a matrix characterization for the dν semiclassical and dν coherent orthogonal polynomials abstract we present a new structure relation for the sequence of orthogonal polynomials associated with a d semiclassical linear functional of class s and then we use it to obtain a matrix characterization of the d semiclassical orthogonal polynomials in terms of the jacobi matrix associated with the multiplication operator in the basis of orthonormal polynomials and the nonsingular lower triangular matrix that represents the orthogonal polynomials with respect to some bases of polynomials we also provide a matrix characterization of d coherent pairs of linear functionals

a high resolution weighted ab semblance for dealing with amplitude variation with offset phenomenon abstractvelocity analysis is an essential step in seismic reflection data processing the conventional and fastest method to estimate how velocity changes with increasing depth is to calculate semblance coefficients traditional semblance has two problems low time and velocity resolution and an inability to handle amplitude variation with offset avo phenomenon although a method known as the ab semblance can arrive at peak velocities in the areas with an avo anomaly it has a lower velocity resolution than conventional semblance we have developed a weighted ab semblance method that can handle both problems simultaneously we have developed two new weighting functions to weight the ab semblance to enhance the resolution of velocity spectra in the time and velocity directions in this way we increase the time and velocity resolution while eliminating the avo problem the first weighting function is defined based on the ratio between the first and the second singular values of the time window to improve

companion orthogonal polynomials we give some properties relating the recurrence relations of orthogonal polynomials associated with any two symmetric distributions email protected 1 x and d 2 x such that email protected 2 x 1 kx 2 d 1 x as applications of properties recurrence relations for many interesting systems of orthogonal polynomials are obtained

asymptotics of sobolev orthogonal polynomials for hermite 1 1 coherent pairs abstract in this paper we will discuss asymptotic properties of monic polynomials s n x n 0 orthogonal with respect to the sobolev inner product p q s r p x q x d 0 r p x q x d 1 with 0 d 0 e x 2 d x d 1 x 2 a x 2 b e x 2 d x a b r and a b it is well known that 0 1 is a pair of symmetric 1 1 coherent measures this means that there exist sequences a n n n b n n n a n b n for every n n such that the algebraic relation h n x b n 2 h n 2 x q n x a n 2 q n 2 x n 2 is satisfied where q n x n 0 is the sequence of monic orthogonal polynomials associated with 1 and h n x n 0 is the sequence of monic hermite polynomials we will study the relative asymptotics for sobolev scaled polynomials and we will obtain mehler heine type formulas among others

signal and traveltime parameter estimation using singular value decomposition abstractsignal detection and traveltime parameter estimation can be performed by computing a coherence function in a data window centered around a traveltime function defined by its parameters we used singular value decomposition of the data matrix not eigendecomposition of a covariance matrix to review the most commonly used coherence measures this resulted in a new reduced semblance coefficient defined from the first eigenimage assuming that the signal amplitude was the same on all data channels as in classical semblance in a second signal model the time signal was constant on each channel but the amplitude changed then the semblance coefficient is the square of the first singular value divided by the energy of the data two normalized crosscorrelation coefficients derived from the first eigenimage can also be used as a coherence measure the normalized crosscorrelation of the spatial singular vector with a vector with all elements equal to one and the normalized crosscorrelation of the tem

m n coherent pairs of order m k and sobolev orthogonal polynomials a pair of regular linear functionals u v is said to be a m n coherent pair of order m k if their corresponding sequences of monic orthogonal polynomials p n x n 0 and q n x n 0 satisfy a structure relation such as i 0ma i np n m i m x i 0nb i nq n k i k x n 0 where a i n and b i n are complex numbers such that a m n 0 if n m b n n 0 if n n and a i n b i n 0 when i n in the first part of this work we focus our attention on the algebraic properties of an m n coherent pair of order m k to be more precise let us assume that m k if m k then u and v are related by a rational factor in the distributional sense if m k then u and v are semiclassical and they are again related by a rational factor in the second part of this work we deal with a sobolev type inner product defined in the linear space of polynomials with real coefficients p as l rp x q x d m 0 x l rp m x q m x d m 1 x p q p where l is a positive real number m is a positive integer number and m 0 m 1 is a m n coherent pair of order m of positive borel measures supported on an infinite subset of the real line meaning that the sequences of monic orthogonal polynomials p n x n 0 and q n x n 0 with respect to m 0 and m 1 respectively satisfy a structure relation as above with k 0 a i n and b i n being real numbers fulfilling the above mentioned conditions we generalize several recent results known in the literature in the framework of sobolev orthogonal polynomials and their connections with coherent pairs introduced in a iserles p e koch s p norsett j m sanz serna on polynomials orthogonal with respect to certain sobolev inner products j approx theory 65 2 1991 151 175 and their extensions in particular we show how to compute the coefficients of the fourier expansion of functions on an appropriate sobolev space defined by the above inner product in terms of the sequence of sobolev orthogonal polynomials s n x l n 0

the complexity of dominating set reconfiguration suppose that we are given two dominating sets d s and d t of a graph g whose cardinalities are at most a given threshold k then we are asked whether there exists a sequence of dominating sets of g between d s and d t such that each dominating set in the sequence is of cardinality at most k and can be obtained from the previous one by either adding or deleting exactly one vertex this decision problem is known to be pspace complete in general in this paper we study the complexity of this problem from the viewpoint of graph classes we first prove that the problem remains pspace complete even for planar graphs bounded bandwidth graphs split graphs and bipartite graphs we then give a general scheme to construct linear time algorithms and show that the problem can be solved in linear time for cographs forests and interval graphs furthermore for these tractable cases we can obtain a desired sequence if it exists such that the number of additions and deletions is bounded by o n where n is the number of vertices in the input graph

the complexity of rerouting shortest paths the shortest path reconfiguration problem has as input a graph g with unit edge lengths with vertices s and t and two shortest st paths p and q the question is whether there exists a sequence of shortest st paths that starts with p and ends with q such that subsequent paths differ in only one vertex this is called a rerouting sequence this problem is shown to be pspace complete for claw free graphs and chordal graphs it is shown that the problem can be solved in polynomial time and that shortest rerouting sequences have linear length for these classes it is also shown that deciding whether a rerouting sequence exists between all pairs of shortest st paths can be done in polynomial time finally a polynomial time algorithm for counting the number of isolated paths is given

complexity of independent set reconfigurability problems we study problems of reconfigurability of independent sets in graphs we consider three different models token jumping token sliding and token addition and removal and analyze relationships between them we prove that independent set reconfigurability in perfect graphs under any of the three models generalizes the shortest path reconfigurability problem in general graphs and is therefore pspace complete on the positive side we give polynomial results for even hole free graphs and p 4 free graphs

shortest paths between shortest paths a b s t r a c t we study the following problem on reconfiguring shortest paths in graphs given two shortest s t paths what is the minimum number of steps required to transform one into the other where each intermediate path must also be a shortest s t path and must differ from the previous one by only one vertex we prove that the shortest reconfiguration sequence can be exponential in the size of the graph and that it is np hard to compute the shortest reconfiguration sequence even when we know that the sequence has polynomial length 2011 elsevier b v all rights reserved

reconfiguration of list l 2 1 labelings in a graph for an integer k 0 suppose that each vertex v of a graph g has a set c v 0 1 k of labels called a list of v a list l 2 1 labeling of g is an assignment of a label in c v to each vertex v of g such that every two adjacent vertices receive labels which differ by at least 2 and every two vertices of distance two receive labels which differ by at least 1 in this paper we study the problem of reconfiguring one list l 2 1 labeling of a graph into another list l 2 1 labeling of the same graph by changing only one label assignment at a time while at all times maintaining a list l 2 1 labeling first we show that this decision problem is pspace complete even for bipartite planar graphs and k 6 in contrast we then show that the problem can be solved in linear time for general graphs if k 4 we finally consider the problem restricted to trees and give a sufficient condition for which any two list l 2 1 labelings of a tree can be transformed into each other

sobolev orthogonal polynomials and m n coherent pairs of measures we introduce the notion of m n coherent pair of measures as a generalization of the concept of coherent pair of measures introduced by iserles et al a iserles p e koch s p norsett j m sanz serna on polynomials orthogonal with respect to certain sobolev inner products j approx theory 65 2 1991 151 175 and subsequently generalized by several authors a pair of measures email protected 0 email protected 1 is called m n coherent if the corresponding orthogonal polynomial sequences p n n and q n n resp satisfy a non zero structure relation such as i 0nr i np n i x email protected i 0ms i nq n i 1 x for all n 0 1 2 where m and n are fixed non negative integer numbers and r i n and s i n are given real parameters satisfying some natural conditions we prove that the regular moment linear functionals associated to an m n coherent pair are semiclassical and they are related by a rational modification in the usual sense of distribution theory we also discuss the converse statement under the assumption that email protected 0 email protected 1 form an m n coherent pair we study the sequence s n l n of the monic orthogonal polynomials with respect to the sobolev inner product l email protected email protected email protected f g email protected 1 defined in the space of all polynomials with real coefficients where l 0 an efficient algorithm is stated to compute the coefficients in the fourier sobolev type series f x email protected n 0 c n ls n l x with respect to l for suitable smooth functions f such that email protected l m 0 2 r and f l m 1 2 r finally some illustrative computational examples are presented

the connectivity of boolean satisfiability computational and structural dichotomies boolean satisfiability problems are an important benchmark for questions about complexity algorithms heuristics and threshold phenomena recent work on heuristics and the satisfiability threshold has centered around the structure and connectivity of the solution space motivated by this work we study structural and connectivity related properties of the space of solutions of boolean satisfiability problems and establish various dichotomies in schaefer s framework on the structural side we obtain dichotomies for the kinds of subgraphs of the hypercube that can be induced by the solutions of boolean formulas as well as for the diameter of the connected components of the solution space on the computational side we establish dichotomy theorems for the complexity of the connectivity and st connectivity questions for the graph of solutions of boolean formulas our results assert that the intractable side of the computational dichotomies is pspace complete while the tractable side which includes but is not limited to all problems with polynomial time algorithms for satisfiability is in p for the st connectivity question and in conp for the connectivity question the diameter of components can be exponential for the pspace complete cases whereas in all other cases it is linear thus diameter and complexity of the connectivity problems are remarkably aligned the crux of our results is an expressibility theorem showing that in the tractable cases the subgraphs induced by the solution space possess certain good structural properties whereas in the intractable cases the subgraphs can be arbitrary

an exact algorithm for the boolean connectivity problem for k cnf we present an exact algorithm for a pspace complete problem denoted by connksat which asks whether the solution space for a given k cnf formula is connected on the n dimensional hypercube the problem is known to be pspace complete for k 3 and polynomial solvable for k 2 gopalan et al 2009 6 we show that connksat for k 3 is solvable in time o 2 e k n for some constant e k 0 where e k depends only on k but not on n this result is considered to be interesting due to the following fact shown by calabro 5 qbf 3 sat which is a typical pspace complete problem is not solvable in time o 2 e n for any constant e 0 provided that the sat problem with no restriction to the clause length is not solvable in time o 2 e n for any constant e 0

a partial k arboretum of graphs with bounded treewidth the notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies this survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class also some mutual relations between such classes are discussed

linear time algorithm for sliding tokens on trees suppose that we are given two independent sets i b and i r of a graph such that i b i r and imagine that a token is placed on each vertex in i b then the sliding token problem is to determine whether there exists a sequence of independent sets which transforms i b into i r so that each independent set in the sequence results from the previous one by sliding exactly one token along an edge in the graph this problem is known to be pspace complete even for planar graphs and also for bounded treewidth graphs in this paper we thus study the problem restricted to trees and give the following three results 1 the decision problem is solvable in linear time 2 for a yes instance we can find in quadratic time an actual sequence of independent sets between i b and i r whose length i e the number of token slides is quadratic and 3 there exists an infinite family of instances on paths for which any sequence requires quadratic length

velocity analysis using similarity weighted semblance weighted semblance can be used for improving the performance of traditional semblance for specific data sets we have developed a novel approach for prestack velocity analysis using weighted semblance the novelty came from a different weighting criteria in which the local similarity between each trace and a reference trace is used on the one hand low similarity corresponded to a noise point or a point indicating incorrect moveout which should be given a small weight on the other hand high similarity corresponded to a point indicating correct moveout that should be given a high weight our approach could also be effectively used for analyzing avo anomalies with increased resolution compared with ab semblance synthetic and field common midpoint gathers demonstrated higher resolution using the approach we developed applications of the proposed method on a prestack data set further confirmed that the stacked data using the similarity weighted semblance could obtain better energy focused events which indicated a more precise velocity picking

reconfiguration of colorable sets in classes of perfect graphs abstract a set of vertices in a graph is c colorable if the subgraph induced by the set has a proper c coloring in this paper we study the problem of finding a step by step transformation called a reconfiguration sequence between two c colorable sets in the same graph this problem generalizes the well studied independent set reconfiguration problem as the first step toward a systematic understanding of the complexity of this general problem we study the problem on classes of perfect graphs we first focus on interval graphs and give a combinatorial characterization of the distance between two c colorable sets this gives a linear time algorithm for finding an actual shortest reconfiguration sequence for interval graphs since interval graphs are exactly the graphs that are simultaneously chordal and co comparability we then complement the positive result by showing that even deciding reachability is pspace complete for chordal graphs and for co comparability graphs the hardness for chordal graphs holds even for split graphs we also consider the case where c is a fixed constant and show that in such a case the reachability problem is polynomial time solvable for split graphs but still pspace complete for co comparability graphs the complexity of this case for chordal graphs remains unsettled as by products our positive results give the first polynomial time solvable cases split graphs and interval graphs for feedback vertex set reconfiguration

on the complexity of reconfiguration problems reconfiguration problems arise when we wish to find a step by step transformation between two feasible solutions of a problem such that all intermediate results are also feasible we demonstrate that a host of reconfiguration problems derived from np complete problems are pspace complete while some are also np hard to approximate in contrast several reconfiguration versions of problems in p are solvable in polynomial time

on an extension of symmetric coherent pairs of orthogonal polynomials given two symmetric and positive definite linear functionals w and v we study the coefficients in the recurrence relation for the system of monic polynomials orthogonal with respect to the second linear functional assuming that the first one is classical and that there exists an algebraic differential relation between these two families of polynomials moreover we determine this companion linear functional as a rational modification of the classical one