using spanning graphs for efficient image registration we provide a detailed analysis of the use of minimal spanning graphs as an alignment method for registering multimodal images this yields an efficient graph theoretic algorithm that for the first time jointly estimates both an alignment measure and a viable descent direction with respect to a parameterized class of spatial transformations we also show how prior information about the interimage modality relationship from prealigned image pairs can be incorporated into the graph based algorithm a comparison of the graph theoretic alignment measure is provided with more traditional measures based on plug in entropy estimators this highlights previously unrecognized similarities between these two registration methods our analysis gives additional insight into the tradeoffs the graph based algorithm is making and how these will manifest themselves in the registration algorithm s performance

on a shallow water model with the coriolis effect abstract in the present study an asymptotic model for wave propagation in shallow water with the effect of the coriolis force is derived from the governing equation in two dimensional flows the transport equation theory is then applied to investigate the local well posedness and wave breaking phenomena for this model the nonexistence of the camassa holm type peaked solution and classification of various traveling wave solutions to the new system are also established moreover it is shown that all the symmetric waves to this model are traveling waves

on unit spherical euclidean distance matrices which differ in one entry abstract a unit spherical euclidean distance matrix edm d is a matrix whose entries can be realized as the interpoint squared euclidean distances of n points on a unit sphere in this paper given such a d and 1 k l n we present a characterization of the set of all unit spherical edms whose entries agree with those of d except possibly with the entry in the klth and lkth positions as a result we show that this set can be discrete consisting of one or two elements or it can be continuous the results are derived using two alternative approaches the second of which is based on cayley menger matrices

existence of a generalized solitary wave solution for water with positive bond number less than 13 abstract the objective of this paper is to give a rigorous answer to the question whether there exists a generalized solitary wave of elevation on water when the nondimensional surface tension coefficient the so called bond number is positive but less than 1 3 and the froude number is near 1 but greater than 1 the main difficulties to overcome are the small amplitude oscillations at infinity and the choice of appropriate banach spaces for the solution of the problem it is shown that an asymptotic expansion developed for this problem indeed yields an approximate solitary wave solution to the exact equations

local well posedness and wave breaking results for periodic solutions of a shallow water equation for waves of moderate amplitude abstract we study the local well posedness of a periodic nonlinear equation for surface waves of moderate amplitude in shallow water we use an approach proposed by kato which is based on semigroup theory for quasi linear equations we also show that singularities for the model equation can occur only in the form of wave breaking in particular surging breakers

global conservative solutions of the camassa holm equation this paper develops a new approach in the analysis of the camassa holm equation by introducing a new set of independent and dependent variables the equation is transformed into a semilinear system whose solutions are obtained as fixed points of a contractive transformation these new variables resolve all singularities due to possible wave breaking returning to the original variables we obtain a semigroup of global solutions depending continuously on the initial data our solutions are conservative in the sense that the total energy equals a constant for almost every time

on properties of cell matrices in this paper properties of cell matrices are studied a determinant of such a matrix is given in a closed form in the proof a general method for determining a determinant of a symbolic matrix with polynomial entries based on multivariate polynomial lagrange interpolation is outlined it is shown that a cell matrix of size n 1 has exactly one positive eigenvalue using this result it is proven that cell matrices are circum euclidean distance matrices c edm and their generalization k cell matrices are cedm under certain natural restrictions a characterization of k cell matrices is outlined

methods for constructing distance matrices and the inverse eigenvalue problem abstract let d 1 r k k and d 2 r l l be two distance matrices we provide necessary conditions on z r k l in order that d d 1 z z t d 2 r n n be a distance matrix we then show that it is always possible to border an n n distance matrix with certain scalar multiples of its perron eigenvector to construct an n 1 n 1 distance matrix we also give necessary and sufficient conditions for two principal distance matrix blocks d 1 and d 2 be used to form a distance matrix as above where z is a scalar multiple of a rank one matrix formed from their perron eigenvectors finally we solve the inverse eigenvalue problem for distance matrices in certain special cases including n 3 4 5 6 any n for which there exists a hadamard matrix and some other cases

asymptotic theory of greedy approximations to minimal k point random graphs let spl chi sub n x sub 1 x sub n be an independent and identically distributed i i d sample having multivariate distribution p we derive almost sure a s limits for the power weighted edge weight function of greedy approximations to a class of minimal graphs spanning k of the n samples the class includes minimal k point graphs constructed by the partitioning method of ravi sundaram marathe rosenkrantz and ravi see proc 5th annu acm siam symp discrete algorithms arlington va p 546 55 1994 where the edge weight function satisfies the quasi additive property of redmond and yukich see ann appl probab vol 4 no 4 p 1057 73 1994 in particular this includes greedy approximations to the k point minimal spanning tree k mst steiner tree k st and the traveling salesman problem k tsp an expression for the influence function of the minimal weight function is given which characterizes the asymptotic sensitivity of the graph weight to perturbations in the underlying distribution the influence function takes a form which indicates that the k point minimal graph in d 1 dimensions has robustness properties in r sup d which are analogous to those of rank order statistics in one dimension a direct result of our theory is that the log weight of the k point minimal graph is a consistent nonparametric estimate of the renyi entropy of the distribution p possible applications of this work include analysis of random communication network topologies estimation of the mixing coefficient in spl epsiv contaminated mixture models outlier discrimination and rejection clustering and pattern recognition robust nonparametric regression two sample matching and image registration

characterization of multispherical and block structures of euclidean distance matrices abstract this paper presents some new characterizations of euclidean distance matrices edms of special structures more specifically we discuss multispherical and block structured edms each of which can be viewed as a generalization of spherical edm we focus on a well known inequality that characterizes spherical edms and extend it to the sets of multispherical and block structured edms some related results are also presented

exact reconstruction of euclidean distance geometry problem using low rank matrix completion the euclidean distance geometry problem arises in a wide variety of applications from determining molecular conformations in computational chemistry to localization in sensor networks when the distance information is incomplete the problem can be formulated as a nuclear norm minimization problem in this paper this minimization program is recast as a matrix completion problem of a low rank r gram matrix with respect to a suitable basis the well known restricted isometry property cannot be satisfied in this scenario instead a dual basis approach is introduced to theoretically analyze the reconstruction problem if the gram matrix satisfies certain coherence conditions with parameter nu the main result shows that the underlying configuration of n points can be recovered with very high probability from o nr nu log 2 n uniformly random samples computationally simple and fast algorithms are designed to solve the euclidean distance geometry problem numerical tests on different 3 d data and protein molecules validate the effectiveness and efficiency of the proposed algorithms

global existence for small data of the viscous green naghdi type equations abstract we consider the cauchy problem for the green naghdi equations with viscosity for small initial data it is well known that adding a second order dissipative term to a hyperbolic system leads to the existence of global smooth solutions once the hyperbolic system is symmetrizable and the so called kawashima shizuta condition is satisfied in a previous work we have proved that the green naghdi equations can be written in a symmetric form using the associated hamiltonian this system being dispersive in the sense that it involves third order derivatives the symmetric form is based on symmetric differential operators in this paper we use this structure for an appropriate change of variable to prove that adding viscosity effects through a second order term leads to global existence of smooth solutions for small data we also deduce that constant solutions are asymptotically stable

faces of the cone of euclidean distance matrices characterizations structure and induced geometry in this paper we obtain new characterizations of the faces of the cone of euclidean distance matrices in one case the characterization is based on a special subspace associated with each distance matrix in other case on linear restrictions of coordinate matrices we also relate the faces to the supporting hyperplanes of the cone and we show how the supporting hyperplanes induce certain geometry on the configurations that belong to that face

well posedness of a highly nonlinear shallow water equation on the circle abstract we present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation furthermore we establish a novel result concerning the local well posedness of the corresponding cauchy problem for space periodic solutions with initial data from the sobolev space h s on the circle for s 3 2

orbital stability of solitary waves of moderate amplitude in shallow water abstract we study the orbital stability of solitary traveling wave solutions of an equation for surface water waves of moderate amplitude in the shallow water regime our approach is based on a method proposed by grillakis shatah and strauss 1987 1 and relies on a reformulation of the evolution equation in hamiltonian form we deduce stability of solitary waves by proving the convexity of a scalar function which is based on two nonlinear functionals that are preserved under the flow

moore penrose inverse of a euclidean distance matrix abstract we obtain expressions for the moore penrose inverse of a euclidean distance matrix edm that are determined only by the positive semidefinite matrix associated with the edm the results complement formulas for the moore penrose inverse of an edm given in balaji and bapat 2007 2 a formula for the inverse of a principal submatrix of an edm is also derived whose expression uses the schur complement of the laplacian of the edm as an application we obtain an expression for the terminal wiener index of a tree

on the nullspace the rangespace and the characteristic polynomial of euclidean distance matrices we present a characterization of the nullspace and the rangespace of a euclidean distance matrix edm d in terms of the vector of all ones and in terms of the gale subspace g d and the realization matrix p corresponding to d this characterization is then used to compute the characteristic polynomial of d we also present some results concerning edms generated by regular figures and edms generated by centrally symmetric points

on a shallow water approximation to the green naghdi equations with the coriolis effect abstract we consider an asymptotic 1d in space rotation camassa holm r ch model which could be used to describe the propagation of long crested shallow water waves in the equatorial ocean regions with allowance for the weak coriolis effect due to the earth s rotation this model equation has similar wave breaking phenomena as the camassa holm equation it is analogous to the rotation green naghdi r gn equations with the weak earth s rotation effect modeling the propagation of wave allowing large amplitude in shallow water we provide here a rigorous justification showing that solutions of the r gn equations tend to associated solution of the r ch model equation in the camassa holm regime with the small amplitude and the larger wavelength furthermore we demonstrate that the r gn model equations are locally well posed in a sobolev space by the refined energy estimates

majorization for the eigenvalues of euclidean distance matrices abstract this paper investigates the relation between the eigenvalues of a euclidean distance matrix edm and those of the corresponding positive semidefinite matrix more precisely let d 1 and d 2 be two edms and let b 1 and b 2 be the corresponding positive semidefinite matrices such that d i b i i 1 2 in this paper when the eigenvalues of b 1 majorizes those of b 2 a condition under which the eigenvalues of d 1 majorizes those of d 2 is derived

graph rigidity via euclidean distance matrices abstract let g v e be an incomplete graph with node set v edge set e and nonnegative weights ij s on the edges let each edge v i v j be viewed as a rigid bar of length ij which can rotate freely around its end nodes a realization of a graph g is an assignment of coordinates in some euclidean space to each node of g in this paper we consider the problem of determining whether or not a given realization of a graph g is rigid we show that each realization of g can be epresented as a point in a compact convex set r m and that a generic realization of g is rigid if and only if its corresponding point is a vertex of i e an extreme point with full dimensional normal cone

a geometrical characterization of strongly regular graphs abstract we give a necessary and sufficient condition of a euclidean representation of a simple graph to be spherical moreover we show a characterization of strongly regular graphs from the view point of euclidean representations of a graph from this characterization we define a natural generalized concept of a strongly regular graph closely related to euclidean designs and codes

large time existence for 1d green naghdi equations we consider here the 1d green naghdi equations that are commonly used in coastal oceanography to describe the propagation of large amplitude surface waves we show that the solution of the green naghdi equations can be constructed by a standard picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition

well posedness and blow up solutions for an integrable nonlinearly dispersive model wave equation abstract we establish local well posedness in the sobolev space hs with any s 3 2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the camassa holm equation however unlike the more familiar korteweg devries model we demonstrate conditions on the initial data that lead to finite time blow up of certain solutions

on cell matrices a class of euclidean distance matrices abstract in this paper we study the set of cell matrices and its relationship with the cone of positive semidefinite diagonal matrices the set forms a convex polyhedral cone in the linear space of symmetric matrices we describe the faces of the cone and its polar we also provide a new linear inequality associated with cell matrices

distributed sensor localization in random environments using minimal number of anchor nodes the paper introduces diloc a distributed iterative algorithm to locate m sensors with unknown locations in rm m ges 1 with respect to a minimal number of m 1 anchors with known locations the sensors and anchors nodes in the network exchange data with their neighbors only no centralized data processing or communication occurs nor is there a centralized fusion center to compute the sensors locations diloc uses the barycentric coordinates of a node with respect to its neighbors these coordinates are computed using the cayley menger determinants i e the determinants of matrices of internode distances we show convergence of diloc by associating with it an absorbing markov chain whose absorbing states are the states of the anchors we introduce a stochastic approximation version extending diloc to random environments i e when the communications among nodes is noisy the communication links among neighbors may fail at random times and the internodes distances are subject to errors we show a s convergence of the modified diloc and characterize the error between the true values of the sensors locations and their final estimates given by diloc numerical studies illustrate diloc under a variety of deterministic and random operating conditions

large time existence for 3d water waves and asymptotics we rigorously justify in 3d the main asymptotic models used in coastal oceanography including shallow water equations boussinesq systems kadomtsev petviashvili kp approximation green naghdi equations serre approximation and full dispersion model we first introduce a variable nondimensionalized version of the water waves equations which vary from shallow to deep water and which involves four dimensionless parameters using a nonlocal energy adapted to the equations we can prove a well posedness theorem uniformly with respect to all the parameters its validity ranges therefore from shallow to deep water from small to large surface and bottom variations and from fully to weakly transverse waves

evaluation of optimization methods for nonrigid medical image registration using mutual information and b splines a popular technique for nonrigid registration of medical images is based on the maximization of their mutual information in combination with a deformation field parameterized by cubic b splines the coordinate mapping that relates the two images is found using an iterative optimization procedure this work compares the performance of eight optimization methods gradient descent with two different step size selection algorithms quasi newton nonlinear conjugate gradient kiefer wolfowitz simultaneous perturbation robbins monro and evolution strategy special attention is paid to computation time reduction by using fewer voxels to calculate the cost function and its derivatives the optimization methods are tested on manually deformed ct images of the heart on follow up ct chest scans and on mr scans of the prostate acquired using a bffe tl and t2 protocol registration accuracy is assessed by computing the overlap of segmented edges precision and convergence properties are studied by comparing deformation fields the results show that the robbins monro method is the best choice in most applications with this approach the computation time per iteration can be lowered approximately 500 times without affecting the rate of convergence by using a small subset of the image randomly selected in every iteration to compute the derivative of the mutual information from the other methods the quasi newton and the nonlinear conjugate gradient method achieve a slightly higher precision at the price of larger computation times

registration of cervical mri using multifeature mutual information radiation therapy for cervical cancer can benefit from image registration in several ways for example by studying the motion of organs or by partially automating the delineation of the target volume and other structures of interest in this paper the registration of cervical data is addressed using mutual information mi of not only image intensity but also features that describe local image structure three aspects of the registration are addressed to make this approach feasible first instead of relying on a histogram based estimation of mutual information which poses problems for a larger number of features a graph based implementation of alpha mutual information alpha mi is employed second the analytical derivative of alpha mi is derived this makes it possible to use a stochastic gradient descent method to solve the registration problem which is substantially faster than non derivative based methods third the feature space is reduced by means of a principal component analysis which also decreases the registration time the proposed technique is compared to a standard approach based on the mutual information of image intensity only experiments are performed on 93 t2 weighted mr clinical data sets acquired from 19 patients with cervical cancer several characteristics of the proposed algorithm are studied on a subset of 19 image pairs one pair per patient on the remaining data 36 image pairs one or two pairs per patient the median overlap is shown to improve significantly compared to standard mi from 0 85 to 0 86 for the clinical target volume ctv p 2 ldr10 2 from 0 75 to 0 81 for the bladder p 8 ldr 10 6 and from 0 76 to 0 77 for the rectum p 2 ldr 10 4 the registration error is improved at important tissue interfaces such as that of the bladder with the ctv and the interface of the rectum with the uterus and cervix

on the diagonal scaling of euclidean distance matrices to doubly stochastic matrices we consider the problem of scaling a nondegenerate predistance matrix a to a doubly stochastic matrix b if a is nondegenerate then there exists a unique positive diagonal matrix c such that b cac we further demonstrate that if a is a euclidean distance matrix then b is a spherical euclidean distance matrix finally we investigate how scaling a nondegenerate euclidean distance matrix a to a doubly stochastic matrix transforms the points that generate a we find that this transformation is equivalent to an inverse stereographic projection

computing the nearest euclidean distance matrix with low embedding dimensions euclidean distance embedding appears in many high profile applications including wireless sensor network localization where not all pairwise distances among sensors are known or accurate the classical multi dimensional scaling cmds generally works well when the partial or contaminated euclidean distance matrix edm is close to the true edm but otherwise performs poorly a natural step preceding cmds would be to calculate the nearest edm to the known matrix a crucial condition on the desired nearest edm is for it to have a low embedding dimension and this makes the problem nonconvex there exists a large body of publications that deal with this problem some try to solve the problem directly and some are the type of convex relaxations of it in this paper we propose a numerical method that aims to solve this problem directly our method is strongly motivated by the majorized penalty method of gao and sun for low rank positive semi definite matrix optimization problems the basic geometric object in our study is the set of edms having a low embedding dimension we establish a zero duality gap result between the problem and its lagrangian dual problem which also motivates the majorization approach adopted numerical results show that the method works well for the euclidean embedding of network coordinate systems and for a class of problems in large scale sensor network localization and molecular conformation

the cone of distance matrices abstract the geometry of the cone of euclidean distance matrices edms is analyzed using a new characterization of an edm the facial structure and the angle that edms of embedding dimension one make with the center ray are found this result follows from a complete analysis of the critical points of the distance function in frobenius norm from the matrix e consisting of zero diagonal and ones elsewhere to the edms of embedding dimension one

a genetic algorithm for circulant euclidean distance matrices this paper presents a fast genetic algorithm to determine three dimensional configurations of points that generate circulant euclidean distance matrices edms a parallel implementation is possible by using the message passing interface mpi standard in addition theoretical results about the polyhedral structure of both the cone of circulant symmetric positive semidefinite matrices and the cone of circulant edms are introduced

corrigendum to local well posedness and wave breaking results for periodic solutions of a shallow water equation for waves of moderate amplitude nonlinear anal 97 2014 145 154 abstract the local well posedness of a periodic nonlinear equation for surface waves of moderate amplitude in shallow water was studied in duruk mutlubas 2014 where an approach proposed by kato based on semigroup theory for quasi linear equations was used it was also shown that singularities for the model equation can occur only in the form of wave breaking in particular surging breakers in this paper we correct the mistake made in the proof of the main result on local well posedness and give the appropriate assumptions followed by the corresponding results

a group majorization ordering for euclidean distance matrices this paper investigates some properties of euclidean distance matrices edms with focus on their ordering structure the ordering treated here is the group majorization ordering induced by the group of permutation matrices by using this notion we establish two monotonicity results for edms i the radius of a spherical euclidean distance matrix spherical edm is increasing with respect to the group majorization ordering ii the larger an edm is in terms of the group majorization ordering the more spread out its eigenvalues are minimal elements with respect to this ordering are also described

on cartesian product of euclidean distance matrices abstract if a r m m and b r n n we define the product a b as a b a j n j m b where denotes the kronecker product and j n is the n n matrix of all ones we refer to this product as the cartesian product of a and b since if d 1 and d 2 are the distance matrices of graphs g 1 and g 2 respectively then d 1 d 2 is the distance matrix of the cartesian product g 1 g 2 we study cartesian products of euclidean distance matrices edms we prove that if a and b are edms then so is the product a b we show that if a is an edm and u is symmetric then a u is an edm if and only if u c j n for some c it is shown that for edms a and b a b is spherical if and only if both a and b are spherical if a and b are edms then we derive expressions for the rank and the moore penrose inverse of a b in the final section we consider the product a b for arbitrary matrices for a r m m b r n n we show that all nonzero minors of a b of order m n 1 are equal an explicit formula for a nonzero minor of order m n 1 is proved the result is shown to generalize the familiar fact that the determinant of the distance matrix of a tree on n vertices does not depend on the tree and is a function only of n

a remark on the faces of the cone of euclidean distance matrices a new characterization of the faces of the cone of euclidean distance matrices edms was recently obtained by tarazaga in terms of lgs d a special subspace associated with each edm d in this note we show that lgs d is nothing but the gale subspace associated with edms

positive definite completions of partial hermitian matrices abstract the question of which partial hermitian matrices some entries specified some free may be completed to positive definite matrices is addressed it is shown that if the diagonal entries are specified and principal minors composed of specified entries are positive then if the undirected graph of the specified entries is chordal a positive definite completion necessarily exists furthermore if this graph is not chordal then examples exist without positive definite completions in case a positive definite completion exists there is a unique matrix in the class of all positive definite completions whose determinant is maximal and this matrix is the unique one whose inverse has zeros in those positions corresponding to unspecified entries in the original partial hermitian matrix additional observations regarding positive definite completions are made

block matrices and multispherical structure of distance matrices abstract the block structure of a matrix and its relation to the block structure of the corresponding eigenvectors is investigated a set of points is said to have multispherical structure if they lie on a collection of concentric spheres when the centroid of each of the clusters lies at the common center the associated distance matrix has a block structure with simple relations between the blocks further such block structure may be recognized from the structure of the eigenvectors of the distance matrix a computational procedure is proposed to find the least number of concentric spheres containing the points represented by a distance matrix

connections between the real positive semidefinite and distance matrix completion problems abstract though the real symmetric positive semidefinite psd matrices and the euclidean distance matrices are closely related exact relationships between the corresponding completion problems are not apparent we establish strong partial relationships of two types this permits the transfer of some insights from one problem to the other and allows computational tools for the psd problem to be used for the distance problem

estimating the gap of finite metric spaces of strict p negative type abstract let x d be a finite metric space this paper first discusses the spectrum of the p distance matrix of a finite metric space of p negative type and then gives upper and lower bounds for the so called gap x p of a finite metric space of strict p negative type furthermore estimations for x p under a certain gluing construction for finite metric spaces are given and finally be applied to finite ultrametric spaces

hadamard inverses square roots and products of almost semidefinite matrices abstract let a aij be an n n symmetric matrix with all positive entries and just one positive eigenvalue bapat proved then that the hadamard inverse of a given by a 1 1 a ij is positive semidefinite we show that if moreover a is invertible then a 1 is positive definite we use this result to obtain a simple proof that with the same hypotheses on a except that all the diagonal entries of a are zero the hadamard square root of a given by a 1 2 a ij 1 2 has just one positive eigenvalue and is invertible finally we show that if a is any positive semidefinite matrix and b is almost positive definite and invertible then a b 1 e t b 1 e a

completely positive factorizations associated with euclidean distance matrices corresponding to an arithmetic progression abstract euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties we exploit those properties to develop completely positive factorizations of translations of those matrices we show that the minimal translation that makes such a matrix positive semidefinite results in a completely positive matrix we also discuss completely positive factorizations of such matrices over the integers methods developed in the paper can be used to find completely positive factorizations of other matrices with similar properties

an optimal algorithm for approximate nearest neighbor searching fixed dimensions consider a set of s of n data points in real d dimensional space r d where distances are measured using any minkowski metric in nearest neighbor searching we preprocess s into a data structure so that given any query point q r d is the closest point of s to q can be reported quickly given any positive real e data point p is a 1 e approximate nearest neighbor of q if its distance from q is within a factor of 1 e of the distance to the true nearest neighbor we show that it is possible to preprocess a set of n points in r d in o dn log n time and o dn space so that given a query point q r d and e 0 a 1 e approximate nearest neighbor of q can be computed in o c d e log n time where c d e d 1 6d e d is a factor depending only on dimension and e in general we show that given an integer k 1 1 e approximations to the k nearest neighbors of q can be computed in additional o kd log n time

optimization of mutual information for multiresolution image registration we propose a new method for the intermodal registration of images using a criterion known as mutual information our main contribution is an optimizer that we specifically designed for this criterion we show that this new optimizer is well adapted to a multiresolution approach because it typically converges in fewer criterion evaluations than other optimizers we have built a multiresolution image pyramid along with an interpolation process an optimizer and the criterion itself around the unifying concept of spline processing this ensures coherence in the way we model data and yields good performance we have tested our approach in a variety of experimental conditions and report excellent results we claim an accuracy of about a hundredth of a pixel under ideal conditions we are also robust since the accuracy is still about a tenth of a pixel under very noisy conditions in addition a blind evaluation of our results compares very favorably to the work of several other researchers

estimating mutual information we present two classes of improved estimators for mutual information m x y from samples of random points distributed according to some joint probability density mu x y in contrast to conventional estimators based on binnings they are based on entropy estimates from k nearest neighbor distances this means that they are data efficient with k 1 we resolve structures down to the smallest possible scales adaptive the resolution is higher where data are more numerous and have minimal bias indeed the bias of the underlying entropy estimates is mainly due to nonuniformity of the density at the smallest resolved scale giving typically systematic errors which scale as functions of k n for n points numerically we find that both families become exact for independent distributions i e the estimator m x y vanishes up to statistical fluctuations if mu x y mu x mu y this holds for all tested marginal distributions and for all dimensions of x and y in addition we give estimators for redundancies between more than two random variables we compare our algorithms in detail with existing algorithms finally we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis ica for improving ica and for estimating the reliability of blind source separation

multispherical euclidean distance matrices abstract in this paper we introduce new necessary and sufficient conditions for an euclidean distance matrix to be multispherical the class of multispherical distance matrices studied in this paper contains not only most of the matrices studied by hayden et al 1996 2 but also many other multispherical structures that do not satisfy the conditions in hayden et al 1996 2 we also study the information provided by the origin of coordinates when it is placed at the center of the spheres and the origin representation property is satisfied these vectors associated with the origin of coordinates generate a number of supporting hyperplanes for a family of multispherical matrices and also describe part of the null space of the corresponding distance matrices

circum euclidean distance matrices and faces abstract we study the structure of circum euclidean distance matrices those euclidean distance matrices generated by points lying on a hypersphere we show for example that such euclidean distance matrices are characterized as having constant row sums and they constitute the interior of the cone of all euclidean distance matrices also we provide a formula for computing the radius of a representing configuration in the smallest embedding dimension r and show that rk d r 1 finally we obtain a geometric characterization of the faces of this cone given a configuration of points and its euclidean distance matrix d any matrix in the minimal face containing d comes from a configuration that is a linear perturbation of the points that generate d

distance matrices and regular figures abstract a regular figure which includes all regular polygons is a set of points on a hypersphere whose center coincides with their centroid we characterize all regular figures as those whose points generate a euclidean distance matrix edm with eigenvector e the vector of all ones restricting the classical maps of schoenberg gower and critchley for all edms to the subcone of edms with eigenvector e yields new geometrical information about the generating points and a simple formula for the radius of the hypersphere

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

a diffusion approach to network localization the localization of nodes on a network is a challenging research topic it arises in a variety of applications such as communications and sensor network analysis we propose a computational approach to recovering the positions of network nodes given partial and corrupted distance measurements and the positions of a small subset of anchor nodes first we show how to derive geometrically adaptive diffusion bases defined over the entire network given only partial distance measurements second we propose to utilize several diffusion bases simultaneously to derive multiscale diffusion frames last we utilize the diffusion frames to formulate a l1 regression based extension of the anchor points coordinates to the entire network we experimentally show that under a wide range of conditions our method compares favorably with state of the art approaches

traveling surface waves of moderate amplitude in shallow water we study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the euler equations for inviscid incompressible and homogeneous fluids we obtain solitary waves of elevation and depression including a family of solitary waves with compact support where the amplitude may increase or decrease with respect to the wave speed our approach is based on techniques from dynamical systems and relies on a reformulation of the evolution equation as an autonomous hamiltonian system which facilitates an explicit expression for bounded orbits in the phase plane to establish existence of the corresponding periodic and solitary traveling wave solutions

the cell matrix closest to a given euclidean distance matrix abstract cell matrix introduced by jaklic and modic 6 is a special euclidean distance matrix edm that has a quite attractive and simple structure it is of interest to approximate an edm by a cell matrix in this paper we consider the problem of finding the cell matrix that is closest to a given edm with respect to the frobenius norm the majorization ordering of the eigenvalues of a cell matrix is also discussed

a shallow water approximation to the full water wave problem we demonstrate that the system of the green naghdi equations as a two directional nonlinearly dispersive wave model is a close approximation to the two dimensional full water wave problem based on the energy estimates and the proof of the well posedness for the green naghdi equations and the water wave problem we compare solutions of the two systems showing that without restrictions on the wave amplitude any two solutions of the two systems remain close at least in some finite time within the shallow water regime provided that their initial data are close in the banach space hs hs 1 for some s as a consequence we show that if the depth of the water compared with the wavelength is sufficiently small the two solutions exist for the same finite time using the uniformly bounded energies defined in the paper 2006 wiley periodicals inc

properties of euclidean and non euclidean distance matrices abstract a distance matrix d of order n is symmetric with elements 1 2 d ij 2 where dii 0 d is euclidean when the 1 2 n n 1 quantities dij can be generated as the distances between a set of n points x n p in a euclidean space of dimension p the dimensionality of d is defined as the least value of p rank x of any generating x in general p 1 and p 2 are also acceptable but may include imaginary coordinates even when d is euclidean basic properties of euclidean distance matrices are established in particular when rank d it is shown that depending on whether etd e is not or is zero the generating points lie in either p 1 dimensions in which case they lie on a hypersphere or in p 2 dimensions in which case they do not the notation e is used for a vector all of whose values are one when d is non euclidean its dimensionality p r s will comprise r real and s imaginary columns of x and r s are invariant for all generating x of minimal rank higher ranking representations can arise only from p 1 r 1 s or p 1 r s 1 or p 2 r 1 s 1 so that not only are r s invariant but they are both minimal for all admissible representations x

well posedness of the water waves equations 1 1 presentation of the problem the water waves problem for an ideal liquid consists of describing the motion of the free surface and the evolution of the velocity field of a layer of perfect incompressible irrotational fluid under the influence of gravity in this paper we restrict our attention to the case when the surface is a graph parameterized by a function x where t denotes the time variable and x xi xd rd the horizontal spatial variables the method developed here works equally well for any integer d 1 but the only physically relevant cases are of course d 1 and d 2 the layer of fluid is also delimited from below by a not necessarily flat bottom parameterized by a time independent function b x we denote by q t the fluid domain at time t the incompressibility of the fluids is expressed by 1 1 div v 0 in qu t 0

numerical simulation of gravity waves abstract we present a new spectral method to simulate numerically the waterwave problem in a channel for a fluid of finite or infinite depth it is formulated in terms of the free surface elevation and the velocity potential the numerical method is based on the reduction of this problem to a lower dimensional computation involving surface variables alone to accomplish this we describe the taylor expansion of the dirichlet neumann operator in homogeneous powers of the surface elevation each term is a concatenation of fourier multipliers with powers of and its derivatives and is valid uniformly in wavenumber these are easily calculated using the fast fourier transform the method is illustrated by computing the long time evolution of modulated wave packets and of approximations to the stokes steady wave train by imposing a surface pressure we observe surface steepening in large amplitude evolution and wake and bow wave development for flows with a close to critical froude number finally we give an example of nonlinear evolution of the distribution of energy among normal modes

on the solutions of a model equation for shallow water waves of moderate amplitude abstract this paper is concerned with the cauchy problem of a model equation for shallow water waves of moderate amplitude which was proposed by a constantin and d lannes the hydrodynamical relevance of the camassa holmand degasperis procesi equations arch ration mech anal 192 2009 165 186 first the local well posedness of the model equation is obtained in besov spaces b p r s p r 1 s max 3 2 1 1 p which generalize the sobolev spaces h s by using littlewood paley decomposition and transport equation theory second the local well posedness in critical case with s 3 2 p 2 r 1 is considered moreover with analytic initial data we show that its solutions are analytic in both variables globally in space and locally in time finally persistence properties on strong solutions are also investigated

coordinate shadows of semidefinite and euclidean distance matrices we consider the projected semidefinite and euclidean distance cones onto a subset of the matrix entries these two sets are precisely the input data defining feasible semidefinite and euclidean distance completion problems we classify when these sets are closed and use the boundary structure of these two sets to elucidate the krislock wolkowicz facial reduction algorithm in particular we show that under a chordality assumption the minimal cones of these problems admit combinatorial characterizations as a by product we record a striking relationship between the complexity of the general facial reduction algorithm singularity degree and facial exposedness of conic images under a linear mapping

inverse eigenvalue problem of distance matrix via orthogonal matrix in this paper for a given list of real numbers 1 2 n with sum zero and some additional more technical conditions specified in the paper we construct a euclidean distance matrix edm having as its list of eigenvalues without using hadamard matrices

growth rates for the linearized motion of fluid interfaces away from equilibrium we consider the motion of a two dimensional interface separating an inviscid incompressible irrotational fluid influenced by gravity from a region of zero density we show that under certain conditions the equations of motion linearized about a presumed time dependent solution are wellposed that is linear disturbances have a bounded rate of growth if surface tension is neglected the linear equations are well posed provided the underlying exact motion satisfies a condition on the acceleration of the interface relative to gravity similar to the criterion formulated by g i taylor if surface tension is included the linear equations are well posed without qualifications whether the fluid is above or below the interface an interesting qualitative structure is found for the linear equations a lagrangian approach is used like that of numerical work such as 3 except that the interface is assumed horizontal at infinity certain integral equations which occur involving double layer potentials are shown to be solvable in the present case 1993 john wiley sons inc

on certain linear mappings between inner product and squared distance matrices abstract we obtain the spectral decomposition of four linear mappings the first is a mapping of the linear hull of all centered inner product matrices onto the linear hull of all the induced squared distance matrices it is based on the natural generalization of the cosine law of elementary euclidean geometry the other three mappings studied are 1 the adjoint and 1 extensions and applications particularly to multidimensional scaling are discussed in some detail

isobe kakinuma model for water waves as a higher order shallow water approximation abstract we justify rigorously an isobe kakinuma model for water waves as a higher order shallow water approximation in the case of a flat bottom it is known that the full water wave equations are approximated by the shallow water equations with an error of order o 2 where is a small nondimensional parameter defined as the ratio of the mean depth to the typical wavelength the green naghdi equations are known as higher order approximate equations to the water wave equations with an error of order o 4 in this paper we show that the isobe kakinuma model is a much higher order approximation to the water wave equations with an error of order o 6

the real positive definite completion problem for a simple cycle abstract we consider the question of whether a real partial positive definite matrix in which the specified off diagonal entries consist of a full n cycle has a positive definite completion this lies in contrast to the previously studied chordal case we give two solutions in one we describe about n 2 independent conditions on angles associated with a normalization of the data that are necessary and sufficient the second is more computational and allows presentation of all positive definite completions as well as answering the existence question

linear stability of solitary waves of the green naghdi equations we investigate the eigenvalue problem obtained from linearizing the green naghdi equations about solitary wave solutions unlike weakly nonlinear water wave models the physical system considered here has nonlinearity in its highest derivative term this results in more detailed asymptotic analysis of the eigenvalue problem in the presence of a large parameter combining the technique of singular perturbation with the evans function we show that for solitary waves of small amplitude the problem has no eigenvalues of positive real part and the evans function is nonvanishing everywhere except the origin this fact then leads to the linear stability of these solitary waves 2001 john wiley sons inc

on the low regularity solutions and wave breaking for an equation modeling shallow water waves of moderate amplitude abstract in this paper we consider a nonlinear evolution equation which models the propagation of surface waves of moderate amplitude in shallow water regime we first prove the existence of the low regularity solutions for the cauchy problem of this equation then we discuss the initial profiles under which the solutions of this equation blow up in finite time

on the long wave approximation for the euler poisson system abstract we study the long wave approximation to the euler poisson system for the ion acoustic wave in cold plasma according to the spatial temporal scale and the amplitude of waves we first justify rigorously that in the long wave limit the one way propagating solutions of the euler poisson system are well approximated by the unidirectional solutions of the burgers or kdv equation with responding to the different parameter scales we then demonstrate that the solutions could be convergent to two wave packets in opposite directions where each wave packet involves independently as a solution of the burgers or kdv equation

on euclidean distance matrices abstract if a is a real symmetric matrix and p is an orthogonal projection onto a hyperplane then we derive a formula for the moore penrose inverse of pap as an application we obtain a formula for the moore penrose inverse of an euclidean distance matrix edm which generalizes formulae for the inverse of a edm in the literature to an invertible spherical edm we associate a laplacian matrix which we define as a positive semidefinite n n matrix of rank n 1 and with zero row sums and prove some properties known results for distance matrices of trees are derived as special cases in particular we obtain a formula due to graham and lovasz for the inverse of the distance matrix of a tree it is shown that if d is a nonsingular edm and l is the associated laplacian then d 1 l is nonsingular and has a nonnegative inverse finally infinitely divisible matrices are constructed using edms

on the blow up structure for the generalized periodic camassa holm and degasperis procesi equations considered herein are the generalized camassa holm and degasperis procesi equations in the spatially periodic setting the precise blow up scenarios of strong solutions are derived for both of equations several conditions on the initial data guaranteeing the development of singularities in finite time for strong solutions of these two equations are established the exact blow up rates are also determined finally geometric descriptions of these two integrable equations from non stretching invariant curve flows in centro equiaffine geometries pseudo spherical surfaces and affine surfaces are given

attribute vector guided groupwise registration abstract groupwise registration has been recently introduced to simultaneously register a group of images by avoiding the selection of a particular template to achieve this several methods have been proposed to take advantage of information theoretic entropy measures based on image intensity however simplistic utilization of voxelwise image intensity is not sufficient to establish reliable correspondences since it lacks important contextual information therefore we explore the notion of attribute vector as the voxel signature instead of image intensity to guide the correspondence detection in groupwise registration in particular for each voxel the attribute vector is computed from its multi scale neighborhoods in order to capture the geometric information at different scales the probability density function pdf of each element in the attribute vector is then estimated from the local neighborhood providing a statistical summary of the underlying anatomical structure in that local pattern eventually with the help of jensen shannon js divergence a group of subjects can be aligned simultaneously by minimizing the sum of js divergences across the image domain and all attributes we have employed our groupwise registration algorithm on both real nirep na0 data set and simulated data 12 pairs of normal control and simulated atrophic data set the experimental results demonstrate that our method yields better registration accuracy compared with a popular groupwise registration method

a contribution to the study of the metric and euclidean structures of dissimilarities this paper is concerned with the geometric properties of dissimilarity coefficients defined on finite sets and especially with their euclidean nature we present several particular transformations which preserve euclideanarity and we complete through the study of a one parameter family the current knowledge of the metric and euclidean structure of coefficients based on binary data these results are directly deduced from two theorems which prove the positive semi definite status of some quadratic forms which play a large role in some definitions of dissimilarity commonly used

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

euclidean graph distance matrices of generalizations of the star graph abstract in this paper a relation between graph distance matrices of the star graph and its generalizations and euclidean distance matrices is considered it is proven that distance matrices of certain families of graphs are circum euclidean their spectrum and generating points are given in a closed form

on super spherical distance matrices and two results from schoenberg abstract a new characterization of simplicial distance matrices is obtained the superspherical semidistance matrices are introduced two results deriving from schoenberg are studied a short proof of the first is obtained before strengthening it to show that every circum euclidean semidistance matrix is superspherical the second that l 2 embeds in l 1 required a very sophisticated proof the relationship between super spherical and euclidean matrices is clarified and in the finite case leads to an elementary proof of this second result finally the classes of matrices studied here are located in the wider context of the classes studied by critchley and fichet 1994

the best euclidian fit to a given distance matrix in prescribed dimensions abstract in this paper we determine the euclidean distance matrix which is closest to a given not necessarily euclidian one we admit a wide class of appropriate matrix norms as measures of closeness majorization results on sums of eigenvalues of symmetric matrices serve as basic tools

well posedness in sobolev spaces of the full water wave problem in 2 d we consider the motion of the interface of 2 d irrotational incompressible inviscid water wave with air above water and surface tension zero we show that the interface is always not accelerating into the water region normal to itself as rapidly as the normal acceleration of gravity as long as the interface is nonself intersect we therefore obtain the existence and uniqueness of solutions of the full water wave problem locally in time for any initial interface which is nonself intersect including the case that the interface is of multiple heights

approximation by matrices positive semidefinite on a subspace abstract we obtain the best approximation to a matrix by matrices positive semidefinite on a subspace as a by product we present two new characterizations of euclidean distance matrices

approximate and exact completion problems for euclidean distance matrices using semidefinite programming abstract a partial pre distance matrix a is a matrix with zero diagonal and with certain elements fixed to given nonnegative values the other elements are considered free the euclidean distance matrix completion problem chooses nonnegative values for the free elements in order to obtain a euclidean distance matrix edm the nearest or approximate euclidean distance matrix problem is to find a euclidean distance matrix edm that is nearest in the frobenius norm to the matrix a when the free variables are discounted in this paper we introduce two algorithms one for the exact completion problem and one for the approximate completion problem both use a reformulation of edm into a semidefinite programming problem sdp the first algorithm is based on an implicit equation for the completion that for many instances provides an explicit solution the other algorithm is based on primal dual interior point methods that exploit the structure and sparsity included are results on maps that arise that keep the edm and sdp cones invariant we briefly discuss numerical tests

the long wave limit for the water wave problem i the case of zero surface tension the korteweg de vries equation boussinesq equation and many other equations can be formally derived as approximate equations for the two dimensional water wave problem in the limit of long waves here we consider the classical problem concerning the validity of these equations for the water wave problem in an infinitely long canal without surface tension we prove that the solutions of the water wave problem in the long wave limit split up into two wave packets one moving to the right and one to the left where each of these wave packets evolves independently as a solution of a korteweg de vries equation our result allows us to describe the nonlinear interaction of solitary waves 2000 john wiley sons inc