.M.
1998-01-01
The Maximum Entropy Technique (MENT) for solution of the inverse problems is explained. The effective computer program for resolution of the nonlinear equations system encountered in the MENT has been developed and tested. The possibilities of the MENT have been demonstrated on the example of the MENT in the doublet structure analysis of noisy experimental data. The comparison of the MENT results with results of the Fourier algorithm technique without regularization is presented. The tolerant noise level is equal to 30% for MENT and only 0.1% for the Fourier algorithm
Twenty-five years of maximum-entropy principle
Kapur, J. N.
1983-04-01
The strengths and weaknesses of the maximum entropy principle (MEP) are examined and some challenging problems that remain outstanding at the end of the first quarter century of the principle are discussed. The original formalism of the MEP is presented and its relationship to statistical mechanics is set forth. The use of MEP for characterizing statistical distributions, in statistical inference, nonlinear spectral analysis, transportation models, population density models, models for brand-switching in marketing and vote-switching in elections is discussed. Its application to finance, insurance, image reconstruction, pattern recognition, operations research and engineering, biology and medicine, and nonparametric density estimation is considered.
Maximum Entropy Closure of Balance Equations for Miniband Semiconductor Superlattices
Directory of Open Access Journals (Sweden)
Luis L. Bonilla
2016-07-01
Full Text Available Charge transport in nanosized electronic systems is described by semiclassical or quantum kinetic equations that are often costly to solve numerically and difficult to reduce systematically to macroscopic balance equations for densities, currents, temperatures and other moments of macroscopic variables. The maximum entropy principle can be used to close the system of equations for the moments but its accuracy or range of validity are not always clear. In this paper, we compare numerical solutions of balance equations for nonlinear electron transport in semiconductor superlattices. The equations have been obtained from Boltzmann–Poisson kinetic equations very far from equilibrium for strong fields, either by the maximum entropy principle or by a systematic Chapman–Enskog perturbation procedure. Both approaches produce the same current-voltage characteristic curve for uniform fields. When the superlattices are DC voltage biased in a region where there are stable time periodic solutions corresponding to recycling and motion of electric field pulses, the differences between the numerical solutions produced by numerically solving both types of balance equations are smaller than the expansion parameter used in the perturbation procedure. These results and possible new research venues are discussed.
Stimulus-dependent maximum entropy models of neural population codes.
Directory of Open Access Journals (Sweden)
Einat Granot-Atedgi
Full Text Available Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME model-a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population.
Maximum entropy networks are more controllable than preferential attachment networks
International Nuclear Information System (INIS)
Hou, Lvlin; Small, Michael; Lao, Songyang
2014-01-01
A maximum entropy (ME) method to generate typical scale-free networks has been recently introduced. We investigate the controllability of ME networks and Barabási–Albert preferential attachment networks. Our experimental results show that ME networks are significantly more easily controlled than BA networks of the same size and the same degree distribution. Moreover, the control profiles are used to provide insight into control properties of both classes of network. We identify and classify the driver nodes and analyze the connectivity of their neighbors. We find that driver nodes in ME networks have fewer mutual neighbors and that their neighbors have lower average degree. We conclude that the properties of the neighbors of driver node sensitively affect the network controllability. Hence, subtle and important structural differences exist between BA networks and typical scale-free networks of the same degree distribution. - Highlights: • The controllability of maximum entropy (ME) and Barabási–Albert (BA) networks is investigated. • ME networks are significantly more easily controlled than BA networks of the same degree distribution. • The properties of the neighbors of driver node sensitively affect the network controllability. • Subtle and important structural differences exist between BA networks and typical scale-free networks
Multi-GPU maximum entropy image synthesis for radio astronomy
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.
Applications of the maximum entropy principle in nuclear physics
International Nuclear Information System (INIS)
Froehner, F.H.
1990-01-01
Soon after the advent of information theory the principle of maximum entropy was recognized as furnishing the missing rationale for the familiar rules of classical thermodynamics. More recently it has also been applied successfully in nuclear physics. As an elementary example we derive a physically meaningful macroscopic description of the spectrum of neutrons emitted in nuclear fission, and compare the well known result with accurate data on 252 Cf. A second example, derivation of an expression for resonance-averaged cross sections for nuclear reactions like scattering or fission, is less trivial. Entropy maximization, constrained by given transmission coefficients, yields probability distributions for the R- and S-matrix elements, from which average cross sections can be calculated. If constrained only by the range of the spectrum of compound-nuclear levels it produces the Gaussian Orthogonal Ensemble (GOE) of Hamiltonian matrices that again yields expressions for average cross sections. Both avenues give practically the same numbers in spite of the quite different cross section formulae. These results were employed in a new model-aided evaluation of the 238 U neutron cross sections in the unresolved resonance region. (orig.) [de
LIBOR troubles: Anomalous movements detection based on maximum entropy
Bariviera, Aurelio F.; Martín, María T.; Plastino, Angelo; Vampa, Victoria
2016-05-01
According to the definition of the London Interbank Offered Rate (LIBOR), contributing banks should give fair estimates of their own borrowing costs in the interbank market. Between 2007 and 2009, several banks made inappropriate submissions of LIBOR, sometimes motivated by profit-seeking from their trading positions. In 2012, several newspapers' articles began to cast doubt on LIBOR integrity, leading surveillance authorities to conduct investigations on banks' behavior. Such procedures resulted in severe fines imposed to involved banks, who recognized their financial inappropriate conduct. In this paper, we uncover such unfair behavior by using a forecasting method based on the Maximum Entropy principle. Our results are robust against changes in parameter settings and could be of great help for market surveillance.
Venus atmosphere profile from a maximum entropy principle
Directory of Open Access Journals (Sweden)
L. N. Epele
2007-10-01
Full Text Available The variational method with constraints recently developed by Verkley and Gerkema to describe maximum-entropy atmospheric profiles is generalized to ideal gases but with temperature-dependent specific heats. In so doing, an extended and non standard potential temperature is introduced that is well suited for tackling the problem under consideration. This new formalism is successfully applied to the atmosphere of Venus. Three well defined regions emerge in this atmosphere up to a height of 100 km from the surface: the lowest one up to about 35 km is adiabatic, a transition layer located at the height of the cloud deck and finally a third region which is practically isothermal.
Conjugate variables in continuous maximum-entropy inference.
Davis, Sergio; Gutiérrez, Gonzalo
2012-11-01
For a continuous maximum-entropy distribution (obtained from an arbitrary number of simultaneous constraints), we derive a general relation connecting the Lagrange multipliers and the expectation values of certain particularly constructed functions of the states of the system. From this relation, an estimator for a given Lagrange multiplier can be constructed from derivatives of the corresponding constraining function. These estimators sometimes lead to the determination of the Lagrange multipliers by way of solving a linear system, and, in general, they provide another tool to widen the applicability of Jaynes's formalism. This general relation, especially well suited for computer simulation techniques, also provides some insight into the interpretation of the hypervirial relations known in statistical mechanics and the recently derived microcanonical dynamical temperature. We illustrate the usefulness of these new relations with several applications in statistics.
Maximum Entropy and Probability Kinematics Constrained by Conditionals
Directory of Open Access Journals (Sweden)
Stefan Lukits
2015-03-01
Full Text Available Two open questions of inductive reasoning are solved: (1 does the principle of maximum entropy (PME give a solution to the obverse Majerník problem; and (2 isWagner correct when he claims that Jeffrey’s updating principle (JUP contradicts PME? Majerník shows that PME provides unique and plausible marginal probabilities, given conditional probabilities. The obverse problem posed here is whether PME also provides such conditional probabilities, given certain marginal probabilities. The theorem developed to solve the obverse Majerník problem demonstrates that in the special case introduced by Wagner PME does not contradict JUP, but elegantly generalizes it and offers a more integrated approach to probability updating.
A maximum entropy reconstruction technique for tomographic particle image velocimetry
International Nuclear Information System (INIS)
Bilsky, A V; Lozhkin, V A; Markovich, D M; Tokarev, M P
2013-01-01
This paper studies a novel approach for reducing tomographic PIV computational complexity. The proposed approach is an algebraic reconstruction technique, termed MENT (maximum entropy). This technique computes the three-dimensional light intensity distribution several times faster than SMART, using at least ten times less memory. Additionally, the reconstruction quality remains nearly the same as with SMART. This paper presents the theoretical computation performance comparison for MENT, SMART and MART, followed by validation using synthetic particle images. Both the theoretical assessment and validation of synthetic images demonstrate significant computational time reduction. The data processing accuracy of MENT was compared to that of SMART in a slot jet experiment. A comparison of the average velocity profiles shows a high level of agreement between the results obtained with MENT and those obtained with SMART. (paper)
Tsallis distribution as a standard maximum entropy solution with 'tail' constraint
International Nuclear Information System (INIS)
Bercher, J.-F.
2008-01-01
We show that Tsallis' distributions can be derived from the standard (Shannon) maximum entropy setting, by incorporating a constraint on the divergence between the distribution and another distribution imagined as its tail. In this setting, we find an underlying entropy which is the Renyi entropy. Furthermore, escort distributions and generalized means appear as a direct consequence of the construction. Finally, the 'maximum entropy tail distribution' is identified as a Generalized Pareto Distribution
Understanding Peripheral Bat Populations Using Maximum-Entropy Suitability Modeling.
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.
Halo-independence with quantified maximum entropy at DAMA/LIBRA
Energy Technology Data Exchange (ETDEWEB)
Fowlie, Andrew, E-mail: andrew.j.fowlie@googlemail.com [ARC Centre of Excellence for Particle Physics at the Tera-scale, Monash University, Melbourne, Victoria 3800 (Australia)
2017-10-01
Using the DAMA/LIBRA anomaly as an example, we formalise the notion of halo-independence in the context of Bayesian statistics and quantified maximum entropy. We consider an infinite set of possible profiles, weighted by an entropic prior and constrained by a likelihood describing noisy measurements of modulated moments by DAMA/LIBRA. Assuming an isotropic dark matter (DM) profile in the galactic rest frame, we find the most plausible DM profiles and predictions for unmodulated signal rates at DAMA/LIBRA. The entropic prior contains an a priori unknown regularisation factor, β, that describes the strength of our conviction that the profile is approximately Maxwellian. By varying β, we smoothly interpolate between a halo-independent and a halo-dependent analysis, thus exploring the impact of prior information about the DM profile.
Bayesian and maximum likelihood estimation of genetic maps
DEFF Research Database (Denmark)
York, Thomas L.; Durrett, Richard T.; Tanksley, Steven
2005-01-01
that makes the Bayesian method applicable to large data sets. We present an extensive simulation study examining the statistical properties of the method and comparing it with the likelihood method implemented in Mapmaker. We show that the Maximum A Posteriori (MAP) estimator of the genetic distances......, corresponding to the maximum likelihood estimator, performs better than estimators based on the posterior expectation. We also show that while the performance is similar between Mapmaker and the MCMC-based method in the absence of genotyping errors, the MCMC-based method has a distinct advantage in the presence...
Application of the maximum entropy method to dynamical fermion simulations
Clowser, Jonathan
This thesis presents results for spectral functions extracted from imaginary-time correlation functions obtained from Monte Carlo simulations using the Maximum Entropy Method (MEM). The advantages this method are (i) no a priori assumptions or parametrisations of the spectral function are needed, (ii) a unique solution exists and (iii) the statistical significance of the resulting image can be quantitatively analysed. The Gross Neveu model in d = 3 spacetime dimensions (GNM3) is a particularly interesting model to study with the MEM because at T = 0 it has a broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are resonances. Results for the elementary fermion, the Goldstone boson (pion), the sigma, the massive pseudoscalar meson and the symmetric phase resonances are presented. UKQCD Nf = 2 dynamical QCD data is also studied with MEM. Results are compared to those found from the quenched approximation, where the effects of quark loops in the QCD vacuum are neglected, to search for sea-quark effects in the extracted spectral functions. Information has been extract from the difficult axial spatial and scalar as well as the pseudoscalar, vector and axial temporal channels. An estimate for the non-singlet scalar mass in the chiral limit is given which is in agreement with the experimental value of Mao = 985 MeV.
Evaluation of hepatic blood flow using maximum entropy methods
International Nuclear Information System (INIS)
Seo, Shinya; Sasaki, Yuichiro; Abe, Yoshinao; Yamada, Kenji; Yoshioka, Seiro; Matsuzawa, Taiju.
1985-01-01
Using spectrum analysis (Maximum entropy methods; MEM), we separated the portal venous and the hepatic arterial components from the time activity curve (TAC) obtained by RI angiography of sup(99m)Tc-phytate. We set the region of interest on the right lobe of the liver and the left kidney, and set the short and the long section to the differentiated TAC of the liver and the TAC of the kidney. Sectioning was done as follows: 1) short section, from the point at 20 % of the peak to the point at the peak of the kidney. 2) long section, from the point at 20 % of the peak to the point at 0 which was extrapolated from the initial slope of the TAC of the kidney. We analysed these sections using MEM. The fast cycle (FC) obtained from the short section was related to the mean transit time (MTT) of the hepatic artery. The slow cycle (SC) obtained from the long section was related to the MTT of the portal vein. FC and SC were calculated on the liver and the kidney. Clinically, we compared the normal liver with liver chirrhosis. In normal, the liver to kidney ratio of FC and SC were 0.90 +- 0.14 and 1.08 +- 0.11, respectively. In cirrhosis, the liver to kidney ratio of FC and SC were 0.66 +- 0.16 and 1.65 +- 0.35, respectively. These results were reasonable for the hemodynamics of the diseased liver. (author)
Maximum Entropy Method for neutron powder diffraction data
International Nuclear Information System (INIS)
Sakata, Makoto; Uno, Tatsuya; Takata, Masaki; Takagi, Masahiro; Kumazawa, Shintaro; Howard, C.J.
1993-01-01
The Maximum Entropy Method (MEM) is powerful method to restore the accurate electron density distribution from X-ray diffraction data. It deals with electron density which is always positive. In order to analyze neutron diffraction data by the MEM, it is necessary to overcome the difficulty of negative scattering length of some atoms, such as Ti, Mn. In this work, a new approach to solving the negative scattering problem is described. It is based on nuclear densities rather than densities of scattering length, because the nuclear densities are always positive. The new method is successfully applied to analyze the neutron powder data from two polymorphs of TiO 2 , i.e. rutile and anatase. The procedure, like its X-ray counter-part, requires no structural model. The nuclear densities of rutile obtained by the present method is compared with the electron density distribution previously obtained by the MEM analysis. In contrast to the electron density distribution, nuclear densities show completely no density between Ti and O nuclei. It is also revealed that both Ti and O nuclear densities are confined within a very limited space. The present analysis provide a good demonstration of complementary nature of neutron and X-ray diffraction. (author)
Maximum entropy formalism for the analytic continuation of matrix-valued Green's functions
Kraberger, Gernot J.; Triebl, Robert; Zingl, Manuel; Aichhorn, Markus
2017-10-01
We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended for spectral functions that are possibly negative in some frequency ranges. In that way, all matrix elements of the Green's function matrix can be analytically continued; we introduce a computationally cheap element-wise method for this purpose. However, this method cannot ensure important constraints on the mathematical properties of the resulting spectral functions, namely positive semidefiniteness and Hermiticity. To improve on this, we present a full matrix formalism, where all matrix elements are treated simultaneously. We show the capabilities of these methods using insulating and metallic dynamical mean-field theory (DMFT) Green's functions as test cases. Finally, we apply the methods to realistic material calculations for LaTiO3, where off-diagonal matrix elements in the Green's function appear due to the distorted crystal structure.
Maximum-entropy principle and its application to the solution of inverse problems
International Nuclear Information System (INIS)
Soroko, L.
1981-01-01
The maximum-entropy principle, which expresses a constraint on the solution to an inverse problem defined by a system of linear equations, is explained. The maximum-entropy principle makes it possible to raise the resolution of an instrument a posteriori and to reconstruct tomographic images from a truncated set of projections
The mechanics of granitoid systems and maximum entropy production rates.
Hobbs, Bruce E; Ord, Alison
2010-01-13
A model for the formation of granitoid systems is developed involving melt production spatially below a rising isotherm that defines melt initiation. Production of the melt volumes necessary to form granitoid complexes within 10(4)-10(7) years demands control of the isotherm velocity by melt advection. This velocity is one control on the melt flux generated spatially just above the melt isotherm, which is the control valve for the behaviour of the complete granitoid system. Melt transport occurs in conduits initiated as sheets or tubes comprising melt inclusions arising from Gurson-Tvergaard constitutive behaviour. Such conduits appear as leucosomes parallel to lineations and foliations, and ductile and brittle dykes. The melt flux generated at the melt isotherm controls the position of the melt solidus isotherm and hence the physical height of the Transport/Emplacement Zone. A conduit width-selection process, driven by changes in melt viscosity and constitutive behaviour, operates within the Transport Zone to progressively increase the width of apertures upwards. Melt can also be driven horizontally by gradients in topography; these horizontal fluxes can be similar in magnitude to vertical fluxes. Fluxes induced by deformation can compete with both buoyancy and topographic-driven flow over all length scales and results locally in transient 'ponds' of melt. Pluton emplacement is controlled by the transition in constitutive behaviour of the melt/magma from elastic-viscous at high temperatures to elastic-plastic-viscous approaching the melt solidus enabling finite thickness plutons to develop. The system involves coupled feedback processes that grow at the expense of heat supplied to the system and compete with melt advection. The result is that limits are placed on the size and time scale of the system. Optimal characteristics of the system coincide with a state of maximum entropy production rate. This journal is © 2010 The Royal Society
On generalized entropies, Bayesian decisions and statistical diversity
Czech Academy of Sciences Publication Activity Database
Vajda, Igor; Zvárová, Jana
2007-01-01
Roč. 43, č. 5 (2007), s. 675-696 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GA102/07/1131; GA MŠk(CZ) 1M06014 Institutional research plan: CEZ:AV0Z10750506; CEZ:AV0Z10300504 Keywords : Generalized information * Generalized entropy * Power entropy * Bayes error * Simpson diversity * Emlen diversity Subject RIV: BD - Theory of Information Impact factor: 0.552, year: 2007
Maximum entropy principle for stationary states underpinned by stochastic thermodynamics.
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.
Exact Maximum-Entropy Estimation with Feynman Diagrams
Netser Zernik, Amitai; Schlank, Tomer M.; Tessler, Ran J.
2018-02-01
A longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using perturbative Feynman calculus. The explicit expression is given as a sum over weighted trees.
Network Inference and Maximum Entropy Estimation on Information Diagrams
Czech Academy of Sciences Publication Activity Database
Martin, E.A.; Hlinka, J.; Meinke, A.; Děchtěrenko, Filip; Tintěra, J.; Oliver, I.; Davidsen, J.
2017-01-01
Roč. 7, č. 1 (2017), s. 1-15, č. článku 7062. ISSN 2045-2322 R&D Projects: GA ČR GA13-23940S Institutional support: RVO:68081740 Keywords : complex networks * mutual information * entropy maximization * fMRI Subject RIV: AN - Psychology OBOR OECD: Cognitive sciences Impact factor: 4.259, year: 2016
Maximum entropy production: Can it be used to constrain conceptual hydrological models?
M.C. Westhoff; E. Zehe
2013-01-01
In recent years, optimality principles have been proposed to constrain hydrological models. The principle of maximum entropy production (MEP) is one of the proposed principles and is subject of this study. It states that a steady state system is organized in such a way that entropy production is maximized. Although successful applications have been reported in...
Network Inference and Maximum Entropy Estimation on Information Diagrams
Czech Academy of Sciences Publication Activity Database
Martin, E.A.; Hlinka, J.; Meinke, A.; Děchtěrenko, Filip; Tintěra, J.; Oliver, I.; Davidsen, J.
2017-01-01
Roč. 7, č. 1 (2017), s. 1-15, č. článku 7062. ISSN 2045-2322 R&D Projects: GA ČR GA13-23940S Institutional support: RVO:68081740 Keywords : complex networks * mutual information * entropy maximization * fMRI Subject RIV: AN - Psychology OBOR OECD: Psychology (including human - machine relations) Impact factor: 4.259, year: 2016
Spectral shaping of a randomized PWM DC-DC converter using maximum entropy probability distributions
CSIR Research Space (South Africa)
Dove, Albert
2017-01-01
Full Text Available Entropy. It is shown that given a pool of randomized parameters, there exists a region through which maximum spreading happens and how this spreading out is compromized by having constraints....
Chen, Yihang; Xiao, Chijie; Yang, Xiaoyi; Wang, Tianbo; Xu, Tianchao; Yu, Yi; Xu, Min; Wang, Long; Lin, Chen; Wang, Xiaogang
2017-10-01
The Laser-driven Ion beam trace probe (LITP) is a new diagnostic method for measuring poloidal magnetic field (Bp) and radial electric field (Er) in tokamaks. LITP injects a laser-driven ion beam into the tokamak, and Bp and Er profiles can be reconstructed using tomography methods. A reconstruction code has been developed to validate the LITP theory, and both 2D reconstruction of Bp and simultaneous reconstruction of Bp and Er have been attained. To reconstruct from experimental data with noise, Maximum Entropy and Gaussian-Bayesian tomography methods were applied and improved according to the characteristics of the LITP problem. With these improved methods, a reconstruction error level below 15% has been attained with a data noise level of 10%. These methods will be further tested and applied in the following LITP experiments. Supported by the ITER-CHINA program 2015GB120001, CHINA MOST under 2012YQ030142 and National Natural Science Foundation Abstract of China under 11575014 and 11375053.
Okada, Kanzo
2018-01-01
Gyarmati's variational principle is generalized to nonlinear cases in the maximum entropy formalism of Jaynes by basing it on a statistical mechanical expression involving the partition function. The force representation for the general solution of the Clausius-Duhem inequality due to Edelen, which is expressed as the sum of the dissipative and non-dissipative parts of the thermodynamic forces, is also found to be derivable from within the maximum entropy formalism.
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 ...
Network Inference and Maximum Entropy Estimation on Information Diagrams
Czech Academy of Sciences Publication Activity Database
Martin, E.A.; Hlinka, Jaroslav; Meinke, A.; Děchtěrenko, Filip; Tintěra, J.; Oliver, I.; Davidsen, J.
2017-01-01
Roč. 7, č. 1 (2017), č. článku 7062. ISSN 2045-2322 R&D Projects: GA ČR GA13-23940S; GA MZd(CZ) NV15-29835A Grant - others:GA MŠk(CZ) LO1611 Institutional support: RVO:67985807 Keywords : complex networks * mutual information * entropy maximization * fMRI Subject RIV: BD - Theory of Information OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 4.259, year: 2016
What is the maximum rate at which entropy of a string can increase?
International Nuclear Information System (INIS)
Ropotenko, Kostyantyn
2009-01-01
According to Susskind, a string falling toward a black hole spreads exponentially over the stretched horizon due to repulsive interactions of the string bits. In this paper such a string is modeled as a self-avoiding walk and the string entropy is found. It is shown that the rate at which information/entropy contained in the string spreads is the maximum rate allowed by quantum theory. The maximum rate at which the black hole entropy can increase when a string falls into a black hole is also discussed.
Directory of Open Access Journals (Sweden)
Zhuofei Xu
2017-01-01
Full Text Available Empirical mode decomposition (EMD is a self-adaptive analysis method for nonlinear and nonstationary signals. It has been widely applied to machinery fault diagnosis and structural damage detection. A novel feature, maximum symbolic entropy of intrinsic mode function based on EMD, is proposed to enhance the ability of recognition of EMD in this paper. First, a signal is decomposed into a collection of intrinsic mode functions (IMFs based on the local characteristic time scale of the signal, and then IMFs are transformed into a serious of symbolic sequence with different parameters. Second, it can be found that the entropies of symbolic IMFs are quite different. However, there is always a maximum value for a certain symbolic IMF. Third, take the maximum symbolic entropy as features to describe IMFs from a signal. Finally, the proposed features are applied to evaluate the effect of maximum symbolic entropy in fault diagnosis of rolling bearing, and then the maximum symbolic entropy is compared with other standard time analysis features in a contrast experiment. Although maximum symbolic entropy is only a time domain feature, it can reveal the signal characteristic information accurately. It can also be used in other fields related to EMD method.
Maximum-entropy networks pattern detection, network reconstruction and graph combinatorics
Squartini, Tiziano
2017-01-01
This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties. After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem o...
A quadratic spline maximum entropy method for the computation of invariant densities
Directory of Open Access Journals (Sweden)
DING Jiu
2015-06-01
Full Text Available The numerical recovery of an invariant density of the Frobenius-Perron operator corresponding to a nonsingular transformation is depicted by using quadratic spline functions. We implement a maximum entropy method to approximate the invariant density. The proposed method removes the ill-conditioning in the maximum entropy method, which arises by the use of polynomials. Due to the smoothness of the functions and a good convergence rate, the accuracy in the numerical calculation increases rapidly as the number of moment functions increases. The numerical results from the proposed method are supported by the theoretical analysis.
Energy and enstrophy spectra of geostrophic turbulent flows derived from a maximum entropy principle
Verkley, W. T. M.; Lynch, P.
2009-04-01
The principle of maximum entropy is used to obtain energy and enstrophy spectra as well as average vorticity fields in the context of geostrophic turbulence on a rotating sphere. In the unforced-undamped (inviscid) case the maximization of entropy is constrained by the (constant) energy and enstrophy of the system, leading to the familiar results of absolute statistical equilibrium. In the damped (freely decaying) and forced-damped case the maximization of entropy is constrained by either the decay rates of energy and enstrophy or by the energy and enstrophy in combination with their decay rates. Integrations with a numerical spectral model are used to check the theoretical results for the different cases. Maximizing the entropy, constrained by the energy and enstrophy, gives a very good description of the energy and enstrophy spectra in the inviscid case, in accordance with known results. Maximizing the entropy, constrained by the energy and enstrophy in combination with their decay rates, also leads to very good descriptions of the energy and enstrophy spectra in the freely decaying case, not too long after the damping has set in. In the forced-damped case, maximizing the entropy with the energy and enstrophy in combination with their (zero) decay rates as constraints, gives a reasonable description of the spectra although discrepancies remain.
Reconstruction of electron beam distribution in phase space by using parallel maximum entropy method
International Nuclear Information System (INIS)
Hajima, R.; Hirotsu, T.; Kondo, S.
1997-01-01
Reconstruction of electron beam distribution in six-dimensional phase space by tomographic approach is presented. Maximum entropy method (MENT) is applied to the reconstruction and compared with filtered back-projection. Finally, MENT is adapted to parallel computing environment with PVM. (orig.)
Using maximum entropy modeling to identify and prioritize red spruce forest habitat in West Virginia
Nathan R. Beane; James S. Rentch; Thomas M. Schuler
2013-01-01
Red spruce forests in West Virginia are found in island-like distributions at high elevations and provide essential habitat for the endangered Cheat Mountain salamander and the recently delisted Virginia northern flying squirrel. Therefore, it is important to identify restoration priorities of red spruce forests. Maximum entropy modeling was used to identify areas of...
Czech Academy of Sciences Publication Activity Database
Palatinus, Lukáš; Amami, M.; van Smaalen, S.
2004-01-01
Roč. 60, - (2004), s. 127-137 ISSN 0108-7681 Grant - others:DFG(DE) XX Institutional research plan: CEZ:AV0Z1010914 Keywords : incommensurate modulation * superspace * maximum entropy method Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 5.418, year: 2004
Maximum-Entropy Models of Sequenced Immune Repertoires Predict Antigen-Antibody Affinity
DEFF Research Database (Denmark)
Asti, Lorenzo; Uguzzoni, Guido; Marcatili, Paolo
2016-01-01
-frequency mutation rate in the genome region that codes for the antibody active site. Eventually, cells that produce antibodies with higher affinity for their cognate antigen are selected and clonally expanded. Here, we propose a new statistical approach based on maximum entropy modeling in which a scoring function...
Incommensurate modulations made visible by the Maximum Entropy Method in superspace
Czech Academy of Sciences Publication Activity Database
Palatinus, Lukáš; van Smaalen, S.
2004-01-01
Roč. 219, - (2004), s. 719-729 ISSN 0044-2968 Grant - others:DFG(DE) XX Institutional research plan: CEZ:AV0Z1010914 Keywords : Maximum Entropy Method * modulated structures * charge density Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.390, year: 2004
The prior-derived F constraints in the maximum-entropy method
Czech Academy of Sciences Publication Activity Database
Palatinus, Lukáš; van Smaalen, S.
2005-01-01
Roč. 61, - (2005), s. 363-372 ISSN 0108-7673 Institutional research plan: CEZ:AV0Z10100521 Keywords : charge density * maximum-entropy method * sodium nitrite Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.791, year: 2005
The generalized F constraint in the maximum-entropy method - a study on simulated data
Czech Academy of Sciences Publication Activity Database
Palatinus, Lukáš; van Smaalen, S.
2002-01-01
Roč. 58, - (2002), s. 559-567 ISSN 0108-7673 Grant - others:DFG(DE) XX Institutional research plan: CEZ:AV0Z1010914 Keywords : maximum-entropy method * electron density * oxalic acid Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.417, year: 2002
Nuclear Enhanced X-ray Maximum Entropy Method Used to Analyze Local Distortions in Simple Structures
DEFF Research Database (Denmark)
Christensen, Sebastian; Bindzus, Niels; Christensen, Mogens
the ideal, undistorted rock-salt structure. NEXMEM employs a simple procedure to normalize extracted structure factors to the atomic form factors. The NDD is reconstructed by performing maximum entropy calculations on the normalized structure factors. NEXMEM has been validated by testing against simulated...
Maximum non-extensive entropy block bootstrap for non-stationary processes
Czech Academy of Sciences Publication Activity Database
Bergamelli, M.; Novotný, Jan; Urga, G.
2015-01-01
Roč. 91, 1/2 (2015), s. 115-139 ISSN 0001-771X R&D Projects: GA ČR(CZ) GA14-27047S Institutional support: RVO:67985998 Keywords : maximum entropy * bootstrap * Monte Carlo simulations Subject RIV: AH - Economics
Comparison of tomography reconstruction by maximum entropy and filtered retro projection
International Nuclear Information System (INIS)
Abdala, F.J.P.; Simpson, D.M.; Roberty, N.C.
1992-01-01
The tomographic reconstruction with few projections is studied, comparing the maximum entropy method with filtered retro projection. Simulations with and without the presence of noise and also with the presence of an object of high density inside of the skull are showed. (C.G.C.)
Predicting the Outcome of NBA Playoffs Based on the Maximum Entropy Principle
Directory of Open Access Journals (Sweden)
Ge Cheng
2016-12-01
Full Text Available Predicting the outcome of National Basketball Association (NBA matches poses a challenging problem of interest to the research community as well as the general public. In this article, we formalize the problem of predicting NBA game results as a classification problem and apply the principle of Maximum Entropy to construct an NBA Maximum Entropy (NBAME model that fits to discrete statistics for NBA games, and then predict the outcomes of NBA playoffs using the model. Our results reveal that the model is able to predict the winning team with 74.4% accuracy, outperforming other classical machine learning algorithms that could only afford a maximum prediction accuracy of 70.6% in the experiments that we performed.
Ugarte, Sergio; Gao, Yue; Metghalchi, Hameed
2010-01-01
The Maximum Entropy Principle has been used to model complex chemical reaction processes. The maximum entropy principle has been employed by the Rate-Controlled Constrained-Equilibrium (RCCE) method to determine concentration of different species during non-equilibrium combustion process. In this model, it is assumed that the system evolves through constrained equilibrium states where entropy of the mixture is maximized subject to constraints. Mixture composition is determined by integrating ...
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.
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.
Derivation of some new distributions in statistical mechanics using maximum entropy approach
Directory of Open Access Journals (Sweden)
Ray Amritansu
2014-01-01
Full Text Available The maximum entropy principle has been earlier used to derive the Bose Einstein(B.E., Fermi Dirac(F.D. & Intermediate Statistics(I.S. distribution of statistical mechanics. The central idea of these distributions is to predict the distribution of the microstates, which are the particle of the system, on the basis of the knowledge of some macroscopic data. The latter information is specified in the form of some simple moment constraints. One distribution differs from the other in the way in which the constraints are specified. In the present paper, we have derived some new distributions similar to B.E., F.D. distributions of statistical mechanics by using maximum entropy principle. Some proofs of B.E. & F.D. distributions are shown, and at the end some new results are discussed.
Takahashi, Osamu; Nomura, Tetsuo; Tabayashi, Kiyohiko; Yamasaki, Katsuyoshi
2008-07-01
We performed spectral analysis by using the maximum entropy method instead of the traditional Fourier transform technique to investigate the short-time behavior in molecular systems, such as the energy transfer between vibrational modes and chemical reactions. This procedure was applied to direct ab initio molecular dynamics calculations for the decomposition of formic acid. More reactive trajectories of dehydrolation than those of decarboxylation were obtained for Z-formic acid, which was consistent with the prediction of previous theoretical and experimental studies. Short-time maximum entropy method analyses were performed for typical reactive and non-reactive trajectories. Spectrograms of a reactive trajectory were obtained; these clearly showed the reactant, transient, and product regions, especially for the dehydrolation path.
Maximum-Entropy Meshfree Method for Compressible and Near-Incompressible Elasticity
Energy Technology Data Exchange (ETDEWEB)
Ortiz, A; Puso, M A; Sukumar, N
2009-09-04
Numerical integration errors and volumetric locking in the near-incompressible limit are two outstanding issues in Galerkin-based meshfree computations. In this paper, we present a modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision. Secondly, a locking-free small-strain elasticity formulation for meshfree methods is proposed, which draws on developments in assumed strain methods and nodal integration techniques. In this study, maximum-entropy basis functions are used; however, the generality of our approach permits the use of any meshfree approximation. Various benchmark problems in two-dimensional compressible and near-incompressible small strain elasticity are presented to demonstrate the accuracy and optimal convergence in the energy norm of the maximum-entropy meshfree formulation.
Use of the maximum entropy method in X-ray astronomy
International Nuclear Information System (INIS)
Willingale, R.
1981-01-01
An algorithm used to apply the maximum entropy method in X-ray astronomy is described. It is easy to programme on a digital computer and fast enough to allow processing of two-dimensional images. The method gives good noise suppression without loss of instrumental resolution and has been successfully applied to several data analysis problems in X-ray astronomy. The restoration of a high-resolution image from the Einstein Observatory demonstrates the use of the algorithm. (author)
L. Jubair Ahmed; A. Ebenezer Jeyakumar
2013-01-01
Thresholding is one of the most important techniques for performing image segmentation. In this paper to compute optimum thresholds for Maximum Tsallis entropy thresholding (MTET) model, a new hybrid algorithm is proposed by integrating the Comprehensive Learning Particle Swarm Optimizer (CPSO) with the Powell’s Conjugate Gradient (PCG) method. Here the CPSO will act as the main optimizer for searching the near-optimal thresholds while the PCG method will be used to fine tune the best solutio...
Bistability, non-ergodicity, and inhibition in pairwise maximum-entropy models.
Rostami, Vahid; Porta Mana, PierGianLuca; Grün, Sonja; Helias, Moritz
2017-10-01
Pairwise maximum-entropy models have been used in neuroscience to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, would produce a bimodal distribution for the population-averaged activity, and for some population sizes the second mode would peak at high activities, that experimentally would be equivalent to 90% of the neuron population active within time-windows of few milliseconds. Several problems are connected with this bimodality: 1. The presence of the high-activity mode is unrealistic in view of observed neuronal activity and on neurobiological grounds. 2. Boltzmann learning becomes non-ergodic, hence the pairwise maximum-entropy distribution cannot be found: in fact, Boltzmann learning would produce an incorrect distribution; similarly, common variants of mean-field approximations also produce an incorrect distribution. 3. The Glauber dynamics associated with the model is unrealistically bistable and cannot be used to generate realistic surrogate data. This bimodality problem is first demonstrated for an experimental dataset from 159 neurons in the motor cortex of macaque monkey. Evidence is then provided that this problem affects typical neural recordings of population sizes of a couple of hundreds or more neurons. The cause of the bimodality problem is identified as the inability of standard maximum-entropy distributions with a uniform reference measure to model neuronal inhibition. To eliminate this problem a modified maximum-entropy model is presented, which reflects a basic effect of inhibition in the form of a simple but non-uniform reference measure. This model does not lead to unrealistic bimodalities, can be found with Boltzmann learning, and has an associated Glauber dynamics which incorporates a minimal asymmetric inhibition.
Hydrodynamic equations for electrons in graphene obtained from the maximum entropy principle
Energy Technology Data Exchange (ETDEWEB)
Barletti, Luigi, E-mail: luigi.barletti@unifi.it [Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134 Firenze (Italy)
2014-08-15
The maximum entropy principle is applied to the formal derivation of isothermal, Euler-like equations for semiclassical fermions (electrons and holes) in graphene. After proving general mathematical properties of the equations so obtained, their asymptotic form corresponding to significant physical regimes is investigated. In particular, the diffusive regime, the Maxwell-Boltzmann regime (high temperature), the collimation regime and the degenerate gas limit (vanishing temperature) are considered.
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 ...
International Nuclear Information System (INIS)
Bastiens, K.; Lemahieu, I.
1994-01-01
The application of a maximum entropy reconstruction algorithm to PET images requires a lot of computing resources. A parallel implementation could seriously reduce the execution time. However, programming a parallel application is still a non trivial task, needing specialized people. In this paper a programming environment based on a visual programming language is used for a parallel implementation of the reconstruction algorithm. This programming environment allows less experienced programmers to use the performance of multiprocessor systems. (authors)
Applications of the principle of maximum entropy: from physics to ecology
International Nuclear Information System (INIS)
Banavar, Jayanth R; Volkov, Igor; Maritan, Amos
2010-01-01
There are numerous situations in physics and other disciplines which can be described at different levels of detail in terms of probability distributions. Such descriptions arise either intrinsically as in quantum mechanics, or because of the vast amount of details necessary for a complete description as, for example, in Brownian motion and in many-body systems. We show that an application of the principle of maximum entropy for estimating the underlying probability distribution can depend on the variables used for describing the system. The choice of characterization of the system carries with it implicit assumptions about fundamental attributes such as whether the system is classical or quantum mechanical or equivalently whether the individuals are distinguishable or indistinguishable. We show that the correct procedure entails the maximization of the relative entropy subject to known constraints and, additionally, requires knowledge of the behavior of the system in the absence of these constraints. We present an application of the principle of maximum entropy to understanding species diversity in ecology and introduce a new statistical ensemble corresponding to the distribution of a variable population of individuals into a set of species not defined a priori. (topical review)
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
Directory of Open Access Journals (Sweden)
Kostas Alexandridis
2013-06-01
Full Text Available Assessing spatial model performance often presents challenges related to the choice and suitability of traditional statistical methods in capturing the true validity and dynamics of the predicted outcomes. The stochastic nature of many of our contemporary spatial models of land use change necessitate the testing and development of new and innovative methodologies in statistical spatial assessment. In many cases, spatial model performance depends critically on the spatially-explicit prior distributions, characteristics, availability and prevalence of the variables and factors under study. This study explores the statistical spatial characteristics of statistical model assessment of modeling land use change dynamics in a seven-county study area in South-Eastern Wisconsin during the historical period of 1963–1990. The artificial neural network-based Land Transformation Model (LTM predictions are used to compare simulated with historical land use transformations in urban/suburban landscapes. We introduce a range of Bayesian information entropy statistical spatial metrics for assessing the model performance across multiple simulation testing runs. Bayesian entropic estimates of model performance are compared against information-theoretic stochastic entropy estimates and theoretically-derived accuracy assessments. We argue for the critical role of informational uncertainty across different scales of spatial resolution in informing spatial landscape model assessment. Our analysis reveals how incorporation of spatial and landscape information asymmetry estimates can improve our stochastic assessments of spatial model predictions. Finally our study shows how spatially-explicit entropic classification accuracy estimates can work closely with dynamic modeling methodologies in improving our scientific understanding of landscape change as a complex adaptive system and process.
From physics to economics: An econometric example using maximum relative entropy
Giffin, Adom
2009-04-01
Econophysics, is based on the premise that some ideas and methods from physics can be applied to economic situations. We intend to show in this paper how a physics concept such as entropy can be applied to an economic problem. In so doing, we demonstrate how information in the form of observable data and moment constraints are introduced into the method of Maximum relative Entropy (MrE). A general example of updating with data and moments is shown. Two specific econometric examples are solved in detail which can then be used as templates for real world problems. A numerical example is compared to a large deviation solution which illustrates some of the advantages of the MrE method.
Principle of maximum entropy for reliability analysis in the design of machine components
Zhang, Yimin
2018-03-01
We studied the reliability of machine components with parameters that follow an arbitrary statistical distribution using the principle of maximum entropy (PME). We used PME to select the statistical distribution that best fits the available information. We also established a probability density function (PDF) and a failure probability model for the parameters of mechanical components using the concept of entropy and the PME. We obtained the first four moments of the state function for reliability analysis and design. Furthermore, we attained an estimate of the PDF with the fewest human bias factors using the PME. This function was used to calculate the reliability of the machine components, including a connecting rod, a vehicle half-shaft, a front axle, a rear axle housing, and a leaf spring, which have parameters that typically follow a non-normal distribution. Simulations were conducted for comparison. This study provides a design methodology for the reliability of mechanical components for practical engineering projects.
Effective updating process of seismic fragilities using Bayesian method and information entropy
International Nuclear Information System (INIS)
Kato, Masaaki; Takata, Takashi; Yamaguchi, Akira
2008-01-01
Seismic probabilistic safety assessment (SPSA) is an effective method for evaluating overall performance of seismic safety of a plant. Seismic fragilities are estimated to quantify the seismically induced accident sequences. It is a great concern that the SPSA results involve uncertainties, a part of which comes from the uncertainty in the seismic fragility of equipment and systems. A straightforward approach to reduce the uncertainty is to perform a seismic qualification test and to reflect the results on the seismic fragility estimate. In this paper, we propose a figure-of-merit to find the most cost-effective condition of the seismic qualification tests about the acceleration level and number of components tested. Then a mathematical method to reflect the test results on the fragility update is developed. A Bayesian method is used for the fragility update procedure. Since a lognormal distribution that is used for the fragility model does not have a Bayes conjugate function, a parameterization method is proposed so that the posterior distribution expresses the characteristics of the fragility. The information entropy is used as the figure-of-merit to express importance of obtained evidence. It is found that the information entropy is strongly associated with the uncertainty of the fragility. (author)
Directory of Open Access Journals (Sweden)
Axel Kleidon
2010-03-01
Full Text Available The Maximum Entropy Production (MEP principle has been remarkably successful in producing accurate predictions for non-equilibrium states. We argue that this is because the MEP principle is an effective inference procedure that produces the best predictions from the available information. Since all Earth system processes are subject to the conservation of energy, mass and momentum, we argue that in practical terms the MEP principle should be applied to Earth system processes in terms of the already established framework of non-equilibrium thermodynamics, with the assumption of local thermodynamic equilibrium at the appropriate scales.
Chaos control of ferroresonance system based on RBF-maximum entropy clustering algorithm
International Nuclear Information System (INIS)
Liu Fan; Sun Caixin; Sima Wenxia; Liao Ruijin; Guo Fei
2006-01-01
With regards to the ferroresonance overvoltage of neutral grounded power system, a maximum-entropy learning algorithm based on radial basis function neural networks is used to control the chaotic system. The algorithm optimizes the object function to derive learning rule of central vectors, and uses the clustering function of network hidden layers. It improves the regression and learning ability of neural networks. The numerical experiment of ferroresonance system testifies the effectiveness and feasibility of using the algorithm to control chaos in neutral grounded system
Ground state of the Hubbard model: a variational approach based on the maximum entropy principle
Energy Technology Data Exchange (ETDEWEB)
Arrachea, L. (Dept. de Fisica, Univ. Nacional de La Plata (Argentina)); Plastino, A. (Dept. de Fisica, Univ. Nacional de La Plata (Argentina)); Canosa, N. (Physik Dept. der Technischen Univ. Muenchen, Garching (Germany)); Rossignoli, R. (Physik Dept. der Technischen Univ. Muenchen, Garching (Germany))
1993-05-17
A variational approach based on maximum entropy considerations is used to approximate the ground state of the Hubbard Hamiltonian. The evaluation of both the ground state energy and the correlation functions is performed with a trial wave function, which is parameterized in terms of a small set of variables associated with the relevant correlation operators of the problem. Results for one-dimensional case are in very good agreement with the exact ones for arbitrary interaction strengths. It is also shown that the method provides us with better evaluations of the ground state energy and correlation functions than those obtained with the Gutzwiller approximation. (orig.)
Ground state of the Hubbard model: a variational approach based on the maximum entropy principle
Arrachea, L.; Canosa, N.; Plastino, A.; Rossignoli, R.
1993-05-01
A variational approach based on maximum entropy considerations is used to approximate the ground state of the Hubbard Hamiltonian. The evaluation of both the ground state energy and the correlation functions is performed with a trial wave function, which is parameterized in terms of a small set of variables associated with the relevant correlation operators of the problem. Results for the one-dimensional case are in very good agreement with the exact ones for arbitrary interaction strengths. It is also shown that the method provides us with better evaluations of the ground state energy and correlation functions than those obtained with the Gutzwiller approximation.
Modelling maximum river flow by using Bayesian Markov Chain Monte Carlo
Cheong, R. Y.; Gabda, D.
2017-09-01
Analysis of flood trends is vital since flooding threatens human living in terms of financial, environment and security. The data of annual maximum river flows in Sabah were fitted into generalized extreme value (GEV) distribution. Maximum likelihood estimator (MLE) raised naturally when working with GEV distribution. However, previous researches showed that MLE provide unstable results especially in small sample size. In this study, we used different Bayesian Markov Chain Monte Carlo (MCMC) based on Metropolis-Hastings algorithm to estimate GEV parameters. Bayesian MCMC method is a statistical inference which studies the parameter estimation by using posterior distribution based on Bayes’ theorem. Metropolis-Hastings algorithm is used to overcome the high dimensional state space faced in Monte Carlo method. This approach also considers more uncertainty in parameter estimation which then presents a better prediction on maximum river flow in Sabah.
Maximum-entropy data restoration using both real- and Fourier-space analysis
International Nuclear Information System (INIS)
Anderson, D.M.; Martin, D.C.; Thomas, E.L.
1989-01-01
An extension of the maximum-entropy (ME) data-restoration method is presented that is sensitive to periodic correlations in data. The method takes advantage of the higher signal-to-noise ratio for periodic information in Fourier space, thus enhancing statistically significant frequencies in a manner which avoids the user bias inherent in conventional Fourier filtering. This procedure incorporates concepts underlying new approaches in quantum mechanics that consider entropies in both position and momentum spaces, although the emphasis here is on data restoration rather than quantum physics. After a fast Fourier transform of the image, the phases are saved and the array of Fourier moduli are restored using the maximum-entropy criterion. A first-order continuation method is introduced that speeds convergence of the ME computation. The restored moduli together with the original phases are then Fourier inverted to yield a new image; traditional real-space ME restoration is applied to this new image completing one stage in the restoration process. In test cases improvement can be obtained from two to four stages of iteration. It is shown that in traditional Fourier filtering spurious features can be induced by selection or elimination of Fourier components without regard to their statistical significance. With the present approach there is no such freedom for the user to exert personal bias, so that features present in the final image and power spectrum are those which have survived the tests of statistical significance in both real and Fourier space. However, it is still possible for periodicities to 'bleed' across sharp boundaries. An 'uncertainty' relation is derived describing the inverse relationship between the resolution of these boundaries and the level of noise that can be eliminated. (orig./BHO)
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M. E. Haji Abadi
2013-09-01
Full Text Available In this paper, the continuous optimal control theory is used to model and solve the maximum entropy problem for a continuous random variable. The maximum entropy principle provides a method to obtain least-biased probability density function (Pdf estimation. In this paper, to find a closed form solution for the maximum entropy problem with any number of moment constraints, the entropy is considered as a functional measure and the moment constraints are considered as the state equations. Therefore, the Pdf estimation problem can be reformulated as the optimal control problem. Finally, the proposed method is applied to estimate the Pdf of the hourly electricity prices of New England and Ontario electricity markets. Obtained results show the efficiency of the proposed method.
Maximum entropy methods for extracting the learned features of deep neural networks.
Finnegan, Alex; Song, Jun S
2017-10-01
New architectures of multilayer artificial neural networks and new methods for training them are rapidly revolutionizing the application of machine learning in diverse fields, including business, social science, physical sciences, and biology. Interpreting deep neural networks, however, currently remains elusive, and a critical challenge lies in understanding which meaningful features a network is actually learning. We present a general method for interpreting deep neural networks and extracting network-learned features from input data. We describe our algorithm in the context of biological sequence analysis. Our approach, based on ideas from statistical physics, samples from the maximum entropy distribution over possible sequences, anchored at an input sequence and subject to constraints implied by the empirical function learned by a network. Using our framework, we demonstrate that local transcription factor binding motifs can be identified from a network trained on ChIP-seq data and that nucleosome positioning signals are indeed learned by a network trained on chemical cleavage nucleosome maps. Imposing a further constraint on the maximum entropy distribution also allows us to probe whether a network is learning global sequence features, such as the high GC content in nucleosome-rich regions. This work thus provides valuable mathematical tools for interpreting and extracting learned features from feed-forward neural networks.
Modelling and Simulation of Seasonal Rainfall Using the Principle of Maximum Entropy
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Jonathan Borwein
2014-02-01
Full Text Available We use the principle of maximum entropy to propose a parsimonious model for the generation of simulated rainfall during the wettest three-month season at a typical location on the east coast of Australia. The model uses a checkerboard copula of maximum entropy to model the joint probability distribution for total seasonal rainfall and a set of two-parameter gamma distributions to model each of the marginal monthly rainfall totals. The model allows us to match the grade correlation coefficients for the checkerboard copula to the observed Spearman rank correlation coefficients for the monthly rainfalls and, hence, provides a model that correctly describes the mean and variance for each of the monthly totals and also for the overall seasonal total. Thus, we avoid the need for a posteriori adjustment of simulated monthly totals in order to correctly simulate the observed seasonal statistics. Detailed results are presented for the modelling and simulation of seasonal rainfall in the town of Kempsey on the mid-north coast of New South Wales. Empirical evidence from extensive simulations is used to validate this application of the model. A similar analysis for Sydney is also described.
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).
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R. Mauda
2014-01-01
Full Text Available 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.
Maximum entropy reconstructions of dynamic signaling networks from quantitative proteomics data.
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Jason W Locasale
2009-08-01
Full Text Available Advances in mass spectrometry among other technologies have allowed for quantitative, reproducible, proteome-wide measurements of levels of phosphorylation as signals propagate through complex networks in response to external stimuli under different conditions. However, computational approaches to infer elements of the signaling network strictly from the quantitative aspects of proteomics data are not well established. We considered a method using the principle of maximum entropy to infer a network of interacting phosphotyrosine sites from pairwise correlations in a mass spectrometry data set and derive a phosphorylation-dependent interaction network solely from quantitative proteomics data. We first investigated the applicability of this approach by using a simulation of a model biochemical signaling network whose dynamics are governed by a large set of coupled differential equations. We found that in a simulated signaling system, the method detects interactions with significant accuracy. We then analyzed a growth factor mediated signaling network in a human mammary epithelial cell line that we inferred from mass spectrometry data and observe a biologically interpretable, small-world structure of signaling nodes, as well as a catalog of predictions regarding the interactions among previously uncharacterized phosphotyrosine sites. For example, the calculation places a recently identified tumor suppressor pathway through ARHGEF7 and Scribble, in the context of growth factor signaling. Our findings suggest that maximum entropy derived network models are an important tool for interpreting quantitative proteomics data.
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S. Pascale
2012-01-01
Full Text Available The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m^{−2} K^{−1} of material entropy production is due to vertical heat transport and 5–7 mW m^{−2} K^{−1} to horizontal heat transport.
Zhao, Quanyu; Kurata, Hiroyuki
2010-08-01
Elementary mode (EM) analysis is potentially effective in integrating transcriptome or proteome data into metabolic network analyses and in exploring the mechanism of how phenotypic or metabolic flux distribution is changed with respect to environmental and genetic perturbations. The EM coefficients (EMCs) indicate the quantitative contribution of their associated EMs and can be estimated by maximizing Shannon's entropy as a general objective function in our previous study, but the use of EMCs is still restricted to a relatively small-scale networks. We propose a fast and universal method that optimizes hundreds of thousands of EMCs under the constraint of the Maximum entropy principle (MEP). Lagrange multipliers (LMs) are applied to maximize the Shannon's entropy-based objective function, analytically solving each EMC as the function of LMs. Consequently, the number of such search variables, the EMC number, is dramatically reduced to the reaction number. To demonstrate the feasibility of the MEP with Lagrange multipliers (MEPLM), it is coupled with enzyme control flux (ECF) to predict the flux distributions of Escherichia coli and Saccharomycescerevisiae for different conditions (gene deletion, adaptive evolution, temperature, and dilution rate) and to provide a quantitative understanding of how metabolic or physiological states are changed in response to these genetic or environmental perturbations at the elementary mode level. It is shown that the ECF-based method is a feasible framework for the prediction of metabolic flux distribution by integrating enzyme activity data into EMs to genetic and environmental perturbations. Copyright 2010 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.
How fast can we learn maximum entropy models of neural populations?
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Ganmor, Elad; Schneidman, Elad; Segev, Ronen
2009-01-01
Most of our knowledge about how the brain encodes information comes from recordings of single neurons. However, computations in the brain are carried out by large groups of neurons. Modelling the joint activity of many interacting elements is computationally hard because of the large number of possible activity patterns and limited experimental data. Recently it was shown in several different neural systems that maximum entropy pairwise models, which rely only on firing rates and pairwise correlations of neurons, are excellent models for the distribution of activity patterns of neural populations, and in particular, their responses to natural stimuli. Using simultaneous recordings of large groups of neurons in the vertebrate retina responding to naturalistic stimuli, we show here that the relevant statistics required for finding the pairwise model can be accurately estimated within seconds. Furthermore, while higher order statistics may, in theory, improve model accuracy, they are, in practice, harmful for times of up to 20 minutes due to sampling noise. Finally, we demonstrate that trading accuracy for entropy may actually improve model performance when data is limited, and suggest an optimization method that automatically adjusts model constraints in order to achieve good performance.
Maximum entropy approach to statistical inference for an ocean acoustic waveguide.
Knobles, D P; Sagers, J D; Koch, R A
2012-02-01
A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations. © 2012 Acoustical Society of America
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.
Modeling the Mass Action Dynamics of Metabolism with Fluctuation Theorems and Maximum Entropy
Cannon, William; Thomas, Dennis; Baxter, Douglas; Zucker, Jeremy; Goh, Garrett
The laws of thermodynamics dictate the behavior of biotic and abiotic systems. Simulation methods based on statistical thermodynamics can provide a fundamental understanding of how biological systems function and are coupled to their environment. While mass action kinetic simulations are based on solving ordinary differential equations using rate parameters, analogous thermodynamic simulations of mass action dynamics are based on modeling states using chemical potentials. The latter have the advantage that standard free energies of formation/reaction and metabolite levels are much easier to determine than rate parameters, allowing one to model across a large range of scales. Bridging theory and experiment, statistical thermodynamics simulations allow us to both predict activities of metabolites and enzymes and use experimental measurements of metabolites and proteins as input data. Even if metabolite levels are not available experimentally, it is shown that a maximum entropy assumption is quite reasonable and in many cases results in both the most energetically efficient process and the highest material flux.
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Urniezius, Renaldas
2011-01-01
The principle of Maximum relative Entropy optimization was analyzed for dead reckoning localization of a rigid body when observation data of two attached accelerometers was collected. Model constraints were derived from the relationships between the sensors. The experiment's results confirmed that accelerometers each axis' noise can be successfully filtered utilizing dependency between channels and the dependency between time series data. Dependency between channels was used for a priori calculation, and a posteriori distribution was derived utilizing dependency between time series data. There was revisited data of autocalibration experiment by removing the initial assumption that instantaneous rotation axis of a rigid body was known. Performance results confirmed that such an approach could be used for online dead reckoning localization.
Urniežius, Renaldas
2011-03-01
The principle of Maximum relative Entropy optimization was analyzed for dead reckoning localization of a rigid body when observation data of two attached accelerometers was collected. Model constraints were derived from the relationships between the sensors. The experiment's results confirmed that accelerometers each axis' noise can be successfully filtered utilizing dependency between channels and the dependency between time series data. Dependency between channels was used for a priori calculation, and a posteriori distribution was derived utilizing dependency between time series data. There was revisited data of autocalibration experiment by removing the initial assumption that instantaneous rotation axis of a rigid body was known. Performance results confirmed that such an approach could be used for online dead reckoning localization.
Cheng, Xiaojun; Ma, Xujun; Yépez, Miztli; Genack, Azriel Z.; Mello, Pier A.
2017-11-01
The single-parameter scaling hypothesis relating the average and variance of the logarithm of the conductance is a pillar of the theory of electronic transport. We use a maximum-entropy ansatz to explore the logarithm of the particle, or energy density lnW (x ) at a depth x into a random one-dimensional system. Single-parameter scaling would be the special case in which x =L (the system length). We find the result, confirmed in microwave measurements and computer simulations, that the average of lnW (x ) is independent of L and equal to -x /ℓ , with ℓ the mean free path. At the beginning of the sample, var [lnW (x )] rises linearly with x and is also independent of L , with a sublinear increase and then a drop near the sample output. At x =L we find a correction to the value of var [lnT ] predicted by single-parameter scaling.
Modelling streambank erosion potential using maximum entropy in a central Appalachian watershed
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J. Pitchford
2015-03-01
Full Text Available We used maximum entropy to model streambank erosion potential (SEP in a central Appalachian watershed to help prioritize sites for management. Model development included measuring erosion rates, application of a quantitative approach to locate Target Eroding Areas (TEAs, and creation of maps of boundary conditions. We successfully constructed a probability distribution of TEAs using the program Maxent. All model evaluation procedures indicated that the model was an excellent predictor, and that the major environmental variables controlling these processes were streambank slope, soil characteristics, bank position, and underlying geology. A classification scheme with low, moderate, and high levels of SEP derived from logistic model output was able to differentiate sites with low erosion potential from sites with moderate and high erosion potential. A major application of this type of modelling framework is to address uncertainty in stream restoration planning, ultimately helping to bridge the gap between restoration science and practice.
Multi-Group Maximum Entropy Model for Translational Non-Equilibrium
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.
Imaging VLBI polarimetry data from Active Galactic Nuclei using the Maximum Entropy Method
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Coughlan Colm P.
2013-12-01
Full Text Available Mapping the relativistic jets emanating from AGN requires the use of a deconvolution algorithm to account for the effects of missing baseline spacings. The CLEAN algorithm is the most commonly used algorithm in VLBI imaging today and is suitable for imaging polarisation data. The Maximum Entropy Method (MEM is presented as an alternative with some advantages over the CLEAN algorithm, including better spatial resolution and a more rigorous and unbiased approach to deconvolution. We have developed a MEM code suitable for deconvolving VLBI polarisation data. Monte Carlo simulations investigating the performance of CLEAN and the MEM code on a variety of source types are being carried out. Real polarisation (VLBA data taken at multiple wavelengths have also been deconvolved using MEM, and several of the resulting polarisation and Faraday rotation maps are presented and discussed.
Implementing and testing Bayesian and maximum-likelihood supertree methods in phylogenetics.
Akanni, Wasiu A; Wilkinson, Mark; Creevey, Christopher J; Foster, Peter G; Pisani, Davide
2015-08-01
Since their advent, supertrees have been increasingly used in large-scale evolutionary studies requiring a phylogenetic framework and substantial efforts have been devoted to developing a wide variety of supertree methods (SMs). Recent advances in supertree theory have allowed the implementation of maximum likelihood (ML) and Bayesian SMs, based on using an exponential distribution to model incongruence between input trees and the supertree. Such approaches are expected to have advantages over commonly used non-parametric SMs, e.g. matrix representation with parsimony (MRP). We investigated new implementations of ML and Bayesian SMs and compared these with some currently available alternative approaches. Comparisons include hypothetical examples previously used to investigate biases of SMs with respect to input tree shape and size, and empirical studies based either on trees harvested from the literature or on trees inferred from phylogenomic scale data. Our results provide no evidence of size or shape biases and demonstrate that the Bayesian method is a viable alternative to MRP and other non-parametric methods. Computation of input tree likelihoods allows the adoption of standard tests of tree topologies (e.g. the approximately unbiased test). The Bayesian approach is particularly useful in providing support values for supertree clades in the form of posterior probabilities.
Targeted search for continuous gravitational waves: Bayesian versus maximum-likelihood statistics
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Prix, Reinhard; Krishnan, Badri
2009-01-01
We investigate the Bayesian framework for detection of continuous gravitational waves (GWs) in the context of targeted searches, where the phase evolution of the GW signal is assumed to be known, while the four amplitude parameters are unknown. We show that the orthodox maximum-likelihood statistic (known as F-statistic) can be rediscovered as a Bayes factor with an unphysical prior in amplitude parameter space. We introduce an alternative detection statistic ('B-statistic') using the Bayes factor with a more natural amplitude prior, namely an isotropic probability distribution for the orientation of GW sources. Monte Carlo simulations of targeted searches show that the resulting Bayesian B-statistic is more powerful in the Neyman-Pearson sense (i.e., has a higher expected detection probability at equal false-alarm probability) than the frequentist F-statistic.
Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle.
Shalymov, Dmitry S; Fradkov, Alexander L
2016-01-01
We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.
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Matteo Polettini
2013-06-01
Full Text Available We challenge claims that the principle of maximum entropy production produces physical phenomenological relations between conjugate currents and forces, even beyond the linear regime, and that currents in networks arrange themselves to maximize entropy production as the system approaches the steady state. In particular: (1 we show that Ziegler’s principle of thermodynamic orthogonality leads to stringent reciprocal relations for higher order response coefficients, and in the framework of stochastic thermodynamics, we exhibit a simple explicit model that does not satisfy them; (2 on a network, enforcing Kirchhoff’s current law, we show that maximization of the entropy production prescribes reciprocal relations between coarse-grained observables, but is not responsible for the onset of the steady state, which is, rather, due to the minimum entropy production principle.
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Argentiero, Amedeo; Bovi, Maurizio; Cerqueti, Roy
2016-01-01
This paper examines psycho-induced overconsumption in a dynamic stochastic context. As emphasized by well-established psychological results, these psycho-distortions derive from a decision making based on simple rules-of-thumb, not on analytically sounded optimizations. To our end, we therefore compare two New Keynesian models. The first is populated by optimizing Muth-rational agents and acts as the normative benchmark. The other is a “psycho-perturbed” version of the benchmark that allows for the potential presence of overoptimism and, hence, of overconsumption. The parameters of these models are estimated through a Bayesian-type procedure, and performances are evaluated by employing an entropy measure. Such methodologies are particularly appropriate here since they take in full consideration the complexity generated by the randomness of the considered systems. In particular, they let to derive a not negligible information on the size and on the cyclical properties of the biases. In line with cognitive psychology suggestions our evidence shows that the overoptimism/overconsumption is: widespread—it is detected in nation-wide data; persistent—it emerges in full-sample estimations; it moves according to the expected cyclical behavior—larger in booms, and it disappears in crises. Moreover, by taking into account the effect of these psycho-biases, the model fits actual data better than the benchmark. All considered, then, enhancing the existing literature our findings: i) sustain the importance of inserting psychological distortions in macroeconomic models and ii) underline that system dynamics and psycho biases have statistically significant and economically important connections.
Non-equilibrium thermodynamics, maximum entropy production and Earth-system evolution.
Kleidon, Axel
2010-01-13
The present-day atmosphere is in a unique state far from thermodynamic equilibrium. This uniqueness is for instance reflected in the high concentration of molecular oxygen and the low relative humidity in the atmosphere. Given that the concentration of atmospheric oxygen has likely increased throughout Earth-system history, we can ask whether this trend can be generalized to a trend of Earth-system evolution that is directed away from thermodynamic equilibrium, why we would expect such a trend to take place and what it would imply for Earth-system evolution as a whole. The justification for such a trend could be found in the proposed general principle of maximum entropy production (MEP), which states that non-equilibrium thermodynamic systems maintain steady states at which entropy production is maximized. Here, I justify and demonstrate this application of MEP to the Earth at the planetary scale. I first describe the non-equilibrium thermodynamic nature of Earth-system processes and distinguish processes that drive the system's state away from equilibrium from those that are directed towards equilibrium. I formulate the interactions among these processes from a thermodynamic perspective and then connect them to a holistic view of the planetary thermodynamic state of the Earth system. In conclusion, non-equilibrium thermodynamics and MEP have the potential to provide a simple and holistic theory of Earth-system functioning. This theory can be used to derive overall evolutionary trends of the Earth's past, identify the role that life plays in driving thermodynamic states far from equilibrium, identify habitability in other planetary environments and evaluate human impacts on Earth-system functioning. This journal is © 2010 The Royal Society
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Carlos A. L. Pires
2013-02-01
Full Text Available The Minimum Mutual Information (MinMI Principle provides the least committed, maximum-joint-entropy (ME inferential law that is compatible with prescribed marginal distributions and empirical cross constraints. Here, we estimate MI bounds (the MinMI values generated by constraining sets Tcr comprehended by mcr linear and/or nonlinear joint expectations, computed from samples of N iid outcomes. Marginals (and their entropy are imposed by single morphisms of the original random variables. N-asymptotic formulas are given both for the distribution of cross expectation’s estimation errors, the MinMI estimation bias, its variance and distribution. A growing Tcr leads to an increasing MinMI, converging eventually to the total MI. Under N-sized samples, the MinMI increment relative to two encapsulated sets Tcr1 ⊂ Tcr2 (with numbers of constraints mcr1
Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood e...
Test the principle of maximum entropy in constant sum 2×2 game: Evidence in experimental economics
International Nuclear Information System (INIS)
Xu, Bin; Zhang, Hongen; Wang, Zhijian; Zhang, Jianbo
2012-01-01
By using laboratory experimental data, we test the uncertainty of strategy type in various competing environments with two-person constant sum 2×2 game in the social system. It firstly shows that, in these competing game environments, the outcome of human's decision-making obeys the principle of the maximum entropy. -- Highlights: ► Test the uncertainty in two-person constant sum games with experimental data. ► On game level, the constant sum game fits the principle of maximum entropy. ► On group level, all empirical entropy values are close to theoretical maxima. ► The results can be different for the games that are not constant sum game.
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Muhammad Shoaib
2016-10-01
Full Text Available Proper knowledge of the wind characteristics of a site is of fundamental importance in estimating wind energy output from a selected wind turbine. The present paper focuses on assessing the suitability and accuracy of the fitted distribution function to the measured wind speed data for Baburband site in Sindh Pakistan. Comparison is made between the wind power densities obtained using the fitted functions based on Maximum Entropy Principle (MEP and Weibull distribution. In case of MEP-based function a system of (N+1 non-linear equations containing (N+1 Lagrange multipliers is defined as probability density function. The maximum entropy probability density functions is calculated for 3–9 low order moments obtained from measured wind speed data. The annual actual wind power density (PA is found to be 309.25 W/m2 while the Weibull based wind power density (PW is 297.25 W/m2. The MEP-based density for orders 5, 7, 8 and 9 (PE is 309.21 W/m2, whereas for order 6 it is 309.43 W/m2. To validate the MEP-based function, the results are compared with the Weibull function and the measured data. Kolmogorov–Smirnov test is performed between the cdf of the measured wind data and the fitted distribution function (Q95 = 0.01457 > Q = 10−4. The test confirms the suitability of MEP-based function for modeling measured wind speed data and for the estimation of wind energy output from a wind turbine. R2 test is also performed giving analogous behavior of the fitted MEP-based pdf to the actual wind speed data (R2 ~ 0.9. The annual energy extracted using the chosen wind turbine based on Weibull function is PW = 2.54 GWh and that obtained using MEP-based function is PE = 2.57–2.67 GWh depending on the order of moments.
Graafsma, H; de Vries, R.Y.
1999-01-01
The maximum-entropy method (MEM) has been applied for the deconvolution of the point-spread function (PSF) of two-dimensional X-ray detectors. The method is robust, model and image independent, and only depends on the correct description of the two-dimensional point-spread function and gain factor
de Vries, R.Y.; Briels, Willem J.; Feil, D.; te Velde, G.; Baerends, E.J.
1996-01-01
1990 Sakata and Sato applied the maximum entropy method (MEM) to a set of structure factors measured earlier by Saka and Kato with the Pendellösung method. They found the presence of non-nuclear attractors, i.e., maxima in the density between two bonded atoms. We applied the MEM to a limited set of
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.
Maximum-Entropy Models of Sequenced Immune Repertoires Predict Antigen-Antibody Affinity.
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Lorenzo Asti
2016-04-01
Full Text Available The immune system has developed a number of distinct complex mechanisms to shape and control the antibody repertoire. One of these mechanisms, the affinity maturation process, works in an evolutionary-like fashion: after binding to a foreign molecule, the antibody-producing B-cells exhibit a high-frequency mutation rate in the genome region that codes for the antibody active site. Eventually, cells that produce antibodies with higher affinity for their cognate antigen are selected and clonally expanded. Here, we propose a new statistical approach based on maximum entropy modeling in which a scoring function related to the binding affinity of antibodies against a specific antigen is inferred from a sample of sequences of the immune repertoire of an individual. We use our inference strategy to infer a statistical model on a data set obtained by sequencing a fairly large portion of the immune repertoire of an HIV-1 infected patient. The Pearson correlation coefficient between our scoring function and the IC50 neutralization titer measured on 30 different antibodies of known sequence is as high as 0.77 (p-value 10-6, outperforming other sequence- and structure-based models.
Analysis of QCD sum rule based on the maximum entropy method
International Nuclear Information System (INIS)
Gubler, Philipp
2012-01-01
QCD sum rule was developed about thirty years ago and has been used up to the present to calculate various physical quantities like hadrons. It has been, however, needed to assume 'pole + continuum' for the spectral function in the conventional analyses. Application of this method therefore came across with difficulties when the above assumption is not satisfied. In order to avoid this difficulty, analysis to make use of the maximum entropy method (MEM) has been developed by the present author. It is reported here how far this new method can be successfully applied. In the first section, the general feature of the QCD sum rule is introduced. In section 2, it is discussed why the analysis by the QCD sum rule based on the MEM is so effective. In section 3, the MEM analysis process is described, and in the subsection 3.1 likelihood function and prior probability are considered then in subsection 3.2 numerical analyses are picked up. In section 4, some cases of applications are described starting with ρ mesons, then charmoniums in the finite temperature and finally recent developments. Some figures of the spectral functions are shown. In section 5, summing up of the present analysis method and future view are given. (S. Funahashi)
Maximum entropy inference of seabed attenuation parameters using ship radiated broadband noise.
Knobles, D P
2015-12-01
The received acoustic field generated by a single passage of a research vessel on the New Jersey continental shelf is employed to infer probability distributions for the parameter values representing the frequency dependence of the seabed attenuation and the source levels of the ship. The statistical inference approach employed in the analysis is a maximum entropy methodology. The average value of the error function, needed to uniquely specify a conditional posterior probability distribution, is estimated with data samples from time periods in which the ship-receiver geometry is dominated by either the stern or bow aspect. The existence of ambiguities between the source levels and the environmental parameter values motivates an attempt to partially decouple these parameter values. The main result is the demonstration that parameter values for the attenuation (α and the frequency exponent), the sediment sound speed, and the source levels can be resolved through a model space reduction technique. The results of this multi-step statistical inference developed for ship radiated noise is then tested by processing towed source data over the same bandwidth and source track to estimate continuous wave source levels that were measured independently with a reference hydrophone on the tow body.
Computational design of hepatitis C vaccines using maximum entropy models and population dynamics
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.
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E. Ridolfi
2011-07-01
Full Text Available Hydrological models are the basis of operational flood-forecasting systems. The accuracy of these models is strongly dependent on the quality and quantity of the input information represented by rainfall height. Finer space-time rainfall resolution results in more accurate hazard forecasting. In this framework, an optimum raingauge network is essential in predicting flood events.
This paper develops an entropy-based approach to evaluate the maximum information content achievable by a rainfall network for different sampling time intervals. The procedure is based on the determination of the coefficients of transferred and nontransferred information and on the relative isoinformation contours.
The nontransferred information value achieved by the whole network is strictly dependent on the sampling time intervals considered. An empirical curve is defined, to assess the objective of the research: the nontransferred information value is plotted versus the associated sampling time on a semi-log scale. The curve has a linear trend.
In this paper, the methodology is applied to the high-density raingauge network of the urban area of Rome.
LQG and maximum entropy control design for the Hubble Space Telescope
Collins, Emmanuel G., Jr.; Richter, Stephen
Solar array vibrations are responsible for serious pointing control problems on the Hubble Space Telescope (HST). The original HST control law was not designed to attenuate these disturbances because they were not perceived to be a problem prior to launch. However, significant solar array vibrations do occur due to large changes in the thermal environment as the HST orbits the earth. Using classical techniques, Marshall Space Flight Center in conjunction with Lockheed Missiles and Space Company developed modified HST controllers that were able to suppress the influence of the vibrations of the solar arrays on the line-of-sight (LOS) performance. Substantial LOS improvement was observed when two of these controllers were implemented on orbit. This paper describes the development of modified HST controllers by using modern control techniques, particularly linear-quadratic-gaussian (LQG) design and Maximum Entropy robust control design, a generalization of LQG that incorporates robustness constraints with respect to modal errors. The fundamental issues are discussed candidly and controllers designed using these modern techniques are described.
Reppert, Michael; Tokmakoff, Andrei
The structural characterization of intrinsically disordered peptides (IDPs) presents a challenging biophysical problem. Extreme heterogeneity and rapid conformational interconversion make traditional methods difficult to interpret. Due to its ultrafast (ps) shutter speed, Amide I vibrational spectroscopy has received considerable interest as a novel technique to probe IDP structure and dynamics. Historically, Amide I spectroscopy has been limited to delivering global secondary structural information. More recently, however, the method has been adapted to study structure at the local level through incorporation of isotope labels into the protein backbone at specific amide bonds. Thanks to the acute sensitivity of Amide I frequencies to local electrostatic interactions-particularly hydrogen bonds-spectroscopic data on isotope labeled residues directly reports on local peptide conformation. Quantitative information can be extracted using electrostatic frequency maps which translate molecular dynamics trajectories into Amide I spectra for comparison with experiment. Here we present our recent efforts in the development of a rigorous approach to incorporating Amide I spectroscopic restraints into refined molecular dynamics structural ensembles using maximum entropy and related approaches. By combining force field predictions with experimental spectroscopic data, we construct refined structural ensembles for a family of short, strongly disordered, elastin-like peptides in aqueous solution.
A Novel Maximum Entropy Markov Model for Human Facial Expression Recognition.
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Muhammad Hameed Siddiqi
Full Text Available Research in video based FER systems has exploded in the past decade. However, most of the previous methods work well when they are trained and tested on the same dataset. Illumination settings, image resolution, camera angle, and physical characteristics of the people differ from one dataset to another. Considering a single dataset keeps the variance, which results from differences, to a minimum. Having a robust FER system, which can work across several datasets, is thus highly desirable. The aim of this work is to design, implement, and validate such a system using different datasets. In this regard, the major contribution is made at the recognition module which uses the maximum entropy Markov model (MEMM for expression recognition. In this model, the states of the human expressions are modeled as the states of an MEMM, by considering the video-sensor observations as the observations of MEMM. A modified Viterbi is utilized to generate the most probable expression state sequence based on such observations. Lastly, an algorithm is designed which predicts the expression state from the generated state sequence. Performance is compared against several existing state-of-the-art FER systems on six publicly available datasets. A weighted average accuracy of 97% is achieved across all datasets.
Using maximum entropy modeling for optimal selection of sampling sites for monitoring networks
Stohlgren, Thomas J.; Kumar, Sunil; Barnett, David T.; Evangelista, Paul H.
2011-01-01
Environmental monitoring programs must efficiently describe state shifts. We propose using maximum entropy modeling to select dissimilar sampling sites to capture environmental variability at low cost, and demonstrate a specific application: sample site selection for the Central Plains domain (453,490 km2) of the National Ecological Observatory Network (NEON). We relied on four environmental factors: mean annual temperature and precipitation, elevation, and vegetation type. A “sample site” was defined as a 20 km × 20 km area (equal to NEON’s airborne observation platform [AOP] footprint), within which each 1 km2 cell was evaluated for each environmental factor. After each model run, the most environmentally dissimilar site was selected from all potential sample sites. The iterative selection of eight sites captured approximately 80% of the environmental envelope of the domain, an improvement over stratified random sampling and simple random designs for sample site selection. This approach can be widely used for cost-efficient selection of survey and monitoring sites.
Maximum entropy analysis of polarized fluorescence decay of (E)GFP in aqueous solution
Novikov, Eugene G.; Skakun, Victor V.; Borst, Jan Willem; Visser, Antonie J. W. G.
2018-01-01
The maximum entropy method (MEM) was used for the analysis of polarized fluorescence decays of enhanced green fluorescent protein (EGFP) in buffered water/glycerol mixtures, obtained with time-correlated single-photon counting (Visser et al 2016 Methods Appl. Fluoresc. 4 035002). To this end, we used a general-purpose software module of MEM that was earlier developed to analyze (complex) laser photolysis kinetics of ligand rebinding reactions in oxygen binding proteins. We demonstrate that the MEM software provides reliable results and is easy to use for the analysis of both total fluorescence decay and fluorescence anisotropy decay of aqueous solutions of EGFP. The rotational correlation times of EGFP in water/glycerol mixtures, obtained by MEM as maxima of the correlation-time distributions, are identical to the single correlation times determined by global analysis of parallel and perpendicular polarized decay components. The MEM software is also able to determine homo-FRET in another dimeric GFP, for which the transfer correlation time is an order of magnitude shorter than the rotational correlation time. One important advantage utilizing MEM analysis is that no initial guesses of parameters are required, since MEM is able to select the least correlated solution from the feasible set of solutions.
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Mona Nazeri
Full Text Available One of the available tools for mapping the geographical distribution and potential suitable habitats is species distribution models. These techniques are very helpful for finding poorly known distributions of species in poorly sampled areas, such as the tropics. Maximum Entropy (MaxEnt is a recently developed modeling method that can be successfully calibrated using a relatively small number of records. In this research, the MaxEnt model was applied to describe the distribution and identify the key factors shaping the potential distribution of the vulnerable Malayan Sun Bear (Helarctos malayanus in one of the main remaining habitats in Peninsular Malaysia. MaxEnt results showed that even though Malaysian sun bear habitat is tied with tropical evergreen forests, it lives in a marginal threshold of bio-climatic variables. On the other hand, current protected area networks within Peninsular Malaysia do not cover most of the sun bears potential suitable habitats. Assuming that the predicted suitability map covers sun bears actual distribution, future climate change, forest degradation and illegal hunting could potentially severely affect the sun bear's population.
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George Kesidis
2008-06-01
Full Text Available In many ensemble classification paradigms, the function which combines local/base classifier decisions is learned in a supervised fashion. Such methods require common labeled training examples across the classifier ensemble. However, in some scenarios, where an ensemble solution is necessitated, common labeled data may not exist: (i legacy/proprietary classifiers, and (ii spatially distributed and/or multiple modality sensors. In such cases, it is standard to apply fixed (untrained decision aggregation such as voting, averaging, or naive Bayes rules. In recent work, an alternative transductive learning strategy was proposed. There, decisions on test samples were chosen aiming to satisfy constraints measured by each local classifier. This approach was shown to reliably correct for class prior mismatch and to robustly account for classifier dependencies. Significant gains in accuracy over fixed aggregation rules were demonstrated. There are two main limitations of that work. First, feasibility of the constraints was not guaranteed. Second, heuristic learning was applied. Here, we overcome these problems via a transductive extension of maximum entropy/improved iterative scaling for aggregation in distributed classification. This method is shown to achieve improved decision accuracy over the earlier transductive approach and fixed rules on a number of UC Irvine datasets.
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.
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.
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Jayajit Das '
2015-07-01
Full Text Available A common statistical situation concerns inferring an unknown distribution Q(x from a known distribution P(y, where X (dimension n, and Y (dimension m have a known functional relationship. Most commonly, n ≤ m, and the task is relatively straightforward for well-defined functional relationships. For example, if Y1 and Y2 are independent random variables, each uniform on [0, 1], one can determine the distribution of X = Y1 + Y2; here m = 2 and n = 1. However, biological and physical situations can arise where n > m and the functional relation Y→X is non-unique. In general, in the absence of additional information, there is no unique solution to Q in those cases. Nevertheless, one may still want to draw some inferences about Q. To this end, we propose a novel maximum entropy (MaxEnt approach that estimates Q(x based only on the available data, namely, P(y. The method has the additional advantage that one does not need to explicitly calculate the Lagrange multipliers. In this paper we develop the approach, for both discrete and continuous probability distributions, and demonstrate its validity. We give an intuitive justification as well, and we illustrate with examples.
Well posedness and maximum entropy approximation for the dynamics of quantitative traits
Boďová, Katarína
2017-11-06
We study the Fokker–Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker–Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain’s boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker–Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.
Reinterpreting maximum entropy in ecology: a null hypothesis constrained by ecological mechanism.
O'Dwyer, James P; Rominger, Andrew; Xiao, Xiao
2017-07-01
Simplified mechanistic models in ecology have been criticised for the fact that a good fit to data does not imply the mechanism is true: pattern does not equal process. In parallel, the maximum entropy principle (MaxEnt) has been applied in ecology to make predictions constrained by just a handful of state variables, like total abundance or species richness. But an outstanding question remains: what principle tells us which state variables to constrain? Here we attempt to solve both problems simultaneously, by translating a given set of mechanisms into the state variables to be used in MaxEnt, and then using this MaxEnt theory as a null model against which to compare mechanistic predictions. In particular, we identify the sufficient statistics needed to parametrise a given mechanistic model from data and use them as MaxEnt constraints. Our approach isolates exactly what mechanism is telling us over and above the state variables alone. © 2017 John Wiley & Sons Ltd/CNRS.
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.
A subjective supply–demand model: the maximum Boltzmann/Shannon entropy solution
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Piotrowski, Edward W; Sładkowski, Jan
2009-01-01
The present authors have put forward a projective geometry model of rational trading. The expected (mean) value of the time that is necessary to strike a deal and the profit strongly depend on the strategies adopted. A frequent trader often prefers maximal profit intensity to the maximization of profit resulting from a separate transaction because the gross profit/income is the adopted/recommended benchmark. To investigate activities that have different periods of duration we define, following the queuing theory, the profit intensity as a measure of this economic category. The profit intensity in repeated trading has a unique property of attaining its maximum at a fixed point regardless of the shape of demand curves for a wide class of probability distributions of random reverse transactions (i.e. closing of the position). These conclusions remain valid for an analogous model based on supply analysis. This type of market game is often considered in research aiming at finding an algorithm that maximizes profit of a trader who negotiates prices with the Rest of the World (a collective opponent), possessing a definite and objective supply profile. Such idealization neglects the sometimes important influence of an individual trader on the demand/supply profile of the Rest of the World and in extreme cases questions the very idea of demand/supply profile. Therefore we put forward a trading model in which the demand/supply profile of the Rest of the World induces the (rational) trader to (subjectively) presume that he/she lacks (almost) all knowledge concerning the market but his/her average frequency of trade. This point of view introduces maximum entropy principles into the model and broadens the range of economic phenomena that can be perceived as a sort of thermodynamical system. As a consequence, the profit intensity has a fixed point with an astonishing connection with Fibonacci classical works and looking for the quickest algorithm for obtaining the extremum of a
Maximum entropy approach to H -theory: Statistical mechanics of hierarchical systems
Vasconcelos, Giovani L.; Salazar, Domingos S. P.; Macêdo, A. M. S.
2018-02-01
A formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small subsystem—representing the region where the measurements are made—in contact with a set of "nested heat reservoirs" corresponding to the hierarchical structure of the system, where the temperatures of the reservoirs are allowed to fluctuate owing to the complex interactions between degrees of freedom at different scales. The probability distribution function (pdf) of the temperature of the reservoir at a given scale, conditioned on the temperature of the reservoir at the next largest scale in the hierarchy, is determined from a maximum entropy principle subject to appropriate constraints that describe the thermal equilibrium properties of the system. The marginal temperature distribution of the innermost reservoir is obtained by integrating over the conditional distributions of all larger scales, and the resulting pdf is written in analytical form in terms of certain special transcendental functions, known as the Fox H functions. The distribution of states of the small subsystem is then computed by averaging the quasiequilibrium Boltzmann distribution over the temperature of the innermost reservoir. This distribution can also be written in terms of H functions. The general family of distributions reported here recovers, as particular cases, the stationary distributions recently obtained by Macêdo et al. [Phys. Rev. E 95, 032315 (2017), 10.1103/PhysRevE.95.032315] from a stochastic dynamical approach to the problem.
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Kai Yan
2015-01-01
Full Text Available A predictive model for droplet size and velocity distributions of a pressure swirl atomizer has been proposed based on the maximum entropy formalism (MEF. The constraint conditions of the MEF model include the conservation laws of mass, momentum, and energy. The effects of liquid swirling strength, Weber number, gas-to-liquid axial velocity ratio and gas-to-liquid density ratio on the droplet size and velocity distributions of a pressure swirl atomizer are investigated. Results show that model based on maximum entropy formalism works well to predict droplet size and velocity distributions under different spray conditions. Liquid swirling strength, Weber number, gas-to-liquid axial velocity ratio and gas-to-liquid density ratio have different effects on droplet size and velocity distributions of a pressure swirl atomizer.
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Nasser, Hassan; Cessac, Bruno; Marre, Olivier
2013-01-01
Understanding the dynamics of neural networks is a major challenge in experimental neuroscience. For that purpose, a modelling of the recorded activity that reproduces the main statistics of the data is required. In the first part, we present a review on recent results dealing with spike train statistics analysis using maximum entropy models (MaxEnt). Most of these studies have focused on modelling synchronous spike patterns, leaving aside the temporal dynamics of the neural activity. However, the maximum entropy principle can be generalized to the temporal case, leading to Markovian models where memory effects and time correlations in the dynamics are properly taken into account. In the second part, we present a new method based on Monte Carlo sampling which is suited for the fitting of large-scale spatio-temporal MaxEnt models. The formalism and the tools presented here will be essential to fit MaxEnt spatio-temporal models to large neural ensembles. (paper)
2012-01-25
An MEP model for remote sensing of evapotranspiration (invited talk), AGU Fall Meeting, San Francisco, 2010. 6. Nieves, V., E. Wood, J. Wang, and R...corresponding field variables; (2) developing a model of evapotranspiration (ET) over the land surfaces using the Principle of Maximum Entropy Production (MEP...scaling moments and geometric mean of the incremental process |z1 – z2|, , where Z is the partition function (normalization factor), ?0 is determined
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Reginatto, M.; Goldhagen, P.
1998-06-01
The problem of analyzing data from a multisphere neutron spectrometer to infer the energy spectrum of the incident neutrons is discussed. The main features of the code MAXED, a computer program developed to apply the maximum entropy principle to the deconvolution (unfolding) of multisphere neutron spectrometer data, are described, and the use of the code is illustrated with an example. A user's guide for the code MAXED is included in an appendix. The code is available from the authors upon request
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Bispo, Heleno; Silva, Nilton; Brito, Romildo; Manzi, João
2013-01-01
Highlights: • Minimum entropy generation (MEG) principle improved the reaction performance. • MEG rate and the maximum conversion equivalence have been analyzed. • Temperature and residence time are used to the domain establishment of MEG. • Satisfying the temperature and residence time relationship results a optimal performance. - Abstract: The analysis of the equivalence between the minimum entropy generation (MEG) rate and the maximum conversion rate for a reactive system is the main purpose of this paper. While being used as a strategy of optimization, the minimum entropy production was applied to the production of propylene glycol in a Continuous Stirred-Tank Reactor (CSTR) with a view to determining the best operating conditions, and under such conditions, a high conversion rate was found. The effects of the key variables and restrictions on the validity domain of MEG were investigated, which raises issues that are included within a broad discussion. The results from simulations indicate that from the chemical reaction standpoint a maximum conversion rate can be considered as equivalent to MEG. Such a result can be clearly explained by examining the classical Maxwell–Boltzmann distribution, where the molecules of the reactive system under the condition of the MEG rate present a distribution of energy with reduced dispersion resulting in a better quality of collision between molecules with a higher conversion rate
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Iwama, N.; Inoue, A.; Tsukishima, T.; Sato, M.; Kawahata, K.
1981-07-01
A new procedure for the maximum entropy spectral estimation is studied for the purpose of data processing in Fourier transform spectroscopy. The autoregressive model fitting is examined under a least squares criterion based on the Yule-Walker equations. An AIC-like criterion is suggested for selecting the model order. The principal advantage of the new procedure lies in the enhanced frequency resolution particularly for small values of the maximum optical path-difference of the interferogram. The usefulness of the procedure is ascertained by some numerical simulations and further by experiments with respect to a highly coherent submillimeter wave and the electron cyclotron emission from a stellarator plasma. (author)
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Aijun Guo
2017-11-01
Full Text Available Copula functions have been extensively used to describe the joint behaviors of extreme hydrological events and to analyze hydrological risk. Advanced marginal distribution inference, for example, the maximum entropy theory, is particularly beneficial for improving the performance of the copulas. The goal of this paper, therefore, is twofold; first, to develop a coupled maximum entropy-copula method for hydrological risk analysis through deriving the bivariate return periods, risk, reliability and bivariate design events; and second, to reveal the impact of marginal distribution selection uncertainty and sampling uncertainty on bivariate design event identification. Particularly, the uncertainties involved in the second goal have not yet received significant consideration. The designed framework for hydrological risk analysis related to flood and extreme precipitation events is exemplarily applied in two catchments of the Loess plateau, China. Results show that (1 distribution derived by the maximum entropy principle outperforms the conventional distributions for the probabilistic modeling of flood and extreme precipitation events; (2 the bivariate return periods, risk, reliability and bivariate design events are able to be derived using the coupled entropy-copula method; (3 uncertainty analysis highlights the fact that appropriate performance of marginal distribution is closely related to bivariate design event identification. Most importantly, sampling uncertainty causes the confidence regions of bivariate design events with return periods of 30 years to be very large, overlapping with the values of flood and extreme precipitation, which have return periods of 10 and 50 years, respectively. The large confidence regions of bivariate design events greatly challenge its application in practical engineering design.
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Hou, Z; Terry, N; Hubbard, S S; Csatho, B
2013-02-12
In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniqueness and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability distribution functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSim) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes
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Hou, Zhangshuan; Terry, Neil C.; Hubbard, Susan S.
2013-02-22
In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniqueness and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability density functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSIM) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of
Bayesian hierarchical models for regional climate reconstructions of the last glacial maximum
Weitzel, Nils; Hense, Andreas; Ohlwein, Christian
2017-04-01
Spatio-temporal reconstructions of past climate are important for the understanding of the long term behavior of the climate system and the sensitivity to forcing changes. Unfortunately, they are subject to large uncertainties, have to deal with a complex proxy-climate structure, and a physically reasonable interpolation between the sparse proxy observations is difficult. Bayesian Hierarchical Models (BHMs) are a class of statistical models that is well suited for spatio-temporal reconstructions of past climate because they permit the inclusion of multiple sources of information (e.g. records from different proxy types, uncertain age information, output from climate simulations) and quantify uncertainties in a statistically rigorous way. BHMs in paleoclimatology typically consist of three stages which are modeled individually and are combined using Bayesian inference techniques. The data stage models the proxy-climate relation (often named transfer function), the process stage models the spatio-temporal distribution of the climate variables of interest, and the prior stage consists of prior distributions of the model parameters. For our BHMs, we translate well-known proxy-climate transfer functions for pollen to a Bayesian framework. In addition, we can include Gaussian distributed local climate information from preprocessed proxy records. The process stage combines physically reasonable spatial structures from prior distributions with proxy records which leads to a multivariate posterior probability distribution for the reconstructed climate variables. The prior distributions that constrain the possible spatial structure of the climate variables are calculated from climate simulation output. We present results from pseudoproxy tests as well as new regional reconstructions of temperatures for the last glacial maximum (LGM, ˜ 21,000 years BP). These reconstructions combine proxy data syntheses with information from climate simulations for the LGM that were
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Chavanis, Pierre-Henri, E-mail: chavanis@irsamc.ups-tlse.fr [Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse (France)
2014-12-01
In the context of two-dimensional (2D) turbulence, we apply the maximum entropy production principle (MEPP) by enforcing a local conservation of energy. This leads to an equation for the vorticity distribution that conserves all the Casimirs, the energy, and that increases monotonically the mixing entropy (H-theorem). Furthermore, the equation for the coarse-grained vorticity dissipates monotonically all the generalized enstrophies. These equations may provide a parametrization of 2D turbulence. They do not generally relax towards the maximum entropy state. The vorticity current vanishes for any steady state of the 2D Euler equation. Interestingly, the equation for the coarse-grained vorticity obtained from the MEPP turns out to coincide, after some algebraic manipulations, with the one obtained with the anticipated vorticity method. This shows a connection between these two approaches when the conservation of energy is treated locally. Furthermore, the newly derived equation, which incorporates a diffusion term and a drift term, has a nice physical interpretation in terms of a selective decay principle. This sheds new light on both the MEPP and the anticipated vorticity method. (paper)
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.
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
Directory of Open Access Journals (Sweden)
Yan Gao
2014-01-01
Full Text Available With the rapid development and application of medical sensor networks, the security has become a big challenge to be resolved. Trust mechanism as a method of “soft security” has been proposed to guarantee the network security. Trust models to compute the trustworthiness of single node and each path are constructed, respectively, in this paper. For the trust relationship between nodes, trust value in every interval is quantified based on Bayesian inference. A node estimates the parameters of prior distribution by using the collected recommendation information and obtains the posterior distribution combined with direct interactions. Further, the weights of trust values are allocated through using the ordered weighted vector twice and overall trust degree is represented. With the associated properties of Tsallis entropy, the definition of path Tsallis entropy is put forward, which can comprehensively measure the uncertainty of each path. Then a method to calculate the credibility of each path is derived. The simulation results show that the proposed models can correctly reflect the dynamic of node behavior, quickly identify the malicious attacks, and effectively avoid such path containing low-trust nodes so as to enhance the robustness.
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Qing Ye
2015-01-01
Full Text Available This research proposes a novel framework of final drive simultaneous failure diagnosis containing feature extraction, training paired diagnostic models, generating decision threshold, and recognizing simultaneous failure modes. In feature extraction module, adopt wavelet package transform and fuzzy entropy to reduce noise interference and extract representative features of failure mode. Use single failure sample to construct probability classifiers based on paired sparse Bayesian extreme learning machine which is trained only by single failure modes and have high generalization and sparsity of sparse Bayesian learning approach. To generate optimal decision threshold which can convert probability output obtained from classifiers into final simultaneous failure modes, this research proposes using samples containing both single and simultaneous failure modes and Grid search method which is superior to traditional techniques in global optimization. Compared with other frequently used diagnostic approaches based on support vector machine and probability neural networks, experiment results based on F1-measure value verify that the diagnostic accuracy and efficiency of the proposed framework which are crucial for simultaneous failure diagnosis are superior to the existing approach.
Bayesian modeling of the assimilative capacity component of nutrient total maximum daily loads
Faulkner, B. R.
2008-08-01
Implementing stream restoration techniques and best management practices to reduce nonpoint source nutrients implies enhancement of the assimilative capacity for the stream system. In this paper, a Bayesian method for evaluating this component of a total maximum daily load (TMDL) load capacity is developed and applied. The joint distribution of nutrient retention metrics from a literature review of 495 measurements was used for Monte Carlo sampling with a process transfer function for nutrient attenuation. Using the resulting histograms of nutrient retention, reference prior distributions were developed for sites in which some of the metrics contributing to the transfer function were measured. Contributing metrics for the prior include stream discharge, cross-sectional area, fraction of storage volume to free stream volume, denitrification rate constant, storage zone mass transfer rate, dispersion coefficient, and others. Confidence of compliance (CC) that any given level of nutrient retention has been achieved is also determined using this approach. The shape of the CC curve is dependent on the metrics measured and serves in part as a measure of the information provided by the metrics to predict nutrient retention. It is also a direct measurement, with a margin of safety, of the fraction of export load that can be reduced through changing retention metrics. For an impaired stream in western Oklahoma, a combination of prior information and measurement of nutrient attenuation was used to illustrate the proposed approach. This method may be considered for TMDL implementation.
McDonald, James G.; Groth, Clinton P. T.
2013-09-01
The ability to predict continuum and transition-regime flows by hyperbolic moment methods offers the promise of several advantages over traditional techniques. These methods offer an extended range of physical validity as compared with the Navier-Stokes equations and can be used for the prediction of many non-equilibrium flows with a lower expense than particle-based methods. Also, the hyperbolic first-order nature of the resulting partial differential equations leads to mathematical and numerical advantages. Moment equations generated through an entropy-maximization principle are particularly attractive due to their apparent robustness; however, their application to practical situations involving viscous, heat-conducting gases has been hampered by several issues. Firstly, the lack of closed-form expressions for closing fluxes leads to numerical expense as many integrals of distribution functions must be computed numerically during the course of a flow computation. Secondly, it has been shown that there exist physically realizable moment states for which the entropy-maximizing problem on which the method is based cannot be solved. Following a review of the theory surrounding maximum-entropy moment closures, this paper shows that both of these problems can be addressed in practice, at least for a simplified one-dimensional gas, and that the resulting flow predictions can be surprisingly good. The numerical results described provide significant motivations for the extension of these ideas to the fully three-dimensional case.
Ishimatsu, N; Takata, M; Nishibori, E; Sakata, M; Hayashi, J; Shirotani, I; Shimomura, O
2002-01-01
The physical properties relating to 4f electrons in cerium phosphide, especially the temperature dependence and the isomorphous transition that occurs at around 10 GPa, were studied by means of x-ray powder diffraction and charge density distribution maps derived by the maximum-entropy method. The compressibility of CeP was exactly determined using a helium pressure medium and the anomaly that indicated the isomorphous transition was observed in the compressibility. We also discuss the anisotropic charge density distribution of Ce ions and its temperature dependence.
Energy Technology Data Exchange (ETDEWEB)
La Rosa, Salvatore; Romano, Vittorio [Dipartimento di Matematica e Informatica, Universita di Catania, viale A Doria 6, 95125 Catania (Italy)], E-mail: larosa@dmi.unict.it, E-mail: romano@dmi.unict.it
2008-05-30
The maximum entropy principle is used to get a consistent hydrodynamical model for the transport of holes in semiconductors. Heavy, light and split-off valence bands are considered. The first two are described by the warped functions while for the split-off band a parabolic approximation is used. Intra- and inter-band scatterings of holes with non-polar optical phonons, acoustic phonons and impurities are taken into account along with the generation-recombination mechanism. Limiting energy-transport and drift-diffusion models are deduced and simulations in bulk silicon are performed.
Laue, Ernest D.; Pollard, Konrad O. B.; Skilling, John; Staunton, James; Sutkowski, Andrew C.
The maximum entropy method (MEM) is shown to be capable of producing spectra of improved clarity from FIDs in which the early points are corrupted by ring-down (which may be caused by acoustic ringing or by pulse breakthrough). The method is evaluated using 17O NMR data. The distortion arising from the ring-down signal is suppressed by ignoring the severely corrupted early points in the FID when evaluating trial MEM spectra. The areas of peaks are best recovered (within 10%) when a suitable degree of line narrowing (equivalent in effect to a matched filter) is used in the MEM spectrum.
Maximum entropy algorithm and its implementation for the neutral beam profile measurement
Energy Technology Data Exchange (ETDEWEB)
Lee, Seung Wook; Cho, Gyu Seong [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of); Cho, Yong Sub [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1997-12-31
A tomography algorithm to maximize the entropy of image using Lagrangian multiplier technique and conjugate gradient method has been designed for the measurement of 2D spatial distribution of intense neutral beams of KSTAR NBI (Korea Superconducting Tokamak Advanced Research Neutral Beam Injector), which is now being designed. A possible detection system was assumed and a numerical simulation has been implemented to test the reconstruction quality of given beam profiles. This algorithm has the good applicability for sparse projection data and thus, can be used for the neutral beam tomography. 8 refs., 3 figs. (Author)
Laplante, Jérémie; Groth, Clinton P. T.
2016-11-01
The Navier-Stokes-Fourier (NSF) equations are conventionally used to model continuum flow near local thermodynamic equilibrium. In the presence of more rarefied flows, there exists a transitional regime in which the NSF equations no longer hold, and where particle-based methods become too expensive for practical problems. To close this gap, moment closure techniques having the potential of being both valid and computationally tractable for these applications are sought. In this study, a number of five-moment closures for a model one-dimensional kinetic equation are assessed and compared. In particular, four different moment closures are applied to the solution of stationary shocks. The first of these is a Grad-type moment closure, which is known to fail for moderate departures from equilibrium. The second is an interpolative closure based on maximization of thermodynamic entropy which has previously been shown to provide excellent results for 1D gaskinetic theory. Additionally, two quadrature methods of moments (QMOM) are considered. One method is based on the representation of the distribution function in terms of a combination of three Dirac delta functions. The second method, an extended QMOM (EQMOM), extends the quadrature-based approach by assuming a bi-Maxwellian representation of the distribution function. The closing fluxes are analyzed in each case and the region of physical realizability is examined for the closures. Numerical simulations of stationary shock structures as predicted by each moment closure are compared to reference kinetic and the corresponding NSF-like equation solutions. It is shown that the bi-Maxwellian and interpolative maximum-entropy-based moment closures are able to closely reproduce the results of the true maximum-entropy distribution closure for this case very well, whereas the other methods do not. For moderate departures from local thermodynamic equilibrium, the Grad-type and QMOM closures produced unphysical subshocks and were
Curtis, Gary P.; Lu, Dan; Ye, Ming
2015-01-01
While Bayesian model averaging (BMA) has been widely used in groundwater modeling, it is infrequently applied to groundwater reactive transport modeling because of multiple sources of uncertainty in the coupled hydrogeochemical processes and because of the long execution time of each model run. To resolve these problems, this study analyzed different levels of uncertainty in a hierarchical way, and used the maximum likelihood version of BMA, i.e., MLBMA, to improve the computational efficiency. This study demonstrates the applicability of MLBMA to groundwater reactive transport modeling in a synthetic case in which twenty-seven reactive transport models were designed to predict the reactive transport of hexavalent uranium (U(VI)) based on observations at a former uranium mill site near Naturita, CO. These reactive transport models contain three uncertain model components, i.e., parameterization of hydraulic conductivity, configuration of model boundary, and surface complexation reactions that simulate U(VI) adsorption. These uncertain model components were aggregated into the alternative models by integrating a hierarchical structure into MLBMA. The modeling results of the individual models and MLBMA were analyzed to investigate their predictive performance. The predictive logscore results show that MLBMA generally outperforms the best model, suggesting that using MLBMA is a sound strategy to achieve more robust model predictions relative to a single model. MLBMA works best when the alternative models are structurally distinct and have diverse model predictions. When correlation in model structure exists, two strategies were used to improve predictive performance by retaining structurally distinct models or assigning smaller prior model probabilities to correlated models. Since the synthetic models were designed using data from the Naturita site, the results of this study are expected to provide guidance for real-world modeling. Limitations of applying MLBMA to the
International Nuclear Information System (INIS)
Papoular, R.J.; Zheludev, A.; Ressouche, E.; Schweizer, J.
1995-01-01
When density distributions in crystals are reconstructed from 3D diffraction data, a problem sometimes occurs when the spatial resolution in one given direction is very small compared to that in perpendicular directions. In this case, a 2D projected density is usually reconstructed. For this task, the conventional Fourier inversion method only makes use of those structure factors measured in the projection plane. All the other structure factors contribute zero to the reconstruction of a projected density. On the contrary, the maximum-entropy method uses all the 3D data, to yield 3D-enhanced 2D projected density maps. It is even possible to reconstruct a projection in the extreme case when not one structure factor in the plane of projection is known. In the case of poor resolution along one given direction, a Fourier inversion reconstruction gives very low quality 3D densities 'smeared' in the third dimension. The application of the maximum-entropy procedure reduces the smearing significantly and reasonably well resolved projections along most directions can now be obtained from the MaxEnt 3D density. To illustrate these two ideas, particular examples based on real polarized neutron diffraction data sets are presented. (orig.)
Directory of Open Access Journals (Sweden)
Gogarten J Peter
2002-02-01
Full Text Available Abstract Background Horizontal gene transfer (HGT played an important role in shaping microbial genomes. In addition to genes under sporadic selection, HGT also affects housekeeping genes and those involved in information processing, even ribosomal RNA encoding genes. Here we describe tools that provide an assessment and graphic illustration of the mosaic nature of microbial genomes. Results We adapted the Maximum Likelihood (ML mapping to the analyses of all detected quartets of orthologous genes found in four genomes. We have automated the assembly and analyses of these quartets of orthologs given the selection of four genomes. We compared the ML-mapping approach to more rigorous Bayesian probability and Bootstrap mapping techniques. The latter two approaches appear to be more conservative than the ML-mapping approach, but qualitatively all three approaches give equivalent results. All three tools were tested on mitochondrial genomes, which presumably were inherited as a single linkage group. Conclusions In some instances of interphylum relationships we find nearly equal numbers of quartets strongly supporting the three possible topologies. In contrast, our analyses of genome quartets containing the cyanobacterium Synechocystis sp. indicate that a large part of the cyanobacterial genome is related to that of low GC Gram positives. Other groups that had been suggested as sister groups to the cyanobacteria contain many fewer genes that group with the Synechocystis orthologs. Interdomain comparisons of genome quartets containing the archaeon Halobacterium sp. revealed that Halobacterium sp. shares more genes with Bacteria that live in the same environment than with Bacteria that are more closely related based on rRNA phylogeny . Many of these genes encode proteins involved in substrate transport and metabolism and in information storage and processing. The performed analyses demonstrate that relationships among prokaryotes cannot be accurately
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S. H. Chiang
2016-06-01
Full Text Available Forest is a very important ecosystem and natural resource for living things. Based on forest inventories, government is able to make decisions to converse, improve and manage forests in a sustainable way. Field work for forestry investigation is difficult and time consuming, because it needs intensive physical labor and the costs are high, especially surveying in remote mountainous regions. A reliable forest inventory can give us a more accurate and timely information to develop new and efficient approaches of forest management. The remote sensing technology has been recently used for forest investigation at a large scale. To produce an informative forest inventory, forest attributes, including tree species are unavoidably required to be considered. In this study the aim is to classify forest tree species in Erdenebulgan County, Huwsgul province in Mongolia, using Maximum Entropy method. The study area is covered by a dense forest which is almost 70% of total territorial extension of Erdenebulgan County and is located in a high mountain region in northern Mongolia. For this study, Landsat satellite imagery and a Digital Elevation Model (DEM were acquired to perform tree species mapping. The forest tree species inventory map was collected from the Forest Division of the Mongolian Ministry of Nature and Environment as training data and also used as ground truth to perform the accuracy assessment of the tree species classification. Landsat images and DEM were processed for maximum entropy modeling, and this study applied the model with two experiments. The first one is to use Landsat surface reflectance for tree species classification; and the second experiment incorporates terrain variables in addition to the Landsat surface reflectance to perform the tree species classification. All experimental results were compared with the tree species inventory to assess the classification accuracy. Results show that the second one which uses Landsat surface
Chung-Wei, Li; Gwo-Hshiung, Tzeng
To deal with complex problems, structuring them through graphical representations and analyzing causal influences can aid in illuminating complex issues, systems, or concepts. The DEMATEL method is a methodology which can be used for researching and solving complicated and intertwined problem groups. The end product of the DEMATEL process is a visual representation—the impact-relations map—by which respondents organize their own actions in the world. The applicability of the DEMATEL method is widespread, ranging from analyzing world problematique decision making to industrial planning. The most important property of the DEMATEL method used in the multi-criteria decision making (MCDM) field is to construct interrelations between criteria. In order to obtain a suitable impact-relations map, an appropriate threshold value is needed to obtain adequate information for further analysis and decision-making. In this paper, we propose a method based on the entropy approach, the maximum mean de-entropy algorithm, to achieve this purpose. Using real cases to find the interrelationships between the criteria for evaluating effects in E-learning programs as an examples, we will compare the results obtained from the respondents and from our method, and discuss that the different impact-relations maps from these two methods.
Wood, Kevin; Nishida, Satoshi; Sontag, Eduardo; Cluzel, Philippe
2012-02-01
Drugs are commonly used in combinations larger than two for treating infectious disease. However, it is generally impossible to infer the net effect of a multi-drug combination on cell growth directly from the effects of individual drugs. We combined experiments with maximum entropy methods to develop a mechanism-independent framework for calculating the response of both bacteria and human cancer cells to a large variety of drug combinations comprised of anti-microbial or anti-cancer drugs. We experimentally show that the cellular responses to drug pairs are sufficient to infer the effects of larger drug combinations in gram negative bacteria, Escherichia coli, gram positive bacteria, Staphylococcus aureus, and also human breast cancer and melanoma cell lines. Remarkably, the accurate predictions of this framework suggest that the multi-drug response obeys statistical rather than chemical laws for combinations larger than two. Consequently, these findings offer a new strategy for the rational design of therapies using large drug combinations.
The effect of the shape function on small-angle scattering analysis by the maximum entropy method
Energy Technology Data Exchange (ETDEWEB)
Jemian, P.R. [Argonne National Lab., IL (United States); Allen, A.J. [Univ. of Maryland, College Park, MD (United States). Department of Physics]|[National Inst. of Standards and Technology, Gaithersburg, MD (United States)
1992-09-15
Analysis of small-angle scattering data to obtain a particle size distribution is dependent upon the shape function used to model the scattering. Using a maximum entropy analysis of small-angle scattering data, the effect of shape function selection on obtained size distribution is demonstrated using three different shape functions to describe the same scattering data from each of two steels. The alloys have been revealed by electron microscopy to contain a distribution of randomly oriented and mainly non-interacting, irregular, ellipsoidal precipitates. Comparison is made between the different forms of the shape function. Effect of an incident wavelength distribution is also shown. The importance of testing appropriate shape functions and validating these against other microstructural studies is discussed.
Maximum entropy as a tool for the determination of the c-axis profile of layered compounds
International Nuclear Information System (INIS)
Depondt, P.; Neumann, D.A.; Trevino, S.F.
1993-01-01
A simple procedure for the determination of the structure normal to the basal plane of layered compounds based on the now ubiquitous maximum-entropy method is presented. It is illustrated by the analysis of room-temperature (00l) elastic neutron-scattering experiments performed on two graphite intercalation compounds, stage 3 C 44.6 MoCl 5 and stage 1 KC 24 (ND 3 ) 4.3 . The former example is quite simple, requiring only a crude heuristic model to determine the structure-factor phases. The latter shows good sensitivity to the orientation of the ND 3 threefold axis with respect to the basal plane, thus providing its first direct determination. (orig.)
Directory of Open Access Journals (Sweden)
Jorge Pereira
2015-12-01
Full Text Available Biological invasion by exotic organisms became a key issue, a concern associated to the deep impacts on several domains described as resultant from such processes. A better understanding of the processes, the identification of more susceptible areas, and the definition of preventive or mitigation measures are identified as critical for the purpose of reducing associated impacts. The use of species distribution modeling might help on the purpose of identifying areas that are more susceptible to invasion. This paper aims to present preliminary results on assessing the susceptibility to invasion by the exotic species Acacia dealbata Mill. in the Ceira river basin. The results are based on the maximum entropy modeling approach, considered one of the correlative modelling techniques with better predictive performance. Models which validation is based on independent data sets present better performance, an evaluation based on the AUC of ROC accuracy measure.
Satuła, D; Szymański, K; Dobrzyński, L
2010-07-28
Determination of the Mössbauer absorption cross section, σ(E), and accurate reconstruction of the hyperfine field distributions of the invar alloy, Fe(64)Ni(36), by the maximum entropy method (MEM) is presented. The procedure consists of three steps: deconvolution of the Mössbauer spectra with the instrumental resolution function using MEM, nonlinear transformation of the deconvoluted spectrum into σ(E), and reconstruction of the hyperfine field distribution. In order to test the procedure of the deconvolution and correction for thickness effect, several simulated spectra with thickness parameter 1 invar alloy, measured with and without application of an external magnetic field, are discussed. The reconstruction has been made to test the earlier postulated non-collinear ferromagnetic state of invar without referring to any specific model in the analysis of the Mössbauer results. It is shown that marginal probability distribution of hyperfine magnetic field consists of the main maximum at about 28 T and a broad tail extending down to 5 T. Observed isomer shift of the main maximum is small and positive. The isomer shift decreases with magnetic field and attains negative values at the lowest fields. It is shown that the magnetic texture parameter does not depend on the hyperfine magnetic field. One thus concludes that in the invar Ni-Fe alloys, in contrast to some theoretical predictions, there is no evidence for different arrangements of the iron magnetic moments as a function of the magnetic hyperfine field.
Energy Technology Data Exchange (ETDEWEB)
Satula, D; Szymanski, K; Dobrzynski, L, E-mail: satula@alpha.uwb.edu.p [Faculty of Physics, University of Bialystok, 41 Lipowa Street, 15-424 Bialystok (Poland)
2010-07-28
Determination of the Moessbauer absorption cross section, {sigma}(E), and accurate reconstruction of the hyperfine field distributions of the invar alloy, Fe{sub 64}Ni{sub 36}, by the maximum entropy method (MEM) is presented. The procedure consists of three steps: deconvolution of the Moessbauer spectra with the instrumental resolution function using MEM, nonlinear transformation of the deconvoluted spectrum into {sigma}(E), and reconstruction of the hyperfine field distribution. In order to test the procedure of the deconvolution and correction for thickness effect, several simulated spectra with thickness parameter 1 < t < 50 and different values of Lorentzian FWHM of the source and absorber were analyzed. It is shown that the procedure of the deconvolution and extraction of {sigma}(E) works well for spectra whose lines contain at least five experimental points per FWHM. Reconstructed distributions of hyperfine field parameters, based on the extracted Moessbauer cross section of the Fe-Ni invar alloy, measured with and without application of an external magnetic field, are discussed. The reconstruction has been made to test the earlier postulated non-collinear ferromagnetic state of invar without referring to any specific model in the analysis of the Moessbauer results. It is shown that marginal probability distribution of hyperfine magnetic field consists of the main maximum at about 28 T and a broad tail extending down to 5 T. Observed isomer shift of the main maximum is small and positive. The isomer shift decreases with magnetic field and attains negative values at the lowest fields. It is shown that the magnetic texture parameter does not depend on the hyperfine magnetic field. One thus concludes that in the invar Ni-Fe alloys, in contrast to some theoretical predictions, there is no evidence for different arrangements of the iron magnetic moments as a function of the magnetic hyperfine field.
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.
DEFF Research Database (Denmark)
Steenstrup, Stig; Hove, Jens D; Kofoed, Klaus
2002-01-01
PTT. It is the purpose here to investigate the possibility of estimating the fPTT in a model-free way. The method employs the maximum entropy principle and is used, in particular, on cardiac positron emission tomographic (PET) studies but is believed to be more generally applicable. Using this principle in a test case...
Armean, Irina M; Lilley, Kathryn S; Trotter, Matthew W B; Pilkington, Nicholas C V; Holden, Sean B
2018-01-30
Protein-protein interactions (PPI) play a crucial role in our understanding of protein function and biological processes. The standardization and recording of experimental findings is increasingly stored in ontologies, with the Gene Ontology (GO) being one of the most successful projects. Several PPI evaluation algorithms have been based on the application of probabilistic frameworks or machine learning algorithms to GO properties. Here, we introduce a new training set design and machine learning based approach that combines dependent heterogeneous protein annotations from the entire ontology to evaluate putative co-complex protein interactions determined by empirical studies. PPI annotations are built combinatorically using corresponding GO terms and InterPro annotation. We use a S. cerevisiae high-confidence complex dataset as a positive training set. A series of classifiers based on Maximum Entropy and support vector machines (SVMs), each with a composite counterpart algorithm, are trained on a series of training sets. These achieve a high performance area under the ROC curve of ≤ 0.97, outperforming go2ppi - a previously established prediction tool for protein-protein interactions (PPI) based on Gene Ontology (GO) annotations. https://github.com/ima23/maxent-ppi. sbh11@cl.cam.ac.uk. Supplementary data are available at Bioinformatics online. © The Author(s) 2018. Published by Oxford University Press.
Directory of Open Access Journals (Sweden)
Chengquan Zhou
2018-02-01
Full Text Available To obtain an accurate count of wheat spikes, which is crucial for estimating yield, this paper proposes a new algorithm that uses computer vision to achieve this goal from an image. First, a home-built semi-autonomous multi-sensor field-based phenotype platform (FPP is used to obtain orthographic images of wheat plots at the filling stage. The data acquisition system of the FPP provides high-definition RGB images and multispectral images of the corresponding quadrats. Then, the high-definition panchromatic images are obtained by fusion of three channels of RGB. The Gram–Schmidt fusion algorithm is then used to fuse these multispectral and panchromatic images, thereby improving the color identification degree of the targets. Next, the maximum entropy segmentation method is used to do the coarse-segmentation. The threshold of this method is determined by a firefly algorithm based on chaos theory (FACT, and then a morphological filter is used to de-noise the coarse-segmentation results. Finally, morphological reconstruction theory is applied to segment the adhesive part of the de-noised image and realize the fine-segmentation of the image. The computer-generated counting results for the wheat plots, using independent regional statistical function in Matlab R2017b software, are then compared with field measurements which indicate that the proposed method provides a more accurate count of wheat spikes when compared with other traditional fusion and segmentation methods mentioned in this paper.
Hoffman, Steven J; Justicz, Victoria
2016-07-01
To develop and validate a method for automatically quantifying the scientific quality and sensationalism of individual news records. After retrieving 163,433 news records mentioning the Severe Acute Respiratory Syndrome (SARS) and H1N1 pandemics, a maximum entropy model for inductive machine learning was used to identify relationships among 500 randomly sampled news records that correlated with systematic human assessments of their scientific quality and sensationalism. These relationships were then computationally applied to automatically classify 10,000 additional randomly sampled news records. The model was validated by randomly sampling 200 records and comparing human assessments of them to the computer assessments. The computer model correctly assessed the relevance of 86% of news records, the quality of 65% of records, and the sensationalism of 73% of records, as compared to human assessments. Overall, the scientific quality of SARS and H1N1 news media coverage had potentially important shortcomings, but coverage was not too sensationalizing. Coverage slightly improved between the two pandemics. Automated methods can evaluate news records faster, cheaper, and possibly better than humans. The specific procedure implemented in this study can at the very least identify subsets of news records that are far more likely to have particular scientific and discursive qualities. Copyright © 2016 Elsevier Inc. All rights reserved.
Westhoff, Martijn; Zehe, Erwin; Erpicum, Sébastien; Archambeau, Pierre; Pirotton, Michel; Dewals, Benjamin
2015-04-01
The Maximum Entropy Production (MEP) principle is a conjecture assuming that a medium is organized in such a way that maximum power is subtracted from a gradient driving a flux (with power being a flux times its driving gradient). This maximum power is also known as the Carnot limit. It has already been shown that the atmosphere operates close to this Carnot limit when it comes to heat transport from the Equator to the poles, or vertically, from the surface to the atmospheric boundary layer. To reach this state close to the Carnot limit, the effective thermal conductivity of the atmosphere is adapted by the creation of convection cells (e.g. wind). The aim of this study is to test if the soil's effective hydraulic conductivity also adapts itself in such a way that it operates close to the Carnot limit. The big difference between atmosphere and soil is the way of adaptation of its resistance. The soil's hydraulic conductivity is either changed by weathering processes, which is a very slow process, or by creation of preferential flow paths. In this study the latter process is simulated in a lab experiment, where we focus on the preferential flow paths created by piping. Piping is the process of backwards erosion of sand particles subject to a large pressure gradient. Since this is a relatively fast process, it is suitable for being tested in the lab. In the lab setup a horizontal sand bed connects two reservoirs that both drain freely at a level high enough to keep the sand bed always saturated. By adding water to only one reservoir, a horizontal pressure gradient is maintained. If the flow resistance is small, a large gradient develops, leading to the effect of piping. When pipes are being formed, the effective flow resistance decreases; the flow through the sand bed increases and the pressure gradient decreases. At a certain point, the flow velocity is small enough to stop the pipes from growing any further. In this steady state, the effective flow resistance of
Agapiou, Sergios; Burger, Martin; Dashti, Masoumeh; Helin, Tapio
2018-04-01
We consider the inverse problem of recovering an unknown functional parameter u in a separable Banach space, from a noisy observation vector y of its image through a known possibly non-linear map {{\\mathcal G}} . We adopt a Bayesian approach to the problem and consider Besov space priors (see Lassas et al (2009 Inverse Problems Imaging 3 87-122)), which are well-known for their edge-preserving and sparsity-promoting properties and have recently attracted wide attention especially in the medical imaging community. Our key result is to show that in this non-parametric setup the maximum a posteriori (MAP) estimates are characterized by the minimizers of a generalized Onsager-Machlup functional of the posterior. This is done independently for the so-called weak and strong MAP estimates, which as we show coincide in our context. In addition, we prove a form of weak consistency for the MAP estimators in the infinitely informative data limit. Our results are remarkable for two reasons: first, the prior distribution is non-Gaussian and does not meet the smoothness conditions required in previous research on non-parametric MAP estimates. Second, the result analytically justifies existing uses of the MAP estimate in finite but high dimensional discretizations of Bayesian inverse problems with the considered Besov priors.
Directory of Open Access Journals (Sweden)
Hannah Slater
Full Text Available Modelling the spatial distributions of human parasite species is crucial to understanding the environmental determinants of infection as well as for guiding the planning of control programmes. Here, we use ecological niche modelling to map the current potential distribution of the macroparasitic disease, lymphatic filariasis (LF, in Africa, and to estimate how future changes in climate and population could affect its spread and burden across the continent. We used 508 community-specific infection presence data collated from the published literature in conjunction with five predictive environmental/climatic and demographic variables, and a maximum entropy niche modelling method to construct the first ecological niche maps describing potential distribution and burden of LF in Africa. We also ran the best-fit model against climate projections made by the HADCM3 and CCCMA models for 2050 under A2a and B2a scenarios to simulate the likely distribution of LF under future climate and population changes. We predict a broad geographic distribution of LF in Africa extending from the west to the east across the middle region of the continent, with high probabilities of occurrence in the Western Africa compared to large areas of medium probability interspersed with smaller areas of high probability in Central and Eastern Africa and in Madagascar. We uncovered complex relationships between predictor ecological niche variables and the probability of LF occurrence. We show for the first time that predicted climate change and population growth will expand both the range and risk of LF infection (and ultimately disease in an endemic region. We estimate that populations at risk to LF may range from 543 and 804 million currently, and that this could rise to between 1.65 to 1.86 billion in the future depending on the climate scenario used and thresholds applied to signify infection presence.
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.
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
Nagy, László G; Urban, Alexander; Orstadius, Leif; Papp, Tamás; Larsson, Ellen; Vágvölgyi, Csaba
2010-12-01
Recently developed comparative phylogenetic methods offer a wide spectrum of applications in evolutionary biology, although it is generally accepted that their statistical properties are incompletely known. Here, we examine and compare the statistical power of the ML and Bayesian methods with regard to selection of best-fit models of fruiting-body evolution and hypothesis testing of ancestral states on a real-life data set of a physiological trait (autodigestion) in the family Psathyrellaceae. Our phylogenies are based on the first multigene data set generated for the family. Two different coding regimes (binary and multistate) and two data sets differing in taxon sampling density are examined. The Bayesian method outperformed Maximum Likelihood with regard to statistical power in all analyses. This is particularly evident if the signal in the data is weak, i.e. in cases when the ML approach does not provide support to choose among competing hypotheses. Results based on binary and multistate coding differed only modestly, although it was evident that multistate analyses were less conclusive in all cases. It seems that increased taxon sampling density has favourable effects on inference of ancestral states, while model parameters are influenced to a smaller extent. The model best fitting our data implies that the rate of losses of deliquescence equals zero, although model selection in ML does not provide proper support to reject three of the four candidate models. The results also support the hypothesis that non-deliquescence (lack of autodigestion) has been ancestral in Psathyrellaceae, and that deliquescent fruiting bodies represent the preferred state, having evolved independently several times during evolution. Copyright © 2010 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Bruce T. Milne
2017-05-01
Full Text Available Stream networks are branched structures wherein water and energy move between land and atmosphere, modulated by evapotranspiration and its interaction with the gravitational dissipation of potential energy as runoff. These actions vary among climates characterized by Budyko theory, yet have not been integrated with Horton scaling, the ubiquitous pattern of eco-hydrological variation among Strahler streams that populate river basins. From Budyko theory, we reveal optimum entropy coincident with high biodiversity. Basins on either side of optimum respond in opposite ways to precipitation, which we evaluated for the classic Hubbard Brook experiment in New Hampshire and for the Whitewater River basin in Kansas. We demonstrate that Horton ratios are equivalent to Lagrange multipliers used in the extremum function leading to Shannon information entropy being maximal, subject to constraints. Properties of stream networks vary with constraints and inter-annual variation in water balance that challenge vegetation to match expected resource supply throughout the network. The entropy-Horton framework informs questions of biodiversity, resilience to perturbations in water supply, changes in potential evapotranspiration, and land use changes that move ecosystems away from optimal entropy with concomitant loss of productivity and biodiversity.
Directory of Open Access Journals (Sweden)
Evgeni B. Starikov
2018-02-01
Full Text Available This work has shown the way to put the formal statistical-mechanical basement under the hotly debated notion of enthalpy-entropy compensation. The possibility of writing down the universal equation of state based upon the statistical mechanics is discussed here.
Simmons, Mark P
2014-11-01
Contrived and simulated examples were used to quantify the range of conditions in which maximum likelihood and Bayesian MCMC methods are biased in favor of phylogenetic signal present in globally sampled characters over that present in conflicting locally sampled characters (those with missing data). The bias occurs in both the optimal tree identified as well as branch supports even when there are more locally sampled characters supporting the conflicting topology. The bias can lead to high bootstrap, SH-like aLRT support (up to 100%), and posterior probabilities for the conflicting clades. The bias can occur even when only a single terminal has missing data. The bias is not limited to likelihood methods that only ever present a single optimal tree that is fully resolved (as in PhyML and RAxML)-it can also occur in branch-and-bound PAUP(∗) searches. The bias persists despite sampling numerous characters, and the bias is consistently unidirectional. The bias may occur in the context of incongruence between gene trees as well as within a single gene wherein terminals have different sequence lengths caused by DNA-amplification differences or gaps caused by indels. This bias is another example wherein commonly implemented parametric phylogenetic methods interpret ambiguity as support. In contrast, parsimony is robust to the bias. Copyright © 2014 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
Alvarez R, J.T.
1998-01-01
This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ( 4 He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator ρhut FP that is evaluated as Wigneris function through ρ CG obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D mn defined with a nonequilibrium coarse grained statistical operator ρhut CG , matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine ρhut CG by means of the local equilibrium statistical operator ρhut l -tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D mn but with aid of a quasi equilibrium statistical operator ρhut qe instead of the local equilibrium operator ρhut l -tilde. Matrix
Furbish, David; Schmeeckle, Mark; Schumer, Rina; Fathel, Siobhan
2016-01-01
We describe the most likely forms of the probability distributions of bed load particle velocities, accelerations, hop distances, and travel times, in a manner that formally appeals to inferential statistics while honoring mechanical and kinematic constraints imposed by equilibrium transport conditions. The analysis is based on E. Jaynes's elaboration of the implications of the similarity between the Gibbs entropy in statistical mechanics and the Shannon entropy in information theory. By maximizing the information entropy of a distribution subject to known constraints on its moments, our choice of the form of the distribution is unbiased. The analysis suggests that particle velocities and travel times are exponentially distributed and that particle accelerations follow a Laplace distribution with zero mean. Particle hop distances, viewed alone, ought to be distributed exponentially. However, the covariance between hop distances and travel times precludes this result. Instead, the covariance structure suggests that hop distances follow a Weibull distribution. These distributions are consistent with high-resolution measurements obtained from high-speed imaging of bed load particle motions. The analysis brings us closer to choosing distributions based on our mechanical insight.
Ainslie, B; Reuten, C; Steyn, D G; Le, Nhu D; Zidek, James V
2009-06-01
We apply the entropy-based Bayesian optimizing approach of Le and Zidek to the spatial redesign of the extensive air pollution monitoring network operated by Metro Vancouver, in the Lower Fraser Valley, British Columbia. This method is chosen because of its statistical sophistication, relative to other possible approaches, and because of the very rich, two-decade long data record available from this network. The redesign analysis is applied to ozone, carbon monoxide and PM(2.5) pollutants. The analysis provides guidance with regard to stations monitoring the three pollutants. For both ozone and PM(2.5), the analysis indicates a need for more stations in the eastern part of the monitoring domain. A parallel analysis indicates that stations may be removed from the more central parts of the domain. An analysis of the carbon monoxide network produces results that are not nearly as clearly defined as those for the other two pollutants, presumably because carbon monoxide is a primary pollutant with many locally important sources. The work demonstrates the great utility of the analysis technique, and also provides statistically defensible guidance on the spatial redesign of this important monitoring network.
Dewar, R
2003-01-01
Jaynes' information theory formalism of statistical mechanics is applied to the stationary states of open, non-equilibrium systems. First, it is shown that the probability distribution p subGAMMA of the underlying microscopic phase space trajectories GAMMA over a time interval of length tau satisfies p subGAMMA propor to exp(tau sigma subGAMMA/2k sub B) where sigma subGAMMA is the time-averaged rate of entropy production of GAMMA. Three consequences of this result are then derived: (1) the fluctuation theorem, which describes the exponentially declining probability of deviations from the second law of thermodynamics as tau -> infinity; (2) the selection principle of maximum entropy production for non-equilibrium stationary states, empirical support for which has been found in studies of phenomena as diverse as the Earth's climate and crystal growth morphology; and (3) the emergence of self-organized criticality for flux-driven systems in the slowly-driven limit. The explanation of these results on general inf...
Moua, Yi; Roux, Emmanuel; Girod, Romain; Dusfour, Isabelle; de Thoisy, Benoit; Seyler, Frédérique; Briolant, Sébastien
2017-05-01
Malaria is an important health issue in French Guiana. Its principal mosquito vector in this region is Anopheles darlingi Root. Knowledge of the spatial distribution of this species is still very incomplete due to the extent of French Guiana and the difficulty to access most of the territory. Species distribution modeling based on the maximal entropy procedure was used to predict the spatial distribution of An. darlingi using 39 presence sites. The resulting model provided significantly high prediction performances (mean 10-fold cross-validated partial area under the curve and continuous Boyce index equal to, respectively, 1.11-with a level of omission error of 20%-and 0.42). The model also provided a habitat suitability map and environmental response curves in accordance with the known entomological situation. Several environmental characteristics that had a positive correlation with the presence of An. darlingi were highlighted: nonpermanent anthropogenic changes of the natural environment, the presence of roads and tracks, and opening of the forest. Some geomorphological landforms and high altitude landscapes appear to be unsuitable for An. darlingi. The species distribution modeling was able to reliably predict the distribution of suitable habitats for An. darlingi in French Guiana. Results allowed completion of the knowledge of the spatial distribution of the principal malaria vector in this Amazonian region, and identification of the main factors that favor its presence. They should contribute to the definition of a necessary targeted vector control strategy in a malaria pre-elimination stage, and allow extrapolation of the acquired knowledge to other Amazonian or malaria-endemic contexts. © The Authors 2016. Published by Oxford University Press on behalf of Entomological Society of America. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Directory of Open Access Journals (Sweden)
Rong Jiang
2014-09-01
Full Text Available As the early design decision-making structure, a software architecture plays a key role in the final software product quality and the whole project. In the software design and development process, an effective evaluation of the trustworthiness of a software architecture can help making scientific and reasonable decisions on the architecture, which are necessary for the construction of highly trustworthy software. In consideration of lacking the trustworthiness evaluation and measurement studies for software architecture, this paper provides one trustworthy attribute model of software architecture. Based on this model, the paper proposes to use the Principle of Maximum Entropy (POME and Grey Decision-making Method (GDMM as the trustworthiness evaluation method of a software architecture and proves the scientificity and rationality of this method, as well as verifies the feasibility through case analysis.
Energy Technology Data Exchange (ETDEWEB)
Kulakhmetov, Marat, E-mail: mkulakhm@purdue.edu; Alexeenko, Alina, E-mail: alexeenk@purdue.edu [Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana 47907 (United States); Gallis, Michael, E-mail: magalli@sandia.gov [Engineering Sciences Center, Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)
2016-05-07
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. 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 × 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.
McGuire, Jimmy A; Witt, Christopher C; Altshuler, Douglas L; Remsen, J V
2007-10-01
Hummingbirds are an important model system in avian biology, but to date the group has been the subject of remarkably few phylogenetic investigations. Here we present partitioned Bayesian and maximum likelihood phylogenetic analyses for 151 of approximately 330 species of hummingbirds and 12 outgroup taxa based on two protein-coding mitochondrial genes (ND2 and ND4), flanking tRNAs, and two nuclear introns (AK1 and BFib). We analyzed these data under several partitioning strategies ranging between unpartitioned and a maximum of nine partitions. In order to select a statistically justified partitioning strategy following partitioned Bayesian analysis, we considered four alternative criteria including Bayes factors, modified versions of the Akaike information criterion for small sample sizes (AIC(c)), Bayesian information criterion (BIC), and a decision-theoretic methodology (DT). Following partitioned maximum likelihood analyses, we selected a best-fitting strategy using hierarchical likelihood ratio tests (hLRTS), the conventional AICc, BIC, and DT, concluding that the most stringent criterion, the performance-based DT, was the most appropriate methodology for selecting amongst partitioning strategies. In the context of our well-resolved and well-supported phylogenetic estimate, we consider the historical biogeography of hummingbirds using ancestral state reconstructions of (1) primary geographic region of occurrence (i.e., South America, Central America, North America, Greater Antilles, Lesser Antilles), (2) Andean or non-Andean geographic distribution, and (3) minimum elevational occurrence. These analyses indicate that the basal hummingbird assemblages originated in the lowlands of South America, that most of the principle clades of hummingbirds (all but Mountain Gems and possibly Bees) originated on this continent, and that there have been many (at least 30) independent invasions of other primary landmasses, especially Central America.
Gotovac, Hrvoje; Cvetkovic, Vladimir; Andricevic, Roko
2010-05-01
The travel time formulation of advective transport in heterogeneous porous media is of interest both conceptually, e.g., for incorporating retention processes, and in applications where typically the travel time peak, early, and late arrivals of contaminants are of major concern in a regulatory or remediation context. Furthermore, the travel time moments are of interest for quantifying uncertainty in advective transport of tracers released from point sources in heterogeneous aquifers. In view of this interest, the travel time distribution has been studied in the literature; however, the link to the hydraulic conductivity statistics has been typically restricted to the first two moments. Here we investigate the influence of higher travel time moments on the travel time probability density function (pdf) in heterogeneous porous media combining Monte Carlo simulations with the maximum entropy principle. The Monte Carlo experimental pdf is obtained by the adaptive Fup Monte Carlo method (AFMCM) for advective transport characterized by a multi-Gaussian structure with exponential covariance considering two injection modes (in-flux and resident) and lnK variance up to 8. A maximum entropy (MaxEnt) algorithm based on Fup basis functions is used for the complete characterization of the travel time pdf. All travel time moments become linear with distance. Initial nonlinearity is found mainly for the resident injection mode, which exhibits a strong nonlinearity within first 5IY for high heterogeneity. For the resident injection mode, the form of variance and all higher moments changes from the familiar concave form predicted by the first-order theory to a convex form; for the in-flux mode, linearity is preserved even for high heterogeneity. The number of moments sufficient for a complete characterization of the travel time pdf mainly depends on the heterogeneity level. Mean and variance completely describe travel time pdf for low and mild heterogeneity, skewness is dominant
Maximizing entropy over Markov processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2014-01-01
computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process...... as a reward function, a polynomial algorithm to verify the existence of a system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...
Maximizing Entropy over Markov Processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2013-01-01
computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process...... as a reward function, a polynomial algorithm to verify the existence of an system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...
Nonparametric bayesian reward segmentation for skill discovery using inverse reinforcement learning
CSIR Research Space (South Africa)
Ranchod, P
2015-10-01
Full Text Available to be optimizing. The skill boundaries and the number of skills making up each demonstration are unknown. We use a Bayesian nonparametric approach to propose skill segmentations and maximum entropy inverse reinforcement learning to infer reward functions from...
On Maximum Entropy Signal Analysis.
1983-06-01
number of time series datai the method is reputed to be superior to Past Fourier Transform (FT) analysis when applied to short data records in that better...implemented on the GENRAD 2508 to determine the auto-power spectrum by applying the PT to small samples of data points. In order to preserve the resolution...Estimation Through Auto Regressive Model Pitting. Ann Inst Stat Math 21,407-419,(1969) 9 IXAXI’H. Stastistical Predictor Identification. Ann Inst Stat Math 22
Directory of Open Access Journals (Sweden)
Matthew W Breece
Full Text Available Atlantic sturgeon (Acipenser oxyrinchus oxyrinchus experienced severe declines due to habitat destruction and overfishing beginning in the late 19(th century. Subsequent to the boom and bust period of exploitation, there has been minimal fishing pressure and improving habitats. However, lack of recovery led to the 2012 listing of Atlantic sturgeon under the Endangered Species Act. Although habitats may be improving, the availability of high quality spawning habitat, essential for the survival and development of eggs and larvae may still be a limiting factor in the recovery of Atlantic sturgeon. To estimate adult Atlantic sturgeon spatial distributions during riverine occupancy in the Delaware River, we utilized a maximum entropy (MaxEnt approach along with passive biotelemetry during the likely spawning season. We found that substrate composition and distance from the salt front significantly influenced the locations of adult Atlantic sturgeon in the Delaware River. To broaden the scope of this study we projected our model onto four scenarios depicting varying locations of the salt front in the Delaware River: the contemporary location of the salt front during the likely spawning season, the location of the salt front during the historic fishery in the late 19(th century, an estimated shift in the salt front by the year 2100 due to climate change, and an extreme drought scenario, similar to that which occurred in the 1960's. The movement of the salt front upstream as a result of dredging and climate change likely eliminated historic spawning habitats and currently threatens areas where Atlantic sturgeon spawning may be taking place. Identifying where suitable spawning substrate and water chemistry intersect with the likely occurrence of adult Atlantic sturgeon in the Delaware River highlights essential spawning habitats, enhancing recovery prospects for this imperiled species.
Ning, Shuoying; Wei, Jiufeng; Feng, Jinian
2017-01-01
Climate change will markedly impact biology, population ecology, and spatial distribution patterns of insect pests because of the influence of future greenhouse effects on insect development and population dynamics. Onion maggot, Delia antiqua, larvae are subterranean pests with limited mobility, that directly feed on bulbs of Allium sp. and render them completely unmarketable. Modeling the spatial distribution of such a widespread and damaging pest is crucial not only to identify current potentially suitable climactic areas but also to predict where the pest is likely to spread in the future so that appropriate monitoring and management programs can be developed. In this study, Maximum Entropy Niche Modeling was used to estimate the current potential distribution of D. antiqua and to predict the future distribution of this species in 2030, 2050, 2070 and 2080 by using emission scenario (A2) with 7 climate variables. The results of this study show that currently highly suitable habitats for D.antiqua occur throughout most of East Asia, some regions of North America, Western Europe, and Western Asian countries near the Caspian sea and Black Sea. In the future, we predict an even broader distribution of this pest spread more extensively throughout Asia, North America and Europe, particularly in most of European countries, Central regions of United States and much of East Asia. Our present day and future predictions can enhance strategic planning of agricultural organizations by identifying regions that will need to develop Integrated Pest Management programs to manage the onion maggot. The distribution forecasts will also help governments to optimize economic investments in management programs for this pest by identifying regions that are or will become less suitable for current and future infestations.
Lombardo, Luigi
2016-07-18
This study aims at evaluating the performance of the Maximum Entropy method in assessing landslide susceptibility, exploiting topographic and multispectral remote sensing predictors. We selected the catchment of the Giampilieri stream, which is located in the north-eastern sector of Sicily (southern Italy), as test site. On 1/10/2009, a storm rainfall triggered in this area hundreds of debris flow/avalanche phenomena causing extensive economical damage and loss of life. Within this area a presence-only-based statistical method was applied to obtain susceptibility models capable of distinguish future activation sites of debris flow and debris slide, which where the main source failure mechanisms for flow or avalanche type propagation. The set of predictors used in this experiment comprised primary and secondary topographic attributes, derived by processing a high resolution digital elevation model, CORINE land cover data and a set of vegetation and mineral indices obtained by processing multispectral ASTER images. All the selected data sources are dated before the disaster. A spatially random partition technique was adopted for validation, generating fifty replicates for each of the two considered movement typologies in order to assess accuracy, precision and reliability of the models. The debris slide and debris flow susceptibility models produced high performances with the first type being the best fitted. The evaluation of the probability estimates around the mean value for each mapped pixel shows an inverted relation, with the most robust models corresponding to the debris flows. With respect to the role of each predictor within the modelling phase, debris flows appeared to be primarily controlled by topographic attributes whilst the debris slides were better explained by remotely sensed derived indices, particularly by the occurrence of previous wildfires across the slope. The overall excellent performances of the two models suggest promising perspectives for
Bayesian image reconstruction: Application to emission tomography
Energy Technology Data Exchange (ETDEWEB)
Nunez, J.; Llacer, J.
1989-02-01
In this paper we propose a Maximum a Posteriori (MAP) method of image reconstruction in the Bayesian framework for the Poisson noise case. We use entropy to define the prior probability and likelihood to define the conditional probability. The method uses sharpness parameters which can be theoretically computed or adjusted, allowing us to obtain MAP reconstructions without the problem of the grey'' reconstructions associated with the pre Bayesian reconstructions. We have developed several ways to solve the reconstruction problem and propose a new iterative algorithm which is stable, maintains positivity and converges to feasible images faster than the Maximum Likelihood Estimate method. We have successfully applied the new method to the case of Emission Tomography, both with simulated and real data. 41 refs., 4 figs., 1 tab.
Chen, Qingxia; Ibrahim, Joseph G
2014-07-01
Multiple Imputation, Maximum Likelihood and Fully Bayesian methods are the three most commonly used model-based approaches in missing data problems. Although it is easy to show that when the responses are missing at random (MAR), the complete case analysis is unbiased and efficient, the aforementioned methods are still commonly used in practice for this setting. To examine the performance of and relationships between these three methods in this setting, we derive and investigate small sample and asymptotic expressions of the estimates and standard errors, and fully examine how these estimates are related for the three approaches in the linear regression model when the responses are MAR. We show that when the responses are MAR in the linear model, the estimates of the regression coefficients using these three methods are asymptotically equivalent to the complete case estimates under general conditions. One simulation and a real data set from a liver cancer clinical trial are given to compare the properties of these methods when the responses are MAR.
Leung, Gabriel M; Woo, Pauline P S; McGhee, Sarah M; Cheung, Annie N Y; Fan, Susan; Mang, Oscar; Thach, Thuan Q; Ngan, Hextan Y S
2006-08-01
To examine the secular effects of opportunistic screening for cervical cancer in a rich, developed community where most other such populations have long adopted organised screening. The analysis was based on 15 140 cases of invasive cervical cancer from 1972 to 2001. The effects of chronological age, time period, and birth cohort were decomposed using both maximum likelihood and Bayesian methods. The overall age adjusted incidence decreased from 24.9 in 1972-74 to 9.5 per 100,000 in 1999-2001, in a log-linear fashion, yielding an average annual reduction of 4.0% (p1920s cohort curve representing an age-period interaction masquerading as a cohort change that denotes the first availability of Pap testing during the 1960s concentrated among women in their 40s; (2) a hook around the calendar years 1982-83 when cervical cytology became a standard screening test for pregnant women. Hong Kong's cervical cancer rates have declined since Pap tests first became available in the 1960s, most probably because of increasing population coverage over time and in successive generations in a haphazard fashion and punctuated by the systematic introduction of routine cytology as part of antenatal care in the 1980s.
Feranec, Robert S.; Kozlowski, Andrew L.
2016-03-01
To understand what factors control species colonization and extirpation within specific paleoecosystems, we analyzed radiocarbon dates of megafaunal mammal species from New York State after the Last Glacial Maximum. We hypothesized that the timing of colonization and extirpation were both driven by access to preferred habitat types. Bayesian calibration of a database of 39 radiocarbon dates shows that caribou (Rangifer tarandus) were the first colonizers, then mammoth (Mammuthus sp.), and finally American mastodon (Mammut americanum). The timing of colonization cannot reject the hypothesis that colonizing megafauna tracked preferred habitats, as caribou and mammoth arrived when tundra was present, while mastodon arrived after boreal forest was prominent in the state. The timing of caribou colonization implies that ecosystems were developed in the state prior to 16,000 cal yr BP. The contemporaneous arrival of American mastodon with Sporormiella spore decline suggests the dung fungus spore is not an adequate indicator of American mastodon population size. The pattern in the timing of extirpation is opposite to that of colonization. The lack of environmental changes suspected to be ecologically detrimental to American mastodon and mammoth coupled with the arrival of humans shortly before extirpation suggests an anthropogenic cause in the loss of the analyzed species.
Liu, Lihong; Xia, Hongyan; Baule, Claudia; Belák, Sándor
2009-01-01
Bovine viral diarrhoea virus 1 (BVDV-1) and Bovine viral diarrhoea virus 2 (BVDV-2) are two recognised bovine pestivirus species of the genus Pestivirus. Recently, a pestivirus, termed SVA/cont-08, was detected in a batch of contaminated foetal calf serum originating from South America. Comparative sequence analysis showed that the SVA/cont-08 virus shares 15-28% higher sequence identity to pestivirus D32/00_'HoBi' than to members of BVDV-1 and BVDV-2. In order to reveal the phylogenetic relationship of SVA/cont-08 with other pestiviruses, a molecular dataset of 30 pestiviruses and 1,896 characters, comprising the 5'UTR, N(pro) and E2 gene regions, was analysed by two methods: maximum likelihood and Bayesian approach. An identical, well-supported tree topology was observed, where four pestiviruses (SVA/cont-08, D32/00_'HoBi', CH-KaHo/cont, and Th/04_KhonKaen) formed a monophyletic clade that is closely related to the BVDV-1 and BVDV-2 clades. The strategy applied in this study is useful for classifying novel pestiviruses in the future.
Säwén, Elin; Massad, Tariq; Landersjö, Clas; Damberg, Peter; Widmalm, Göran
2010-08-21
The conformational space available to the flexible molecule α-D-Manp-(1-->2)-α-D-Manp-OMe, a model for the α-(1-->2)-linked mannose disaccharide in N- or O-linked glycoproteins, is determined using experimental data and molecular simulation combined with a maximum entropy approach that leads to a converged population distribution utilizing different input information. A database survey of the Protein Data Bank where structures having the constituent disaccharide were retrieved resulted in an ensemble with >200 structures. Subsequent filtering removed erroneous structures and gave the database (DB) ensemble having three classes of mannose-containing compounds, viz., N- and O-linked structures, and ligands to proteins. A molecular dynamics (MD) simulation of the disaccharide revealed a two-state equilibrium with a major and a minor conformational state, i.e., the MD ensemble. These two different conformation ensembles of the disaccharide were compared to measured experimental spectroscopic data for the molecule in water solution. However, neither of the two populations were compatible with experimental data from optical rotation, NMR (1)H,(1)H cross-relaxation rates as well as homo- and heteronuclear (3)J couplings. The conformational distributions were subsequently used as background information to generate priors that were used in a maximum entropy analysis. The resulting posteriors, i.e., the population distributions after the application of the maximum entropy analysis, still showed notable deviations that were not anticipated based on the prior information. Therefore, reparameterization of homo- and heteronuclear Karplus relationships for the glycosidic torsion angles Φ and Ψ were carried out in which the importance of electronegative substituents on the coupling pathway was deemed essential resulting in four derived equations, two (3)J(COCC) and two (3)J(COCH) being different for the Φ and Ψ torsions, respectively. These Karplus relationships are denoted
Spectral analysis of the IntCal98 calibration curve: a Bayesian view
International Nuclear Information System (INIS)
Palonen, V.; Tikkanen, P.
2004-01-01
Preliminary results from a Bayesian approach to find periodicities in the IntCal98 calibration curve are given. It has been shown in the literature that the discrete Fourier transform (Schuster periodogram) corresponds to the use of an approximate Bayesian model of one harmonic frequency and Gaussian noise. Advantages of the Bayesian approach include the possibility to use models for variable, attenuated and multiple frequencies, the capability to analyze unevenly spaced data and the possibility to assess the significance and uncertainties of spectral estimates. In this work, a new Bayesian model using random walk noise to take care of the trend in the data is developed. Both Bayesian models are described and the first results of the new model are reported and compared with results from straightforward discrete-Fourier-transform and maximum-entropy-method spectral analyses
Energy Technology Data Exchange (ETDEWEB)
Boyaval, S.
2000-06-15
This PhD presents a study on a series of high pressure swirl atomizers dedicated to Gasoline Direct Injection (GDI). Measurements are performed in stationary and pulsed working conditions. A great aspect of this thesis is the development of an original experimental set-up to correct multiple light scattering that biases the drop size distributions measurements obtained with a laser diffraction technique (Malvern 2600D). This technique allows to perform a study of drop size characteristics near the injector tip. Correction factors on drop size characteristics and on the diffracted intensities are defined from the developed procedure. Another point consists in applying the Maximum Entropy Formalism (MEF) to calculate drop size distributions. Comparisons between experimental distributions corrected with the correction factors and the calculated distributions show good agreement. This work points out that the mean diameter D{sub 43}, which is also the mean of the volume drop size distribution, and the relative volume span factor {delta}{sub v} are important characteristics of volume drop size distributions. The end of the thesis proposes to determine local drop size characteristics from a new development of deconvolution technique for line-of-sight scattering measurements. The first results show reliable behaviours of radial evolution of local characteristics. In GDI application, we notice that the critical point is the opening stage of the injection. This study shows clearly the effects of injection pressure and nozzle internal geometry on the working characteristics of these injectors, in particular, the influence of the pre-spray. This work points out important behaviours that the improvement of GDI principle ought to consider. (author)
Adjoint entropy vs topological entropy
Giordano Bruno, Anna
2012-01-01
Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...
On the prior probabilities for two-stage Bayesian estimates
International Nuclear Information System (INIS)
Kohut, P.
1992-01-01
The method of Bayesian inference is reexamined for its applicability and for the required underlying assumptions in obtaining and using prior probability estimates. Two different approaches are suggested to determine the first-stage priors in the two-stage Bayesian analysis which avoid certain assumptions required for other techniques. In the first scheme, the prior is obtained through a true frequency based distribution generated at selected intervals utilizing actual sampling of the failure rate distributions. The population variability distribution is generated as the weighed average of the frequency distributions. The second method is based on a non-parametric Bayesian approach using the Maximum Entropy Principle. Specific features such as integral properties or selected parameters of prior distributions may be obtained with minimal assumptions. It is indicated how various quantiles may also be generated with a least square technique
Applications of Entropy in Finance: A Review
Directory of Open Access Journals (Sweden)
Guanqun Tong
2013-11-01
Full Text Available Although the concept of entropy is originated from thermodynamics, its concepts and relevant principles, especially the principles of maximum entropy and minimum cross-entropy, have been extensively applied in finance. In this paper, we review the concepts and principles of entropy, as well as their applications in the field of finance, especially in portfolio selection and asset pricing. Furthermore, we review the effects of the applications of entropy and compare them with other traditional and new methods.
Entropy and transverse section reconstruction
International Nuclear Information System (INIS)
Gullberg, G.T.
1976-01-01
A new approach to the reconstruction of a transverse section using projection data from multiple views incorporates the concept of maximum entropy. The principle of maximizing information entropy embodies the assurance of minimizing bias or prejudice in the reconstruction. Using maximum entropy is a necessary condition for the reconstructed image. This entropy criterion is most appropriate for 3-D reconstruction of objects from projections where the system is underdetermined or the data are limited statistically. This is the case in nuclear medicine time limitations in patient studies do not yield sufficient projections
Entropy: From Thermodynamics to Hydrology
Directory of Open Access Journals (Sweden)
Demetris Koutsoyiannis
2014-02-01
Full Text Available Some known results from statistical thermophysics as well as from hydrology are revisited from a different perspective trying: (a to unify the notion of entropy in thermodynamic and statistical/stochastic approaches of complex hydrological systems and (b to show the power of entropy and the principle of maximum entropy in inference, both deductive and inductive. The capability for deductive reasoning is illustrated by deriving the law of phase change transition of water (Clausius-Clapeyron from scratch by maximizing entropy in a formal probabilistic frame. However, such deductive reasoning cannot work in more complex hydrological systems with diverse elements, yet the entropy maximization framework can help in inductive inference, necessarily based on data. Several examples of this type are provided in an attempt to link statistical thermophysics with hydrology with a unifying view of entropy.
Lechner, Joseph H.
1999-10-01
This report describes two classroom activities that help students visualize the abstract concept of entropy and apply the second law of thermodynamics to real situations. (i) A sealed "rainbow tube" contains six smaller vessels, each filled with a different brightly colored solution (low entropy). When the tube is inverted, the solutions mix together and react to form an amorphous precipitate (high entropy). The change from low entropy to high entropy is irreversible as long as the tube remains sealed. (ii) When U.S. currency is withdrawn from circulation, intact bills (low entropy) are shredded into small fragments (high entropy). Shredding is quick and easy; the reverse process is clearly nonspontaneous. It is theoretically possible, but it is time-consuming and energy-intensive, to reassemble one bill from a pile that contains fragments of hundreds of bills. We calculate the probability P of drawing pieces of only one specific bill from a mixture containing one pound of bills, each shredded into n fragments. This result can be related to Boltzmann's entropy formula S?=klnW.
Bayesian Recurrent Neural Network for Language Modeling.
Chien, Jen-Tzung; Ku, Yuan-Chu
2016-02-01
A language model (LM) is calculated as the probability of a word sequence that provides the solution to word prediction for a variety of information systems. A recurrent neural network (RNN) is powerful to learn the large-span dynamics of a word sequence in the continuous space. However, the training of the RNN-LM is an ill-posed problem because of too many parameters from a large dictionary size and a high-dimensional hidden layer. This paper presents a Bayesian approach to regularize the RNN-LM and apply it for continuous speech recognition. We aim to penalize the too complicated RNN-LM by compensating for the uncertainty of the estimated model parameters, which is represented by a Gaussian prior. The objective function in a Bayesian classification network is formed as the regularized cross-entropy error function. The regularized model is constructed not only by calculating the regularized parameters according to the maximum a posteriori criterion but also by estimating the Gaussian hyperparameter by maximizing the marginal likelihood. A rapid approximation to a Hessian matrix is developed to implement the Bayesian RNN-LM (BRNN-LM) by selecting a small set of salient outer-products. The proposed BRNN-LM achieves a sparser model than the RNN-LM. Experiments on different corpora show the robustness of system performance by applying the rapid BRNN-LM under different conditions.
Directory of Open Access Journals (Sweden)
Tommaso Toffoli
2016-06-01
Full Text Available Here we deconstruct, and then in a reasoned way reconstruct, the concept of “entropy of a system”, paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a count associated with a description; this count (traditionally expressed in logarithmic form for a number of good reasons is in essence the number of possibilities—specific instances or “scenarios”—that match that description. Very natural (and virtually inescapable generalizations of the idea of description are the probability distribution and its quantum mechanical counterpart, the density operator. We track the process of dynamically updating entropy as a system evolves. Three factors may cause entropy to change: (1 the system’s internal dynamics; (2 unsolicited external influences on it; and (3 the approximations one has to make when one tries to predict the system’s future state. The latter task is usually hampered by hard-to-quantify aspects of the original description, limited data storage and processing resource, and possibly algorithmic inadequacy. Factors 2 and 3 introduce randomness—often huge amounts of it—into one’s predictions and accordingly degrade them. When forecasting, as long as the entropy bookkeping is conducted in an honest fashion, this degradation will always lead to an entropy increase. To clarify the above point we introduce the notion of honest entropy, which coalesces much of what is of course already done, often tacitly, in responsible entropy-bookkeping practice. This notion—we believe—will help to fill an expressivity gap in scientific discourse. With its help, we shall prove that any dynamical system—not just our physical universe—strictly obeys Clausius’s original formulation of the second law of thermodynamics if and only if it is invertible. Thus this law is a tautological property of invertible systems!
Indian Academy of Sciences (India)
It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf that satisfy ∫ f h i d = i for i = 1 , 2 , … , … k the maximizer of entropy is an f 0 that is proportional to exp ( ∑ c i h i ) for some choice of c i . An extension of this to a continuum of ...
Indian Academy of Sciences (India)
It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf that satisfy ∫ f h i d = i for i = 1 , 2 , … , … k the maximizer of entropy is an f 0 that is proportional to exp ( ∑ c i h i ) for some choice of c i . An extension of this to a continuum of ...
Indian Academy of Sciences (India)
Abstract. It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf f that satisfy. ∫ fhi dμ = λi for i = 1, 2,...,...k the maximizer of entropy is an f0 that is pro- portional to exp(. ∑ ci hi ) for some choice of ci . An extension of this to a continuum of.
Air kerma rate estimation by means of in-situ gamma spectrometry: A Bayesian approach
International Nuclear Information System (INIS)
Cabal, Gonzalo; Kluson, Jaroslav
2008-01-01
Full text: Bayesian inference is used to determine the Air Kerma Rate based on a set of in situ environmental gamma spectra measurements performed with a NaI(Tl) scintillation detector. A natural advantage of such approach is the possibility to quantify uncertainty not only in the Air Kerma Rate estimation but also for the gamma spectra which is unfolded within the procedure. The measurements were performed using a 3'' x 3'' NaI(Tl) scintillation detector. The response matrices of such detection system were calculated using a Monte Carlo code. For the calculations of the spectra as well as the Air Kerma Rate the WinBugs program was used. WinBugs is a dedicated software for Bayesian inference using Monte Carlo Markov chain methods (MCMC). The results of such calculations are shown and compared with other non-Bayesian approachs such as the Scofield-Gold iterative method and the Maximum Entropy Method
Spatial data modelling and maximum entropy theory
Czech Academy of Sciences Publication Activity Database
Klimešová, Dana; Ocelíková, E.
2005-01-01
Roč. 51, č. 2 (2005), s. 80-83 ISSN 0139-570X Institutional research plan: CEZ:AV0Z10750506 Keywords : spatial data classification * distribution function * error distribution Subject RIV: BD - Theory of Information
Maximum entropy analysis of cosmic ray composition
Czech Academy of Sciences Publication Activity Database
Nosek, D.; Ebr, Jan; Vícha, Jakub; Trávníček, Petr; Nosková, J.
2016-01-01
Roč. 76, Mar (2016), s. 9-18 ISSN 0927-6505 R&D Projects: GA ČR(CZ) GA14-17501S Institutional support: RVO:68378271 Keywords : ultra-high energy cosmic rays * extensive air showers * cosmic ray composition Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 3.257, year: 2016
A comparison of maximum entropy and maximum likelihood estimation
Oude Lansink, A.G.J.M.
1999-01-01
Gegevens betreffende het ondernemerschap op Nederlandse akkerbouwbedrijven zijn in 2 benaderingsmethodes verwerkt, welke onderling op voorspellende nauwkeurigheid en op prijs-elasticiteit zijn vergeleken
Compressive sensing and entropy in seismic signals
Marinho, Eberton S.; Rocha, Tiago C.; Corso, Gilberto; Lucena, Liacir S.
2017-09-01
This work analyzes the correlation between the seismic signal entropy and the Compressive Sensing (CS) recovery index. The recovery index measures the quality of a signal reconstructed by the CS method. We analyze the performance of two CS algorithms: the ℓ1-MAGIC and the Fast Bayesian Compressive Sensing (BCS). We have observed a negative correlation between the performance of CS and seismic signal entropy. Signals with low entropy have small recovery index in their reconstruction by CS. The rationale behind our finding is: a sparse signal is easy to recover by CS and, besides, a sparse signal has low entropy. In addition, ℓ1-MAGIC shows a more significant correlation between entropy and CS performance than Fast BCS.
Upper entropy axioms and lower entropy axioms
International Nuclear Information System (INIS)
Guo, Jin-Li; Suo, Qi
2015-01-01
The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak upper entropy axioms and weak lower entropy axioms. Their conditions are weaker than those of Shannon–Khinchin axioms and Tsallis axioms, while these conditions are stronger than those of the axiomatics based on the first three Shannon–Khinchin axioms. The subadditivity and strong subadditivity of entropy are obtained in the new axiomatics. Tsallis statistics is a special case of satisfying our axioms. Moreover, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics
Bayesian networks in overlay recipe optimization
Binns, Lewis A.; Reynolds, Greg; Rigden, Timothy C.; Watkins, Stephen; Soroka, Andrew
2005-05-01
Currently, overlay measurements are characterized by "recipe", which defines both physical parameters such as focus, illumination et cetera, and also the software parameters such as algorithm to be used and regions of interest. Setting up these recipes requires both engineering time and wafer availability on an overlay tool, so reducing these requirements will result in higher tool productivity. One of the significant challenges to automating this process is that the parameters are highly and complexly correlated. At the same time, a high level of traceability and transparency is required in the recipe creation process, so a technique that maintains its decisions in terms of well defined physical parameters is desirable. Running time should be short, given the system (automatic recipe creation) is being implemented to reduce overheads. Finally, a failure of the system to determine acceptable parameters should be obvious, so a certainty metric is also desirable. The complex, nonlinear interactions make solution by an expert system difficult at best, especially in the verification of the resulting decision network. The transparency requirements tend to preclude classical neural networks and similar techniques. Genetic algorithms and other "global minimization" techniques require too much computational power (given system footprint and cost requirements). A Bayesian network, however, provides a solution to these requirements. Such a network, with appropriate priors, can be used during recipe creation / optimization not just to select a good set of parameters, but also to guide the direction of search, by evaluating the network state while only incomplete information is available. As a Bayesian network maintains an estimate of the probability distribution of nodal values, a maximum-entropy approach can be utilized to obtain a working recipe in a minimum or near-minimum number of steps. In this paper we discuss the potential use of a Bayesian network in such a capacity
Maximum auto-mutual-information factor analysis
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg
2017-01-01
Based on the information theoretical measure mutual information derived from entropy and Kullback-Leibler divergence, an alternative to maximum autocorrelation factor analysis is sketched.......Based on the information theoretical measure mutual information derived from entropy and Kullback-Leibler divergence, an alternative to maximum autocorrelation factor analysis is sketched....
Fully probabilistic design of hierarchical Bayesian models
Czech Academy of Sciences Publication Activity Database
Quinn, A.; Kárný, Miroslav; Guy, Tatiana Valentine
2016-01-01
Roč. 369, č. 1 (2016), s. 532-547 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Fully probabilistic design * Ideal distribution * Minimum cross- entropy principle * Bayesian conditioning * Kullback-Leibler divergence * Bayesian nonparametric modelling Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.832, year: 2016 http://library.utia.cas.cz/separaty/2016/AS/karny-0463052.pdf
Minimal entropy approximation for cellular automata
International Nuclear Information System (INIS)
Fukś, Henryk
2014-01-01
We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)
Directory of Open Access Journals (Sweden)
Ingo Klein
2016-07-01
Full Text Available A new kind of entropy will be introduced which generalizes both the differential entropy and the cumulative (residual entropy. The generalization is twofold. First, we simultaneously define the entropy for cumulative distribution functions (cdfs and survivor functions (sfs, instead of defining it separately for densities, cdfs, or sfs. Secondly, we consider a general “entropy generating function” φ, the same way Burbea et al. (IEEE Trans. Inf. Theory 1982, 28, 489–495 and Liese et al. (Convex Statistical Distances; Teubner-Verlag, 1987 did in the context of φ-divergences. Combining the ideas of φ-entropy and cumulative entropy leads to the new “cumulative paired φ-entropy” ( C P E φ . This new entropy has already been discussed in at least four scientific disciplines, be it with certain modifications or simplifications. In the fuzzy set theory, for example, cumulative paired φ-entropies were defined for membership functions, whereas in uncertainty and reliability theories some variations of C P E φ were recently considered as measures of information. With a single exception, the discussions in the scientific disciplines appear to be held independently of each other. We consider C P E φ for continuous cdfs and show that C P E φ is rather a measure of dispersion than a measure of information. In the first place, this will be demonstrated by deriving an upper bound which is determined by the standard deviation and by solving the maximum entropy problem under the restriction of a fixed variance. Next, this paper specifically shows that C P E φ satisfies the axioms of a dispersion measure. The corresponding dispersion functional can easily be estimated by an L-estimator, containing all its known asymptotic properties. C P E φ is the basis for several related concepts like mutual φ-information, φ-correlation, and φ-regression, which generalize Gini correlation and Gini regression. In addition, linear rank tests for scale that
Small-signal analysis in high-energy physics: A Bayesian approach
International Nuclear Information System (INIS)
Prosper, H.B.
1988-01-01
The statistics of small signals masked by a background of imprecisely known magnitude is addressed from a Bayesian viewpoint using a simple statistical model which may be derived from the principle of maximum entropy. The issue of the correct assignment of prior probabilities is resolved by invoking an invariance principle proposed by Jaynes. We calculate the posterior probability and use it to calculate point estimates and upper limits for the magnitude of the signal. The results are applicable to high-energy physics experiments searching for new phenomena. We illustrate this by reanalyzing some published data from a few experiments
Excess Entropy and Diffusivity
Indian Academy of Sciences (India)
First page Back Continue Last page Graphics. Excess Entropy and Diffusivity. Excess entropy scaling of diffusivity (Rosenfeld,1977). Analogous relationships also exist for viscosity and thermal conductivity.
Energy Technology Data Exchange (ETDEWEB)
Alvarez R, J.T
1998-10-01
This thesis presents a microscopic model for the non-linear fluctuating hydrodynamic of superfluid helium ({sup 4} He), model developed by means of the Maximum Entropy Method (Maxent). In the chapter 1, it is demonstrated the necessity to developing a microscopic model for the fluctuating hydrodynamic of the superfluid helium, starting from to show a brief overview of the theories and experiments developed in order to explain the behavior of the superfluid helium. On the other hand, it is presented the Morozov heuristic method for the construction of the non-linear hydrodynamic fluctuating of simple fluid. Method that will be generalized for the construction of the non-linear fluctuating hydrodynamic of the superfluid helium. Besides, it is presented a brief summary of the content of the thesis. In the chapter 2, it is reproduced the construction of a Generalized Fokker-Planck equation, (GFP), for a distribution function associated with the coarse grained variables. Function defined with aid of a nonequilibrium statistical operator {rho}hut{sub FP} that is evaluated as Wigneris function through {rho}{sub CG} obtained by Maxent. Later this equation of GFP is reduced to a non-linear local FP equation from considering a slow and Markov process in the coarse grained variables. In this equation appears a matrix D{sub mn} defined with a nonequilibrium coarse grained statistical operator {rho}hut{sub CG}, matrix elements are used in the construction of the non-linear fluctuating hydrodynamics equations of the superfluid helium. In the chapter 3, the Lagrange multipliers are evaluated for to determine {rho}hut{sub CG} by means of the local equilibrium statistical operator {rho}hut{sub l}-tilde with the hypothesis that the system presents small fluctuations. Also are determined the currents associated with the coarse grained variables and furthermore are evaluated the matrix elements D{sub mn} but with aid of a quasi equilibrium statistical operator {rho}hut{sub qe} instead
Lesaffre, Emmanuel
2012-01-01
The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets. Through examples, exercises and a combination of introd
Entropy Bounds for Constrained Two-Dimensional Fields
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Justesen, Jørn
1999-01-01
The maximum entropy and thereby the capacity of 2-D fields given by certain constraints on configurations are considered. Upper and lower bounds are derived.......The maximum entropy and thereby the capacity of 2-D fields given by certain constraints on configurations are considered. Upper and lower bounds are derived....
Black hole entropy, curved space and monsters
International Nuclear Information System (INIS)
Hsu, Stephen D.H.; Reeb, David
2008-01-01
We investigate the microscopic origin of black hole entropy, in particular the gap between the maximum entropy of ordinary matter and that of black holes. Using curved space, we construct configurations with entropy greater than the area A of a black hole of equal mass. These configurations have pathological properties and we refer to them as monsters. When monsters are excluded we recover the entropy bound on ordinary matter S 3/4 . This bound implies that essentially all of the microstates of a semiclassical black hole are associated with the growth of a slightly smaller black hole which absorbs some additional energy. Our results suggest that the area entropy of black holes is the logarithm of the number of distinct ways in which one can form the black hole from ordinary matter and smaller black holes, but only after the exclusion of monster states
Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.
Carroll, Carlos; Johnson, Devin S; Dunk, Jeffrey R; Zielinski, William J
2010-12-01
Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies
Directory of Open Access Journals (Sweden)
Hea-Jung Kim
2017-06-01
Full Text Available This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT models with stochastic (or uncertain constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT models (such as log-normal, log-Cauchy, and log-logistic FT models as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.
Entropy estimates for simple random fields
DEFF Research Database (Denmark)
Forchhammer, Søren; Justesen, Jørn
1995-01-01
We consider the problem of determining the maximum entropy of a discrete random field on a lattice subject to certain local constraints on symbol configurations. The results are expected to be of interest in the analysis of digitized images and two dimensional codes. We shall present some examples...... of binary and ternary fields with simple constraints. Exact results on the entropies are known only in a few cases, but we shall present close bounds and estimates that are computationally efficient...
MERGING DIGITAL SURFACE MODELS IMPLEMENTING BAYESIAN APPROACHES
Directory of Open Access Journals (Sweden)
H. Sadeq
2016-06-01
Full Text Available In this research different DSMs from different sources have been merged. The merging is based on a probabilistic model using a Bayesian Approach. The implemented data have been sourced from very high resolution satellite imagery sensors (e.g. WorldView-1 and Pleiades. It is deemed preferable to use a Bayesian Approach when the data obtained from the sensors are limited and it is difficult to obtain many measurements or it would be very costly, thus the problem of the lack of data can be solved by introducing a priori estimations of data. To infer the prior data, it is assumed that the roofs of the buildings are specified as smooth, and for that purpose local entropy has been implemented. In addition to the a priori estimations, GNSS RTK measurements have been collected in the field which are used as check points to assess the quality of the DSMs and to validate the merging result. The model has been applied in the West-End of Glasgow containing different kinds of buildings, such as flat roofed and hipped roofed buildings. Both quantitative and qualitative methods have been employed to validate the merged DSM. The validation results have shown that the model was successfully able to improve the quality of the DSMs and improving some characteristics such as the roof surfaces, which consequently led to better representations. In addition to that, the developed model has been compared with the well established Maximum Likelihood model and showed similar quantitative statistical results and better qualitative results. Although the proposed model has been applied on DSMs that were derived from satellite imagery, it can be applied to any other sourced DSMs.
Entropy, Perception, and Relativity
National Research Council Canada - National Science Library
Jaegar, Stefan
2006-01-01
.... Shannon's notion of entropy is a special case of my more general definition of entropy. I define probability using a so-called performance function, which is de facto an exponential distribution...
Abolishing the maximum tension principle
Directory of Open Access Journals (Sweden)
Mariusz P. Da̧browski
2015-09-01
Full Text Available We find the series of example theories for which the relativistic limit of maximum tension Fmax=c4/4G represented by the entropic force can be abolished. Among them the varying constants theories, some generalized entropy models applied both for cosmological and black hole horizons as well as some generalized uncertainty principle models.
Ben-Naim, Arieh
2011-01-01
Changes in entropy can "sometimes" be interpreted in terms of changes in disorder. On the other hand, changes in entropy can "always" be interpreted in terms of changes in Shannon's measure of information. Mixing and demixing processes are used to highlight the pitfalls in the association of entropy with disorder. (Contains 3 figures.)
Quantum chaos: entropy signatures
International Nuclear Information System (INIS)
Miller, P.A.; Sarkar, S.; Zarum, R.
1998-01-01
A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)
Maximizing entropy of image models for 2-D constrained coding
DEFF Research Database (Denmark)
Forchhammer, Søren; Danieli, Matteo; Burini, Nino
2010-01-01
This paper considers estimating and maximizing the entropy of two-dimensional (2-D) fields with application to 2-D constrained coding. We consider Markov random fields (MRF), which have a non-causal description, and the special case of Pickard random fields (PRF). The PRF are 2-D causal finite...... context models, which define stationary probability distributions on finite rectangles and thus allow for calculation of the entropy. We consider two binary constraints and revisit the hard square constraint given by forbidding neighboring 1s and provide novel results for the constraint that no uniform 2...... £ 2 squares contains all 0s or all 1s. The maximum values of the entropy for the constraints are estimated and binary PRF satisfying the constraint are characterized and optimized w.r.t. the entropy. The maximum binary PRF entropy is 0.839 bits/symbol for the no uniform squares constraint. The entropy...
RNA Thermodynamic Structural Entropy.
Directory of Open Access Journals (Sweden)
Juan Antonio Garcia-Martin
Full Text Available Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs. However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
RNA Thermodynamic Structural Entropy.
Garcia-Martin, Juan Antonio; Clote, Peter
2015-01-01
Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http
International Nuclear Information System (INIS)
Markvardsen, A.J.
2000-01-01
The physics of the series Pr y Y 1-y Ba 2 CU 3 O 6+x , and ability of Pr to suppress superconductivity, has been a subject of frequent discussions in the literature for more than a decade. This thesis describes a polarised neutron diffraction (PND) experiment performed on PrBa 2 Cu 3 O 6.24 designed to find out something about the electron structure. This experiment pushed the limits of what can be done using the PND technique. The problem is one of a limited number of measured Fourier components that need to be inverted to form a real space image. To accomplish this inversion the maximum entropy technique has been employed. In some cases, the maximum entropy technique has the ability to increase the resolution of 'inverted' data immensely, but this ability is found to depend critically on the choice of constants used in the method. To investigate this a Bayesian robustness analysis of the maximum entropy method is carried out, resulting in an improvement of the maximum entropy technique for analysing PND data. Some results for nickel in the literature have been te-analysed and a comparison is made with different maximum entropy algorithms. Equipped with an improved data analysis technique and carefully measured PND data for PrBa 2 Cu 3 O 6.24 a number of new interesting features are observed, putting constraints on existing theoretical models of Pr y Y 1-y Ba 2 Cu 3 O 6+x and leaving room for more questions to be answered. (author)
Towards operational interpretations of generalized entropies
International Nuclear Information System (INIS)
Topsoee, Flemming
2010-01-01
The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.
Coarse Graining Shannon and von Neumann Entropies
Directory of Open Access Journals (Sweden)
Ana Alonso-Serrano
2017-05-01
Full Text Available The nature of coarse graining is intuitively “obvious”, but it is rather difficult to find explicit and calculable models of the coarse graining process (and the resulting entropy flow discussed in the literature. What we would like to have at hand is some explicit and calculable process that takes an arbitrary system, with specified initial entropy S, and that monotonically and controllably drives the entropy to its maximum value. This does not have to be a physical process, in fact for some purposes it is better to deal with a gedanken-process, since then it is more obvious how the “hidden information” is hiding in the fine-grain correlations that one is simply agreeing not to look at. We shall present several simple mathematically well-defined and easy to work with conceptual models for coarse graining. We shall consider both the classical Shannon and quantum von Neumann entropies, including models based on quantum decoherence, and analyse the entropy flow in some detail. When coarse graining the quantum von Neumann entropy, we find it extremely useful to introduce an adaptation of Hawking’s super-scattering matrix. These explicit models that we shall construct allow us to quantify and keep clear track of the entropy that appears when coarse graining the system and the information that can be hidden in unobserved correlations (while not the focus of the current article, in the long run, these considerations are of interest when addressing the black hole information puzzle.
Thermoeconomic diagnosis and entropy generation paradox
DEFF Research Database (Denmark)
Sigthorsson, Oskar; Ommen, Torben Schmidt; Elmegaard, Brian
2017-01-01
In the entropy generation paradox, the entropy generation number, as a function of heat exchanger effectiveness, counter-intuitively approaches zero in two limits symmetrically from a single maximum. In thermoeconomic diagnosis, namely in the characteristic curve method, the exergy destruction...... to the entropy generation paradox, as a decreased heat exchanger effectiveness (as in the case of an operation anomaly in the component) can counter-intuitively result in decreased exergy destruction rate of the component. Therefore, along with an improper selection of independent variables, the heat exchanger...... increases in case of an operation anomaly in a component. The normalised exergy destruction rate as the dependent variable therefore resolves the relation of the characteristic curve method with the entropy generation paradox....
Fused Entropy Algorithm in Optical Computed Tomography
Directory of Open Access Journals (Sweden)
Xiong Wan
2014-02-01
Full Text Available In most applications of optical computed tomography (OpCT, limited-view problems are often encountered, which can be solved to a certain extent with typical OpCT reconstructive algorithms. The concept of entropy first emerged in information theory has been introduced into OpCT algorithms, such as maximum entropy (ME algorithms and cross entropy (CE algorithms, which have demonstrated their superiority over traditional OpCT algorithms, yet have their own limitations. A fused entropy (FE algorithm, which follows an optimized criterion combining self-adaptively ME with CE, is proposed and investigated by comparisons with ME, CE and some traditional OpCT algorithms. Reconstructed results of several physical models show this FE algorithm has a good convergence and can achieve better precision than other algorithms, which verifies the feasibility of FE as an approach of optimizing computation, not only for OpCT, but also for other image processing applications.
Applications of quantum entropy to statistics
International Nuclear Information System (INIS)
Silver, R.N.; Martz, H.F.
1994-01-01
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 heirarchical Bayes methods
Bayesian structural equation modeling in sport and exercise psychology.
Stenling, Andreas; Ivarsson, Andreas; Johnson, Urban; Lindwall, Magnus
2015-08-01
Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.
Directory of Open Access Journals (Sweden)
Øyvind Grøn
2012-12-01
Full Text Available The effect of gravity upon changes of the entropy of a gravity-dominated system is discussed. In a universe dominated by vacuum energy, gravity is repulsive, and there is accelerated expansion. Furthermore, inhomogeneities are inflated and the universe approaches a state of thermal equilibrium. The difference between the evolution of the cosmic entropy in a co-moving volume in an inflationary era with repulsive gravity and a matter-dominated era with attractive gravity is discussed. The significance of conversion of gravitational energy to thermal energy in a process with gravitational clumping, in order that the entropy of the universe shall increase, is made clear. Entropy of black holes and cosmic horizons are considered. The contribution to the gravitational entropy according to the Weyl curvature hypothesis is discussed. The entropy history of the Universe is reviewed.
Rosser, J. Barkley
2016-12-01
Entropy is a central concept of statistical mechanics, which is the main branch of physics that underlies econophysics, the application of physics concepts to understand economic phenomena. It enters into econophysics both in an ontological way through the Second Law of Thermodynamics as this drives the world economy from its ecological foundations as solar energy passes through food chains in dissipative process of entropy rising and production fundamentally involving the replacement of lower entropy energy states with higher entropy ones. In contrast the mathematics of entropy as appearing in information theory becomes the basis for modeling financial market dynamics as well as income and wealth distribution dynamics. It also provides the basis for an alternative view of stochastic price equilibria in economics, as well providing a crucial link between econophysics and sociophysics, keeping in mind the essential unity of the various concepts of entropy.
Conservative models: parametric entropy vs. temporal entropy in outcomes.
Huang, Lumeng; Ritzi, Robert W; Ramanathan, Ramya
2012-01-01
The geologic architecture in aquifer systems affects the behavior of fluid flow and the dispersion of mass. The spatial distribution and connectivity of higher-permeability facies play an important role. Models that represent this geologic structure have reduced entropy in the spatial distribution of permeability relative to models without structure. The literature shows that the stochastic model with the greatest variance in the distribution of predictions (i.e., the most conservative model) will not simply be the model representing maximum disorder in the permeability field. This principle is further explored using the Shannon entropy as a single metric to quantify and compare model parametric spatial disorder to the temporal distribution of mass residence times in model predictions. The principle is most pronounced when geologic structure manifests as preferential-flow pathways through the system via connected high-permeability sediments. As per percolation theory, at certain volume fractions the full connectivity of the high-permeability sediments will not be represented unless the model is three-dimensional. At these volume fractions, two-dimensional models can profoundly underrepresent the entropy in the real, three-dimensional, aquifer system. Thus to be conservative, stochastic models must be three-dimensional and include geologic structure. © 2011, The Author(s). Ground Water © 2011, National Ground Water Association.
Bessiere, Pierre; Ahuactzin, Juan Manuel; Mekhnacha, Kamel
2013-01-01
Probability as an Alternative to Boolean LogicWhile logic is the mathematical foundation of rational reasoning and the fundamental principle of computing, it is restricted to problems where information is both complete and certain. However, many real-world problems, from financial investments to email filtering, are incomplete or uncertain in nature. Probability theory and Bayesian computing together provide an alternative framework to deal with incomplete and uncertain data. Decision-Making Tools and Methods for Incomplete and Uncertain DataEmphasizing probability as an alternative to Boolean
Acoustic Entropy of the Materials in the Course of Degradation
Directory of Open Access Journals (Sweden)
Ali Kahirdeh
2016-07-01
Full Text Available We report experimental observations on the evolution of acoustic entropy in the course of cyclic loading as degradation occurs due to fatigue. The measured entropy is a result of the materials’ microstructural changes that occur as degradation due to cyclic mechanical loading. Experimental results demonstrate that maximum acoustic entropy emanating from materials during the course of degradation remains similar. Experiments are shown for two different types of materials: Aluminum 6061 (a metallic alloy and glass/epoxy (a composite laminate. The evolution of the acoustic entropy demonstrates a persistent trend over the course of degradation.
Information entropy and its application in heat conduction
Su, C. Q.; Wu, Y.; Fan, X. Y.; Guo, P.
2017-11-01
In this paper, heat conduction problems are analyzed from the view of information entropy. The variation law of temperature with time in the lumped-heat-capacity system can be expressed in the form of exponential distribution. It is proved that exponential distribution is the solution of a conditional extreme value problem with information entropy as an objective function. The general analysis procedure of heat conduction problems from the view of information entropy is proposed. Fundamental solution of heat conduction equation can be written in the form of normal distribution, and normal distribution can be derived from the maximum entropy principle.
International Nuclear Information System (INIS)
Zhu, Qingjun; Song, Fengquan; Ren, Jie; Chen, Xueyong; Zhou, Bin
2014-01-01
To further expand the application of an artificial neural network in the field of neutron spectrometry, the criteria for choosing between an artificial neural network and the maximum entropy method for the purpose of unfolding neutron spectra was presented. The counts of the Bonner spheres for IAEA neutron spectra were used as a database, and the artificial neural network and the maximum entropy method were used to unfold neutron spectra; the mean squares of the spectra were defined as the differences between the desired and unfolded spectra. After the information entropy of each spectrum was calculated using information entropy theory, the relationship between the mean squares of the spectra and the information entropy was acquired. Useful information from the information entropy guided the selection of unfolding methods. Due to the importance of the information entropy, the method for predicting the information entropy using the Bonner spheres' counts was established. The criteria based on the information entropy theory can be used to choose between the artificial neural network and the maximum entropy method unfolding methods. The application of an artificial neural network to unfold neutron spectra was expanded. - Highlights: • Two neutron spectra unfolding methods, ANN and MEM, were compared. • The spectrum's entropy offers useful information for selecting unfolding methods. • For the spectrum with low entropy, the ANN was generally better than MEM. • The spectrum's entropy was predicted based on the Bonner spheres' counts
Entropy - Some Cosmological Questions Answered by Model of Expansive Nondecelerative Universe
Directory of Open Access Journals (Sweden)
Miroslav Sukenik
2003-01-01
Full Text Available Abstract: The paper summarizes the background of Expansive Nondecelerative Universe model and its potential to offer answers to some open cosmological questions related to entropy. Three problems are faced in more detail, namely that of Hawkings phenomenon of black holes evaporation, maximum entropy of the Universe during its evolution, and time evolution of specific entropy.
The Bayesian Covariance Lasso.
Khondker, Zakaria S; Zhu, Hongtu; Chu, Haitao; Lin, Weili; Ibrahim, Joseph G
2013-04-01
Estimation of sparse covariance matrices and their inverse subject to positive definiteness constraints has drawn a lot of attention in recent years. The abundance of high-dimensional data, where the sample size ( n ) is less than the dimension ( d ), requires shrinkage estimation methods since the maximum likelihood estimator is not positive definite in this case. Furthermore, when n is larger than d but not sufficiently larger, shrinkage estimation is more stable than maximum likelihood as it reduces the condition number of the precision matrix. Frequentist methods have utilized penalized likelihood methods, whereas Bayesian approaches rely on matrix decompositions or Wishart priors for shrinkage. In this paper we propose a new method, called the Bayesian Covariance Lasso (BCLASSO), for the shrinkage estimation of a precision (covariance) matrix. We consider a class of priors for the precision matrix that leads to the popular frequentist penalties as special cases, develop a Bayes estimator for the precision matrix, and propose an efficient sampling scheme that does not precalculate boundaries for positive definiteness. The proposed method is permutation invariant and performs shrinkage and estimation simultaneously for non-full rank data. Simulations show that the proposed BCLASSO performs similarly as frequentist methods for non-full rank data.
Entropy resistance analyses of a two-stream parallel flow heat exchanger with viscous heating
International Nuclear Information System (INIS)
Cheng Xue-Tao; Liang Xin-Gang
2013-01-01
Heat exchangers are widely used in industry, and analyses and optimizations of the performance of heat exchangers are important topics. In this paper, we define the concept of entropy resistance based on the entropy generation analyses of a one-dimensional heat transfer process. With this concept, a two-stream parallel flow heat exchanger with viscous heating is analyzed and discussed. It is found that the minimization of entropy resistance always leads to the maximum heat transfer rate for the discussed two-stream parallel flow heat exchanger, while the minimizations of entropy generation rate, entropy generation numbers, and revised entropy generation number do not always. (general)
Entropy and Kolmogorov complexity
Moriakov, N.V.
2016-01-01
This thesis is dedicated to studying the theory of entropy and its relation to the Kolmogorov complexity. Originating in physics, the notion of entropy was introduced to mathematics by C. E. Shannon as a way of measuring the rate at which information is coming from a data source. There are, however,
International Nuclear Information System (INIS)
Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael
2015-01-01
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.
Indian Academy of Sciences (India)
Enthalpy–entropy compensation is the name given to the correlation sometimes observed between the estimates of the enthalpy and entropy of a reaction obtained from temperature-dependence data. Although the mainly artefactual nature of this correlation has been known for many years, the subject enjoys periodical ...
Indian Academy of Sciences (India)
entropy loss during protein folding plays a much larger role in determining the shape of the free energy reaction landscape than it does in most small molecule reactions. For a protein to fold, the loss of entropy must be balanced by the gain in enthalpy for the free energy to favor folding. Strong non- covalent forces from ...
Metrics for evaluating performance and uncertainty of Bayesian network models
Bruce G. Marcot
2012-01-01
This paper presents a selected set of existing and new metrics for gauging Bayesian network model performance and uncertainty. Selected existing and new metrics are discussed for conducting model sensitivity analysis (variance reduction, entropy reduction, case file simulation); evaluating scenarios (influence analysis); depicting model complexity (numbers of model...
Nonsymmetric entropy I: basic concepts and results
Liu, Chengshi
2006-01-01
A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally from maximal nonsymmetric entropy principle.
Entropy Inequality Violations from Ultraspinning Black Holes.
Hennigar, Robie A; Mann, Robert B; Kubizňák, David
2015-07-17
We construct a new class of rotating anti-de Sitter (AdS) black hole solutions with noncompact event horizons of finite area in any dimension and study their thermodynamics. In four dimensions these black holes are solutions to gauged supergravity. We find that their entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality, which states that for a given thermodynamic volume, the black hole entropy is maximized for Schwarzschild-AdS space. We use this result to suggest more stringent conditions under which this conjecture may hold.
International Nuclear Information System (INIS)
Baccetti, Valentina; Visser, Matt
2013-01-01
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context. (paper)
Entropy of the Mixture of Sources and Entropy Dimension
Smieja, Marek; Tabor, Jacek
2011-01-01
We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based on measures instead of partitions.
Entropy Coherent and Entropy Convex Measures of Risk
Laeven, R.J.A.; Stadje, M.A.
2011-01-01
We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences,
Entropy coherent and entropy convex measures of risk
Laeven, R.J.A.; Stadje, M.
2013-01-01
We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex
Measurement Invariance, Entropy, and Probability
Directory of Open Access Journals (Sweden)
D. Eric Smith
2010-02-01
Full Text Available We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use measurement scale as a type of information constraint. We argue that a very common measurement scale is linear at small magnitudes grading into logarithmic at large magnitudes, leading to observations that often follow Student’s probability distribution which has a Gaussian shape for small fluctuations from the mean and a power law shape for large fluctuations from the mean. An inverse scaling often arises in which measures naturally grade from logarithmic to linear as one moves from small to large magnitudes, leading to observations that often follow a gamma probability distribution. A gamma distribution has a power law shape for small magnitudes and an exponential shape for large magnitudes. The two measurement scales are natural inverses connected by the Laplace integral transform. This inversion connects the two major scaling patterns commonly found in nature. We also show that superstatistics is a special case of an integral transform, and thus can be understood as a particular way in which to change the scale of measurement. Incorporating information about measurement scale into maximum entropy provides a general approach to the relations between measurement, information and probability.
Directory of Open Access Journals (Sweden)
Leonid M. Martyushev
2015-06-01
Full Text Available The entropy production (inside the volume bounded by a photosphere of main-sequence stars, subgiants, giants, and supergiants is calculated based on B–V photometry data. A non-linear inverse relationship of thermodynamic fluxes and forces as well as an almost constant specific (per volume entropy production of main-sequence stars (for 95% of stars, this quantity lies within 0.5 to 2.2 of the corresponding solar magnitude is found. The obtained results are discussed from the perspective of known extreme principles related to entropy production.
Bayesian optimization for computationally extensive probability distributions.
Tamura, Ryo; Hukushima, Koji
2018-01-01
An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of acquisition functions by Gaussian processes for the next training phase, which should be located near a local maximum or a global maximum of the probability distribution. Our Bayesian optimization technique is applied to the posterior distribution in the effective physical model estimation, which is a computationally extensive probability distribution. Even when the number of sampling points on the posterior distributions is fixed to be small, the Bayesian optimization provides a better maximizer of the posterior distributions in comparison to those by the random search method, the steepest descent method, or the Monte Carlo method. Furthermore, the Bayesian optimization improves the results efficiently by combining the steepest descent method and thus it is a powerful tool to search for a better maximizer of computationally extensive probability distributions.
A Bayesian approach to extracting meaning from system behavior
Energy Technology Data Exchange (ETDEWEB)
Dress, W.B.
1998-08-01
The modeling relation and its reformulation to include the semiotic hierarchy is essential for the understanding, control, and successful re-creation of natural systems. This presentation will argue for a careful application of Rosen`s modeling relationship to the problems of intelligence and autonomy in natural and artificial systems. To this end, the authors discuss the essential need for a correct theory of induction, learning, and probability; and suggest that modern Bayesian probability theory, developed by Cox, Jaynes, and others, can adequately meet such demands, especially on the operational level of extracting meaning from observations. The methods of Bayesian and maximum Entropy parameter estimation have been applied to measurements of system observables to directly infer the underlying differential equations generating system behavior. This approach by-passes the usual method of parameter estimation based on assuming a functional form for the observable and then estimating the parameters that would lead to the particular observed behavior. The computational savings is great since only location parameters enter into the maximum-entropy calculations; this innovation finesses the need for nonlinear parameters altogether. Such an approach more directly extracts the semantics inherent in a given system by going to the root of system meaning as expressed by abstract form or shape, rather than in syntactic particulars, such as signal amplitude and phase. Examples will be shown how the form of a system can be followed while ignoring unnecessary details. In this sense, the authors are observing the meaning of the words rather than being concerned with their particular expression or language. For the present discussion, empirical models are embodied by the differential equations underlying, producing, or describing the behavior of a process as measured or tracked by a particular variable set--the observables. The a priori models are probability structures that
Entropy in Corporate Information Systems
Directory of Open Access Journals (Sweden)
Victor Y. Tsvetkov
2014-03-01
Full Text Available This paper describes the stages of entropy formation. It depicts the basic definitions of the corporate information systems. This paper describes the quality of entropy, the duration of the entropy in the corporate information system. The article also gives a paradigmatic description of the action of information entropy in time.
Minimum entropy production principle
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel
2013-01-01
Roč. 8, č. 7 (2013), s. 9664-9677 ISSN 1941-6016 Institutional support: RVO:68378271 Keywords : MINEP Subject RIV: BE - Theoretical Physics http://www.scholarpedia.org/article/Minimum_entropy_production_principle
Energy Technology Data Exchange (ETDEWEB)
Estes, John [Blackett Laboratory, Imperial College,London SW7 2AZ (United Kingdom); Jensen, Kristan [Department of Physics and Astronomy, University of Victoria,Victoria, BC V8W 3P6 (Canada); C.N. Yang Institute for Theoretical Physics, SUNY Stony Brook,Stony Brook, NY 11794-3840 (United States); O’Bannon, Andy [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom); Tsatis, Efstratios [8 Kotylaiou Street, Athens 11364 (Greece); Wrase, Timm [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States)
2014-05-19
We study a number of (3+1)- and (2+1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3+1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1+1)-dimensional field theories generalizes to higher dimensions.
Estes, John; Jensen, Kristan; O'Bannon, Andy; Tsatis, Efstratios; Wrase, Timm
2014-05-01
We study a number of (3 + 1)- and (2 + 1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3 + 1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1 + 1)-dimensional field theories generalizes to higher dimensions.
Microcanonical entropy for classical systems
Franzosi, Roberto
2018-03-01
The entropy definition in the microcanonical ensemble is revisited. We propose a novel definition for the microcanonical entropy that resolve the debate on the correct definition of the microcanonical entropy. In particular we show that this entropy definition fixes the problem inherent the exact extensivity of the caloric equation. Furthermore, this entropy reproduces results which are in agreement with the ones predicted with standard Boltzmann entropy when applied to macroscopic systems. On the contrary, the predictions obtained with the standard Boltzmann entropy and with the entropy we propose, are different for small system sizes. Thus, we conclude that the Boltzmann entropy provides a correct description for macroscopic systems whereas extremely small systems should be better described with the entropy that we propose here.
Introduction to Bayesian statistics
Bolstad, William M
2017-01-01
There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this Third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian staistics. The author continues to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inferenfe cfor discrete random variables, bionomial proprotion, Poisson, normal mean, and simple linear regression. In addition, newly-developing topics in the field are presented in four new chapters: Bayesian inference with unknown mean and variance; Bayesian inference for Multivariate Normal mean vector; Bayesian inference for Multiple Linear RegressionModel; and Computati...
Entropy Is Simple, Qualitatively
Lambert, Frank L.
2002-10-01
Qualitatively, entropy is simple. What it is, why it is useful in understanding the behavior of macro systems or of molecular systems is easy to state: Entropy increase from a macro viewpoint is a measure of the dispersal of energy from localized to spread out at a temperature T. The conventional q in qrev/T is the energy dispersed to or from a substance or a system. On a molecular basis, entropy increase means that a system changes from having fewer accessible microstates to having a larger number of accessible microstates. Fundamentally based on statistical and quantum mechanics, this approach is superior to the non-fundamental "disorder" as a descriptor of entropy change. The foregoing in no way denies the subtlety or the difficulty presented by entropy in thermodynamics—to first-year students or to professionals. However, as an aid to beginners in their quantitative study of thermodynamics, the qualitative conclusions in this article give students the advantage of a clear bird’s-eye view of why entropy increases in a wide variety of basic cases: a substance going from 0 K to T, phase change, gas expansion, mixing of ideal gases or liquids, colligative effects, and the Gibbs equation. See Letter re: this article.
Renormalized entanglement entropy
Energy Technology Data Exchange (ETDEWEB)
Taylor, Marika; Woodhead, William [Mathematical Sciences and STAG Research Centre, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom)
2016-08-29
We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement entropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renormalization group flows. The renormalized entanglement entropy for disk regions in AdS{sub 4} spacetimes agrees precisely with the holographically renormalized action for AdS{sub 4} with spherical slicing and hence with the F quantity, in accordance with the Casini-Huerta-Myers map. We present a generic class of holographic RG flows associated with deformations by operators of dimension 3/2<Δ<5/2 for which the F quantity increases along the RG flow, hence violating the strong version of the F theorem. We conclude by explaining how the renormalized entanglement entropy can be derived directly from the renormalized partition function using the replica trick i.e. our renormalization method for the entanglement entropy is inherited directly from that of the partition function. We show explicitly how the entanglement entropy counterterms can be derived from the standard holographic renormalization counterterms for asymptotically locally anti-de Sitter spacetimes.
International Nuclear Information System (INIS)
Lemos, Jose P. S.; Zaslavskii, Oleg B.
2010-01-01
We trace the origin of the black hole entropy S, replacing a black hole by a quasiblack hole. Let the boundary of a static body approach its own gravitational radius, in such a way that a quasihorizon forms. We show that if the body is thermal with the temperature taking the Hawking value at the quasihorizon limit, it follows, in the nonextremal case, from the first law of thermodynamics that the entropy approaches the Bekenstein-Hawking value S=A/4. In this setup, the key role is played by the surface stresses on the quasihorizon and one finds that the entropy comes from the quasihorizon surface. Any distribution of matter inside the surface leads to the same universal value for the entropy in the quasihorizon limit. This can be of some help in the understanding of black hole entropy. Other similarities between black holes and quasiblack holes such as the mass formulas for both objects had been found previously. We also discuss the entropy for extremal quasiblack holes, a more subtle issue.
Bayesian artificial intelligence
Korb, Kevin B
2003-01-01
As the power of Bayesian techniques has become more fully realized, the field of artificial intelligence has embraced Bayesian methodology and integrated it to the point where an introduction to Bayesian techniques is now a core course in many computer science programs. Unlike other books on the subject, Bayesian Artificial Intelligence keeps mathematical detail to a minimum and covers a broad range of topics. The authors integrate all of Bayesian net technology and learning Bayesian net technology and apply them both to knowledge engineering. They emphasize understanding and intuition but also provide the algorithms and technical background needed for applications. Software, exercises, and solutions are available on the authors' website.
Bayesian artificial intelligence
Korb, Kevin B
2010-01-01
Updated and expanded, Bayesian Artificial Intelligence, Second Edition provides a practical and accessible introduction to the main concepts, foundation, and applications of Bayesian networks. It focuses on both the causal discovery of networks and Bayesian inference procedures. Adopting a causal interpretation of Bayesian networks, the authors discuss the use of Bayesian networks for causal modeling. They also draw on their own applied research to illustrate various applications of the technology.New to the Second EditionNew chapter on Bayesian network classifiersNew section on object-oriente
On the Conditional Rényi Entropy
S. Fehr (Serge); S. Berens (Stefan)
2014-01-01
htmlabstractThe Rényi entropy of general order unifies the well-known Shannon entropy with several other entropy notions, like the min-entropy or the collision entropy. In contrast to the Shannon entropy, there seems to be no commonly accepted definition for the conditional Rényi entropy: several
Scaling of the magnetic entropy change of Fe3−xMnxSi
International Nuclear Information System (INIS)
Said, M.R.; Hamam, Y.A.; Abu-Aljarayesh, I.
2014-01-01
The magnetic entropy change of Fe 3−x Mn x Si (for x=1.15, 1.3 and 1.5) has been extracted from isothermal magnetization measurements near the Curie temperature. We used the scaling hypotheses of the thermodynamic potentials to scale the magnetic entropy change to a single universal curve for each sample. The effect of the exchange field and the Curie temperature on the maximum entropy change is discussed. - Highlights: • The maximum of the magnetic entropy change occurs at temperatures T>T C . • The exchange field enhances the magnetic entropy change. • The magnetic entropy change at T C is inversely proportional to T C . • Scaling hypothesis is used to scale the magnetic entropy change
2D Tsallis Entropy for Image Segmentation Based on Modified Chaotic Bat Algorithm
Directory of Open Access Journals (Sweden)
Zhiwei Ye
2018-03-01
Full Text Available Image segmentation is a significant step in image analysis and computer vision. Many entropy based approaches have been presented in this topic; among them, Tsallis entropy is one of the best performing methods. However, 1D Tsallis entropy does not consider make use of the spatial correlation information within the neighborhood results might be ruined by noise. Therefore, 2D Tsallis entropy is proposed to solve the problem, and results are compared with 1D Fisher, 1D maximum entropy, 1D cross entropy, 1D Tsallis entropy, fuzzy entropy, 2D Fisher, 2D maximum entropy and 2D cross entropy. On the other hand, due to the existence of huge computational costs, meta-heuristics algorithms like genetic algorithm (GA, particle swarm optimization (PSO, ant colony optimization algorithm (ACO and differential evolution algorithm (DE are used to accelerate the 2D Tsallis entropy thresholding method. In this paper, considering 2D Tsallis entropy as a constrained optimization problem, the optimal thresholds are acquired by maximizing the objective function using a modified chaotic Bat algorithm (MCBA. The proposed algorithm has been tested on some actual and infrared images. The results are compared with that of PSO, GA, ACO and DE and demonstrate that the proposed method outperforms other approaches involved in the paper, which is a feasible and effective option for image segmentation.
Aspects of entanglement entropy for gauge theories
International Nuclear Information System (INIS)
Soni, Ronak M.; Trivedi, Sandip P.
2016-01-01
A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of the Hilbert space of states on each link of the lattice. This extended Hilbert space admits a tensor product decomposition by definition and allows a density matrix and entanglement entropy for the set of links of interest to be defined. Here, we continue the study of this extended Hilbert space definition with particular emphasis on the case of Non-Abelian gauge theories. We extend the electric centre definition of Casini, Huerta and Rosabal to the Non-Abelian case and find that it differs in an important term. We also find that the entanglement entropy does not agree with the maximum number of Bell pairs that can be extracted by the processes of entanglement distillation or dilution, and give protocols which achieve the maximum bound. Finally, we compute the topological entanglement entropy which follows from the extended Hilbert space definition and show that it correctly reproduces the total quantum dimension in a class of Toric code models based on Non-Abelian discrete groups.
Applicability of the minimum entropy generation method for optimizing thermodynamic cycles
International Nuclear Information System (INIS)
Cheng Xue-Tao; Liang Xin-Gang
2013-01-01
Entropy generation is often used as a figure of merit in thermodynamic cycle optimizations. In this paper, it is shown that the applicability of the minimum entropy generation method to optimizing output power is conditional. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power when the total heat into the system of interest is not prescribed. For the cycles whose working medium is heated or cooled by streams with prescribed inlet temperatures and prescribed heat capacity flow rates, it is theoretically proved that both the minimum entropy generation rate and the minimum entropy generation number correspond to the maximum output power when the virtual entropy generation induced by dumping the used streams into the environment is considered. However, the minimum principle of entropy generation is not tenable in the case that the virtual entropy generation is not included, because the total heat into the system of interest is not fixed. An irreversible Carnot cycle and an irreversible Brayton cycle are analysed. The minimum entropy generation rate and the minimum entropy generation number do not correspond to the maximum output power if the heat into the system of interest is not prescribed. (general)
Coupling diffusion and maximum entropy models to estimate thermal inertia
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...
Application of maximum entropy method for the study of electron ...
Indian Academy of Sciences (India)
density at the mid-bond (0.003 e/Е3) at 2.118 Е from the origin leaving it more ionic than the other two sulphides studied .... (called RS refinements) using a code by the author in which the individual thermal parameters were ..... predicting metallurgical behaviour of the elements in binary alloy systems, LA-2345. (Los Alamos ...
Adaptive Statistical Language Modeling; A Maximum Entropy Approach
1994-04-19
WORKS PAINTED PAINTER LYRICAL DRAWINGS SCULP- TURES SURFACES WORK COLORS IMAGERY ABU *= ABU NIDAL TERRORIST PALESTINIAN SYRIA LIBYA INTELLIGENCE ARAB...CRUDE GASOLINE SEA MERCANTILE DELIVERY ABUSE .= ABUSE ABUSED DRUG ALCOHOL CHILDREN ABUSING CHILD COCAINE DRUGS CASES TREATMENT CARE SEXUALLY PHYSICAL...REALLY I’VE GO NEVER THINK BETMR YOUNG #= YOUNG OLD AGE MAN HER CHILDREN LIFE HIM I MEN SCHOOL SHE WOMEN COLLEGE POINT TEEN DAE STOCK YOUNG’S KIM YOUNG’S
Combining Experiments and Simulations Using the Maximum Entropy Principle
DEFF Research Database (Denmark)
Boomsma, Wouter; Ferkinghoff-Borg, Jesper; Lindorff-Larsen, Kresten
2014-01-01
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...
Application of maximum entropy method for the study of electron ...
Indian Academy of Sciences (India)
demonstrate that the integrated powder data can be used for the analysis of electron density distribution using MEM and the bonding features can be understood in a better manner. However, the limitations lie in the quality of powder data sets used for the analysis. 2. Data treatment. The powder data of SrS, BaS and PuS ...
A general maximum entropy framework for thermodynamic variational principles
International Nuclear Information System (INIS)
Dewar, Roderick C.
2014-01-01
Minimum free energy principles are familiar in equilibrium thermodynamics, as expressions of the second law. They also appear in statistical mechanics as variational approximation schemes, such as the mean-field and steepest-descent approximations. These well-known minimum free energy principles are here unified and extended to any system analyzable by MaxEnt, including non-equilibrium systems. The MaxEnt Lagrangian associated with a generic MaxEnt distribution p defines a generalized potential Ψ for an arbitrary probability distribution p-hat, such that Ψ is a minimum at (p-hat) = p. Minimization of Ψ with respect to p-hat thus constitutes a generic variational principle, and is equivalent to minimizing the Kullback-Leibler divergence between p-hat and p. Illustrative examples of min–Ψ are given for equilibrium and non-equilibrium systems. An interpretation of changes in Ψ is given in terms of the second law, although min–Ψ itself is an intrinsic variational property of MaxEnt that is distinct from the second law
Farokhi, Saeed; Taghavi, Ray; Keshmiri, Shawn
2015-11-01
Stealth technology is developed for military aircraft to minimize their signatures. The primary attention was focused on radar signature, followed by the thermal and noise signatures of the vehicle. For radar evasion, advanced configuration designs, extensive use of carbon composites and radar-absorbing material, are developed. On thermal signature, mainly in the infra-red (IR) bandwidth, the solution was found in blended rectangular nozzles of high aspect ratio that are shielded from ground detectors. For noise, quiet and calm jets are integrated into vehicles with low-turbulence configuration design. However, these technologies are totally incapable of detecting new generation of revolutionary aircraft. These shall use all electric, distributed, propulsion system that are thermally transparent. In addition, composite skin and non-emitting sensors onboard the aircraft will lead to low signature. However, based on the second-law of thermodynamics, there is no air vehicle that can escape from leaving an entropy trail. Entropy is thus the only inevitable signature of any system, that once measured, can detect the source. By characterizing the entropy field based on its statistical properties, the source may be recognized, akin to face recognition technology. Direct measurement of entropy is cumbersome, however as a derived property, it can be easily measured. The measurement accuracy depends on the probe design and the sensors onboard. One novel air data sensor suite is introduced with promising potential to capture the entropy trail.
Entropy Production in Stochastics
Directory of Open Access Journals (Sweden)
Demetris Koutsoyiannis
2017-10-01
Full Text Available While the modern definition of entropy is genuinely probabilistic, in entropy production the classical thermodynamic definition, as in heat transfer, is typically used. Here we explore the concept of entropy production within stochastics and, particularly, two forms of entropy production in logarithmic time, unconditionally (EPLT or conditionally on the past and present having been observed (CEPLT. We study the theoretical properties of both forms, in general and in application to a broad set of stochastic processes. A main question investigated, related to model identification and fitting from data, is how to estimate the entropy production from a time series. It turns out that there is a link of the EPLT with the climacogram, and of the CEPLT with two additional tools introduced here, namely the differenced climacogram and the climacospectrum. In particular, EPLT and CEPLT are related to slopes of log-log plots of these tools, with the asymptotic slopes at the tails being most important as they justify the emergence of scaling laws of second-order characteristics of stochastic processes. As a real-world application, we use an extraordinary long time series of turbulent velocity and show how a parsimonious stochastic model can be identified and fitted using the tools developed.
BAYESIAN ENTROPY FOR SPATIAL SAMPLING DESIGN OF ENVIRONMENTAL DATA
Particulate Matter (PM) has been linked to widespread public health effects, including a range of serious respiratory and cardiovascular problems, and to reduced visibility in may parts of the United States, see the Environmental Protection Agency (EPA) report (2004) and relevant...
Bayesian Cross-Entropy Reconstruction of Complex Images
1992-11-16
over that in Fig. 4. The isolated point source is restored, and the edges are crisper , but suffer from overshoot artifacts just within the airplane...outline. 6. GMEMK-median window output from data in Fig. 3. The modulus is shown. The ref- erence image was as before. The edges are crisper than in Fig
Entropy conservative finite element schemes
Tadmor, E.
1986-01-01
The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.
Quantum entropy and uncertainty for two-mode squeezed, coherent and intelligent spin states
Aragone, C.; Mundarain, D.
1993-01-01
We compute the quantum entropy for monomode and two-mode systems set in squeezed states. Thereafter, the quantum entropy is also calculated for angular momentum algebra when the system is either in a coherent or in an intelligent spin state. These values are compared with the corresponding values of the respective uncertainties. In general, quantum entropies and uncertainties have the same minimum and maximum points. However, for coherent and intelligent spin states, it is found that some minima for the quantum entropy turn out to be uncertainty maxima. We feel that the quantum entropy we use provides the right answer, since it is given in an essentially unique way.
Microscopic entropy and nonlocality
International Nuclear Information System (INIS)
Karpov, E.; Ordonets, G.; Petroskij, T.; Prigozhin, I.
2003-01-01
We have obtained a microscopic expression for entropy in terms of H function based on nonunitary Λ transformation which leads from the time evolution as a unitary group to a Markovian dynamics and unifies the reversible and irreversible aspects of quantum mechanics. This requires a new representation outside the Hilbert space. In terms of H, we show the entropy production and the entropy flow during the emission and absorption of radiation by an atom. Analyzing the time inversion experiment, we emphasize the importance of pre- and postcollisional correlations, which break the symmetry between incoming and outgoing waves. We consider the angle dependence of the H function in a three-dimensional situation. A model including virtual transitions is discussed in a subsequent paper
A gravitational entropy proposal
International Nuclear Information System (INIS)
Clifton, Timothy; Tavakol, Reza; Ellis, George F R
2013-01-01
We propose a thermodynamically motivated measure of gravitational entropy based on the Bel–Robinson tensor, which has a natural interpretation as the effective super-energy–momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein–Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson–Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein’s field equations. It is also in keeping with Penrose’s Weyl curvature hypothesis. (paper)
Linking entropy flow with typhoon evolution: a case-study
International Nuclear Information System (INIS)
Liu, C; Xu, H; Liu, Y
2007-01-01
This paper is mainly aimed at investigating the relationship of entropy flow with an atmospheric system (typhoon), based on the observational analyses covering its whole life-cycle. The formula for calculating entropy flow is derived starting with the Gibbs relation with data from the NCEP/NCAR reanalysis. The results show that: (i) entropy flow characteristics at different vertical layers of the system are heterogeneous with predominant negative entropy flow in the large portion of the troposphere and positive ones at upper levels during its development; (ii) changes in the maximum surface wind velocity or the intensity of a typhoon are synchronous with the total entropy flow around the typhoon centre and its neighbourhood, suggesting that the growth of a severe atmospheric system relies greatly upon the negative entropy flow being strong enough, and that entropy flow analysis might provide a particular point of view and a powerful tool to understand the mechanism responsible for the life-cycle of an atmospheric system and associated weather events; and (iii) the horizontal pattern of negative entropy flow near the surface might contain some significant information conducive to the track forecast of typhoons
EEG entropy measures in anesthesia
Liang, Zhenhu; Wang, Yinghua; Sun, Xue; Li, Duan; Voss, Logan J.; Sleigh, Jamie W.; Hagihira, Satoshi; Li, Xiaoli
2015-01-01
Highlights: ► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents. Methods: Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared. Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R2) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation
Thinning, photonic beamsplitting, and a general discrete entropy power inequality
Guha, Saikat; Shapiro, Jeffrey H.; Sanchez, Raul Garcia-Patron
2016-01-01
Many partially-successful attempts have been made to find the most natural discrete-variable version of Shannon's entropy power inequality (EPI). We develop an axiomatic framework from which we deduce the natural form of a discrete-variable EPI and an associated entropic monotonicity in a discrete-variable central limit theorem. In this discrete EPI, the geometric distribution, which has the maximum entropy among all discrete distributions with a given mean, assumes a role analogous to the Ga...
Quantum Entropy and Complexity
Benatti, F.; Oskouei, S. Khabbazi; Abad, A. Shafiei Deh
We study the relations between the recently proposed machine-independent quantum complexity of P. Gacs [1] and the entropy of classical and quantum systems. On one hand, by restricting Gacs complexity to ergodic classical dynamical systems, we retrieve the equality between the Kolmogorov complexity rate and the Shannon entropy rate derived by A. A. Brudno [2]. On the other hand, using the quantum Shannon-McMillan theorem [3], we show that such an equality holds densely in the case of ergodic quantum spin chains.
DEFF Research Database (Denmark)
Yuri, Shtarkov; Justesen, Jørn
1997-01-01
The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions.......The concept of entropy for an image on a discrete two dimensional grid is introduced. This concept is used as an information theoretic bound on the coding rate for the image. It is proved that this quantity exists as a limit for arbitrary sets satisfying certain conditions....
Polytomies and Bayesian phylogenetic inference.
Lewis, Paul O; Holder, Mark T; Holsinger, Kent E
2005-04-01
Bayesian phylogenetic analyses are now very popular in systematics and molecular evolution because they allow the use of much more realistic models than currently possible with maximum likelihood methods. There are, however, a growing number of examples in which large Bayesian posterior clade probabilities are associated with very short branch lengths and low values for non-Bayesian measures of support such as nonparametric bootstrapping. For the four-taxon case when the true tree is the star phylogeny, Bayesian analyses become increasingly unpredictable in their preference for one of the three possible resolved tree topologies as data set size increases. This leads to the prediction that hard (or near-hard) polytomies in nature will cause unpredictable behavior in Bayesian analyses, with arbitrary resolutions of the polytomy receiving very high posterior probabilities in some cases. We present a simple solution to this problem involving a reversible-jump Markov chain Monte Carlo (MCMC) algorithm that allows exploration of all of tree space, including unresolved tree topologies with one or more polytomies. The reversible-jump MCMC approach allows prior distributions to place some weight on less-resolved tree topologies, which eliminates misleadingly high posteriors associated with arbitrary resolutions of hard polytomies. Fortunately, assigning some prior probability to polytomous tree topologies does not appear to come with a significant cost in terms of the ability to assess the level of support for edges that do exist in the true tree. Methods are discussed for applying arbitrary prior distributions to tree topologies of varying resolution, and an empirical example showing evidence of polytomies is analyzed and discussed.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy à la Boltzmann. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September 2001 pp 19-34. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/09/0019-0034. Author Affiliations.
Aur, Dorian; Vila-Rodriguez, Fidel
2017-01-01
Complexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical systems are spatially distributed multidimensional systems. We introduced Dynamic Cross-Entropy (DCE) a novel multidimensional complexity measure that quantifies the degree of regularity of EEG signals in selected frequency bands. Time series generated by discrete logistic equations with varying control parameter r are used to test DCE measures. Sliding window DCE analyses are able to reveal specific period doubling bifurcations that lead to chaos. A similar behavior can be observed in seizures triggered by electroconvulsive therapy (ECT). Sample entropy data show the level of signal complexity in different phases of the ictal ECT. The transition to irregular activity is preceded by the occurrence of cyclic regular behavior. A significant increase of DCE values in successive order from high frequencies in gamma to low frequencies in delta band reveals several phase transitions into less ordered states, possible chaos in the human brain. To our knowledge there are no reliable techniques able to reveal the transition to chaos in case of multidimensional times series. In addition, DCE based on sample entropy appears to be robust to EEG artifacts compared to DCE based on Shannon entropy. The applied technique may offer new approaches to better understand nonlinear brain activity. Copyright Â© 2016 Elsevier B.V. All rights reserved.
Rescaling Temperature and Entropy
Olmsted, John, III
2010-01-01
Temperature and entropy traditionally are expressed in units of kelvin and joule/kelvin. These units obscure some important aspects of the natures of these thermodynamic quantities. Defining a rescaled temperature using the Boltzmann constant, T' = k[subscript B]T, expresses temperature in energy units, thereby emphasizing the close relationship…
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy à la Boltzmann. Jayanta K Bhattacharjee. General Article Volume 6 Issue 9 September 2001 pp 19-34. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/006/09/0019-0034 ...
DEFF Research Database (Denmark)
Hansen, Britt Rosendahl; Kuhn, Luise Theil; Bahl, Christian Robert Haffenden
2010-01-01
the eect: the isothermal magnetic entropy change and the adiabatic temperature change. Some of the manifestations and utilizations of the MCE will be touched upon in a general way and nally I will talk about the results I have obtained on a sample of Gadolinium Iron Garnet (GdIG, Gd3Fe5O12), which...
Indian Academy of Sciences (India)
Consider the integral. taken over a reversible transformation. We shall call this function the entropy of state A.” 'Thermodynamics' by Enrico Fermi. “Let Γ be the volume of the region of motion of the states, and. This is the basic assumption of ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 9. Entropy in Biology. Jayant B Udgaonkar. General Article Volume 6 Issue 9 September 2001 pp 61-66. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/09/0061-0066. Author Affiliations.
Zucker, M. H.
This paper is a critical analysis and reassessment of entropic functioning as it applies to the question of whether the ultimate fate of the universe will be determined in the future to be "open" (expanding forever to expire in a big chill), "closed" (collapsing to a big crunch), or "flat" (balanced forever between the two). The second law of thermodynamics declares that entropy can only increase and that this principle extends, inevitably, to the universe as a whole. This paper takes the position that this extension is an unwarranted projection based neither on experience nonfact - an extrapolation that ignores the powerful effect of a gravitational force acting within a closed system. Since it was originally presented by Clausius, the thermodynamic concept of entropy has been redefined in terms of "order" and "disorder" - order being equated with a low degree of entropy and disorder with a high degree. This revised terminology more subjective than precise, has generated considerable confusion in cosmology in several critical instances. For example - the chaotic fireball of the big bang, interpreted by Stephen Hawking as a state of disorder (high entropy), is infinitely hot and, thermally, represents zero entropy (order). Hawking, apparently focusing on the disorderly "chaotic" aspect, equated it with a high degree of entropy - overlooking the fact that the universe is a thermodynamic system and that the key factor in evaluating the big-bang phenomenon is the infinitely high temperature at the early universe, which can only be equated with zero entropy. This analysis resolves this confusion and reestablishes entropy as a cosmological function integrally linked to temperature. The paper goes on to show that, while all subsystems contained within the universe require external sources of energization to have their temperatures raised, this requirement does not apply to the universe as a whole. The universe is the only system that, by itself can raise its own
A Bayesian Framework of Uncertainties Integration in 3D Geological Model
Liang, D.; Liu, X.
2017-12-01
3D geological model can describe complicated geological phenomena in an intuitive way while its application may be limited by uncertain factors. Great progress has been made over the years, lots of studies decompose the uncertainties of geological model to analyze separately, while ignored the comprehensive impacts of multi-source uncertainties. Great progress has been made over the years, while lots of studies ignored the comprehensive impacts of multi-source uncertainties when analyzed them item by item from each source. To evaluate the synthetical uncertainty, we choose probability distribution to quantify uncertainty, and propose a bayesian framework of uncertainties integration. With this framework, we integrated data errors, spatial randomness, and cognitive information into posterior distribution to evaluate synthetical uncertainty of geological model. Uncertainties propagate and cumulate in modeling process, the gradual integration of multi-source uncertainty is a kind of simulation of the uncertainty propagation. Bayesian inference accomplishes uncertainty updating in modeling process. Maximum entropy principle makes a good effect on estimating prior probability distribution, which ensures the prior probability distribution subjecting to constraints supplied by the given information with minimum prejudice. In the end, we obtained a posterior distribution to evaluate synthetical uncertainty of geological model. This posterior distribution represents the synthetical impact of all the uncertain factors on the spatial structure of geological model. The framework provides a solution to evaluate synthetical impact on geological model of multi-source uncertainties and a thought to study uncertainty propagation mechanism in geological modeling.
Force-Time Entropy of Isometric Impulse.
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.
The Entropy-Based Quantum Metric
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Roger Balian
2014-07-01
Full Text Available The von Neumann entropy S( D ^ generates in the space of quantum density matrices D ^ the Riemannian metric ds2 = −d2S( D ^ , which is physically founded and which characterises the amount of quantum information lost by mixing D ^ and D ^ + d D ^ . A rich geometric structure is thereby implemented in quantum mechanics. It includes a canonical mapping between the spaces of states and of observables, which involves the Legendre transform of S( D ^ . The Kubo scalar product is recovered within the space of observables. Applications are given to equilibrium and non equilibrium quantum statistical mechanics. There the formalism is specialised to the relevant space of observables and to the associated reduced states issued from the maximum entropy criterion, which result from the exact states through an orthogonal projection. Von Neumann’s entropy specialises into a relevant entropy. Comparison is made with other metrics. The Riemannian properties of the metric ds2 = −d2S( D ^ are derived. The curvature arises from the non-Abelian nature of quantum mechanics; its general expression and its explicit form for q-bits are given, as well as geodesics.
Entropy, neutro-entropy and anti-entropy for neutrosophic information
Patrascu, Vasile
2017-01-01
This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: e...
Prior sensitivity analysis in default Bayesian structural equation modeling
van Erp, S.J.; Mulder, J.; Oberski, Daniel L.
2018-01-01
Bayesian structural equation modeling (BSEM) has recently gained popularity because it enables researchers to fit complex models while solving some of the issues often encountered in classical maximum likelihood (ML) estimation, such as nonconvergence and inadmissible solutions. An important
Entropy, neutro-entropy and anti-entropy for neutrosophic information
Vasile Patrascu
2017-01-01
This article shows a deca-valued representation of neutrosophic information in which are defined the following features: truth, falsity, weak truth, weak falsity, ignorance, contradiction, saturation, neutrality, ambiguity and hesitation. Using these features, there are constructed computing formulas for entropy, neutro-entropy and anti-entropy.
Entropy Measures vs. Kolmogorov Complexity
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Luís Antunes
2011-03-01
Full Text Available Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for R´enyi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we show that, for some distributions we have a similar result. We prove that, for universal time-bounded distribution mt(x, Tsallis and Rényi entropies converge if and only if α is greater than 1. We also establish the uniform continuity of these entropies.
Information Distances versus Entropy Metric
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Bo Hu
2017-06-01
Full Text Available Information distance has become an important tool in a wide variety of applications. Various types of information distance have been made over the years. These information distance measures are different from entropy metric, as the former is based on Kolmogorov complexity and the latter on Shannon entropy. However, for any computable probability distributions, up to a constant, the expected value of Kolmogorov complexity equals the Shannon entropy. We study the similar relationship between entropy and information distance. We also study the relationship between entropy and the normalized versions of information distances.
Energy Technology Data Exchange (ETDEWEB)
Weinberg, A.M.
1982-10-01
Utopians who use entropy to warn of a vast deterioration of energy and mineral resources seek a self-fulfilling prophesy when they work to deny society access to new energy sources, particularly nuclear power. While theoretically correct, entropy is not the relevant factor for the rest of this century. The more extreme entropists call for a return to an eotechnic society based on decentralized, renewable energy technologies, which rests on the assumptions of a loss in Gibbs Free Energy, a mineral depletion that will lead to OPEC-like manipulation, and a current technology that is destroying the environment. The author challenges these assumptions and calls for an exorcism of public fears over reactor accidents. He foresees a resurgence in public confidence in nuclear power by 1990 that will resolve Western dependence on foreign oil. (DCK)
Holographic Entanglement Entropy
Rangamani, Mukund
2016-01-01
We review the developments in the past decade on holographic entanglement entropy, a subject that has garnered much attention owing to its potential to teach us about the emergence of spacetime in holography. We provide an introduction to the concept of entanglement entropy in quantum field theories, review the holographic proposals for computing the same, providing some justification for where these proposals arise from in the first two parts. The final part addresses recent developments linking entanglement and geometry. We provide an overview of the various arguments and technical developments that teach us how to use field theory entanglement to detect geometry. Our discussion is by design eclectic; we have chosen to focus on developments that appear to us most promising for further insights into the holographic map. This is a preliminary draft of a few chapters of a book which will appear sometime in the near future, to be published by Springer. The book in addition contains a discussion of application o...
Entropy region and convolution
Czech Academy of Sciences Publication Activity Database
Matúš, František; Csirmaz, L.
2016-01-01
Roč. 62, č. 11 (2016), s. 6007-6018 ISSN 0018-9448 R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : entropy region * information-theoretic inequality * polymatroid Subject RIV: BD - Theory of Information Impact factor: 2.679, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/matus-0465564.pdf
Equipartition of entropy production
International Nuclear Information System (INIS)
Tondeur, D.
1990-01-01
This paper deals with the optimal design or operation of heat and mass transfer processes and develops the following conjecture: for a given duty, the best configuration of the process is that in which the entropy production rate is most uniformly distributed. This principle is first analyzed in detail on the simple example of tubular heat exchangers, and within the framework of linear irreversible thermodynamics. A main result is established, which states that the total entropy production is minimal when the local production is uniformly distributed (equipartition). Corollaries then result, which relate the entropy production and the variance of its distribution to economic factors such as the duty, the exchange area, the fluid flow-rates, and the temperature changes. The equipartition principle is then extended to multiple independent variables (time and space), multicomponent transfer, and non-linear but concave flux vs force relationship. Chemical Engineering examples are discussed, where the equipartition property has been applied implicitly or explicitly: design of distillation plates, cyclic distillation, optimal state of feed, and flow-sheets in chromatographic separations. Finally, a generalization of the equipartition principle is proposed, for systems with a distributed design variable (such as the size of the various elements of a system). The optimal distribution of investment is such that the investment in each element (properly amortized) is equal to the cost of irreversible energy degradation in this element. This is equivalent to saying that the ratio of these two quantities is uniformly distributed over the system, and reduces to equipartition of entropy production when the cost factors are constant over the whole system
Understanding Computational Bayesian Statistics
Bolstad, William M
2011-01-01
A hands-on introduction to computational statistics from a Bayesian point of view Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common statistic
Bayesian statistics an introduction
Lee, Peter M
2012-01-01
Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee’s book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as wel
Holographic entanglement entropy
Rangamani, Mukund
2017-01-01
This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part f...
Directory of Open Access Journals (Sweden)
Bernard S. Kay
2015-12-01
Full Text Available We give a review, in the style of an essay, of the author’s 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state—entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author’s recent arguments based on this alternative description which suggest that the Anti de Sitter space (AdS/conformal field theory (CFT correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory.
Thermodynamic Efficiency and Entropy Production in the Climate System
Lucarini, V.
2009-04-01
We present a succinct analysis of the thermodynamics of the climate system, studying some of its macroscopic properties in terms of the 1st law and the 2nd law of thermodynamics. We first review and clarify the notion of efficiency of the climate system treated formally as a thermal machine, and show how the Lorenz energy cycle can be framed in a macro-scale thermodynamic context. We then exploit a thermodynamic inequality to relate the Carnot efficiency of the climate system to the lower bound to the amount of entropy production. Since entropy production due to heat transport from hot to cold regions is basically the difference between the actual and the minimal entropy production, the controversial principle of maximum entropy production is given a rigorous interpretation.
Preimage entropy dimension of topological dynamical systems
Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao
2014-01-01
We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated system...
Quantum Dynamical Entropies and Gács Algorithmic Entropy
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Fabio Benatti
2012-07-01
Full Text Available Several quantum dynamical entropies have been proposed that extend the classical Kolmogorov–Sinai (dynamical entropy. The same scenario appears in relation to the extension of algorithmic complexity theory to the quantum realm. A theorem of Brudno establishes that the complexity per unit time step along typical trajectories of a classical ergodic system equals the KS-entropy. In the following, we establish a similar relation between the Connes–Narnhofer–Thirring quantum dynamical entropy for the shift on quantum spin chains and the Gács algorithmic entropy. We further provide, for the same system, a weaker linkage between the latter algorithmic complexity and a different quantum dynamical entropy proposed by Alicki and Fannes.
Entanglement entropy and differential entropy for massive flavors
International Nuclear Information System (INIS)
Jones, Peter A.R.; Taylor, Marika
2015-01-01
In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.
Entanglement entropy and differential entropy for massive flavors
Energy Technology Data Exchange (ETDEWEB)
Jones, Peter A.R. [Physics and Astronomy and STAG Research Centre, University of Southampton, Highfield, Southampton, SO17 1BJ (United Kingdom); Taylor, Marika [Mathematical Sciences and STAG Research Centre, University of Southampton, Highfield, Southampton, SO17 1BJ (United Kingdom)
2015-08-04
In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.
Scaling-Laws of Flow Entropy with Topological Metrics of Water Distribution Networks
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Giovanni Francesco Santonastaso
2018-01-01
Full Text Available Robustness of water distribution networks is related to their connectivity and topological structure, which also affect their reliability. Flow entropy, based on Shannon’s informational entropy, has been proposed as a measure of network redundancy and adopted as a proxy of reliability in optimal network design procedures. In this paper, the scaling properties of flow entropy of water distribution networks with their size and other topological metrics are studied. To such aim, flow entropy, maximum flow entropy, link density and average path length have been evaluated for a set of 22 networks, both real and synthetic, with different size and topology. The obtained results led to identify suitable scaling laws of flow entropy and maximum flow entropy with water distribution network size, in the form of power–laws. The obtained relationships allow comparing the flow entropy of water distribution networks with different size, and provide an easy tool to define the maximum achievable entropy of a specific water distribution network. An example of application of the obtained relationships to the design of a water distribution network is provided, showing how, with a constrained multi-objective optimization procedure, a tradeoff between network cost and robustness is easily identified.
Logarithmic black hole entropy corrections and holographic Renyi entropy
International Nuclear Information System (INIS)
Mahapatra, Subhash
2018-01-01
The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G D 0 . The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)
Directory of Open Access Journals (Sweden)
David W Redding
Full Text Available Statistical approaches for inferring the spatial distribution of taxa (Species Distribution Models, SDMs commonly rely on available occurrence data, which is often clumped and geographically restricted. Although available SDM methods address some of these factors, they could be more directly and accurately modelled using a spatially-explicit approach. Software to fit models with spatial autocorrelation parameters in SDMs are now widely available, but whether such approaches for inferring SDMs aid predictions compared to other methodologies is unknown. Here, within a simulated environment using 1000 generated species' ranges, we compared the performance of two commonly used non-spatial SDM methods (Maximum Entropy Modelling, MAXENT and boosted regression trees, BRT, to a spatial Bayesian SDM method (fitted using R-INLA, when the underlying data exhibit varying combinations of clumping and geographic restriction. Finally, we tested how any recommended methodological settings designed to account for spatially non-random patterns in the data impact inference. Spatial Bayesian SDM method was the most consistently accurate method, being in the top 2 most accurate methods in 7 out of 8 data sampling scenarios. Within high-coverage sample datasets, all methods performed fairly similarly. When sampling points were randomly spread, BRT had a 1-3% greater accuracy over the other methods and when samples were clumped, the spatial Bayesian SDM method had a 4%-8% better AUC score. Alternatively, when sampling points were restricted to a small section of the true range all methods were on average 10-12% less accurate, with greater variation among the methods. Model inference under the recommended settings to account for autocorrelation was not impacted by clumping or restriction of data, except for the complexity of the spatial regression term in the spatial Bayesian model. Methods, such as those made available by R-INLA, can be successfully used to account
DEFF Research Database (Denmark)
Jensen, Finn Verner; Nielsen, Thomas Dyhre
2016-01-01
is largely due to the availability of efficient inference algorithms for answering probabilistic queries about the states of the variables in the network. Furthermore, to support the construction of Bayesian network models, learning algorithms are also available. We give an overview of the Bayesian network...
Kleibergen, F.R.; Kleijn, R.; Paap, R.
2000-01-01
We propose a novel Bayesian test under a (noninformative) Jeffreys'priorspecification. We check whether the fixed scalar value of the so-calledBayesian Score Statistic (BSS) under the null hypothesis is aplausiblerealization from its known and standardized distribution under thealternative. Unlike
Yuan, Ying; MacKinnon, David P.
2009-01-01
In this article, we propose Bayesian analysis of mediation effects. Compared with conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian…
DEFF Research Database (Denmark)
Müller-Lennert, Martin; Dupont-Dupuis, Fréderic; Szehr, Oleg
2013-01-01
in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new...... quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data...
Editorial: Entropy in Landscape Ecology
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Samuel A. Cushman
2018-04-01
Full Text Available Entropy and the second law of thermodynamics are the central organizing principles of nature, but the ideas and implications of the second law are poorly developed in landscape ecology. The purpose of this Special Issue “Entropy in Landscape Ecology” in Entropy is to bring together current research on applications of thermodynamics in landscape ecology, to consolidate current knowledge and identify key areas for future research. The special issue contains six articles, which cover a broad range of topics including relationships between entropy and evolution, connections between fractal geometry and entropy, new approaches to calculate configurational entropy of landscapes, example analyses of computing entropy of landscapes, and using entropy in the context of optimal landscape planning. Collectively these papers provide a broad range of contributions to the nascent field of ecological thermodynamics. Formalizing the connections between entropy and ecology are in a very early stage, and that this special issue contains papers that address several centrally important ideas, and provides seminal work that will be a foundation for the future development of ecological and evolutionary thermodynamics.
Entanglement Entropy of Black Holes
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Sergey N. Solodukhin
2011-10-01
Full Text Available The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as ’t Hooft’s brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the black-hole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.
Katona, Gyula O H; Tardos, Gábor
2007-01-01
The present volume is a collection of survey papers in the fields of entropy, search and complexity. They summarize the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively. Search theory has variegated applications, among others in bioinformatics. Some of these papers also have links to linear statistics and communicational complexity. Further works survey the fundamentals of information theory and quantum source coding. The volume is recommended to experienced researchers as well as young scientists and students both in mathematics and computer science
Steinberg, Peter
2008-06-01
Who is the blog written by? Peter Steinberg is a nuclear physicist at the Brookhaven National Laboratory in New York, US. He is acting project manager of the PHOBOS experiment, which used Brookhaven's Relativistic Heavy Ion Collider (RHIC) to search for unusual events produced during collisions between gold nuclei. He is also involved with the PHENIX experiment, which seeks to discover a new state of matter known as the quark-gluon plasma. In addition to his own blog Entropy Bound, Steinberg is currently blogging on a website that was set up last year to publicize the involvement of US scientists with the Large Hadron Collider (LHC) at CERN.
Minimum Error Entropy Classification
Marques de Sá, Joaquim P; Santos, Jorge M F; Alexandre, Luís A
2013-01-01
This book explains the minimum error entropy (MEE) concept applied to data classification machines. Theoretical results on the inner workings of the MEE concept, in its application to solving a variety of classification problems, are presented in the wider realm of risk functionals. Researchers and practitioners also find in the book a detailed presentation of practical data classifiers using MEE. These include multi‐layer perceptrons, recurrent neural networks, complexvalued neural networks, modular neural networks, and decision trees. A clustering algorithm using a MEE‐like concept is also presented. Examples, tests, evaluation experiments and comparison with similar machines using classic approaches, complement the descriptions.
Nonextensive entropy interdisciplinary applications
Tsallis, Constantino
2004-01-01
A great variety of complex phenomena in many scientific fields exhibit power-law behavior, reflecting a hierarchical or fractal structure. Many of these phenomena seem to be susceptible to description using approaches drawn from thermodynamics or statistical mechanics, particularly approaches involving the maximization of entropy and of Boltzmann-Gibbs statistical mechanics and standard laws in a natural way. The book addresses the interdisciplinary applications of these ideas, and also on various phenomena that could possibly be quantitatively describable in terms of these ideas.
Renormalization group flow of entanglement entropy to thermal entropy
Kim, Ki-Seok; Park, Chanyong
2017-05-01
Utilizing the holographic technique, we investigate how the entanglement entropy evolves along the renormalization group flow. After introducing a new generalized temperature which satisfies the thermodynamicslike law even in the IR regime, we find that the renormalized entropy and the generalized temperature in the IR limit approach the thermal entropy and thermodynamic temperature of a real thermal system. This result implies that the microscopic quantum entanglement entropy in the IR region leads to the thermodynamic relation up to small quantum corrections caused by the quantum entanglement near the entangling surface. Intriguingly, this IR feature of the entanglement entropy universally happens regardless of the detail of the dual field theory and the shape of the entangling surface. We check this IR universality with a most general geometry called the hyperscaling violation geometry which is dual to a relativistic nonconformal field theory.
Directory of Open Access Journals (Sweden)
John Scales Avery
2012-04-01
Full Text Available In this essay, human society is regarded as a “superorganism”, analogous to colonies of social insects. The digestive system of the human superorganism is the global economy, which ingests both free energy and resources, and later excretes them in a degraded form. This process involves an increase in entropy. Early in the 20th century, both Frederick Soddy and Nicholas Georgescu-Roegen discussed the relationship between entropy and economics. Soddy called for an index system to regulate the money supply and a reform of the fractional reserve banking system, while Georgescu-Roegen pointed to the need for Ecological Economics, a steady-state economy, and population stabilization. As we reach the end of the fossil fuel era and as industrial growth falters, massive unemployment can only be avoided by responsible governmental action. The necessary steps include shifting labor to projects needed for a sustainable economy, dividing the available work fairly among those seeking employment, and reforming the practices of the financial sector.
A Note on Burg’s Modified Entropy in Statistical Mechanics
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Amritansu Ray
2016-02-01
Full Text Available Burg’s entropy plays an important role in this age of information euphoria, particularly in understanding the emergent behavior of a complex system such as statistical mechanics. For discrete or continuous variable, maximization of Burg’s Entropy subject to its only natural and mean constraint always provide us a positive density function though the Entropy is always negative. On the other hand, Burg’s modified entropy is a better measure than the standard Burg’s entropy measure since this is always positive and there is no computational problem for small probabilistic values. Moreover, the maximum value of Burg’s modified entropy increases with the number of possible outcomes. In this paper, a premium has been put on the fact that if Burg’s modified entropy is used instead of conventional Burg’s entropy in a maximum entropy probability density (MEPD function, the result yields a better approximation of the probability distribution. An important lemma in basic algebra and a suitable example with tables and graphs in statistical mechanics have been given to illustrate the whole idea appropriately.
On weighted cumulative residual Tsallis entropy and its dynamic version
Khammar, A. H.; Jahanshahi, S. M. A.
2018-02-01
Recently, Sati and Gupta (2015) have introduced a generalized cumulative residual entropy based on the non-additive Tsallis entropy. The cumulative residual entropy, introduced by Rao et al. (2004) is a generalized measure of uncertainty which is applied in reliability and image alignment and non-additive measures of entropy. This entropy finds justifications in many physical, biological and chemical phenomena. In this paper, we derive the weighted form of this measure and call it Weighted Cumulative Residual Tsallis Entropy (WCRTE). Being a "length-biased" shift-dependent information measure, WCRTE is related to the differential information in which higher weight is assigned to large values of observed random variables. Based on the dynamic version of this new information measure, we propose ageing classes and it is shown that it can uniquely determine the survival function and Rayleigh distribution. Several properties, including linear transformations, bounds and related results to stochastic orders are obtained for these measures. Also, we identify classes of distributions in which some well-known distributions are maximum dynamic version of WCRTE. The empirical WCRTE is finally proposed to estimate the new information measure.
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Prasad Radha K.
2017-09-01
Full Text Available This paper presents mathematical modelling and numerical analysis to evaluate entropy generation analysis (EGA by considering pressure drop and second law efficiency based on thermodynamics for forced convection heat transfer in rectangular duct of a solar air heater with wire as artificial roughness in the form of arc shape geometry on the absorber plate. The investigation includes evaluations of entropy generation, entropy generation number, Bejan number and irreversibilities of roughened as well as smooth absorber plate solar air heaters to compare the relative performances. Furthermore, effects of various roughness parameters and operating parameters on entropy generation have also been investigated. Entropy generation and irreversibilities (exergy destroyed has its minimum value at relative roughness height of 0.0422 and relative angle of attack of 0.33, which leads to the maximum exergetic efficiency. Entropy generation and exergy based analyses can be adopted for the evaluation of the overall performance of solar air heaters.
Prasad, Radha K.; Sahu, Mukesh K.
2017-09-01
This paper presents mathematical modelling and numerical analysis to evaluate entropy generation analysis (EGA) by considering pressure drop and second law efficiency based on thermodynamics for forced convection heat transfer in rectangular duct of a solar air heater with wire as artificial roughness in the form of arc shape geometry on the absorber plate. The investigation includes evaluations of entropy generation, entropy generation number, Bejan number and irreversibilities of roughened as well as smooth absorber plate solar air heaters to compare the relative performances. Furthermore, effects of various roughness parameters and operating parameters on entropy generation have also been investigated. Entropy generation and irreversibilities (exergy destroyed) has its minimum value at relative roughness height of 0.0422 and relative angle of attack of 0.33, which leads to the maximum exergetic efficiency. Entropy generation and exergy based analyses can be adopted for the evaluation of the overall performance of solar air heaters.
Entropy-based probabilistic fatigue damage prognosis and algorithmic performance comparison
National Aeronautics and Space Administration — In this paper, a maximum entropy-based general framework for probabilistic fatigue damage prognosis is investigated. The proposed methodology is based on an...
Entropy-based Probabilistic Fatigue Damage Prognosis and Algorithmic Performance Comparison
National Aeronautics and Space Administration — In this paper, a maximum entropy-based general framework for probabilistic fatigue damage prognosis is investigated. The proposed methodology is based on an...
Giant onsite electronic entropy enhances the performance of ceria for water splitting.
Naghavi, S Shahab; Emery, Antoine A; Hansen, Heine A; Zhou, Fei; Ozolins, Vidvuds; Wolverton, Chris
2017-08-18
Previous studies have shown that a large solid-state entropy of reduction increases the thermodynamic efficiency of metal oxides, such as ceria, for two-step thermochemical water splitting cycles. In this context, the configurational entropy arising from oxygen off-stoichiometry in the oxide, has been the focus of most previous work. Here we report a different source of entropy, the onsite electronic configurational entropy, arising from coupling between orbital and spin angular momenta in lanthanide f orbitals. We find that onsite electronic configurational entropy is sizable in all lanthanides, and reaches a maximum value of ≈4.7 k B per oxygen vacancy for Ce 4+ /Ce 3+ reduction. This unique and large positive entropy source in ceria explains its excellent performance for high-temperature catalytic redox reactions such as water splitting. Our calculations also show that terbium dioxide has a high electronic entropy and thus could also be a potential candidate for solar thermochemical reactions.Solid-state entropy of reduction increases the thermodynamic efficiency of ceria for two-step thermochemical water splitting. Here, the authors report a large and different source of entropy, the onsite electronic configurational entropy arising from coupling between orbital and spin angular momenta in f orbitals.
International Nuclear Information System (INIS)
Arjmandi, H.R.; Amani, E.
2015-01-01
In this study, we are simulating the turbulent combustion of a mixed bluff-body swirl stabilized flame in a gas turbine combustion chamber and investigating the effects of different parameters, including the swirl number, distance between the air and fuel nozzle which is called bluff size, equivalence ratio, inlet fuel flow rate, and the inlet air velocity, on the entropy generation. We perform the process of the design of the combustion chamber by proposing the optimal value of each parameter based on the EGM (entropy generation minimization) method under the two maximum allowable temperature and size constraints. Two common methods of entropy generation calculation, one based on the overall entropy balance on a system and the other based on the local entropy generation rate calculation, are used and compared in this study. Our results show that the deviation between the total entropy generations calculated by the two methods is 6.4% in average which is an acceptable error in turbulent combustion simulations. Also, the two opposing factors, namely chemical reaction and heat transfer, have the main contribution to the total entropy generation. - Highlights: • We perform the design of a combustion chamber using CFD and based on the EGM method. • We use and compare two methods for computing the total entropy generation. • We also study the entropy generation due to different phenomena separately. • Reaction and heat transfer have the dominant contribution to the entropy generation
Black brane entropy and hydrodynamics
Booth, I.; Heller, M.P.; Spaliński, M.
2010-01-01
A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics
Sample entropy analysis of cervical neoplasia gene-expression signatures
Directory of Open Access Journals (Sweden)
Salama Salama A
2009-02-01
Full Text Available Abstract 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.
Entropy Budget for Hawking Evaporation
Directory of Open Access Journals (Sweden)
Ana Alonso-Serrano
2017-07-01
Full Text Available Blackbody radiation, emitted from a furnace and described by a Planck spectrum, contains (on average an entropy of 3 . 9 ± 2 . 5 bits per photon. Since normal physical burning is a unitary process, this amount of entropy is compensated by the same amount of “hidden information” in correlations between the photons. The importance of this result lies in the posterior extension of this argument to the Hawking radiation from black holes, demonstrating that the assumption of unitarity leads to a perfectly reasonable entropy/information budget for the evaporation process. In order to carry out this calculation, we adopt a variant of the “average subsystem” approach, but consider a tripartite pure system that includes the influence of the rest of the universe, and which allows “young” black holes to still have a non-zero entropy; which we identify with the standard Bekenstein entropy.
Entropy inequalities from reflection positivity
International Nuclear Information System (INIS)
Casini, H
2010-01-01
We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for the correlators are mapped into inequalities for the entropies. We write them using a real-time version of reflection positivity, which can be generalized to general quantum systems. Using this generalization we can prove an infinite sequence of inequalities which are obeyed by the Renyi entropies of integer index. There is one independent inequality involving any number of different subsystems. In quantum field theory the inequalities acquire a simple geometrical form and are consistent with the integer index Renyi entropies being given by vacuum expectation values of twisting operators in the Euclidean formulation. Several possible generalizations and specific examples are analyzed
Bayesian data analysis for newcomers.
Kruschke, John K; Liddell, Torrin M
2018-02-01
This article explains the foundational concepts of Bayesian data analysis using virtually no mathematical notation. Bayesian ideas already match your intuitions from everyday reasoning and from traditional data analysis. Simple examples of Bayesian data analysis are presented that illustrate how the information delivered by a Bayesian analysis can be directly interpreted. Bayesian approaches to null-value assessment are discussed. The article clarifies misconceptions about Bayesian methods that newcomers might have acquired elsewhere. We discuss prior distributions and explain how they are not a liability but an important asset. We discuss the relation of Bayesian data analysis to Bayesian models of mind, and we briefly discuss what methodological problems Bayesian data analysis is not meant to solve. After you have read this article, you should have a clear sense of how Bayesian data analysis works and the sort of information it delivers, and why that information is so intuitive and useful for drawing conclusions from data.
Maximum mutual information regularized classification
Wang, Jim Jing-Yan
2014-09-07
In this paper, a novel pattern classification approach is proposed by regularizing the classifier learning to maximize mutual information between the classification response and the true class label. We argue that, with the learned classifier, the uncertainty of the true class label of a data sample should be reduced by knowing its classification response as much as possible. The reduced uncertainty is measured by the mutual information between the classification response and the true class label. To this end, when learning a linear classifier, we propose to maximize the mutual information between classification responses and true class labels of training samples, besides minimizing the classification error and reducing the classifier complexity. An objective function is constructed by modeling mutual information with entropy estimation, and it is optimized by a gradient descend method in an iterative algorithm. Experiments on two real world pattern classification problems show the significant improvements achieved by maximum mutual information regularization.
Bayesian methods for data analysis
Carlin, Bradley P.
2009-01-01
Approaches for statistical inference Introduction Motivating Vignettes Defining the Approaches The Bayes-Frequentist Controversy Some Basic Bayesian Models The Bayes approach Introduction Prior Distributions Bayesian Inference Hierarchical Modeling Model Assessment Nonparametric Methods Bayesian computation Introduction Asymptotic Methods Noniterative Monte Carlo Methods Markov Chain Monte Carlo Methods Model criticism and selection Bayesian Modeling Bayesian Robustness Model Assessment Bayes Factors via Marginal Density Estimation Bayes Factors
Statistics: a Bayesian perspective
National Research Council Canada - National Science Library
Berry, Donald A
1996-01-01
...: it is the only introductory textbook based on Bayesian ideas, it combines concepts and methods, it presents statistics as a means of integrating data into the significant process, it develops ideas...
Noncausal Bayesian Vector Autoregression
DEFF Research Database (Denmark)
Lanne, Markku; Luoto, Jani
We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution...
Granade, Christopher; Combes, Joshua; Cory, D. G.
2016-03-01
In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of-the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we address all three problems. First, we use modern statistical methods, as pioneered by Huszár and Houlsby (2012 Phys. Rev. A 85 052120) and by Ferrie (2014 New J. Phys. 16 093035), to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first priors on quantum states and channels that allow for including useful experimental insight. Finally, we develop a method that allows tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.
Vlad, Marcel Ovidiu; Tsuchiya, Masa; Oefner, Peter; Ross, John
2002-01-01
We investigate the statistical properties of systems with random chemical composition and try to obtain a theoretical derivation of the self-similar Dirichlet distribution, which is used empirically in molecular biology, environmental chemistry, and geochemistry. We consider a system made up of many chemical species and assume that the statistical distribution of the abundance of each chemical species in the system is the result of a succession of a variable number of random dilution events, which can be described by using the renormalization-group theory. A Bayesian approach is used for evaluating the probability density of the chemical composition of the system in terms of the probability densities of the abundances of the different chemical species. We show that for large cascades of dilution events, the probability density of the composition vector of the system is given by a self-similar probability density of the Dirichlet type. We also give an alternative formal derivation for the Dirichlet law based on the maximum entropy approach, by assuming that the average values of the chemical potentials of different species, expressed in terms of molar fractions, are constant. Although the maximum entropy approach leads formally to the Dirichlet distribution, it does not clarify the physical origin of the Dirichlet statistics and has serious limitations. The random theory of dilution provides a physical picture for the emergence of Dirichlet statistics and makes it possible to investigate its validity range. We discuss the implications of our theory in molecular biology, geochemistry, and environmental science.
Variational Bayesian Filtering
Czech Academy of Sciences Publication Activity Database
Šmídl, Václav; Quinn, A.
2008-01-01
Roč. 56, č. 10 (2008), s. 5020-5030 ISSN 1053-587X R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : Bayesian filtering * particle filtering * Variational Bayes Subject RIV: BC - Control Systems Theory Impact factor: 2.335, year: 2008 http://library.utia.cas.cz/separaty/2008/AS/smidl-variational bayesian filtering.pdf
Bayesian Networks An Introduction
Koski, Timo
2009-01-01
Bayesian Networks: An Introduction provides a self-contained introduction to the theory and applications of Bayesian networks, a topic of interest and importance for statisticians, computer scientists and those involved in modelling complex data sets. The material has been extensively tested in classroom teaching and assumes a basic knowledge of probability, statistics and mathematics. All notions are carefully explained and feature exercises throughout. Features include:.: An introduction to Dirichlet Distribution, Exponential Families and their applications.; A detailed description of learni
Revisiting sample entropy analysis
Govindan, R. B.; Wilson, J. D.; Eswaran, H.; Lowery, C. L.; Preißl, H.
2007-03-01
We modify the definition of sample entropy (SaEn) by incorporating a time delay between the components of the block (from which the densities are estimated) and show that the modified method characterizes the complexity of the system better than the original version. We apply the modified SaEn to the standard deterministic systems and stochastic processes (uncorrelated and long range correlated (LRC) processes) and show that the underlying complexity of the system is better quantified by the modified method. We extend this analysis to the RR intervals of the normal and congestive heart failure (CHF) subjects (available via www.physionet.org) and show that there is a good degree of separation between the two groups.
Tsallis-like entropies in quantum scattering
International Nuclear Information System (INIS)
Ion, D.B.; Ion, M.L.
1998-01-01
In this work, the following entropies in quantum scattering are defined: the informational angular entropy, S θ ; Tsallis-like angular entropies, S q (θ); the angular momentum entropy, S L ; the Tsallis-like angular momentum entropies, S q (L); the angle-angular momentum entropy, S θL . These entropies are defined as natural measures of the uncertainties corresponding to the distribution probabilities. If we are interested in obtaining a measure of uncertainty of the simultaneous realization of the probability distributions, than, we have to calculate the entropy corresponding to these distributions. The expression of angle-angular momentum entropy is given. The relation between the Tsallis entropies and the angle-angular momentum entropy is derived
The Role of Configurational Entropy in Amorphous Systems
Directory of Open Access Journals (Sweden)
Kirsten A. Graeser
2010-05-01
Full Text Available Configurational entropy is an important parameter in amorphous systems. It is involved in the thermodynamic considerations, plays an important role in the molecular mobility calculations through its appearance in the Adam-Gibbs equation and provides information on the solubility increase of an amorphous form compared to its crystalline counterpart. This paper presents a calorimetric method which enables the scientist to quickly determine the values for the configurational entropy at any temperature and obtain the maximum of information from these measurements.
Entropy Bounds and Field Equations
Directory of Open Access Journals (Sweden)
Alessandro Pesci
2015-08-01
Full Text Available For general metric theories of gravity, we compare the approach that describes/derives the field equations of gravity as a thermodynamic identity with the one which looks at them from entropy bounds. The comparison is made through the consideration of the matter entropy flux across (Rindler horizons, studied by making use of the notion of a limiting thermodynamic scale l* of matter, previously introduced in the context of entropy bounds. In doing this: (i a bound for the entropy of any lump of matter with a given energy-momentum tensor Tab is considered, in terms of a quantity, which is independent of the theory of gravity that we use; this quantity is the variation of the Clausius entropy of a suitable horizon when the element of matter crosses it; (ii by making use of the equations of motion of the theory, the same quantity is then expressed as the variation of Wald’s entropy of that horizon (and this leads to a generalized form of the generalized covariant entropy bound, applicable to general diffeomorphism-invariant theories of gravity; and (iii a notion of l* for horizons, as well as an expression for it, is given.
Population entropies estimates of proteins
Low, Wai Yee
2017-05-01
The Shannon entropy equation provides a way to estimate variability of amino acids sequences in a multiple sequence alignment of proteins. Knowledge of protein variability is useful in many areas such as vaccine design, identification of antibody binding sites, and exploration of protein 3D structural properties. In cases where the population entropies of a protein are of interest but only a small sample size can be obtained, a method based on linear regression and random subsampling can be used to estimate the population entropy. This method is useful for comparisons of entropies where the actual sequence counts differ and thus, correction for alignment size bias is needed. In the current work, an R based package named EntropyCorrect that enables estimation of population entropy is presented and an empirical study on how well this new algorithm performs on simulated dataset of various combinations of population and sample sizes is discussed. The package is available at https://github.com/lloydlow/EntropyCorrect. This article, which was originally published online on 12 May 2017, contained an error in Eq. (1), where the summation sign was missing. The corrected equation appears in the Corrigendum attached to the pdf.
Bubble Entropy: An Entropy Almost Free of Parameters.
Manis, George; Aktaruzzaman, Md; Sassi, Roberto
2017-11-01
Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors. Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation
The concept of entropy. Relation between action and entropy
Directory of Open Access Journals (Sweden)
J.-P.Badiali
2005-01-01
Full Text Available The Boltzmann expression for entropy represents the traditional link between thermodynamics and statistical mechanics. New theoretical developments like the Unruh effect or the black hole theory suggest a new definition of entropy. In this paper we consider the thermodynamics of black holes as seriously founded and we try to see what we can learn from it in the case of ordinary systems for which a pre-relativistic description is sufficient. We introduce a space-time model and a new definition of entropy considering the thermal equilibrium from a dynamic point of view. Then we show that for black hole and ordinary systems we have the same relation relating a change of entropy to a change of action.
Interval Entropy and Informative Distance
Directory of Open Access Journals (Sweden)
Fakhroddin Misagh
2012-03-01
Full Text Available The Shannon interval entropy function as a useful dynamic measure of uncertainty for two sided truncated random variables has been proposed in the literature of reliability. In this paper, we show that interval entropy can uniquely determine the distribution function. Furthermore, we propose a measure of discrepancy between two lifetime distributions at the interval of time in base of Kullback-Leibler discrimination information. We study various properties of this measure, including its connection with residual and past measures of discrepancy and interval entropy, and we obtain its upper and lower bounds.
Dynamical entropy for infinite quantum systems
International Nuclear Information System (INIS)
Hudetz, T.
1990-01-01
We review the recent physical application of the so-called Connes-Narnhofer-Thirring entropy, which is the successful quantum mechanical generalization of the classical Kolmogorov-Sinai entropy and, by its very conception, is a dynamical entropy for infinite quantum systems. We thus comparingly review also the physical applications of the classical dynamical entropy for infinite classical systems. 41 refs. (Author)
Vector entropy imaging theory with application to computerized tomography
International Nuclear Information System (INIS)
Wang Yuanmei; Cheng Jianping; Heng, Pheng Ann
2002-01-01
Medical imaging theory for x-ray CT and PET is based on image reconstruction from projections. In this paper a novel vector entropy imaging theory under the framework of multiple criteria decision making is presented. We also study the most frequently used image reconstruction methods, namely, least square, maximum entropy, and filtered back-projection methods under the framework of the single performance criterion optimization. Finally, we introduce some of the results obtained by various reconstruction algorithms using computer-generated noisy projection data from the Hoffman phantom and real CT scanner data. Comparison of the reconstructed images indicates that the vector entropy method gives the best in error (difference between the original phantom data and reconstruction), smoothness (suppression of noise), grey value resolution and is free of ghost images. (author)
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.
Directory of Open Access Journals (Sweden)
Izaak Neri
2017-02-01
Full Text Available 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.
Rodrigues da Silva, Vicente de P; Belo Filho, Adelgcio F; Rodrigues Almeida, Rafaela S; de Holanda, Romildo Morant; da Cunha Campos, João Hugo Baracuy
2016-02-15
The principle of maximum entropy can provide consistent basis to analyze water resources and geophysical processes in general. In this paper, we propose to assess the space-time variability of rainfall and streamflow in northeastern region of Brazil using the Shannon entropy. Mean values of marginal and relative entropies were computed for a 10-year period from 189 stations in the study area and entropy maps were then constructed for delineating annual and seasonal characteristics of rainfall and streamflow. The Mann-Kendall test was used to evaluate the long-term trend in marginal entropy as well as relative entropy for two sample stations. High degree of similarity was found between rainfall and streamflow, particularly during dry season. Both rainfall and streamflow variability can satisfactorily be obtained in terms of marginal entropy as a comprehensive measure of the regional uncertainty of these hydrological events. The Shannon entropy produced spatial patterns which led to a better understanding of rainfall and streamflow characteristics throughout the northeastern region of Brazil. The total relative entropy indicated that rainfall and streamflow carried the same information content at annual and rainy season time scales. Copyright © 2015 Elsevier B.V. All rights reserved.
Multi-Level Wavelet Shannon Entropy-Based Method for Single-Sensor Fault Location
Directory of Open Access Journals (Sweden)
Qiaoning Yang
2015-10-01
Full Text Available In actual application, sensors are prone to failure because of harsh environments, battery drain, and sensor aging. Sensor fault location is an important step for follow-up sensor fault detection. In this paper, two new multi-level wavelet Shannon entropies (multi-level wavelet time Shannon entropy and multi-level wavelet time-energy Shannon entropy are defined. They take full advantage of sensor fault frequency distribution and energy distribution across multi-subband in wavelet domain. Based on the multi-level wavelet Shannon entropy, a method is proposed for single sensor fault location. The method firstly uses a criterion of maximum energy-to-Shannon entropy ratio to select the appropriate wavelet base for signal analysis. Then multi-level wavelet time Shannon entropy and multi-level wavelet time-energy Shannon entropy are used to locate the fault. The method is validated using practical chemical gas concentration data from a gas sensor array. Compared with wavelet time Shannon entropy and wavelet energy Shannon entropy, the experimental results demonstrate that the proposed method can achieve accurate location of a single sensor fault and has good anti-noise ability. The proposed method is feasible and effective for single-sensor fault location.
Phase transitions and quantum entropy
International Nuclear Information System (INIS)
Arrachea, L.; Canosa, N.; Plastino, A.; Portesi, M.; Rossignoli, R.
1990-01-01
An examination is made of the possibility to predict phase transitions of the fundamental state of finite quantum system, knowing the quantum entropy of these states, defined on the basis of the information theory. (Author). 7 refs., 3 figs
Quantum entropy and special relativity.
Peres, Asher; Scudo, Petra F; Terno, Daniel R
2002-06-10
We consider a single free spin- 1 / 2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.
Mixing, entropy and competition
International Nuclear Information System (INIS)
Klimenko, A Y
2012-01-01
Non-traditional thermodynamics, applied to random behaviour associated with turbulence, mixing and competition, is reviewed and analysed. Competitive mixing represents a general framework for the study of generic properties of competitive systems and can be used to model a wide class of non-equilibrium phenomena ranging from turbulent premixed flames and invasion waves to complex competitive systems. We demonstrate consistency of the general principles of competition with thermodynamic description, review and analyse the related entropy concepts and introduce the corresponding competitive H-theorem. A competitive system can be characterized by a thermodynamic quantity—competitive potential—which determines the likely direction of evolution of the system. Contested resources tend to move between systems from lower to higher values of the competitive potential. There is, however, an important difference between conventional thermodynamics and competitive thermodynamics. While conventional thermodynamics is constrained by its zeroth law and is fundamentally transitive, the transitivity of competitive thermodynamics depends on the transitivity of the competition rules. Intransitivities are common in the real world and are responsible for complex behaviour in competitive systems. This work follows ideas and methods that have originated from the analysis of turbulent combustion, but reviews a much broader scope of issues linked to mixing and competition, including thermodynamic characterization of complex competitive systems with self-organization. The approach presented here is interdisciplinary and is addressed to the general educated readers, whereas the mathematical details can be found in the appendices. (comment)
Information entropy analysis of leopard seal vocalization bouts
Buck, John R.; Rogers, Tracey L.; Cato, Douglas H.
2004-05-01
Leopard seals (Hydrurga leptonyx) are solitary pinnipeds who are vocally active during their brief breeding season. The seals produce vocal bouts consisting of a sequence of distinct sounds, with an average length of roughly ten sounds. The sequential structure of the bouts is thought to be individually distinctive. Bouts recorded from five leopard seals during 1992-1994 were analyzed using information theory. The first-order Markov model entropy estimates were substantially smaller than the independent, identically distributed model entropy estimates for all five seals, indicative of constraints on the sequential structure of each seal's bouts. Each bout in the data set was classified using maximum-likelihood estimates from the first-order Markov model for each seal. This technique correctly classified 85% of the bouts, comparable to results in Rogers and Cato [Behaviour (2002)]. The relative entropies between the Markov models were found to be infinite in 18/20 possible cross-comparisons, indicating there is no probability of misclassifying the bouts in these 18 comparisons in the limit of long data sequences. One seal has sufficient data to compare a nonparametric entropy estimate with the Markov entropy estimate, finding only a small difference. This suggests that the first-order Markov model captures almost all the sequential structure in this seal's bouts.
A simple method for estimating the entropy of neural activity
International Nuclear Information System (INIS)
Berry II, Michael J; Tkačik, Gašper; Dubuis, Julien; Marre, Olivier; Da Silveira, Rava Azeredo
2013-01-01
The number of possible activity patterns in a population of neurons grows exponentially with the size of the population. Typical experiments explore only a tiny fraction of the large space of possible activity patterns in the case of populations with more than 10 or 20 neurons. It is thus impossible, in this undersampled regime, to estimate the probabilities with which most of the activity patterns occur. As a result, the corresponding entropy—which is a measure of the computational power of the neural population—cannot be estimated directly. We propose a simple scheme for estimating the entropy in the undersampled regime, which bounds its value from both below and above. The lower bound is the usual ‘naive’ entropy of the experimental frequencies. The upper bound results from a hybrid approximation of the entropy which makes use of the naive estimate, a maximum entropy fit, and a coverage adjustment. We apply our simple scheme to artificial data, in order to check their accuracy; we also compare its performance to those of several previously defined entropy estimators. We then apply it to actual measurements of neural activity in populations with up to 100 cells. Finally, we discuss the similarities and differences between the proposed simple estimation scheme and various earlier methods. (paper)
Minimal length, Friedmann equations and maximum density
International Nuclear Information System (INIS)
Awad, Adel; Ali, Ahmed Farag
2014-01-01
Inspired by Jacobson’s thermodynamic approach, Cai et al. have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation http://dx.doi.org/10.1103/PhysRevD.75.084003 of Friedmann equations to accommodate a general entropy-area law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ,a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p=ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.
Minimal length, Friedmann equations and maximum density
Energy Technology Data Exchange (ETDEWEB)
Awad, Adel [Center for Theoretical Physics, British University of Egypt,Sherouk City 11837, P.O. Box 43 (Egypt); Department of Physics, Faculty of Science, Ain Shams University,Cairo, 11566 (Egypt); Ali, Ahmed Farag [Centre for Fundamental Physics, Zewail City of Science and Technology,Sheikh Zayed, 12588, Giza (Egypt); Department of Physics, Faculty of Science, Benha University,Benha, 13518 (Egypt)
2014-06-16
Inspired by Jacobson’s thermodynamic approach, Cai et al. have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation http://dx.doi.org/10.1103/PhysRevD.75.084003 of Friedmann equations to accommodate a general entropy-area law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ,a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p=ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.
Bayesian Exploratory Factor Analysis
DEFF Research Database (Denmark)
Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corr......This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor......, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study confirms the validity of the approach. The method is used to produce interpretable low dimensional aggregates...
Berliner, M.
2017-12-01
Bayesian statistical decision theory offers a natural framework for decision-policy making in the presence of uncertainty. Key advantages of the approach include efficient incorporation of information and observations. However, in complicated settings it is very difficult, perhaps essentially impossible, to formalize the mathematical inputs needed in the approach. Nevertheless, using the approach as a template is useful for decision support; that is, organizing and communicating our analyses. Bayesian hierarchical modeling is valuable in quantifying and managing uncertainty such cases. I review some aspects of the idea emphasizing statistical model development and use in the context of sea-level rise.
Bayesian Exploratory Factor Analysis
Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.; Piatek, Rémi
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study confirms the validity of the approach. The method is used to produce interpretable low dimensional aggregates from a high dimensional set of psychological measurements. PMID:25431517
Energy conservation and maximal entropy production in enzyme reactions.
Dobovišek, Andrej; Vitas, Marko; Brumen, Milan; Fajmut, Aleš
2017-08-01
A procedure for maximization of the density of entropy production in a single stationary two-step enzyme reaction is developed. Under the constraints of mass conservation, fixed equilibrium constant of a reaction and fixed products of forward and backward enzyme rate constants the existence of maximum in the density of entropy production is demonstrated. In the state with maximal density of entropy production the optimal enzyme rate constants, the stationary concentrations of the substrate and the product, the stationary product yield as well as the stationary reaction flux are calculated. The test, whether these calculated values of the reaction parameters are consistent with their corresponding measured values, is performed for the enzyme Glucose Isomerase. It is found that calculated and measured rate constants agree within an order of magnitude, whereas the calculated reaction flux and the product yield differ from their corresponding measured values for less than 20 % and 5 %, respectively. This indicates that the enzyme Glucose Isomerase, considered in a non-equilibrium stationary state, as found in experiments using the continuous stirred tank reactors, possibly operates close to the state with the maximum in the density of entropy production. Copyright © 2017 Elsevier B.V. All rights reserved.
Derivation of Hunt equation for suspension distribution using Shannon entropy theory
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.
Giant onsite electronic entropy enhances the performance of ceria for water splitting
DEFF Research Database (Denmark)
Naghavi, S. Shahab; Emery, Antoine A.; Hansen, Heine Anton
2017-01-01
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 kB per oxygen vacancy for Ce4+/Ce3+ 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....
Bayesian methods for hackers probabilistic programming and Bayesian inference
Davidson-Pilon, Cameron
2016-01-01
Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples a...
Electron density distribution in Si and Ge using multipole, maximum ...
Indian Academy of Sciences (India)
The local, average and electronic structure of the semiconducting materials Si and Ge has been studied using multipole, maximum entropy method (MEM) and pair distribution function (PDF) analyses, using X-ray powder data. The covalent nature of bonding and the interaction between the atoms are clearly revealed by the ...
Bayesian logistic regression analysis
Van Erp, H.R.N.; Van Gelder, P.H.A.J.M.
2012-01-01
In this paper we present a Bayesian logistic regression analysis. It is found that if one wishes to derive the posterior distribution of the probability of some event, then, together with the traditional Bayes Theorem and the integrating out of nuissance parameters, the Jacobian transformation is an
Bayesian statistical inference
Directory of Open Access Journals (Sweden)
Bruno De Finetti
2017-04-01
Full Text Available This work was translated into English and published in the volume: Bruno De Finetti, Induction and Probability, Biblioteca di Statistica, eds. P. Monari, D. Cocchi, Clueb, Bologna, 1993.Bayesian statistical Inference is one of the last fundamental philosophical papers in which we can find the essential De Finetti's approach to the statistical inference.
Czech Academy of Sciences Publication Activity Database
Domesová, Simona; Beres, Michal
2017-01-01
Roč. 15, č. 2 (2017), s. 258-266 ISSN 1336-1376 R&D Projects: GA MŠk LQ1602 Institutional support: RVO:68145535 Keywords : Bayesian statistics * Cross-Entropy method * Darcy flow * Gaussian random field * inverse problem Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics http://advances.utc.sk/index.php/AEEE/article/view/2236
Entropy corresponding to the interior of a Schwarzschild black hole
Directory of Open Access Journals (Sweden)
Bibhas Ranjan Majhi
2017-07-01
Full Text Available Interior volume within the horizon of a black hole is a non-trivial concept which turns out to be very important to explain several issues in the context of quantum nature of black hole. Here we show that the entropy, contained by the maximum interior volume for massless modes, is proportional to the Bekenstein–Hawking expression. The proportionality constant is less than unity implying the horizon bears maximum entropy than that by the interior. The derivation is very systematic and free of any ambiguity. To do so the precise value of the energy of the modes, living in the interior, is derived by constraint analysis. Finally, the implications of the result are discussed.
Entropy corresponding to the interior of a Schwarzschild black hole
Majhi, Bibhas Ranjan; Samanta, Saurav
2017-07-01
Interior volume within the horizon of a black hole is a non-trivial concept which turns out to be very important to explain several issues in the context of quantum nature of black hole. Here we show that the entropy, contained by the maximum interior volume for massless modes, is proportional to the Bekenstein-Hawking expression. The proportionality constant is less than unity implying the horizon bears maximum entropy than that by the interior. The derivation is very systematic and free of any ambiguity. To do so the precise value of the energy of the modes, living in the interior, is derived by constraint analysis. Finally, the implications of the result are discussed.
Disentangling Complexity in Bayesian Automatic Adaptive Quadrature
Adam, Gheorghe; Adam, Sanda
2018-02-01
The paper describes a Bayesian automatic adaptive quadrature (BAAQ) solution for numerical integration which is simultaneously robust, reliable, and efficient. Detailed discussion is provided of three main factors which contribute to the enhancement of these features: (1) refinement of the m-panel automatic adaptive scheme through the use of integration-domain-length-scale-adapted quadrature sums; (2) fast early problem complexity assessment - enables the non-transitive choice among three execution paths: (i) immediate termination (exceptional cases); (ii) pessimistic - involves time and resource consuming Bayesian inference resulting in radical reformulation of the problem to be solved; (iii) optimistic - asks exclusively for subrange subdivision by bisection; (3) use of the weaker accuracy target from the two possible ones (the input accuracy specifications and the intrinsic integrand properties respectively) - results in maximum possible solution accuracy under minimum possible computing time.
Bayesian optimization for materials science
Packwood, Daniel
2017-01-01
This book provides a short and concise introduction to Bayesian optimization specifically for experimental and computational materials scientists. After explaining the basic idea behind Bayesian optimization and some applications to materials science in Chapter 1, the mathematical theory of Bayesian optimization is outlined in Chapter 2. Finally, Chapter 3 discusses an application of Bayesian optimization to a complicated structure optimization problem in computational surface science. Bayesian optimization is a promising global optimization technique that originates in the field of machine learning and is starting to gain attention in materials science. For the purpose of materials design, Bayesian optimization can be used to predict new materials with novel properties without extensive screening of candidate materials. For the purpose of computational materials science, Bayesian optimization can be incorporated into first-principles calculations to perform efficient, global structure optimizations. While re...
Lemons, Don S
2013-01-01
Striving to explore the subject in as simple a manner as possible, this book helps readers understand the elusive concept of entropy. Innovative aspects of the book include the construction of statistical entropy, the derivation of the entropy of classical systems from purely classical assumptions, and a statistical thermodynamics approach to the ideal Fermi and ideal Bose gases. Derivations are worked through step-by-step and important applications are highlighted in over 20 worked examples. Nearly 50 end-of-chapter exercises test readers' understanding. The book also features a glossary giving definitions for all essential terms, a time line showing important developments, and list of books for further study. It is an ideal supplement to undergraduate courses in physics, engineering, chemistry and mathematics.
Formulating the shear stress distribution in circular open channels based on the Renyi entropy
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.
Sonnino, Giorgio; Steinbrecher, György; Cardinali, Alessandro; Sonnino, Alberto; Tlidi, Mustapha
2013-01-01
Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing the minimum entropy production and the maximum entropy principle under the scale invariance restrictions. The obtained probability distribution presents a singularity that has immediate physical interpretation in terms of the intermittency models. The derived reference probability distribution function is interpreted as time and ensemble average of the real physical one. A generic family of stochastic processes describing noise-driven intermittency, where the stationary density distribution coincides exactly with the one resulted from entropy maximization, is presented.
DEFF Research Database (Denmark)
Hansen, Niels Christian; Loui, Psyche; Vuust, Peter
Statistical learning underlies the generation of expectations with different degrees of uncertainty. In music, uncertainty applies to expectations for pitches in a melody. This uncertainty can be quantified by Shannon entropy from distributions of expectedness ratings for multiple continuations...... of each melody, as obtained with the probe-tone paradigm. We hypothesised that statistical learning of music can be modelled as a process of entropy reduction. Specifically, implicit learning of statistical regularities allows reduction in the relative entropy (i.e. symmetrised Kullback-Leibler Divergence...... of musical training, and within-participant decreases in entropy after short-term statistical learning of novel music. Thus, whereas inexperienced listeners make high-entropy predictions, following the Principle of Maximum Entropy, statistical learning over varying timescales enables listeners to generate...
Catching homologies by geometric entropy
Felice, Domenico; Franzosi, Roberto; Mancini, Stefano; Pettini, Marco
2018-02-01
A geometric entropy is defined in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size networks by analytical methods and then large size networks by numerical techniques. Two different classes of networks, the random graphs and the scale-free networks, are investigated computing their Betti numbers and then showing the capability of geometric entropy of detecting homologies.
Text mining by Tsallis entropy
Jamaati, Maryam; Mehri, Ali
2018-01-01
Long-range correlations between the elements of natural languages enable them to convey very complex information. Complex structure of human language, as a manifestation of natural languages, motivates us to apply nonextensive statistical mechanics in text mining. Tsallis entropy appropriately ranks the terms' relevance to document subject, taking advantage of their spatial correlation length. We apply this statistical concept as a new powerful word ranking metric in order to extract keywords of a single document. We carry out an experimental evaluation, which shows capability of the presented method in keyword extraction. We find that, Tsallis entropy has reliable word ranking performance, at the same level of the best previous ranking methods.
Methods for calculating nonconcave entropies
International Nuclear Information System (INIS)
Touchette, Hugo
2010-01-01
Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and techniques: (i) microcanonical contraction, (ii) metastable branches of the free energy, (iii) generalized canonical ensembles with specific illustrations involving the so-called Gaussian and Betrag ensembles, (iv) the restricted canonical ensemble, and (v) the inverse Laplace transform. A simple long-range spin model having a nonconcave entropy is used to illustrate each method
Approximate maximum parsimony and ancestral maximum likelihood.
Alon, Noga; Chor, Benny; Pardi, Fabio; Rapoport, Anat
2010-01-01
We explore the maximum parsimony (MP) and ancestral maximum likelihood (AML) criteria in phylogenetic tree reconstruction. Both problems are NP-hard, so we seek approximate solutions. We formulate the two problems as Steiner tree problems under appropriate distances. The gist of our approach is the succinct characterization of Steiner trees for a small number of leaves for the two distances. This enables the use of known Steiner tree approximation algorithms. The approach leads to a 16/9 approximation ratio for AML and asymptotically to a 1.55 approximation ratio for MP.
International Nuclear Information System (INIS)
Sheikhzadeh, G. A.; Nikfar, M.
2013-01-01
In the present study, aspect ratio (AR) effects of a centered adiabatic rectangular obstacle numerically investigated on natural convection and entropy generation in a differentially heated enclosure filled with either water or nanofluid (Cu-water). The governing equations are solved numerically with finite volume method using the SIMPLER algorithm. The study has been done for Rayleigh numbers between 10 3 and 10 6 , the aspect ratio of 1/3, 1/2, 1, 2 and 3 and for base fluid as well as nanofluid. It is found that, using the nanofluid leads to increase the flow strength, average Nusselt number and entropy generation and decrease the Bejan number especially at high Rayleigh numbers. At low Rayleigh numbers entropy generation is very low. By increasing Rayleigh number, entropy generation and Bejan number increases. It is observed that the viscose entropy generation is more considerable than the thermal entropy generation and has dominant role in total entropy generation. The maximum entropy generation occurs at AR = 1/3 and 3 and the minimum entropy generation occurs at AR = 1 and 1/2. It is observed that the effect of AR on Nusselt number, entropy generation and Bejan number depends on Rayleigh number.
Maximum Autocorrelation Factorial Kriging
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg; Conradsen, Knut; Pedersen, John L.
2000-01-01
This paper describes maximum autocorrelation factor (MAF) analysis, maximum autocorrelation factorial kriging, and its application to irregularly sampled stream sediment geochemical data from South Greenland. Kriged MAF images are compared with kriged images of varimax rotated factors from...
Multivariate refined composite multiscale entropy analysis
Energy Technology Data Exchange (ETDEWEB)
Humeau-Heurtier, Anne, E-mail: anne.humeau@univ-angers.fr
2016-04-01
Multiscale entropy (MSE) has become a prevailing method to quantify signals complexity. MSE relies on sample entropy. However, MSE may yield imprecise complexity estimation at large scales, because sample entropy does not give precise estimation of entropy when short signals are processed. A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. Nevertheless, RCMSE is for univariate signals only. The simultaneous analysis of multi-channel (multivariate) data often over-performs studies based on univariate signals. We therefore introduce an extension of RCMSE to multivariate data. Applications of multivariate RCMSE to simulated processes reveal its better performances over the standard multivariate MSE. - Highlights: • Multiscale entropy quantifies data complexity but may be inaccurate at large scale. • A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. • Nevertheless, RCMSE is adapted to univariate time series only. • We herein introduce an extension of RCMSE to multivariate data. • It shows better performances than the standard multivariate multiscale entropy.
The entropy principle thermodynamics for the unsatisfied
Thess, André
2011-01-01
Entropy is the most important and the most difficult to understand term of thermodynamics. This book helps make this key concept understandable. It includes seven illustrative examples of applications of entropy, which are presented step by step.
Using entropy measures to characterize human locomotion.
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.
On thermodynamic limits of entropy densities
Moriya, H; Van Enter, A
We give some sufficient conditions which guarantee that the entropy density in the thermodynamic limit is equal to the thermodynamic limit of the entropy densities of finite-volume (local) Gibbs states.
Examples of Entropy-driven Ordering
Indian Academy of Sciences (India)
driven Ordering. Orientational ordering of long objects. Entropy of sliding increases. Freezing in hard-sphere systems. Vibrational entropy increases. Phase separation in hard-sphere binary mixtures with disparate sizes. More room for smaller ...
Bayesian Independent Component Analysis
DEFF Research Database (Denmark)
Winther, Ole; Petersen, Kaare Brandt
2007-01-01
In this paper we present an empirical Bayesian framework for independent component analysis. The framework provides estimates of the sources, the mixing matrix and the noise parameters, and is flexible with respect to choice of source prior and the number of sources and sensors. Inside the engine...... in a Matlab toolbox, is demonstrated for non-negative decompositions and compared with non-negative matrix factorization.......In this paper we present an empirical Bayesian framework for independent component analysis. The framework provides estimates of the sources, the mixing matrix and the noise parameters, and is flexible with respect to choice of source prior and the number of sources and sensors. Inside the engine...
Arregui, Iñigo
2018-01-01
In contrast to the situation in a laboratory, the study of the solar atmosphere has to be pursued without direct access to the physical conditions of interest. Information is therefore incomplete and uncertain and inference methods need to be employed to diagnose the physical conditions and processes. One of such methods, solar atmospheric seismology, makes use of observed and theoretically predicted properties of waves to infer plasma and magnetic field properties. A recent development in solar atmospheric seismology consists in the use of inversion and model comparison methods based on Bayesian analysis. In this paper, the philosophy and methodology of Bayesian analysis are first explained. Then, we provide an account of what has been achieved so far from the application of these techniques to solar atmospheric seismology and a prospect of possible future extensions.
Mørup, Morten; Schmidt, Mikkel N
2012-09-01
Many networks of scientific interest naturally decompose into clusters or communities with comparatively fewer external than internal links; however, current Bayesian models of network communities do not exert this intuitive notion of communities. We formulate a nonparametric Bayesian model for community detection consistent with an intuitive definition of communities and present a Markov chain Monte Carlo procedure for inferring the community structure. A Matlab toolbox with the proposed inference procedure is available for download. On synthetic and real networks, our model detects communities consistent with ground truth, and on real networks, it outperforms existing approaches in predicting missing links. This suggests that community structure is an important structural property of networks that should be explicitly modeled.