regular orbits on symplectic modules let g be a finite group and let v be a faithful kg module k a field the question is does v contain a regular g orbit the problem has been widely studied in the literature in l berger proves that the answer is positive when a is nilpotent c 1 c free for every p and char k 1 a in 6 hargraves drops the condition of being a c c free for odd primes which are not mersenne primes a simplified proof of the main results of hargraves may be found in fleischmann s paper 3 in s gow shows that the conclusion holds when a is nilpotent char k j j a 1 and both 1 a i and char k are odd in io turull studies the case in which a is supersolvable and v is a completely reducible a module theorem 2 2 of lo extends berger s result in z the author studies a particular situation in which char k 1 1 a it is proven that if h k is a p chief factor of a solvable group g p odd and a is a p subgroup of g acting faithfully on h k then h k contains a regular a orbit the nilpotent case is open in this note we suppose that v is endowed with a g invariant nonsingular symplectic form this allows us to obtain stronger results

on a conjecture of gluck let mathbf f g and b g respectively denote the fitting subgroup and the largest degree of an irreducible complex character of a finite group g a well known conjecture of d gluck claims that if g is solvable then g mathbf f g le b g 2 we confirm this conjecture in the case where mathbf f g is coprime to 6 we also extend the problem to arbitrary finite groups and prove several results showing that the largest irreducible character degree of a finite group strongly controls the group structure

large orbits of odd order subgroups of solvable linear groups abstract suppose that g is a finite solvable group and v is a finite faithful and completely reducible g module let h be an odd order subgroup of g then h has at least two regular orbits on v v suppose in addition that v is odd then there exists v v in a regular orbit of f g h such that c h v f 2 g let g be a solvable group h be an odd order hall subgroup of g v be a faithful g module over possibly different finite fields of odd characteristic and assume that v o g is completely reducible then there exists v v such that c h v o g

nonsolvable groups with no prime dividing three character degrees abstract in this paper we complete a study that is originated by lewis and white of finite nonsolvable groups where no prime divides three irreducible character degrees

dimensional reduction of the master equation for stochastic chemical networks the reduced multiplane method chemical reaction networks which exhibit strong fluctuations are common in microscopic systems in which reactants appear in low copy numbers the analysis of these networks requires stochastic methods which come in two forms direct integration of the master equation and monte carlo simulations the master equation becomes infeasible for large networks because the number of equations increases exponentially with the number of reactive species monte carlo methods which are more efficient in integrating over the exponentially large phase space also become impractical due to the large amounts of noisy data that need to be stored and analyzed the recently introduced multiplane method a lipshtat and o biham phys rev lett 93 170601 2004 is an efficient framework for the stochastic analysis of large reaction networks it is a dimensional reduction method based on the master equation which provides a dramatic reduction in the number of equations without compromising the accuracy of the results the reduction is achieved by breaking the network into a set of maximal fully connected subnetworks maximal cliques a separate master equation is written for the reduced probability distribution associated with each clique with suitable coupling terms between them this method is highly efficient in the case of sparse networks in which the maximal cliques tend to be small however in dense networks some of the cliques may be rather large and the dimensional reduction is not as effective furthermore the derivation of the multiplane equations from the master equation is tedious and difficult here we present the reduced multiplane method in which the maximal cliques are broken down to the fundamental two vertex cliques the number of equations is further reduced making the method highly efficient even for dense networks moreover the equations take a simpler form which can be easily constructed using a diagrammatic procedure for any desired network architecture it is shown that the method provides accurate results for the population sizes of the reactive species and their reaction rates

variational region based segmentation using multiple texture statistics this paper investigates variational region level criterion for supervised and unsupervised texture based image segmentation the focus is given to the demonstration of the effectiveness and robustness of this region based formulation compared to most common variational approaches the main contributions of this global criterion are twofold first the proposed methods circumvent a major problem related to classical texture based segmentation approaches existing methods even if they use different and various texture features are mainly stated as the optimization of a criterion evaluating punctual pixel likelihoods or similarity measure computed within a local neighborhood these approaches require sufficient dissimilarity between the considered texture features an additional limitation is the choice of the neighborhood size and shape these two parameters and especially the neighborhood size significantly influence the classification performances the neighborhood must be large enough to capture texture structures and small enough to guarantee segmentation accuracy these parameters are often set experimentally these limitations are mitigated with the proposed variational methods stated at the region level it resorts to an energy criterion defined on image where regions are characterized by nonparametric distributions of their responses to a set of filters in the supervised case the segmentation algorithm consists in the minimization of a similarity measure between region level statistics and texture prototypes and a boundary based functional that imposes smoothness and regularity on region boundaries in the unsupervised case the data driven term involves the maximization of the dissimilarity between regions the proposed similarity measure is generic and permits optimally fusing various types of texture features it is defined as a weighted sum of kullback leibler divergences between feature distributions the optimization of the proposed variational criteria is carried out using a level set formulation the effectiveness and the robustness of this formulation at region level compared to classical active contour methods are evaluated for various brodatz and natural images

zeros of brauer characters and linear actions of finite groups small primes abstract we describe the finite groups whose p brauer character table for p 2 or p 3 does not contain any zero this completes the analysis in 6 where we considered the case p 5

structural matching by discrete relaxation this paper describes a bayesian framework for performing relational graph matching by discrete relaxation our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching broadly speaking there are two main aspects to this study firstly we focus on the issue of how relational inexactness may be quantified we illustrate that several popular relational distance measures can be recovered as specific limiting cases of the bayesian consistency measure the second aspect of our comparison concerns the way in which structural inexactness is controlled we investigate three different realizations of the matching process which draw on contrasting control models the main conclusion of our study is that the active process of graph editing outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter

polyhedral object recognition by indexing in computer vision the indexing problem is the problem of recognizing a few objects in a large database of objects while avoiding the help of the classical image feature to object feature matching paradigm in this paper we address the problem of recognizing three dimensional 3 d polyhedral objects from 2 d images by indexing both the objects to be recognized and the images are represented by weighted graphs the indexing problem is therefore the problem of determining whether a graph extracted from the image is present or absent in a database of model graphs we introduce a novel method for performing this graph indexing process which is based both on polynomial characterization of binary and weighted graphs and on hashing we describe in detail this polynomial characterization and then we show how it can be used in the context of polyhedral object recognition next we describe a practical recognition by indexing system that includes the organization of the database the representation of polyhedral objects in terms of 2 d characteristic views the representation of this views in terms of weighted graphs and the associated image processing finally some experimental results allow the evaluation of the system performance

object recognition using shape from shading investigates whether surface topography information extracted from intensity images using a shape from shading sfs algorithm can be used for the purposes of 3d object recognition we consider how curvature and shape index information delivered by this algorithm can be used to recognize objects based on their surface topography we explore two contrasting object recognition strategies the first of these is based on a low level attribute summary and uses histograms of curvature and orientation measurements the second approach is based on the structural arrangement of constant shape index maximal patches and their associated region attributes we show that region curvedness and a string ordering of the regions according to size provides recognition accuracy of about 96 percent by polling various recognition schemes including a graph matching method we show that a recognition rate of 98 99 percent is achievable

induction and restriction of characters and hall subgroups abstract let h be a hall subgroup of a separable group g given a character irr g we determine when it happens that g for every irreducible constituent of h and dually given a character irr h we determine when it happens that h for every irreducible constituent of g we also study some related questions

statistical motion model based on the change of feature relationships human gait based recognition we offer a novel representation scheme for view based motion analysis using just the change in the relational statistics among the detected image features without the need for object models perfect segmentation or part level tracking we model the relational statistics using the probability that a random group of features in an image would exhibit a particular relation to reduce the representational combinatorics of these relational distributions we represent them in a space of probability functions sopf where the euclidean distance is related to the bhattacharya distance between probability functions different motion types sweep out different traces in this space we demonstrate and evaluate the effectiveness of this representation in the context of recognizing persons from gait in particular on outdoor sequences 1 we demonstrate the possibility of recognizing persons from not only walking gait but running and jogging gaits as well 2 we study recognition robustness with respect to view point variation and 3 we benchmark the recognition performance on a database of 71 subjects walking on soft grass surface where we achieve around 90 percent recognition rates in the presence of viewpoint variation

robust image modeling techniques with an image restoration application a robust parameter estimation algorithm for a nonsymmetric half plane nshp autoregressive model where the driving noise is a mixture of a gaussian and an outlier process is presented the convergence of the estimation algorithm is proved an algorithm to estimate parameters and original image intensity simultaneously from the impulse noise corrupted image where the model governing the image is not available is also presented the robustness of the parameter estimates is demonstrated by simulation finally an algorithm to restore realistic images is presented the entire image generally does not obey a simple image model but a small portion e g 8 8 of the image is assumed to obey an nshp model the original image is divided into windows and the robust estimation algorithm is applied for each window the restoration algorithm is tested by comparing it to traditional methods on several different images

texture synthesis textons revisited this paper introduces a technique for synthesizing natural textures with emphasis on quasiperiodic and structural textures textures are assumed to be composed of three components namely illumination structure and stochastic the contribution of this work is that in contrast to previous techniques it proposes a joint approach for handling the texture s global illumination irregular structure and stochastic component which may be correlated to the other two components furthermore the proposed technique does not produce verbatim copies in the synthesized texture more specifically a top down approach is used for extraction of texture elements textons in which in contrast to previous texton based approaches no assumptions regarding perfect periodicity are made the structure itself can be modeled as a stochastic process consequently textons are allowed to have irregular and nonidentical shapes in the synthesis stage a new nonregular textural structure is designed from the original one that defines the place holders for textons we call such place holders empty textons e textons the e textons are filled in by a representative texton since e textons do not have identical shapes a texton shape matching procedure is required after adding the illumination to the structural component a strictly localized version of a block sampling technique is applied to add the stochastic component the block sampling technique combined with the addition of the illumination component provides a significant improvement in the appearance of synthesized textures results show that the proposed method is successful in synthesizing structural textures visually indistinguishable to the original moreover the method is successful in synthesizing a variety of stochastic textures

groups whose degree graph has three independent vertices abstract let g be a finite group and let cd g denote the set of degrees of the irreducible complex characters of g this paper is a contribution to the study of the degree graph of g that is the prime graph built on the set cd g namely we characterize finite groups whose degree graph has three independent vertices i e three vertices that are pairwise non adjacent our result turns out to be a generalization of several previously known theorems concerning the structure of the degree graph

an efficiently computable metric for comparing polygonal shapes a method for comparing polygons that is a metric invariant under translation rotation and change of scale reasonably easy to compute and intuitive is presented the method is based on the l sub 2 distance between the turning functions of the two polygons it works for both convex and nonconvex polygons and runs in time o mn log mn where m is the number of vertices in one polygon and n is the number of vertices in the other some examples showing that the method produces answers that are intuitively reasonable are presented

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

stochastic analysis of complex reaction networks using binomial moment equations the stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species direct integration of the master equation is thus infeasible and is most often replaced by monte carlo simulations while monte carlo simulations are a highly effective tool equation based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network here we present a highly efficient equation based method for the analysis of stochastic reaction networks the method is based on the recently introduced binomial moment equations barzel and biham phys rev lett 106 150602 2011 the binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species they capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure this leads to a simple and transparent form of the equations and allows a highly efficient and surprisingly simple truncation scheme unlike ordinary moment equations in which the inclusion of high order moments is prohibitively complicated the binomial moment equations can be easily constructed up to any desired order the result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions the number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial and often quadratic dependence on the number of reactive species in the binomial moment equations the aim of this paper is twofold to present a complete derivation of the binomial moment equations to demonstrate the applicability of the moment equations for a representative set of example networks in which stochastic effects play an important role

retrieval of textured images through the use of quantization and modal analysis this paper proposes a new method for textured image retrieval by the modal analysis of quantized spectral point patterns as the modal correspondence method of shapiro and brady to match point sets by comparing the eigenvectors of a pairwise point proximity matrix taken from the power spectrum peaks a variant of the carcassoni ribeiro and hancock method for performing recognition is taken into account for choosing image features to represent an image a quantization scheme is applied this quantization scheme acts in the spectral space given by the fourier transform of each image its goal is to find a small set which represents an image efficiently where the most important features are presented the proposed technique is invariant to rotation and is robust in the presence of noise and damaged images the techniques here presented are compared and the commonly used retrieval performance measurement precision and recall is used as evaluation of the query results

minimizing nonsubmodular functions with graph cuts a review optimization techniques based on graph cuts have become a standard tool for many vision applications these techniques allow to minimize efficiently certain energy functions corresponding to pairwise markov random fields mrfs currently there is an accepted view within the computer vision community that graph cuts can only be used for optimizing a limited class of mrf energies e g submodular functions in this survey we review some results that show that graph cuts can be applied to a much larger class of energy functions in particular nonsubmodular functions while these results are well known in the optimization community to our knowledge they were not used in the context of computer vision and mrf optimization we demonstrate the relevance of these results to vision on the problem of binary texture restoration

an answer to a question of isaacs on character degree graphs abstract let n be a normal subgroup of a finite group g we consider the graph g n whose vertices are the prime divisors of the degrees of the irreducible characters of g whose kernel does not contain n and two vertices are joined by an edge if the product of the two primes divides the degree of some of the characters of g whose kernel does not contain n we prove that if g n is disconnected then g n is solvable this proves a strong form of a conjecture of isaacs

line pattern retrieval using relational histograms this paper presents a new compact shape representation for retrieving line patterns from large databases the basic idea is to exploit both geometric attributes and structural information to construct a shape histogram we realize this goal by computing the n nearest neighbor graph for the lines segments for each pattern the edges of the neighborhood graphs are used to gate contributions to a two dimensional pairwise geometric histogram shapes are indexed by searching for the line pattern that maximizes the cross correlation of the normalized histogram bin contents we evaluate the new method on a database containing over 2 500 line patterns each composed of hundreds of lines

large orbits in coprime actions of solvable groups let g be a solvable group of automorphisms of a finite group k if g and k are coprime then there exists an orbit of g on k of size at least g it is also proved that in a solvable group the largest normal subgroup is the intersection of at most three hall subgroups

a variation on theorems of jordan and gluck abstract gluck proved that any finite group g has an abelian subgroup a such that g a is bounded by a polynomial function of the largest degree of the complex irreducible characters of g this improved on a previous bound of isaacs and passman in this paper we present a variation of this result that looks at the number of prime factors all these results in turn may be seen as variations on the classical theorem of jordan on linear groups

texture modeling by multiple pairwise pixel interactions a markov random field model with a gibbs probability distribution gpd is proposed for describing particular classes of grayscale images which can be called spatially uniform stochastic textures the model takes into account only multiple short and long range pairwise interactions between the gray levels in the pixels an effective learning scheme is introduced to recover structure and strength of the interactions using maximal likelihood estimates of the potentials in the gpd as desired parameters the scheme is based on an analytic initial approximation of the estimates and their subsequent refinement by a stochastic approximation experiments in modeling natural textures show the utility of the proposed model

gibbs random fields cooccurrences and texture modeling gibbs random field grf models and features from cooccurrence matrices are typically considered as separate but useful tools for texture discrimination the authors show an explicit relationship between cooccurrences and a large class of grf s this result comes from a new framework based on a set theoretic concept called the aura set and on measures of this set aura measures this framework is also shown to be useful for relating different texture analysis tools the authors show how the aura set can be constructed with morphological dilation how its measure yields cooccurrences and how it can be applied to characterizing the behavior of the gibbs model for texture in particular they show how the aura measure generalizes to any number of gray levels and neighborhood order some properties previously known for just the binary nearest neighbor grf finally the authors illustrate how these properties can guide one s intuition about the types of grf patterns which are most likely to form

on retrieving textured images from an image database abstract we discuss the problem of an image based query for retrieving images represented by sufficiently large regions of uniform textures from image data bases a distance measure to match the query image to the database content under possible orientation and scale differences between the textures of the same type is proposed the measure is based on comparing the gray level difference histograms collected in accord with the structure of multiple pairwise pixel interactions in the subimages to be matched the interaction structure is recovered with a proposed learning scheme for a markov random field image model with gibbs probability distribution texture rotation and scaling are handled to some extent by similar transformations of the interaction structures several results on experimental databases containing digitized textured images are presented

diameters of degree graphs of nonsolvable groups ii let g be a finite group and let cd g be the set of irreducible character degrees of g the degree graph g is the graph whose set of vertices is the set of primes that divide degrees in cd g with an edge between p and q if pq divides a for some degree a cd g it is shown using the degree graphs of the finite simple groups that if g is a nonsolvable group then the diameter of g is at most 3

nonsolvable normal subgroups and irreducible character degrees abstract let the nonsolvable n be a normal subgroup of the finite group g and cd g n denote the irreducible character degrees of g such that there exist respectively corresponding character kernels not containing n write cd g n to stand for the cardinality of cd g n suppose that cd g n 5 in this paper we prove that if n is a minimal normal subgroup then n is a simple group of lie type when n is a normal subgroup we prove that g has a normal series 1 v u n g such that v is solvable u v is a simple group of lie type and the cardinality cd g u 3 as an application we investigate the structure of g when 5 cd g 6 here cd g denotes the set of irreducible character degrees of g

regular orbits of finite primitive solvable groups abstract suppose that a finite solvable group g acts faithfully irreducibly and quasi primitively on a finite vector space v then g has a uniquely determined normal subgroup e which is a direct product of extraspecial p groups for various p and we denote e e z e we prove that when e 5 6 7 g will have regular orbits on v this result combined with a previous result of the author will give a complete list of e such that g will have regular orbits on v

bounding graph diameters of nonsolvable groups abstract associated with the character degrees of a finite group is the common divisor graph where the nontrivial degrees are the vertices and distinct degrees are adjacent when they have a common nontrivial divisor the author has shown that common divisor graphs for solvable groups have diameters of at most 3 the present paper extends this result to nonsolvable groups by showing that their common divisor graphs also have diameters bounded above by 3

noisy logo recognition using line segment hausdorff distance logo recognition is of great interest in the document and shape analysis domain in order to develop a recognition method that is robust to employ under adverse conditions such as different scale orientation broken curves added noise and occlusion a modified line segment hausdorff distance is proposed in this paper the new approach has the advantage to incorporate structural and spatial information to compute dissimilarity between two sets of line segments rather than two sets of points the proposed technique has been applied on line segments generated from logos with encouraging results clear cut distinction between the correct and incorrect matches has been observed this suggests a strong potential for logo and shape recognition system

geometric hashing with line features abstract geometric hashing is a model based object recognition technique for detecting objects which can be partially overlapping or partly occluded in its simplest form the geometric hashing method assumes relatively noise free data and is applied to objects with points as local features however extracting of the locations of point features is inherently error prone line features compared with point features can generally be extracted with greater accuracy the application of line features for geometric hashing to the recognition of two dimensional 2d or flat 3d objects undergoing various geometric transformations is investigated

graph characteristics from the heat kernel trace graph structures have been proved important in high level vision since they can be used to represent structural and relational arrangements of objects in a scene one of the problems that arises in the analysis of structural abstractions of objects is graph clustering in this paper we explore how permutation invariants computed from the trace of the heat kernel can be used to characterize graphs for the purposes of measuring similarity and clustering the heat kernel is the solution of the heat equation and is a compact representation of the path length distribution on a graph the trace of the heat kernel is given by the sum of the laplacian eigenvalues exponentiated with time we explore three different approaches to characterizing the heat kernel trace as a function of time our first characterization is based on the zeta function which from the mellin transform is the moment generating function of the heat kernel trace our second characterization is unary and is found by computing the derivative of the zeta function at the origin the third characterization is derived from the heat content i e the sum of the elements of the heat kernel we show how the heat content can be expanded as a power series in time and the coefficients of the series can be computed using the laplacian spectrum we explore the use of these characterizations as a means of representing graph structure for the purposes of clustering and compare them with the use of the laplacian spectrum experiments with the synthetic and real world databases reveal that each of the three proposed invariants is effective and outperforms the traditional laplacian spectrum moreover the heat content invariants appear to consistently give the best results in both synthetic sensitivity studies and on real world object recognition problems

degree graphs of simple orthogonal and symplectic groups abstract let g be a finite group and let cd g be the set of irreducible ordinary character degrees of g the degree graph of g is the graph g whose set of vertices is the set of primes dividing degrees in cd g with an edge between primes p 1 and p 2 if p 1 p 2 divides some degree in cd g we determine the graph g for the finite simple groups of types b l c l d l and d l 2 that is for the simple orthogonal and symplectic groups

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

fields of experts we develop a framework for learning generic expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks the approach provides a practical method for learning high order markov random field mrf models with potential functions that extend over large pixel neighborhoods these clique potentials are modeled using the product of experts framework that uses non linear functions of many linear filter responses in contrast to previous mrf approaches all parameters including the linear filters themselves are learned from training data we demonstrate the capabilities of this field of experts model with two example applications image denoising and image inpainting which are implemented using a simple approximate inference scheme while the model is trained on a generic image database and is not tuned toward a specific application we obtain results that compete with specialized techniques

groups whose prime graphs have no triangles abstract let g be a finite group and let cd g be the set of all complex irreducible character degrees of g let g be the set of all primes which divide some character degree of g the prime graph g attached to g is a graph whose vertex set is g and there is an edge between two distinct primes u and v if and only if the product uv divides some character degree of g in this paper we show that if g is a finite group whose prime graph g has no triangles then g has at most 5 vertices we also obtain a classification of all finite graphs with 5 vertices and having no triangles which can occur as prime graphs of some finite groups finally we show that the prime graph of a finite group can never be a cycle nor a tree with at least 5 vertices

large character degrees of solvable groups with abelian sylow 2 subgroups abstract we prove that if g is a solvable group with abelian sylow 2 subgroups the index of the fitting subgroup of g is at most the square of the largest irreducible character degree of g

nonparametric motion characterization using causal probabilistic models for video indexing and retrieval this paper describes an original approach for content based video indexing and retrieval we aim at providing a global interpretation of the dynamic content of video shots without any prior motion segmentation and without any use of dense optic flow fields to this end we exploit the spatio temporal distribution within a shot of appropriate local motion related measurements derived from the spatio temporal derivatives of the intensity function these distributions are then represented by causal gibbs models to be independent of camera movement the motion related measurements are computed in the image sequence generated by compensating the estimated dominant image motion in the original sequence the statistical modeling framework considered makes the exact computation of the conditional likelihood of a video shot belonging to a given motion or more generally to an activity class feasible this property allows us to develop a general statistical framework for video indexing and retrieval with query by example we build a hierarchical structure of the processed video database according to motion content similarity this results in a binary tree where each node is associated to an estimated causal gibbs model we consider a similarity measure inspired from kullback leibler divergence then retrieval with query by example is performed through this binary tree using the maximum a posteriori map criterion we have obtained promising results on a set of various real image sequences

on a conjecture of alvis we exhibit for each integer n 15 an ordinary irreducible character of the symmetric group sn which restricts irreducibly to an with the property that its degree is divisible by every prime less than or equal to n thereby proving a conjecture of d l alvis 2005 elsevier inc all rights reserved

structural matching in computer vision using probabilistic relaxation in this paper we develop the theory of probabilistic relaxation for matching features extracted from 2d images derive as limiting cases the various heuristic formulae used by researchers in matching problems and state the conditions under which they apply we successfully apply our theory to the problem of matching and recognizing aerial road network images based on road network models and to the problem of edge matching in a stereo pair for this purpose each line network is represented by an attributed relational graph where each node is a straight line segment characterized by certain attributes and related with every other node via a set of binary relations

direct products of groups and regular orbits abstract we prove the following result let p be a prime and let g be a finite p solvable group that is a direct product of two non cyclic subgroups of coprime order and let v be some faithful irreducible module for g over some field in characteristic p then g has a regular orbit that is there exists some v v such that c g v 1

validity of rate equation results for reaction rates in reaction networks with fluctuations systems of reacting particles which are well mixed or distributed homogeneously in space are commonly modeled by deterministic rate equations these equations which are based on the mean field approximation are valid for macroscopic systems however they neglect fluctuations in the particle populations as a result under conditions of strong fluctuations the reaction rates obtained from the rate equations are highly inaccurate to account for the fluctuations stochastic methods are required however these methods are computationally intensive and may become infeasible for complex reaction networks therefore it is useful to identify the conditions under which the rate equations provide accurate results naively one expects strong fluctuations when the average population sizes of some of the reactants are of order one or lower here we present a systematic approach for testing the validity of the rate equations in which we define characteristic scales in terms of the rate constants of the network we show that the rate equations fail to accurately reproduce the reaction rates when the system size is reduced below these scales surprisingly the rate equations are found to be applicable in a wider range than expected their validity depends not only on the population sizes of the reactive species but also on the kinetic properties of the reaction network

finite groups whose all irreducible character degrees are hall numbers abstract we call m is a hall number for g if m is the order of a hall subgroup of g that is gcd g m m 1 the aim of this paper is to investigate the structure of the finite group g whose all irreducible character degrees are hall numbers for g

structural indexing efficient 3 d object recognition the authors present an approach for the recognition of multiple 3 d object models from three 3 d scene data the approach uses two different types of primitives for matching small surface patches where differential properties can be reliably computed and lines corresponding to depth or orientation discontinuities these are represented by splashes and 3 d curves respectively it is shown how both of these primitives can be encoded by a set of super segments consisting of connected linear segments these super segments are entered into a table and provide the essential mechanism for fast retrieval and matching the issues of robustness and stability of the features are addressed in detail the acquisition of the 3 d models is performed automatically by computing splashes in highly structured areas of the objects and by using boundary and surface edges for the generation of 3 d curves the authors present results with the current system 3 d object recognition based on super segments and discuss further extensions

four vertex degree graphs of nonsolvable groups for a finite group g the character degree graph g is the graph whose vertices are the primes dividing the degrees of the ordinary irreducible characters of g with distinct primes p and q joined by an edge if pq divides some character degree of g we determine all graphs with four vertices that occur as g for some nonsolvable group g along with previously known results on character degree graphs of solvable groups this completes the classification of all four vertex graphs that occur as g for some finite group g

evaluation of the multiplane method for efficient simulations of reaction networks reaction networks in the bulk and on surfaces are widespread in physical chemical and biological systems in macroscopic systems which include large populations of reactive species stochastic fluctuations are negligible and the reaction rates can be evaluated using rate equations however many physical systems are partitioned into microscopic domains where the number of molecules in each domain is small and fluctuations are strong under these conditions the simulation of reaction networks requires stochastic methods such as direct integration of the master equation however direct integration of the master equation is infeasible for complex networks because the number of equations proliferates as the number of reactive species increases recently the multiplane method which provides a dramatic reduction in the number of equations was introduced lipshtat and biham phys rev lett 93 170601 2004 the reduction is achieved by breaking the network into a set of maximal fully connected subnetworks maximal cliques lower dimensional master equations are constructed for the marginal probability distributions associated with the cliques with suitable couplings between them in this paper we test the multiplane method and examine its applicability we show that the method is accurate in the limit of small domains where fluctuations are strong it thus provides an efficient framework for the stochastic simulation of complex reaction networks with strong fluctuations for which rate equations fail and direct integration of the master equation is infeasible the method also applies in the case of large domains where it converges to the rate equation results

upper bounds for the number of irreducible character degrees of a group abstract let g be a p solvable group for some prime p and suppose that the largest irreducible character degree of g is kp where k p is an integer we obtain an upper bound on the total number of different irreducible character degrees of g where the bound depends on k but not on p

a cumulant expansion technique for simultaneous markov random field image restoration and hyperparameter estimation we investigate hyperparameter estimation for incomplete data in markov random field image restoration assuming linear dependence of energies with respect to hyperparameters framework we use a cumulant expansion technique widely known in statistical physics and signal processing new insight is given on maximum likelihood estimation of hyperparameters of the prior regularization and contour probability distribution functions pdfs for an explicit joint boundary pixel process aimed to preserve discontinuities in particular the case where the prior regularization potential is an homogeneous function of pixels is fully analyzed a generalized stochastic gradient gsg algorithm with a fast sampling technique is devised aiming to achieve simultaneous hyperparameter estimation and pixel restoration image restoration performances of posterior mean performed during gsg convergence and of simulated annealing performed after gsg convergence are compared experimentally results and perspectives are given

large varvec p prime orbits for varvec p p nilpotent linear groups let g be a p nilpotent linear group on a finite vector space v of characteristic p suppose that g v is odd let p be a sylow p subgroup of g we show that there exist vectors v 1 and v 2 in v such that c g v 1 cap c g v 2 p a striking conjecture of malle and navarro offers a simple global criterion for the nilpotence in the sense of broue and puig of a p block of a finite group our result implies that this conjecture holds for groups of odd order

simple groups and strong covers given a finite nonabelian simple group s and labelling as the set of prime divisors of s a set c of character degrees of s strongly covers if some fixed prime divides every member of c and every prime in divides at least one member of c in this article we classify the simple groups s for which there is such a set when there is such a set we associate a strong covering number scn s with s by letting this be the cardinality of a smallest set c of degrees which strongly covers finding a set c which strongly covers establishes an upper bound on scn s but in many cases our set c has minimal cardinality and so scn s c in addition if cd s has a subset c which strongly covers c can be chosen so c 3 showing scn s 3 and we furthermore classify which simple groups have a strong covering number of 3 for all the sporadic and alternating groups and several families of groups of lie type we calculate the exact strong covering number several consequences of these facts are also presented

finite groups with consecutive nonlinear character degrees abstract the aim of this paper is to investigate structure of the finite groups whose nonlinear irreducible character degrees are consecutive integers