distributional strategies for games with incomplete information we study games with incomplete information from a point of view which emphasizes the empirical predictions arising from game theoretic models using the notion of distributional strategies we prove four main theorems i a mixed strategy nash equilibrium existence theorem ii a pure strategy equilibrium existence theorem iii a pure strategy equilibrium existence theorem and iv a theorem describing how the set of equilibria of a game varies with the parameters of the game

communication and equilibrium in discontinuous games of incomplete information this paper offers a new approach to the study of economic problems usually modeled as games of incomplete information with discontinuous payoffs typically the discontinuities arise from indeterminacies ties in the underlying problem the point of view taken here is that the tie breaking rules that resolve these indeterminacies should be viewed as part of the solution rather than part of the description of the model a solution is therefore a tie breaking rule together with strategies satisfying the usual best response criterion when information is incomplete solutions need not exist that is there may be no tie breaking rule that is compatible with the existence of strategy profiles satisfying the usual best response criteria it is shown that the introduction of incentive compatible communication cheap talk restores existence

effective nonparametric estimation in the case of severely discretized data often economic data are discretized or rounded to some extent this paper proposes a regression and a density estimator that work especially well when discretization causes conventional kernel based estimators to behave poorly the estimator proposed here is a weighted average of neighboring frequency estimators and the weights are composed of cubic b splines interestingly we show that this estimator can have both a smaller bias and variance than frequency estimators as a means to obtain asymptotic normality and rates of convergence we assume that the discreteness becomes finer as the sample size increases

multi level monte carlo weak galerkin method with nested meshes for stochastic brinkman problem abstract this paper is devoted to the numerical analysis of a multi level monte carlo weak galerkin mlmcwg approximation with nested meshes for solving stochastic brinkman equations with two dimensional spatial domain with weak gradient operator and a stabilizer at hand the weak galerkin wg technique is a high order accurate and stable method which can easily handle deterministic partial differential equations with complex geometries flows with jump fluid viscosity coefficients or high contrast permeability fields given by each sample the multi level monte carlo mlmc technique with nested meshes balances the sampling error and the spatial approximation error where the computational cost can be sharply reduced to log linear complexity with respect to the degree of freedom in spatial direction the nested meshes requirement is introduced here in order to simplify the analysis which can be generalized to mlmc with non nested meshes error estimates are derived in terms of the spatial meshsize and the number of samples the numerical tests are provided to illustrate the behavior of the mlmcwg method and verify our theoretical results regarding optimal convergence of the approximate solutions

numerical simulation of creeping fluid flow in reconstruction models of porous media abstract in this paper we examine representative examples of realistic three dimensional models for porous media by comparing their geometry and permeability with those of the original experimental specimen the comparison is based on numerically exact evaluations of permeability porosity specific internal surface mean curvature euler number and local percolation probabilities the experimental specimen is a three dimensional computer tomographic image of fontainebleau sandstone the three models are stochastic reconstructions for which many of the geometrical characteristics coincide with those of the experimental specimen we find that in spite of the similarity in the geometrical properties the permeability and formation factor can differ greatly between models and the experiment

pore network extraction from micro computerized tomography images network models that represent the void space of a rock by a lattice of pores connected by throats can predict relative permeability once the pore geometry and wettability are known micro computerized tomography scanning provides a three dimensional image of the pore space however these images cannot be directly input into network models in this paper a modified maximal ball algorithm extending the work of silin and patzek d silin and t patzek physica a 371 336 2006 is developed to extract simplified networks of pores and throats with parametrized geometry and interconnectivity from images of the pore space the parameters of the pore networks such as coordination number and pore and throat size distributions are computed and compared to benchmark data from networks extracted by other methods experimental data and direct computation of permeability and formation factor on the underlying images good agreement is reached in most cases allowing networks derived from a wide variety of rock types to be used for predictive modeling

using convex quadratic programming to model random media with gaussian random fields excursion sets of gaussian random fields grfs have been frequently used in the literature to model two phase random media with measurable phase autocorrelation functions the goal of successful modeling is finding the optimal field autocorrelation function that best approximates the prescribed phase autocorrelation function in this paper we present a technique which uses convex quadratic programming to find the best admissible field autocorrelation function under a prescribed discretization unlike previous methods this technique efficiently optimizes over all admissible field autocorrelation functions instead of optimizing only over a predetermined parametrized family the results from using this technique indicate that the grf model is significantly more versatile than observed in previous studies an application to modeling a base catalyzed tetraethoxysilane aerogel system given small angle neutron scattering data is also presented

a stochastic ansatz and its relationship with the dichotomic markov process abstract it is shown that a simple stochastic ansatz for the solution of a stochastic differential equation leads to exact results for the dichotomic markov process this has implications for more complex problems where the ansatz leads to a simplified approach to the solution of stochastic equations in engineering and applied physics

development of optimal models of porous media by combining static and dynamic data the permeability and porosity distributions we describe a method for the development of the optimal spatial distributions of the porosity phi and permeability k of a large scale porous medium the optimal distributions are constrained by static and dynamic data the static data that we utilize are limited data for phi and k which the method honors in the optimal model and utilizes their correlation functions in the optimization process the dynamic data include the first arrival fa times at a number of receivers of seismic waves that have propagated in the porous medium and the time dependent production rates of a fluid that flows in the medium the method combines the simulated annealing method with a simulator that solves numerically the three dimensional 3d acoustic wave equation and computes the fa times and a second simulator that solves the 3d governing equation for the fluid s pressure as a function of time to our knowledge this is the first time that an optimization method has been developed to determine simultaneously the global minima of two distinct total energy functions as a stringent test of the method s accuracy we solve for flow of two immiscible fluids in the same porous medium without using any data for the two phase flow problem in the optimization process we show that the optimal model in addition to honoring the data also yields accurate spatial distributions of phi and k as well as providing accurate quantitative predictions for the single and two phase flow problems the efficiency of the computations is discussed in detail

microstructure reconstruction using entropic descriptors a multi scale approach to the inverse reconstruction of a pattern s microstructure is reported instead of a correlation function a pair of entropic descriptors eds is proposed for a stochastic optimization method the first of them measures a spatial inhomogeneity for a binary pattern or compositional one for a greyscale image the second one quantifies a spatial or compositional statistical complexity the eds reveal structural information that is dissimilar at least in part to that given by correlation functions at almost all discrete length scales the method is tested on a few digitized binary and greyscale images in each of the cases the persuasive reconstruction of the microstructure is found

classification of missing values in spatial data using spin models a problem of current interest is the estimation of spatially distributed processes at locations where measurements are missing linear interpolation methods rely on the gaussian assumption which is often unrealistic in practice or normalizing transformations which are successful only for mild deviations from the gaussian behavior we propose to address the problem of missing value estimation on two dimensional grids by means of spatial classification methods based on spin ising potts and clock models the spin variables provide an interval discretization of the process values and the spatial correlations are captured in terms of interactions between the spins the spins at the unmeasured locations are classified by means of the energy matching principle the correlation energy of the entire grid including prediction sites is estimated from the sample based correlations we investigate the performance of the spin classifiers in terms of computational speed misclassification rate class histogram and spatial correlations reproduction using simulated realizations of spatial random fields real rainfall data and a digital test image we also compare the spin based methods with standard classifiers such as the k nearest neighbor the fuzzy k nearest neighbor and the support vector machine we find that the spin based classifiers provide competitive choices

consistency of orthogonal series density estimators based on grouped observations in this correspondence we show that nonparametric orthogonal series estimators of probability densities retain the mean integrated square error mise consistency when observations are grouped to the points of a uniform grid prebinned this kind of grouping is typical for computer rounding errors and may also be useful in data compression before calculating estimates e g using the fft the main result shows that mise consistency holds for all square integrable densities under mild conditions on the grid step size

effect of the image resolution on the statistical descriptors of heterogeneous media the characterization and reconstruction of heterogeneous materials such as porous media and electrode materials involve the application of image processing methods to data acquired by scanning electron microscopy or other microscopy techniques among them binarization and decimation are critical in order to compute the correlation functions that characterize the microstructure of the above mentioned materials in this study we present a theoretical analysis of the effects of the image size reduction due to the progressive and sequential decimation of the original image three different decimation procedures random bilinear and bicubic were implemented and their consequences on the discrete correlation functions two point line path and pore size distribution and the coarseness derived from the local volume fraction are reported and analyzed the chosen statistical descriptors correlation functions and coarseness are typically employed to characterize and reconstruct heterogeneous materials a normalization for each of the correlation functions has been performed when the loss of statistical information has not been significant for a decimated image its normalized correlation function is forecast by the trend of the original image reference function in contrast when the decimated image does not hold statistical evidence of the original one the normalized correlation function diverts from the reference function moreover the equally weighted sum of the average of the squared difference between the discrete correlation functions of the decimated images and the reference functions leads to a definition of an overall error during the first stages of the gradual decimation the error remains relatively small and independent of the decimation procedure above a threshold defined by the correlation length of the reference function the error becomes a function of the number of decimation steps at this stage some statistical information is lost and the error becomes dependent on the decimation procedure these results may help us to restrict the amount of information that one can afford to lose during a decimation process in order to reduce the computational and memory cost when one aims to diminish the time consumed by a characterization or reconstruction technique yet maintaining the statistical quality of the digitized sample

microstructural degeneracy associated with a two point correlation function and its information content a two point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function in an earlier letter gommes jiao and torquato phys rev lett 108 080601 2012 we addressed the microstructural degeneracy question what is the number of microstructures compatible with a specified correlation function we computed this degeneracy i e configurational entropy in the framework of reconstruction methods which enabled us to map the problem to the determination of ground state degeneracies here we provide a more comprehensive presentation of the methodology and analyses as well as additional results since the configuration space of a reconstruction problem is a hypercube on which a hamming distance is defined we can calculate analytically the energy profile of any reconstruction problem corresponding to the average energy of all microstructures at a given hamming distance from a ground state the steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem which can be used as a proxy for the ground state degeneracy the relationship between this roughness metric and the ground state degeneracy is calibrated using a monte carlo algorithm for determining the ground state degeneracy of a variety of microstructures including realizations of hard disks and poisson point processes at various densities as well as those with known degeneracies e g single disks of various sizes and a particular crystalline microstructure we show that our results can be expressed in terms of the information content of the two point correlation functions from this perspective the a priori condition for a reconstruction to be accurate is that the information content expressed in bits should be comparable to the number of pixels in the unknown microstructure we provide a formula to calculate the information content of any two point correlation function which makes our results broadly applicable to any field in which correlation functions are employed

on the realizability of pair correlation functions abstract the pair correlation function g 2 r provides a basic geometric descriptor for many particle systems it must obey two necessary conditions i non negativity for all distances r and ii non negativity of its associated structure factor s k for all k here we utilize an improved stochastic construction algorithm for particle configurations to establish conditions in which i and ii are also sufficient i e g 2 r is in fact realizable two types of target pair correlation functions have been investigated in one two and three dimensions for hard core particles specifically a unit step function and a contact plus step pair correlation function results indicate that the former target function is realizable up to a terminal density set by necessary condition ii at which the particle core packing fraction equals 2 d in d dimensions furthermore results are consistent with the proposition that for d 1 the contact plus step function is realizable up to a terminal density due to condition ii at which the packing fraction of cores is d 2 2 d 1 torquato and stillinger j phys chem b 106 2000 8354 11406

efficient uncertainty quantification for permeability of three dimensional porous media through image analysis and pore scale simulations in this paper we propose an efficient coupled approach for uncertainty quantification of permeability for randomly reconstructed three dimensional 3d pore images where the porosity and two point correlations of a realistic sandstone sample are honored the joshi quiblier adler approach and karhunen loeve expansion are utilized for quick reconstruction of 3d pore images with reduced random dimensionality the eigenvalue problem for the covariance matrix of 3d intermediate gaussian random fields is solved equivalently by a kernel method then the lattice boltzmann method is adopted to simulate fluid flow in reconstructed pore space and evaluate permeability lastly the sparse polynomial chaos expansion sparse pce integrated with a feature selection method is employed to predict permeability distributions incurred by the randomness in microscopic pore structures the feature selection process which is intended to discard redundant basis functions is carried out by the least absolute shrinkage and selection operator modified least angle regression along with cross validation the competence of our proposed approach is validated by the results from monte carlo simulation it reveals that a small number of samples is sufficient for sparse pce with feature selection to produce convincing results then we utilize our method to quantify the uncertainty of permeability under different porosities and correlation parameters it is found that the predicted permeability distributions for reconstructed 3d pore images are close to experimental measurements of berea sandstones in the literature in addition the results show that porosity and correlation length are the critical influence factors for the uncertainty of permeability

boolean reconstructions of complex materials integral geometric approach we show that for the boolean model of random composite media one can from a single image of a system at any particle fraction define a set of parameters which allows one to accurately reconstruct the medium for all other phase fractions the morphological characterization is based on a family of measures known in integral geometry which provides powerful formulas for the boolean model the percolation thresholds of either phase are obtained with good accuracy from the reconstructions one can subsequently predict property curves for the material across all phase fractions from the single three dimensional image we illustrate this for transport and mechanical properties of complex boolean systems and for experimental sandstone samples

the existence of subgame perfect equilibrium in continuous games with almost perfect information a case for public randomization the starting point of this paper is a simple regular dynamic game in which subgame perfect equilibrium fails to exist examination of this example shows that existence would be restored if players were allowed to observe the output of a public randomization device the main result of the paper shows that the introduction of public randomization yields existence not only in the example but also in a large class of dynamic games it is also argued that the introduction of public randomization is the minimal robust extension of subgame perfect equilibrium in this class of games

multi level monte carlo weak galerkin method for elliptic equations with stochastic jump coefficients in this paper we present a multi level monte carlo weak galerkin method for solving elliptic equations with stochastic jump coefficients the multi level monte carlo technique balances the spatial approximation error and the sampling error the weak galerkin technique is a stable and high order accurate method which can easily handle deterministic partial differential equations with complex geometries or jump coefficients given by each sample and this method is also able to capture highly complex solutions exhibiting discontinuities or oscillations with high resolution comparing with the standard monte carlo method by using the multi level monte carlo weak galerkin method the computational cost can be sharply reduced to log linear complexity with respect to the degree of freedom in spatial direction the numerical experiments verify the efficiency of our algorithms

entropic descriptor of a complex behaviour abstract we propose a new type of entropic descriptor that is able to quantify the statistical complexity a measure of complex behaviour by taking simultaneously into account the average departures of a system s entropy s from both its maximum possible value s max and its minimum possible value s min when these two departures are similar to each other the statistical complexity is maximal we apply the new concept to the variability over a range of length scales of spatial or grey level pattern arrangements in simple models the pertinent results confirm the fact that a highly non trivial length scale dependence of the entropic descriptor makes it an adequate complexity measure able to distinguish between structurally distinct configurational macrostates with the same degree of disorder a feature that makes it a good tool for discerning structures in complex patterns

estimation of the influence of second and third order moments on random sets reconstructions abstract to characterize a random image we often limit ourselves to the use of two functions the first one is the histogram or grey level distribution the other is the covariance function which allows the study of the spatial grey level distribution one evaluation of the relevance of these two functions to describe the morphology of images is presented especially we show the importance of having recourse to the centered third order moment in addition to these two functions to obtain a fine characterization of images this study is done for binary random images generated from the same primary grains poisson polygons or discs that are implanted in different ways we simulate with the gagalowicz s procedure some textures respecting the same second or third order moments we study the resemblance in term of the morphology described with erosion and dilation curves and with granulometry by opening and pseudo granulometry by closing with squares the analysis of the results of these measurements is carried out with the help of correspondence analysis that allows a quantitative and qualitative approach of the differences of morphology

modeling multiscale diffusion processes in random heterogeneous media a simple stochastic up scaling strategy is presented for incorporating the effects of micro scale variations of thermal conductivity in the thermal analysis of macro scale systems incomplete characterization of the fine scale variation necessitates posing the thermal conductivity as a stochastic multiscale random field a data driven approach coupled with a non linear dimension reduction algorithm is used to construct a low dimensional stochastic descriptor of the fine scale variation of the stochastic conductivity a representative volume element rve argument is utilized to construct a simple model for up scaling the stochastic thermal conductivity in this model the effective stochastic thermal conductivity is estimated by virtually interrogating the stochastic rv a realistic example of the proposed stochastic multiscale diffusion strategy is illustrated utilizing limited experimental data

on the existence of nash equilibrium in bayesian games we furnish conditions on the primitives of a bayesian game that guarantee the existence of a bayes nash equilibrium by allowing for payoff discontinuities in actions we cover various applications that cannot be handled by extant results

compressing random microstructures via stochastic wang tilings this rapid communication presents a stochastic wang tiling based technique to compress or reconstruct disordered microstructures on the basis of given spatial statistics unlike the existing approaches based on a single unit cell it utilizes a finite set of tiles assembled by a stochastic tiling algorithm thereby allowing to accurately reproduce long range orientation orders in a computationally efficient manner although the basic features of the method are demonstrated for a two dimensional particulate suspension the present framework is fully extensible to generic multidimensional media

on locally adaptive density estimation abstract theoretical and practical aspects of the sample point adaptive positive kernel density estimator are examined a closed form expression for the mean integrated squared error is obtained through the device of preprocessing the data by binning with this expression the exact behavior of the optimally adaptive smoothing parameter function is studied for the first time the approach differs from most earlier techniques in that bias of the adaptive estimator remains o h 2 and is not improved to the rate o h 4 a practical algorithm is constructed using a modification of least squares cross validation simulated and real examples are presented including comparisons with a fixed bandwidth estimator and a fully automatic version of abramson s adaptive estimator the results are very promising

modeling heterogeneous materials via two point correlation functions ii algorithmic details and applications in the first part of this series of two papers we proposed a theoretical formalism that enables one to model and categorize heterogeneous materials media via two point correlation functions s2 and introduced an efficient heterogeneous medium reconstruction algorithm called the lattice point algorithm here we discuss the algorithmic details of the lattice point procedure and an algorithm modification using surface optimization to further speed up the reconstruction process the importance of the error tolerance which indicates to what accuracy the media are reconstructed is also emphasized and discussed we apply the algorithm to generate three dimensional digitized realizations of a fontainebleau sandstone and a boron carbide aluminum composite from the two dimensional tomographic images of their slices through the materials to ascertain whether the information contained in s2 is sufficient to capture the salient structural features we compute the two point cluster functions of the media which are superior signatures of the microstructure because they incorporate topological connectedness information we also study the reconstruction of a binary laser speckle pattern in two dimensions in which the algorithm fails to reproduce the pattern accurately we conclude that in general reconstructions using s2 only work well for heterogeneous materials with single scale structures however two point information via s2 is not sufficient to accurately model multiscale random media moreover we construct realizations of hypothetical materials with desired structural characteristics obtained by manipulating their two point correlation functions

discretized and interpolated kernel density estimates abstract the kernel estimate of a probability density function inherits its smoothness properties from the kernel density chosen by the investigator nevertheless for computational and especially graphical reasons exact kernel density estimates are often presented in piecewise constant discretized or piecewise linear interpolated form using the exact estimate only at some grid of points the asymptotic integrated mean squared error properties of these modifications are studied it is seen that discretization may adversely affect the order of magnitude of this risk criterion so care needs to be taken in practice to limit the degree of discretization employed this roughness effect essentially disappears when interpolation is used instead then it takes a remarkably coarse grid to result in more than a negligible deterioration in the estimate s performance data discretization prior to applying the kernel density estimation prescription is also addressed such prebinning does not affect the smoot

pore space reconstruction of vuggy carbonates using microtomography and multiple point statistics 1 to reconstruct complex porous media such as carbonates we propose a two step approach to combine different types of images microtomography at the resolution of a few microns to resolve large pores and vugs with statistically reconstructed high resolution images for smaller features two dimensional 2 d thin sections provide multiple point statistics which describe the statistical relation between multiple spatial locations that can be used to generate 3 d images with accurate connectivity these statistical reconstructions are combined with images directly measured by microtomography the integrated method is tested on carbonates for which 3 d images of disconnected vugs are captured while 2 d thin sections characterize the small scale structure the integrated images have permeabilities computed using the lattice boltzmann method that are similar to laboratory measured values

equilibrium refinement for infinite normal form games we present three distinct approaches to perfect and proper equilibria for infinite normal form games in the first two approaches players tremble in the infinite games playing full support approximate best responses to others strategies in the strong approach a tremble assigns high probability to the set of pure best responses in the weak approach it assigns high probability to a neighborhood of this set the third limit of finite approach applies traditional refinements to sequences of successively larger finite games overall the strong approach to equilibrium refinement most fully respects the structure of infinite games

prediction of permeability for porous media reconstructed using multiple point statistics to predict multiphase flow through geologically realistic porous media it is necessary to have a three dimensional 3d representation of the pore space we use multiple point statistics based on two dimensional 2d thin sections as training images to generate geologically realistic 3d pore space representations thin section images can provide multiple point statistics which describe the statistical relation between multiple spatial locations and use the probability of occurrence of particular patterns assuming that the medium is isotropic a 3d image can be generated that preserves typical patterns of the void space seen in the thin sections the method is tested on berea sandstone for which a 3d image from micro ct computerized tomography scanning is available and shows that the use of multiple point statistics allows the long range connectivity of the structure to be preserved in contrast to two point statistics methods that tend to underestimate the connectivity furthermore a high resolution 2d thin section image of a carbonate reservoir rock is used to reconstruct 3d structures by the proposed method the permeabilities of the statistical images are computed using the lattice boltzmann method lbm the results are similar to the measured values to the permeability directly computed on the micro ct image for berea and to predictions using analysis of the 2d images and the effective medium approximation

the influence of rounding errors on some nonparametric estimators of a density and its derivatives all continuous data is rounded to some extent and this rounding introduces errors into the estimation of the parent density and its derivatives in this paper we examine the influence of rounding errors on the two most popular types of nonparametric density estimator those based on kernels and those based on generalized fourier series our results lead directly to several important conclusions which are very relevant to the practical problems of density estimation

achieving higher order convergence rates for density estimation with binned data abstract a method is proposed for achieving fast o n 8 9 and faster asymptotic mean integrated squared error amise convergence rates in density estimation using data condensed to standard histogram bin counts and edges the method involves the two elements of b splines and the correct mass proportions property in which the probability mass for the histogram bins equals exactly the fraction of the data found in those bins it is shown that the asymptotic bias of such an estimate using a spline of order p and bin width h will be o hp resulting in optimal amise of o n 2p 2p 1 form theoretical and numeric comparisons to kernel based and other estimators show that the histospline estimator is usually comparable and often superior an extension to the multivariate density estimation setting is described

reconstructing random media we formulate a procedure to reconstruct the structure of general random heterogeneous media from limited morphological information by extending the methodology of rintoul and torquato j colloid interface sci bold 186 467 1997 developed for dispersions the procedure has the advantages that it is simple to implement and generally applicable to multidimensional multiphase and anisotropic structures furthermore an extremely useful feature is that it can incorporate any type and number of correlation functions in order to provide as much morphological information as is necessary for accurate reconstruction we consider a variety of one and two dimensional reconstructions including periodic and random arrays of rods various distribution of disks debye random media and a fontainebleau sandstone sample we also use our algorithm to construct heterogeneous media from specified hypothetical correlation functions including an exponentially damped oscillating function as well as physically unrealizable ones copyright ital 1998 ital the american physical society

fractal heterogeneous media a method is presented for generating compact fractal disordered media by generalizing the random midpoint displacement algorithm the obtained structures are invasive stochastic fractals with the hurst exponent varying as a continuous parameter as opposed to lacunar deterministic fractals such as the menger sponge by employing the detrending moving average algorithm a carbone phys rev e 76 056703 2007 the hurst exponent of the generated structure can be subsequently checked the fractality of such a structure is referred to a property defined over a three dimensional topology rather than to the topology itself consequently in this framework the hurst exponent should be intended as an estimator of compactness rather than of roughness applications can be envisaged for simulating and quantifying complex systems characterized by self similar heterogeneity across space for example exploitation areas range from the design and control of multifunctional self assembled artificial nanostructures and microstructures to the analysis and modeling of complex pattern formation in biology environmental sciences geomorphological sciences etc

on the generation of periodic discrete structures with identical two point correlation strategies for the generation of periodic discrete structures with identical two point correlation called 2pc equivalent are developed it is shown that starting from a set of 2pc equivalent root structures 2pc equivalent child structures of arbitrary resolution and number of phases e g material phases can be generated based on phase extension through trivial embeddings kernel based extension and phase coalescence proofs are provided by means of discrete fourier transform theory a python 3 implementation is offered for reproduction of examples and future applications

development of optimal models of porous media by combining static and dynamic data the porosity distribution this paper is part of a project the goal of which is the development of the optimal spatial distributions of the porosity and permeability of a large scale porous medium by using complementary static and dynamic data for the medium the data include limited measurements of the porosity which the method honors preserves in the optimal model and utilizes its correlation function together with the first arrival fa times at a certain number of receivers of seismic waves that have propagated in the medium and the time dependence of the pressure of a fluid flowing in the medium the method uses the simulated annealing sa technique in order to develop the optimal model in the present paper we utilize the porosity and fa times data in order to develop the optimal spatial distribution of the porosity this is accomplished by combining the sa method with a simulator that solves for the numerical solution of the acoustic wave equation from which the fa times are estimated limited porosity and fa times data we show that the optimal model not only honors the data but also provides accurate estimates of the porosities in the rest of the porous medium the efficiency of the computations is discussed in detail

modeling heterogeneous materials via two point correlation functions basic principles heterogeneous materials abound in nature and man made situations examples include porous media biological materials and composite materials diverse and interesting properties exhibited by these materials result from their complex microstructures which also make it difficult to model the materials yeong and torquato phys rev e 57 495 1998 introduced a stochastic optimization technique that enables one to generate realizations of heterogeneous materials from a prescribed set of correlation functions in this first part of a series of two papers we collect the known necessary conditions on the standard two point correlation function s2 r and formulate a conjecture in particular we argue that given a complete two point correlation function space s2 r of any statistically homogeneous material can be expressed through a map on a selected set of bases of the function space we provide examples of realizable two point correlation functions and suggest a set of analytical basis functions we also discuss an exact mathematical formulation of the re construction problem and prove that s2 r cannot completely specify a two phase heterogeneous material alone moreover we devise an efficient and isotropy preserving construction algorithm namely the lattice point algorithm to generate realizations of materials from their two point correlation functions based on the yeong torquato technique subsequent analysis can be performed on the generated images to obtain desired macroscopic properties these developments are integrated here into a general scheme that enables one to model and categorize heterogeneous materials via two point correlation functions we will mainly focus on basic principles in this paper the algorithmic details and applications of the general scheme are given in the second part of this series of two papers

cheap talk and sequential equilibria in signaling games well behaved infinite signaling games may have no sequential equilibria we prove that adding cheap talk to these games solves the nonexistence problem the limit of sequential equilibrium outcomes of finite approximating games is a sequential equilibrium outcome of the cheap talk extension of the limit game in addition when the signaling space has no isolated points any cheap talk sequential equilibrium outcome can be approximated by a sequential e equilibrium of the game without cheap talk

geometrical ambiguity of pair statistics ii heterogeneous media in the first part of this series of two papers y jiao f h stillinger and s torquato phys rev e 81 011105 2010 we considered the geometrical ambiguity of pair statistics associated with point configurations here we focus on the analogous problem for heterogeneous media materials heterogeneous media are ubiquitous in a host of contexts including composites and granular media biological tissues ecological patterns and astrophysical structures the complex structures of heterogeneous media are usually characterized via statistical descriptors such as the n point correlation function s n an intricate inverse problem of practical importance is to what extent a medium can be reconstructed from the two point correlation function s 2 of a target medium recently general claims of the uniqueness of reconstructions using s 2 have been made based on numerical studies which implies that s 2 suffices to uniquely determine the structure of a medium within certain numerical accuracy in this paper we provide a systematic approach to characterize the geometrical ambiguity of s 2 for both continuous two phase heterogeneous media and their digitized representations in a mathematically precise way in particular we derive the exact conditions for the case where two distinct media possess identical s 2 i e they form a degenerate pair the degeneracy conditions are given in terms of integral and algebraic equations for continuous media and their digitized representations respectively by examining these equations and constructing their rigorous solutions for specific examples we conclusively show that in general s 2 is indeed not sufficient information to uniquely determine the structure of the medium which is consistent with the results of our recent study on heterogeneous media reconstruction y jiao f h stillinger and s torquato proc natl acad sci u s a 106 17634 2009 the analytical examples include complex patterns composed of building blocks bearing the letter t and the word water as well as degenerate stacking variants of the densest sphere packing in three dimensions barlow films several numerical examples of degeneracy e g reconstructions of polycrystal microstructures laser speckle patterns and sphere packings are also given which are virtually exact solutions of the degeneracy equations the uniqueness issue of multiphase media reconstructions and additional structural information required to characterize heterogeneous media are discussed including two point quantities that contain topological connectedness information about the phases