forced lattice vibrations part ii this is the first part of a two part series on forced lattice vibrations in which a semi infinite lattice of one dimensional particles xn n 1 is driven from one end by a particle x0 this particle undergoes a given periodically perturbed uniform motion x0 t at h yt where a and are constants and h has period 2 for a wide variety of restoring forces f i e f 0 numerical calculations indicate the existence of a sequence of thresholds 1 1 a h f 2 2 a h f k k a h f k 0 as k if k k 1 a k phase wave that is well described by the wave form emerges and travels through the lattice the goal of this series is to describe the emergence and calculate some properties of these wave forms in part i the authors first consider the case where f x ex i e toda forces but h is arbitrary and show how to compute a basic diagnostic see j formula 1 26 for the system in terms of the solution of an associated scalar riemann hilbert problem once a certain finite set of numbers is known in another direction the authors consider the case where f x is restoring but arbitrary and h is small here the authors prove a general result asserting that if there exists a sufficiently ample family of traveling wave solutions of the doubly infinite lattice then it is possible to construct time periodic k phase wave solutions with asymptotics in n of type iii for the driven system i in part ii the authors prove that sufficiently ample families of traveling wave solutions of the system iv exist in the cases 1 and 1 2 for general restoring forces f in the case with toda forces f x ex the authors prove that sufficiently ample families of traveling wave solutions

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

multi phase computations of the semiclassical limit of the schrodinger equation and related problems whitham vs wigner abstract we present and compare two different techniques to obtain the multi phase solutions for the schrodinger equation in the semiclassical limit the first is whitham s averaging method which gives the modulation equations governing the evolution of multi phase solutions the second is the wigner transform a convenient tool to derive the semiclassical limit equation in the phase space the vlasov equation for the linear schrodinger equation motivated by the linear superposition principle we derive and prove the multi phase ansatz for the wigner function by the stationary phase method and then use the ansatz to close the moment equations of the vlasov equation and obtain the multi phase equations in the physical space we show that the multi phase equations so derived agree with those derived by whitham s averaging method which can be proved using different arguments generic way of obtaining and computing the multi phase equations by the wigner function is given and kinetic schemes are introduced to solve the multi phase equations the numerical schemes based on multiphase closure of the liouville equation are purely eulerian and only operate in the physical space several numerical examples are given to explore the validity of this approach similar studies are conducted for the linearized korteweg de vries equation and the linear wave equation

enumerative counting is hard abstract an n variable boolean formula may have anywhere from 0 to 2n satisfying assignments can a polynomial time machine given such a formula reduce this exponential number of possibilities to a small number of possibilities we call such a machine an enumerator and prove that if there is a good polynomial time enumerator for p i e one where for every boolean formula f the small set has at most o f 1 e numbers then p np p p and probabilistic polynomial time equals polynomial time furthermore we show that p polynomial time turing reduces to enumerating p

whitham systems and deformations we consider the deformations of whitham systems including the dispersion terms and having the form of dubrovin zhang deformations of frobenius manifolds the procedure is connected with the b a dubrovin problem of deformations of frobenius manifolds corresponding to the whitham systems of integrable hierarchies under some nondegeneracy requirements we suggest a general scheme of the deformation of the hyperbolic whitham systems using the initial nonlinear system the general form of the deformed whitham system coincides with the form of the low dispersion asymptotic expansions used by b a dubrovin and y zhang in the theory of deformations of frobenius manifolds

on a class of solutions of kdv abstract practically every book on the inverse scattering transform method for solving the cauchy problem for kdv and other integrable systems refers to this method as nonlinear fourier transform if this is indeed so the method should lead to a nonlinear analogue of the fourier expansion formula u t x u k e i kx k t dk in this paper a special class of solutions of kdv whose role is similar to that of e i kx k t is discussed the theory of these solutions referred to here as harmonic breathers is developed and it is shown that these solutions may be used to construct more general solutions of kdv similarly to how the functions e i kx t are used to perform the same task in the theory of fourier transform a nonlinear superposition formula for general solutions of kdv similar to the fourier expansion formula is conjectured

binary and ternary oscillations in a cubic numerical scheme abstract we study a central difference semi discretization of the cubic scalar conservation law both spatial period 2 binary and period 3 ternary oscillations are stationary solutions of this scheme and we find where each type is linearly stable we observe numerically the formation of ternary oscillations to the left of riemann shock initial data with ur 0 while binary oscillations form to the right of riemann rarefaction data having ul 0 we derive modulation equations for both wave patterns using them to show that binary oscillations generated by the scheme are numerical artifacts while computing an explicit solution for the ternary modulation equations for positive initial data the ternary modulation equations remain hyperbolic while the solutions enter an elliptic region for data of both signs conditions under which solutions of the ternary modulation equations can be inverted to yield period 3 oscillations are also discussed

rejecting mismatches by correspondence function a novel method icf identifying point correspondences by correspondence function is proposed for rejecting mismatches from given putative point correspondences by analyzing the connotation of homography we introduce a novel concept of correspondence function for two images of a general 3d scene which captures the relationships between corresponding points by mapping a point in one image to its corresponding point in another since the correspondence functions are unknown in real applications we also study how to estimate them from given putative correspondences and propose an algorithm iecf iteratively estimate correspondence function based on diagnostic technique and svm then the proposed icf method is able to reject the mismatches by checking whether they are consistent with the estimated correspondence functions extensive experiments on real images demonstrate the excellent performance of our proposed method in addition the icf is a general method for rejecting mismatches and it is applicable to images of rigid objects or images of non rigid objects with unknown deformation

existence and modulation of traveling waves in particles chains we consider an infinite particle chain whose dynamics are governed by the following system of differential equations where qn t is the displacement of the nth particle at time t along the chain axis and denotes differentiation with respect to time we assume that all particles have unit mass and that the interaction potential v between adjacent particles is a convex c function for this system we prove the existence of c time periodic traveling wave solutions of the form qn t q wt kn where q is a periodic function q z q z 1 the period is normalized to equal 1 and k are respectively the frequency and the wave number is the mean particle spacing and can be chosen to be an arbitrary parameter we present two proofs one based on a variational principle and the other on topological methods in particular degree theory for small amplitude waves based on perturbation techniques we describe the form of the traveling waves and we derive the weakly nonlinear dispersion relation for the fully nonlinear case when the amplitude of the waves is high we use numerical methods to compute the traveling wave solution and the non linear dispersion relation we finally apply whitham s method of averaged lagrangian to derive the modulation equations for the wave parameters k and 1999 john wiley sons inc

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

modified bounds for covering codes the covering radius of binary codes is studied bounds on k n r the minimum cardinality of any binary code of length n and covering radius r are found modifications of the van wee lower bounds are proved for k n r the minimal number of codewords in any binary code of length n and covering radius r the first of the two van wee bounds is based on studying the hamming spheres of radius 1 centered at the points which have distance r to the code c the points covered by more than one codeword are divided into several classes and better estimates for some of these classes are obtained using a suitable averaging process the lower bound for k n r when r or 2 is improved the second van wee bound studies spheres of radius 2 centered at the points which have distance r 1 or r to the code c these points are divided essentially into two classes the points that are covered by only one codeword of c and the points that are covered by more than one codeword

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

shock waves in the dissipative toda lattice we consider the propagation of a shock wave sw in the damped toda lattice the sw is a moving boundary between two semi infinite lattice domains with different densities a steadily moving sw may exist if the damping in the lattice is represented by an inner friction which is a discrete analogue of the second viscosity in hydrodynamics the problem can be considered analytically in the continuum approximation and the analysis produces an explicit relation between the sw s velocity and the densities of the two phases numerical simulations of the lattice equations of motion demonstrate that a stable sw establishes if the initial velocity is directed towards the less dense phase in the opposite case the wave gradually spreads out the numerically found equilibrium velocity of the sw turns out to be in very good agreement with the analytical formula even in a strongly discrete case if the initial velocity is essentially different from the one determined by the densities but has the correct sign the velocity does not alter significantly but instead the sw adjusts itself to the given velocity by sending another sw in the opposite direction

the zero dispersion limit of the korteweg de vries equation with periodic initial data on etudie le probleme aux valeurs initiales pour l equation de korteweg de vries u t 6uu x e 2 u xxx 0 dans la limite e 0 on calcul la limite faible de la solution pour des donnees initiales periodiques quand e 0

large oscillations arising in a dispersive numerical scheme abstract we study the oscillatory behavior that arises in solutions of a dispersive numerical scheme for the hopf equation whenever the classical solution of the equation develops a singularity modulation equations are derived that describe period two oscillations so long as the solution of those equations takes values for which the equations are hyperbolic however those equations have an elliptic region that may be entered by its solutions in a finite time after which the corresponding period two oscillations are seen to break down this kind of phenomenon has not been observed for integrable schemes the generation and propagation of period two oscillations are asymptotically analyzed and a matching formula is found for the transition between oscillatory and nonoscillatory regions modulation equations are also presented for period three oscillations numerical experiments are carried out that illustrate our analysis

the small dispersion limit of the korteweg de vries equation ii in part i the scattering transform method is used to study the weak limit of solutions to the initial value problem for the korteweg devries kdv equation as the dispersion tends to zero in that limit the associated schrodinger operator becomes semiclassical so the exact scattering data is replaced by its corresponding wkb expressions only nonpositive initial data are considered in that case the limiting reflection coefficient vanishes the explicit solution of kay and moses for the reflectionless inverse transform is then analyzed and the weak limit valid for all time is characterized by a quadratic minimum problem with constraints this minimum problem is reduced to a riemann hilbert problem in function theory in parts ii and iii we use function theoretical methods to solve the riemann hilbert problem in terms of solutions to an auxiliary initial value problem the weak limit satisfies the kdv equation with the dispersive term dropped until its derivatives become infinite up to that time the weak limit is a strong l2 limit at later times the weak limit is locally described by whitham s averaged equations or more generally by the equations found by flaschka et al using multiphase averaging for large times behavior of the weak limit is studied directly from the minimum problem

the generation of modulated wavetrains in the solution of the korteweg de vries equation on demontre une relation entre la methode des ondes modulees de whitham et la methode de lax et levermore contenant la limite de petite dispersion

modulation of multiphase waves in the presence of resonance the phenomenon of spatio temporal phase modulation made possible by resonance is investigated in detail through the analysis of an example problem a simple family of exact solutions to the ablowitz ladik equations is found to be modulationally stable in some regimes this family of solutions is determined by fixing antiperiod 2 boundary conditions which determines two wavenumbers within the family of solutions the frequencies do not depend on amplitude this feature ensures that the antiperiod 2 boundary conditions will be enforced under modulation the family of solutions is described by four parameters two being actions that foliate the phase space and two being macroscopically observable functions of the phase constants the modulation of the actions is described by a closed hyperbolic system of first order equations which is consistent with the full set of four genus 1 modulation equations the modulation of the phase information easily observed due to the presence of two resonances is described by two more equations that are driven by the actions the results are confirmed by numerical experiments

macroscopic lattice dynamics abstract fully nonlinear modulation equations are presented that govern the slow evolution of single phase harmonic wavetrains under a large family of spatially discrete nonintegrable flows among which is the discrete nonlinear schrodinger equation dnls these modulation equations are a pair of partial differential equations in conservation form that are hyperbolic for some data and elliptic for other data in some cases these equations are capable of dynamically changing type from hyperbolic to elliptic a phenomenon that has been associated with the modulational instability of the underlying wavetrain by putting the modulation equations in riemann invariant form one can select initial data that avoid this dynamic change of type numerical experiments demonstrating the theoretical results are presented

generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields the equilibrium measure in the presence of an external field plays a role in a number of areas in analysis for example in random matrix theory the limiting mean density of eigenvalues is precisely the density of the equilibrium measure typical behavior for the equilibrium measure is 1 it is positive on the interior of a finite number of intervals 2 it vanishes like a square root at endpoints and 3 outside the support there is strict inequality in the euler lagrange variational conditions if these conditions hold then the limiting local eigenvalue statistics is loosely described by a bulk in which there is universal behavior involving the sine kernel and edge effects in which there is a universal behavior involving the airy kernel through techniques from potential theory and integrable systems we show that this regular behavior is generic for equilibrium measures associated with real analytic external fields in particular we show that for any one parameter family of external fields v c the equilibrium measure exhibits this regular behavior except for an at most countable number of values of c we discuss applications of our results to random matrices orthogonal polynomials and integrable systems 2000 john wiley sons inc

on semiclassical zero dispersion limit solutions of the focusing nonlinear schrodinger equation we calculate the leading order term of the solution of the focusing nonlinear cubic schrodinger equation nls in the semiclassical limit for a certain one parameter family of initial conditions this family contains both solitons and pure radiation in the pure radiation case our result is valid for all times t 0 we utilize the riemann hilbert problem formulation of the inverse scattering problem to obtain the leading order term of the solution error estimates are provided 2004 wiley periodicals inc

stereo processing by semiglobal matching and mutual information this paper describes the semiglobal matching sgm stereo method it uses a pixelwise mutual information ml based matching cost for compensating radiometric differences of input images pixelwise matching is supported by a smoothness constraint that is usually expressed as a global cost function sgm performs a fast approximation by pathwise optimizations from all directions the discussion also addresses occlusion detection subpixel refinement and multibaseline matching additionally postprocessing steps for removing outliers recovering from specific problems of structured environments and the interpolation of gaps are presented finally strategies for processing almost arbitrarily large images and fusion of disparity images using orthographic projection are proposed a comparison on standard stereo images shows that sgm is among the currently top ranked algorithms and is best if subpixel accuracy is considered the complexity is linear to the number of pixels and disparity range which results in a runtime of just 1 2 seconds on typical test images an in depth evaluation of the ml based matching cost demonstrates a tolerance against a wide range of radiometric transformations finally examples of reconstructions from huge aerial frame and pushbroom images demonstrate that the presented ideas are working well on practical problems

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

the behavior of the weyl function in the zero dispersion kdv limit the moment formulas that globally characterize the zero dispersion limit of the korteweg devries kdv equation are known to be expressed in terms of the solution of a maximization problem here we establish a direct relation between this maximizer and the zero dispersion limit of the logarithm of the jost functions associated with the inverse spectral transform all the kdv conserved densities are encoded in the spatial derivative of these functions known as weyl functions we show the weyl functions are densities of measures that converge in the weak sense to a limiting measure this limiting measure encodes all of the weak limits of the kdv conserved densities moreover we establish the weak limit of spectral measures associated with the dirichlet problem

robust point matching via vector field consensus in this paper we propose an efficient algorithm called vector field consensus for establishing robust point correspondences between two sets of points our algorithm starts by creating a set of putative correspondences which can contain a very large number of false correspondences or outliers in addition to a limited number of true correspondences inliers next we solve for correspondence by interpolating a vector field between the two point sets which involves estimating a consensus of inlier points whose matching follows a nonparametric geometrical constraint we formulate this a maximum a posteriori map estimation of a bayesian model with hidden latent variables indicating whether matches in the putative set are outliers or inliers we impose nonparametric geometrical constraints on the correspondence as a prior distribution using tikhonov regularizers in a reproducing kernel hilbert space map estimation is performed by the em algorithm which by also estimating the variance of the prior model initialized to a large value is able to obtain good estimates very quickly e g avoiding many of the local minima inherent in this formulation we illustrate this method on data sets in 2d and 3d and demonstrate that it is robust to a very large number of outliers even up to 90 we also show that in the special case where there is an underlying parametric geometrical model e g the epipolar line constraint that we obtain better results than standard alternatives like ransac if a large number of outliers are present this suggests a two stage strategy where we use our nonparametric model to reduce the size of the putative set and then apply a parametric variant of our approach to estimate the geometric parameters our algorithm is computationally efficient and we provide code for others to use it in addition our approach is general and can be applied to other problems such as learning with a badly corrupted training data set

non rigid visible and infrared face registration via regularized gaussian fields criterion registration of multi sensor data particularly visible color sensors and infrared sensors is a prerequisite for multimodal image analysis such as image fusion typically the relationships between image pairs are modeled by rigid or affine transformations however this cannot produce accurate alignments when the scenes are not planar for example face images in this paper we propose a regularized gaussian fields criterion for non rigid registration of visible and infrared face images the key idea is to represent an image by its edge map and align the edge maps by a robust criterion with a non rigid model we model the transformation between images in a reproducing kernel hilbert space and a sparse approximation is applied to the transformation to avoid high computational complexity moreover a coarse to fine strategy by applying deterministic annealing is used to overcome local convergence problems the qualitative and quantitative comparisons on two publicly available databases demonstrate that our method significantly outperforms the state of the art method with an affine model as a result our method will be beneficial for fusion based face recognition highlightswe analyze the robustness of gaussian fields criterion both in theory and experiment the gaussian fields criterion is generalized from rigid to the non rigid case we propose a new non rigid registration method to deal with more real world problems a sparse approximation on the transformation is applied to speed up the method we customize and apply the proposed method to visible thermal ir face registration

further results on the covering radius of codes a number of upper and lower bounds are obtained for k n r the minimal number of codewords in any binary code of length n and covering radius r several new constructions are used to derive the upper bounds including an amalgamated direct sum construction for nonlinear codes this construction works best when applied to normal codes and we give some new and stronger conditions which imply that a linear code is normal an upper bound is given for the density of a covering code over any alphabet and it is shown that k n 2 r 1 leq k n r holds for sufficiently large n

matching widely separated views based on affine invariant regions invariant regions are self adaptive image patches that automatically deform with changing viewpoint as to keep on covering identical physical parts of a scene such regions can be extracted directly from a single image they are then described by a set of invariant features which makes it relatively easy to match them between views even under wide baseline conditions in this contribution two methods to extract invariant regions are presented the first one starts from corners and uses the nearby edges while the second one is purely intensity based as a matter of fact the goal is to build an opportunistic system that exploits several types of invariant regions as it sees fit this yields more correspondences and a system that can deal with a wider range of images to increase the robustness of the system two semi local constraints on combinations of region correspondences are derived one geometric the other photometric they allow to test the consistency of correspondences and hence to reject falsely matched regions experiments on images of real world scenes taken from substantially different viewpoints demonstrate the feasibility of the approach

the zero dispersion limit of the korteweg de vries equation for initial potentials with non trivial reflection coefficient the inverse scattering method is used to determine the distribution limit as 0 of the solution u x t of the initial value problem ut 6uux 2uxxx 0 u x 0 v x where v x is a positive bump which decays sufficiently fast as x x the case v x 0 has been solved by peter d lax and c david levermore 8 9 10 the computation of the distribution limit of u x t as 0 is reduced to a quadratic maximization problem which is then solved

a new integrable equation in the 2 1 dimension dispersionless limit of the bkp equation a new integrable equation is obtained as the dispersionless limit of the bkp equation it is then studied in the framework of kodama s approach 1988 the new equation also turns out to be completely integrable with an infinite number of conservation laws the hodograph transformation method is applied to obtain exact solutions in various cases

improved sphere bounds on the covering radius of codes the sphere bound is a trivial lower bound on k n r the minimal cardinality of any binary code of length n and with covering radius r by simple arguments it is considerably improved to k n 1 or 2 sup n n for n even a table of lower and upper bounds on k n r for n

robust l_ 2 e estimation of transformation for non rigid registration we introduce a new transformation estimation algorithm using the l 2 e estimator and apply it to non rigid registration for building robust sparse and dense correspondences in the sparse point case our method iteratively recovers the point correspondence and estimates the transformation between two point sets feature descriptors such as shape context are used to establish rough correspondence we then estimate the transformation using our robust algorithm this enables us to deal with the noise and outliers which arise in the correspondence step the transformation is specified in a functional space more specifically a reproducing kernel hilbert space in the dense point case for nonrigid image registration our approach consists of matching both sparsely and densely sampled sift features and it has particular advantages in handling significant scale changes and rotations the experimental results show that our approach greatly outperforms state of the art methods particularly when the data contains severe outliers

dispersive regularization of the whitham equation for the toda lattice in this paper the averaged whitham equations for the slow modulations of multi phase wavetrains for the toda lattice are studied our main result is showing how the solution with step initial conditions may be regularized by choosing an appropriate riemann surface on which the whitham equation is defined

robust and efficient estimation by minimising a density power divergence a minimum divergence estimation method is developed for robust parameter estimation the proposed approach uses new density based divergences which unlike existing methods of this type such as minimum hellinger distance estimation avoid the use of nonparametric density estimation and associated complications such as bandwidth selection the proposed class of density power divergences is indexed by a single parameter which controls the trade off between robustness and efficiency the methodology affords a robust extension of maximum likelihood estimation for which 0 choices of near zero afford considerable robustness while retaining efficiency close to that of maximum likelihood

algebraic varieties in the birkhoff strata of the grassmannian gr 2 harrison cohomology and integrable systems the local properties of the families of algebraic subsets wg in the birkhoff strata 2g of gr 2 containing the hyperelliptic curves of genus g are studied it is shown that the tangent spaces tg for wg are isomorphic to the linear spaces of 2 coboundaries particular subsets in wg are described by the integrable dispersionless coupled kdv systems of hydrodynamical type defining a special class of 2 cocycles and 2 coboundaries in tg it is demonstrated that the blows ups of such 2 cocycles and 2 coboundaries and gradient catastrophes for associated integrable systems are interrelated

on geometric phases for soliton equations this paper develops a new complex hamiltonian structure forn soliton solutions for a class of integrable equations such as the nonlinear schrodinger sine gordon and korteweg de vries hierarchies of equations that yields amongst other things geometric phases in the sense of hannay and berry for example one of the possible soliton geometric phases is manifested by the well known phase shift that occurs for interacting solitons the main new tools are complex angle representations that linearize the corresponding hamiltonian flows on associated noncompact jacobi varieties this new structure is obtained by taking appropriate limits of the differential equations describing the class of quasi periodic solutions a method of asymptotic reduction of the angle representations is introduced for investigating soliton geometric phases that are related to the presence of monodromy at singularities in the space of parameters in particular the phase shift of interacting solitons can be expressed as an integral over a cycle on an associated riemann surface in this setting soliton geometric asymptotics are constructed for studying geometric phases in the quantum case the general approach is worked out in detail for the three specific hierarchies of equations mentioned some links with functions the braid group and geometric quantization are pointed out as well

guided mlesac faster image transform estimation by using matching priors mlesac is an established algorithm for maximum likelihood estimation by random sampling consensus devised for computing multiview entities like the fundamental matrix from correspondences between image features a shortcoming of the method is that it assumes that little is known about the prior probabilities of the validities of the correspondences this paper explains the consequences of that omission and describes how the algorithm s theoretical standing and practical performance can be enhanced by deriving estimates of these prior probabilities using the priors in guided mlesac is found to give an order of magnitude speed increase for problems where the correspondences are described by one image transformation and clutter this paper describes two further modifications to guided mlesac the first shows how all putative matches rather than just the best from a particular feature can be taken forward into the sampling stage albeit at the expense of additional computation the second suggests how to propagate the output from one frame forward to successive frames the additional information makes guided mlesac computationally realistic at video rates for correspondence sets modeled by two transformations and clutter

regularized vector field learning with sparse approximation for mismatch removal in vector field learning regularized kernel methods such as regularized least squares require the number of basis functions to be equivalent to the training sample size n the learning process thus has o n 3 and o n 2 in the time and space complexity respectively this poses significant burden on the vector learning problem for large datasets in this paper we propose a sparse approximation to a robust vector field learning method sparse vector field consensus sparsevfc and derive a statistical learning bound on the speed of the convergence we apply sparsevfc to the mismatch removal problem the quantitative results on benchmark datasets demonstrate the significant speed advantage of sparsevfc over the original vfc algorithm two orders of magnitude faster without much performance degradation we also demonstrate the large improvement by sparsevfc over traditional methods like ransac moreover the proposed method is general and it can be applied to other applications in vector field learning

frequency computation and bounded queries there have been several papers over the last ten years that consider the number of queries needed to compute a function as a measure of its complexity the following function has been studied extensively in that light faa x1 xa a x1 a xa we are interested in the complexity in terms of the number of queries of approximating faa let b a and let f be any function such that faa x1 xa and f x1 xa agree on at least b bits for a general set a we have matching upper and lower bounds on f that depend on coding theory these are applied to get exact bounds for the case where a is semirecursive a is superterse and assuming p np a sat we obtain exact bounds when a is the halting problem using different methods

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

hamiltonian structure for the modulation equations of a sine gordon wavetrain on etudie l equation sinus gordon e 2 t 2 x 2 u sin u 0 ou e est un petit parametre on construit une solution asymptotique sous la forme d un train d onde n phase variant lentement

on the generation of dispersive shock waves abstract we review various methods for the analysis of initial value problems for integrable dispersive equations in the weak dispersion or semiclassical regime some methods are sufficiently powerful to rigorously explain the generation of modulated wavetrains so called dispersive shock waves as the result of shock formation in a limiting dispersionless system they also provide a detailed description of the solution near caustic curves that delimit dispersive shock waves revealing fascinating universal wave patterns

robust non rigid point set registration using spatially constrained gaussian fields estimating transformations from degraded point sets is necessary for many computer vision and pattern recognition applications in this paper we propose a robust non rigid point set registration method based on spatially constrained context aware gaussian fields we first construct a context aware representation e g shape context for assignment initialization then we use a graph laplacian regularized gaussian fields to estimate the underlying transformation from the likely correspondences on the one hand the intrinsic manifold is considered and used to preserve the geometrical structure and a priori knowledge of the point set is extracted on the other hand by using the deterministic annealing the presented method is extended to a projected high dimensional feature space i e reproducing kernel hilbert space through a kernel trick to solve the transformation in which the local structure is propagated by the coarse to fine scaling strategy in this way the proposed method gradually recovers much more correct correspondences and then estimates the transformation parameters accurately and robustly when facing degradations experimental results on 2d and 3d synthetic and real data point sets demonstrate that the proposed method reaches better performance than the state of the art algorithms

semiclassical eigenvalue distribution of the zakharov shabat eigenvalue problem abstract in this paper we consider the semi classical limit of the non self adjoint zakharov shabat eigenvalue problem we conduct a series of careful numerical experiments which provide strong evidence that the number of eigenvalues scales like 1 just as in the self adjoint case and that the eigenvalues appear to approach a limiting curve one general choice of potential functions produces a y shaped spectrum we give an asymptotic argument which predicts a critical value for the phase for which the straight line spectra bifurcates to produce the y shaped spectra this asymptotic prediction agrees quite well with numerical experiments the asymptotic argument also predicts a symmetry breaking in the eigenfunctions which we are able to observe numerically we also show that the number of eigenvalues living away from the real axis for a restricted class of potentials is bounded by c 1 where c is an explicit constant a complete theory of the shape of the eigenvalue curve and a general bound on the number of eigenvalues is still lacking

gaussian field consensus a robust nonparametric matching method for outlier rejection abstract in this paper we propose a robust method called gaussian field consensus gfc for outlier rejection from given putative point set matching correspondences finding correct correspondences inliers is a key component in many computer vision and pattern recognition tasks and the goal of outlier mismatch rejection is to fit the transformation function that maps one feature point set to another our gfc starts by inputting a putative correspondence set which is contaminated by many outliers and the main task of our gfc is to identify the underlying true correspondences from outliers then we formulate this challenging problem by gaussian field nonparametric matching model which bases on the exponential distance loss and kernel method in a reproducing kernel hilbert space next we introduce a local linear constraint based on the regularization theory to preserve the topological structure of the feature points moreover the sparse approximation is used to reduce the search space in this way we can handle a large number of points easily finally we test the gfc method on several real image datasets in the presence of outliers where the experimental results show that our proposed method outperforms current state of the art methods in most test scenarios

binary modulated oscillations in a semi discrete version of burgers equation abstract in this paper we study both analytically and numerically the binary modulated oscillations which arise in an integrable semi discrete approximation to inviscid burgers explicit solutions of the binary modulation equations derived in goodman and lax 1988 are found for several choices of initial data observations based on numerical experiments are presented as to which initial data lead to solutions containing purely binary oscillations comparisons are made to the integrable theory of the kac van moerbeke and toda lattices non integrable schemes for which the binary oscillations also remain hyperbolic are presented and explicit solutions of their binary modulation equations are found

point set registration coherent point drift point set registration is a key component in many computer vision tasks the goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other multiple factors including an unknown nonrigid spatial transformation large dimensionality of point set noise and outliers make the point set registration a challenging problem we introduce a probabilistic method called the coherent point drift cpd algorithm for both rigid and nonrigid point set registration we consider the alignment of two point sets as a probability density estimation problem we fit the gaussian mixture model gmm centroids representing the first point set to the data the second point set by maximizing the likelihood we force the gmm centroids to move coherently as a group to preserve the topological structure of the point sets in the rigid case we impose the coherence constraint by reparameterization of gmm centroid locations with rigid parameters and derive a closed form solution of the maximization step of the em algorithm in arbitrary dimensions in the nonrigid case we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation we also introduce a fast algorithm that reduces the method computation complexity to linear we test the cpd algorithm for both rigid and nonrigid transformations in the presence of noise outliers and missing points where cpd shows accurate results and outperforms current state of the art methods

a mathematical analysis of the motion coherence theory in motion perception there are a number of important phenomena involving coherence examples include motion capture and motion cooperativity we propose a theoretical model called the motion coherence theory that gives a possible explanation for these effects 1 2 in this framework the aperture problem can also be thought of as a problem of coherence and given a similar explanation we propose the concept of a velocity field defined everywhere in the image even where there is no explicit motion information available theough a cost function the model imposes smoothness on the velocity field in a more general way than in previous theories in this paper we provide a detailed theoretical analysis of the motion coherence theory we discuss its relations with previous theories and show that some of them are approximations to it a second paper 3 provides extensions for temporal coherence and comparisons to psychophysical phenomena the theory applies to both short range and long range motion it places them in the same computational framework and provides a way to define interactions between the two processes

from boltzmann to euler hilbert s 6th problem revisited abstract this article addresses the hydrodynamic limit of the boltzmann equation namely the compressible euler equations of gas dynamics an exact summation of the chapman enskog expansion originally given by gorban and karlin is the key to the analysis an appraisal of the role of viscosity and capillarity in the limiting process is then given where the analogy is drawn to the limit of the korteweg de vries burgers equations as a small parameter tends to zero

terse superterse and verbose sets abstract let a be a subset of the natural numbers and let f a n x 1 x n a x 1 a x n where a is the characteristic function of a an oracle turing machine with oracle a could certainly compute f a n with n queries to a there are some sets a e g the halting set for which f a n can be computed with substantially fewer than n queries one key reason for this is that the questions asked to the oracle can depend on previous answers i e the questions are adaptive we examine when it is possible to save queries a set a is terse if the computation of f a n from a requires n queries a set a is superterse if the computation of f a n from any set requires n queries a set a is verbose if f a 2 n 1 can be computed with n queries to a the range of possible query savings is limited by the following theorem f a n cannot be computed with only log n queries to a set x unless a is recursive in addition we produce the following 1 a verbose set in each truth table degree and a superterse set in each nonzero truth table degree and 2 an r e verbose set in each r e truth table degree and an r e terse set in each nonzero r e turing degree

kinetic decomposition for singularly perturbed higher order partial differential equations abstract in this paper we consider singularly perturbed higher order partial differential equations we establish the condition under which the approximate solutions converge in a strong topology to the entropy solution of a scalar conservation laws using methodology developed in hwang and tzavaras comm partial differential equations 27 2002 1229 first we obtain the approximate transport equation for the given dispersive equations then using the averaging lemma we obtain the convergence

robust point matching for nonrigid shapes by preserving local neighborhood structures in previous work on point matching a set of points is often treated as an instance of a joint distribution to exploit global relationships in the point set for nonrigid shapes however the local relationship among neighboring points is stronger and more stable than the global one in this paper we introduce the notion of a neighborhood structure for the general point matching problem we formulate point matching as an optimization problem to preserve local neighborhood structures during matching our approach has a simple graph matching interpretation where each point is a node in the graph and two nodes are connected by an edge if they are neighbors the optimal match between two graphs is the one that maximizes the number of matched edges existing techniques are leveraged to search for an optimal solution with the shape context distance used to initialize the graph matching followed by relaxation labeling updates for refinement extensive experiments show the robustness of our approach under deformation noise in point locations outliers occlusion and rotation it outperforms the shape context and tps rpm algorithms on most scenarios

covering radius survey and recent results all known results on covering radius are presented as well as some new results there are a number of upper and lower bounds including asymptotic results a few exact determinations of covering radius some extensive relations with other aspects of coding theory through the reed muller codes and new results on the least covering radius of any linear n k code there is also a recent result on the complexity of computing the covering radius

on the nonlinear schro dinger limit of the korteweg de vries equation abstract using the multiscale approach of zakharov and kuznetsov it is shown that the nonlinear schrodinger periodic scattering data is related to the korteweg de vries periodic scattering data via an average over the korteweg de vries carrier oscillation this allows a complete elucidation of the physical meaning of the nonlinear schrodinger scattering data conservation laws theta function solutions and reality constraint

bifurcations of new eigenvalues for the benjamin ono equation a criterion for the emergence of new eigenvalues is found for the linear scattering problem associated with the benjamin ono bo equation this bifurcation occurs due to perturbations of nongeneric potentials which include the soliton solutions of the bo equation the asymptotic approximation of an exponentially small new eigenvalue is derived the method is based on the expansion of a localized function through a complete set of unperturbed eigenfunctions explicit expressions are obtained for the soliton potentials

hilbert s 6th problem exact and approximate hydrodynamic manifolds for kinetic equations the problem of the derivation of hydrodynamics from the boltz mann equation and related dissipative systems is formulated as the problem of slow invariant manifold in the space of distributions we review a few in stances where such hydrodynamic manifolds were found analytically both as the result of summation of the chapman enskog asymptotic expansion and by the direct solution of the invariance equation these model cases comprising grad s moment systems both linear and nonlinear are studied in depth in order to gain understanding of what can be expected for the boltzmann equa tion particularly the dispersive dominance and saturation of dissipation rate of the exact hydrodynamics in the short wave limit and the viscosity modifica tion at high divergence of the flow velocity are indicated as severe obstacles to the resolution of hilbert s 6th problem furthermore we review the derivation of the approximate hydrodynamic manifold for the boltzmann equation using newton s iteration and avoiding smallness parameters and compare this to the exact solutions additionally we discuss the problem of projection of the boltzmann equation onto the approximate hydrodynamic invariant manifold using entropy concepts finally a set of hypotheses is put forward where we describe open questions and set a horizon for what can be derived exactly or proven about the hydrodynamic manifolds for the boltzmann equation in the future

robust point set registration using gaussian mixture models in this paper we present a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers the key idea of this registration framework is to represent the input point sets using gaussian mixture models then the problem of point set registration is reformulated as the problem of aligning two gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized we show that the popular iterative closest point icp method and several existing point set registration methods in the field are closely related and can be reinterpreted meaningfully in our general framework our instantiation of this general framework is based on the the l2 distance between two gaussian mixtures which has the closed form expression and in turn leads to a computationally efficient registration algorithm the resulting registration algorithm exhibits inherent statistical robustness has an intuitive interpretation and is simple to implement we also provide theoretical and experimental comparisons with other robust methods for point set registration

dispersive shock waves and modulation theory there is growing physical and mathematical interest in the hydrodynamics of dissipationless dispersive media since g b whitham s seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics there has been a significant body of work in this area however there has been no comprehensive survey of the field of dispersive hydrodynamics utilizing whitham s averaging theory as the primary mathematical tool we review the rich mathematical developments over the past fifty years with an emphasis on physical applications the fundamental large scale coherent excitation in dispersive hydrodynamic systems is an expanding oscillatory dispersive shock wave or dsw both the macroscopic and microscopic properties of dsws are analyzed in detail within the context of the universal integrable and foundational models for uni directional korteweg de vries equation and bi directional nonlinear schrodinger equation dispersive hydrodynamics a dsw fitting procedure that does not rely upon integrable structure yet reveals important macroscopic dsw properties is described dsw theory is then applied to a number of physical applications superfluids nonlinear optics geophysics and fluid dynamics finally we survey some of the more recent developments including non classical dsws dsw interactions dsws in perturbed and inhomogeneous environments and two dimensional oblique dsws

diffusion dispersion limits for multidimensional scalar conservation laws with source terms abstract in this paper we consider conservation laws with diffusion and dispersion terms we study the convergence for approximation applied to conservation laws with source terms the proof is based on the hwang and tzavaras s new approach seok hwang athanasios e tzavaras kinetic decomposition of approximate solutions to conservation laws application to relaxation and diffusion dispersion approximations comm partial differential equations 27 5 6 2002 1229 1254 and the kinetic formulation developed by lions perthame and tadmor p l lions b perthame e tadmor a kinetic formulation of multidimensional scalar conservation laws and related equations j amer math soc 7 1 1994 169 191

painleve ii asymptotics near the leading edge of the oscillatory zone for the korteweg de vries equation in the small dispersion limit in the small dispersion limit solutions to the korteweg de vries equation develop an interval of fast oscillations after a certain time we obtain a universal asymptotic expansion for the korteweg de vries solution near the leading edge of the oscillatory zone up to second order corrections this expansion involves the hastings mcleod solution of the painleve ii equation we prove our results using the riemann hilbert approach c 2009 wiley periodicals inc

an extension of the steepest descent method for riemann hilbert problems the small dispersion limit of the korteweg de vries kdv equation this paper extends the steepest descent method for riemann hilbert problems introduced by deift and zhou in a critical new way we present in particular an algorithm to obtain the support of the riemann hilbert problem for leading asymptotics applying this extended method to small dispersion kdv korteweg de vries equation we i recover the variational formulation of p d lax and c d levermore 1979 proc natl acad sci usa 76 3602 3606 for the weak limit of the solution ii derive without using an ansatz the hyperelliptic asymptotic solution of s venakides that describes the oscillations and iii are now able to compute the phase shifts integrating the modulation equations exactly the procedure of this paper is a version of fully nonlinear geometrical optics for integrable systems with some additional analysis the theory can provide rigorous error estimates between the solution and its computed asymptotic expression

object matching using a locally affine invariant and linear programming techniques in this paper we introduce a new matching method based on a novel locally affine invariant geometric constraint and linear programming techniques to model and solve the matching problem in a linear programming formulation all geometric constraints should be able to be exactly or approximately reformulated into a linear form this is a major difficulty for this kind of matching algorithm we propose a novel locally affine invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming based methods do the key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points whose weights can be solved easily by least squares errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points the resulting overall objective function can be solved efficiently by linear programming techniques our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm

removing mismatches for retinal image registration via multi attribute driven regularized mixture model in order to address the problem of retinal image registration this paper proposes and analyzes a novel and general matching algorithm called multi attribute driven regularized mixture model mad rmm mismatches removal can play a key role in image registration which refers to establish reliable matches between two point sets here the presented approach starts from multi feature attributes which are used to guide the feature matching to identify inliers correct matches from outliers incorrect matches and then estimates the spatial transformation in this paper motivated by the problem of feature matching that the initial correspondence is always contaminated by outliers thereby we formulate this issue as a probability deformable mixture model which consists of gaussian components for inliers and uniform components for outliers moreover the algorithm takes full advantage of using multiple attributes for better general matching performance here we are assuming all inliers are mapped into a high dimensional feature space namely reproducing kernel hilbert space rkhs and the closed form solution to the mapping function is given by the representation theorem with l2 norm regularization under the expectation maximization em algorithm finally we evaluate the performance of the algorithm by applying it to retinal image registration on several datasets where experimental results demonstrate that the mad rmm outperforms current state of the art methods and shows the robustness to outliers on real retinal images

the whitham equations for optical communications mathematical theory of nrz we present a model of optical communication system for high bit rate data transmission in the nonreturn to zero nrz format over transoceanic distance the system operates in a small group velocity dispersion regime and the model equation is given by the well known whitham equations describing the slow modulation of multiphase wavetrains of the defocusing nonlinear schrodinger nls equation the model equation is of hyperbolic type and nrz pulse with certain initial phase modulation develops a shock we then show how one can obtain a global solution by choosing an appropriate riemann surface on which the whitham equation is defined we also discuss the effect of third order dispersion by using an integrable hierarchy of the nls equation and we give a condition to avoid a shock formation

unified approach to kdv modulations we develop a unified approach to integrating the whitham modulation equations our approach is based on the formulation of the initial value problem for the zero dispersion kdv as the steepest descent for the scalar riemann hilbert problem 6 and on the method of generating differentials for the kdv whitham hierarchy 9 by assuming the hyperbolicity of the zero dispersion limit for the kdv with general initial data we bypass the inverse scattering transform and produce the symmetric system of algebraic equations describing motion of the modulation parameters plus the system of inequalities determining the number the oscillating phases at any fixed point on the x t plane the resulting system effectively solves the zero dispersion kdv with an arbitrary initial datum c 2001 john wiley sons inc

tip splitting evolution in the idealized saffman taylor problem we derive a formula describing the evolution of tip splittings of saffman taylor fingers in a hele shaw cell at zero surface tension

the korteweg de vries equation with small dispersion higher order lax levermore theory we utilize the inverse scattering transformation to study the rapid oscillations which arise in the solution of the initial value problem begin gathered u t 6u u x in 2 u xxx 0 hfill u left x 0 right v left x right hfill end gathered when 0 we refine the lax levermore theory which gives the weak limit of the solution as 0 by introducing a quantum condition this allows us to calculate the waveform of the local oscillations up to phase shifts when is small