singular continuous spectrum for palindromic schrodinger operators we give new examples of discrete schrodinger operators with potentials taking finitely many values that have purely singular continuous spectrum if the hullx of the potential is strictly ergodic then the existence of just one potentialx inx for which the operator has no eigenvalues implies that there is a generic set inx for which the operator has purely singular continuous spectrum a sufficient condition for the existence of such anx is that there is az x that contains arbitrarily long palindromes thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset inx the class includes well known substitutions like fibonacci thue morse period doubling binary non pisot and ternary non pisot we also show that the operator has no absolutely continuous spectrum for allx x ifx derives from a primitive substitution for potentials defined by circle maps x n 1 j 0 n we show that the operator has purely singular continuous spectrum for a generic subset inx for all irrational and every half open intervalj

patrolling a perimeter abstract in this paper we study the problem of patrolling a perimeter the general situation considered here can correspond to different tactical problems and it is studied from the point of view of game theory to put the ideas in a context we describe it as follows an intruder seeks to carry out a sabotage on the perimeter of a protected zone he has to perform the action along n consecutive days and has to position himself each day at one of m strategic points placed on this border the first day he can take his place at any of the m points but on successive days he can move only to adjacent points furthermore the perimeter is protected by a patroller who will select each day one of the m points to inspect the strategic situation is modeled as a two person zero sum game which is developed on a cyclic set of m points over n time units we prove some interesting properties of the strategies solve the game in closed form under certain constraints and obtain bounds for the value of the game in several non solved cases

the transformation of polynomial eigenfunctions of linear second order difference operators a special case of meixner polynomials as polynomial eigenfunctions of a linear second order difference operator a special case of the meixner polynomials m 2 c n x 1 is transformed explicitly into new complete sequences of non classical orthogonal polynomials

positive lyapunov exponents for schrodinger operators with quasi periodic potentials we present a new simple way to estimate the rate of exponential growth lyapunov exponent of solutions of the finite difference schrodinger equation h e psi n mathop limits def psi n 1 psi n 1 lambda f alpha n theta psi n heref is a non constant real analytic function of period 1 and is irrational for large we prove that the lyapunov exponent is positive for every energye in the spectrum ofh and a e in particular the absolutely continuous spectrum ofh is empty in the continuum we study the quasi periodic operator onl2 r h frac d 2 dx 2 k 2 cos x cos alpha x theta for largek and show that for wide intervals of low energies the lyapunov exponent is positive the main idea which originated from m herman s subharmonic argument 11 is to deform the phase to the complex plane this enables us to avoid small denominator problems by moving them off the axis making estimates much easier to perform we recover the information for real using an elementary extension of jensen s formula subharmonicity

characterization theorem for laguerre hahn orthogonal polynomials on non uniform lattices abstract a characterization theorem for laguerre hahn orthogonal polynomials on non uniform lattices is stated and proved this theorem proves the equivalence between the riccati equation for the formal stieltjes function linear first order difference relations for the orthogonal polynomials as well as for the associated polynomials of the first kind and linear first order difference relations for the functions of the second kind

holder continuity of the spectral measures for one dimensional schrodinger operator in exponential regime avila and jitomirskaya prove that the spectral measure v xf of quasi periodic schrodinger operator is 1 2 holder continuous with appropriate initial vector f if satisfies diophantine condition and is small in the present paper the conclusion is extended to that for all with the spectral measure v xf is 1 2 holder continuous with small if v is real analytic in a neighbor of x c where c is a large absolute constant in particular the spectral measure xf of almost mathieu operator is 1 2 holder continuous if e c with c a large absolute constant

epipolar plane image analysis an approach to determining structure from motion we present a technique for building a three dimensional description of a static scene from a dense sequence of images these images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image the technique utilizes knowledge of the camera motion to form and analyze slices of this solid these slices directly encode not only the three dimensional positions of objects but also such spatiotemporal events as the occlusion of one object by another for straight line camera motions these slices have a simple linear structure that makes them easier to analyze the analysis computes the three dimensional positions of object features marks occlusion boundaries on the objects and builds a three dimensional map of free space in our article we first describe the application of this technique to a simple camera motion and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects

diagonalization of certain integral operators abstract we study integral representations of formal inverses of the differential operator and the askey wilson divided difference operators in different polynomial bases the eigenvalues are related to zeros of bessel functions q bessel functions and confluent hypergeometric functions the eigenfunctions are exponential functions and in the case of the askey wilson operator are new types of q exponential functions we also found new q analogs of the sine and cosine functions

robust and dense depth estimation for light field images we propose a depth estimation method for light field images light field images can be considered as a collection of 2d images taken from different viewpoints arranged in a regular grid we exploit this configuration and compute the disparity maps between specific pairs of views this computation is carried out by a state of the art two view stereo method providing a nondense disparity estimation we propose a disparity interpolation method increasing the density and improving the accuracy of this initial estimate disparities obtained from several pairs of views are fused to obtain a unique and robust estimation finally different experiments on synthetic and real images show how the proposed method outperforms the state of the art results

reflection symmetries of almost periodic functions abstract we study global reflection symmetries of almost periodic functions in the non limit periodic case we establish an upper bound on the haar measure of the set of those elements in the hull which are almost symmetric about the origin as an application of this result we prove that in the non limit periodic case the criterion of jitomirskaya and simon ensuring absence of eigenvalues for almost periodic schrodinger operators is only applicable on a set of zero haar measure we complement this by giving examples of limit periodic functions where the jitomirskaya simon criterion can be applied to every element of the hull

variational calculus on q nonuniform lattices abstract we introduce the variational calculus on q nonuniform lattices in particular we discuss the basic concepts such as the euler lagrange equation and its applications to the isoperimetric the lagrange and the optimal control problems on q nonuniform lattices

searching for an agent who may or may not want to be found there is an extensive theory regarding optimal continuous path search for a mobile or immobile target the traditional theory assumes that the target is one of three types i an object with a known distribution of paths ii a mobile or immobile hider who wants to avoid or delay capture or iii a rendezvouser who wants to find the searcher this paper introduces a new type of search problem by assuming that aims of the target are not known to the searcher the target may be either a type iii cooperator with a known cooperation probabilityc or a type ii evader this formulation models search problems like that for a lost teenager who may be a runaway or a lost intelligence agent who may be a defector in any given search context it produces a continuum of search problems g c 0 c 1 linking a zero sum searchgame withc 0 to a rendezvous problem withc 1 these models thus provide a theoretical bridge between two previously distinct parts of search theory namely searchgames and rendezvous search

singular continuous spectrum is generic in a variety of contexts we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators those with singular spectrum are a dense g delta

two point one sided rendezvous abstract in a rendezvous search two or more teams called seekers try to minimize the time needed to find each other in this paper we consider two seekers in the plane this is a one sided problem since seeker 1 begins at a predetermined point o seeker 2 begins at one of a finite set of points x i with probability p i we first discuss the general situation and then consider the specific case when seeker 2 can begin from one of two points

localization for a class of one dimensional quasi periodic schrodinger operators we prove for small and satisfying a certain diophantine condition the operator h varepsilon 2 delta frac 1 2 pi cos 2 pi j alpha theta j in mathbb z has pure point spectrum for almost all a similar result is established at low energy for h frac d 2 dx 2 k 2 cos 2 pi x cos 2 pi alpha x theta providedk is sufficiently large

second phase transition line we study the phase transion line of the almost mathieu operator that separates arithmetic regions corresponding to singular continuous and a e pure point regimes and prove that both purely singular continuous and a e pure point spectrum occur for dense sets of frequencies

anderson localization for the almost mathieu equation a nonperturbative proof we prove that for any diophantine rotation angle and a e phase the almost mathieu operator h n n 1 n 1 cos 2 n n has pure point spectrum with exponentially decaying eigenfunctions for 15 we also prove the existence of some pure point spectrum for any 5 4

a linear programming approach to the search game on a network with mobile hider this paper discusses a search game on a network q with two players a searcher and a hider who each move with continuous trajectories starting from different points subject to a maximal speed and termination time t this is a zero sum game with payoff given by the time elapsed until the searcher reaches a point that is occupied by the hider if this happens and t otherwise the problem is formulated as an infinite dimensional linear program and the extreme points and the reduced cost functional are studied an algorithm is derived for this problem and how it works on an example is demonstrated

geometric occlusion analysis in depth estimation using integral guided filter for light field image unlike traditional multi view images sampling in angular domain of light field images is distributed in different directions therefore an angular sampling image asi comprising of possible matching points extracted from each view is available for each point in this paper we analyze the geometric relationship between asis and reference sub aperture images and then prove the occlusion boundary similarity based on the geometric relationship in extreme cases we show that some points in asi have higher reliability than other points for depth calculation an integral guided filter is then built based on the sub aperture image to predict occlusion probabilities in asis the filter is independent of asis and has no requirement for high angular resolution so that it is easy to apply to the cost volume calculation we integrate the filter into our depth estimation framework and other state of the art depth estimation frameworks experimental results demonstrate that the proposed filter is more effective to occluded point detection in asis than other methods results from different data sets show that our method outperforms the existing state of the art depth estimation methods especially along occlusion boundaries

discrete darboux transformation for discrete polynomials of hypergeometric type the darboux transformation well known in second order differential operator theory is applied to the difference equations satisfied by the discrete hypergeometric polynomials charlier meixner kravchuk hahn

infiltration games on arbitrary graphs the purpose of this note is to extend the work of lalley l and auger a on infiltration games on certain classes of graphs to an arbitrary graph by a simple application of menger s theorem h theorem 5 91 infiltration games as proposed by gal g sect 4 61 and generalized by auger a are determined by specifying two vertices a and b of a connected graph g and a capture probability 1 2 in the infiltration game r f g a b 2 the infiltrator chooses a path p a p o p l p t b from a to b in g of any length and the guard chooses a map g 1 2 v a b where v denotes the vertex set of g the interpretation is that at time t the infiltrator and guard are at the vertices p t and g t and the guard will capture the inliltrato i with probability 1 a if they coincide in the zero sum game r the payoff i7 is the probability that the infiltrator maximizer safely reaches the target vertex b z7 p g a where q is the number of times p and g coincide in some versions a time bound n is put on the length t of infiltrator paths p and the game is denoted f g a b 1 n related searchlight games are discussed in bb opl op2 r recently auger a has extended the work of lalley l by giving a complete solution for arbitrary time bounds n of the infiltration games on the graphs l lk mi m2 mk consisting of two vertices a and b joined by k vertex disjoint paths with m mk total m c mi interior vertices the value of the game t l a b a n is given by

pure point spectrum under 1 parameter perturbations and instability of anderson localization we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic fora we study the set of all eigenvalues of the operatora t a tp t that belong to its essential spectrum which does not depend on the parametert we prove that this set is empty for a dense set of values oft then we apply this result or its idea to questions of anderson localization for 1 dimensional schrodinger operators discrete and continuous

rational spectral transformations and orthogonal polynomials abstract we show that generic rational transformations of the stieltjes function with polynomial coefficients st can be presented as a finite superposition of four fundamental elementary transforms christoffel transform ct geronimus transform gt and forward and backward associated transformations a t a t it is shown that the laguerre hahn polynomials lhp on arbitrary nonuniform lattice are covariant with respect to st i e st of a lhp yields another lhp whereas the semi classical polynomials are covariant with respect to a subclass of linear st some applications of these results to the theory of the semi classical polynomials are considered

on ruckle s conjecture on accumulation games in an accumulation game the hider secretly distributes his given total wealth h among n locations while the searcher picks r locations and confiscates the material placed there the hider wins if what is left at the remaining n r locations is at least 1 otherwise the searcher wins ruckle s conjecture says that an optimal hider strategy is to put an equal amount h k at k randomly chosen locations for some k we extend the work of kikuta and ruckle by proving the conjecture for several cases e g r 2 or n 2 n leq7 n 2r 1 h leq2 1 n r and n leq2r the last result uses the erdos ko rado theorem we establish a connection between ruckle s conjecture and the hoeffding problem of bounding tail probabilities of sums of random variables

diagonalizaton of certain integral operators ii abstract we establish an integral representation of a right inverse of the askey wilson finite difference operator in an l 2 space weighted by the weight function of the continuous q jacobi polynomials we characterize the eigenvalues of this integral operator and prove a q analog of the expansion of e ixy in jacobi polynomials of argument x we also outline a general procedure of finding integral representations for inverses of linear operators

special nonuniform lattice snul orthogonal polynomials on discrete dense sets of points difference calculus compatible with polynomials i e such that the divided difference operator of first order applied to any polynomial must yield a polynomial of lower degree can only be made on special lattices well known in contemporary q calculus orthogonal polynomials satisfying difference relations on such lattices are presented in particular lattices which are dense on intervals q 1 are considered

light field reconstruction using shearlet transform in this article we develop an image based rendering technique based on light field reconstruction from a limited set of perspective views acquired by cameras our approach utilizes sparse representation of epipolar plane images epi in shearlet transform domain the shearlet transform has been specifically modified to handle the straight lines characteristic for epi the devised iterative regularization algorithm based on adaptive thresholding provides high quality reconstruction results for relatively big disparities between neighboring views the generated densely sampled light field of a given 3d scene is thus suitable for all applications which require light field reconstruction the proposed algorithm compares favorably against state of the art depth image based rendering techniques and shows superior performance specifically in reconstructing scenes containing semi transparent objects

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

operators with singular continuous spectrum i general operators the baire category theorem implies that the family f of dense sets g in fixed metric space x is a candidate for generic sets since it is closed under countable intersections and if x is perfect has no isolated point then a f has uncountable intersections with any open ball in x

the factorization method for the askey wilson polynomials a special infeld hull factorization is given for the askey wilson second order q difference operator it is then shown how to deduce a generalization of the corresponding askey wilson polynomials c 1999 elsevier science b v all rights reserved

static search games played over graphs and general metric spaces we define a general game which forms a basis for modelling situations of static search and concealment over regions with spatial structure the game involves two players the searching player and the concealing player and is played over a metric space each player simultaneously chooses to deploy at a point in the space the searching player receiving a payoff of 1 if his opponent lies within a predetermined radius r of his position the concealing player receiving a payoff of 1 otherwise the concepts of dominance and equivalence of strategies are examined in the context of this game before focusing on the more specific case of the game played over a graph methods are presented to simplify the analysis of such games both by means of the iterated elimination of dominated strategies and through consideration of automorphisms of the graph lower and upper bounds on the value of the game are presented and optimal mixed strategies are calculated for games played over a particular family of graphs

fugitive search games on graphs and related parameters abstract the goal of a fugitive search game on a graph is to trap a fugitive that hides on the vertices of the graph by systematically placing searchers on the vertices the fugitive is assumed to have complete knowledge of the graph and of the searchers moves but is restricted to move only along paths whose vertices are not guarded by searchers the search number of the graph is the least number of searchers necessary to trap the fugitive variants of the fugitive search game have been related to important graph parameters like treewidth and pathwidth in this paper we introduce a class of fugitive search games where the searchers do not see the fugitive and the fugitive can only move just before a searcher is placed on the vertex it occupies letting the fugitive s speed i e the maximum number of edges the fugitive can traverse at a single move vary we get different games we show that if the speed of the fugitive is unbounded then the search number minus 1 is equal to the treewidth of the graph while if the speed is 1 then the search number minus 1 is equal to a polynomially computable graph parameter which is called width or alternatively linkage and is studied in the context of the constraint satisfaction and boolean satisfiability problems we also show that in the above two cases the search number remains the same even if we consider only search strategies that at every step further restrict the fugitive s possible resorts this monotonicity property is usually expressed as recontamination does not help moreover we give an equivalent characterization of the search number for any given fugitive speed in terms of an elimination ordering of the vertices of the graph using this characterization we show that for any graph if the length of any chordless cycle is bounded by a constant s s 3 then the treewidth of the graph plus 1 is equal to the search number for fugitive speed s 2

operators with singular continuous spectrum ii rank one operators for an operator a with cyclic vector we studya p wherep is the rank one projection onto multiples of if spec a anda has no a c spectrum we prove thata p has purely singular continuous spectrum on for a denseg of s

recontamination does not help to search a graph this paper is concerned with a game on graphs called graph searching the object of this game is to clear all edges of a contaminated graph clearing is achieved by moving searchers a kind of token along the edges of the graph according to clearing rules certain search strategies cause edges that have been cleared to become contaminated again megiddo et al 9 conjectured that every graph can be searched using a minimum number of searchers without this recontamination occurring that is without clearing any edge twice in this paper this conjecture is proved this places the graph searching problem in np completing the proof by megiddo et al that the graph searching problem is np complete furthermore by eliminating the need to consider recontamination this result simplifies the analysis of searcher requirements with respect to other properties of graphs

minimax rendezvous on the line suppose that n players are placed randomly on the real line at consecutive integers and faced in random directions each player has maximum speed one cannot see the others and doesn t know his relative position what is the minimum time m n required to ensure that all the players can meet together at a single point regardless of their initial placement we prove that m 2 3 m 3 4 and m n is asymptotic to n 2 we also consider a variant of the problem which requires players who meet to stick together and find in this case that three players require 5 time units to ensure a meeting this paper is thus a minimax version of the rendezvous search problem which has hitherto been studied only in terms of minimizing the expected meeting time

the princess and monster game on an interval a minimizing searcher s and a maximizing hider h move at unit speed on a closed interval until the first capture or payoff time t min t s t h t that they meet this zero sum princess and monster game or less colorfully search game with mobile hider was proposed by rufus isaacs for general networks q while the existence and finiteness of the value v v q has been established for such games only the circle network has been solved value and optimal mixed strategies it seems that the interval network q 1 1 had not been studied because it was assumed to be trivial with value 3 2 and obvious searcher mixed strategy going equiprobably from one end to the other we establish that this game is in fact nontrivial by showing that v 3 2 using a combination of continuous and discrete mixed strategies for both players we show that 15 11 leq v leq 13 9 the full solution of this very simple game is still open and appears difficult though many properties of the optimal strategies are derived here

spectral transformation chains and some new biorthogonal rational functions a discrete time chain associated with the generalized eigenvalue problem for two jacobi matrices is derived various discrete and continuous symmetries of this integrable equation are revealed a class of its rational elementary and elliptic functions solutions appearing from a similarity reduction are constructed the latter lead to large families of biorthogonal rational functions based upon the very well poised balanced hypergeometric series of three types the standard hypergeometric series 9 f 8 basic series 10 9 and its elliptic analogue 10 e 9 for an important subclass of the elliptic biorthogonal rational functions the weight function and normalization constants are determined explicitly

the rendezvous search problem the author considers the problem faced by two people who are placed randomly in a known search region and move about at unit speed to find each other in the least expected time this time is called the rendezvous value of the region it is shown how symmetries in the search region may hinder the process by preventing coordination based on concepts such as north or clockwise a general formulation of the rendezvous search problem is given for a compact metric space endowed with a group of isometrics which represents the spatial uncertainties of the players these concepts are illustrated by considering upper bounds for various rendezvous values for the circle and an arbitrary metric network the discrete rendezvous problem on a cycle graph for players restricted to symmetric markovian strategies is then solved finally the author considers the problem faced by two people on an infinite line who each know the distribution of the distance but not the direction to each other

stereo matching using belief propagation in this paper we formulate the stereo matching problem as a markov network and solve it using bayesian belief propagation the stereo markov network consists of three coupled markov random fields that model the following a smooth field for depth disparity a line process for depth discontinuity and a binary process for occlusion after eliminating the line process and the binary process by introducing two robust functions we apply the belief propagation algorithm to obtain the maximum a posteriori map estimation in the markov network other low level visual cues e g image segmentation can also be easily incorporated in our stereo model to obtain better stereo results experiments demonstrate that our methods are comparable to the state of the art stereo algorithms for many test cases

rendezvous on a planar lattice we analyze the optimal behavior of two players who are lost on a planar surface and who want to meet each other in least expected time they each know the initial distribution of the other s location but have no common labeling of points and so cannot simply go to a location agreed to in advance they have no compasses so do not even have a common notion of north for simplicity we restrict their motions to the integer lattice z2 graph paper and their motions to horizontal and vertical directions as in the original work of anderson and fekete 2001

rendezvous search on the line with distinguishable players two players are placed on the real line at a distance d with a distribution f known to both neither knows the direction of the other nor do they have a common notion of a positive direction on the line we seek the least expected rendezvous time r r left f right in which they can meet given maximum speeds of one we consider the cases where f is a bounded point discrete or finite mean distribution we obtain upper bounds or exact values for r and in one case an optimality condition for search strategies a connection with beck s linear search problem is established

on search games that include ambush we present a stochastic game that models ambush search in a finite region q which has area but no other structure the searcher can search a unit area of q in unit time or adopt an ambush mode for a certain period the searcher captures the hider when the searched region contains the hider s location or if the hider moves while the searcher is in ambush mode the payoff in this zero sum game is the capture time our game is motivated by the still unsolved princess and monster game on a star graph with a large number of leaves

sharp phase transitions for the almost mathieu operator it is known that the spectral type of the almost mathieu operator amo depends in a fundamental way on both the strength of the coupling constant and the arithmetic properties of the frequency we study the competition between those factors and locate the point where the phase transition from singular continuous spectrum to pure point spectrum takes place which solves jitomirskaya s conjecture together with a previous work by avila this gives the sharp description of phase transitions for the amo for the a e phase

search hide games on trees abstract in this paper we consider search hide games on trees there are two players player h the hider or inspectee selects one of m vertices of the tree for hiding undeclared objects permanently player i the inspector is allowed to search some vertices of the tree trying to find the hidden objects however player i can only examine exactly k m vertices lying on a subtree with k vertices because of certain limitations player i wants to maximize the probability of detecting the undeclared objects and player h to minimize it this problem can be described by a fractional covering problem fc and its dual dfc an algorithm based on the revised simplex method with implicit column generation is proposed for solving fc and dfc the all possible strategies of the player i all possible subtree with k vertices is not necessary listed explicitly in order to find a profitable column a polynomial algorithm is developed by utilizing the structure of the underlying tree

raid games across a set with cyclic order abstract in this paper we shall deal with two person zero sum games where the strategies of the players are intervals on a set with cyclic order and the payoff function is a function depending on the intersection of the strategies for the players these games correspond to similar tactical problems we give a general method to obtain a solution of the discrete games of this kind this method is applied to solve the games with monotonic payoff function and a game with no monotonic one we also solve a continuous game

operators with singular continuous spectrum iii almost periodic schrodinger operators we prove that one dimensional schrodinger operators with even almost periodic potential have no point spectrum for a dense g in the hull this implies purely singular continuous spectrum for the almost mathieu equation for coupling larger than 2 and a dense g in even if the frequency is an irrational with good diophantine properties

orthogonal polynomials on systems of non uniform lattices from compatibility conditions abstract we deduce difference equations in the matrix form for laguerre hahn orthogonal polynomials on systems of non uniform lattices the so called compatibility conditions involving the transfer matrices as a consequence we obtain closed form expressions for the recurrence relation coefficients of the laguerre hahn polynomials of class zero

ambush strategies in search games on graphs a blind searcher and a blind hider move at below unit speed along a finite length graph q known to both until the first time t when they meet a two person zero sum game arises if the searcher pays the hider t units we consider circumstances under which it may be optimal for the searcher to lie in wait at a node of q hoping the hider will come to him we also explicitly define a notion of equilibrium in distribution for such games which has been implicit in the literature we show that for the graph consisting of two nodes connected by three arcs of equal length there are optimal ambush strategies but there is no equilibrium in distribution

a search game when a search path is given abstract in this paper we investigate a search game in discrete time and space a searcher is given a search path in advance and his look on the path is determined by a randomized look strategy a target selects a path from some options the searcher gains a value on the detection of the target but expends search cost by the look a pay off function of the game for the searcher is the expected reward which is defined as the expected value minus the expected search cost first we show a recursive relation for the conditional optimal look strategy of the searcher given a target path we prove its np completeness though it looks simple and clarify some characteristics of the solution then our original continuous game is converted to a matrix game from these facts we consider a relationship between the game and the one sided optimizing problem and examine some examples

occlusion aware depth estimation for light field using multi orientation epis abstract epipolar plane images epis contain special linear structures that reflect the disparity of a 3d point and are widely used in light field depth estimation however previous epi based approaches only utilize horizontal and vertical epis to estimate local disparities and ignore diagonal directions in order to make full use of the regular grid light field images we develop a strategy to extract epipolar plane images in all available directions based on the multi orientation epis a specific epi in which the point is not occluded is found and used to calculate robust depth estimation we also design a novel framework to estimate the depth information which combines the local depth with edge orientation the multi orientation epis and optimal orientation selection are proved to be effective in detecting and excluding occlusions experimental results show that the proposed method outperforms state of the art depth estimation methods especially near occlusion boundaries

spectral transformations self similar reductions and orthogonal polynomials we study spectral transformations in the theory of orthogonal polynomials which are similar to darboux transformations for the schr dinger equation linear transformations of the stieltjes function with coefficients that are rational in the argument are constructed as iterations of the christoffel and geronimus transformations we describe a characteristic property of semi classical orthogonal polynomials scop on the uniform and the exponential lattice namely that all these polynomials can be obtained through simple quasi periodic and q periodic self similar closures of the chain of linear spectral transformations in the self similar setting a characterization of the laguerre hahn polynomials on linear and q linear lattices is obtained by considering rational transformations of the stieltjes function generated by transitions to the associated polynomials

a generalization of ruckle s results for an ambush game abstract this article considers a two person zero sum game in which a traveller player i chooses a point in the closed unit interval 0 1 so as to minimise the probability of being ambushed by two obstacles placed there by his adversary player ii the payoff to player i equals 1 if the point chosen by him is not in either of the intervals chosen by player ii and 0 otherwise this paper complements the results obtained by ruckle baston and bostock and lee

quantum models with spectrum generated by the flows of polynomial zeros a class of purely bosonic models is characterized having the following properties in a hilbert space of analytic functions i wave function is the generating function for orthogonal polynomials of a discrete energy variable ii any hamiltonian has nondegenerate purely point spectrum that corresponds to infinite discrete support of measure in the orthogonality relation of the polynomials iii the support is determined exclusively by the points of discontinuity of iv the spectrum of can be numerically determined as fixed points of monotonic flows of the zeros of orthogonal polynomials v one can compute practically an unlimited number of energy levels e g in double precision if a model of is exactly solvable its spectrum can only assume one of four qualitatively different types the results are applied to spin boson quantum models that are at least partially diagonalizable and have at least single one dimensional irreducible component in the spin subspace examples include the rabi model and its various generalizations

variational light field analysis for disparity estimation and super resolution we develop a continuous framework for the analysis of 4d light fields and describe novel variational methods for disparity reconstruction as well as spatial and angular super resolution disparity maps are estimated locally using epipolar plane image analysis without the need for expensive matching cost minimization the method works fast and with inherent subpixel accuracy since no discretization of the disparity space is necessary in a variational framework we employ the disparity maps to generate super resolved novel views of a scene which corresponds to increasing the sampling rate of the 4d light field in spatial as well as angular direction in contrast to previous work we formulate the problem of view synthesis as a continuous inverse problem which allows us to correctly take into account foreshortening effects caused by scene geometry transformations all optimization problems are solved with state of the art convex relaxation techniques we test our algorithms on a number of real world examples as well as our new benchmark data set for light fields and compare results to a multiview stereo method the proposed method is both faster as well as more accurate data sets and source code are provided online for additional evaluation

rational interpolation to solutions of riccati difference equations on elliptic lattices it is shown how to define difference equations on particular lattices x n email protected z where the x ns are values of an elliptic function at a sequence of arguments in arithmetic progression elliptic lattice solutions to special difference equations elliptic riccati equations have remarkable simple interpolatory continued fraction expansions

schrodinger operators in the twentieth century this paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics

optimal trade off between speed and acuity when searching for a small object a searcher seeks to find a stationary hider located at some point h not necessarily a node on a given network q the searcher can move along the network from a given starting point at unit speed but to actually find the hider she must pass it while moving at a fixed slower speed which may depend on the arc in this bimodal search game the payoff is the first time the searcher passes the hider while moving at her slow speed this game models the search for a small or well hidden object e g a contact lens improvised explosive device predator search for camouflaged prey we define a bimodal chinese postman tour as a tour of minimum time i which traverses every point of every arc at least once in the slow mode for trees and weakly eulerian networks networks containing a number of disjoint eulerian cycles connected in a tree like fashion the value of the bimodal search game is i 2 for trees the optimal hider strategy has full support on the network this differs from traditional search games where it is optimal for him to hide only at leaf nodes we then consider the notion of a lucky searcher who can also detect the hider with a positive probability q even when passing him at her fast speed this paper has particular importance for demining problems

search games on trees with asymmetric travel times a point h is hidden in a rooted tree q which is endowed with asymmetric distances travel times between nodes we determine the randomized search strategy starting from the root which minimizes the expected time to reach h in the worst case this is equivalent to a zero sum search game gamma left q right with minimizing searcher maximizing hider and payoff equal to the capture time the worst hiding distribution over the leaves from the searcher s viewpoint is one where at every node i the probability of each branch is proportional to the minimum time required to tour it from i the optimal randomized search is a mixture over depth first searches we also consider briefly some other networks and the possibility of a mobile hider our formulation with asymmetric travel times generalizes that of gal siam j control optim 17 1979 pp 99 122 for symmetric travel times and also the search games of kikuta j oper res 38 1995 pp 70 88 and kikuta and ruckle naval res logist 41 1994 pp 821 831 who posited search costs c i at each node i which were added to the travel time to obtain the payoff we also briefly consider what happens if we allow the searcher hider to start hide at any leaf node we determine when properties found by dagan and gal networks 52 2008 pp 156 161 for the symmetric version of such games hold in our asymmetric context

continuous depth map reconstruction from light fields in this paper we investigate how the recently emerged photography technology the light field can benefit depth map estimation a challenging computer vision problem a novel framework is proposed to reconstruct continuous depth maps from light field data unlike many traditional methods for the stereo matching problem the proposed method does not need to quantize the depth range by making use of the structure information amongst the densely sampled views in light field data we can obtain dense and relatively reliable local estimations starting from initial estimations we go on to propose an optimization method based on solving a sparse linear system iteratively with a conjugate gradient method two different affinity matrices for the linear system are employed to balance the efficiency and quality of the optimization then a depth assisted segmentation method is introduced so that different segments can employ different affinity matrices experiment results on both synthetic and real light fields demonstrate that our continuous results are more accurate efficient and able to preserve more details compared with discrete approaches

stochastic search in a convex region a stochastic search strategy is proposed for locating a possibility mobile target in a bounded convex region of the plane the strategy is asymptotically minimax as e 0 with respect to the time required to get within e of the target the proof involves the study of first passages to time dependent boundaries by a certain semi markov process

global stereo reconstruction under second order smoothness priors second order priors on the smoothness of 3d surfaces are a better model of typical scenes than first order priors however stereo reconstruction using global inference algorithms such as graph cuts has not been able to incorporate second order priors because the triple cliques needed to express them yield intractable nonsubmodular optimization problems this paper shows that inference with triple cliques can be effectively performed our optimization strategy is a development of recent extensions to alpha expansion based on the ldquo qpbordquo algorithm the strategy is to repeatedly merge proposal depth maps using a novel extension of qpbo proposal depth maps can come from any source for example frontoparallel planes as in alpha expansion or indeed any existing stereo algorithm with arbitrary parameter settings

depth estimation with occlusion modeling using light field cameras light field cameras have become widely available in both consumer and industrial applications however most previous approaches do not model occlusions explicitly and therefore fail to capture sharp object boundaries a common assumption is that for a lambertian scene a pixel will exhibit photo consistency which means all viewpoints converge to a single point when focused to its depth however in the presence of occlusions this assumption fails to hold making most current approaches unreliable precisely where accurate depth information is most important at depth discontinuities in this paper an occlusion aware depth estimation algorithm is developed the method also enables identification of occlusion edges which may be useful in other applications it can be shown that although photo consistency is not preserved for pixels at occlusions it still holds in approximately half the viewpoints moreover the line separating the two view regions occluded object versus occluder has the same orientation as that of the occlusion edge in the spatial domain by ensuring photo consistency in only the occluded view region depth estimation can be improved occlusion predictions can also be computed and used for regularization experimental results show that our method outperforms current state of the art light field depth estimation algorithms especially near occlusion boundaries