lower semicontinuity property of multiparameter optimal stopping value and its application to multiparameter prophet inequalities abstract this paper is concerned with the optimal stopping problem for discrete time multiparameter stochastic processes with the index set n d the optimal stopping value of a discrete time multiparameter integrable stochastic process whose negative part is uniformly integrable is lower semicontinuous for the topology of convergence in distribution the multiparameter version of prophet inequality for the one parameter optimal stopping problem is formulated and the lower semicontinuity property of the optimal stopping value is applied to the multiparameter prophet inequality

fast surface interpolation using hierarchical basis functions an alternative to multigrid relaxation that is much easier to implement and more generally applicable is presented conjugate gradient descent is used in conjunction with a hierarchical multiresolution set of basis functions the resultant algorithm uses a pyramid to smooth the residual vector before the direction is computed simulation results showing the speed of convergence and its dependence on the choice of interpolator the number of smoothing levels and other factors are presented the relationship of this approach to other multiresolution relaxation and representation schemes is also discussed

a phase transition for the coupled branching process part i the ergodic theory in the range of finite second moments we consider a particular markov process tu on s s n the random variable tu x is interpreted as the number of particles atx at timet the initial distribution of this process is a translation invariant measure withf x d the evolution is as follows at rateb x a particle is born atx but moves instantaneously toy chosen with probabilityq x y all particles at a site die at ratepd withp 0 1 d and individual particles die independently from each other at rate 1 p d every particle moves independently of everything else according to a continuous time random walk

varying complexity in tree structured image distribution models probabilistic models of image statistics underlie many approaches in image analysis and processing an important class of such models have variables whose dependency graph is a tree if the hidden variables take values on a finite set most computations with the model can be performed exactly including the likelihood calculation training with the em algorithm etc crouse et al developed one such model the hidden markov tree hmt they took particular care to limit the complexity of their model we argue that it is beneficial to allow more complex tree structured models describe the use of information theoretic penalties to choose the model complexity and present experimental results to support these proposals for these experiments we use what we call the hierarchical image probability hip model the differences between the hip and the hmt models include the use of multivariate gaussians to model the distributions of local vectors of wavelet coefficients and the use of different numbers of hidden states at each resolution we demonstrate the broad utility of image distributions by applying the hip model to classification synthesis and compression across a variety of image types namely electrooptical synthetic aperture radar and mammograms digitized x rays in all cases we compare with the hmt

fuzzy multiresolution signal representation we present a multiresolution signal representation technique which uses fuzzy rules a fuzzy tree is used to connect different levels of resolution we apply our representation to several random processes and demonstrate some useful properties of our representation when applied to fractals

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

ml parameter estimation of a multiscale stochastic process using the em algorithm an algorithm for estimation of the parameters of a multiscale stochastic process based on scale recursive dynamics on trees is presented the expectation maximization algorithm is used to provide maximum likelihood estimates for the general case of a nonhomogeneous tree with no fixed structure for the process dynamics experimental results are presented using synthetic data

a karhunen loeve like expansion for 1 f processes via wavelets while so called 1 f or scaling processes emerge regularly in modeling a wide range of natural phenomena as yet no entirely satisfactory framework has been described for the analysis of such processes orthonormal wavelet bases are used to provide a new construction for nearly 1 f processes from a set of uncorrelated random variables

discrete multi armed bandits and multi parameter processes the general multi armed bandit problem is reformulated and solved as a control problem over a partially ordered set the approach taken provides a technically convenient framework for bandit like problems it also adds insight to the structure of strategies over partially ordered sets

on the normal exponential map in singular conformal metrics abstract brake orbits and homoclinics of autonomous dynamical systems correspond via maupertuis principle to geodesics in riemannian manifolds endowed with a metric which is singular on the boundary jacobi metric motivated by the classical yet still intriguing in many aspects problem of establishing multiplicity results for brake orbits and homoclinics as done in giambo et al 2005 2010 2011 and by the development of a morse theory in giambo et al 2014 for geodesics in such kind of metric in this paper we study the related normal exponential map from a global perspective

multiscale recursive estimation data fusion and regularization we describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and or noisy measurements which may also be at several scales in particular multiscale signal representations lead naturally to pyramidal or tree like data structures in which each level in the tree corresponds to a particular scale of representation a class of multiscale dynamic models evolving on dyadic trees is introduced the main focus of this paper is on the description analysis and application of an extremely efficient optimal estimation algorithm for this class of models this algorithm consists of a fine to coarse filtering sweep followed by a coarse to fine smoothing step corresponding to the dyadic tree generalization of kalman filtering and rauch tung striebel smoothing the kalman filtering sweep consists of the recursive application of three steps a measurement update step a fine to coarse prediction step and a fusion step we illustrate the use of our methodology for the fusion of multiresolution data and for the efficient solution of fractal regularizations of ill posed signal and image processing problems encountered

estimation of fractal signals from noisy measurements using wavelets the role of the wavelet transformation as a whitening filter for 1 f processes is exploited to address problems of parameter and signal estimations for 1 f processes embedded in white background noise robust computationally efficient and consistent iterative parameter estimation algorithms are derived based on the method of maximum likelihood and cramer rao bounds are obtained included among these algorithms are optimal fractal dimension estimators for noisy data algorithms for obtaining bayesian minimum mean square signal estimates are also derived together with an explicit formula for the resulting error these smoothing algorithms find application in signal enhancement and restoration the parameter estimation algorithms find application in signal enhancement and restoration the parameter estimation algorithms in addition to solving the spectrum estimation problem and to providing parameters for the smoothing process are useful in problems of signal detection and classification results from simulations are presented to demonstrated the viability of the algorithms

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

gaussian multiresolution models exploiting sparse markov and covariance structure in this paper we consider the problem of learning gaussian multiresolution mr models in which data are only available at the finest scale and the coarser hidden variables serve to capture long distance dependencies tree structured mr models have limited modeling capabilities as variables at one scale are forced to be uncorrelated with each other conditioned on other scales we propose a new class of gaussian mr models in which variables at each scale have sparse conditional covariance structure conditioned on other scales our goal is to learn a tree structured graphical model connecting variables across scales which translates into sparsity in inverse covariance while at the same time learning sparse structure for the conditional covariance not its inverse within each scale conditioned on other scales this model leads to an efficient new inference algorithm that is similar to multipole methods in computational physics we demonstrate the modeling and inference advantages of our approach over methods that use mr tree models and single scale approximation methods that do not use hidden variables

closed characteristics on compact convex hypersurfaces in r 2n for any given compact c 2 hypersurface in r 2n bounding a strictly convex set with nonempty interior in this paper an invariant n is defined and satisfies n n 2 1 where a denotes the greatest integer which is not greater than a r the following results are proved in this paper there always exist at least n geometrically distinct closed characteristics on if all the geometrically distinct closed characteristics on are nondegenerate then n n if the total number of geometrically distinct closed characteristics on is finite there exists at least an elliptic one among them and there exist at least n 1 of them possessing irrational mean indices if this total number is at most 2 n 2 there exist at least two elliptic ones among them

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

multiscale methods for the segmentation and reconstruction of signals and images this paper addresses the problem of both segmenting and reconstructing a noisy signal or image the work is motivated by large problems arising in certain scientific applications such as medical imaging two objectives for a segmentation and denoising algorithm are laid out it should be computationally efficient and capable of generating statistics for the errors in the reconstruction and estimates of the boundary locations the starting point for the development of a suitable algorithm is a variational approach to segmentation shah 1992 this paper then develops a precise statistical interpretation of a one dimensional 1 d version of this variational approach to segmentation the 1 d algorithm that arises as a result of this analysis is computationally efficient and capable of generating error statistics a straightforward extension of this algorithm to two dimensions would incorporate recursive procedures for computing estimates of inhomogeneous gaussian markov random fields such procedures require an unacceptably large number of operations to meet the objective of developing a computationally efficient algorithm the use of previously developed multiscale statistical methods is investigated this results in the development of an algorithm for segmenting and denoising which is not only computationally efficient but also capable of generating error statistics as desired

correlation structure of the discrete wavelet coefficients of fractional brownian motion it is shown that the discrete wavelet coefficients of fractional brownian motion at different scales are correlated and that their auto and cross correlation functions decay hyperbolically fast at a rate much faster than that of the autocorrelation of the fractional brownian motion itself the rate of decay of the correlation function in the wavelet domain is primarily determined by the number of vanishing moments of the analyzing wavelet

multiple brake orbits in bounded convex symmetric domains abstract in this paper we prove that there exist at least two geometrically distinct brake orbits in every bounded convex symmetric domain in r n for n 2

multiscale autoregressive processes ii lattice structures for whitening and modeling for pt i see ibid vol 40 no 8 p 1915 34 1992 lattice structures for the whitening and modeling of isotropic processes on trees are developed and a result relating the stability properties of these models to the reflection coefficient sequence introduced in pt i is presented this framework allows one to obtain a detailed analysis of the wold decomposition of processes on trees one interesting aspect of this is that there is a significantly larger class of singular processes on dyadic trees than on the integers

noniterative manipulation of discrete energy based models for image analysis abstract with emphasis on the graph structure of energy based models devoted to image analysis we investigate efficient procedures for sampling and inferring we show that triangulated graphs whom trees are simple instances of always support causal models for which noniterative procedures can be devised to minimize the energy to extract probabilistic descriptions to sample from corresponding prior and posterior distributions or to infer from local marginals the relevance and efficiency of these procedures are illustrated for classification problems

functions on the sphere with critical points in pairs and orthogonal geodesic chords abstract using an estimate on the number of critical points for a morse even function on the sphere s m m 1 we prove a multiplicity result for orthogonal geodesic chords in riemannian manifolds with boundary that are diffeomorphic to euclidean balls this yields also a multiplicity result for brake orbits in a potential well

predictability and stopping on lattices of sets as a first step in the development of a general theory of set indexed martingales we define predictability on a general space with respect to a filtration indexed by a lattice of sets we prove a characterization of the predictable algebra in terms of adapted and left continuous processes without any form of topology for the index set we then define a stopping set and show that it is a natural generalization of the stopping time in particular the predictable algebra can be characterized by various stochastic intervals generated by stopping sets

continuous multi armed bandits and multiparameter processes a general framework is proposed for continuous time dynamic allocation models of a scarce resource among competing projects the allocation model is formulated as a multi armed bandit model and solved as a control problem of a multiparameter process in contrast to discrete time bandits where only one arm can be pulled at a time the continuous time bandit must allow simultaneous pulls the multiparameter approach allows a strong solution of diffusion type bandits here the main problem is to define precisely how to switch among arms and the solution involves local times

optimal stopping of two parameter processes on nonstandard probability spaces keywords nonstandard analysis optimal stopping problem randomized stopping times nonstandard probability theory loeb spaces conditional independence property reference prob article 1989 001doi 10 2307 2001425 record created on 2008 12 01 modified on 2017 05 12

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

on the spectrum of fractional brownian motions fractional brownian motions fbms provide useful models for a number of physical phenomena whose empirical spectra obey power laws of fractional order however due to the nonstationary nature of these processes the precise meaning of such spectra remains generally unclear two complementary approaches are proposed which are intended to clarify this point the first one based on a time frequency analysis takes into account the nonstationary nature of fbm and puts emphasis on time averaged measurements the second one based on a time scale analysis is matched to self similarity properties of fbm and reveals an underlying stationary structure relative to each time scaling

new fast smoothers for multiscale systems we consider the smoothing problem for multiscale stochastic systems based on the wavelet transform these models involve processes indexed by the nodes of a dyadic tree each level of the dyadic tree represents one scale or resolution of the process therefore moving upward on the tree divides the resolution by 2 whereas moving downward multiplies it by 2 the processes are built according to a recursion in scale from coarse to fine to which random details are added to operate the change in scale one must perform an interpolation this is achieved using the qmf pair of operators attached to a wavelet transform these models have proved to be of great value to capture textures or fractal like processes as well as to perform multiresolution sensor fusion an example of which is given here up to now however only subclasses of multiscale systems were amenable to fast algorithms and through different formalisms those relying on haar s wavelet and those involving only one of the two wavelet interpolators we provide here a unifying framework that handles any system based on orthogonal wavelets a smoothing theory is presented to define the field of fast algorithms for markov random fields and give intuition on how to design them this theory reveals the difficulties arising with general multiscale systems we then prove that orthogonality properties of wavelets are the gate to fastness

efficient multiscale regularization with applications to the computation of optical flow a new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence the solution of the new problem formulation is computed with an efficient multiscale algorithm experiments on several image sequences demonstrate the substantial computational savings that can be achieved due to the fact that the algorithm is noniterative and in fact has a per pixel computational complexity that is independent of image size the new approach also has a number of other important advantages specifically multiresolution flow field estimates are available allowing great flexibility in dealing with the tradeoff between resolution and accuracy multiscale error covariance information is also available which is of considerable use in assessing the accuracy of the estimates in particular these error statistics can be used as the basis for a rational procedure for determining the spatially varying optimal reconstruction resolution furthermore if there are compelling reasons to insist upon a standard smoothness constraint the new algorithm provides an excellent initialization for the iterative algorithms associated with the smoothness constraint problem formulation finally the usefulness of the approach should extend to a wide variety of ill posed inverse problems in which variational techniques seeking a smooth solution are generally used

two parameter optimal stopping and bi markov processes in this paper the optimal stopping problem is solved for particular two parameter processes here called bi markov processes a subsequent potential theory is developed with respect to a pair of one parameter semi groups we introduce a new notion of harmonicity for two variable functions and we interpret it in the framework of the theory of bi markov processes

prophet inequalities for finite stage multiparameter optimal stopping problems abstract this paper is concerned with the optimal stopping problem for discrete time multiparameter stochastic processes with the index set n d in the classical optimal stopping problems the comparisons between the expected reward of a player with complete foresight and the expected reward of a player using nonanticipating stop rules known as prophet inequalities have been studied by many authors prophet inequalities in the case of finite stage two parameter optimal stopping problems are extended to the case of finite stage general multiparameter optimal stopping problems

optional sampling of submartingales indexed by partially ordered sets the optional sampling theorem for martingales indexed by a partially ordered set is true if the index set is directed however the corresponding result for submartingales indexed by a partially ordered set is not true in general in this paper we completely characterize the class of stopping times for which the optional sampling theorem is true for all uniformly bounded submartingales indexed by countable partially ordered sets by assuming a conditional independence property we show that when the index set is r 2 the optional sampling theorem is true for all uniformly bounded right continuous submartingales and all stopping times this conditional independence property is satisfied in cases where the submartingales and stopping times are measurable with respect to the two parameter wiener process a counterexample shows that the optional sampling result is false for r n when n 2 even if the conditional independence property is satisfied

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

multiply rooted multiscale models for large scale estimation divide and conquer or multiscale techniques have become popular for solving large statistical estimation problems the methods rely on defining a state which conditionally decorrelates the large problem into multiple subproblems each more straightforward than the original however this step cannot be carried out for asymptotically large problems since the dimension of the state grows without bound leading to problems of computational complexity and numerical stability in this paper we propose a new approach to hierarchical estimation in which the conditional decorrelation of arbitrarily large regions is avoided and the problem is instead addressed piece by piece the approach possesses promising attributes it is not a local method the estimate at every point is based on all measurements it is numerically stable for problems of arbitrary size and the approach retains the benefits of the multiscale framework on which it is based a broad class of statistical models a stochastic realization theory an algorithm to calculate statistical likelihoods and the ability to fuse local and nonlocal measurements

bayesian multiscale models for poisson processes abstract i introduce a class of bayesian multiscale models bmsm s for one dimensional inhomogeneous poisson processes the focus is on estimating the discretized intensity function underlying the process unlike the usual transform based approach at the heart of most wavelet based methods for gaussian data these bmsm s are constructed using recursive dyadic partitions rdp s within an entirely likelihood based framework each rdp may be associated with a binary tree and a new multiscale prior distribution is introduced for the unknown intensity through the placement of mixture distributions at each of the nodes of the tree the concept of model mixing is then applied to a complete collection of such trees in addition to allowing for the inclusion of full location scale information in the model this last step also is fundamental both in inducing stationarity in the prior distribution and in enabling a given intensity function to be approximated at the resolution of the data under squared error lo

modeling and estimation of multiresolution stochastic processes an overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing a natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image in particular it is shown how the wavelet transform directly suggests such a modeling paradigm this perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time like variable the investigation of models on homogeneous trees is emphasized the framework examined here allows for consideration in a very natural way of the fusion of data from sensors with differing resolutions also thanks to the fact that wavelet transforms do an excellent job of compressing large classes of covariance kernels it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect

additive comparisons of stopping values and supremum values for finite stage multiparameter stochastic processes abstract this paper concerns the optimal stopping problem for discrete time multiparameter stochastic processes with the index set n d in the classical optimal stopping problems the comparisons between the expected reward of a player with complete foresight and the expected reward of a player using nonanticipating stop rules known as prophet inequalities have been studied by many authors ratio comparisons between these values in the case of multiparameter optimal stopping problems are studied by krengel and sucheston 1981 9 and tanaka 2007 2006 14 15 in this paper an additive comparison in the case of finite stage multiparameter optimal stopping problems is given

optimal stopping problems for multiarmed bandit processes with arms independence abstract this paper deals with the optimal stopping problem for multiarmed bandit processes under the assumption of independence of arms we show that optimal strategies and stopping times are expressed by the dynamic allocation indices for each arm this paper reduces this problem to several independent one parameter optimal stopping problems on the basis of these results we characterize optimal strategies and stopping times moreover this paper also extends those to the case allowing time constraints in the case where arm s state evolve according to markov chains with finite state linear programming calculation of optimal strategies and stopping times is discussed

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

arret optimal sur le plan the optimal stopping problem by stopping points for processes indexed by a partially ordered set 2 is stated in a quite general frame an optimality criterion concerned with conditional pay off is established by studying the maximal elements of the set of stopping points where the snell enveloppe preserves the martingale property the problem is solved on the one point compactification of 2

wavelets and dilation equations a brief introduction wavelets are new families of basis functions that yield the representation f x sum b jk w 2 j x k their construction begins with the solution phi x to a dilation equation with coefficients c k then w comes from phi and the basis comes by translation and dilation of w it is shown in part 1 how conditions on the c k lead to approximation properties and orthogonality properties of the wavelets part 2 describes the recursive algorithms also based on the c k that decompose and reconstruct f the object of wavelets is to localize as far as possible in both time and frequency with efficient algorithms

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

multiscale systems kalman filters and riccati equations an algorithm analogous to the rauch tung striebel algorithm spl minus consisting of a fine to coarse kalman filter like sweep followed by a coarse to fine smoothing step spl minus was developed previously by the authors ibid vol 39 no 3 p 464 78 1994 in this paper they present a detailed system theoretic analysis of this filter and of the new scale recursive riccati equation associated with it while this analysis is similar in spirit to that for standard kalman filters the structure of the dyadic tree leads to several significant differences in particular the structure of the kalman filter error dynamics leads to the formulation of an ml version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the hamiltonian for the smoothing problem in addition the notion of stability for dynamics requires some care as do the concepts of reachability and observability using these system theoretic constructs the stability and steady state behavior of the fine to coarse kalman filter and its riccati equation are analysed

wavelet analysis and synthesis of fractional brownian motion fractional brownian motion fbm offers a convenient modeling for nonstationary stochastic processes with long term dependencies and 1 f type spectral behavior over wide ranges of frequencies statistical self similarity is an essential feature of fbm and makes natural the use of wavelets for both its analysis and its synthesis a detailed second order analysis is carried out for wavelet coefficients of fbm it reveals a stationary structure at each scale and a power law behavior of the coefficients variance from which the fractal dimension of fbm can be estimated conditions for using orthonormal wavelet decompositions as approximate whitening filters are discussed consequences of discretization are considered and some connections between the wavelet point of view and previous approaches based on length measurements analysis or dyadic interpolation synthesis are briefly pointed out

semi infinite arrays of isotropic point scatterers a unified approach we solve the two dimensional problem of acoustic scattering by a semi infinite pe riodic array of identical isotropic point scatterers i e objects whose size is negligible compared to the incident wavelength and which are assumed to scatter incident waves uniformly in all directions this model is appropriate for scatterers on which dirichlet boundary conditions are applied in the limit as the ratio of wavelength to body size tends to infinity the problem is also relevant to the scattering of an e polarized electromagnetic wave by an array of highly conducting wires the actual geometry of each scatterer is characterized by a single parameter in the equations related to the single body scattering problem and determined from a harmonic boundary value problem using a mixture of analytical and numerical techniques we confirm that a number of phenomena reported for specific geometries are in fact present in the general case such as the presence of shadow boundaries in the far field and the vanishing of the circular wave scattered by the end of the array in certain specific directions we show that the semi infinite array problem is equivalent to that of inverting an infinite toeplitz matrix which in turn can be formulated as a discrete wiener hopf problem numerical results are presented which compare the amplitude of the wave diffracted by the end of the array for scatterers having different shapes

iteration theory of l index and multiplicity of brake orbits abstract in this paper we first establish the bott type iteration formulas and some abstract precise iteration formulas of the maslov type index theory associated with a lagrangian subspace for symplectic paths as an application we prove that there exist at least n 2 1 geometrically distinct brake orbits on every c 2 compact convex symmetric hypersurface in r 2 n satisfying the reversible condition n furthermore if all brake orbits on this hypersurface are nondegenerate then there are at least n geometrically distinct brake orbits on it as a consequence we show that there exist at least n 2 1 geometrically distinct brake orbits in every bounded convex symmetric domain in r n furthermore if all brake orbits in this domain are nondegenerate then there are at least n geometrically distinct brake orbits in it in the symmetric case we give a positive answer to the seifert conjecture of 1948 under a generic condition

examples with minimal number of brake orbits and homoclinics in annular potential regions abstract we use a geometric construction to exhibit examples of autonomous lagrangian systems admitting exactly two homoclinics emanating from a nondegenerate maximum of the potential energy and reaching a regular level of the potential having the same value of the maximum point similarly we show examples of hamiltonian systems that admit exactly two brake orbits in an annular potential region connecting the two connected components of the boundary of the potential well these examples show that the estimates proven in 2 are sharp

wave diffraction by semi infinite venetian blind type grating the h polarized electromagnetic wave diffraction by semi infinite periodic venetian blind type grating is considered the grating consists of strips placed in the parallel planes the problem is reduced to a nonlinear operator equation with respect to the unknown reflection operator of a structure for its solution a complex approach which consists in using the successive over relaxation method and the gauss seidel method is suggested the near and far fields scattered by the grating are calculated the dependences of the reflection coefficient and diffraction patterns are analyzed for different incidence angles width of strips and distance between them

multiple brake orbits and homoclinics in riemannian manifolds let m g be a complete riemannian manifold omega subset m an open subset whose closure is homeomorphic to an annulus we prove that if is smooth and it satisfies a strong concavity assumption then there are at least two distinct geodesics in overline omega omega cup partial omega starting orthogonally to one connected component of and arriving orthogonally onto the other one using the results given in giambo et al adv differ equ 10 931 960 2005 we then obtain a proof of the existence of two distinct homoclinic orbits for an autonomous lagrangian system emanating from a nondegenerate maximum point of the potential energy and a proof of the existence of two distinct brake orbits for a class of hamiltonian systems under a further symmetry assumption the result is improved by showing the existence of at least dim m pairs of geometrically distinct geodesics as above brake orbits and homoclinic orbits in our proof we shall use recent deformation results proved in giambo et al nonlinear anal ser a theory methods appl 73 290 337 2010

electromagnetic wave diffraction by semi infinite strip grating a nonlinear operator equation in terms of the operator of reflection by a plane periodic semi infinite grating of thin metal strips is obtained for the h polarized electromagnetic wave incidence this equation is solved numerically for an incident plane wave the algorithm created allows the solution of a nonlinear operator equation in the fourier amplitude of the reflected field with the method of successive iterations the initial approach chosen is substantiated and the solution convergence is numerically verified the field reflected by a semi infinite grating is calculated and analyzed for different numerical values of the exciting wave angle of incidence the strip width and the incident field wavelength

reciprocal processes on a tree modeling and estimation issues motivated by multiresolution decomposition methods such as the discrete wavelet transformation the authors introduce reciprocal processes on truncated n ary trees the authors discuss the relationship between such processes and nearest neighbor models the authors show that they can derive a recursive description of the process and that all reciprocal processes on n ary trees reduce to autoregressive processes in the case of zero valued boundary values at the bottom of the tree corresponding to truncation of the tree the authors then study the smoothing equations associated with such models

multiscale autoregressive processes i schur levinson parametrizations in many applications it is of interest to analyze and recognize phenomena occurring at different scales the recently introduced wavelet transforms provide a time and scale decomposition of signals that offers the possibility of such analysis a corresponding statistical framework to support the development of optimal multiscale statistical signal processing algorithms is described the theory of multiscale signal representation leads naturally to models of signals on trees and this provides the framework for investigation in particular the class of isotropic processes on homogeneous trees is described and a theory of autoregressive models is developed in this context this leads to generalizations of schur and levinson recursions associated properties of the resulting reflection coefficients and the initial pieces in a system theory for multiscale modeling

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed