isotropic random motion at finite speed with k erlang distributed direction alternations we study uniformly distributed direction of motion at finite speed where the direction alternations occur according to the renewal epochs of a k erlang pdf at first sight our generalizations of previous markovian results appears to be a small step however it must be seen as an important non markovian case where we have found closed form expressions for the pdf and the conditional characteristic function of this semi markov transport process we present detailed calculations of a three dimensional example for the 2 erlang case which is important not only from physical applications point of view but also to understand more general models for instance in principle the example of the 2 erlang case can be extended to a k erlang case k 3 4 but some of the mathematical expressions may be cumbersome

a new family of solvable pearson dirichlet random walks an n step pearson gamma random walk in d starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations the gamma distribution of each step length has a shape parameter q 0 constrained random walks of n steps in d are obtained from the latter walks by imposing that the sum of the step lengths is equal to a fixed value simple closed form expressions were obtained in particular for the distribution of the endpoint of such constrained walks for any d d0 and any n 2 when q is either q frac d 2 1 d0 3 or q d 1 d0 2 le caer in j stat phys 140 728 751 2010 when the total walk length is chosen without loss of generality to be equal to 1 then the constrained step lengths have a dirichlet distribution whose parameters are all equal to q and the associated walk is thus named a pearson dirichlet random walk the density of the endpoint position of a n step planar walk of this type n 2 with q d 2 was shown recently to be a weighted mixture of 1 floor n 2 endpoint densities of planar pearson dirichlet walks with q 1 beghin and orsingher in stochastics 82 201 229 2010 the previous result is generalized to any walk space dimension and any number of steps n 2 when the parameter of the pearson dirichlet random walk is q d 1 we rely on the connection between an unconstrained random walk and a constrained one which have both the same n and the same q d to obtain a closed form expression of the endpoint density the latter is a weighted mixture of 1 floor n 2 densities with simple forms equivalently expressed as a product of a power and a gauss hypergeometric function the weights are products of factors which depends both on d and n and bessel numbers independent of d

a pearson random walk with steps of uniform orientation and dirichlet distributed lengths a constrained diffusive random walk of n steps in d and a random flight in d which are equivalent were investigated independently in recent papers j stat phys 127 813 2007 j theor probab 20 769 2007 and j stat phys 131 1039 2008 the n steps of the walk are independent and identically distributed random vectors of exponential length and uniform orientation conditioned on the sum of their lengths being equal to a given value l closed form expressions for the distribution of the endpoint of the walk were obtained altogether for any n for d 1 2 4 uniform distributions of the endpoint inside a ball of radius l were evidenced for a walk of three steps in 2d and of two steps in 4d

when a random walk of fixed length can lead uniformly anywhere inside a hypersphere a variation of the pearson rayleigh random walk in which the steps are i i d random vectors of exponential length and uniform orientation is considered conditioned on the total path length the probability density function of the position of the walker after n steps is determined analytically in one and two dimensions it is shown that in two dimensions n 3 marks a critical transition point in the behavior of the random walk by taking less than three steps and walking a total length l one is more likely to end the walk near the boundary of the disc of radius l while by taking more than three steps one is more likely to end near the origin somehow surprisingly by taking exactly three steps one can end uniformly anywhere inside the disc of radius l this means that conditioned on l the sum of three vectors of exponential length and uniform direction has a uniform probability density

random motions at finite speed in higher dimensions we present a general method of studying the transport process bold x t t 0 in the euclidean space m m 2 based on the analysis of the integral transforms of its distributions we show that the joint characteristic functions of bold x t are connected with each other by a convolution type recurrent relation this enables us to prove that the characteristic function fourier transform of bold x t in any dimension m 2 satisfies a convolution type volterra integral equation of second kind we give its solution and obtain the characteristic function of bold x t in terms of the multiple convolutions of the kernel of the equation with itself an explicit form of the laplace transform of the characteristic function in any dimension is given the complete solution of the problem of finding the initial conditions for the governing partial differential equations is given

residence time and collision statistics for exponential flights the rod problem revisited many random transport phenomena such as radiation propagation chemical biological species migration or electron motion can be described in terms of particles performing exponential flights for such processes we sketch a general approach based on the feynman kac formalism that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution we then illustrate the proposed method in the case of the so called rod problem a one dimensional system and discuss the relevance of the obtained results in the context of monte carlo estimators

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

saddles arrows and spirals deterministic trajectories in cyclic competition of four species population dynamics in systems composed of cyclically competing species has been of increasing interest recently here we investigate a system with four or more species using mean field theory we study in detail the trajectories in configuration space of the population fractions we discover a variety of orbits shaped like saddles spirals and straight lines many of their properties are found explicitly most remarkably we identify a collective variable that evolves simply as an exponential q e t where is a function of the reaction rates it provides information on the state of the system for late times as well as for t we discuss implications of these results for the evolution of a finite stochastic system a generalization to an arbitrary number of cyclically competing species yields valuable insights into universal properties of such systems

strong continuation contrast invariant inpainting with a third order optimal pde pde based image inpainting has become a very active area of research after the pioneering works of masnou and morel bertalm spl inodot spl acute o et al and ballester et al in this paper we take a different approach inspired by the excellent work of caselles et al we view the inpainting problem as a particular case of image interpolation in which we intend to propagate level lines expressing this in terms of local neighborhoods and using a taylor expansion we derive a third order pde that performs inpainting this pde is optimal in the sense that it is the most accurate third order pde which can ensure continuation of level lines the continuation is strong allowing the restoration of thin structures occluded by a wide gap the result is also contrast invariant this is a novel pde which in both its accuracy and contrast invariance outperforms the approaches cited above

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

image inpainting by patch propagation using patch sparsity this paper introduces a novel examplar based inpainting algorithm through investigating the sparsity of natural image patches two novel concepts of sparsity at the patch level are proposed for modeling the patch priority and patch representation which are two crucial steps for patch propagation in the examplar based inpainting approach first patch structure sparsity is designed to measure the confidence of a patch located at the image structure e g the edge or corner by the sparseness of its nonzero similarities to the neighboring patches the patch with larger structure sparsity will be assigned higher priority for further inpainting second it is assumed that the patch to be filled can be represented by the sparse linear combination of candidate patches under the local patch consistency constraint in a framework of sparse representation compared with the traditional examplar based inpainting approach structure sparsity enables better discrimination of structure and texture and the patch sparse representation forces the newly inpainted regions to be sharp and consistent with the surrounding textures experiments on synthetic and natural images show the advantages of the proposed approach

role separating ordering in social dilemmas controlled by topological frustration three is a crowd is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models accordingly social relations within a triangle deserve special attention with this motivation we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice this topology provides an irreconcilable frustration which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game by using different strategy updating protocols we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb like organization which helps to minimize the negative consequence of the topological frustration we relate the emergence of these patterns to the microscopic dynamics of the evolutionary process both by means of mean field approximations and monte carlo simulations for comparison we also consider the same evolutionary dynamics on the square lattice where of course the topological frustration is absent however with the deletion of diagonal links of the triangular lattice we can gradually bridge the gap to the square lattice interestingly in this case the level of cooperation in the system is a direct indicator of the level of topological frustration thus providing a method to determine frustration levels in an arbitrary interaction network

segregation process and phase transition in cyclic predator prey models with an even number of species we study a spatial cyclic predator prey model with an even number of species for n 4 6 and 8 that allows the formation of two defensive alliances consisting of the even and odd label species the species are distributed on the sites of a square lattice the evolution of spatial distribution is governed by iteration of two elementary processes on neighboring sites chosen randomly if the sites are occupied by a predator prey pair then the predator invades the prey s site otherwise the species exchange their sites with a probability x for low x values a self organizing pattern is maintained by cyclic invasions if x exceeds a threshold value then two types of domain grow up that are formed by the odd and even label species respectively monte carlo simulations indicate the blocking of this segregation process within a range of x for n 8

two stage image denoising by principal component analysis with local pixel grouping this paper presents an efficient image denoising scheme by using principal component analysis pca with local pixel grouping lpg for a better preservation of image local structures a pixel and its nearest neighbors are modeled as a vector variable whose training samples are selected from the local window by using block matching based lpg such an lpg procedure guarantees that only the sample blocks with similar contents are used in the local statistics calculation for pca transform estimation so that the image local features can be well preserved after coefficient shrinkage in the pca domain to remove the noise the lpg pca denoising procedure is iterated one more time to further improve the denoising performance and the noise level is adaptively adjusted in the second stage experimental results on benchmark test images demonstrate that the lpg pca method achieves very competitive denoising performance especially in image fine structure preservation compared with state of the art denoising algorithms

interfaces with internal structures in generalized rock paper scissors models in this work we investigate the development of stable dynamical structures along interfaces separating domains belonging to enemy partnerships in the context of cyclic predator prey models with an even number of species n 8 we use both stochastic and field theory simulations in one and two spatial dimensions as well as analytical arguments to describe the association at the interfaces of mutually neutral individuals belonging to enemy partnerships and to probe their role in the development of the dynamical structures at the interfaces we identify an interesting behavior associated with the symmetric or asymmetric evolution of the interface profiles depending on whether n 2 is odd or even respectively we also show that the macroscopic evolution of the interface network is not very sensitive to the internal structure of the interfaces although this work focuses on cyclic predator prey models with an even number of species we argue that the results are expected to be quite generic in the context of spatial stochastic may leonard models

exemplar based inpainting technical review and new heuristics for better geometric reconstructions this paper proposes a technical review of exemplar based inpainting approaches with a particular focus on greedy methods several comparative and illustrative experiments are provided to deeply explore and enlighten these methods and to have a better understanding on the state of the art improvements of these approaches from this analysis three improvements over criminisi et al algorithm are then presented and detailed 1 a tensor based data term for a better selection of pixel candidates to fill in 2 a fast patch lookup strategy to ensure a better global coherence of the reconstruction and 3 a novel fast anisotropic spatial blending algorithm that reduces typical block artifacts using tensor models relevant comparisons with the state of the art inpainting methods are provided that exhibit the effectiveness of our contributions

iterative kernel principal component analysis for image modeling in recent years kernel principal component analysis kpca has been suggested for various image processing tasks requiring an image model such as e g denoising or compression the original form of kpca however can be only applied to strongly restricted image classes due to the limited number of training examples that can be processed we therefore propose a new iterative method for performing kpca the kernel hebbian algorithm which iteratively estimates the kernel principal components with only linear order memory complexity in our experiments we compute models for complex image classes such as faces and natural images which require a large number of training examples the resulting image models are tested in single frame super resolution and denoising applications the kpca model is not specifically tailored to these tasks in fact the same model can be used in super resolution with variable input resolution or denoising with unknown noise characteristics in spite of this both super resolution and denoising performance are comparable to existing methods

random motion with uniformly distributed directions and random velocity in this paper we deal with uniformly distributed direction of motion or isotropic motion at random speed or velocity where the direction alternations occur according to the renewal epochs of a general distribution we derive the renewal equation for the characteristic function of the transition density of the multidimensional motion then by using the renewal equation we study the behavior of the transition density near the sphere of its singularity for one two three and four dimensional cases to illustrate our solution methodology we present detailed calculations of many solvable examples

collision statistics for random flights with anisotropic scattering and absorption for a broad class of random walks with anisotropic scattering kernels and absorption we derive explicit formulas that allow expressing the moments of the collision number n v performed in a volume v as a function of the particle equilibrium distribution our results apply to arbitrary domains v and boundary conditions and allow assessing the hitting statistics for systems where the typical displacements are comparable to the domain size so that the diffusion limit is possibly not attained an example is discussed for one dimensional random flights with exponential displacements where analytical calculations can be carried out

predominance of the weakest species in lotka volterra and may leonard formulations of the rock paper scissors model we revisit the problem of the predominance of the weakest species in the context of lotka volterra and may leonard formulations of a spatial stochastic rock paper scissors model in which one of the species has its predation probability reduced by 0l mathcal p w l1 we show that despite the different population dynamics and spatial patterns these two formulations lead to qualitatively similar results for the late time values of the relative abundances of the three species as a function of mathcal p w as long as the simulation lattices are sufficiently large for coexistence to prevail the weakest species generally having an advantage over the others specially over its predator however for smaller simulation lattices we find that the relatively large oscillations at the initial stages of simulations with random initial conditions may result in a significant dependence of the probability of species survival on the lattice size

twice scattered particles in a plane are uniformly distributed it was recently shown physica a 216 299 315 1995 that in two dimensions the sum of three vectors each of whose lengths is exponentially distributed whose direction is uniformly distributed and such that the sum of their lengths is l is uniformly distributed on a disk of radius l we state here this random walk result in terms of scattering of particles as follows in two dimensions twice isotropically scattered particles by random i e poisson distributed scatterers are uniformly distributed we show that there is no other dimension d and no other number of scatterings s for which the corresponding result i e uniform distribution on a d dimensional sphere after s scatterings holds

missing intensity interpolation using a kernel pca based pocs algorithm and its applications a missing intensity interpolation method using a kernel principal component analysis pca based projection onto convex sets pocs algorithm and its applications are presented in this paper in order to interpolate missing intensities within a target image the proposed method reconstructs local textures containing the missing pixels by using the pocs algorithm in this reconstruction process a nonlinear eigenspace is constructed from each kind of texture and the optimal subspace for the target local texture is introduced into the constraint of the pocs algorithm in the proposed method the optimal subspace can be selected by monitoring errors converged in the reconstruction process this approach provides a solution to the problem in conventional methods of not being able to effectively perform adaptive reconstruction of the target textures due to missing intensities and successful interpolation of the missing intensities by the proposed method can be realized furthermore since our method can restore any images including arbitrary shaped missing areas its potential in two image reconstruction tasks image enlargement and missing area restoration is also shown in this paper

spirals and coarsening patterns in the competition of many species a complex ginzburg landau approach in order to model real ecological systems one has to consider many species that interact in complex ways however most of the recent theoretical studies have been restricted to few species systems with rather trivial interactions the few studies dealing with larger number of species and or more complex interaction schemes are mostly restricted to numerical explorations in this paper we determine starting from the deterministic mean field rate equations for large classes of systems the space of coexistence fixed points at which biodiversity is maximal for systems with a single coexistence fixed point we derive complex ginzburg landau equations that allow to describe space time pattern realized in two space dimensions for selected cases we compare the theoretical predictions with the pattern observed in numerical simulations

pattern transitions and complexity for a nonlocal logistic map abstract we examine the pattern solutions in a generalized nonlocal logistic map that includes spatial kernels in both growth and competition terms we show that this map includes as a particular case the nonlocal fisher kolmogorov equation and we demonstrate the existence of three kinds of stationary nonlinear solutions one uniform one cosine type that we refer to as wavelike solution and another in the form of gaussian we also obtain analytical expressions that describe the nonlinear pattern behavior in the system and we establish the stability criterion we define thermodynamics quantities such as entropy and the order parameter based on this the pattern no pattern and pattern pattern transitions are properly analyzed we show that these pattern solutions may be related to the recently observed peak adding phenomenon in nonlinear optics

asymptotic relation for the transition density of the three dimensional markov random flight on small time intervals we consider the markov random flight varvec x t t 0 in the three dimensional euclidean space mathbb r 3 with constant finite speed c 0 and the uniform choice of the initial and each new direction at random time instants that form a homogeneous poisson flow of rate lambda 0 series representations for the conditional characteristic functions of varvec x t corresponding to two and three changes of direction are obtained based on these results an asymptotic formula as t rightarrow 0 for the unconditional characteristic function of varvec x t is derived by inverting it we obtain an asymptotic relation for the transition density of the process we show that the error in this formula has the order o t 3 and therefore it gives a good approximation on small time intervals whose lengths depend on lambda an asymptotic formula as t rightarrow 0 for the probability of being in a three dimensional ball of radius r ct is also derived estimate of the accuracy of the approximation is analysed

interplay between partnership formation and competition in generalized may leonard games in order to better understand the interplay of partnership and competition in population dynamics we study a family of generalized may leonard models with n species these models have a very rich structure characterized by different types of space time patterns interesting partnership formations emerge following the maxim that the enemy of my enemy is my friend in specific cases cyclic dominance within coarsening clusters yields a peculiar coarsening behavior with intriguing pattern formation we classify the different types of dynamics through the analysis of the square of the adjacency matrix the dependence of the population densities on emerging pattern and propagating wave fronts is elucidated through a fourier analysis finally after having identified collaborating teams we study interface fluctuations where we initially populate different parts of the system with different teams

a global approach for solving evolutive heat transfer for image denoising and inpainting this paper proposes an alternative to partial differential equations pdes for solving problems in computer vision based on evolutive heat transfer traditionally the method for solving such physics based problems is to discretize and solve a pde by a purely mathematical process instead of using the pde we propose to use the global heat principle and to decompose it into basic laws we show that some of these laws admit an exact global version since they arise from conservative principles we also show that the assumptions made about the other basic laws can be made wisely taking into account knowledge about the problem and the domain the numerical scheme is derived in a straightforward way from the modeled problem thus providing a physical explanation for each step in the solution the advantage of such an approach is that it minimizes the approximations made during the whole process and it modularizes it allowing changing the application to a great number of problems we apply the scheme to two applications image denoising and inpainting which are modeled with heat transfer for denoising we propose a new approximation for the conductivity coefficient and we add thin lines to the features in order to block diffusion

the pre image problem in kernel methods in this paper we address the problem of finding the pre image of a feature vector in the feature space induced by a kernel this is of central importance in some kernel applications such as on using kernel principal component analysis pca for image denoising unlike the traditional method in which relies on nonlinear optimization our proposed method directly finds the location of the pre image based on distance constraints in the feature space it is noniterative involves only linear algebra and does not suffer from numerical instability or local minimum problems evaluations on performing kernel pca and kernel clustering on the usps data set show much improved performance

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

sparse representation for color image restoration sparse representations of signals have drawn considerable interest in recent years the assumption that natural signals such as images admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data in particular the design of well adapted dictionaries for images has been a major challenge the k svd has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks in this paper we address the problem of learning dictionaries for color images and extend the k svd based grayscale image denoising algorithm that appears in this work puts forward ways for handling nonhomogeneous noise and missing information paving the way to state of the art results in applications such as color image denoising demosaicing and inpainting as demonstrated in this paper

filling in by joint interpolation of vector fields and gray levels a variational approach for filling in regions of missing data in digital images is introduced the approach is based on joint interpolation of the image gray levels and gradient isophotes directions smoothly extending in an automatic fashion the isophote lines into the holes of missing data this interpolation is computed by solving the variational problem via its gradient descent flow which leads to a set of coupled second order partial differential equations one for the gray levels and one for the gradient orientations the process underlying this approach can be considered as an interpretation of the gestaltist s principle of good continuation no limitations are imposed on the topology of the holes and all regions of missing data can be simultaneously processed even if they are surrounded by completely different structures applications of this technique include the restoration of old photographs and removal of superimposed text like dates subtitles or publicity examples of these applications are given we conclude the paper with a number of theoretical results on the proposed variational approach and its corresponding gradient descent flow

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

color direction patch sparsity based image inpainting using multidirection features this paper proposes a color direction patch sparsity based image inpainting method to better maintain structure coherence texture clarity and neighborhood consistence of the inpainted region of an image the method uses super wavelet transform to estimate the multi direction features of a degraded image and combines with color information to construct the weighted color direction distance wcdd to measure the difference between two patches based on the wcdd the color direction structure sparsity is defined to obtain a more robust filling order and more suitable multiple candidate patches are searched then the target patches are sparsely represented by the multiple candidate patches under neighborhood consistency constraints in both the color and the multi direction spaces experimental results are presented to demonstrate the effectiveness of the proposed approach on tasks such as scratch removal text removal block removal and object removal the effects of super wavelet transforms and direction features are also investigated

probability law for the euclidean distance between two planar random flights we consider two independent symmetric markov random flights z1 t and z2 t performed by the particles that simultaneously start from the origin of the euclidean plane mathbb r 2 in random directions distributed uniformly on the unit circumference s1 and move with constant finite velocities c1 0 c2 0 respectively the new random directions are taking uniformly on s1 at random time instants that form independent homogeneous poisson flows of rates 1 0 2 0

two step dirichlet random walks abstract random walks of n steps taken into independent uniformly random directions in a d dimensional euclidean space d 2 which are characterized by a sum of step lengths which is fixed and taken to be 1 without loss of generality are named dirichlet when this constraint is realized via a dirichlet law of step lengths the latter continuous multivariate distribution which depends on n positive parameters generalizes the beta distribution n 2 it is simply obtained from n independent gamma random variables with identical scale factors previous literature studies of these random walks dealt with symmetric dirichlet distributions whose parameters are all equal to a value q which takes half integer or integer values in the present work the probability density function of the distance from the endpoint to the origin is first made explicit for a symmetric dirichlet random walk of two steps it is valid for any positive value of q and for all d 2 the latter pdf is used in turn to express the related density of a random walk of two steps whose step length is distributed according to an asymmetric beta distribution which depends on two parameters namely q and q s where s is a positive integer

random flights through spaces of different dimensions we shall study random flights that start in a space of one given dimension and after performing a definite number of steps continue to develop in a space of higher dimension we show that if the difference of the dimension of spaces is even then the probability density describing the composite flight can be expressed as marginalizations of the probability density associated to a random flight in the space of less dimensions this dimensional reduction is a consequence of gegenbauer addition theorem

statistical aspects of random fragmentations three random fragmentation of an interval processes are investigated for each of them there is a splitting probability and a probability not to split at each step of the fragmentation process whose overall effect is to stabilize the global number of splitting events some of their statistical features are studied in each case among which fragments size distribution partition function structure of the underlying random fragmentation tree occurrence of a phase transition in the first homogeneous model splitting probability does not depend on fragments size at each step in the next two fragmentation models splitting probability is fragments length dependent in the first such models fragments further split with probability one if their sizes exceed some cutoff value only in a second model considered splitting probability of finite size objects is assumed to increase algebraically with fragments size at each step the impact of these dependencies on statistical properties of the resulting random partitions are studied several examples are supplied

edge based image restoration in this paper we propose a new image inpainting algorithm that relies on explicit edge information the edge information is used both for the reconstruction of a skeleton image structure in the missing areas as well as for guiding the interpolation that follows the structure reconstruction part exploits different properties of the edges such as the colors of the objects they separate an estimate of how well one edge continues into another one and the spatial order of the edges with respect to each other in order to preserve both sharp and smooth edges the areas delimited by the recovered structure are interpolated independently and the process is guided by the direction of the nearby edges the novelty of our approach lies primarily in exploiting explicitly the constraint enforced by the numerical interpretation of the sequential order of edges as well as in the pixel filling method which takes into account the proximity and direction of edges extensive experiments are carried out in order to validate and compare the algorithm both quantitatively and qualitatively they show the advantages of our algorithm and its readily application to real world cases

synchronization and extinction in cyclic games with mixed strategies we consider cyclic lotka volterra models with three and four strategies where at every interaction agents play a strategy using a time dependent probability distribution agents learn from a loss by reducing the probability to play a losing strategy at the next interaction for that an agent is described as an urn containing balls of three and four types respectively where after a loss one of the balls corresponding to the losing strategy is replaced by a ball representing the winning strategy using both mean field rate equations and numerical simulations we investigate a range of quantities that allows us to characterize the properties of these cyclic models with time dependent probability distributions for the three strategy case in a spatial setting we observe a transition from neutrally stable to stable when changing the level of discretization of the probability distribution for large values of yielding a good approximation to a continuous distribution spatially synchronized temporal oscillations dominate the system for the four strategy game the system is always neutrally stable but different regimes emerge depending on the size of the system and the level of discretization

on random flights with non uniformly distributed directions this paper deals with a new class of random flights in d d 2 characterized by non uniform probability distributions on the multidimensional sphere these random motions differ from similar models appeared in literature where the directions are taken according to the uniform law the family of angular probability distributions introduced in this paper depends on a parameter 0 which gives the anisotropy of the motion furthermore we assume that the number of changes of direction performed by the random flight is fixed the time lengths between two consecutive changes of orientation have joint probability distribution given by a dirichlet density function

adaptive subspace based inverse projections via division into multiple sub problems for missing image data restoration this paper presents adaptive subspace based inverse projections via division into multiple sub problems asip dimss for missing image data restoration in the proposed method a target problem for estimating missing image data is divided into multiple sub problems and each sub problem is iteratively solved with the constraints of other known image data by projection into a subspace model of image patches the solution of each sub problem is calculated where we call this procedure subspace based inverse projection for simplicity the proposed method can use higher dimensional subspaces for finding unique solutions in each sub problem and successful restoration becomes feasible since a high level of image representation performance can be preserved this is the biggest contribution of this paper furthermore the proposed method generates several subspaces from known training examples and enables derivation of a new criterion in the above framework to adaptively select the optimal subspace for each target patch in this way the proposed method realizes missing image data restoration using asip dims since our method can estimate any kind of missing image data its potential in two image restoration tasks image inpainting and super resolution based on several methods for multivariate analysis is also shown in this paper

cyclic competition of mobile species on continuous space pattern formation and coexistence we propose a model for cyclically competing species on continuous space and investigate the effect of the interplay between the interaction range and mobility on coexistence a transition from coexistence to extinction is uncovered with a strikingly nonmonotonic behavior in the coexistence probability about the minimum in the probability switches between spiral and plane wave patterns arise a strong mobility can either promote or hamper coexistence depending on the radius of the interaction range these phenomena are absent in any lattice based model and we demonstrate that they can be explained using nonlinear partial differential equations our continuous space model is more physical and we expect the findings to generate experimental interest

beyond rock paper scissors systems deterministic models of cyclic ecological systems with more than three species abstract we consider cyclic ecological systems consisting of more than three species extending the well studied three species rock paper scissors rps system for such systems alliance and partial alliance states consisting of non competing species can form a phenomenon not present in classical rps systems we develop analyze and simulate a may leonard type model accounting for cyclic dynamics and spatial diffusion we analyze in detail four species and five species systems determine dynamics for both spatially homogeneous initial conditions i e ode models and the propagation and interaction of patches of different species driven by diffusion and the cyclic dynamics pde models we show markedly different behavior between the four and five species models with alliance states as stable steady states for the former whereas both coexistence of all species and heteroclinic cycles are possible stable outcomes for the latter finally we discuss the extension of this even odd split to systems with more than five species

image super resolution via sparse representation this paper presents a new approach to single image superresolution based upon sparse signal representation research on image statistics suggests that image patches can be well represented as a sparse linear combination of elements from an appropriately chosen over complete dictionary inspired by this observation we seek a sparse representation for each patch of the low resolution input and then use the coefficients of this representation to generate the high resolution output theoretical results from compressed sensing suggest that under mild conditions the sparse representation can be correctly recovered from the downsampled signals by jointly training two dictionaries for the low and high resolution image patches we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries therefore the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch the learned dictionary pair is a more compact representation of the patch pairs compared to previous approaches which simply sample a large amount of image patch pairs reducing the computational cost substantially the effectiveness of such a sparsity prior is demonstrated for both general image super resolution sr and the special case of face hallucination in both cases our algorithm generates high resolution images that are competitive or even superior in quality to images produced by other similar sr methods in addition the local sparse modeling of our approach is naturally robust to noise and therefore the proposed algorithm can handle sr with noisy inputs in a more unified framework

the exact probability distribution of a two dimensional random walk a calculation is made of the exact probability distribution of the two dimensional displacement of a particle at timet that starts at the origin moves in straight line paths at constant speed and changes its direction after exponentially distributed time intervals where the lengths of the straight line paths and the turn angles are independent the angles being uniformly distributed this random walk is the simplest model for the locomotion of microorganisms on surfaces its weak convergence to a wiener process is also shown

input space versus feature space in kernel based methods this paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector sv kernel functions we first discuss the geometry of feature space in particular we review what is known about the shape of the image of input space under the feature space map and how this influences the capacity of sv methods following this we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel using the example of the class of inhomogeneous polynomial kernels which are often used in sv pattern recognition we then discuss the connection between feature space and input space by dealing with the question of how one can given some vector in feature space find a preimage exact or approximate in input space we describe algorithms to tackle this issue and show their utility in two applications of kernel methods first we use it to reduce the computational complexity of sv decision functions second we combine it with the kernel pca algorithm thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real world data

performance of weak species in the simplest generalization of the rock paper scissors model to four species we investigate the problem of the predominance and survival of weak species in the context of the simplest generalization of the spatial stochastic rock paper scissors model to four species by considering models in which one two or three species have a reduced predation probability we show using lattice based spatial stochastic simulations with random initial conditions that if only one of the four species has its probability reduced then the most abundant species is the prey of the weakest assuming that the simulations are large enough for coexistence to prevail also among the remaining cases we present examples in which weak and strong species have similar average abundances and others in which either of them dominates the most abundant species being always a prey of a weak species with which it maintains a unidirectional predator prey interaction however in contrast to the three species model we find no systematic difference in the global performance of weak and strong species and we conjecture that a similar result will hold if the number of species is further increased we also determine the probability of single species survival and coexistence as a function of the lattice size discussing its dependence on initial conditions and on the change to the dynamics of the model which results from the extinction of one of the species

time evolution of the rule 150 cellular automaton activity from a fibonacci iteration the rule 150 cellular automaton is a remarkable discrete dynamical system as it shows 1 f spectra if started from a single seed j nagler and j c claussen phys rev e 71 067103 2005 despite its simplicity a feasible solution for its time behavior is not obvious its self similarity does not follow a one step iteration like other elementary cellular automata here it is shown how its time behavior can be solved as a two step vectorial or string iteration which can be viewed as a generalization of fibonacci iteration generating the time series from a sequence of vectors of increasing length this allows us to compute the total activity time series more efficiently than by simulating the whole spatiotemporal process or even by using the closed expression the results are further extended to the generalization of rule 150 to the two dimensional case and to bethe lattices and the relation to corresponding integer sequences is discussed