relation of signal set choice to the performance of optimal non gaussian detectors the optimal procedure for detecting the presence of discrete time signals in additive noise can be derived from the likelihood ratio test when the noise has statistically independent identically distributed components the dependence of the detector s performance on signal characteristics can be related to the kullback leibler kl distance between the distributions governing the hypotheses performance predictions based on the central limit theorem are shown to be poor approximations to the true performance performance of the optimal detector has long been known to increase exponentially with increasing kl distance symmetric noise amplitude distributions yield a symmetric dependence on the difference between the signals amplitudes at each time index small signal locally optimal detection performance is shown to depend on signal energy whereas large signal performance depends on the signal waveform when a distance measure can be defined performance depends on a different measure than that used in the detector with one exception the gaussian

from one cell to the whole froth a dynamical map we investigate two and three dimensional shell structured inflatable froths which can be constructed by a recursion procedure adding successive layers of cells around a germ cell we prove that any froth can be reduced into a system of concentric shells there is only a restricted set of local configurations for which the recursive inflation transformation is not applicable these configurations are inclusions between successive layers and can be treated as vertices and edges decorations of a shell structured inflatable skeleton the recursion procedure is described by a logistic map which provides a natural classification into euclidean hyperbolic and elliptic froths froths tiling manifolds with different curvatures can be classified simply by distinguishing between those with a bounded or unbounded number of elements per shell without any a priori knowledge on their curvature a result associated with maximal orientational entropy is obtained on topological properties of natural cellular systems the topological characteristics of all experimentally known tetrahedrally close packed structures are retrieved

exact two cell correlations in random cellular structures generated from a 2d ising ferromagnet abstract random 2d cellular structures are generated from distributions of spins given by a ferromagnetic ising model with nearest neighbour couplings on a square lattice topological correlations between pairs of neighbouring cells are expressed as rational functions of even number spin correlations involving two four and six spins which are exactly known for the square ising model the latter correlations have been calculated numerically in the vicinity of the curie point they agree with computer simulation results

long range geometrical correlations in two dimensional foams the statistical properties of two dimensional space filling random cellular structures foams or their dual random triangulations in statistical equilibrium are obtained by maximum entropy inference and topological simulations we show by maximum entropy inference that for a broad class of foams shell structured including three sided cell inclusions all two cell topological correlators aj k n average number of pairs of k cell and n cell at a topological distance j are linear in n and k the numbers of neighbours of the cells this generalizes a correlation known for neighbouring cells j d 1 which implies the linearity of aboav s relation between the total number of neighbours of the cells adjacent to a n neighboured cell andn our results verified by simulations also build up gauss s theorem for cellular structures any additional restriction in exploring local cell configurations besides the constraints of filling space at random will manifest itself through a deviation from linearity of the correlators aj k n and the aboav relation notably foams made of feynman diagrams have additional context dependent restrictions and their aboav relation is slightly curved it is essential that the local random variablen denotes the number of neighbours of the cell and not that of its sides whenever the two are different

topological models of cellular structures a method for constructing topological models of cellular structures is described it is based on lattices with topologically unstable sites which belong to more than zs polygons zs 3 in 2d and on rules which allow removing this degeneracy for every value of the coordination number z and for a given rule there are q z stable configurations called states cellular models are associated with distributions of states on the lattice sites the distribution of cell sides as well as other characteristics such as the correlations among cells can be derived many models of statistical physics may be used ising potts cellular automata the case z 4 is discussed and observed to agree with some experimental or simulation results

universal properties of voronoi tessellations of hard discs the authors describe a 2d mosaic obtained by the voronoi tessellation of a monosize assembly of discs at different packing fractions the experimental device hard discs moving on an air table produces for every packing fraction a succession of mosaics in statistical equilibrium which constitutes a statistical ensemble this ensemble is large enough for fluctuations from the most probable distributions to be negligible they use the maximum entropy principle to get the distribution of the polygons in 2d mosaics generated from an assembly of hard discs steric exclusion yields an extra conservation law which is sufficient to give a good agreement with the experimental data a similar behaviour in the six fold parameter seems to hold for other mosaics

tessellation of a stripe this paper describes enumeration of a class of topologically distinct periodic divisions of a stripe optimization of the geometry of these periodic tilings optimization that yields minimum total perimeter of the tiles gives a set of physically plausible periodic structures of monodisperse two dimensional foams bounded by two parallel walls evaluation of the minimum total perimeters of the lattices that we enumerated suggests two possible lower bounds for the mean perimeter of tiles forming periodic coverings of a stripe

towards statistical mechanics of a 2d random cellular structure using the methods of statistical mechanics the authors construct the partition function of a system of a large number of 2d cells that covers without pores or overlaps a flat surface each cell is defined by its position area perimeter and number of sides besides topological and space filling constraints they impose new ones regarding the energy and maximum area of the cells the entropy and free energy of the system are calculated and the mean values of the macroscopic parameters are determined in the equilibrium configuration the results are compared with experimental ones for soap froths and metallurgical aggregates

a comparative study of synchrony measures for the early diagnosis of alzheimer s disease based on eeg it is well known that eeg signals of alzheimer s disease ad patients are generally less synchronous than in age matched control subjects however this effect is not always easily detectable this is especially the case for patients in the pre symptomatic phase commonly referred to as mild cognitive impairment mci during which neuronal degeneration is occurring prior to the clinical symptoms appearance in this paper various synchrony measures are studied in the context of ad diagnosis including the correlation coefficient mean square and phase coherence granger causality phase synchrony indices information theoretic divergence measures state space based measures and the recently proposed stochastic event synchrony measures experiments with eeg data show that many of those measures are strongly correlated or anti correlated with the correlation coefficient and hence provide little complementary information about eeg synchrony measures that are only weakly correlated with the correlation coefficient include the phase synchrony indices granger causality measures and stochastic event synchrony measures in addition those three families of synchrony measures are mutually uncorrelated and therefore they each seem to capture a specific kind of interdependence for the data set at hand only two synchrony measures are able to convincingly distinguish mci patients from age matched control patients i e granger causality in particular full frequency directed transfer function and stochastic event synchrony those two measures are used as features to distinguish mci patients from age matched control subjects yielding a leave one out classification rate of 83 the classification performance may be further improved by adding complementary features from eeg this approach may eventually lead to a reliable eeg based diagnostic tool for mci and ad

the voronoi tessellation generated from eigenvalues of complex random matrices the voronoi froth generated from eigenvalues of asymmetric complex random matrices is studied by numerical simulation it is more regular than the random voronoi froth irvf generated from a poisson process the existence of a unique tessellation called here random matrix voronoi froth rmvf follows from the universality of the distribution of eigenvalues which is also briefly commented on the geometrical and topological properties of the rmvf have been characterised an empirical and accurate distribution function is also proposed for the cell side length of a rvf deviations from the aboav weaire law are discussed their magnitude may be interpreted as a measure ofthe departure from an equilibrium structure in the frame of the statistical crystallography theory of rivier

a comment on rivier s maximum entropy method of statistical crystallography in the literature rivier s maximum entropy method was used to prove lewis law and a linear aboav s law in this paper we show that the functional forms of these two laws for a statistically equilibrated cellular network even if such a network really exists cannot be derived or proved by this method for example within the maximum entropy method we demonstrate that a quadratic aboav s or lewis s law is as probable as a linear one

symmetrizing the kullback leibler distance we define a new distance measure the resistor average distance between two probability distributions that is closely related to the kullback leibler distance while the kullbackleibler distance is asymmetric in the two distributions the resistor average distance is not it arises from geometric considerations similar to those used to derive the chernoff distance determining its relation to well known distance measures reveals a new way to depict how commonly used distance measures relate to each other

model for coarsening froths and foams the coarsening process of froths and foams is described statistically in two dimensions by a random neighbor model this nonlinear dynamical model contains no free parameters all rates are determined dynamically it describes normal growth agrees with experimental results throws light on old data and hopefully inspires new simulations and measurements lewis s law anat rec 38 341 1928 am j bot 30 74 1943 and some other properties can be derived analytically from the model

some inequalities for information divergence and related measures of discrimination inequalities which connect information divergence with other measures of discrimination or distance between probability distributions are used in information theory and its applications to mathematical statistics ergodic theory and other scientific fields we suggest new inequalities of this type often based on underlying identities as a consequence we obtain certain improvements of the well known pinsker inequality our study depends on two measures of discrimination called capacitory discrimination and triangular discrimination the discussion contains references to related research and comparison with other measures of discrimination e g ali silvey csiszar 1996 1966 divergences and in particular the hellinger distance

statistical properties and shell analysis in random cellular structures we investigate the statistical properties of two dimensional random cellular systems froths in terms of their shell structure the froth is analyzed as a system of concentric layers of cells around a given central cell we derive exact analytical relations for the topological properties of the sets of cells belonging to these layers experimental observations of the shell structure of two dimensional soap froth are made and compared with the results on two kinds of voronoi constructions it is found that there are specific differences between soap froths and purely geometrical constructions in particular these systems differ in the topological charge of clusters as a function of shell number in the asymptotic values of defect concentrations and in the number of cells in a given layer we derive approximate expressions with no free parameters which correctly explain these different behaviors s1063 651x 96 13111 1

calibrated steganalysis of mp3stego in multi encoder scenario abstract experimenting with different mp3 encoders shows subtle differences in their outputs indicating they have been implemented differently if this characteristic is not addressed properly it could degrade performance of mp3 steganalysis additionally calibration is a powerful technique which has not found its true potential in mp3 steganalysis this paper tries to fill these gaps first we propose a new set of calibrated features based on quantization step to that end we show that quantization steps of mp3 bit stream and steganography induced noise are respectively band limited and wide band signals we use this observation and apply a low pass filter on quantization steps of mp3 bit stream and then use the result for calibrating of features then we present our analysis on different encoders and show that their statistical properties are quite dissimilar for all fields of mp3 bitstream we use this observation and propose an encoder classifier that have near perfect accuracy this accuracy is achieved after testing a wide range of feature selection methods and finally using genetic algorithm due to its superior performance our simulations show that the proposed method achieved accuracy of 95 8 and 95 2 at 3 12 of maximum embedding rate in the single and multi encoder scenarios respectively

shape error concealment based on a shape preserving boundary approximation in object based video representation video scenes are composed of several arbitrarily shaped video objects vos defined by their texture shape and motion in error prone communications packet loss results in missing information at the decoder the impact of transmission errors is minimized through error concealment in this paper we propose a spatial error concealment technique for recovering lost shape data we consider a geometric shape representation consisting of the object boundary which can be extracted from the plane missing macroblocks result in a broken boundary a b spline curve is constructed to replace a missing boundary segment based on a t spline representation of the received boundary we use t splines because they produce shape preserving approximations and do not change the characteristics of the original boundary the representation ensures a good estimation of the first derivatives at the points touching the missing segment applying smoothing conditions we manage to construct a new spline that joins smoothly with the received boundary leading to successful concealment results experimental results on object shapes with different concealment difficulty demonstrate the performance of the proposed method comparisons with prior proposed methods are also presented

roundness of grains in cellular microstructures many physical systems are composed of polyhedral cells of varying sizes and shapes these structures are simple in the sense that no more than three faces meet at an edge and no more than four edges meet at a vertex this means that individual cells can usually be considered as simple three dimensional polyhedra this paper is concerned with determining the distribution of combinatorial types of such polyhedral cells we introduce the terms fundamental and vertex truncated types and apply these concepts to the grain growth microstructure as a testing ground for these microstructures we demonstrate that most grains are of particular fundamental types whereas the frequency of vertex truncated types decreases exponentially with the number of truncations this can be explained by the evolutionary process through which grain growth structures are formed and in which energetically unfavorable surfaces are quickly eliminated furthermore we observe that these grain types are round in a combinatorial sense there are no short separating cycles that partition the polyhedra into two parts of similar sizes a particular microstructure derived from the poisson voronoi initial condition is identified as containing an unusually large proportion of round grains this microstructure has an average of 14 036 faces per grain and is conjectured to be more resistant to topological change than the steady state grain growth microstructure

annihilating filter based low rank hankel matrix approach for image inpainting in this paper we propose a patch based image inpainting method using a low rank hankel structured matrix completion approach the proposed method exploits the annihilation property between a shift invariant filter and image data observed in many existing inpainting algorithms in particular by exploiting the commutative property of the convolution the annihilation property results in a low rank block hankel structure data matrix and the image inpainting problem becomes a low rank structured matrix completion problem the block hankel structured matrices are obtained patch by patch to adapt to the local changes in the image statistics to solve the structured low rank matrix completion problem we employ an alternating direction method of multipliers with factorization matrix initialization using the low rank matrix fitting algorithm as a side product of the matrix factorization locally adaptive dictionaries can be also easily constructed despite the simplicity of the algorithm the experimental results using irregularly subsampled images as well as various images with globally missing patterns showed that the proposed method outperforms existing state of the art image inpainting methods

random cellular structures generated from a 2d ising ferromagnet topological models of 2d cellular structures are associated with distributions of spins given by a ferromagnetic ising model with nearest neighbour interactions on a square lattice every vertex of a square lattice is topologically unstable as it belongs to more than three polygons there are two ways associated with the spin states to remove this degeneracy by replacing every vertex by one side topological properties such as the distribution p n of the number n of cell sides the two cell correlation mk n p k akn which is the average number of k sided neighbours of a cell with n sides n cell the mean number m n of sides of the first neighbour cells of n cells are characterized as a function of t tc by direct calculations and by monte carlo and q2r simulations the correlations akn of a biological tissue are compared with the akn of a ferromagnetic ising cellular structure and with the akn expected from the maximum entropy model

choice of a pertinent color space for color texture characterization using parametric spectral analysis this article presents a comparison of different color spaces including rgb ihls and email protected a b for color texture characterization this comparison is based on the fusion of the independent spatial structure and color feature cues in ihls and l a b two channel complex color images are created from the luminance and the chrominance values for such images two dimensional complex multichannel linear prediction models are used to perform parametric power spectrum estimation and the structure feature cues are computed from this estimated power spectrum quantitative comparison of auto spectra of luminance and combined chrominance channels for different color spaces is done this comparison is based on the degree of decorrelation between luminance and chrominance information provided by different color space transformations three dimensional histograms are used as color feature cues then to classify color textures kullback leibler divergence based symmetric distance measures are calculated for pure color luminance structure and chrominance structure feature cues individual as well as combined effect of information from all feature cues on classification results is then compared for different color spaces and different color texture data sets the proposed color texture classification method performs better than the state of the art methods in certain cases the l a b color space gives us a better characterization of the chrominance spatial structure as well as the overall spatial structure for all of the chosen data sets experimental results on pixel classification of color textures are also presented and discussed

ring correlations in random networks we examine the correlations between rings in random network glasses in two dimensions as a function of their separation initially we use the topological separation measured by the number of intervening rings but this leads to pseudo long range correlations due to a lack of topological charge neutrality in the shells surrounding a central ring this effect is associated with the noncircular nature of the shells it is therefore necessary to use the geometrical distance between ring centers hence we find a generalization of the aboav weaire law out to larger distances with the correlations between rings decaying away when two rings are more than about three rings apart

the effects of regularity on the geometrical properties of voronoi tessellations this study comprehensively quantifies the effects of regularity on the geometrical properties of a random three dimensional voronoi tessellation vt where regularity was defined as the ratio of the minimum seed distance to the seed distance of the correlated body centred cubic lattice a scheme to generate voronoi tessellations with controlled regularity is proposed which was used to simulate 106 cells for a series of regularities the results were used to derive probability distributions for the properties of the tessellation including faces and edges per cell vertex and dihedral cell angles cell areas and volumes etc an understanding of the relation between a simple measurable parameter characterizing the degree of regularity of a voronoi tessellation and its geometrical properties is essential in generating virtual microstructures that are statistically representative of reality the statistical results are also relevant to all other applications involving random voronoi tessellations finally an application is presented of the proposed voronoi tessellation generation scheme applied to micromechanical modelling of grain structures with defined regularities for crystal plasticity finite element analysis

topological models of 2d cellular structure ii z 5 for pt i see ibid vol 24 p 1307 1991 topological models of 2d cellular structures are associated with planar tessellations with topologically unstable sites which belong to z 3 polygons this degeneracy is removed by replacing every z vertex by z 3 added sides a method which uses the diagonal triangulation of the dual tiling is also described the number of stable configurations called states is calculated as a function of z topological properties of the associated cellular structures are derived for a distribution of equiprobable and independent states on the various sites and for z ranging from 5 to infinity the distributions p n of the number n of cell sides for the latter distribution of states are typical of the p n of planar cuts of polycrystals and differ from the p n of soap froths deviations from the aboav weaire relation which describes the correlations between nearest neighbour cells occur mainly for n 3 and n 9

stochastic geometry of polygonal networks an alternative approach to the hexagon square transition in benard convection we apply stochastic geometry to the transition from hexagonal to square cells recently observed in surface tension driven benard convection in particular we study the metric and topological evolution of benard patterns as a function of the temperature difference dt across the layer the preference of square benard cells at higher dt is a consequence of both a higher efficiency in heat transfer and more favorable metric properties most notably the perimeter area ratio of a square cell exceeds that of a hexagonal cell by an unexpectedly high value from a topological point of view the benard pattern obeys the aboav weaire law at all times even in the presence of threefold and fourfold vertices the regimes above and below the transition are characterized by different topological correlations between neighboring cells with the appearance of fourfold vertices the topological correlation changes from negative to positive s1063 651x 98 14709 8

applicability of the lewis and aboav weaire laws to 2d and 3d cellular structures based on poisson partitions two and three dimensional networks of a columnar type are described which result from partitions based on poisson point distributions the metric and topological properties of such laminated poisson networks are derived and the applicability of the lewis and aboav weaire laws to them is tested the 2d poisson network contains cells with i or 4 i is the number of sides and both laws are obeyed the 3d poisson networks are of various types and have f or 6 f is the number of faces in a cell and f 14 in one particular type of 3d poisson network the two laws are again exactly obeyed in another type the laws show large deviations at low f but are asymptotically obeyed when f tends to infinite

random line tessellations of the plane statistical properties of many sided cells we consider a family of random line tessellations of the euclidean plane introduced in a more formal context by hug and schneider geom funct anal 17 156 2007 and described by a parameter 1 for 1 the zero cell that is the cell containing the origin coincides with the crofton cell of a poisson line tessellation and for 2 it coincides with the typical poisson voronoi cell let pn be the probability for the zero cell to have n sides we construct the asymptotic expansion of log pn up to terms that vanish as n our methods are nonrigorous but of the kind commonly accepted in theoretical physics as leading to exact results in the large n limit the cell is shown to become circular the circle is centered at the origin when 1 but gets delocalized for the crofton cell 1 which is a singular point of the parameter range the large n expansion of log pn 1 is therefore different from that of the general case and we show how to carry it out as a corollary we obtain the analogous expansion for the typicaln sided cell of a poisson line tessellation

on the size distribution of poisson voronoi cells abstract poisson voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices although this particular space tessellation is intensively studied by mathematicians in two and three dimensional 3d spaces there is no exact result known for the size distribution of voronoi cells motivated by the simple form of the distribution function in the 1d case a simple and compact analytical formula is proposed for approximating the voronoi cell s size distribution function in the practically important 2d and 3d cases as well denoting the dimensionality of the space by d d 1 2 3 the f y const y 3 d 1 2 exp 3 d 1 y 2 compact form is suggested for the normalized cell size distribution function by using large scale computer simulations the viability of the proposed distribution function is studied and critically discussed

on the correlation between sizes and shapes of cells in epithelial mosaics it is shown that lewis s empirical linear relationship between the average area of a cell and the number of its sides in two dimensional mosaics corresponds to maximal arbitrariness in the cellular distribution an expression for the distribution is given in the general case

high resolution local structure constrained image upsampling with the development of ultra high resolution display devices the visual perception of fine texture details is becoming more and more important a method of high quality image upsampling with a low cost is greatly needed in this paper we propose a fast and efficient image upsampling method that makes use of high resolution local structure constraints the average local difference is used to divide a bicubic interpolated image into a sharp edge area and a texture area and these two areas are reconstructed separately with specific constraints for reconstruction of the sharp edge area a high resolution gradient map is estimated as an extra constraint for the recovery of sharp and natural edges for the reconstruction of the texture area a high resolution local texture structure map is estimated as an extra constraint to recover fine texture details these two reconstructed areas are then combined to obtain the final high resolution image the experimental results demonstrated that the proposed method recovered finer pixel level texture details and obtained top level objective performance with a low time cost compared with state of the art methods

scaling properties of three dimensional foams we obtain the scaling states of three dimensional soap foams by using equilibrium statistical mechanics techniques we consider a phase space where each bubble is characterized by its center of mass position volume surface and number of faces a gibbs entropy function is then defined and as done in standard statistical mechanics we obtain the probability density function defined in the phase space by maximizing the entropy subject to convenient constraints the froth is supposed to completely fill the available volume and we consider energy terms accounting for surface tension and the thermal energy of the gas inside the bubbles we find that the volume distribution presents an exponential decay with cell size and the correlation between cell volume and number of faces fits very well the available numerical data additional distribution functions and average values are also in good agreement with numerical simulations

simulations of aggregation in 2d a study of kinetics structure and topological properties abstract colloidal aggregation in 2d has been studied using off lattice simulations structural kinetic and topological properties these last using the voronoi construction have been analysed in diffusion limited cluster aggregation dlca and reaction limited cluster aggregation rlca the simulations show dynamic scaling of the cluster size distribution for large sizes and times it has been observed that when the system reaches dynamic scaling some topological properties become stationary furthermore kinetic and topological aspects are related among them

a universal variational framework for sparsity based image inpainting in this paper we extend an existing universal variational framework for image inpainting with new numerical algorithms given certain regularization operator and denoting u the latent image the basic model is to minimize the l p p 0 1 norm of u preserving the pixel values outside the inpainting region utilizing the operator splitting technique the original problem can be approximated by a new problem with extra variable with the alternating minimization method the new problem can be decomposed as two subproblems with exact solutions there are many choices for in our approach such as gradient operator wavelet transform framelet transform or other tight frames moreover with slight modification we can decouple our framework into two relatively independent parts 1 denoising and 2 linear combination therefore we can take any denoising method including bm3d filter in the denoising step the numerical experiments on various image inpainting tasks such as scratch and text removal randomly missing pixel filling and block completion clearly demonstrate the super performance of the proposed methods furthermore the theoretical convergence of the proposed algorithms is proved

topological correlations in soap froths correlation in two dimensional soap froth is analyzed with the introduction of two point correlators and topological distance cells with an equal number of sides repel with linear correlation while cells with a different number of sides attract with nonbilinear correlation for nearest neighbors which cannot be explained by the maximum entropy argument also the analysis indicates that froth is correlated up to the third shell neighbors at least s 1063 651x 98 07108 6

analytical results for size topology correlations in 2d disk and cellular packings random tilings or packings in the plane are characterized by a size distribution of individual elements domains and by the statistics of neighbor relations between the domains most systems occurring in nature or technology have a unimodal distribution of both areas and number of neighbors empirically strong correlations between these distributions have been observed and formulated as universal laws using only the local correlation free granocentric model approach with no free parameters we construct accurate analytical descriptions for disk crystallization size topology correlations and lemaitre s law

spatial correlations in polydisperse frictionless two dimensional packings we investigate next nearest neighbor correlations of the contact number in simulations of polydisperse frictionless packings in two dimensions we find that disks with few contacting neighbors are predominantly in contact with disks that have many neighbors and vice versa at all packing fractions this counterintuitive result can be explained by drawing a direct analogy to the aboav weaire law in cellular structures we find an empirical one parameter relation similar to the aboav weaire law that satisfies an exact sum rule constraint surprisingly there are no correlations in the radii between neighboring particles despite correlations between contact number and radius

context aware patch based image inpainting using markov random field modeling in this paper we first introduce a general approach for context aware patch based image inpainting where textural descriptors are used to guide and accelerate the search for well matching candidate patches a novel top down splitting procedure divides the image into variable size blocks according to their context constraining thereby the search for candidate patches to nonlocal image regions with matching context this approach can be employed to improve the speed and performance of virtually any patch based inpainting method we apply this approach to the so called global image inpainting with the markov random field mrf prior where mrf encodes a priori knowledge about consistency of neighboring image patches we solve the resulting optimization problem with an efficient low complexity inference method experimental results demonstrate the potential of the proposed approach in inpainting applications like scratch text and object removal improvement and significant acceleration of a related global mrf based inpainting method is also evident

boosted manifold principal angles for image set based recognition in this paper we address the problem of classifying vector sets we motivate and introduce a novel method based on comparisons between corresponding vector subspaces in particular there are two main areas of novelty i we extend the concept of principal angles between linear subspaces to manifolds with arbitrary nonlinearities ii it is demonstrated how boosting can be used for application optimal principal angle fusion the strengths of the proposed method are empirically demonstrated on the task of automatic face recognition afr in which it is shown to outperform state of the art methods in the literature

planar voronoi cells the violation of aboav s law explained in planar cellular systems mn denotes the average sidedness of a cell neighbouring an n sided cell aboav s empirical law states that nmn is linear in n a downward curvature is nevertheless observed in the numerical nmn data of the random voronoi froth the exact large n expansion of mn obtained in the present work namely explains this curvature its inverse square root dependence on n sets a new theoretical paradigm similar curved behaviour may be expected and must indeed be looked for in experimental data of sufficiently high resolution we argue that it occurs in particular in diffusion limited colloidal aggregation on the basis of recent simulation data due to fernandez toledano et al 2005 phys rev e 71 041401 and earlier experimental results by earnshaw and robinson 1994 phys rev lett 72 3682

scaling at the rod to flexible chain crossover in the stiff limit the authors critically examine the present theoretical understanding of the conformational rod to flexible chain crossover of a linear chain polymer in dilute solution with a good solvent there is good evidence for weak universality in this crossover while strong universality seems unlikely from available evidence in addition this system should exhibit a second crossover from a gaussian to an excluded volume they present a scaling hypothesis for the behaviour of this second crossover and compare with the initial results of numerical simulations and with the experiment of murakami et al 1980

how to explain individual classification decisions after building a classifier with modern tools of machine learning we typically have a black box at hand that is able to predict well for unseen data thus we get an answer to the question what is the most likely label of a given unseen data point however most methods will provide no answer why the model predicted a particular label for a single instance and what features were most influential for that particular instance the only method that is currently able to provide such explanations are decision trees this paper proposes a procedure which based on a set of assumptions allows to explain the decisions of any classification method

properties of a three dimensional poisson voronoi tesselation a monte carlo study a complete statistical description of the properties of a cellular microstructure generated by a three dimensional poisson voronoi tesselation has been obtained by a rigorous computer simulation involving several hundred thousand cells a two parameter gamma distribution is found to be a good fit to the cell s face volume and surface area distributions for a sample size of several thousand cells or less a lognormal distribution can also be used to approximate these distributions the individual face area and edge length distributions are also obtained

a note on the aboav weaire law abstract in this paper we present an alternative derivation of the aboav weaire law by first making the assumption that the mean of the number of sides surrounding a cell is a function of the time leads to mn the mean number of sides surrounding a cell of sides n as a linear function of the second moment and is independent of n this indicates that the local mean increases with time when written in the form of the general aboav weaire relation we find in their notation that a 1 and b 6 7 the analysis also leads to the relation that the deviation from the ensemble average 6 is proportional to and b is the coefficient of proportionality the initial assumption is removed and the assumption that mn is now a function of time and the number of sides is made this assumption leads to mn as a linear function of the ratio n 1 this applies in the limit of small and the assumption that mn can be expanded as a maclaurin series when written in the form of the general aboav weaire law a 1 and b 0 this implies that the deviation from the mean 6 is then proportional to n 1 a similar analysis is applied to three dimensions and when the faces of the cells are considered we find that the average number of faces of the cells surrounding a cell of face is a linear function of 1 where is the second moment of the faces with mean 14 this analysis of the mean number of sides surrounding a cell is extended to finding the mean area surrounding a cell of sides n and area a man it is found that the mean area of the cells man is given by man aa aa a n where aa is the local cell area average which in the first approximation can be treated as the ensemble average area similarly the mean volume of cells surrounding a cell of faces and volume v is given by m v v a v a v where va is the average local volume in this case cells of small areas volumes are surrounded by cells of areas volumes greater than the average area volume we can reverse the argument to show that the large area volume cells are surrounded by small area volume cells the results of this analysis indicates that the cells are not randomly distributed

structure of random cellular networks and their evolution abstract the methods of statistical mechanics are applied to the structure of random space filling cellular structures foams metallurgical grain aggregates biological tissues microreversibility of the structural properties under elementary transformations is demonstrated maximum entropy inference under a few constraints yields structural equations of state relating the size of cells to their topological shape these equations of state classify the structures and are criteria for their randomness quasistatic evolution is obtained if the structure remains in statistical equilibrium at all times in 2d it is governed by von neumann s law

3 d carotid multi region mri segmentation by globally optimal evolution of coupled surfaces in this paper we propose a novel global optimization based 3 d multi region segmentation algorithm for t1 weighted black blood carotid magnetic resonance mr images the proposed algorithm partitions a 3 d carotid mr image into three regions wall lumen and background the algorithm performs such partitioning by simultaneously evolving two coupled 3 d surfaces of carotid artery adventitia boundary ab and lumen intima boundary lib while preserving their anatomical inter surface consistency such that the lib is always located within the ab in particular we show that the proposed algorithm results in a fully time implicit scheme that propagates the two linearly ordered surfaces of the ab and lib to their globally optimal positions during each discrete time frame by convex relaxation in this regard we introduce the continuous max flow model and prove its duality equivalence to the convex relaxed optimization problem with respect to each evolution step we then propose a fully parallelized continuous max flow based algorithm which can be readily implemented on a gpu to achieve high computational efficiency extensive experiments with four users using 12 3t mr and 26 1 5t mr images demonstrate that the proposed algorithm yields high accuracy and low operator variability in computing vessel wall volume in addition we show the algorithm outperforms previous methods in terms of high computational efficiency and robustness with fewer user interactions

damage spreading in the q2r ising model abstract we find evidence of metastability in the spreading of damage in the q2r cellular automaton approximation for a 2d ising system which is first equilibrated with a standard metropolis simulation a subsequent study of both single site and whole line damage spreading in metropolis q2r systems as well as in pure q2r systems shows a logarithmic dependence of the damage spreading threshold on time and saturation effects in single site damage suggest a transition in the damage spreading threshold at low initial energy values examination of the magnetization as a function of energy in pure q2r shows extremely long relaxation times for p

scaling behavior of two dimensional domain growth computer simulation of vertex models computer simulations are performed for vertex models which are coarse grained models for dynamical cellular patterns in two dimensions by simulating large systems we obtain conclusive evidence of scaling behavior that is a power law for the growth of the average cell size and the scaling properties for the distribution functions of edge number and size of cells several versions of the vertex models are obtained by making some approximations for the equation of motion of a vertex and we compare the statistical properties of the patterns in the scaling regime

integrable structure of ginibre s ensemble of real random matrices and a pfaffian integration theorem in the recent publication e kanzieper and g akemann in phys rev lett 95 230201 2005 an exact solution was reported for the probability pn k to find exactly k real eigenvalues in the spectrum of an n n real asymmetric matrix drawn at random from ginibre s orthogonal ensemble ginoe in the present paper we offer a detailed derivation of the above result by concentrating on the proof of the pfaffian integration theorem the key ingredient of our analysis of the statistics of real eigenvalues in the ginoe we also initiate a study of the correlations of complex eigenvalues and derive a formula for the joint probability density function of all complex eigenvalues of a ginoe matrix restricted to have exactly k real eigenvalues in the particular case of k 0 all correlation functions of complex eigenvalues are determined

a geometric formulation of the law of aboav weaire in two and three dimensions the law of aboav weaire is a simple mathematical expression deriving from empirical observations that the number of sides of a grain is related to the average number of sides of the neighboring grains and is usually restricted to natural two dimensional microstructures numerous attempts have been made to justify this relationship theoretically or to derive an analogous relation in three dimensions this paper provides several exact geometric results with expressions similar to that of the usual law of aboav weaire though with additional terms that may be used to establish when the law of abaov weaire is a suitable approximation specifically we derive several local relations that apply to individual grain clusters and a corresponding global relation that is identical in two and three dimensions except for a single parameter the derivation requires the definition and investigation of the average excess curvature a previously unconsidered physical quantity an approximation to our exact result is compared to the results of extensive simulations in two and three dimensions and we provide a compact expression that strikes a balance between complexity and accuracy

lewis law versus feltham s law in soap froth abstract the scaling of area and perimeter of n sided cells versus n in a two dimensional cellular pattern are investigated lewis law states that a n is linear in n while feltham s law states that the perimeter e n is linear in n we have tested these two different predictions on soap froth for large samples starting with approximately 5000 cells at different times and different gap thicknesses we conclude that feltham s law has a smaller statistical error than lewis law we also compared the results with several two dimensional voronoi constructions of random points and perturbed triangular lattice we found that the error bars of the lewis s law and feltham s law are comparable in the voronoi constructions using geometric constraints we argue and verified by experimental data that there is a universal law obeyed by the slopes and intercepts of these laws on all samples

effect of packing method on the randomness of disc packings the randomness of disc packings generated by random sequential adsorption rsa random packing under gravity rpg and mason packing mp which gives a packing density close to that of the rsa packing has been analysed based on the delaunay tessellation and is evaluated at two levels i e the randomness at individual subunit level which relates to the construction of a triangle from a given edge length distribution and the randomness at network level which relates to the connection between triangles from a given triangle frequency distribution the delaunay tessellation itself is also analysed and its almost perfect randomness at the two levels is demonstrated which verifies the proposed approach and provides a random reference system for the present analysis it is found that i the construction of a triangle subunit is not random for the rsa mp and rpg packings with the degree of randomness decreasing from the rsa to mp and then to rpg packing ii the connection of triangular subunits in the network is almost perfectly random for the rsa packing acceptable for the mp packing and not good for the rpg packing packing method is an important factor governing the randomness of disc packings

new monte carlo method for planar poisson voronoi cells by a new monte carlo algorithm we evaluate the sidedness probability pn of a planar poisson voronoi cell in the range 3 n 1600 the algorithm is developed on the basis of earlier theoretical work it exploits in particular the known asymptotic behaviour of pn as n our pn values all have between four and six significant digits accurate n dependent averages second moments and variances are obtained for the cell area and the cell perimeter the numerical large n behaviour of these quantities is analysed in terms of an asymptotic power series in n 1 snapshots are shown of typical occurrences of extremely rare events implicating cells of up to n 1600 sides embedded in an ordinary poisson voronoi diagram we reveal and discuss the characteristic features of such many sided cells and their immediate environment their relevance for observable properties is stressed

bubble size topology correlations in two dimensional foams derived from surface energy minimization we obtain the number fractions xi the average areas a i and the average perimeters p i of i sided bubbles in a two dimensional foam by minimizing the total surface energy and assuming a simple relation between p i and a i calculations for linear and weibull distributions of the square root of the bubble area yield large deviations particularly at small i from lewis s and desch s laws which linearly relate a i and p i respectively to i nevertheless we find good agreement with experimental results for xi p i and a i in foams

correlations in topological models of 2d random cellular structures general relations and constraints which must be satisfied by the topological correlations in 2d space filling random cellular structures are discussed and a topological short range order coefficient is defined topological models of 2d structures are associated with planar tessellations with topologically unstable sites which belong to z 3 polygons the stable configurations called states are obtained by replacing every vertex by z 3 added sides the topological properties of the latter models are calculated exactly for a distribution of independent and equiprobable states on the various sites and for any value of z the case of the structures associated with tilings by triangles is thoroughly considered the calculated correlations are compared with the correlations in alumina cuts and in random voronoi froths the variability of the topological properties of 2d random cellular structures is discussed

inter cluster scaling in two dimensional colloidal aggregation abstract cluster cluster aggregation has been studied experimentally in two dimensional colloidal systems of moderately high area fraction in the diffusion limited regime the system spontaneously exhibits ordering beyond the scale of the fractal aggregates which persists into the gelled state this ordering arises from an effective inter cluster repulsion due to the mutually exclusive depletion zones surrounding each cluster various metrical and topological properties of the system indicate that this long range order is stationary apart from the inherent change of scale as the clusters grow topological correlations show that the inter cluster self organization is compatible with maximum entropy the non equilibrium system behaves as if it were in statistical equilibrium and no physical forces are involved in the long range order for the reaction limited case no such inter cluster ordering is evident at any stage the system is nonstationary and the aggregation is governed by specific physical forces

sided and symmetrized bregman centroids in this paper we generalize the notions of centroids and barycenters to the broad class of information theoretic distortion measures called bregman divergences bregman divergences form a rich and versatile family of distances that unifies quadratic euclidean distances with various well known statistical entropic measures since besides the squared euclidean distance bregman divergences are asymmetric we consider the left sided and right sided centroids and the symmetrized centroids as minimizers of average bregman distortions we prove that all three centroids are unique and give closed form solutions for the sided centroids that are generalized means furthermore we design a provably fast and efficient arbitrary close approximation algorithm for the symmetrized centroid based on its exact geometric characterization the geometric approximation algorithm requires only to walk on a geodesic linking the two left right sided centroids we report on our implementation for computing entropic centers of image histogram clusters and entropic centers of multivariate normal distributions that are useful operations for processing multimedia information and retrieval these experiments illustrate that our generic methods compare favorably with former limited ad hoc methods

voronoi cell properties from simulated and real random spheres and points results are reported of a computer aided study of the properties of voronoi cells generated from randomly placed impenetrable uniform spheres which saturate a space and of poisson points in three dimensional space an empirical expression is suggested for the volume distribution function and an expression for the probability of thenth nearest neighbor of a voronoi cell nucleus forming a cell face comparison is made with the work of meijering philips res rep 8 270 1953 finney proc r soc london a319 479 495 1970 kiang z astrophys 64 433 1966 and others radial distributions coordination number and packing density are discussed for the spheres

recovery of lost color and depth frames in multiview videos in this paper we consider an integrated error concealment system for lost color frames and lost depth frames in multiview videos with depths we first proposed a pixel based color error concealment method with the use of depth information instead of assuming that the same moving object in consecutive frames has minimal depth difference as is done in a state of the art method a more realistic situation in which the same moving object in consecutive frames can be in different depths is considered in the derived motion vector candidate set we consider all the candidate motion vectors in the set and weight the reference pixels by the depth differences to obtain the final recovered pixel compared with the two state of the art methods the proposed method has average peak signal to noise ratio gains of up to 8 73 and 3 98 db respectively second we proposed an iterative depth frame error concealment method the initial recovered depth frame is obtained by depth image based rendering from another available view the holes in the recovered depth frame are then filled in the proposed priority order preprocessing methods depth difference compensation and inconsistent pixel removal are performed to improve the performance compared with a method that uses the available motion vector in a color frame to recover the lost depth pixels the hybrid motion vector extrapolation method the inpainting method and the proposed method have gains of up to 4 31 10 29 and 6 04 db respectively finally for the situation in which the color and the depth frames are lost at the same time our two methods jointly perform better with a gain of up to 7 79 db