quasi invariant parameterisations and matching of curves in images in this paper we investigate quasi invariance on a smooth manifold and show that there exist quasi invariant parameterisations which are not exactly invariant but approximately invariant under group transformations and do not require high order derivatives the affine quasi invariant parameterisation is investigated in more detail and exploited for defining general affine semi local invariants from second order derivatives only the new invariants are implemented and used for matching curve segments under general affine motions and extracting symmetry axes of objects with 3d bilateral symmetry

universality at the edge of the spectrum for unitary orthogonal and symplectic ensembles of random matrices we prove universality at the edge of the spectrum for unitary 2 orthogonal 1 and symplectic 4 ensembles of random matrices in the scaling limit for a class of weights w x e v x where v is a polynomial v x 2mx2m 2m 0 the precise statement of our results is given in theorem 1 1 and corollaries 1 2 and 1 4 below for the same class of weights a proof of universality in the bulk of the spectrum is given in 12 for the unitary ensembles and in 9 for the orthogonal and symplectic ensembles our starting point in the unitary case is 12 and for the orthogonal and symplectic cases we rely on our recent work 9 which in turn depends on the earlier work of widom 46 and tracy and widom 42 as in 9 the uniform plancherel rotach type asymptotics for the orthogonal polynomials found in 12 plays a central role the formulae in 46 express the correlation kernels for 1 4 as a sum of a christoffel darboux cd term as in the case 2 together with a correction term in the bulk scaling limit 9 the correction term is of lower order and does not contribute to the limiting form of the correlation kernel by contrast in the edge scaling limit considered here the cd term and the correction term contribute to the same order this leads to additional technical difficulties over and above 49 2006 wiley periodicals inc

multivalued continuum systems this paper deals with continuum systems where a continuous degree of performance levels between perfect functioning and complete failure is allowed here we shall assume that the system can be modeled as a structure function given by a mapping from the n dimensional unit hypercube into a k dimensional unit hypercube in such a way that the performance of the system is described according to k single continuum valued criteria some basic concepts relative to these continuum multivalued systems are discussed and general reliability bounds are obtained based upon the minimal paths and minimal cuts of the k associated single valued continuum systems

on the toda and kac van moerbeke systems given a solution of the toda lattice we explicitly construct a solution of the kac van moerbeke system related to each other by a miura type transformation as an illustration of our method we derive the n soliton solutions of the kac van moerbeke lattice

asymptotics and integrable structures for biorthogonal polynomials associated to a random two matrix model abstract we give a rigorous construction of complete families of biorthonormal polynomials associated to a planar measure of the form e n v x w y 2 xy d x d y for polynomial v and w we are further able to show that the zeroes of these polynomials are all real and distinct a complex analytical construction of the biorthonormal polynomials is given in terms of a non local riemann hilbert problem which given our prior result provides an avenue for developing uniform asymptotics for the statistical distributions of these zeroes as n becomes large the biorthonormal polynomials considered here play a fundamental role in the analysis of certain random multi matrix models we show that the evolutions of the recursion matrices for the polynomials induced by linear deformations of v and w coincide with a semi infinite generalization of the completely integrable full kostant toda lattice this connection could be relevant for understanding aspects of scaling limits for the multi matrix model

how many entries of a typical orthogonal matrix can be approximated by independent normals we solve an open problem of diaconis that asks what are the largest orders of p n and q n such that z n the p n x q n upper left block of a random matrix r n which is uniformly distributed on the orthogonal group o n can be approximated by independent standard normals this problem is solved by two different approximation methods first we show that the variation distance between the joint distribution of entries of z n and that of p n q n independent standard normals goes to zero provided p n o n and q n o n we also show that the above variation distance does not go to zero if p n x n and q n y n for any positive numbers x and y this says that the largest orders of p n and q n are o n 1 2 in the sense of the above approximation second suppose n ij n n is generated by performing the gram schmidt algorithm on the columns of y n y ij n n where y ij 1 i j n are i i d standard normals we show that e n m max 1 i n 1 j m n ij y ij goes to zero in probability as long as m m n o n log n we also prove that e n m n 2 in probability when m n n logn for any a 0 this says that m n o n log n is the largest order such that the entries of the first m n columns of n can be approximated simultaneously by independent standard normals

long time behaviour for a class of low regularity solutions of the camassa holm equation in this paper we investigate the long time behaviour for a class of low regularity solutions of the camasssa holm equation given by the superposition of infinitely many interacting traveling waves with corners at their peaks

some perspectives on the eigenvalue problem this expository paper explores the relationships among a number of algorithms for solving eigenvalue problems including the power method subspace iteration the qr algorithm and the arnoldi and symmetric lanczos algorithms the symmetric lanczos algorithm is shown to be identical to the three term recursion stieltjes procedure for computing orthogonal polynomials with respect to a measure on the real line the connection between measures on the line and symmetric tridiagonal jacobi matrices is investigated if such a matrix is transformed by a step of the qr algorithm there is a corresponding transformation in the measure the tridiagonal matrices are also exploited for the construction of gaussian quadrature formulas for measures on the line the developments on the real line are replicated with suitable modifications on the unit circle via lanczos like procedures for unitary operators the best known procedure of this type is the recursion of szego for computing orthogonal polynomials on the

cmv the unitary analogue of jacobi matrices we discuss a number of properties of cmv matrices by which we mean the class of unitary matrices studied recently by cantero moral and velazquez we argue that they play an equivalent role among unitary matrices to that of jacobi matrices among all hermitian matrices in particular we describe the analogues of well known properties of jacobi matrices foliation by co adjoint orbits a natural symplectic structure algorithmic reduction to this shape lax representation for an integrable lattice system ablowitz ladik and the relation to orthogonal polynomials as offshoots of our analysis we will construct action angle variables for the finite ablowitz ladik hierarchy and describe the long time behavior of this system 2006 wiley periodicals inc

nonabelian nonlinear lattice equations on finite interval we apply the inverse spectral problem method to the class of non abelian nonlinear lattice equations on the finite interval the integrable discrete nonlinear schrodinger and discrete modified korteveg de vries equations are considered as examples in the latter case the large time asymptotics for solutions are found

foundations of semi differential invariants this paper elaborates the theoretical foundations of a semi differential framework for invariance semi differential invariants combine coordinates and their derivatives with respect to some contour parameter at several points of the image contour thus allowing for an optimal trade off between identification of points and the calculation of derivatives a systematic way of generating complete and independent sets of such invariants is presented it is also shown that invariance under reparametrisation can be cast in the same framework the theory is illustrated by a complete analysis of 2d affine transformations in a companion paper pauwels et al 1995 these affine semi differential invariants are implemented in the computer program form flat object recognition method for the recognition of planar contours under pseudo perspective projection

on the toda and kac van moerbeke hierarchies we provide a comprehensive treatment of the single and double commutation method as a tool for constructing soliton solutions of the toda and kac van moerbeke hierarchy on arbitrary background in addition we present a novel construction based on the single commutation method as an illustration we compute the n soliton solution of the toda and kac van moerbeke hierarchy

a systematic approach to the soliton equations of a discrete eigenvalue problem the ablowitz ladik al problem is a linear vector difference equation whose isospectral flow equations include several important soliton equations e g the discrete nonlinear schrodinger equation iqn qn 1 2qn qn 1 qn 2 qn 1 qn 1 there is an established procedure for describing the soliton hierarchy of the more familiar akns ablowitz kaup newell and segur problem it is based on the notion of a generator for the hierarchy in this paper the soliton equations of the al hierarchy are described and characterized by a generator pair a new continuous spectral problem is introduced and the akns hierarchy is embedded in its hierarchy as a specialization

scale invariance of the png droplet and the airy process we establish that the static height fluctuations of a particular growth model the png droplet converges upon proper rescaling to a limit process which we call the airy process a y the airy process is stationary it has continuous sample paths its single time fixed y distribution is the tracy widom distribution of the largest eigenvalue of a gue random matrix and the airy process has a slow decay of correlations as y 2 roughly the airy process describes the last line of dyson s brownian motion model for random matrices our construction uses a multi layer version of the png model which can be analyzed through fermionic techniques specializing our result to a fixed value of y one reobtains the celebrated result of baik deift and johansson on the length of the longest increasing subsequence of a random permutation

new classes of toda soliton solutions we provide a detailed investigation of limits of n soliton solutions of the toda lattice as n tends to infinity our principal results yield new classes of toda solutions including in particular new kinds of soliton like i e reflectionless solutions as a byproduct we solve an inverse spectral problem for one dimensional jacobi operators and explicitly construct tri diagonal matrices that yield a purely absolutely continuous spectrum in 1 1 and give rise to an eigenvalue spectrum that includes any prescribed countable and bounded subset of mr bs 1 1

generalized information theory abstract generalized information theory is viewed in this paper as an information theory that is liberated from the boundaries of probability theory after overviewing classical probabilistic information theory the paper examines recent developments regarding nonprobabilistic measures and principles of uncertainty based information which form a nucleus of the emerging generalized information theory

on modeling possibilistic uncertainty in two state reliability theory in this paper we show how a possibilistic uncertainty model can be used to represent and manipulate uncertainty about the states of a system and of its components at the same time we present a thorough study of the incorporation of this possibilistic uncertainty model in classical two state reliability theory the possibilistic reliability of a component or system is introduced and studied furthermore we introduce the important notion of a possibilistic structure function based upon the concept of a classical two valued structure function under certain conditions of possibilistic independence it allows us to calculate the possibilistic reliability of a system in terms of the possibilistic reliabilities of its components finally we give straightforward methods for determining a possibilistic structure function from its classical two valued counterpart in this way we intend to show that a possibilistic uncertainty model in two state reliability theory is formally analogous to and certainly not more complicated than a probabilistic uncertainty model

fuzzy contactibility and fuzzy variables abstract this paper gives some advanced developments of possibility measure theory there are two problems being solved in this paper 1 1 what is the most essential property of the possibility measures 2 2 what is the measure extension theorem concering the possibility measures finally a structure which is analogous to the probability measure theory becomes more clear

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

edge universality of beta ensembles we prove the edge universality of the beta ensembles for any beta ge 1 provided that the limiting spectrum is supported on a single interval and the external potential is fancyscript c 4 and regular we also prove that the edge universality holds for generalized wigner matrices for all symmetry classes moreover our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class fancyscript c 4

the toda rarefaction problem in the toda shock problem see 7 1 11 s and also 131 one considers a driving particle moving with a fixed velocity 2a and impinging on a one dimensional semi infinite lattice of particles initially equally spaced and at rest and interacting with exponential forces in this paper we consider the related toda rarefaction problem in which the driving particle now moves away from the lattice at fixed speed in analogy with a piston being withdrawn as it were from a container filled with gas we make use of the riemann hilbert factorization formulation of the related inverse scattering problem in the case where the speed 21al of the driving particle is sufficiently large la1 l we show that the particle escapes from the lattice which then executes a free motion of the type studied for example in 5 in other words in analogy with a piston being withdrawn too rapidly from a container filled with gas cavitation develops 0 1996 john wiley sons inc

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

differential and numerically invariant signature curves applied to object recognition we introduce a new paradigm the differential invariant signature curve or manifold for the invariant recognition of visual objects a general theorem of e cartan implies that two curves are related by a group transformation if and only if their signature curves are identical the important examples of the euclidean and equi affine groups are discussed in detail secondly we show how a new approach to the numerical approximation of differential invariants based on suitable combination of joint invariants of the underlying group action allows one to numerically compute differential invariant signatures in a fully group invariant manner applications to a variety of fundamental issues in vision including detection of symmetries visual tracking and reconstruction of occlusions are discussed

an efficient approach for design optimization of structures involving fuzzy variables abstract we propose a new approach for solving design optimization problems of structures involving fuzzy variables first the possibilistic safety model of structures with fuzzy variables is investigated a possibilistic safety index psi is presented to compare different designs this paper then presents the psi based design optimization psibdo model for structures with fuzzy variables the optimization problem is a triple loop nested problem and the computational cost is high to reduce the computation time a technique called target performance based design approach tpbda is proposed to overcome difficulties encountered by the psibdo with the proposed tpbda the triple loop nested problem is reduced to a double loop one and the computational time is considerably reduced several examples are given to demonstrate the efficiency of the proposed approach

universality in numerical computations with random data the authors present evidence for universality in numerical computations with random data given a possibly stochastic numerical algorithm with random input data the time or number of iterations to convergence within a given tolerance is a random variable called the halting time two component universality is observed for the fluctuations of the halting time i e the histogram for the halting times centered by the sample average and scaled by the sample variance collapses to a universal curve independent of the input data distribution as the dimension increases thus up to two components the sample average and the sample variance the statistics for the halting time are universally prescribed the case studies include six standard numerical algorithms as well as a model of neural computation and decision making a link to relevant software is provided for readers who would like to do computations of their own

perceptually relevant and piecewise linear matching of silhouettes in this paper a novel alignment method for silhouettes is proposed this method is based on the establishment of correspondences between landmarks on their boundaries and in turn on the establishment of correspondences of the boundary pieces in between these landmarks the method yields more correct correspondences than conventional methods that scale the arc length descriptions of silhouettes to align them the selection of landmarks is investigated as to the robustness of their localization and their perceptual relevance matching of silhouettes is then achieved by quantifying the dissimilarity of a pair of silhouette boundaries based on a novel dissimilarity metric the matching procedure is evaluated based on retrieval experiments and it is concluded that the precision of the results is higher than that obtained by conventional pointwise comparison methods

skew symmetry detection via invariant signatures we propose a new approach to skew symmetry detection based on the theory of invariant signatures for planar objects invariant signatures associated to object boundaries are generalizations of the curvature versus arclength description of curves invariant under geometric transformations more complex than the euclidean ones we show that symmetries of objects and hence of closed boundaries translate into simple structures in the invariant signature functions and are therefore in principle readily detectable

spectral properties of certain tridiagonal matrices abstract we study spectral properties of irreducible tridiagonal k toeplitz matrices and certain matrices which arise as perturbations of them

on the infinite dimensional qr algorithm spectral computations of infinite dimensional operators are notoriously difficult yet ubiquitous in the sciences indeed despite more than half a century of research it is still unknown which classes of operators allow for the computation of spectra and eigenvectors with convergence rates and error control recent progress in classifying the difficulty of spectral problems into complexity hierarchies has revealed that the most difficult spectral problems are so hard that one needs three limits in the computation and no convergence rates nor error control is possible this begs the question which classes of operators allow for computations with convergence rates and error control in this paper we address this basic question and the algorithm used is an infinite dimensional version of the qr algorithm indeed we generalise the qr algorithm to infinite dimensional operators we prove that not only is the algorithm executable on a finite machine but one can also recover the extremal parts of the spectrum and corresponding eigenvectors with convergence rates and error control this allows for new classification results in the hierarchy of computational problems that existing algorithms have not been able to capture the algorithm and convergence theorems are demonstrated on a wealth of examples with comparisons to standard approaches that are notorious for providing false solutions we also find that in some cases the iqr algorithm performs better than predicted by theory and make conjectures for future study

schwarps locally projective image warps based on 2d schwarzian derivatives image warps or just warps capture the geometric deformation existing between two images of a deforming surface the current approach to enforce a warp s smoothness is to penalize its second order partial derivatives bookstein in ieee trans pattern anal mach intell 11 567 585 1989 rueckert et al in ieee trans med imaging 18 712 721 1999 because this favors locally affine warps this fails to capture the local projective component of the image deformation this may have a negative impact on applications such as image registration and deformable 3d reconstruction we propose a novel penalty designed to smooth the warp while capturing the deformation s local projective structure our penalty is based on equivalents to the schwarzian derivatives which are projective differential invariants exactly preserved by homographies we propose a methodology to derive a set of partial differential equations with only homographies as solutions we call this system the schwarzian equations and we explicitly derive them for 2d functions using differential properties of homographies we name as schwarp a warp which is estimated by penalizing the residual of schwarzian equations experimental evaluation shows that schwarps outperform existing warps in modeling and extrapolation power and lead to better results in three deformable reconstruction methods namely shape reconstruction in shape from template camera calibration in shape from template and non rigid structure from motion

the local projective shape of smooth surfaces and their outlines this article examines projectively invariant local geometric properties of smooth curves and surfaces oriented projective differential geometry is proposed as a general framework for establishing such invariants and characterizing the local projective shape of surfaces and their outlines it is applied to two problems 1 the projective generalization of koenderink s famous characterization of convexities concavities and inflections of the apparent contours of solids bounded by smooth surfaces and 2 the image based construction of rim meshes which provide a combinatorial description of the arrangement induced on the surface of an object by the contour generators associated with multiple cameras observing it

structural properties of continuum systems abstract this paper deals with monotonic systems where the performance levels of the system and its components range from perfect functioning to complete failure allowing any intermediate state in the unit interval in particular general bounds are found for the reliability of such systems moreover it is shown how these continuum systems can be approached by finite multistate systems

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

possibility and necessity integrals abstract in this paper we introduce seminormed and semiconormed fuzzy integrals associated with confidence measures these confidence measures have a field of sets as their domain and a complete lattice as their codomain in introducing these integrals the analogy with the classical introduction of lebesgue integrals is explored and exploited it is amongst other things shown that our integrals are the most general integrals that satisfy a number of natural basic properties in this way our dual classes of fuzzy integrals constitute a significant generalization of sugeno s fuzzy integrals a large number of important general properties of these integrals is studied furthermore and most importantly the combination of seminormed fuzzy integrals and possibility measures on the one hand and semiconormed fuzzy integrals and necessity measures on the other hand is extensively studied it is shown that these combinations are very natural and have properties which are analogous to the combination of lebesgue integrals and classical measures using these results the very basis is laid for a unifying measure and integral theoretic account of possibility and necessity theory in very much the same way as the theory of lebesgue integration provides a proper framework for a unifying and formal account of probability theory

long time behaviour of an infinite particle system the long time behaviour of the semi infinite toda lattice is deduced from a set of identities for the squared eigenfunctions of the toda flow

recognition of planar shapes under affine distortion methods for the recognition ofplanar shapes from arbitrary viewpoints are described the adopted model of projection is orthographic the invariant descriptions derived for this group are one dimensional shape signatures comparable to the well known curvature as a function of arc length description of euclidean geometry since the use of such differential invariants in the affine case would lead to unacceptably high orders of derivatives affine invariant descriptions based onsemi differential invariants are proposed as an alternative a systematic discussion of different types of these invariants is given the usefulness and viability of this methodology is demonstrated on a database containing more than 40 objects

matrix models for beta ensembles this paper constructs tridiagonal random matrix models for general 0 hermite gaussian and laguerre wishart ensembles these generalize the well known gaussian and wishart models for 1 2 4 furthermore in the cases of the laguerre ensembles we eliminate the exponent quantization present in the previously known models we further discuss applications for the new matrix models and present some open problems

beta ensembles stochastic airy spectrum and a diffusion we prove that the largest eigenvalues of the beta ensembles of random matrix theory converge in distribution to the low lying eigenvalues of the random schrodinger operator d2 dx2 x 2 bx restricted to the positive half line where b x is white noise in doing so we extend the definition of the tracy widom distributions to all 0 and also analyze their tails last in a parallel development we provide a second characterization of these laws in terms of a one dimensional diffusion the proofs rely on the associated tridiagonal matrix models and a universality result showing that the spectrum of such models converge to that of their continuum operator limit in particular we show how tracy widom laws arise from a functional central limit theorem

q scale measures of fuzzy sets abstract in an attempt to generalize nahmias scale measure to apply to fuzzy sets in this paper we introduce the notion of q scale measure a q scale measure is slightly different from a crisp valued possibility measure in several ways we use a number of examples to demonstrate the validity of the notion of q scale measure in various circumstances and give preliminary discussions on basic properties of q scale measure induced q scale measure semigroup of q scale measures q scale measure of probabilistic sets and q scale measure of l fuzzy sets

universality at the edge of the spectrum in wigner random matrices we prove universality at the edge for rescaled correlation functions of wigner random matrices in the limit n as a corollary we show that after proper rescaling the 1th 2nd 3rd etc eigenvalues of wigner random hermitian resp real symmetric matrix weakly converge to the distributions established by tracy and widom in g u e g o e cases

system failure engineering and fuzzy methodology an introductory overview abstract system failure engineering may encompass reliability safety security maintainability risk and quality control in this paper we pay a unified view i e a failure oriented view to system failure engineering the notion of failure can be represented in terms of fuzzy sets and widely interpreted we then discuss various application aspects of fuzzy methodology in system failure engineering which include fuzzy methodology in fault diagnosis in probist systems in structural reliability in software reliability in human reliability in safety engineering in security engineering in risk engineering and in quality control as well as profust posbist and posfust reliability theories engineering case studies and mathematical problems raised by applications of fuzzy methodology in system failure engineering are also addressed in this paper

the toda flow on a generic orbit is integrable pour l orbite generique de l action coadjointe du groupe triangulaire inferieur sur son algebre de lie duale on presente un ensemble complet d integrales en involution pour le flot de toda associe

on the solvability complexity index the n pseudospectrum and approximations of spectra of operators we show that it is possible to compute spectra and pseudospectra of linear operators on separable hilbert spaces given their matrix elements the core in the theory is pseudospectral analysis and in particular the n pseudospectrum and the residual pseudospectrum we also introduce a new classification tool for spectral problems namely the solvability complexity index this index is an indicator of the difficultness of different computational spectral problems

the toda flow on a generic orbit is integrable on construit des variables action angle pour le flot de toda sur des orbites generiques de l action coadjointe du groupe triangulaire inferieur sur son algebre de lie duale

nonintersecting brownian motions on the half line and discrete gaussian orthogonal polynomials we study the distribution of the maximal height of the outermost path in the model of n nonintersecting brownian motions on the half line as n showing that it converges in the proper scaling to the tracy widom distribution for the largest eigenvalue of the gaussian orthogonal ensemble this is as expected from the viewpoint that the maximal height of the outermost path converges to the maximum of the airy2 process minus a parabola our proof is based on riemann hilbert analysis of a system of discrete orthogonal polynomials with a gaussian weight in the double scaling limit as this system approaches saturation we consequently compute the asymptotics of the free energy and the reproducing kernel of the corresponding discrete orthogonal polynomial ensemble in the critical scaling in which the density of particles approaches saturation both of these results can be viewed as dual to the case in which the mean density of eigenvalues in a random matrix model is vanishing at one point

isospectral deformations of random jacobi operators we show the integrability of infinite dimensional hamiltonian systems obtained by making isospectral deformations of random jacobi operators over an abstract dynamical system the time 1 map of these so called random toda flows can be expressed by aqr decomposition

toda flows with infinitely many variables abstract the toda flow and related flows extend naturally to operators in hilbert space and the purpose of this paper is to describe these flows and to analyse some of their special properties

cmv matrices in random matrix theory and integrable systems a survey we present a survey of recent results concerning a remarkable class of unitary matrices the cmv matrices we are particularly interested in the role they play in the theory of random matrices and integrable systems throughout the paper we also emphasize the analogies and connections to jacobi matrices

possibility theory an integral theoretic approach this paper introduces possibility integrals as fuzzy integrals w r t possibility measures it is shown that this concept can be used to unify a lot of known results in possibility theory that up to now have been introduced on a more ad hoc basis the integral theoretic approach allows us amongst other things to introduce product and conditional possibility measures in very much the same way as product lebesgue measures and conditional probability measures are introduced furthermore to stress the fact that the concept of order relations is basic for possibility theory all the results are proved for a complete lattice as the evaluation set instead of the more familiar unit interval 0 1

affine invariant geometry for non rigid shapes shape recognition deals with the study geometric structures modern surface processing methods can cope with non rigidity by measuring the lack of isometry deal with similarity or scaling by multiplying the euclidean arc length by the gaussian curvature and manage equi affine transformations by resorting to the special affine arc length definition in classical equi affine differential geometry here we propose a computational framework that is invariant to the full affine group of transformations similarity and equi affine thus by construction it can handle non rigid shapes technically we add the similarity invariant property to an equi affine invariant one and establish an affine invariant pseudo metric as an example we show how diffusion geometry can encapsulate the proposed measure to provide robust signatures and other analysis tools for affine invariant surface matching and comparison

ordinary differential equations and the symmetric eigenvalue problem in this paper the authors develop a general framework for calculating the eigenvalues of a symmetric matrix using ordinary differential equations new algorithms are suggested and old algorithms including qr are interpreted

fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context abstract conventional reliability theory is based on the binary state assumption and the probability assumption namely 1 the systems are precisely defined as functioning or failed 2 the system behavior is fully characterized in the context of probability measures however the probability assumption is no longer reasonable in the case of small size of samples since the term probability stems from the sample generality in this way possibility measures should be used to characterize the sample particularity in this paper the binary state assumption is reserved and the possibility assumption is taken in place of the probability assumption thus a concept of fuzzy reliability i e posbist reliability is introduced and a theory of fuzzy reliability i e posbist reliability theory is established various conclusions which are contrary to statements in conventional reliability theory i e probist reliability theory are then drawn

on the approximation of spectra of linear operators on hilbert spaces abstract we present several new techniques for approximating spectra of linear operators not necessarily bounded on an infinite dimensional separable hilbert space our approach is to take well known techniques from finite dimensional matrix analysis and show how they can be generalized to an infinite dimensional setting to provide approximations of spectra of elements in a large class of operators we conclude by proposing a solution to the general problem of approximating the spectrum of an arbitrary bounded operator by introducing the n pseudospectrum and argue how that can be used as an approximation to the spectrum

application of affine invariant fourier descriptors to recognition of 3 d objects the method of fourier descriptors is extended to produce a set of normalized coefficients which are invariant under any affine transformation translation rotation scaling and shearing the method is based on a parameterized boundary description which is transformed to the fourier domain and normalized there to eliminate dependencies on the affine transformation and on the starting point invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions as is demonstrated by processing silhouettes of aircraft maneuvering in three space