exact energy and momentum conserving algorithms for general models in nonlinear elasticity implicit time integration schemes that inherit the conservation laws of total energy linear and angular momentum are considered for initial boundary value problems in finite deformation elastodynamics conserving schemes are constructed for general hyperelastic material models both compressible and incompressible and are formulated in a way that is independent of spatial discretization three numerical examples for ogden type material models implemented using a finite element discretization in space are given to illustrate the performance of the proposed schemes these examples show that relative to the standard implicit mid point rule the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy

modeling orientation fields of fingerprints with rational complex functions abstract in this paper a novel model is proposed for the orientation field of fingerprints which can be expressed as the argument of a rational complex function it is suitable for all types of fingerprints experimental results show that it performs much better than the previous works

multi multiplier ambient space formulations of constrained dynamical systems with an application to elastodynamics various formulations of the equations of motion for both finite and infinite dimensional constrained lagrangian dynamical systems are studied the different formulations correspond to different ways of enforcing constraints through multiplier fields all the formulations considered are posed on ambient spaces whose members are unrestricted by the need to satisfy constraint equations but each formulation is shown to possess an invariant set on which the constraint equations and physical balance laws are satisfied the stability properties of the invariant set within its ambient space are shown to be different in each case we use the specific model problem of linearized incompressible elastodynamics to compare properties of three different ambient space formulations we establish the well posedness of one formulation in the particular case of a homogeneous isotropic body subject to specified tractions on its boundary

long time numerical solution of the navier stokes equations based on a sequential regularization formulation the sequential regularization method is a reformulation of the unsteady navier stokes equations from the viewpoint of constrained dynamical systems or the approximate helmholtz hodge projection in this paper we study the long time behavior of the sequential regularization formulation we give a uniform in time estimate between the solution of the reformulated system and that of the navier stokes equations we also conduct an error analysis for the temporal discrete system and show that the error bound is independent of time a couple of long time flow examples are computed to demonstrate this method

differential algebraic systems as differential equations on manifolds based on the theory of differential equations on manifolds existence and uniqueness results are proved for a class of mixed systems of differential and algebraic equations as they occur in various applications both the autonomous and nonautonomous case are considered moreover a class of algebraically incomplete systems is introduced for which existence and uniqueness results only hold on certain lower dimensional manifolds this class includes systems for which the application of ode solvers is known to lead to difficulties finally some solution approach based on continuation techniques is outlined

global models for the orientation field of fingerprints an approach based on quadratic differentials quadratic differentials naturally define analytic orientation fields on planar surfaces we propose to model orientation fields of fingerprints by specifying quadratic differentials models for all fingerprint classes such as arches loops and whorls are laid out these models are parametrised by few geometrically interpretable parameters which are invariant under euclidean motions we demonstrate their ability in adapting to given observed orientation fields and we compare them to existing models using the fingerprint images of the nist special database 4 we also illustrate that these model allow for extrapolation into unobserved regions this goes beyond the scope of earlier models for the orientation field as those are restricted to the observed planar fingerprint region within the framework of quadratic differentials we are able to verify analytically penrose s formula for the singularities on a palm l s penrose dermatoglyphics scientific american vol 221 no 6 pp 73 84 1969 potential applications of these models are the use of their parameters as indices of large fingerprint databases as well as the definition of intrinsic coordinates for single fingerprint images

fingerprint pattern classification abstract this paper presents a new method for fingerprint classification in this method fingerprint images are divided into 32 32 subregions to obtain direction pattern next the relaxation smoothing process with singularity detection and convergency checking is performed starting from the singular regions found feature parameters of the fingerprint are obtained by extracting major flow line traces the result of the experiments shows that this approach is capable of classifying fingerprint patterns into more than ten categories

modelling fingerprint ridge orientation using legendre polynomials the estimation of fingerprint ridge orientation is an essential step in every automatic fingerprint verification system the importance of ridge orientation can be deflected from the fact that it is inevitably used for detecting describing and matching fingerprint features such as minutiae and singular points in this paper we propose a novel method for fingerprint ridge orientation modelling using legendre polynomials one of the main problems it addresses is smoothing orientation data while preserving details in high curvature areas especially singular points we show that singular points which result in a discontinuous orientation field can be modelled by the zero poles of legendre polynomials the models parameters are obtained in a two staged optimization procedure another advantage of the proposed method is a very compact representation of the orientation field using only 56 coefficients we have carried out extensive experiments using a state of the art fingerprint matcher and a singular point detector moreover we compared the proposed method with other state of the art fingerprint orientation estimation algorithms we can report significant improvements in both singular point detection and matching rates

convergence of gradient descent for low rank matrix approximation this paper provides a proof of global convergence of gradient search for low rank matrix approximation such approximations have recently been of interest for large scale problems as well as for dictionary learning for sparse signal representations and matrix completion the proof is based on the interpretation of the problem as an optimization on the grassmann manifold and fubiny study distance on this space

finite difference schemes for incompressible flows in the velocity impulse density formulation we consider finite difference schemes based on the impulse density variable we show that the original velocity impulse density formulation of oseledets is marginally ill posed for the inviscid flow and this has the consequence that some ordinarily stable numerical methods in other formulations become unstable in the velocity impulse density formulation we present numerical evidence of this instability we then discuss the construction of stable finite difference schemes by requiring that at the numerical level the nonlinear terms be convertible to similar terms in the primitive variable formulation finally we give a simplified velocity impulse density formulation which is free of these complications and yet retains the nice features of the original velocity impulse density formulation with regard to the treatment of boundary we present numerical results on this simplified formulation for the driven cavity flow on both the staggered and non staggered grids

global solutions of the equations of elastodynamics of incompressible neo hookean materials abstract i prove that the initial value problem for the motion of a certain type of elastic body has a solution for all time if the initial data are sufficiently small the body must fill all of three space obey a neo hookean stress strain law and be incompressible the proof takes advantage of the delayed singularity formation which occurs for solutions of quasilinear hyperbolic equations in more than one space dimension it turns out that the curl of the displacement of the body obeys such an equation thus using klainerman s inequality one derives the necessary estimates to guarantee that solutions persist for all time

an unconstrained hamiltonian formulation for incompressible fluid flow the equations governing the time evolution of an ideal fluid in material coordinates are expressed as an unconstrained canonical hamiltonian system the incompressibility of the flow is consequent upon certain first integrals of the motion the variable conjugate to the configuration field is not the usual linear momentum but is instead a quantity that is related to linear momentum through an auxiliary scalar field whose time derivative is the pressure the definition of the hamiltonian involves a minimization with respect to this auxiliary field the method of derivation may be generally applied to obtain unconstrained hamiltonian descriptions of lagrangian field equations subject to pointwise constraints

special functions of matrix argument i algebraic induction zonal polynomials and hypergeometric functions hypergeometric functions of matrix argument arise in a diverse range of applications in harmonic analysis multivariate statistics quantum physics molecular chemistry and number theory this paper presents a general theory of such functions for real division algebras these functions which generalize the classical hypergeometric functions are defined by infinite series on the space s s n f of all n x n hermitian matrices over the division algebra f the theory depends intrinsically upon the representation theory of the general linear group g gl n f of invertible n x n matrices over f and the theme of this work is the full exploitation of the inherent group theory the main technique is the use of the method of algebraic induction to realize explicitly the appropriate representations of g to decompose the space of polynomial functions on s and to describe the zonal polynomials from which the hypergeometric functions are constructed detailed descriptions of the convergence properties of the series expansions are given and integral representations are provided future papers in this series will develop the fine structure of these functions 0 introduction we begin a series of articles in which we develop the fine structure of generalized hypergeometric functions of matrix argument by fine structure we allude to the analogues of such classical results as series expansions integral formulas asymptotics differential equations summation formulas addition theorems composition formulas and recurrence relations this first paper in which we simultaneously treat real complex and quaternionic analysis is the result of our desire to present a complete theory of hypergeometric functions of matrix argument over real division algebras not only as a framework for the body of detailed results to follow in later papers but also to clarify the representationtheoretic foundation for such a theory although these hypergeometric functions are of interest on purely analytic grounds they arise in a wide range of applications indeed various classes of received by the editors may 19 1986 1980 malhema1zics s ject claszficain 1985 ren primary 22e30 22e45 33a75 43a85 43a90 62h10 secondary 20g20 32a07 32m15 44a10 62e15 key w and phrases generalized hypergeometric functions zonal polynomials representation theory algebraic induction multivariate statistics general linear group generalized gamma functions pochhammer symbols laplace transforms maximal compact subgroup invariant polynomials positive cones symmetric spaces schur functions special functions of matrix argument the first author is on leave from the university of wyoming the second author was partially supported by the national science foundation under grant mcs 8403381 and by the research council of the university of north carolina b1987 american mathematical society 0002 9947 87 1 00 25 per page

stabilization of daes and invariant manifolds many methods have been proposed for the stabilization of higher index differential algebraic equations daes such methods often involve constraint differentiation and problem stabilization thus obtaining a stabilized index reduction a popular method is baumgarte stabilization but the choice of parameters to make it robust is unclear in practice here we explain why the baumgarte method may run into trouble we then show how to improve it we further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature our approach is to i consider stabilization of odes with invariants ii discretize the stabilizing term in a simple way generally different from the ode discretization and iii use orthogonal projections whenever possible the best methods thus obtained are related to methods of coordinate projection we discuss them and make concrete algorithmic suggestions

on the largest principal angle between random subspaces formulas are derived for the probability density function and the probability distribution function of the largest canonical angle between two p dirnensional subspaces of r n chosen from the uniform distribution on the grassmann manifold which is the unique distribution invariant by orthogonal transformations of r n the formulas involve the gamma function and the hypergeometric function of a matrix argument c 2005 elsevier inc all rights reserved

analysis of a sequential regularization method for the unsteady navier stokes equations the incompressibility constraint makes navier stokes equations difficult a reformulation to a better posed problem is needed before solving it numerically the sequential regularization method srm is a reformulation which combines the penalty method with a stabilization method in the context of constrained dynamical systems and has the benefit of both methods in the paper we study the existence and uniqueness for the solution of the srm and provide a simple proof of the convergence of the solution of the srm to the solution of the navier stokes equations we also give error estimates for the time discretized srm formulation

coherence enhancing diffusion filtering the completion of interrupted lines or the enhancement of flow like structures is a challenging task in computer vision human vision and image processing we address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so called interest operator second moment matrix structure tensor an m dimensional formulation of this method is analysed with respect to its well posedness and scale space properties an efficient scheme is presented which uses a stabilization by a semi implicit additive operator splitting aos and the scale space behaviour of this method is illustrated by applying it to both 2 d and 3 d images

energy methods for quasilinear hyperbolic initial boundary value problems applications to elastodynamics the aim of this paper is to show how energy methods can be used to establish local in time existence of smooth solutions to certain initial boundary value problems for systems of quasilinear hyperbolic partial differential equations our particular objective is to treat the equations of nonlinear elastodynamics

hamiltonian dynamics of an elastica and the stability of solitary waves a method is presented for deriving unconstrained hamiltonian systems of partial differential equations equivalent to given constrained lagrangian systems the method is applied to the theory of planar finite amplitude motions of inextensible and unshearable elastic rods the constraints of inextensibility and unshearability become integrals of motion in the hamiltonian formulation

quasi static multiple antenna fading channels at finite blocklength this paper investigates the maximal achievable rate for a given blocklength and error probability over quasi static multiple input multiple output fading channels with and without channel state information at the transmitter and or the receiver the principal finding is that outage capacity despite being an asymptotic quantity is a sharp proxy for the finite blocklength fundamental limits of slow fading channels specifically the channel dispersion is shown to be zero regardless of whether the fading realizations are available at both transmitter and receiver at only one of them or at neither of them these results follow from analytically tractable converse and achievability bounds numerical evaluation of these bounds verifies that zero dispersion may indeed imply fast convergence to the outage capacity as the blocklength increases in the example of a particular 1 times 2 single input multiple output rician fading channel the blocklength required to achieve 90 of capacity is about an order of magnitude smaller compared with the blocklength required for an awgn channel with the same capacity for this specific scenario the coding decoding schemes adopted in the lte advanced standard are benchmarked against the finite blocklength achievability and converse bounds

systematic methods for the computation of the directional fields and singular points of fingerprints the first subject of the paper is the estimation of a high resolution directional field of fingerprints traditional methods are discussed and a method based on principal component analysis is proposed the method not only computes the direction in any pixel location but its coherence as well it is proven that this method provides exactly the same results as the averaged square gradient method that is known from literature undoubtedly the existence of a completely different equivalent solution increases the insight into the problem s nature the second subject of the paper is singular point detection a very efficient algorithm is proposed that extracts singular points from the high resolution directional field the algorithm is based on the poincare index and provides a consistent binary decision that is not based on postprocessing steps like applying a threshold on a continuous resemblance measure for singular points furthermore a method is presented to estimate the orientation of the extracted singular points the accuracy of the methods is illustrated by experiments on a live scanned fingerprint database

accurate and efficient evaluation of schur and jack functions we present new algorithms for computing the values of the schur s x 1 x 2 x n and jack j x 1 x 2 x n functions in floating point arithmetic these algorithms deliver guaranteed high relative accuracy for positive data x i a 0 and run in time that is only linear in n

symplectic integration of constrained hamiltonian systems a hamiltonian system in potential form h q p ptmp 2 f q subject to smooth constraints on q can be viewed as a hamiltonian system on a manifold but numerical computations must be performed in rn in this paper methods which reduce hamiltonian differential algebraic equations to odes in euclidean space are examined the authors study the construction of canonical parametrizations or local charts as well as methods based on the construction of ode systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold in each case a hamiltonian system of ordinary differential equations is produced the stability of the constraint invariants and the behavior of the original hamiltonian along solutions are investigated both numerically and analytically

a geometric newton method for oja s vector field newton s method for solving the matrix equation runs up against the fact that its zeros are not isolated this is due to a symmetry of f by the action of the orthogonal group we show how differential geometric techniques can be exploited to remove this symmetry and obtain a geometric newton algorithm that finds the zeros of f the geometric newton method does not suffer from the degeneracy issue that stands in the way of the original newton method

geometry and radiometry invariant matched manifold detection consider a set of deformable objects undergoing geometric and radiometric transformations as a result of the action of these transformations the set of different realizations of each object is generally a manifold in the space of observations assuming the geometric deformations an object undergoes belong to some finite dimensional family it has been shown that the universal manifold embedding ume provides a set of nonlinear operators that universally maps each of the different manifolds where each manifold is generated by the set all of possible appearances of a single object into a distinct linear subspace of an euclidean space in this paper we generalize this framework to the case where the observed object undergoes both an affine geometric transformation and a monotonic radiometric transformation and present a novel framework for the detection and recognition of the deformable objects applying to each of the observations an operator that makes it invariant to monotonic amplitude transformations but is geometry covariant with the affine transformation the set of all possible observations on that object is mapped by the ume into a single linear subspace invariant with respect to both the geometric and radiometric transformations the embedding of the space of observations is independent of the specific observed object hence it is universal the invariant representation of the object is the basis of a matched manifold detection and tracking framework of objects that undergo complex geometric and radiometric deformations the observed surface is tessellated into a set of tiles such that the deformation of each one is well approximated by an affine geometric transformation and a monotonic transformation of the measured intensities since each tile is mapped by the radiometry invariant ume to a distinct linear subspace the detection and tracking problems are solved by evaluating distances between linear subspaces classification in this context becomes a problem of determining which labeled subspace in a grassmannian is closest to a subspace in the same grassmannian where the latter has been generated by radiometry invariant ume from an unlabeled observation

the initial value problem for elastodynamics of incompressible bodies we prove short time well posedness of the cauchy problem for incompressible strongly elliptic hyperelastic materials

a grassmann rayleigh quotient iteration for computing invariant subspaces the classical rayleigh quotient iteration rqi allows one to compute a one dimensional invariant subspace of a symmetric matrix a here we propose a generalization of the rqi which computes a p dimensional invariant subspace of a cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature

a nonlinear orientation model for global description of fingerprints a nonlinear orientation model for the representation of the orientation matrix of a fingerprint image is presented a general procedure to obtain the set of parameters describing this model is shown particularly a piecewise linear orientation function is analysed the model compared with a previous zero pole model shows substantial decrease in the orientation error the application of this model for efficient identity verification based on the ridge orientation is explored

stability of computational methods for constrained dynamics systems many methods have been proposed for numerically integrating the differential algebraic systems arising from the euler lagrange equations for constrained motion these are based on various problem formulations and discretizations we offer a critical evaluation of these methods from the standpoint of stability nconsidering a linear model we first give conditions under which the differential algebraic problem is well conditioned this involves the concept of an essential underlying ode we review a variety of reformulations which have been proposed in the literature and show that most of them preserve the well conditioning of the original problem then we consider stiff and nonstiff discretizations of such reformulated models in some cases the same implicit discretization may behave in a very different way when applied to different problem formulations acting as a stiff integrator on some formulations and as a nonstiff integrator on others we present the approach of projected invariants as a method for yielding problem reformulations which are desirable in this sense

numerical integration of constrained hamiltonian systems using dirac brackets we study the numerical properties of the equations of motion of constrained systems derived with dirac brackets this formulation is compared with one based on the extended hamiltonian as concrete examples a pendulum in cartesian coordinates and a chain molecule are treated

interference alignment for partially connected mimo cellular networks in this paper we propose an iterative interference alignment ia algorithm for mimo cellular networks with partial connectivity which is induced by heterogeneous path losses and spatial correlation such systems impose several key technical challenges in the ia algorithm design namely the overlapping between the direct and interfering links due to the mimo cellular topology as well as how to exploit the partial connectivity we shall address these challenges and propose a three stage ia algorithm as illustration we analyze the achievable degree of freedom dof of the proposed algorithm for a symmetric partially connected mimo cellular network we show that there is significant dof gain compared with conventional ia algorithms due to partial connectivity the derived dof bound is also backward compatible with that achieved on fully connected k pair mimo interference channels

enhanced local subspace affinity for feature based motion segmentation we present a new motion segmentation algorithm the enhanced local subspace affinity elsa unlike local subspace affinity elsa is robust in a variety of conditions even without manual tuning of its parameters this result is achieved thanks to two improvements the first is a new model selection technique for the estimation of the trajectory matrix rank the second is an estimation of the number of motions based on the analysis of the eigenvalue spectrum of the symmetric normalized laplacian matrix results using the hopkins155 database and synthetic sequences are presented and compared with state of the art techniques

multivariate analysis and jacobi ensembles largest eigenvalue tracy widom limits and rates of convergence abstract let a and b be independent central wishart matrices in p variables with common covariance and having m and n degrees of freedom respectively the distribution of the largest eigenvalue of a b 1 b has numerous applications in multivariate statistics but is difficult to calculate exactly suppose that m and n grow in proportion to p we show that after centering and scaling the distribution is approximated to second order o p 2 3 by the tracy widom law the results are obtained for both complex and then real valued data by using methods of random matrix theory to study the largest eigenvalue of the jacobi unitary and orthogonal ensembles asymptotic approximations of jacobi polynomials near the largest zero play a central role

symplectic numerical integrators in constrained hamiltonian systems recent work reported in the literature suggests that for the long time integration of hamiltonian dynamical systems one should use methods that preserve the symplectic or canonical structure of the flow here we investigate the symplecticness of numerical integrators for constrained dynamics such as occur in molecular dynamics when bond lengths are made rigid in order to overcome stepsize limitations due to the highest frequencies this leads to a constrained hamiltonian system of smaller dimension previous work has shown that it is possible to have methods which are symplectic on the constraint manifold in phase space here it is shown that the very popular verlet method with shake type constraints is equivalent to the same method with rattle type constraints and that the latter is symplectic and time reversible this assumes that the iteration is carried to convergence we also demonstrate the global convergence of the verlet scheme in the presence of shake type and rattle type constraints we perform numerical experiments to compare these methods with the second order backward differentiation method commonly recommended for ordinary differential equations with constraints

approximation of haar distributed matrices and limiting distributions of eigenvalues of jacobi ensembles we develop a tool to approximate the entries of a large dimensional complex jacobi ensemble with independent complex gaussian random variables based on this and the author s earlier work in this direction we obtain the tracy widom law of the largest singular values of the jacobi emsemble moreover the circular law the marchenko pastur law the central limit theorem and the laws of large numbers for the spectral norms are also obtained

the incompressible limit in nonlinear elasticity the incompressible limit in nonlinear elasticity is shown to fall under the theory of singular limits of quasilinear symmetric hyperbolic systems developed by klainerman and majda specifically initial value problems for a family of hyperelastic materials with stored energy functions w left frac partial x partial x right w infty left frac partial x partial x right lambda 2 w left det frac partial x partial x right are considered wherex andx are reference and deformed coordinates respectively under the assumption that the elasticity tensor a kl ij equiv frac partial 2 w infty partial left frac partial x i partial x k right partial left frac partial x j partial x l right is positive definite near the identity matrix and thatw 1 0 the following results are proven for appropriate initial data

a variational formulation for fingerprint orientation modeling orientation pattern is an important feature for characterizing fingerprint and plays critical roles in fingerprint recognition and fingerprint classification this paper proposes a framework for modeling the fingerprint orientation field based on the variational principle where the orientation pattern can be estimated through solving the associated euler lagrange equation compared with existing methods our proposed method has the following features firstly it does not require any prior information about the structure of the acquired fingerprint such as location of singular point s secondly it explicitly provides freedom for modeling the singularity in the orientation field thirdly it has less number of parameters comparison has been made with respect to state of the arts in fingerprint orientation modeling in terms of modeling accuracy fingerprint enhancement and singular point detection advantages of the proposed method are demonstrated

an ergodic sampling scheme for constrained hamiltonian systems with applications to molecular dynamics this article addresses the problem of computing the gibbs distribu tion of a hamiltonian system that is subject to holonomic constraints in doing so we extend recent ideas of cances et al m2an vol 41 no 2 pp 351 389 2007 who could prove a law of large numbers for unconstrained molecular systems with a separable hamiltonian em ploying a discrete version of hamilton s principle studying ergodicity for constrained hamiltonian systems we specifically focus on the numerical discretization error even if the continuous system is perfectly ergodic this property is typically not preserved by the numerical discretization the discretization error is taken care of by means of a hybrid monte carlo al gorithm that allows for sampling bias free expectation values with respect to the gibbs measure independently of the stable step size we give a demonstration of the sampling algorithm by calculating the free energy profile of a small peptide

extracting image orientation feature by using integration operator this paper presents an orientation operator to extract image local orientation features we show that a proper employment of image integration leads to an unbiased orientation estimate based on which an orientation operator is proposed the resulting discrete operator has flexibility in the scale selection as the scale change does not violate the bias minimization criteria an analytical formula is developed to compare orientation biases of various discrete operators the proposed operator shows lower bias than eight well known gradient operators experiments further demonstrate higher orientation accuracy of the proposed operator than these gradient operators

mathematical models for local nontexture inpaintings dedicated to stanley osher on the occasion of his 60th birthday abstract inspired by the recent work of bertalmio et al on digital inpaintings siggraph 2000 we develop general mathematical models for local inpaintings of nontexture images on smooth regions inpaintings are connected to the harmonic and biharmonic extensions and inpainting orders are analyzed for inpaintings involving the recovery of edges we study a variational model that is closely connected to the classical total variation tv denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 other models are also discussed based on the mumford shah regularity comm pure appl math xlii 1989 pp 577 685 and curvature driven diffusions cdd of chan and shen j visual comm image rep 12 2001 the broad applications of the inpainting models are demonstrated through restoring scratched old photos disocclusion in vision analysis text removal digital zooming and edge based image coding