a higher order weak approximation scheme of multidimensional stochastic differential equations using malliavin weights we show a new higher order weak approximation with malliavin weights for multidimensional stochastic differential equations by extending the method in takahashi and yamada 2016 the estimate of global error of the discretization is based on a sharp small time expansion using a malliavin calculus approach we give explicit malliavin weights for second order discretization as polynomials of brownian motions the effectiveness is illustrated through an example in option pricing

hermite polynomial based expansion of european option prices abstract we seek a closed form series approximation of european option prices under a variety of diffusion models the proposed convergent series are derived using the hermite polynomial approach departing from the usual option pricing routine in the literature our model assumptions have no requirements for affine dynamics or explicit characteristic functions moreover convergent expansions provide a distinct insight into how and on which order the model parameters affect option prices in contrast with small time asymptotic expansions in the literature with closed form expansions we explicitly translate model features into option prices such as mean reverting drift and self exciting or skewed jumps numerical examples illustrate the accuracy of this approach and its advantage over alternative expansion methods

an alternative proof for the recursive formulae for computing the moore penrose m inverse of a matrix in this paper we provide an alternative proof for the recursive formulae for the determination of the generalized moore penrose m inverse of a matrix through the direct verification of the four properties of moore penrose m inverse

inequality constraints in the process of jumping abstract this work presents a study of jumping through a biomechanical model of a leg which is subjected to an inequality constraint the activation and deactivation of an equality constraint reproduce the inequality constraint within the framework of the generalized inverse equations of motion it is shown that the activation of this additional constraint can be implemented by greville s formulae

brownian motion on the hyperbolic plane and selberg trace formula abstract we will show that the relation of the heat kernels for the schrodinger operators with uniform magnetic fields on the hyperbolic plane h 2 the maass laplacians and for the schrodinger operators with morse potentials on r is given by means of a one dimensional fourier transform in the framework of stochastic analysis where the brownian motion on h 2 plays an important role by using this relation we will give the explicit forms of the green functions as a typical related problem we will discuss the selberg trace formula the close relation of the trace formula with the corresponding classical mechanics will also be discussed

a new perspective on the tracking control of nonlinear structural and mechanical systems based on recent results from analytical dynamics this paper develops a class of tracking controllers for controlling general nonlinear structural and mechanical systems unlike most control methods that perform some kind of linearization and or nonlinear cancellation the methodology developed herein views the nonlinear control problem from a different perspective this leads to a simple and new control methodology that is capable of exactly maintaining the nonlinear system along a certain trajectory which in general may be described by a set of differential equations in the observations measurements the approach requires very little computation compared with standard approaches it is therefore useful for online real time control of nonlinear systems the methodology is illustrated with two examples

on constrained motion the general explicit equations of motion for constrained discrete dynamical systems are obtained these new equations lead to a simple and new fundamental view of constrained motion where the forces of constraint may be ideal and or non ideal

stochastic calculus of variations abstract a theory of stochastic calculus of variations is presented which generalizes the ordinary calculus of variations to stochastic processes generalizations of the euler equation and noether s theorem are obtained and several conservation laws are discussed an application to nelson s probabilistic framework of quantum mechanics is also given

decroissance exponentielle du noyau de la chaleur sur la diagonale i we give examples based upon large deviation s theory where the heat kernel of a degenerate diffusion has an exponential decay over the diagonal using malliavin calculus we give conditions for a more generalized heat kernel to have an exponential decay over the diagonal we give lower bound in some particular case by using the bismut s condition

berry esseen theorems for quadratic forms of gaussian stationary processes letx1 x2 be a gaussian stationary process with spectral densityf and let z j frac 1 sqrt t left sum limits l 1 t j 1 left x l x l j 1 ex l x l j 1 right right j 1 p the present paper gives a berry esseen type theorem for the joint distribution of z1 zp

analyse quasi sure et l estimation du noyau de la chaleur pour temps petit the ito functionals can be redefined out of a slim set by the natural way quasi sure analysis is used to deal with the heat kernel asymptotic problems

analysis of wiener functionals malliavin calculus and its applications to heat kernels on donne un expose facilement accessible du calcul de malliavin du calcul differentiel de dimension infinie sur l espace de wiener

pricing approximations and error estimates for local levy type models with default we find approximate solutions of partial integro differential equations which arise in financial models when defaultable assets are described by general scalar levy type stochastic processes we derive rigorous error bounds for the approximate solutions we also provide numerical examples illustrating the usefulness and versatility of our methods in a variety of financial settings

a unified approach for the recursive determination of generalized inverses abstract using a unified approach simple derivations for the recursive determination of different types of generalized inverses of a matrix are presented these include results for the generalized inverse the least squares generalized inverse the minimum norm generalized inverse and the moore penrose inverse of a matrix

the bellman gauss principle for constrained motion gauss principle of least constraint is solved in a sequential fashion via dynamic programming in this paper the solution itself constitutes a new principle for constrained motion which we may name the bellman gauss principle for constrained motion

stokes formula on the wiener space and n dimensional nourdin peccati analysis extensions of the nourdin peccati analysis to rn valued random variables are obtained by taking conditional expectation on the wiener space several proof techniques are explored from infinitesimal geometry to quasi sure analysis including a connection to stein s lemma to classical analysis on wiener space partial differential equations for the density of an rn valued centered random variable z z1 zn are obtained of particular importance is the function defined by the conditional expectation given z of the auxiliary random matrix dl 1zi dzj i j 1 2 n where d and l are respectively the derivative operator and the generator of the ornstein uhlenbeck semigroup on wiener space

closed form expansion conditional expectation and option valuation enlightened by the theory of watanabe watanabe s 1987 analysis of wiener functionals malliavin calculus and its applications to heat kernels ann probab 15 1 39 for analyzing generalized random variables and its further development in yoshida yoshida n 1992a asymptotic expansions for statistics related to small diffusions j japan statist soc 22 139 159 takahashi takahashi a 1995 essays on the valuation problems of contingent claims ph d thesis haas school of business university of california berkeley takahashi a 1999 an asymptotic expansion approach to pricing contingent claims asia pacific financial markets 6 115 151 as well as kunitomo and takahashi kunitomo n takahashi a 2001 the asymptotic expansion approach to the valuation of interest rate contingent claims math finance 11 1 117 151 kunitomo n takahashi a 2003 on validity of the asymptotic expansion approach in contingent claim analysis ann appl probab 13 3 914 952 etc we focus on a wide range of mult

small time fluctuations for sub riemannian diffusion loops we study the small time fluctuations for diffusion processes which are conditioned by their initial and final positions under the assumptions that the diffusivity has a sub riemannian structure and that the drift vector field lies in the span of the sub riemannian structure in the case where the endpoints agree and the generator of the diffusion process is non elliptic at that point the deterministic malliavin covariance matrix is always degenerate we identify after a suitable rescaling another limiting malliavin covariance matrix which is non degenerate and we show that with the same scaling the diffusion malliavin covariance matrices are uniformly non degenerate we further show that the suitably rescaled fluctuations of the diffusion loop converge to a limiting diffusion loop which is equal in law to the loop we obtain by taking the limiting process of the unconditioned rescaled diffusion processes and condition it to return to its starting point the generator of the unconditioned limiting rescaled diffusion process can be described in terms of the original generator

asymptotic distribution of statistics in time series veritable conditions are given for the validity of formal edgeworth expansions for the distribution of sums x 1 x n where x i f z i z i p 1 and z 1 z 2 is a strict sense stationary sequence that can be written as z j g e j k k 0 with an iid sequence e i of innovations these models include nonlinear functions of arma processes z i as well as certain nonlinear ar processes the results apply to many statistics in nonlinear time series models

chaotic field theory a sketch abstract spatio temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio temporally periodic solutions the periodic orbit theory yields the global averages characterizing the chaotic dynamics as well as the starting semiclassical approximation to the quantum theory new methods for computing corrections to the semiclassical approximation are developed in particular a nonlinear field transformation yields the perturbative corrections in a form more compact than the feynman diagram expansions

estimation de varadhan pour des diffusions a deux parametres sous des conditions de hormander generalisees la loi d une diffusion a parametre planaire possede une densite lisse en dehors des axes dans le cas elliptique nous etablissons une estimation de cette densite pur des petites valeurs du parametre celle ci constitue l analogue de l estimation de varadhan objet qui est bien connu dans le cas des diffusions ordinaires

global bifurcation sets and stable projections of nonsingular algebraic surfaces the view graph of a surface is a planar graph whose nodes are the stable views projections of the surface and whose edges represent transitional views of codimension one the space of all directions of orthogonal projection can be identified with the projective plane the set of bad projection directions associated with the degenerate views of positive codimension forms a graph in the projective plane the view bifurcation set this graph is dual to the view graph and divides the projective plane into a certain number of connected regions whose representatives are the nodes of the view graph we assume that the projected surface is nonsingular and parameterized by polynomials of degree d we present an estimate for the number of nodes in the view graph in terms of d and describe symbolic algorithms for computing the bifurcation set and the view graph of a surface from a parametrization

stochastic oscillatory integrals with quadratic phase function and jacobi equations an evaluation of a stochastic oscillatory integral with quadratic phase function and analytic amplitude function is given by using solutions of jacobi equations the evaluation will be obtained as an application of real change of variable formulas and holomorphic prolongations of analytic functions on a real wiener space on the way we shall see how a jacobi equation appears in the evaluation by using the malliavin calculus

malliavin calculus and asymptotic expansion for martingales we present an asymptotic expansion of the distribution of a random variable which admits a stochastic expansion around a continuous martingale the emphasis is put on the use of the malliavin calculus the uniform nondegeneracy of the malliavin covariance under certain truncation plays an essential role as the cramer condition did in the case of independent observations applications to statistics are presented

on error estimates for asymptotic expansions with malliavin weights application to stochastic volatility model this paper proposes a unified method for precise estimates of the error bounds in asymptotic expansions of an option price and its greeks sensitivities under a stochastic volatility model more generally we also derive an error estimate for an asymptotic expansion around a general partially elliptic diffusion and a more general wiener functional which is applicable to various important valuation and risk management tasks in the financial business such as the ones for multidimensional diffusion and nondiffusion models in particular we take the malliavin calculus approach and estimate the error bounds for the malliavin weights of both the coefficient and the residual terms in the expansions by effectively applying the properties of kusuoka stroock functions introduced by kusuoka kusuoka s 2003 malliavin calculus revisited j math sci univ tokyo 10 261 277 functions moreover a numerical experiment under the heston type model confirms the effectiveness of our method

analytic functions on abstract wiener spaces abstract let x h be a real abstract wiener space a new definition of analytic functions on x is introduced and it is shown that stochastic line integrals of real analytic 1 forms along brownian motion and solutions to stochastic differential equations with real analytic coefficients are analytic wiener functionals an l p theoretical sufficient condition for wiener functionals to be analytic and an associated cauchy formula are also established

asymptotic expansions of maximum likelihood estimators for small diffusions via the theory of malliavin watanabe the asymptotic expansions of the probability distributions of statistics for the small diffusion are derived by means of the malliavin calculus from this the second order efficiency of the maximum likelihood estimator is proved

a new delta expansion for multivariate diffusions via the ito taylor expansion abstract in this paper we develop a new delta expansion approach to deriving analytical approximation to the transition densities of multivariate diffusions using the ito taylor expansion of the conditional expectation of the dirac delta function our approach yields an explicit recursive formulas for the expansion coefficients and is universally applicable for a wide spectrum of models particularly the time inhomogeneous non affine irreducible multivariate diffusions we show that this new approach can be viewed as an extension of ait sahalia 2002 and lee et al 2014 to the case of multivariate models the derived expansions are proved to converge to the true probability density as the observational time interval shrinks the obtained approximations can thereby be used to carry out the maximum likelihood estimation for the diffusions with discretely observed data extensive numerical experiments demonstrate the accuracy and effectiveness of our approach

on the exponential decay of oscillatory integrals on an abstract wiener space abstract let x h be a real abstract wiener space the saddle point method is carried out on x and an exact formula for deformation of contour integration that is a formula transferring a fourier type integral to a fourier laplace one will be concluded as an application an exponentially fast decay of stochastic oscillatory integrals on x is studied

the visual hull of smooth curved objects the visual hull is a geometric entity that relates the shape of an object to its silhouettes or shadows this paper develops the theory of the visual hull of generic smooth objects we show that the visual hull can be constructed using surfaces which partition the viewpoint space of the aspect graph of the object the surfaces are those generated by the visual events tangent crossing and triple point an analysis based on the shape of the object at the tangency points of these surfaces allows pruning away many surfaces and patches not relevant to the construction an algorithm for computing the visual hull is outlined

explicit form of approximate transition probability density functions of diffusion processes abstract a continuous time diffusion process is very popular in modeling and provides useful tools to analyze particularly but not restricted to a variety of economic and financial variables the transition probability density function tpdf of a diffusion process plays an important role in understanding and explaining the dynamics of the process a new way to find closed form approximate tpdfs for multivariate diffusions is proposed in this paper this method can be applied to general multivariate time inhomogeneous diffusion processes as long as roughly speaking they have smooth drift and volatility functions a diffusion process is said to be reducible if it can be converted into a unit diffusion process where the volatility is the identity matrix we have established how to obtain the approximate tpdf of a reducible diffusion explicitly when a diffusion process is not reducible an explicit form of approximate tpdf can be obtained by using the results in ait sahalia 2008 and choi 2013 the tpdf expansion suggested here enables us to obtain a recursive formula for the coefficient of the approximate tpdf for a multivariate jump diffusion monte carlo simulation studies of conducting maximum likelihood estimation mle using our approximations provide convincing evidence that our tpdf expansion can be used for the mle when the true tpdf is unavailable we also applied our approximate tpdfs to option pricing the differences between our option prices and those from the extended black scholes formula are shown to be quite small this implies that our methods can be employed to price assets whose underlying state variables follow general diffusion models

computing exact aspect graphs of curved objects algebraic surfaces this article presents an algorithm for computing the exact aspect graph of an opaque solid bounded by a smooth algebraic surface orthographic projection is assumed the algorithm is based on a catalog of visual events available from singularity theory it uses curve tracing cell decomposition homotopy continuation and ray tracing to construct the regions of the view sphere delineated by visual event curves the algorithm has been fully implemented and examples are presented

a remark on the asymptotic expansion of density function of wiener functionals abstract we consider the asymptotic expansion of density function of wiener functionals as time tends to zero as in s kusuoka d w stroock precise asymptotics of certain wiener functionals j funct anal 99 1991 1 74 and give an explicit formula for the first coefficient

hypoelliptic heat kernel inequalities on the heisenberg group we study the existence of l p type gradient estimates for the heat kernel of the natural hypoelliptic laplacian on the real three dimensional heisenberg lie group using malliavin calculus methods we verify that these estimates hold in the case

asymptotic expansion of bayes estimators for small diffusions using the malliavin calculus we derived asymptotic expansion of the distributions of the bayes estimators for small diffusions the second order efficiency of the bayes estimator is proved

levy s stochastic area and the principle of stationary phase abstract let w 0 h 0 0 be the 2 dimensional classical pinned wiener space over 0 1 a localization phenomenon will be shown for stochastic oscillatory integrals with levy s stochastic area as phase function

optimal instrumental variables estimation for arma models in this paper a new class of instrumental variables iv estimators for linear processes and in particular arma models is developed previously iv estimators based on lagged observations as instruments have been used to account for unmodelled ma q errors in the estimation of the ar parameters here it is shown that these iv methods can be used to improve efficiency of linear time series estimators in the presence of unmodelled conditional heteroskedasticity moreover an iv estimator for both the ar and ma part is developed estimators based on a gaussian likelihood are inefficient members of the class of iv estimators analyzed here when the innovations are conditionally heteroskedastic

closed form expansions of discretely monitored asian options in diffusion models in this paper we propose a closed form asymptotic expansion approach to pricing discretely monitored asian options in general one dimensional diffusion models our expansion is a small time expansion because the expansion parameter is selected to be the square root of the length of monitoring interval this expansion method is distinguished from many other pricing oriented expansion algorithms in the literature because of two appealing features first we illustrate that it is possible to explicitly calculate not only the first several expansion terms but also any general expansion term in a systematic way second the convergence of the expansion is proved rigorously under some regularity conditions numerical experiments suggest that the closed form expansion formula with only a few terms e g four terms up to the third order is accurate fast and easy to implement for a broad range of diffusion models even including those violating the regularity conditions

an alternative proof for the explicit equations of motion for mechanical systems with independent non ideal constraints an alternative proof for the explicit equations of motion for mechanical systems with independent non ideal constraints is proposed in this paper these equations are derived without the use of generalized inverse matrices and based on the decomposition of the constraint forces along the acceleration constrained flat surface and its normal plane

the debiased whittle likelihood the whittle likelihood is a widely used and computationally efficient pseudolikelihood however it is known to produce biased parameter estimates with finite sample sizes for large classes of models we propose a method for debiasing whittle estimates for second order stationary stochastic processes the debiased whittle likelihood can be computed in the same o n log n operations as the standard whittle approach we demonstrate the superior performance of our method in simulation studies and in application to a large scale oceanographic dataset where in both cases the debiased approach reduces bias by up to two orders of magnitude achieving estimates that are close to those of the exact maximum likelihood at a fraction of the computational cost we prove that the method yields estimates that are consistent at an optimal convergence rate of n 1 2 for gaussian processes and for certain classes of non gaussian or nonlinear processes this is established under weaker assumptions than in the standard theory and in particular the power spectral density is not required to be continuous in frequency we describe how the method can be readily combined with standard methods of bias reduction such as tapering and differencing to further reduce bias in parameter estimates

the scale space aspect graph currently the aspect graph is computed from the theoretical standpoint of perfect resolution in object shape the viewpoint and the projected image this means that the aspect graph may include details that an observer could never see in practice introducing the notion of scale into the aspect graph framework provides a mechanism for selecting a level of detail that is large enough to merit explicit representation this effectively allows control over the number of nodes retained in the aspect graph this paper introduces the concept of the scale space aspect graph defines three different interpretations of the scale dimension and presents a detailed example for a simple class of objects with scale defined in terms of the spatial extent of features in the image

a stochastic approach to the poincare hopf theorem in this paper the poincare hopf theorem hopf 8 is proved by a probabilistic method the proof of this theorem is reduced to an estimate of a supertrace of the fundamental solution we use the malliavian calculus to estimate the fundametal solution our proof can be applied to the case that the zero point set is the union of the submanifolds under some conditions

on wiener functionals of order 2 associated with soliton solutions of the kdv equation abstract the eigenvalues and eigenvectors of the hilbert schmidt operators corresponding to the wiener functionals of order 2 which give a rise of soliton solutions of the kdv equation are determined two explicit expressions of the stochastic oscillatory integral with such wiener functional as phase function are given one is of infinite product type and the other is of levy s formula type as an application the asymptotic behavior of the stochastic oscillatory integral will be discussed

estimating jump diffusions using closed form likelihood expansions the indispensable role of likelihood expansions in financial econometrics for continuous time models has been established since the ground breaking work of ait sahalia 1999 2002a 2008 jump diffusions play an important role in modeling a variety of economic and financial variables as a significant generalization of li 2013 we propose a new closed form expansion for transition density of poisson driven jump diffusion models and its application in maximum likelihood estimation based on discretely sampled data technically speaking our expansion is obtained by perturbing paths of the underlying model correction terms can be calculated explicitly using any symbolic software numerical examples and monte carlo evidence for illustrating the performance of density expansion and the resulting approximate mle are provided in order to demonstrate the practical applicability of the method using the theoretical results in hayashi and ishikawa 2012 some convergence properties related to the density expansion and the approximate mle method can be justified under some standard sufficient but not necessary conditions

arch models as diffusion approximations abstract this paper investigates the convergence of stochastic difference equations e g arch to stochastic differential equations as the length of the discrete time intervals between observations goes to zero these results are applied to the garch 1 1 model of bollerslev 1986 and to the ar 1 exponential arch model of nelson 1989 in their continuous time limits the conditional variance processes in these models have stationary distributions that are inverted gamma and lognormal respectively in addition a class of diffusion approximations based on the exponential arch model is developed

perturbative analysis of anharmonic chains of oscillators out of equilibrium we compute the first order correction to the correlation functions of the stationary state of a stochastically forced harmonic chain out of equilibrium when a small on site anharmonic potential is added this is achieved by deriving a suitable formula for the covariance matrix of the invariant state we find that the first order correction of the heat current does not depend on the size of the system second the temperature profile is linear when the harmonic part of the on site potential is zero the sign of the gradient of the profile however is opposite to the sign of the temperature difference of the two heat baths

using the fundamental equation of constrained motion with inequality constraints in this paper we investigate a computational approach to keeping a moving particle within a predefined annulus or a predefined bounded space formed by two concentric spheres with radii l m i n and l m a x respectively assuming that said particle cannot maintain a perfectly circular trajectory the study develops an algorithm for dealing with a system in which constraints are expressed as inequalities the proposed approach expresses the trajectory in terms of winding unwinding logarithmic spirals with transitions expressed as damped vibrations between them these transitions are necessary to resolve incompatibility between initial conditions for winding unwinding spirals equations of motion for the particle are obtained by using the fundamental equation of constrained motion the obtained simulation results show that such an approach produces the desired pseudo periodic type of motion and the particle stays within the predefined region of space for a long duration although no cycle of its trajectory is repeated

computing the generalized aspect graph for objects with moving parts algorithms for computing the aspect graph representation are generalized to include a larger more realistic domain of objects known as articulated assemblies those objects composed of rigid parts with articulated connections allowed between parts the generalization suggests two slightly different representations one that directly summarizes the possible general views of the object and another hierarchical form summarizing the possible general configurations and their respective views algorithms are outlined for computing both representations the generalized aspect graphs of assemblies formed using translational connections are examined

asymptotic behavior of divergences and cameron martin theorem on loop spaces we first prove the lp convergence p 1 and a fernique type exponential integrability of divergence functionals for all cameron martin vector fields with respect to the pinned wiener measure on loop spaces over a compact riemannian manifold we then prove that the driver flow is a smooth transform on path spaces in the sense of the malliavin calculus and has an quasi continuous modification which can be quasi surely well defined on path spaces this leads us to construct the driver flow on loop spaces through the corresponding flow on path spaces combining these two results with the cruzeiro lemma j funct anal 54 1983 206 227 we give an alternative proof of the quasi invariance of the pinned wiener measure under driver s flow on loop spaces which was established earlier by driver trans amer math soc 342 1994 375 394 and enchev and stroock adv math 119 1996 127 154 by doob s h processes approach together with the short time estimates of the gradient and the hessian of the logarithmic heat kernel on compact riemannian manifolds we also establish the lp convergence p 1 and a fernique type exponential integrability theorem for the stochastic anti development of pinned brownian motions on compact riemannian manifold with an explicit exponential exponent our results generalize and sharpen some earlier results due to gross j funct anal 102 1991 268 313 and hsu math ann 309 1997 331 339 our method does not need any heat kernel estimate and is based on quasi sure analysis and sobolev estimates on path spaces

estimates for the density of a nonlinear landau process abstract the aim of this paper is to obtain estimates for the density of the law of a specific nonlinear diffusion process at any positive bounded time this process is issued from kinetic theory and is called landau process by analogy with the associated deterministic fokker planck landau equation it is not markovian its coefficients are not bounded and the diffusion matrix is degenerate nevertheless the specific form of the diffusion matrix and the nonlinearity imply the non degeneracy of the malliavin matrix and then the existence and smoothness of the density in order to obtain a lower bound for the density the known results do not apply however our approach follows the main idea consisting in discretizing the interval time and developing a recursive method to this aim we prove and use refined results on conditional malliavin calculus the lower bound implies the positivity of the solution of the landau equation and partially answers to an analytical conjecture we also obtain an upper bound for the density which again leads to an unusual estimate due to the bad behavior of the coefficients

a new perspective on constrained motion the explicit general equations of motion for constrained discrete dynamical systems are obtained these new equations lead to a simple and new fundamental view of lagrangian mechanics

functional ito calculus and stochastic integral representation of martingales we develop a non anticipative calculus for functionals of a continuous semimartingale using an extension of the ito formula to path dependent functionals which possess certain directional derivatives the construction is based on a pathwise derivative introduced by b dupire for functionals on the space of right continuous functions with left limits we show that this functional derivative admits a suitable extension to the space of square integrable martingales this extension denes a weak derivative which is shown to be the inverse of the ito integral and which may be viewed as a non anticipative lifting of the malliavin derivative these results lead to a constructive martingale representation formula for ito processes by contrast with the clark haussmann ocone formula this representation only involves nonanticipative quantities which may be computed pathwise

interpreting line drawings of curved objects in this thesis we study the problem of interpreting line drawings of scenes composed or opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them it is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint that the line drawing is error free and that there are no lines due to shadows or specularities our definition implicitly excludes laminae wires and the apices of cones a major component of the interpretation of line drawings is line labelling by line labelling we mean a classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene and b further subclassification of each kind of discontinuity for a depth discontinuity we determine whether it is a limb a locus of points on the surface where the line of sight is tangent to the surface or an occluding edge a tangent plane discontinuity of the surface for an orientation discontinuity we determine whether it corresponds to a convex or concave edge this thesis presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described by analysing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing an algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing a local minimum complexity rule at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex is used in order to prune highly counter intuitive interpretations the labelling scheme was implemented and tested on a number of line drawings the labellings obtained are few and by and large in accordance with human interpretations

horizontal lift of the brownian motion on the hyperbolic plane and the selberg trace formula by using an explicit representation for the horizontal lift of the brownian motion on the poincare upper half plane h2 we show an expression for the heat kernel for the de rham kodaira laplacian on h2 we apply the result to a study on the selberg trace formula

decroissance non exponentielle du noyau de la chaleur in this paper we give estimates on the heat kernel on the diagonal in terms of exp logt 1 when1 vanishes moreover we compute by means of the stochastic calculus of variations the decay of the flatness of some heat kernels on the other hand we show that the computations in both cases are very similar

approximations for the inverse of toeplitz matrices with applications to stationary processes abstract several approximations for the inverse of symmetric toeplitz matrices are compared by a new approximation criterion the criterion requires the approximation to be uniformly good over a set of matrices which increases with the size furthermore a new approximation is introduced by applying a taper to the classical whittle approximation

the geometry of view space of opaque objects bounded by smooth surfaces abstract a view of a smooth opaque object is a line drawing consisting of contour fragments which form closed loops terminate or form t junctions given a compact object we have a global decomposition of the space of camera positions into cells from which topologically equivalent views are obtained to apply certain image based object recognition techniques based on characteristic views of an object one needs to know this cellular decomposition of view space the boundaries of such cells of stable views are formed by the view bifurcation set from which transitional degenerate views are seen we derive a finite list of geometrical models of the view bifurcation set the view bifurcation set of any particular object is a combination of such model surfaces from this list to match a characteristic view with an image one has to find the visible fragments of the apparent contour in the image and we briefly describe an observation which might lead to an algorithm for finding such contour fragments

spectral embedding of graphs in this paper we explore how to embed symbolic relational graphs with unweighted edges in a pattern space we adopt a graph spectral approach we use the leading eigenvectors of the graph adjacency matrix to define eigenmodes of the adjacency matrix for each eigenmode we compute vectors of spectral properties these include the eigenmode perimeter eigenmode volume cheeger number inter mode adjacency matrices and intermode edge distance we embed these vectors in a pattern space using two contrasting approaches the first of these involves performing principal or independent components analysis on the covariance matrix for the spectral pattern vectors the second approach involves performing multidimensional scaling on the l2 norm for pairs of pattern vectors we illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2d images of 3d polyhedral objects two problems are investigated the first of these is the clustering of graphs representing distinct objects viewed from different directions the second is the identification of characteristic views of single objects these two studies reveal that both embedding methods result in well structured view spaces for graph data extracted from 2d views of 3d objects

asymptotics of spectral gaps on loop spaces over a class of riemannian manifolds abstract we prove the existence of spectral gaps of ornstein uhlenbeck operators on loop spaces over a class of riemannian manifolds which include hyperbolic spaces this is an alternative proof and an extension of a result in chen et al 13 further we study the asymptotic behavior of the spectral gap