vicious walkers and hook young tableaux we consider a generalization of the vicious walker model using a bijection map between the path configuration of the non intersecting random walkers and the hook young diagram we compute the probability concerning the number of movements of the walker applying the saddle point method we reveal that the scaling limit gives the tracy widom distribution which is the same with the limit distribution of the largest eigenvalues of the gaussian unitary ensemble

a finitization of the bead process the bead process is the particle system defined on parallel lines with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace and zero weight otherwise motivated by the statistical mechanical model of the tiling of an abc hexagon by three species of rhombi a finitized version of the bead process is defined the corresponding joint distribution can be realized as an eigenvalue probability density function for a sequence of random matrices the finitized bead process is determinantal and we give the correlation kernel in terms of jacobi polynomials two scaling limits are considered a global limit in which the spacing between lines goes to zero and a certain bulk scaling limit in the global limit the shape of the support of the particles is determined while in the bulk scaling limit the bead process kernel of boutillier is reclaimed after appropriate identification of the anisotropy parameter therein

applying property testing to an image partitioning problem property testing is a rapidly growing field of research typically a property testing algorithm proceeds by quickly determining whether an input can satisfy some condition under the assumption that most inputs do not satisfy it if the input is far from satisfying the condition the algorithm is guaranteed to reject it with high probability applying this paradigm to image detection is desirable since images are large objects and a lot of time can be saved by quickly rejecting images which are far from satisfying a certain condition the user is interested in further typically most inputs are indeed far from the sought images we demonstrate this by analyzing the problem of deciding whether a binary image can be partitioned according to a template represented by a rectangular grid and introduce a quick rejector which tests an image extracted from the input image but whose size as well as the time required to construct it are constants which are independent of the input image size with high probability the rejector dismisses the inputs which are far from the template

symmetrized models of last passage percolation and non intersecting lattice paths it has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups u l sp 2l and o l we present a theory of such results based on non intersecting lattice paths and integration techniques familiar from the theory of random matrices detailed derivations of probabilities relating to two further symmetrizations are also given

random matrix ensembles associated to compact symmetric spaces we introduce random matrix ensembles that correspond to the infinite families of irreducible riemannian symmetric spaces of type i in particular we recover the circular orthogonal and symplectic ensembles of dyson and find other families of unitary orthogonal and symplectic ensembles of jacobi type we discuss the universal and weakly universal features of the global and local correlations of the levels in the bulk and at the hard edge of the spectrum i e at the central points 1 on the unit circle previously known results are extended and we find new simple formulas for the bessel kernels that describe the local correlations at a hard edge

non intersecting paths random tilings and random matrices we investigate certain measures induced by families of non intersecting paths in domino tilings of the aztec diamond rhombus tilings of an abc hexagon a dimer model on a cylindrical brick lattice and a growth model the measures obtained e g the krawtchouk and hahn ensembles have the same structure as the eigenvalue measures in random matrix theory like gue which can in fact can be obtained from non intersecting brownian motions the derivations of the measures are based on the karlin mcgregor or lindstrom gessel viennot method we use the measures to show some asymptotic results for the models

operators associated with soft and hard spectral edges from unitary ensembles abstract using hankel operators and shift invariant subspaces on hilbert space this paper develops the theory of the integrable operators associated with soft and hard edges of eigenvalue distributions of random matrices such tracy widom operators are realized as controllability operators for linear systems and are reproducing kernels for weighted hardy spaces known as sonine spaces periodic solutions of hill s equation give a new family of tracy widom type operators this paper identifies a pair of unitary groups that satisfy the von neumann weyl anti commutation relations and leave invariant the subspaces of l 2 that are the ranges of projections given by the tracy widom operators for the soft edge of the gaussian unitary ensemble and hard edge of the jacobi ensemble

correlation kernels for discrete symplectic and orthogonal ensembles in 49 h widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials we obtain similar results for discrete ensembles with rational discrete logarithmic derivative and compute explicitly correlation kernels associated to the classical meixner and charlier orthogonal polynomials

the asymptotics of monotone subsequences of involutions we compute the limiting distributions of the lengths of the longest monotone subsequences of random signed involutions with or without conditions on the number of fixed points and negated points as the sizes of the involutions tend to infinity the resulting distributions are depending on the number of fixed points 1 the tracy widom distributions for the largest eigenvalues of random goe gue gse matrices 2 the normal distribution or 3 new classes of distributions which interpolate between pairs of the tracy widom distributions we also consider the second rows of the corresponding young diagrams in each case the convergence of moments is also shown the proof is based on the algebraic work of j baik and e rains in 7 which establishes a connection between the statistics of random involutions and a family of orthogonal polynomials and an asymptotic analysis of the orthogonal polynomials which is obtained by extending the riemann hilbert analysis for the orthogonal polynomials by p deift k johansson and baik in 3

on the distribution of the largest eigenvalue in principal components analysis let x 1 denote the square of the largest singular value of an n p matrix x all of whose entries are independent standard gaussian variates equivalently x 1 is the largest principal component variance of the covariance matrix x x or the largest eigenvalue of a p variate wishart distribution on n degrees of freedom with identity covariance consider the limit of large p and n with n p gamma ge 1 when centered by mu p sqrt n 1 sqrt p 2 and scaled by sigma p sqrt n 1 sqrt p 1 sqrt n 1 1 sqrt p 1 3 the distribution of x 1 approaches the tracey widom law of order 1 which is defined in terms of the painleve ii differential equation and can be numerically evaluated and tabulated in software simulations show the approximation to be informative for n and p as small as 5 the limit is derived via a corresponding result for complex wishart matrices using methods from random matrix theory the result suggests that some aspects of large p multivariate distribution theory may be easier to apply in practice than their fixed p counterparts

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

an integrated model for evaluating the amount of data required for reliable recognition many recognition procedures rely on the consistency of a subset of data features with a hypothesis as the sufficient evidence to the presence of the corresponding object we analyze here the performance of such procedures using a probabilistic model and provide expressions for the sufficient size of such data subsets that if consistent guarantee the validity of the hypotheses with arbitrary confidence we focus on 2d objects and the affine transformation class and provide for the first time an integrated model which takes into account the shape of the objects involved the accuracy of the data collected the clutter present in the scene the class of the transformations involved the accuracy of the localization and the confidence we would like to have in our hypotheses increasingly it turns out that most of these factors can be quantified cumulatively by one parameter denoted effective similarity which largely determines the sufficient subset size the analysis is based on representing the class of instances corresponding to a model object and a group of transformations as members of a metric space and quantifying the variation of the instances by a metric cover

preferential urn model and nongrowing complex networks a preferential urn model which is based on the concept the rich get richer is proposed from a relationship between a nongrowing model for complex networks and the preferential urn model in regard to degree distributions it is revealed that a fitness parameter in the nongrowing model is interpreted as an inverse local temperature in the preferential urn model furthermore it is clarified that the preferential urn model with randomness generates a fat tailed occupation distribution the concept of the local temperature enables us to understand the fat tailed occupation distribution intuitively since the preferential urn model is a simple stochastic model it can be applied to research on not only the nongrowing complex networks but also many other fields such as econophysics and social sciences

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

computing the aspect graph for line drawings of polyhedral objects an algorithm for computing the aspect graph for polyhedral objects is described the aspects graph is a representation of three dimensional objects by a set of two dimensional views the set of viewpoints on the gaussian sphere is partitioned into regions such that in each region the qualitative structure of the line drawing remains the same at the boundaries between adjacent regions are the accidental viewpoints where the structure for the line drawing changes it is shown that for polyhedral objects there are two fundamental visual events 1 the projections of an edge and a vertex coincide and 2 the projections of three nonadjacent edges intersect at a point the geometry of the object is reflected in the locus of the accidental viewpoints the algorithm computes the partition together with a representative view for each region of the partition

interpretations of some parameter dependent generalizations of classical matrix ensembles two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions pdfs as the parameter is varied one interpolates between the eigenvalue pdf for the superposition of two classical ensembles with orthogonal symmetry and the eigenvalue pdf for a single classical ensemble with unitary symmetry while the other interpolates between a classical ensemble with orthogonal symmetry and a classical ensemble with symplectic symmetry we give interpretations of these pdfs in terms of probabilities associated to the continuous robinson schensted knuth correspondence between matrices with entries chosen from certain exponential distributions and non intersecting lattice paths and in the course of this probability measures on partitions and pairs of partitions are identified the latter are generalized by using macdonald polynomial theory and a particular continuum limit the jacobi limit of the resulting measures is shown to give pdfs related to those appearing in the work of anderson on the selberg integral and also in some classical work of dixon by interpreting anderson s and dixon s work as giving the pdf for the zeros of a certain rational function it is then possible to identify random matrices whose eigenvalue pdfs realize the original parameter dependent pdfs this line of theory allows sampling of the original parameter dependent pdfs their dixon anderson type generalizations and associated marginal distributions from the zeros of certain polynomials defined in terms of random three term recurrences

condensation phenomena with distinguishable particles we study real space condensation phenomena in types of classical stochastic processes site particle system such as zero range processes and urn models we study a stochastic process in the ehrenfest class i e particles in a site are distinguishable in terms of the statistical mechanical analog the ehrenfest class obeys the maxwell boltzmann statistics we analytically clarify conditions for condensation phenomena in disordered cases in the ehrenfest class in addition we discuss the preferential urn model as an example of the disordered urn model it becomes clear that the quenched disorder property plays an important role in the occurrence of the condensation phenomenon in the preferential urn model it is revealed that the preferential urn model shows three types of condensation depending on the disorder parameters

application of the τ function theory of painleve equations to random matrices pv piii the lue jue and cue with denoting an average with respect to the eigenvalue pdf for the laguerre unitary ensemble the object of our study is e n i a x l i l 0 i l for i 0 s and i s where x i l 1 for l i and x i l 0 other wise using okamoto s development of the theory of the painleve v equation it is shown that e n i a is a function associated with the hamiltonian therein and so can be characterized as the solution of a certain second order second degree differential equation or in terms of the solution of certain difference equations the cases 0 and 2 are of particular interest because they correspond to the cumulative distribution and density function respectively for the smallest and largest eigenvalue in the case i s e n i a is simply related to an average in the jacobi unitary ensemble and this in turn is simply related to certain averages over the orthogonal group the unitary symplectic group and the circular unitary ensemble the latter integrals are of interest for their combinatorial content also considered are the hard edge and soft edge scaled limits of e n i a in particular in the hard edge scaled limit it is shown that the limiting quantity e hard 0 s a can be evaluated as a function associated with the hamiltonian in okamoto s theory of the painleve iii equation

a computational learning theory of active object recognition under uncertainty we present some theoretical results related to the problem of actively searching a 3d scene to determine the positions of one or more pre specified objects we investigate the effects that input noise occlusion and the vc dimensions of the related representation classes have in terms of localizing all objects present in the search region under finite computational resources and a search cost constraint we present a number of bounds relating the noise rate of low level feature detection to the vc dimension of an object representable by an architecture satisfying the given computational constraints we prove that under certain conditions the corresponding classes of object localization and recognition problems are efficiently learnable in the presence of noise and under a purposive learning strategy as there exists a polynomial upper bound on the minimum number of examples necessary to correctly localize the targets under the given models of uncertainty we also use these arguments to show that passive approaches to the same problem do not necessarily guarantee that the problem is efficiently learnable under this formulation we prove the existence of a number of emergent relations between the object detection noise rate the scene representation length the object class complexity and the representation class complexity which demonstrate that selective attention is not only necessary due to computational complexity constraints but it is also necessary as a noise suppression mechanism and as a mechanism for efficient object class learning these results concretely demonstrate the advantages of active purposive and attentive approaches for solving complex vision problems

on the relation between orthogonal symplectic and unitary matrix ensembles for the unitary ensembles of n n hermitian matrices associated with a weight function w there is a kernel expressible in terms of the polynomials orthogonal with respect to the weight function which plays an important role for the orthogonal and symplectic ensembles of hermitian matrices there are 2 2 matrix kernels usually constructed using skew orthogonal polynomials which play an analogous role these matrix kernels are determined by their upper left hand entries we derive formulas expressing these entries in terms of the scalar kernel for the corresponding unitary ensembles we also show that whenever w w is a rational function the entries are equal to the scalar kernel plus some extra terms whose number equals the order of w w general formulas are obtained for these extra terms we do not use skew orthogonal polynomials in the derivations

random walks and random permutations a connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences consequently the scaled distribution of the maximum displacements in a particular asymmeteric version of the model can be determined to be the same as the scaled distribution of the eigenvalues at the soft edge of the gue random hermitian matrices the scaling of the distribution gives the maximum mean displacement after t time steps as 2t 1 2 with standard deviation proportional to 1 3 the exponent 1 3 is typical of a large class of two dimensional growth problems

vicious walkers and young tableaux i without walls we rederive previously known results for the number of star and watermelon configurations by showing that these follow immediately from standard results in the theory of young tableaux and integer partitions in this way we provide a proof of a result previously only conjectured for the total number of stars

visibility occlusion and the aspect graph this chapter studies the ways in which the topology of the image of a polyhedron changes with changing viewpoint we catalog the ways that the topological appearance or aspect can change this enables us to find maximal regions of viewpoints of the same aspect we use these techniques to construct the viewpoint space partition vsp a partition of viewpoint space into maximal regions of constant aspect and its dual the aspect graph here we present tight bounds on the maximum size of the vsp and the aspect graph and give algorithms for their construction first in the convex case and then in the general case in particular we give bounds on the maximum size of n 2 and n 6 under an orthographic projection viewing model and of n 3 and n 9 under a perspective viewing model the algorithms make use of a new representation of the appearance of polyhedra from all viewpoints called the aspect representation or asp we believe that this representation is one of the significant contributions of this paper

a computational model of view degeneracy we quantify the observation by kender and freudenstein 1987 that degenerate views occupy a significant fraction of the viewing sphere surrounding an object for a perspective camera geometry we introduce a computational model that can be used to estimate the probability that a view degeneracy will occur in a random view of a polyhedral object for a typical recognition system parameterization view degeneracies typically occur with probabilities of 20 percent and depending on the parameterization as high as 50 percent we discuss the impact of view degeneracy on the problem of object recognition and for a particular recognition framework relate the cost of object disambiguation to the probability of view degeneracy to reduce this cost we incorporate our model of view degeneracy in an active focal length control paradigm that balances the probability of view degeneracy with the camera field of view in order to validate both our view degeneracy model as well as our active focal length control model a set of experiments are reported using a real recognition system operating on real images

ehrenfest urn revisited playing the game on a realistic fluid model the ehrenfest urn process also known as the dogs and fleas model is realistically simulated by molecular dynamics of the lennard jones fluid the key variable is delta z i e the absolute value of the difference between the number of particles in one half of the simulation box and in the other half this is a pure jump stochastic process induced under coarse graining by the deterministic time evolution of the atomic coordinates we discuss the markov hypothesis by analyzing the statistical properties of the jumps and of the waiting times between jumps in the limit of a vanishing integration time step the distribution of waiting times becomes closer to an exponential and therefore the continuous time jump stochastic process is markovian the random variable delta z behaves as a markov chain and in the gas phase the observed transition probabilities follow the predictions of the ehrenfest theory

classical skew orthogonal polynomials and random matrices skew orthogonal polynomials arise in the calculation of the n point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry in particular the distribution functions are completely determined by a certain sum involving the skew orthogonal polynomials in the case that the eigenvalue probability density function involves a classical weight function explicit formulas for the skew orthogonal polynomials are given in terms of related orthogonal polynomials and the structure is used to give a closed form expression for the sum this theory treates all classical cases on an equal footing giving formulas applicable at once to the hermite laguerre and jacobi cases

algebraic aspects of increasing subsequences we present a number of results relating partial cauchy littlewood sums integrals over the compact classical groups and increasing subsequences of permutations these include integral formulae for the distribution of the longest increasing subsequence of a random involution with constrained number of fixed points new formulae for partial cauchy littlewood sums as well as new proofs of old formulae relations of these expressions to orthogonal polynomials on the unit circle and explicit bases for invariant spaces of the classical groups together with appropriate generalizations of the straightening algorithm

3 d shape recovery using distributed aspect matching an approach to the recovery of 3 d volumetric primitives from a single 2 d image is presented the approach first takes a set of 3 d volumetric modeling primitives and generates a hierarchical aspect representation based on the projected surfaces of the primitives conditional probabilities capture the ambiguity of mappings between levels of the hierarchy from a region segmentation of the input image the authors present a formulation of the recovery problem based on the grouping of the regions into aspects no domain independent heuristics are used only the probabilities inherent in the aspect hierarchy are exploited once the aspects are recovered the aspect hierarchy is used to infer a set of volumetric primitives and their connectivity as a front end to an object recognition system the approach provides the indexing power of complex 3 d object centered primitives while exploiting the convenience of 2 d viewer centered aspect matching aspects are used to represent a finite vocabulary of 3 d parts from which objects can be constructed

learning small gallery size for prediction of recognition performance on large populations this paper addresses the estimation of a small gallery size that can generate the optimal error estimate and its confidence on a large population relative to the size of the gallery which is one of the fundamental problems encountered in performance prediction for object recognition it uses a generalized two dimensional prediction model that combines a hypergeometric probability distribution model with a binomial model and also considers the data distortion problem in large populations learning is incorporated in the prediction process in order to find the optimal small gallery size and to improve the prediction the chernoff and chebychev inequalities are used as a guide to obtain the small gallery size during the prediction the expectation maximization em algorithm is used to learn the match score and the non match score distributions that are represented as a mixture of gaussians the optimal size of the small gallery is learned by comparing it with the sizes obtained by the statistical approaches and at the same time the upper and lower bounds for the prediction on large populations are obtained results for the prediction are presented for the nist 4 fingerprint database

fluctuations in time intervals of financial data from the view point of the gini index abstract we propose an approach to explain fluctuations in time intervals of financial markets data from the view point of the gini index we show the explicit form of the gini index for a weibull distribution a good candidate to describe the first passage time of foreign exchange rate the analytical expression of the gini index compares well with the value obtained from empirical data

power law behavior and condensation phenomena in disordered urn models we investigate the equilibrium statistical properties of urn models with disorder two urn models are proposed one belongs to the ehrenfest class and the other corresponds to the monkey class these models are introduced from the view point of the power law behavior and randomness it is clarified that quenched random parameters play an important role in generating the power law behavior we evaluate the occupation probability p k with which an urn has k balls by using the concept of statistical physics of disordered systems in the disordered urn model belonging to the monkey class we find that above critical density c for a given temperature condensation phenomenon occurs and the occupation probability changes its scaling behavior from an exponential law to a heavy tailed power law in large k regime we also discuss an interpretation of our results for explaining macro economy in particular the emergence of wealth differentials

correlations for superpositions and decimations of laguerre and jacobi orthogonal matrix ensembles with a parameter a superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original while a decimation refers to the formation of a new ensemble by observing only every second eigenvalue in the cases of the classical matrix ensembles with orthogonal symmetry it is known that forming superpositions and decimations gives rise to classical matrix ensembles with unitary and symplectic symmetry the basic identities expressing these facts can be extended to include a parameter which in turn provides us with probability density functions which we take as the definition of special parameter dependent matrix ensembles the parameter dependent ensembles relating to superpositions interpolate between superimposed orthogonal ensembles and a unitary ensemble while the parameter dependent ensembles relating to decimations interpolate between an orthogonal ensemble with an even number of eigenvalues and a symplectic ensemble of half the number of eigenvalues by the construction of new families of biorthogonal and skew orthogonal polynomials we are able to compute the corresponding correlation functions both in the finite system and in various scaled limits specializing back to the cases of orthogonal and symplectic symmetry we find that our results imply different functional forms to those known previously

classical discrete symplectic ensembles on the linear and exponential lattice skew orthogonal polynomials and correlation functions the eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalized to discrete settings involving either a linear or an exponential lattice the corresponding correlation functions can be expressed in terms of certain discrete and q skew orthogonal polynomials respectively we give a theory of both of these classes of polynomials and the correlation kernels determining the correlation functions in the cases in which the weights for the corresponding discrete unitary ensembles are classical crucial for this are certain difference operators which relate the relevant symmetric inner products to the skew symmetric ones and have a tridiagonal action on the corresponding discrete or q orthogonal polynomials

the effect of gaussian error in object recognition in model based recognition the goal is to locate an instance of one or more known objects in an image the problem is compounded in real images by the presence of clutter occlusion and sensor error which can lead to false negatives failures to recognize the presence of the object and false positives in which the algorithm incorrectly identifies an occurrence of the object the probability of either event is affected by parameters within the recognition algorithm which are almost always chosen in an ad hoc fashion the effect of the parameter values on the likelihood that the recognition algorithm will make a mistake are usually not understood explicitly to address the problem we explicitly model the noise that occurs in the image in a typical recognition algorithm hypotheses about the position of the object are tested against the evidence in the image and an overall score is assigned to each hypothesis we use a statistical model to determine what score a correct or incorrect hypothesis is likely to have and use standard binary hypothesis testing techniques to distinguish correct from incorrect hypotheses using this approach we can compare algorithms and noise models and automatically choose values for internal system thresholds to minimize the probability of making a mistake

increasing subsequences and the hard to soft edge transition in matrix ensembles our interest is in the cumulative probabilities pr l t l for the maximum length of increasing subsequences in poissonized ensembles of random permutations random fixed point free involutions and reversed random fixed point free involutions it is shown that these probabilities are equal to the hard edge gap probability for matrix ensembles with unitary orthogonal and symplectic symmetry respectively the gap probabilities can be written as a sum over correlations for certain determinantal point processes from these expressions a proof can be given that the limiting form of pr l t l in the three cases is equal to the soft edge gap probability for matrix ensembles with unitary orthogonal and symplectic symmetry respectively thereby reclaiming theorems due to baik deift johansson and baik rains

pfaffian expressions for random matrix correlation functions it is well known that pfaffian formulas for eigenvalue correlations are useful in the analysis of real and quaternion random matrices moreover the parametric correlations in the crossover to complex random matrices are evaluated in the forms of pfaffians in this article we review the formulations and applications of pfaffian formulas for that purpose we first present the general pfaffian expressions in terms of the corresponding skew orthogonal polynomials then we clarify the relation to eynard and mehta s determinant formula for hermitian matrix models and explain how the evaluation is simplified in the cases related to the classical orthogonal polynomials applications of pfaffian formulas to random matrix theory and other fields are also mentioned

recognizing solid objects by alignment with an image in this paper we consider the problem of recognizing solid objects from a single two dimensional image of a three dimensional scene we develop a new method for computing a transformation from a three dimensional model coordinate frame to the two dimensional image coordinate frame using three pairs of model and image points we show that this transformation always exists for three noncollinear points and is unique up to a reflective ambiguity the solution method is closed form and only involves second order equations we have implemented a recognition system that uses this transformation method to determine possible alignments of a model with an image each of these hypothesized matches is verified by comparing the entire edge contours of the aligned object with the image edges using the entire edge contours for verification rather than a few local feature points reduces the chance of finding false matches the system has been tested on partly occluded objects in highly cluttered scenes

wealth condensation in a simple model of economy abstract we introduce a simple model of economy where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading in such a way that the fundamental symmetry of the economy under an arbitrary change of monetary units is insured we investigate a mean field limit of this equation and show that the distribution of wealth is of the pareto power law type the pareto behaviour of the tails of this distribution appears to be robust for finite range models as shown using both a mapping to the random directed polymer problem as well as numerical simulations in this context a phase transition between an economy dominated by a few individuals and a situation where the wealth is more evenly spread out is found an interesting outcome is that the distribution of wealth tends to be very broadly distributed when exchanges are limited either in amplitude or topologically favouring exchanges and less surprisingly increasing taxes seems to be an efficient way to reduce inequalities

computing exact aspect graphs of curved objects solid of revolution this paper introduces a new approach to computing the exact orthographic aspect graph of curved objects curves corresponding to various visual events partition the view sphere into regions where the image structure is stable a catalog of these events for piecewise smooth objects is available from singularity theory for a solid of revolution whose generator is an algebraic curve each visual event is characterized by a system of polynomial equations whose roots can be computed by continuation methods within each region the stable image structure is characterized by a variation of cylindrical algebraic decomposition and ray tracing this approach has been implemented and several examples are presented

grouping based nonadditive verification verification is the final decision stage in many object recognition processes it is carried out by evaluating a score for every hypothesis and choosing the hypotheses associated with the highest score this paper suggests a grouping based verification paradigm relying on the observation that a group of data features belonging to a hypothesized object instance should be a good group therefore it should support perceptual grouping information available from the image by grouping relations the proposed score which is the joint likelihood of these grouping cues quantifies this observation in a probabilistic framework experiments with synthetic and real images show that the proposed method performs better in difficult cases

probabilistic analysis of the application of the cross ratio to model based vision the probability density function for the cross ratio is obtained under the hypothesis that the four image points have independent identical gaussian distributions the density function has six symmetries which are closely linked to the six different values of the cross ratio obtained by permuting the quadruple of points from which the cross ratio is calculated the density function has logarithmic singularities corresponding to values of the cross ratio for which two of the four points are coincident the cross ratio forms the basis of a simple system for recognising or classifying quadruples of collinear image points the performance of the system depends on the choice of rule for deciding whether four image points have a given cross ratio a rule is stated which is computationally straightforward and which takes into account the effects on the cross ratio of small errors in locating the image points two key properties of the rule are the probabilityr of rejection and the probabilityf of a false alarm the probabilitiesr andf depend on a thresholdt in the decision rule there is a trade off betweenr andf obtained by varyingt it is shown that the trade off is insensitive to the given cross ratio letf w max o f thenr f w are related approximately by sqrt ln r 1 sqrt 2 varepsilon r f 1 f w provided e 1f w 4 in the equation e is the accuracy with which image points can be located relative to the width of the image andr f is a constant known as the normalised false alarm rate in the range e 1f w 4 the probabilitiesr andf w are related approximately by r 1 sqrt 2 pi 1 varepsilon 1 r f 1 f w the value ofr f is 14 37 the consequences of these relations between r and fw are discussed it is conjectured that the above general form of the trade off betweenr andf w holds for a wide class of scalar invariants that could be used for model based object recognition invariants with the same type of trade off between the probability of rejection and the probability of false alarm are said to be nondegenerate for model based vision

an a contrario decision method for shape element recognition shape recognition is the field of computer vision which addresses the problem of finding out whether a query shape lies or not in a shape database up to a certain invariance most shape recognition methods simply sort shapes from the database along some dis similarity measure to the query shape their main weakness is the decision stage which should aim at giving a clear cut answer to the question do these two shapes look alike in this article the proposed solution consists in bounding the number of false correspondences of the query shape among the database shapes ensuring that the obtained matches are not likely to occur by chance as an application one can decide with a parameterless method whether any two digital images share some shapes or not