inference of the sparse kinetic ising model using the decimation method in this paper we study the inference of the kinetic ising model on sparse graphs by the decimation method the decimation method which was first proposed in decelle and ricci tersenghi phys rev lett 112 070603 2014 for the static inverse ising problem tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively during the decimation process the likelihood function is maximized over the remaining couplings unlike the l 1 optimization based methods the decimation method does not use the laplace distribution as a heuristic choice of prior to select a sparse solution in our case the whole process can be done auto matically without fixing any parameters by hand we show that in the dynamical inference problem where the task is to reconstruct the couplings of an ising model given the data the decimation process can be applied naturally into a maximum likelihood optimization algorithm as opposed to the static case where pseudolikelihood method needs to be adopted we also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems our results illustrate that on various topologies and with different distribution of couplings the decimation method outperforms the widely used l 1 optimization based methods

improvement on dynamic elastic interpolation technique for reconstructing 3 d objects from serial cross sections an improved method for automatically reconstructing a three dimensional object from serial cross sections is presented in this paper the method improves the dynamic elastic contour interpolation technique 21 there are two major improvements 1 in the case of branching that involves concave contours instead of pairwise inter polation between the start contour and each goal contour the goal im age is considered globally and local constraints are imposed on the forces exerting upon the vertices 2 it takes the continuity of high order derivatives into consideration and incorporates the schemes of spline theory quadratic variation based surface interpolation and fi nite element based multilevel surface interpolation to create smoother surfaces of the reconstructed object in the proposed method the ini tial description of the object is formed by applying the elastic inter polation algorithm to generate a series of intermediate contours be tween each input pair of consecutive cross sections after this a preliminary processing for surface computation is carried out by map ping the contours onto the domain of surface function and then using spline functions to calculate the initial surface values based on the output from the preliminary processing two alternatives viz qua dratic variation based surface interpolation algorithm and finite ele ment based multilevel surface interpolation algorithm can he adopted to obtain the final surface representation

dynamic behavior for a system of neutral functional differential equations consider the system of neutral functional differential equations x 1 t x 2 t r f x 1 t g x 2 t r x 2 t x 1 t r f x 2 t g x 1 t r where r 0 f g c r it is shown that if f is nondecreasing on r and some additional assumptions hold then the w limit set of every bounded solution of such a system with some initial conditions is composed of 2r periodic solutions our results are new and complement some corresponding ones already known

three dimensional shape description using the symmetric axis transform i theory blum s two dimensional shape description method based on the symmetric axis transform sat is generalized to three dimensions the method uniquely decomposes an object into a collection of sub objects each drawn from three separate but not completely independent primitive sets defined in the paper width primitives based on radius function properties axis primitives based on symmetric axis curvatures and boundary primitives based on boundary surface curvatures width primitives are themselves comprised of two components slope districts and curvature districts visualizing the radius function as if it were the height function of some mountainous terrain each slope district corresponds to a mountain face together with the valley below it curvature districts further partition each slope district into regions that are locally convex concave or saddle like similarly axis boundary primitives are regions of the symmetric surface where the symmetric surface boundary surfaces are locally convex concave or saddle like relations among the primitive sets are discussed

interpolation of 3 d binary images based on morphological skeletonization the morphological skeleton interpolation msi algorithm is presented it is an efficient shape based interpolation method used for interpolating slices in a three dimensional 3 d binary object it is based on morphological skeletonization which is used for two dimensional 2 d slice representation the proposed morphological skeleton matching process provides translation rotation and scaling information at the same time the interpolated slices preserve the shape of the original object slices when the slices have similar shapes it can also modify the shape of an object when the successive slices do not have similar shapes applications on artificial and real data are also presented

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

surface interpolation from sparse cross sections using region correspondence the ability to estimate a surface from a set of cross sections allows calculation of the enclosed volume and the display of the surface in three dimensions this process has increasingly been used to derive useful information from medical data however extracting the cross sections segmenting can be very difficult and automatic segmentation methods are not sufficiently robust to handle all situations hence it is an advantage if the surface reconstruction algorithm can work effectively on a small number of cross sections in addition cross sections of medical data are often quite complex shape based interpolation is a simple and elegant solution to this problem although it has known limitations when handling complex shapes in this paper the shape based interpolation paradigm is extended to interpolate a surface through sparse complex cross sections providing a significant improvement over the authors previously published maximal disc guided interpolation the performance of this algorithm is demonstrated on various types of medical data x ray computed tomography magnetic resonance imaging and three dimensional ultrasound although the correspondence problem in general remains unsolved it is demonstrated that correct surfaces can be estimated from a limited amount of real data through the use of region rather than object correspondence

parameter inference in a probabilistic model using clustered data abstract we propose a method to infer the parameters of a probabilistic model from given data samples our method is based on the pseudolikelihood and composite likelihood methods we cluster the given data samples and apply the clustered data samples to the pseudolikelihood and composite likelihood methods from an expansion of the pseudolikelihood method around the mean of a cluster the mean field and thouless anderson palmer equations are derived likewise from an expansion of the composite likelihood method around the mean of a cluster a method that is similar to the bethe approximation is derived we then perform numerical simulations using our method we find that our method gives an accurate estimate in the range of weak coupling parameters but has an inferior accuracy compared to the pseudolikelihood and composite likelihood methods in the range of strong coupling parameters in the range of strong coupling parameters as the number of clusters increases the inference accuracy of our method improves compared to the pseudolikelihood and composite likelihood methods our method reduces the number of computational tasks for the estimation therefore sacrificing the inference accuracy

pattern spectrum and multiscale shape representation the results of a study on multiscale shape description smoothing and representation are reported multiscale nonlinear smoothing filters are first developed using morphological opening and closings g matheron 1975 used openings and closings to obtain probabilistic size distributions of euclidean space sets continuous binary images these distributions are used to develop a concept of pattern spectrum a shape size descriptor a pattern spectrum is introduced for continuous graytone images and arbitrary multilevel signals as well as for discrete images by developing a discrete size family of patterns large jumps in the pattern spectrum at a certain scale indicate the existence of major protruding or intruding substructures of the signal at the scale an entropy like shape size complexity measure is also developed based on the pattern spectrum for shape representation a reduced morphological skeleton transform is introduced for discrete binary and graytone images this transform is a sequence of skeleton components sparse images which represent the original shape at various scales it is shown that the partially reconstructed images from the inverse transform on subsequences of skeleton components are the openings of the image at a scale determined by the number of eliminated components in addition two way correspondences are established among the degree of shape smoothing via multiscale openings or closings the pattern spectrum zero values and the elimination or nonexistence of skeleton components at certain scales

ranks for pairs of spatial fields via metric based on grayscale morphological distances based on a set of morphological distances computed between the grayscale images spatial fields of similar size specifications the ratios of selected morphological distances and the ratios of areas of infima and suprema of grayscale images a new metric to quantify the degree of similarity between the grayscale images is proposed we denote the two spatial fields grayscale images respectively with f i and f j and the infima and suprema of these spatial fields with f i wedge f j and f i vee f j the three morphology based distances include 1 dilation distance d f i f j 2 erosion distance e f i f j and 3 median based distance m n f i f j by employing these parameters which play vital role in construction of parameter specific interaction matrices we provide a metric to designate every possible pair of images that can be considered out of a database consisting of a huge number of images we demonstrate the whole approach on 1 synthetic spatial fields 2 a set of 12 similar sized grayscale images representing cloud top temperatures of a specific region for 12 different time instants and 3 four spatial elevation fields to rank possible pairs of images

a min max medial axis transformation blum s medial axis transformation mat of the set s of 1 s in a binary picture can be defined by an iterative shrinking and reexpanding process which detects corners on the contours of constant distance from s and thereby yields a skeleton of s for unsegmented gray level pictures one can use an analogous definition in which local min and max operations play the roles of shrinking and expanding to compute a mmmat value at each point of the picture the set of points having high values defines a good skeleton for the set of high gray level points in the given picture

improvement on dynamic elastic interpolation technique for reconstructing 3 d objects from serial cross sections biomedical application an improved method for automatically reconstructing a three dimensional object from serial cross sections is presented the method improves the dynamic elastic contour interpolation technique there are two major improvements 1 in the case of branching that involves concave contours instead of pairwise interpolation between the start contour and each goal contour the goal image is considered globally and local constraints are imposed on the forces exerting upon the vertices and 2 it takes the continuity of high order derivatives into consideration and incorporates the schemes of spline theory quadratic variation based surface interpolation and finite element based multilevel surface interpolation to create smoother surfaces of the reconstructed object based on the output from the preliminary processing two alternatives a quadratic variation based surface interpolation algorithm and a finite element based multilevel surface interpolation algorithm can be adopted to obtain the final surface representation

simple method for inference in inverse ising problem using full data abstract we consider inference in the inverse ising problem using full data which means incorporating sets of spin configurations we approximate the boltzmann distribution of the system to generate a frequency distribution derived from the given data then the ratio between two boltzmann distributions with different spin configurations eliminates the partition function and we obtain linear equations which can be solved to yield statistical parameters our method is applicable to cases where the absolute values of the coupling parameters and external fields are large compared to pseudolikelihood maximization the accuracy of the inference obtained from our method is similar although our approach is less labor intensive

threshold superposition in morphological image analysis systems it is shown that four composite morphological systems namely morphological edge detection peak valley extraction skeletonization and shape size distributions obey a weak linear superposition called threshold linear superposition the output image signal or measurement from each system is shown to be the sum of outputs due to input binary images that result from thresholding the input gray level image at all levels these results are generalized to a vector space formulation e g to any finite linear combination of simple morphological systems thus many such systems processing gray level images are reduced to corresponding binary image processing systems which are easier to analyze and implement

asymptotic behavior of bounded solutions for a system of neutral functional differential equations abstract consider the system of neutral functional differential equations x 1 t c x 2 t r f x 1 t g x 2 t r x 2 t c x 1 t r f x 2 t g x 1 t r where r 0 c 0 1 f g c r 1 and f is strictly increasing on r 1 it is shown that if f x g x for all x r 1 or f x g x for all x r 1 then every bounded solution of such a system tends to an equilibrium our results improve and extend some corresponding ones already known

some properties of interpolations using mathematical morphology the problem of interpolation between two images is defined as given two images one at time t 0 and another at t t one must estimate the series of intermediate images for all intermediate time steps this problem is not well posed in the sense that without further constraints there are many possible solutions the solution is thus usually dictated by the choice of the constraints assumptions which in turn relies on the domain of application in this article we follow the approach of obtaining a solution to the interpolation problem using the operators from mathematical morphology mm these operators have an advantage of preserving structures since the operators are defined on sets in this paper we explore the solutions obtained using mm and provide several results along with proofs which corroborates the validity of the assumptions provide links among existing methods and intuition about them we also summarize few possible extensions and prospective problems of current interest

min max operators in texture analysis a signature is generated for a given picture by operating on it with different masks the operations are gray level generalizations of shrink and expand for binary pictures using serra s morphological methods 10 the signature is a set of numbers each corresponding to an application of an operator at a certain scale and direction and can be used to analyze the discriminate textures it is shown that this family of signatures includes as special cases several currently used texture descriptors

nonlinear filtering approach to 3 d gray scale image interpolation three dimensional 3 d images are now common in radiology a 3 d image is formed by stacking a contiguous sequence of two dimensional cross sectional images or slices typically the spacing between known slices is greater than the spacing between known points on a slice many visualization and image analysis tasks however require the 3 d image to have equal sample spacing in all directions to meet this requirement one applies an interpolation technique to the known 3 d image to generate a new uniformly sampled 3 d image the authors propose a nonlinear filter based approach to gray scale interpolation of 3 d images the method referred to as column fitting interpolation is reminiscent of the maximum homogeneity filter used for image enhancement the authors also draw upon the paradigm of relaxation labeling to devise an improved column fitting interpolator both methods are typically more effective than traditional gray scale interpolation techniques

improved contact prediction in proteins using pseudolikelihoods to infer potts models spatially proximate amino acids in a protein tend to coevolve a protein s three dimensional 3d structure hence leaves an echo of correlations in the evolutionary record reverse engineering 3d structures from such correlations is an open problem in structural biology pursued with increasing vigor as more and more protein sequences continue to fill the data banks within this task lies a statistical inference problem rooted in the following correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network propagated via intermediate sites observed correlation is not enough to guarantee proximity to separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics where the task is to learn model parameters fields couplings from observables magnetizations correlations samples in large systems in the context of protein sequences the approach has been referred to as direct coupling analysis here we show that the pseudolikelihood method applied to 21 state potts models describing the statistical properties of families of evolutionarily related proteins significantly outperforms existing approaches to the direct coupling analysis the latter being based on standard mean field techniques this improved performance also relies on a modified score for the coupling strength the results are verified using known crystal structures of specific sequence instances of various protein families code implementing the new method can be found at http plmdca csc kth se

a 3 d reconstruction algorithm for interpolation and extrapolation of planar cross sectional data a three dimensional 3 d reconstruction algorithm utilizing both linear interpolation and linear extrapolation was developed for the study of human prostatic cancer the algorithm was validated by comparing the volumes and shapes of original to reconstructed objects synthetic objects of known geometry and wax models with shapes characteristic of prostatic carcinomas were assessed with standard planimetry and by the digital interpolation extrapolation method volume and multifocality measurements obtained by reconstructing excised prostate glands using histologic maps obtained from whole mount sections were tested the new algorithm provided greater accuracy in determining tumor volumes than conventional methods this model provides a basis for mathematical analysis of prostate cancer lesions

erratum to visualization of spatiotemporal behavior of discrete maps via generation of recursive median elements spatial interpolation is one of the demanding techniques in geographic information science gisci to generate interpolated maps in a continuous manner by using two discrete spatial and or temporal data sets noise free data thematic layers depicting a specific theme at varied spatial or temporal resolutions consist of connected components either in aggregated or in disaggregated forms this short paper provides a simple framework 1 to categorize the connected components of layered sets of two different time instants through their spatial relationships and the hausdorff distances between the companion connected components and 2 to generate sequential maps interpolations between the discrete thematic maps development of the median set using hausdorff erosion and dilation distances to interpolate between temporal frames is demonstrated on lake geometries mapped at two different times and also on the bubonic plague epidemic spread data available for 11 consecutive years we documented the significantly fair quality of the median sets generated for epidemic data between alternative years by visually comparing the interpolated maps with actual maps they can be used to visualize animate the spatiotemporal behavior of a specific theme in a continuous sequence

shape based interpolation of multidimensional objects a shape based interpolation scheme for multidimensional images is presented this scheme consists of first segmenting the given image data into a binary image converting the binary image back into a gray image wherein the gray value of a point represents its shortest distance positive value for points of the object and negative for those outside from the cross sectional boundary and then interpolating the gray image the set of all points with nonnegative values associated with them in the interpolated image constitutes the interpolated object the method not only minimizes user involvement in interactive segmentation but also leads to more accurate representation and depiction of dynamic as well as static objects the general methodology and the implementation details of the method are presented and compared on a qualitative and quantitative basis to the existing methods the generality of the proposed scheme is illustrated with a number of medical imaging examples

on perturbed proximal gradient algorithms we study a version of the proximal gradient algorithm for which the gradient is intractable and is approximated by monte carlo methods and in particular markov chain monte carlo we derive conditions on the step size and the monte carlo batch size under which convergence is guaranteed both increasing batch size and constant batch size are considered we also derive non asymptotic bounds for an averaged version our results cover both the cases of biased and unbiased monte carlo approximation to support our findings we discuss the inference of a sparse generalized linear model with random effect and the problem of learning the edge structure and parameters of sparse undirected graphical models

convergence for pseudo monotone semiflows on product ordered topological spaces in this paper we consider a class of pseudo monotone semiflows which only enjoy some weak monotonicity properties and are defined on product ordered topological spaces under certain conditions several convergence principles are established for each precompact orbit of such a class of semiflows to tend to an equilibrium which improve and extend some corresponding results already known some applications to delay differential equations are presented

parameter inference in a probabilistic model from data regulation of transition rate in the monte carlo method abstract we consider the inference of parameters in a probabilistic model from a data set which is generated by an unknown probabilistic model the monte carlo method is a tool for obtaining a data set obeying a given probability distribution a set of transition rates is required to satisfy three conditions irreducible aperiodic and stationary for a sampled data set to represent a probability distribution we utilize the stationary condition of a probability distribution with respect to transition rates to infer parameters a frequency distribution by a data set substitutes for an unknown probability distribution in the condition our method includes minimum probability flow as a special case and becomes superior to it as the number of samples increases

shape based interpolation of tree like structures in three dimensional images many three dimensional 3 d medical images have lower resolution in the z direction than in the x or y directions before extracting and displaying objects in such images an interpolated 3 d gray scale image is usually generated via a technique such as linear interpolation to fill in the missing slices unfortunately when objects are extracted and displayed from the interpolated image they often exhibit a blocky and generally unsatisfactory appearance a problem that is particularly acute for thin treelike structures such as the coronary arteries two methods for shape based interpolation that offer an improvement to linear interpolation are presented in shape based interpolation the object of interest is first segmented extracted from the initial 3 d image to produce a low z resolution binary valued image and the segmented image is interpolated to produce a high resolution binary valued 3 d image the first method incorporates geometrical constraints and takes as input a segmented version of the original 3 d image the second method builds on the first in that it also uses the original gray scale image as a second input tests with 3 d images of the coronary arterial tree demonstrate the efficacy of the methods

influence of multiple sequence alignment depth on potts statistical models of protein covariation potts statistical models have become a popular and promising way to analyze mutational covariation in protein multiple sequence alignments msas in order to understand protein structure function and fitness but the statistical limitations of these models which can have millions of parameters and are fit to msas of only thousands or hundreds of effective sequences using a procedure known as inverse ising inference are incompletely understood in this work we predict how model quality degrades as a function of the number of sequences n sequence length l amino acid alphabet size q and the degree of conservation of the msa in different applications of the potts models in fitness predictions of individual protein sequences in predictions of the effects of single point mutations in double mutant cycle predictions of epistasis and in 3d contact prediction in protein structure we show how as msa depth n decreases an overfitting effect occurs such that sequences in the training msa have overestimated fitness and we predict the magnitude of this effect and discuss how regularization can help correct for it using a regularization procedure motivated by statistical analysis of the effects of finite sampling we find that as n decreases the quality of point mutation effect predictions degrade least fitness and epistasis predictions degrade more rapidly and contact predictions are most affected however overfitting becomes negligible for msa depths of more than a few thousand effective sequences as often used in practice and regularization becomes less necessary we discuss the implications of these results for users of potts covariation analysis

power law tails in phylogenetic systems covariance analysis of protein sequence alignments uses coevolving pairs of sequence positions to predict features of protein structure and function however current methods ignore the phylogenetic relationships between sequences potentially corrupting the identification of covarying positions here we use random matrix theory to demonstrate the existence of a power law tail that distinguishes the spectrum of covariance caused by phylogeny from that caused by structural interactions the power law is essentially independent of the phylogenetic tree topology depending on just two parameters the sequence length and the average branch length we demonstrate that these power law tails are ubiquitous in the large protein sequence alignments used to predict contacts in 3d structure as predicted by our theory this suggests that to decouple phylogenetic effects from the interactions between sequence distal sites that control biological function it is necessary to remove or down weight the eigenvectors of the covariance matrix with largest eigenvalues we confirm that truncating these eigenvectors improves contact prediction

monotone semiflows generated by functional differential equations abstract this obtains sufficient condition for an autonomous functional differential equation to generate a strongly monotone semiflow on a suitable state space this allows the application to functional differential equations of very powerful recent results on strongly monotone semiflows due to hirsch and matano in addition a very striking relationship is established between such functional differential equations and corresponding ordinary differential equations an example involving a biochemical feedback loop is considered keywords stability steady states

consistent inference of a general model using the pseudolikelihood method recently a maximum pseudolikelihood mpl inference method has been successfully applied to statistical physics models with intractable likelihoods we use information theory to derive a relation between the pseudolikelihood and likelihood functions furthermore we show the consistency of the pseudolikelihood method for a general model

binary morphological shape based interpolation applied to 3 d tooth reconstruction in this paper we propose an interpolation algorithm using a mathematical morphology morphing approach the aim of this algorithm is to reconstruct the n dimensional object from a group of n 1 dimensional sets representing sections of that object the morphing transformation modifies pairs of consecutive sets such that they approach in shape and size the interpolated set is achieved when the two consecutive sets are made idempotent by the morphing transformation we prove the convergence of the morphological morphing the entire object is modeled by successively interpolating a certain number of intermediary sets between each two consecutive given sets we apply the interpolation algorithm for three dimensional tooth reconstruction