pricing geometric asian rainbow options under the mixed fractional brownian motion abstract we deal with the pricing of geometric asian rainbow options under the mixed fractional brownian motion based on standard no arbitrage arguments we obtain a partial differential problem in several independent variables which we solve by employing suitable changes of variables and analytical results derived in bos and ware 2001 and stulz 1982b numerical test cases are presented in which the pricing formula obtained is applied to geometric asian rainbow options on two and three underlying assets monte carlo simulations are also performed which confirm the correctness of the proposed closed form solution

limited path percolation in complex networks we study the stability of network communication after removal of a fraction q 1 p of links under the assumption that communication is effective only if the shortest path between nodes i and j after removal is shorter than al ij a or 1 where l ij is the shortest path before removal for a large class of networks we find analytically and numerically a new percolation transition at p c kappa 0 1 1 a a where kappa 0 triple bond and k is the node degree above p c order n nodes can communicate within the limited path length al ij while below p c n delta delta 1 nodes can communicate we expect our results to influence network design routing algorithms and immunization strategies where short paths are most relevant

3 d shape from a shaded and textural surface image a new 3d texture model is developed by considering the scene image as the superposition of a random texture image on a smooth shaded image the whole image is analyzed using a patch by patch process each patch is assumed to be a tilted and slanted texture plane a modified reflectance map function is applied to describe the deterministic part and the fractional differencing periodic model is chosen to describe the random texture because of its good performance in texture synthesis and its ability to represent the coarseness and the pattern of the surface at the same time an orthographical projection technique is developed to deal with this particular random model which has a nonisotropically distributed texture pattern for estimating the parameter a hybrid method that uses both the least square and the maximum likelihood estimates is applied directly to the given intensity function by using these parameters the synthesized image is obtained and used to reconstruct the original image

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

noise reduction in surface reconstruction from a given gradient field we present a gradient space technique for noise reduction in surfaces reconstructed from a noisy gradient field we first analyze the error sources in the recovered gradient field of a surface using a three image photometric stereo method based on this analysis we propose an additive noise model to describe the errors in the surface gradient estimates we then use a vector space formulation and construct a multiscale orthonormal expansion for gradient fields using the sparse representation properties of this expansion we develop techniques for reducing the gradient field noise by coefficient selection with thresholding the simulation results indicate that the proposed technique provides significant improvement on the noise levels of both the estimated gradient fields and the reconstructed surfaces under heavy noise levels furthermore the experiments using noisy photometric stereo image triplets of real range data suggest that the additive model remains viable after the nonlinear photometric stereo operation to provide accurate noise removal

shape from recognition a novel approach for 3 d face shape recovery in this paper we develop a novel framework for robust recovery of three dimensional 3 d surfaces of faces from single images the underlying principle is shape from recognition i e the idea that pre recognizing face parts can constrain the space of possible solutions to the image irradiance equation thus allowing robust recovery of the 3 d structure of a specific part parts of faces like nose lips and eyes are recognized and localized using robust expansion matching filter templates under varying pose and illumination specialized backpropagation based neural networks are then employed to recover the 3 d shape of particular face parts representation using principal components allows to efficiently encode classes of objects such as nose lips etc the specialized networks are designed and trained to map the principal component coefficients of the part images to another set of principal component coefficients that represent the corresponding 3 d surface shapes to achieve robustness to viewing conditions the network is trained with a wide range of illumination and viewing directions a method for merging recovered 3 d surface regions by minimizing the sum squared error in overlapping areas is also derived quantitative analysis of the reconstruction of the surface parts in varying illumination and pose show relatively small errors indicating that the method is robust and accurate several examples showing recovery of the complete face also illustrate the efficacy of the approach

a probabilistic framework for specular shape from shading one of the problems that hinders conventional methods for shape from shading is the presence of local specularities which may be misidentified as high curvature surface features in this paper we address the problem of estimating the proportions of lambertian and specular reflection components in order to improve the quality of surface normal information recoverable using shape from shading the framework for our study is provided by the iterated conditional modes algorithm we develop a maximum a posteriori probability map estimation method for estimating the mixing proportions for lambertian and specular reflectance and also for recovering local surface normals the map estimation scheme has two model ingredients first there are separate conditional measurement densities which describe the distributions of surface normal directions for the lambertian and specular reflectance components we experimentally compare three different models for the specular component the second ingredient is a smoothness prior which models the distribution of surface normal directions over local image regions we demonstrate the utility of method on real world data ground truth data is provided by imagery obtained with crossed polaroid filters this reveals not only that the method accurately estimates the proportion of specular reflection but that it also results in good surface normal reconstruction in the proximity of specular highlights

nonlinear non negative component analysis algorithms in this paper general solutions for nonlinear non negative component analysis for data representation and recognition are proposed motivated by a combination of the non negative matrix factorization nmf algorithm and kernel theory which has lead to a recently proposed nmf algorithm in a polynomial feature space we propose a general framework where one can build a nonlinear non negative component analysis method using kernels the so called projected gradient kernel non negative matrix factorization pgknmf in the proposed approach arbitrary positive definite kernels can be adopted while at the same time it is ensured that the limit point of the procedure is a stationary point of the optimization problem moreover we propose fixed point algorithms for the special case of gaussian radial basis function rbf kernels we demonstrate the power of the proposed methods in face and facial expression recognition applications

improved methods of estimating shape from shading using the light source coordinate system abstract this paper develops improved methods of estimating local surface orientation from shading information with the aid of a coordinate system having one axis in the assumed direction of the light source in this system the surface tilt is related to the direction of the gray level gradient at the given point an alternative formulation of the surface slant probability density is developed that takes the discrete nature of digital images into account and that yields a better estimate of the light source direction

nonlinear multiresolution a shape from shading example a method for image resolution reduction that simulates the reduction of shape resolution and is to be used with shape from shading algorithms is presented resolution reduction is used for accelerating shape from shading algorithms using multiresolution pyramids the goal of this correspondence is to show that resolution reduction based only on image intensities can be inferior to resolution reduction using knowledge of the surface reflectance this is true for all cases of parameter estimation from intensity images when the intensity is not a linear function of the parameters since optical reduction of images as when moving a camera away from the object is a simple gray level averaging a question is cast on the general scheme of shape from shading it is concluded that for accurate shape from shading one needs to know the distance from the object and the shape should also be known in advance

surface from gradients without discrete integrability enforcement a gaussian kernel approach representative surface reconstruction algorithms taking a gradient field as input enforce the integrability constraint in a discrete manner while enforcing integrability allows the subsequent integration to produce surface heights existing algorithms have one or more of the following disadvantages they can only handle dense per pixel gradient fields smooth out sharp features in a partially integrable field or produce severe surface distortion in the results in this paper we present a method which does not enforce discrete integrability and reconstructs a 3d continuous surface from a gradient or a height field or a combination of both which can be dense or sparse the key to our approach is the use of kernel basis functions which transfer the continuous surface reconstruction problem into high dimensional space where a closed form solution exists by using the gaussian kernel we can derive a straightforward implementation which is able to produce results better than traditional techniques in general an important advantage of our kernel based method is that the method does not suffer discretization and finite approximation both of which lead to surface distortion which is typical of fourier or wavelet bases widely adopted by previous representative approaches we perform comparisons with classical and recent methods on benchmark as well as challenging data sets to demonstrate that our method produces accurate surface reconstruction that preserves salient and sharp features the source code and executable of the system are available for downloading

a multigrid method for shape from shading the shape from shading problem has received much attention in the computer vision literature in recent years the basic problem is to recover the em shape z x y of a surface from a given map of its em shading i e its variation of brightness over a given domain mathematically one has to solve approximately the em image irradiance equation begin center e x y end center relating a given image irradiance em e x y to the radiance of the surface at each point em x y with em r p q a given em reflectance z x and q z y na possible presence of noise and lack of adequate boundary conditions adds to the difficulty of this problem a number of different approaches towards its solution have been proposed in the vision literature including various regularization models however a reliable efficient solution method for practical instances has remained elusive so far nin this paper we analyze the various solution models proposed with the aim of applying an efficient multigrid solver a combination of an fmg continuation technique with an appropriate discretization of one such solution model proposed by b horn yields an efficient solver our results are demonstrated by examples

a multiresolution approach for shape from shading coupling deterministic and stochastic optimization shape from shading is an ill posed inverse problem for which there is no completely satisfactory solution in the existing literature in this paper we address shape from shading as an energy minimization problem we first show that the deterministic approach provides efficient algorithms in terms of cpu time but reaches its limits since the energy associated with shape from shading can contain multiple deep local minima we derive an alternative stochastic approach using simulated annealing the obtained results strongly outperform the results of the deterministic approach the shortcoming is an extreme slowness of the optimization therefore we propose a hybrid approach which combines the deterministic and stochastic approaches in a multiresolution framework

recovery of surfaces with discontinuities by fusing shading and range data within a variational framework this work provides a variational framework for fusing range and intensity data for recovering regularized surfaces it is shown that this framework provides natural boundary conditions for the shape from shading problem results in a new shape from shading formulation in the absence of range data and provides a new fusion paradigm when range data is incorporated the approach is demonstrated on simulated range and intensity images error analysis with respect to the ground truth surface is presented it is shown that the formulation performs well even in very noisy images

fast facial shape recovery from a single image with general unknown lighting by using tensor representation in this paper we propose a fast 3 d facial shape recovery algorithm from a single image with general unknown lighting in order to derive the algorithm we formulate a nonlinear least square problem with two parameter vectors which are related to personal identity and light conditions we then combine the spherical harmonics for the surface normals of a human face with tensor algebra and show that in a certain condition the dimensionality of the least square problem can be further reduced to one tenth of the regular subspace based model by using tensor decomposition n mode svd which greatly speeds up the computations in order to enhance the shape recovery performance we have incorporated prior information in updating the parameters in the experiment the proposed algorithm takes less than 0 4s to reconstruct a face and shows a significant performance improvement over other reported schemes

reconstruction of consistent shape from inconsistent data optimization of 2 raise0 5ex hbox scriptstyle 1 kern 0 1em kern 0 15em lower0 25ex hbox scriptstyle 2 d sketches although the 3d orientations of edges and surfaces are theoretically sufficient for reconstructing the 3d object shape this does not mean that the 3d object shape can actually be reconstructed specifying the edge and surface orientations is often overspecification and inconsistency may result if image data contain errors we propose a scheme of optimization to construct a consistent polyhedron shape from inconsistent data our optimization is achieved by solving a set of linear equations no searchers and iterations are necessary this technique is first applied to the problem of shape from motion and then to the 3d recovery based on the rectangularity hypothesis and the parallelism hypothesis we also present a strategy of heuristic reasoning on rectangularity and parallelism

on the removal of shadows from images this paper is concerned with the derivation of a progression of shadow free image representations first we show that adopting certain assumptions about lights and cameras leads to a 1d gray scale image representation which is illuminant invariant at each image pixel we show that as a consequence images represented in this form are shadow free we then extend this 1d representation to an equivalent 2d chromaticity representation we show that in this 2d representation it is possible to relight all the image pixels in the same way effectively deriving a 2d image representation which is additionally shadow free finally we show how to recover a 3d full color shadow free image representation by first with the help of the 2d representation identifying shadow edges we then remove shadow edges from the edge map of the original image by edge in painting and we propose a method to reintegrate this thresholded edge map thus deriving the sought after 3d shadow free image

surface reconstruction in gradient field domain using compressed sensing surface reconstruction from measurements of spatial gradient is an important computer vision problem with applications in photometric stereo and shape from shading in the case of morphologically complex surfaces observed in the presence of shadowing and transparency artifacts a relatively large dense gradient measurements may be required for accurate surface reconstruction consequently due to hardware limitations of image acquisition devices situations are possible in which the available sampling density might not be sufficiently high to allow for recovery of essential surface details in this paper the above problem is resolved by means of derivative compressed sensing dcs dcs can be viewed as a modification of the classical cs which is particularly suited for reconstructions involving image surface gradients in dcs a standard cs setting is augmented through incorporation of additional constraints arising from some intrinsic properties of potential vector fields we demonstrate that using dcs results in reduction in the number of measurements as compared with the standard dense sampling while producing estimates of higher accuracy and smaller variability as compared with cs based estimates the results of this study are further supported by a series of numerical experiments

dynamic vaccination in partially overlapped multiplex network in this work we propose and investigate a strategy of vaccination which we call dynamic vaccination in our model susceptible people become aware that one or more of their contacts are infected and thereby get vaccinated with probability ensuremath omega before having physical contact with any infected patient then the nonvaccinated individuals will be infected with probability ensuremath beta we apply the strategy to the susceptible infected recovered epidemic model in a multiplex network composed by two networks where a fraction q of the nodes acts in both networks we map this model of dynamic vaccination into bond percolation model and use the generating functions framework to predict theoretically the behavior of the relevant magnitudes of the system at the steady state we find a perfect agreement between the solutions of the theoretical equations and the results of stochastic simulations in addition we find an interesting phase diagram in the plane ensuremath beta text ensuremath ensuremath omega which is composed of an epidemic and a nonepidemic phase separated by a critical threshold line ensuremath beta c which depends on q as q decreases ensuremath beta c increases i e as the overlap decreases the system is more disconnected and therefore more virulent diseases are needed to spread epidemics surprisingly we find that for all values of q a region in the diagram where the vaccination is so efficient that regardless of the virulence of the disease it never becomes an epidemic we compare our strategy with random immunization and find that using the same amount of vaccines for both scenarios we obtain that the spread of disease is much lower in the case of dynamic vaccination when compared to random immunization furthermore we also compare our strategy with targeted immunization and we find that depending on ensuremath omega dynamic vaccination will perform significantly better and in some cases will stop the disease before it becomes an epidemic

pricing geometric asian rainbow options under fractional brownian motion abstract in this paper we explore the pricing of the assets of asian rainbow options under the condition that the assets have self similar and long range dependence characteristics based on the principle of no arbitrage stochastic differential equation and partial differential equation we obtain the pricing formula for two asset rainbow options under fractional brownian motion next our monte carlo simulation experiments show that the derived pricing formula is accurate and effective finally our sensitivity analysis of the influence of important parameters such as the risk free rate hurst exponent and correlation coefficient on the prices of asian rainbow options further illustrate the rationality of our pricing model

intermittent social distancing strategy for epidemic control we study the critical effect of an intermittent social distancing strategy on the propagation of epidemics in adaptive complex networks we characterize the effect of our strategy in the framework of the susceptible infected recovered model in our model based on local information a susceptible individual interrupts the contact with an infected individual with a probability ensuremath sigma and restores it after a fixed time t b we find that depending on the network topology in our social distancing strategy there exists a cutoff threshold ensuremath sigma c beyond which the epidemic phase disappears our results are supported by a theoretical framework and extensive simulations of the model furthermore we show that this strategy is very efficient because it leads to a susceptible herd behavior that protects a large fraction of susceptible individuals we explain our results using percolation arguments

direct analytical methods for solving poisson equations in computer vision problems direct analytical methods are discussed for solving poisson equations of the general form delta u f on a rectangular domain some embedding techniques that may be useful when boundary conditions obtained from stereo and occluding boundary are defined on arbitrary contours are described the suggested algorithms are computationally efficient owing to the use of fast orthogonal transforms applications to shape from shading lightness and optical flow problems are also discussed a proof for the existence and convergence of the flow estimates is given experiments using synthetic images indicate that results comparable to those using multigrid can be obtained in a very small number of iterations

subpixel photometric stereo conventional photometric stereo recovers one normal direction per pixel of the input image this fundamentally limits the scale of recovered geometry to the resolution of the input image and cannot model surfaces with subpixel geometric structures in this paper we propose a method to recover subpixel surface geometry by studying the relationship between the subpixel geometry and the reflectance properties of a surface we first describe a generalized physically based reflectance model that relates the distribution of surface normals inside each pixel area to its reflectance function the distribution of surface normals can be computed from the reflectance functions recorded in photometric stereo images a convexity measure of subpixel geometry structure is also recovered at each pixel through an analysis of the shadowing attenuation then we use the recovered distribution of surface normals and the surface convexity to infer subpixel geometric structures on a surface of homogeneous material by spatially arranging the normals among pixels at a higher resolution than that of the input image finally we optimize the arrangement of normals using a combination of belief propagation and mcmc based on a minimum description length criterion on 3d textons over the surface the experiments demonstrate the validity of our approach and show superior geometric resolution for the recovered surfaces

angular embedding a robust quadratic criterion given the size and confidence of pairwise local orderings angular embedding ae finds a global ordering with a near global optimal eigensolution as a quadratic criterion in the complex domain ae is remarkably robust to outliers unlike its real domain counterpart ls the least squares embedding our comparative study of ls and ae reveals that ae s robustness is due not to the particular choice of the criterion but to the choice of representation in the complex domain when the embedding is encoded in the angular space we not only have a nonconvex error function that delivers robustness but also have a hermitian graph laplacian that completely determines the optimum and delivers efficiency the high quality of embedding by ae in the presence of outliers can hardly be matched by ls its corresponding l1 norm formulation or their bounded versions these results suggest that the key to overcoming outliers lies not with additionally imposing constraints on the embedding solution but with adaptively penalizing inconsistency between measurements themselves ae thus significantly advances statistical ranking methods by removing the impact of outliers directly without explicit inconsistency characterization and advances spectral clustering methods by covering the entire size confidence measurement space and providing an ordered cluster organization

the feasible solution in signal restoration the feasible solution to the signal restoration problem is defined as the one which satisfies all constraints which can be imposed on the true solution a very important set of constraints can be obtained by examining the statistics of the noise these and other constraints can be described as closed convex sets thus projection onto closed convex sets is the numerical method used to obtain a feasible solution examples of this method demonstrate its usefulness in one and two dimensional signal restoration the limitations of the method are discussed

arithmetic brownian motion subordinated by tempered stable and inverse tempered stable processes abstract in the last decade the subordinated processes have become popular and have found many practical applications therefore in this paper we examine two processes related to time changed subordinated classical brownian motion with drift called arithmetic brownian motion the first one so called normal tempered stable is related to the tempered stable subordinator while the second one to the inverse tempered stable process we compare the main properties such as probability density functions laplace transforms ensemble averaged mean squared displacements of such two subordinated processes and propose the parameters estimation procedures moreover we calibrate the analyzed systems to real data related to indoor air quality

a physics based analysis of image appearance models linear and multilinear models pca 3dmm aam asm and multilinear tensors of object shape appearance have been very popular in computer vision in this paper we analyze the applicability of these heuristic models from the fundamental physical laws of object motion and image formation we prove that under suitable conditions the image appearance space can be closely approximated to be multilinear with the illumination and texture subspaces being trilinearly combined with the direct sum of the motion and deformation subspaces this result provides a physics based understanding of many of the successes and limitations of the linear and multilinear approaches existing in the computer vision literature and also identifies some of the conditions under which they are valid it provides an analytical representation of the image space in terms of different physical factors that affect the image formation process numerical analysis of the accuracy of the physics based models is performed and tracking results on real data are presented

shape from shading level set propagation and viscosity solutions we present a new implementation of an algorithm aimed at recovering a 3d shape from its 2d gray level picture in order to reconstruct the shape of the object an almost arbitrarily initialized 3d function is propagated on a rectangular grid so that a level set of this function tracks the height contours of the shape the method imports techniques from differential geometry fluid dynamics and numerical analysis and provides an accurate shape from shading algorithm the method solves some topological problems and gracefully handles cases of non smooth surfaces that give rise to shocks in the propagating contours real and synthetic images of 3d profiles were submitted to the algorithm and the reconstructed surfaces are presented demonstrating the effectiveness of the proposed method

photometric stereo via expectation maximization this paper presents a robust and automatic approach to photometric stereo where the two main components namely surface normals and visible surfaces are respectively optimized by expectation maximization em a dense set of input images is conveniently captured using a digital video camera while a handheld spotlight is being moved around the target object and a small mirror sphere in our approach the inherently complex optimization problem is simplified into a two step optimization where em is employed in each step 1 using the dense input the weight or importance of each observation is alternately optimized with the normal and albedo at each pixel and 2 using the optimized normals and employing the markov random fields mrfs surface integrabilities and discontinuities are alternately optimized in visible surface reconstruction our mathematical derivation gives simple updating rules for the em algorithms leading to a stable practical and parameter free implementation that is very robust even in the presence of complex geometry shadows highlight and transparency we present high quality results on normal and visible surface reconstruction where fine geometric details are automatically recovered by our method

a coupled statistical model for face shape recovery from brightness images we focus on the problem of developing a coupled statistical model that can be used to recover facial shape from brightness images of faces we study three alternative representations for facial shape these are the surface height function the surface gradient and a fourier basis representation we jointly capture variations in intensity and the surface shape representations using a coupled statistical model the model is constructed by performing principal components analysis on sets of parameters describing the contents of the intensity images and the facial shape representations by fitting the coupled model to intensity data facial shape is implicitly recovered from the shape parameters experiments show that the coupled model is able to generate accurate shape from out of training sample intensity images

numerical shape from shading for discontinuous photographic images the height u x y of a continuous lambertian surface of known albedo i e grayness is related to u x y information recoverable from a black and white flash photograph of the surface by the partial differential equation sqrt u 2 x u 2 y n 0 we review the notion of a unique viscosity solution for this equation when n is continuous and a recent unique extension of the viscosity solution when n is discontinuous we prove convergence to this extension for a wide class of the numerical algorithms that converge when n is continuous after discussing the properties of the extension and the order of error in the algorithms simulating the extension we point out warning signs which when observed in the numerical solution usually indicate that the surface is not continuous or that the viscosity solution or its extension does not correspond to the actual surface finally we discuss a method that in some of these cases allows us to correct the simulation and recover the actual surface again

maximum likelihood estimation of depth maps using photometric stereo photometric stereo and depth map estimation provide a way to construct a depth map from images of an object under one viewpoint but with varying illumination directions while estimating surface normals using the lambertian model of reflectance is well established depth map estimation is an ongoing field of research and dealing with image noise is an active topic using the zero mean gaussian model of image noise this paper introduces a method for maximum likelihood depth map estimation that accounts for the propagation of noise through all steps of the estimation process solving for maximum likelihood depth map estimates involves an independent sequence of nonlinear regression estimates one for each pixel followed by a single large and sparse linear regression estimate the linear system employs anisotropic weights which arise naturally and differ in value to related work the new depth map estimation method remains efficient and fast making it practical for realistic image sizes experiments using synthetic images demonstrate the method s ability to robustly estimate depth maps under the noise model practical benefits of the method on challenging imaging scenarios are illustrated by experiments using the extended yale face database b and an extensive data set of 500 reflected light microscopy image sequences

a method for enforcing integrability in shape from shading algorithms an approach for enforcing integrability a particular implementation of the approach an example of its application to extending an existing shape from shading algorithm and experimental results showing the improvement that results from enforcing integrability are presented a possibly nonintegrable estimate of surface slopes is represented by a finite set of basis functions and integrability is enforced by calculating the orthogonal projection onto a vector subspace spanning the set of integrable slopes the integrability projection constraint was applied to extending an iterative shape from shading algorithm of m j brooks and b k p horn 1985 experimental results show that the extended algorithm converges faster and with less error than the original version good surface reconstructions were obtained with and without known boundary conditions and for fairly complicated surfaces

symmetric shape from shading using self ratio image in this paper we present a symmetric shape from shading sfs approach to recover both shape and albedo for symmetric objects lambertian surfaces with unknown varying albedo and orthographic projections are assumed in our formulation of symmetric sfs we have two image irradiance equations one is the standard equation used in sfs and the other is a self ratio image irradiance equation this new image irradiance equation relates the self ratio image which is defined as the ratio of two halves of the input image to light source and surface shape the introduction of the self ratio image facilitates the direct use of symmetry cue based on the self ratio image a new model based symmetric source from shading algorithm is also presented we then propose symmetric sfs algorithms to recover both shape and albedo from a single image and present experimental results the new symmetric sfs scheme has one important property the existence of a unique global solution which consists of unique local solutions at each point simultaneously obtained using the intensity information at that point and the surrounding local region and the assumption of a cal c 2 surface proofs for the existence of a unique solution in the cases of unknown constant and non constant albedos are provided

appearance characterization of linear lambertian objects generalized photometric stereo and illumination invariant face recognition traditional photometric stereo algorithms employ a lambertian reflectance model with a varying albedo field and involve the appearance of only one object in this paper we generalize photometric stereo algorithms to handle all appearances of all objects in a class in particular the human face class by making use of the linear lambertian property a linear lambertian object is one which is linearly spanned by a set of basis objects and has a lambertian surface the linear property leads to a rank constraint and consequently a factorization of an observation matrix that consists of exemplar images of different objects e g faces of different subjects under different unknown illuminations integrability and symmetry constraints are used to fully recover the subspace bases using a novel linearized algorithm that takes the varying albedo field into account the effectiveness of the linear lambertian property is further investigated by using it for the problem of illumination invariant face recognition using just one image attached shadows are incorporated in the model by a careful treatment of the inherent nonlinearity in lambert s law this enables us to extend our algorithm to perform face recognition in the presence of multiple illumination sources experimental results using standard data sets are presented

depth and image recovery using a mrf model this paper deals with the problem of depth recovery and image restoration from sparse and noisy image data the image is modeled as a markov random field and a new energy function is developed to effectively detect discontinuities in highly sparse and noisy images the model provides an alternative to the use of a line process interpolation over missing data sites is first done using local characteristics to obtain initial estimates and then simulated annealing is used to compute the maximum a posteriori map estimate a threshold on energy reduction per iteration is used to speed up simulated annealing by avoiding computation that contributes little to the energy minimization moreover a minor modification of the posterior energy function gives improved results for random as well as structured sparsing problems results of simulations carried out on real range and intensity images along with details of the simulations are presented

generalized fractional diffusion equations for accelerating subdiffusion and truncated levy flights fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time for processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order such equations were introduced in a v chechkin r gorenflo and i sokolov phys rev e 66 046129 2002 for the description of the processes getting more anomalous in the course of time decelerating subdiffusion and accelerating superdiffusion here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time which we call respectively accelerating subdiffusion and decelerating superdiffusion for the former process by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time for the latter process we demonstrate by a particular example how the power law truncated levy stable distribution evolves in time to the distribution with power law asymptotics and gaussian shape in the central part the special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics

applying greek letters to robust option price modeling by binomial tree abstract in this paper a new model is proposed for pricing a european option using the binomial tree method in conjunction with the greek letters in the proposed method the covariance matrix of high and low stock prices was calculated in an uncertainty region applying robust option pricing model an interval of prices instead of spot prices for an option was obtained greek letters were incorporated into a robust option model to ameliorate the accuracy of the interval price it was found out that the interval prices obtained by the present model were flexible with increased accuracy compared with those obtained by the robust option using the binomial tree model it is also indicated that the advantage of the present model over existing models is more tangible in the event of out of the money call option furthermore the accuracy improvement was found to be less noticeable when the maximum costs were equal to each other

estimating planar surface orientation using bispectral analysis in this correspondence we propose a direct method for estimating the orientation of a plane from a single view under perspective projection assuming that the underlying planar texture has random phase we show that the nonlinearities introduced by perspective projection lead to higher order correlations in the frequency domain we also empirically show that these correlations are proportional to the orientation of the plane minimization of these correlations using tools from polyspectral analysis yields the orientation of the plane we show the efficacy of this technique on synthetic and natural images

fokker planck type equations associated with fractional brownian motion controlled by infinitely divisible processes abstract in this paper we study the anomalous diffusion process driven by fractional brownian motion delayed by general infinitely divisible subordinator we show the analyzed process is the stochastic representation of the fokker planck type equation that describes the probability density function of an introduced model moreover we study main characteristics of the examined process the first two moments that allow us in special cases for classification of it as a system with accelerating subdiffusion property

tempered stable levy motion driven by stable subordinator a b s t r a c t in this article we propose a new model for financial data description combining two independent mechanisms namely the tempered stable process and inverse stable subordinator we obtain a new model which captures not only the tempered stable character of the underlying data but also such a property as periods in which the values of an asset stay on the same level moreover we classify our system to the family of subdiffusive processes and investigate its tail behavior we describe in detail testing and estimation procedures for the proposed model in the last step we calibrate our model to the real data

height and gradient from shading the method described here for recovering the shape of a surface from a shaded image can deal with complex wrinkled surfaces integrability can be enforced easily because both surface height and gradient are represented the robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell the new scheme can find an exact solution of a given shape from shading problem even though a regularizing term is included this is a reflection of the fact that shape from shading problems are it not ill posed when boundary conditions are available or when the image contains singular points

a graph spectral approach to shape from shading in this paper we explore how graph spectral methods can be used to develop a new shape from shading algorithm we characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction modeling the blocks of the weight matrix as distinct surface patches we use a graph seriation method to find a surface integration path that maximizes the sum of curvature dependent weights and that can be used for the purposes of height reconstruction to smooth the reconstructed surface we fit quadrics to the height data for each patch the smoothed surface normal directions are updated ensuring compliance with lambert s law the processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained we provide results on synthetic and real world imagery

recovering three dimensional shape from a single image of curved objects an algorithm to recover three dimensional shape i e surface orientation and relative depth from a single segmented image is presented it is assumed that the scene is composed of opaque regular solid objects bounded by piecewise smooth surfaces with no markings or textures it is also assumed that the reflectance map r n is known for the canonical case of lambertian surfaces illuminated by a point light source this implies knowing the light source direction a variational formulation of line drawing and shading constraints in a common framework is developed the global constraints are partitioned into constraint sets corresponding to the faces edges and vertices in the scene for a face the constraints are given by horn s image irradiance equation a variational formulation of the constraints at an edge both from the known direction of the image curve corresponding to the edge and shading is developed at a vertex the constraints are modeled by a system of nonlinear equations an algorithm is presented to solve this system of constraints

a non local low rank approach to enforce integrability we propose a new approach to enforce integrability using recent advances in non local methods our formulation consists in a sparse gradient data fitting term to handle outliers together with a gradient domain non local low rank prior this regularization has two main advantages 1 the low rank prior ensures similarity between non local gradient patches which helps recovering high quality clean patches from severe outliers corruption and 2 the low rank prior efficiently reduces dense noise as it has been shown in recent image restoration works we propose an efficient solver for the resulting optimization formulation using alternate minimization experiments show that the new method leads to an important improvement compared with previous optimization methods and is able to efficiently handle both outliers and dense noise mixed together

effects of epidemic threshold definition on disease spread statistics we study the statistical properties of sir epidemics in random networks when an epidemic is defined as only those sir propagations that reach or exceed a minimum size sc using percolation theory to calculate the average fractional size view the mathml source of an epidemic we find that the strength of the spanning link percolation cluster p is an upper bound to view the mathml source for small values of sc p is no longer a good approximation and the average fractional size has to be computed directly we find that the choice of sc is generally but not always guided by the network structure and the value of t of the disease in question if the goal is to always obtain p as the average epidemic size one should choose sc to be the typical size of the largest percolation cluster at the critical percolation threshold for the transmissibility we also study q the probability that an sir propagation reaches the epidemic mass sc and find that it is well characterized by percolation theory we apply our results to real networks dimes and tracerouter to measure the consequences of the choice sc on predictions of average outcome sizes of computer failure epidemics

crossover from weak to strong disorder regime in the duration of epidemics abstract we study the susceptible infected recovered sir model in complex networks considering that not all individuals in the population interact in the same way this heterogeneity between contacts is modeled by a continuous disorder in our model the disorder represents the contact time or the closeness between individuals we find that the duration time of an epidemic has a crossover with the system size from a power law regime to a logarithmic regime depending on the transmissibility related to the strength of the disorder using percolation theory we find that the duration of the epidemic scales as the average length of the branches of the infection our theoretical findings supported by simulations explains the crossover between the two regimes

lookup table based gradient field reconstruction in computer vision there are many applications where it is advantageous to process an image in the gradient domain and then reintegrate the gradient field important examples include shadow removal lightness calculation and data fusion a serious problem with this approach is that the reconstruction step often introduces artefacts commonly smoothed and smeared edges to the recovered image this is a result of the inherent ill posedness of reintegrating a nonintegrable field artefacts can be diminished but not removed by using complex to highly complex reintegration techniques here we present a remarkably simple and on the face of it naive algorithm for reconstructing gradient fields suppose we start with a multichannel original and from it derive a possibly one of many 1 d gradient field for many applications the derived gradient field will be nonintegrable here we propose a lookup table based map relating the multichannel original to a reconstructed scalar output image whose gradient best matches the target gradient field the idea at base is that if we learn how to map the gradients of the multichannel original onto the desired output gradient and then using the lookup table lut constraint we effectively derive the mapping from the multichannel input to the desired reintegrated image output while this map could take a variety of forms here we derive the best map from the multichannel gradient as a nonlinear function of the input to each of the target scalar gradients in this framework reconstruction is a simple equation solving exercise of low dimensionality one obvious application of our method is to the image fusion problem e g the problem of converting a color or higher d image into grayscale we will show through extensive experiments and complementary theoretical arguments that our straightforward method preserves the target contrast as well as do complex previous reintegration methods but without artefacts and with a substantially cheaper computational cost finally we demonstrate the generality of the method by applying it to gradient field reconstruction in an additional area the shading recovery problem

a graph spectral method for surface height recovery this paper describes a graph spectral method for 3d surface integration the algorithm takes as its input a 2d field of surface normal estimates delivered for instance by a shape from shading or shape from texture procedure we commence by using the surface normals to obtain an affinity weight matrix whose elements are related to the surface curvature the weight matrix is used to compute a row normalized transition probability matrix and we pose the recovery of the integration path as that of finding the steady state random walk for the markov chain defined by this matrix the steady state random walk is given by the leading eigenvector of the original affinity weight matrix by threading the surface normals together along the path specified by the magnitude order of the components of the leading eigenvector we perform surface integration the height increments along the path are simply related to the traversed path length and the slope of the local tangent plane the method is evaluated on needle maps delivered by a shape from shading algorithm applied to real world data and also on synthetic data the method is compared with the local geometric height reconstruction method of bors hancock and wilson and the global methods of horn and brooks and frankot and chellappa

shape from shading using the heat equation this paper offers two new directions to shape from shading namely the use of the heat equation to smooth the field of surface normals and the recovery of surface height using a low dimensional embedding turning our attention to the first of these contributions we pose the problem of surface normal recovery as that of solving the steady state heat equation subject to the hard constraint that lambert s law is satisfied we perform our analysis on a plane perpendicular to the light source direction where the z component of the surface normal is equal to the normalized image brightness the x y or azimuthal component of the surface normal is found by computing the gradient of a scalar field that evolves with time subject to the heat equation we solve the heat equation for the scalar potential and hence recover the azimuthal component of the surface normal from the average image brightness making use of a simple finite difference method the second contribution is to pose the problem of recovering the surface height function as that of embedding the field of surface normals on a manifold so as to preserve the pattern of surface height differences and the lattice footprint of the surface normals we experiment with the resulting method on a variety of real world image data where it produces qualitatively good reconstructed surfaces

langevin picture of subdiffusion with infinitely divisible waiting times in this paper we study a langevin approach to modeling of subdiffusion in the presence of time dependent external forces we construct a subordinated langevin process whose probability density function solves the subdiffusive fractional fokker planck equation we generalize the results known for the levy stable waiting times to the case of infinitely divisible waiting time distributions our approach provides a complete mathematical description of subdiffusion with time dependent forces moreover it allows to study the trajectories of the constructed process both analytically and numerically via monte carlo methodology

incorporating illumination constraints in deformable models for shape from shading and light direction estimation we present a method for the integration of nonlinear holonomic constraints in deformable models and its application to the problems of shape and illuminant direction estimation from shading experimental results demonstrate that our method performs better than previous shape from shading algorithms applied to images of lambertian objects under known illumination it is also more general as it can be applied to non lambertian surfaces and it does not require knowledge of the illuminant direction in this paper 1 we first develop a theory for the numerically robust integration of nonlinear holonomic constraints within a deformable model framework in this formulation we use lagrange multipliers and a baumgarte stabilization approach 1972 2 we also describe a fast new method for the computation of constraint based forces in the case of high numbers of local parameters 3 we demonstrate how any type of illumination constraint from the simple lambertian model to more complex highly nonlinear models can be incorporated in a deformable model framework 4 we extend our method to work when the direction of the light source is not known we couple our shape estimation method with a method for light estimation in an iterative process where improved shape estimation results in improved light estimation and vice versa 5 we perform a series of experiments

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

shape from shading using graph cuts in this paper we investigate the applicability of graph cuts to the sfs shape from shading problem we propose a new semi global method for sfs using graph cuts the new algorithm combines the local method proposed by lee and rosenfeld c h lee a rosenfeld improved methods of estimating shape from shading using the light source coordinate system artif intell 26 1985 125 143 and a global method using an energy minimization technique by employing a new global energy minimization formulation the convex concave ambiguity problem of lee and rosenfeld s method can be resolved efficiently a new combinatorial optimization technique the graph cuts method is used for the minimization of the proposed energy functional experimental results on a variety of synthetic and real world images show that the proposed algorithm reconstructs the 3 d shape of objects very efficiently

parametric shape from shading by radial basis functions we present a new method of shape from shading by using radial basis functions to parameterize the object depth the radial basis functions are deformed by adjusting their centers widths and weights such that the intensity errors are minimized the initial centers and widths are arranged hierarchically to speed up convergence and to stabilize the solution although the smoothness constraint is used it can be eventually dropped out without causing instabilities in the solution an important feature of our parametric shape from shading method is that it offers a unified framework for integration of multiple sensory information we show that knowledge about surface depth and or surface normals anywhere in the image can be easily incorporated into the shape from shading process it is further demonstrated that even qualitative knowledge can be used in shape from shading to improve 3d reconstruction experimental comparisons of our method with several existing ones are made by using both synthetic and real images results show that our solution is more accurate than the others

facial shape from shading and recognition using principal geodesic analysis and robust statistics the aim in this paper is to use principal geodesic analysis to model the statistical variations for sets of facial needle maps we commence by showing how to represent the distribution of surface normals using the exponential map shape deformations are described using principal geodesic analysis on the exponential map using ideas from robust statistics we show how this deformable model may be fitted to facial images in which there is significant self shadowing moreover we demonstrate that the resulting shape from shading algorithm can be used to recover accurate facial shape and albedo from real world images in particular the algorithm can effectively fill in the facial surface when more than 30 of its area is subject to self shadowing to investigate the utility of the shape parameters delivered by the method we conduct experiments with illumination insensitive face recognition we present a novel recognition strategy in which similarity is measured in the space of the principal geodesic parameters we also use the recovered shape information to generate illumination normalized prototype images on which recognition can be performed finally we show that from a single input image we are able to generate the basis images employed by a number of well known illumination insensitive recognition algorithms we also demonstrate that the principal geodesics provide an efficient parameterization of the space of harmonic basis images

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

recovering facial shape using a statistical model of surface normal direction in this paper we show how a statistical model of facial shape can be embedded within a shape from shading algorithm we describe how facial shape can be captured using a statistical model of variations in surface normal direction to construct this model we make use of the azimuthal equidistant projection to map the distribution of surface normals from the polar representation on a unit sphere to cartesian points on a local tangent plane the distribution of surface normal directions is captured using the covariance matrix for the projected point positions the eigenvectors of the covariance matrix define the modes of shape variation in the fields of transformed surface normals we show how this model can be trained using surface normal data acquired from range images and how to fit the model to intensity images of faces using constraints on the surface normal direction provided by lambert s law we demonstrate that the combination of a global statistical constraint and local irradiance constraint yields an efficient and accurate approach to facial shape recovery and is capable of recovering fine local surface details we assess the accuracy of the technique on a variety of images with ground truth and real world images

measuring the self similarity exponent in levy stable processes of financial time series abstract geometric method based procedures which will be called gm algorithms herein were introduced in m a sanchez granero j e trinidad segovia j garcia perez some comments on hurst exponent and the long memory processes on capital markets phys a 387 2008 5543 5551 to efficiently calculate the self similarity exponent of a time series in that paper the authors showed empirically that these algorithms based on a geometrical approach are more accurate than the classical algorithms especially with short length time series the authors checked that gm algorithms are good when working with fractional brownian motions moreover in j e trinidad segovia m fernandez martinez m a sanchez granero a note on geometric method based procedures to calculate the hurst exponent phys a 391 2012 2209 2214 a mathematical background for the validity of such procedures to estimate the self similarity index of any random process with stationary and self affine increments was provided in particular they proved theoretically that gm algorithms are also valid to explore long memory in fractional levy stable motions in this paper we prove empirically by monte carlo simulation that gm algorithms are able to calculate accurately the self similarity index in levy stable motions and find empirical evidence that they are more precise than the absolute value exponent denoted by ave onwards and the multifractal detrended fluctuation analysis mf dfa algorithms especially with a short length time series we also compare them with the generalized hurst exponent ghe algorithm and conclude that both gm2 and ghe algorithms are the most accurate to study financial series in addition to that we provide empirical evidence based on the accuracy of gm algorithms to estimate the self similarity index in levy motions that the evolution of the stocks of some international market indices such as u s small cap and nasdaq100 cannot be modelized by means of a brownian motion

estimation of illuminant direction albedo and shape from shading a robust approach to the recovery of shape from shading information is presented assuming uniform albedo and lambertian surface for the imaging model two methods for estimating the azimuth of the illuminant are presented one is based on local estimates on smooth patches and the other method uses shading information along image contours the elevation of the illuminant and surface albedo are estimated from image statistics taking into consideration the effect of self shadowing with the estimated reflectance map parameters the authors then compute the surface shape using a procedure that implements the smoothness constraint by requiring the gradients of reconstructed density to be close to the gradients of the input image the algorithm is data driven stable updates the surface slope and height maps simultaneously and significantly reduces the residual errors in irradiance and integrability terms a hierarchical implementation of the algorithm is presented typical results on synthetic and images are given to illustrate the usefulness of the approach

shape from shading with a linear triangular element surface model the authors propose to combine a triangular element surface model with a linearized reflectance map to formulate the shape from shading problem the main idea is to approximate a smooth surface by the union of triangular surface patches called triangular elements and express the approximating surface as a linear combination of a set of nodal basis functions since the surface normal of a triangular element is uniquely determined by the heights of its three vertices or nodes image brightness can be directly related to nodal heights using the linearized reflectance map the surface height can then be determined by minimizing a quadratic cost functional corresponding to the squares of brightness errors and solved effectively with the multigrid computational technique the proposed method does not require any integrability constraint or artificial assumptions on boundary conditions simulation results for synthetic and real images are presented to illustrate the performance and efficiency of the method

pricing geometric asian power options under mixed fractional brownian motion environment abstract it has been observed that the stock price process can be modeled with driving force as a mixed fractional brownian motion with hurst index h 3 4 whenever long range dependence is possibly present we obtain a closed form expression for the price of a geometric asian option under the mixed fractional brownian motion environment we consider also asian power options when the payoff function is a power function

models of anomalous diffusion the subdiffusive case abstract the paper discusses a model for anomalous diffusion processes their one point probability density functions p d f are exact solutions of fractional diffusion equations the model reflects the asymptotic behavior of a jump anomalous random walk process with random jump sizes and random inter jump time intervals with infinite means and variances which do not satisfy the law of large numbers in the case when these intervals have a fractional exponential p d f the fractional komogorov feller equation for the corresponding anomalous diffusion is provided and methods of finding its solutions are discussed finally some statistical properties of solutions of the related langevin equation are studied the subdiffusive case is explored in detail the emphasis is on a rigorous presentation which however would be accessible to the physical sciences audience

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

shape from shading using probability functions and belief propagation shape from shading sfs aims to reconstruct the three dimensional shape of an object from a single shaded image this article proposes an improved framework based on belief propagation for computing sfs the implementation of the well known brightness integrability and smoothness constraints inside this framework is shown we implement the constraints as probability density functions for example the brightness constraint is a two dimensional probability density function that relates all possible surface gradients at a pixel to their probability given the pixel intensity a straightforward extension of the framework to photometric stereo is presented where multiple images of the same scene taken under different lighting conditions are available the results are promising especially since the solution is obtained by iteratively applying simple operations on a regular grid of points the presented framework therefore can be implemented in parallel and is a reasonably likely biological scheme

learning shape from shading by a multilayer network the multilayer feedforward network has often been used for learning a nonlinear mapping based on a set of examples of the input output data in this paper we present a novel use of the network in which the example data are not explicitly given we consider the problem of shape from shading in computer vision where the input image coordinates and the output surface depth satisfy only a known differential equation we use the feedforward network as a parametric representation of the object surface and reformulate the shape from shading problem as the minimization of an error function over the network weights the stochastic gradient and conjugate gradient methods are used for the minimization boundary conditions for either surface depth or surface normal or both can be imposed by adjusting the same network at different levels it is further shown that the light source direction can be estimated based on an initial guess by integrating the source estimation with the surface estimation extensions of the method to a wider class of problems are discussed the efficiency of the method is verified by examples of both synthetic and real images

self similar gaussian processes for modeling anomalous diffusion we study some gaussian models for anomalous diffusion which include the time rescaled brownian motion two types of fractional brownian motion and models associated with fractional brownian motion based on the generalized langevin equation gaussian processes associated with these models satisfy the anomalous diffusion relation which requires the mean square displacement to vary with t ensuremath alpha 0l ensuremath alpha l2 however these processes have different properties thus indicating that the anomalous diffusion relation with a single parameter is insufficient to characterize the underlying mechanism although the two versions of fractional brownian motion and time rescaled brownian motion all have the same probability distribution function the slepian theorem can be used to compare their first passage time distributions which are different finally in order to model anomalous diffusion with a variable exponent ensuremath alpha t it is necessary to consider the multifractional extensions of these gaussian processes

second look at the spread of epidemics on networks in an important paper newman phys rev e66 016128 2002 claimed that a general network based stochastic susceptible infectious removed sir epidemic model is isomorphic to a bond percolation model where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor in this paper we show that this isomorphism is incorrect and define a semidirected random network we call the epidemic percolation network that is exactly isomorphic to the sir epidemic model in any finite population in the limit of a large population i the distribution of self limited outbreak sizes is identical to the size distribution of small out components ii the epidemic threshold corresponds to the phase transition where a giant strongly connected component appears iii the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in component and iv the relative final size of an epidemic is equal to the proportion of the network contained in the giant out component for the sir model considered by newman we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold the same epidemic threshold and the same final size of an epidemic as the bond percolation model however the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution we confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations in the appendix we show that an isomorphism to an epidemic percolation network can be defined for any time homogeneous stochastic sir model

globally optimal estimation of nonrigid image distortion image alignment in the presence of non rigid distortions is a challenging task typically this involves estimating the parameters of a dense deformation field that warps a distorted image back to its undistorted template generative approaches based on parameter optimization such as lucas kanade can get trapped within local minima on the other hand discriminative approaches like nearest neighbor require a large number of training samples that grows exponentially with respect to the dimension of the parameter space and polynomially with the desired accuracy 1 in this work we develop a novel data driven iterative algorithm that combines the best of both generative and discriminative approaches for this we introduce the notion of a pull back operation that enables us to predict the parameters of the test image using training samples that are not in its neighborhood not close in the parameter space we prove that our algorithm converges to the global optimum using a significantly lower number of training samples that grows only logarithmically with the desired accuracy we analyze the behavior of our algorithm extensively using synthetic data and demonstrate successful results on experiments with complex deformations due to water and clothing