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Logit dynamics is a form of randomized game dynamics in which players have a bias toward strategic deviations that give a higher improvement in cost. It is used extensively in practice. In congestion (or potential) games, the dynamics converge to the so-called Gibbs distribution over the set of all strategy profiles when interpreted as a Markov chain. In general, logit dynamics can converge slowly to the Gibbs distribution, but beyond that, not much is known about its algorithmic aspects, nor that of the Gibbs distribution. In this work, we are interested in the following two questions for congestion games: (i) Is there an efficient algorithm for sampling from the Gibbs distribution? (ii) If yes, does there also exist natural randomized dynamics that converge quickly to the Gibbs distribution? We first study these questions in extension parallel congestion games, a well-studied special case of symmetric network congestion games. As our main result, we show that there is a simple variation on the logit dynamics that converges quickly to the Gibbs distribution in such games. We also address the first question for the class of so-called capacitated uniform congestion games and the second question for max cut games played on a complete graph. To prove our results, we rely on the recent breakthrough work of Anari et al. (2019) regarding the approximate sampling of a base of a matroid according to a strongly log-concave probability distribution. [ABSTRACT FROM AUTHOR]

Markov random fields (MRFs) are well studied during the past 50 years. Their success are mainly due to their flexibility and to the fact that they gives raise to stochastic image models. In this work, we will consider a stochastic differential equation (SDE) driven by Lévy noise. We will show that the solution $ X_v $ of the SDE is a MRF satisfying the Markov property. We will prove that the Gibbs distribution of the process $ X_v $ can be represented graphically through Feynman graphs, which are defined as a set of cliques, then we will provide applications of MRFs in image processing where the image intensity at a particular location depends only on a neighborhood of pixels.

A Gibbs distribution based combinatorial optimization algorithm for joint antenna splitting and user scheduling problem in full duplex massive multiple-input multiple-output (MIMO) system is proposed in this paper. The optimal solution of this problem can be determined by exhaustive search. However, the complexity of this approach becomes prohibitive in practice when the sample space is large, which is usually the case in massive MIMO systems. Our algorithm overcomes this drawback by converting the original problem into a Kullback-Leibler (KL) divergence minimization problem, and solving it through a related dynamical system via a stochastic gradient descent method. Using this approach, we improve the spectral efficiency (SE) of the system by performing joint antenna splitting and user scheduling. Additionally, numerical results show that the SE curves obtained with our proposed algorithm overlap with the curves achieved by exhaustive search for user scheduling. [ABSTRACT FROM AUTHOR]

Suppose n particles xi in a region of the plane (possibly representing biological individuals such as trees or smaller organisms) have a joint density proportional to exp{- Σi

We investigate a probabilistic model for routeing in a multihop ad hoc communication network, where each user sends a message to the base station. Messages travel in hops via other users, used as relays. Their trajectories are chosen at random according to a Gibbs distribution, which favors trajectories with low interference, measured in terms of signal-to-interference ratio. This model was introduced in our earlier paper, where we expressed, in the limit of a high density of users, the typical distribution of the family of trajectories in terms of a law of large numbers. In this paper, we derive its qualitative properties. We analytically identify the emerging typical scenarios in three extreme regimes. We analyze the typical number of hops and the typical length of a hop and the deviation of the trajectory from the straight line, regime 1 in the limit of a large communication area and large distances and regime 2 in the limit of a strong interference weight. In both the regimes, the typical trajectory approaches a straight line quickly, in regime 1 with equal hop lengths. Interestingly, in regime 2, the typical length of a hop diverges logarithmically in the distance of the transmitter to the base station. We further analyze (regime 3) local and global repulsive effects of a densely populated subarea on the trajectories. [ABSTRACT FROM AUTHOR]

Synthetic aperture radar (SAR) provides rich information about the Earth’s surface under all-weather and day-and-night conditions, and is applied in many relevant fields. SAR imagery semantic segmentation, which can be a final product for end users and a fundamental procedure to support other applications, is one of the most difficult challenges. This paper proposes an encoding-decoding network based on Deeplabv3+ to semantically segment SAR imagery. A new potential energy loss function based on the Gibbs distribution is proposed here to establish the semantic dependence among different categories through the relationship among different cliques in the neighborhood system. This paper introduces an improved channel and spatial attention module to the Mobilenetv2 backbone to improve the recognition accuracy of small object categories in SAR imagery. The experimental results show that the proposed method achieves the highest mean intersection over union (mIoU) and global accuracy (GA) with the least running time, which verifies the effectiveness of our method.

Abstract Most real world combinatorial optimization problems are affected by noise in the input data, thus behaving in the high noise limit like large disordered particle systems, e.g. spin glasses or random networks. Due to uncertainty in the input, optimization of such disordered instances should infer stable posterior distributions of solutions conditioned on the noisy input instance. The maximum entropy principle states that the most stable distribution given the noise influence is defined by the Gibbs distribution and it is characterized by the free energy. In this paper, we first provide rigorous asymptotics of the difficult problem to compute the free energy for two combinatorial optimization problems, namely the sparse Minimum Bisection Problem (sMBP) and Lawler's Quadratic Assignment Problem (LQAP). We prove that both problems exhibit phase transitions equivalent to the discontinuous behavior of Derrida's Random Energy Model (REM). Furthermore, the derived free energy asymptotics lead to a theoretical justification of a recently introduced concept [3] of Gibbs posterior agreement that measures stability of the Gibbs distributions when the cost function fluctuates due to randomness in the input. This relatively new stability concept may potentially provide a new method to select robust solutions for a large class of optimization problems. [ABSTRACT FROM AUTHOR]

We propose a numerical method to learn maximum entropy (MaxEnt) distributions with spatio-temporal constraints from experimental spike trains. This is an extension of two papers, [10] and [4], which proposed the estimation of parameters where only spatial constraints were taken into account. The extension we propose allows one to properly handle memory effects in spike statistics, for large-sized neural networks.

Image segmentation plays a fundamental role in many computer vision applications . It is challenging because of the vast variety of images involved and the diverse segmentation requirements in different applications. As a result, it remains an open problem after so many years of study by researchers all over the world. In this paper, we propose to segment the image by combing its global and local properties. The global properties of the image are characterized by the mean values of different pixel classes and the continuous boundary of the object or region. The local properties are characterized by the interactions of neighboring pixels and the image edge. The proposed approach consists of four basic parts corresponding to the global or local property of the image respectively: (1) The slope difference distribution that is used to compute the global mean values of different pixel classes; (2) Energy minimization to remove inhomogeneity based on Gibbs distribution that complies with local interactions of neighboring pixels; (3) The Canny operator that is used to detect the local edge of the object or the region; (4) The polynomial spline that is used to smooth the boundary of the object or the region. These four basic parts are applied one by one and each of them is indispensable for the achieved high accuracy. A large variety of images are used to validate the proposed approach and the results are favorable. [ABSTRACT FROM AUTHOR]

A novel video motion object segmentation algorithm was proposed under spatial-temporal framework. First, the inter-frame image was partitioned into some regions by the improved watershed algorithm, and the initial segmentation mask was obtained after combining the spatial and temporal segmentation results. Then a model of Markov random field was built based on regions, and the corresponding Gibbs potential energy function was defined. The optimization of solution was carried out by iterated conditional mode （ICM） method. The experiment results show that the algorithm is more effective than COST 211 analysis model.

Molecular dynamic simulations are performed to investigate a long-time evolution of different initial signals in nonlinear acoustic chains with realistic Exp-6 potential and with power potentials. First, in the chain with realistic potential, long-lifetime kink-shaped excitations are found in the system in thermodynamic equilibrium. They give sharp peaks on high-energy tile of Gibbs distribution. Travelling along the chain, each kink collects the energy from the background atoms, and, consequently, transfers it to small-amplitude phonons. Dynamic equilibrium is observed between the processes of growth and decay of the kinks.

This paper presents different recursive formulas for computing the marginals and the normalizing constant of a Gibbs distribution $$\pi $$ . The common thread is the use of the underlying Markov properties of such processes. The procedures are illustrated with several examples, particularly the Ising model. [ABSTRACT FROM AUTHOR]

We propose a numerical method to learn maximum entropy (MaxEnt) distributions with spatio-temporal constraints from experimental spike trains. This is an extension of two papers, [10] and [4], which proposed the estimation of parameters where only spatial constraints were taken into account. The extension we propose allows one to properly handle memory effects in spike statistics, for large-sized neural networks. [ABSTRACT FROM AUTHOR]

This paper elucidates the relationship between the paper [1] and the standard approach in probability theory. [ABSTRACT FROM AUTHOR]

We prove that a stochastic process of pure coagulation has at any time t ≥ 0 a time-dependent Gibbs distribution if and only if the rates ψ(i, j) of single coagulations are of the form ψ(i; j) = if(j) + jf(i), where f is an arbitrary nonnegative function on the set of positive integers. We also obtain a recurrence relation for weights of these Gibbs distributions that allow us to derive the general form of the solution and the explicit solutions in three particular cases of the function f. For the three corresponding models, we study the probability of coagulation into one giant cluster by time t > 0. [ABSTRACT FROM AUTHOR]

Abstract: Syndromic surveillance has, so far, considered only simple models for Bayesian inference. This paper details the methodology for a serious, scalable solution to the problem of combining symptom data from a network of US hospitals for early detection of disease outbreaks. The approach requires high-end Bayesian modeling and significant computation, but the strategy described in this paper appears to be feasible and offers attractive advantages over the methods that are currently used in this area. The method is illustrated by application to ten quarters worth of data on opioid drug abuse surveillance from 636 reporting centers, and then compared to two other syndromic surveillance methods using simulation to create known signal in the drug abuse database. [Copyright &y& Elsevier]

Medical image segmentation is one of the difficult tasks in image processing since the accuracy of segmentation determines the eventual success or failure of proper diagnosis. In medical imaging identification of each pixel in a region has vital importance since it can increase the standard of evaluation criteria. In this respect segmentation of brain MR images has become more significant in research and medical applications related to diagnosis of abnormality and diseases appearing in human brain. Segmentation initiates the process of extraction of various cortical tissues which is a key issue in neuroscience, to detect early neural disorders. The aim of present study is to comprehensively evaluate intensity based fuzzy C-means and Markov random field approaches, both stochastic and deterministic, for the segmentation of brain MR images into three different cortical tissues-gray matter, white matter and cerebrospinal fluid. Along with the analytical assessment of the segmentation techniques including efficiency and user interaction, this work is concentrated on empirical evaluation based on area based matrix. The results illustrate that in all respects, Markov Random field based approaches are showing better performance as compared to fuzzy C-means. Further, the Markov random field approaches are compared to find out which segmentation technique will suit which initial conditions. [ABSTRACT FROM AUTHOR]

We construct an integrated probabilistic model to capture interactions between atoms of a nanocomponent. We then use this model to assess reliabilities of nanocomponents with different structures. Several properties of our proposed model are also described under a sparseness condition. The model is an extension of our previous model based on Markovian random field theory. The proposed integrated model is flexible in that pairwise relationship information among atoms as well as features of individual atoms can be easily incorporated. An important feature that distinguishes the integrated probabilistic model from our previous model is that the integrated approach uses all available sources of information with different weights for different types of interaction. In this paper we consider the nanocomponent at a fixed moment of time, say the present moment, and we assume that the present state of the nanocomponent depends only on the present states of its atoms. [ABSTRACT FROM AUTHOR]

This paper presents a statistical-mechanics-inspired procedure for optimization of the sensor field configuration to detect mobile targets. The key idea is to capture the low-dimensional behavior of the sensor field configurations across the Pareto front in a multiobjective scenario for optimal sensor deployment, where the nondominated points are concentrated within a small region of the large-dimensional decision space. The sensor distribution is constructed using location-dependent energy-like functions and intensive temperature-like parameters in the sense of statistical mechanics. This low-dimensional representation is shown to permit rapid optimization of the sensor field distribution on a high-fidelity simulation test bed of distributed sensor networks. [ABSTRACT FROM PUBLISHER]

Backbone anatomical structure detection and labeling is a necessary step for various analysis tasks of the vertebral column. Appearance, shape and geometry measurements are necessary for abnormality detection locally at each disc and vertebrae (such as herniation) as well as globally for the whole spine (such as spinal scoliosis). We propose a two-level probabilistic model for the localization of discs from clinical magnetic resonance imaging (MRI) data that captures both pixel- and object-level features. Using a Gibbs distribution, we model appearance and spatial information at the pixel level, and at the object level, we model the spatial distribution of the discs and the relative distances between them. We use generalized expectation-maximization for optimization, which achieves efficient convergence of disc labels. Our two-level model allows the assumption of conditional independence at the pixel-level to enhance efficiency while maintaining robustness. We use a dataset that contains 105 MRI clinical normal and abnormal cases for the lumbar area. We thoroughly test our model and achieve encouraging results on normal and abnormal cases. [ABSTRACT FROM AUTHOR]

We present a number of contributions to the LP relaxation approach to weighted constraint satisfaction (= Gibbs energy minimization). We link this approach to many works from constraint programming, which relation has so far been ignored in machine vision and learning. While the approach has been mostly considered only for binary constraints, we generalize it to n-ary constraints in a simple and natural way. This includes a simple algorithm to minimize the LP-based upper bound, n-ary max-sum diffusion-however, we consider using other bound-optimizing algorithms as well. The diffusion iteration is tractable for a certain class of high-arity constraints represented as a black box, which is analogical to propagators for global constraints CSP. Diffusion exactly solves permuted n-ary supermodular problems. A hierarchy of gradually tighter LP relaxations is obtained simply by adding various zero constraints and coupling them in various ways to existing constraints. Zero constraints can be added incrementally, which leads to a cutting-plane algorithm. The separation problem is formulated as finding an unsatisfiable subproblem of a CSP. [ABSTRACT FROM AUTHOR]

Maximization of the information divergence from any hierarchical log-linear model is studied. A new upper bound on the maximum is presented and its tightness analyzed. For the models given by the bases of a matroid, the latter is related to matroid representations by partitions or, equivalently, to ideal secret-sharing schemes. A new link between the divergence maximization, the maximum-likelihood principle, and secret sharing is established. [ABSTRACT FROM AUTHOR]

In this paper, starting from Jaynes' MaxEnt methodology [10, 11], we follow the original idea of Aoki [1] to implement a canonical MaxEnt inference model for the replication of industrial firms' dynamics over a space of economic states. We develop an aggregate model to infer the distributions of agents at meso level using representative states. In particular, we estimate the access probability for agents in different states consistently with macroscopic economic constraints. The model is calibrated on the basis of a sample of firms, drawn from the AMADEUS database, within the manufacturing industry made up of nine sectors of economic activity from 1995 to 2004, and results come to experimental proof at aggregate macroscopic level. [ABSTRACT FROM AUTHOR]

The article demonstrates that a nanostructure model in statistical physics in which the interaction potential is dependent only on coordinates is very limited. Focus is made on particular interaction that is of the Lennard-Jones potential type for the fractal dimension for a nanoporous medium. Thermodynamic relations were adjusted to take into account the interaction for nanostructures.

The article deals with the new distributions in classical physics. It considers a sufficiently general classical Hamilton function and makes three assumptions concerning it. It presents theorems how the three equations given related to each other. Further, it considers a rigid constraint, which is related to the fact that although the volume is large, it is bounded. Therefore, the impact parameter cannot tend to infinity. For two particles, it is limited by the volume.

Abstract: In this paper the design of maximally flat linear phase finite impulse response (FIR) filters is considered. The problem with using the genetic algorithm (GA) in this kind of problems is the high cost of evaluating the fitness for each string in the population. The designing of optimum FIR filters under given constraints and required criteria includes exhaustive number of evaluations for filter coefficients, and the repetitive evaluations of objective functions that implicitly constitutes construction of the filter transfer functions. This problem is handled here with acceptable results utilizing Markov random fields (MRF''s) approach. We establish a new theoretical approach here and we apply it on the design of FIR filters. This approach allows us to construct an explicit probabilistic model of the GA fitness function forming what is called the “Ising GA” that is based on sampling from a Gibbs distribution. Ising GA avoids the exhaustive design of suggested FIR filters (solutions) for every string of coefficients in every generation and replace this by a probabilistic model of fitness every gap (period) of iterations. Experimentations done with Ising GA of probabilistic fitness models are less costly than those done with standard GA and with high quality solutions. [Copyright &y& Elsevier]

It has been shown that the approaches based on the postulate of equiprobability of all acceptable microstates of a dynamical system (the Gibbs distributions and the Boltzmann method) do not satisfy criteria for a theory to be applicable (specifically, agreement with experimental data and inherent consistency), unlike the approach based on the Boltzmann equation. An approach that satisfies these criteria and that is based on the abandonment of the equiprobability postulate is offered. Concepts of spontaneous and stimulated microstates, which imply the failure of the equiprobability of microstates, are introduced. The arguments for the following assertions are suggested: probability and, consequently, one-particle and many-particle distribution functions in principle cannot depend on time; the molecular chaos hypothesis leads to the inherent inconsistency of the Boltzmann equation; the relaxation process results in some ordering of gas particle behavior; the distinguishability of identical particles is a necessary condition to describe the behavior of ensemble particles in terms of probability. [ABSTRACT FROM AUTHOR]

Two measures of the influence of the prior distribution p( θ) in Bayes estimation are proposed. Both involve comparing with alternative prior distributions proportional to p( θ) s , for s ≥ 0. The first one, the influence curve for the prior distribution, is simply the curve of parameter values which are obtained as estimates when the estimation is made using p( θ) s instead of p( θ). It measures the overall influence of the prior. The second one, it the influence rate for the prior, is the derivative of this curve at s = 1, and quantifies the sensitivity to small changes or inaccuracies in the prior distribution. We give a simple formula for the influence rate in marginal posterior mean estimation, and discuss how the influence measures may be computed and used in image processing with Markov random field priors. The results are applied to an image reconstruction problem from visual field testing and to a stylized image analysis problem. [ABSTRACT FROM AUTHOR]

Our aim is to produce a tessellation of space into small voxels and, based on only a few tomographic projections of an object, assign to each voxel a label that indicates one of the components of interest constituting the object. Traditional methods are not reliable in applications, such as electron microscopy in which (due to the damage by radiation) only a few projections are available. We postulate a low level prior knowledge regarding the underlying distribution of label images, and then directly estimate the label image based on the prior and the projections. We use a relatively efficient approximation to a global search for the optimal estimate. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes how a visual system can automatically define features of interest from the observation of a large enough number of natural images. The principle complements the low-level feature extractors provided by PCA filters by analyzing their spatial interactions. This is achieved by modeling an internal representation in the system, composed with ternary variables obtained by thresholding the filters, using a Markov Random Field model. A stochastic gradient algorithm, based on statistics computed from an image database, is used to train this model. The result is a probability distribution on the internal state of the system which adjusts with its environment, under what is referred to as a principle of homeostasis. When new images enter the system, they are confronted to this internal distribution, and images which appear as salient in this regard are detected as visually relevant. A classification of these relevant images is provided, as an illustration of the model. [Copyright &y& Elsevier]

The notion of density of a finite set is introduced. We prove a general theorem of set theory which refines the Gibbs, Bose-Einstein, and Pareto distributions as well as the Zipf law. [ABSTRACT FROM AUTHOR]

Let n S‐valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r+1 of the n components in the joint distribution, we term this a lag‐r model, whose normalising constant can be computed using a forward recursion in O(Sr+1) computations, as opposed to O(Sn) for the direct computation. We show how a lag‐r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed. [ABSTRACT FROM AUTHOR]

Image modeling using Gibbs priors was previously shown, based on experiments, to be effective in image reconstruction problems. This motivated us to evaluate three methods for estimating the priors. Two of them accurately recover the parameters of the priors; however, all of them are useful for binary tomography. This is demonstrated by two sets of experiments: in one the images are from a Gibbs distribution and in the other they are typical cardiac phantom images. [Copyright &y& Elsevier]

The autologistic model is commonly used to model spatial binary data on the lattice. However, if the lattice size is too large, then exact calculation of its normalizing constant poses a major difficulty. Various different methods for estimation of model parameters, such as pseudo-likelihood, have been proposed to overcome this problem. This article presents a method to estimate the normalizing constant in an efficient manner. In particular, this allows tasks such as maximum likelihood estimation and inference for model parameters. We also consider the true likelihood approximated by the product of likelihoods for which the normalizing constant can be found by an analytic computational method by wrapping the lattice on the cylinder. This gives a simulation-free method of inference. We compare estimates of model parameters based on our new methods with the commonly used pseudo-likelihood approach. Although we have not considered Bayesian inferences here, the method can be straightforwardly extended to find posterior distributions. We apply our methods to the well-known endive data and to simulated data and find that our methods give substantially increased accuracy of estimation of model parameters. [ABSTRACT FROM AUTHOR]

Motivated by the autologistic model for the analysis of spatial binary data on the two–dimensional lattice, we develop efficient computational methods for calculating the normalizing constant for models for discrete data defined on the cylinder and lattice. Because the normalizing constant is generally unknown analytically, statisticians have developed various ad hoc methods to overcome this difficulty. Our aim is to provide computationally and statistically efficient methods for calculating the normalizing constant so that efficient likelihood–based statistical methods are then available for inference. We extend the so–called transition method to find a feasible computational method of obtaining the normalizing constant for the cylinder boundary condition. To extend the result to the free–boundary condition on the lattice we use an efficient path sampling Markov chain Monte Carlo scheme. The methods are generally applicable to association patterns other than spatial, such as clustered binary data, and to variables taking three or more values described by, for example, Potts models. [ABSTRACT FROM AUTHOR]

In this Letter, a new approach to build a neural model for the fast identification of spatiotemporal sequences is proposed. Such a model, the Stochastic Neural Sequence Identifier (SNSI), is simple and rapidly learns and identifies a given sequence. The SNSI receives as input several patterns belonging to a particular spatiotemporal sequence and produces as output a label for the sequence identified and a probability of this classification being correct. The SNSI is able to identify a sequence from patterns learned during training or novel ones, i.e., combinations of the sequence items distinct from those belonging to the trained set. The SNSI was tested on a 2D set of both closed and open trajectories with varying levels of complexity. The results suggest that the SNSI is able to recognize all the patterns presented in the training and most of the novel patterns used for testing. [ABSTRACT FROM AUTHOR]

Wavelet threshold algorithms replace small magnitude wavelet coefficients with zero and keep or shrink the other coefficients. This is basically a local procedure, because wavelet coefficients characterize the local regularity of a function. Although a wavelet transform has decorrelating properties, structures in images, like edges, are never decorrelated completely, and these structures appear in the wavelet coefficients: a classification based on a local criterion-like coefficient magnitude is not the perfect method to distinguish important, uncorrupted coefficients from coefficients dominated by noise. We therefore introduce a geometrical prior model for configurations of important wavelet coefficients and combine this with local characterization of a classical threshold procedure into a Bayesian framework. The local characterization is incorporated into the conditional model, whereas the prior model describes only configurations, not coefficient values. More precisely, local characterization favors configurations with clusters of important coefficients. In this way, we can compute, for each coefficient, the posterior probability of being "sufficiently clean." This article proposes and motivates the particular and original choice of the conditional model. Instead of introducing this Bayesian framework, we could also apply heuristic image processing techniques to find clustered configurations of large coefficients. This article also explains the benefits of the Bayesian approach compared to these simple techniques. The parameter of the prior model is estimated on an empirical basis using a pseudolikelihood criterion. [ABSTRACT FROM AUTHOR]

Markov random field(MRF) models for segmentation of noisy images are discussed. According to the maximum a posteriori criterion a configuration of an image field is regarded as an optimal estimate of the original scene when its energy is minimized. However, the minimum energy configuration does not correspond to the scene on edges of a given image, which results in errors of segmentation. Improvements of the model are made and a relaxation algorithm based on the improved model is presented using the edge information obtained by a coarse-to-fine procedure. Some examples are presented to illustrate the applicability of the algorithm to segmentation of noisy images. [ABSTRACT FROM AUTHOR]

This paper presents a reduced-complexity deterministic annealing (DA) approach for vector quantizer (VQ) design by using soft information processing with simplified assignment measures. Low-complexity distributions are designed to mimic the Gibbs distribution, where the latter is the optimal distribution used in the standard DA method. These low-complexity distributions are simple enough to facilitate fast computation, but at the same time they can closely approximate the Gibbs distribution to result in near-optimal performance. We have also derived the theoretical performance loss at a given system entropy due to using the simple soft measures instead of the optimal Gibbs measure. We use thederived result to obtain optimal annealing schedules for the simple soft measures that approximate the annealing schedule for the optimal Gibbs distribution. The proposed reduced-complexity DA algorithms have significantly improved the quality of the final codebooks compared to the generalized Lloyd algorithm and standard stochastic relaxation techniques, both with and without the pairwise nearest neighbor (PNN) codebook initialization. The proposed algorithms are able to evade the local minima and the results show that they are not sensitive to the choice of the initial codebook. Compared to the standard DA approach, the reduced-complexity DA algorithms can operate over 100 times faster with negligible performance difference. For example, for the design of a 16-dimensional vector quantizer having a rate of 0.4375 bit/sample for Gaussian source, the standard DA algorithm achieved 3.60 dB performance in 16 483 CPU seconds, whereas the reduced-complexity DA algorithm achieved the same performance in 136 CPU seconds. Other than VQ design, the DA techniques are applicable to problems such as classification, clustering, and resource allocation.

Synthetic aperture radar (SAR) provides rich information about the Earth's surface under all-weather and day-and-night conditions, and is applied in many relevant fields. SAR imagery semantic segmentation, which can be a final product for end users and a fundamental procedure to support other applications, is one of the most difficult challenges. This paper proposes an encoding-decoding network based on Deeplabv3+ to semantically segment SAR imagery. A new potential energy loss function based on the Gibbs distribution is proposed here to establish the semantic dependence among different categories through the relationship among different cliques in the neighborhood system. This paper introduces an improved channel and spatial attention module to the Mobilenetv2 backbone to improve the recognition accuracy of small object categories in SAR imagery. The experimental results show that the proposed method achieves the highest mean intersection over union (mIoU) and global accuracy (GA) with the least running time, which verifies the effectiveness of our method. [ABSTRACT FROM AUTHOR]