2d and 3d elastic wavefield vector decomposition in the wavenumber domain for vti media a pragmatic decomposition of a vector wavefield into p and s waves is based on the helmholtz theory and the christoffel equation it is applicable to vti media when the plane wave polarization is continuous in the vicinity of a given wavenumber and is uniquely defined by that wavenumber except for the kiss singularities on the vti symmetry axis unlike divergence and curl which separate the wavefield into a scalar and a vector field the decomposed p and s wavefields are both vector fields with correct amplitude phase and physical units if the vector components of decomposed wavefields are added they reconstruct those of the original input wavefield wavefield propagation in any portions of a vti medium that have the same polarization distribution i e the same eigenvector in the wavenumber domain have the same decomposition operators and can be recon structed with a single 3d fourier transform for each operator e g one for p waves and one for s waves this applies to isotropic wavefields a

on the convergence of linear switched systems this paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems we provide a collection of results that use weak dwell time dwell time strong dwell time permanent and persistent activation hypothesis the obtained results are shown to be tight by counterexample finally we apply our result to the three cell converter

on the imaging of reflectors in the earth in this paper i present a modification of the beylkin inversion operator this modification accounts for the band limited nature of the data and makes the role of discontinuities in the sound speed more precise the inversion presented here partially dispenses with the small parameter constraint of the born approximation this is shown by applying the proposed inversion operator to upward scattered data represented by the kirchhoff approximation using the angularly dependent geometrical optics reflection coefficient a fully nonlinear estimate of the jump in sound speed may be extracted from the output of this algorithm interpreted in the context of these kirchhoff approximate data for the forward problem the inversion of these data involves integration over the source receiver surface the reflecting surface and frequency the spatial integrals are computed by the method of stationary phase the output is asymptotically a scaled singular function of the reflecting surface the singular function of a

invariance principles for hybrid systems with connections to detectability and asymptotic stability this paper shows several versions of the lasalle s invariance principle for general hybrid systems the broad framework allows for nonuniqueness of solutions zeno behaviors and does not insist on continuous dependence of solutions on initial conditions instead only a mild structural property involving graphical convergence of solutions is posed the general invariance results are then specified to hybrid systems given by set valued data further results involving invariance as well as observability detectability and asymptotic stability are given

convergence rate of nonlinear switched systems abstract this paper is concerned with the convergence rate of the solutions of nonlinear switched systems we first consider a switched system which is asymptotically stable for a class of switching signals but not for all switching signals we show that solutions corresponding to that class of switching signals converge arbitrarily slowly to the origin then we consider analytic switched systems for which a common weak quadratic lyapunov function exists under two different sets of assumptions we provide explicit exponential convergence rates for switching signals with a fixed dwell time

scalar reverse time depth migration of prestack elastic seismic data reflected p to p and p to s converted seismic waves in a two component elastic common source gather generated with a p wave source in a two dimensional model can be imaged by two independent scalar reverse time depth migrations the inputs to migration are pure p and s waves that are extracted by divergence and curl calculations during shallow extrapolation of the elastic data recorded at the earth s surface for both p to p and p to s converted reflected waves the imaging time at each point is the p wave traveltime from the source to that point the extracted p wave is reverse time extrapolated and imaged with a p velocity model using a finite difference solution of the scalar wave equation the extracted s wave is reverse time extrapolated and imaged similarly but with an s velocity model converted s wave data requires a polarity correction prior to migration to ensure constructive interference between data from adjacent sources synthetic examples show that the algorithm gives satisfactory resul

elastic least squares one way wave equation migration abstractleast squares migration seeks a reflectivity model that fits the observed data it is used to compensate for acquisition noise poor sampling of sources and receivers on the surface as well as poor illumination of the subsurface to date least squares migration has been mainly restricted to the imaging of acoustic wavefields we have developed an extension of one way wave equation least squares migration for elastic wavefields in isotropic media least squares migration is an iterative method that requires a forward and an adjoint operator in elastic least squares one way wave equation migration the forward operator generates data components from multiparameter images by recursive wavefield decomposition extrapolation and recomposition conversely the adjoint operator generates multiparameter images from data components by recursively applying the adjoint of the wavefield recomposition extrapolation and wavefield decomposition operators we use an extended imaging condition and regularize

dynamical properties of hybrid automata hybrid automata provide a language for modeling and analyzing digital and analogue computations in real time systems hybrid automata are studied here from a dynamical systems perspective necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized the results on existence uniqueness and continuity serve as a starting point for stability analysis lyapunov s theorem on stability via linearization and lasalle s invariance principle are generalized to hybrid automata

fourth order finite difference p sv seismograms i describe the properties of a fourth order accurate space second order accurate time two dimensional p sk finite difference scheme based on the madariagavirieux staggered grid formulation the numerical scheme is developed from the first order system of hyperbolic elastic equations of motion and constitutive laws expressed in particle velocities and stresses the madariaga virieux staggered grid scheme has the desirable quality that it can correctly model any variation in material properties including both large and small poisson s ratio materials with minimal numerical dispersion and numerical anisotropy dispersion analysis indicates that the shortest wavelengths in the model need to be sampled at 5 gridpoints wavelength the scheme can be used to accurately simulate wave propagation in mixed acoustic elastic media making it ideal for modeling marine problems explicitly calculating both velocities and stresses makes it relatively simple to initiate a source at the free surface or within a layer and to satisfy free surface boundary conditions benchmark comparisons of finite difference and analytical solutions to lamb s problem are almost identical as are comparisons of finite difference and reflectivity solutions for elastic elastic and acoustic elastic layered models

sets of matrices all infinite products of which converge an infinite product iit lmi of matrices converges on the right if limi m mi exists a set z ai i l of n x n matrices is called an rcp set rightconvergent product set if all infinite products with each element drawn from z converge such sets of matrices arise in constructing self similar objects like von koch s snowflake curve in various interpolation schemes in constructing wavelets of compact support and in studying nonhomogeneous markov chains this paper gives necessary conditions and also some sufficient conditions for a set x to be an rcp set these are conditions on the eigenvalues and left eigenspaces of matrices in 2 and finite products of these matrices necessary and sufficient conditions are given for a finite set z to be an rcp set having a limit function m d rit lad where d d d which is a continuous function on the space of all sequences d with the sequence topology finite rcp sets of column stochastic matrices are completely characterized some results are given on the problem of algorithmically deciding if a given set x is an rcp set

faster algorithms for max product message passing maximum a posteriori inference in graphical models is often solved via message passing algorithms such as the junction tree algorithm or loopy belief propagation the exact solution to this problem is well known to be exponential in the size of the maximal cliques of the triangulated model while approximate inference is typically exponential in the size of the model s factors in this paper we take advantage of the fact that many models have maximal cliques that are larger than their constituent factors and also of the fact that many factors consist only of latent variables i e they do not depend on an observation this is a common case in a wide variety of applications that deal with grid tree and ring structured models in such cases we are able to decrease the exponent of complexity for message passing by 0 5 for both exact and approximate inference we demonstrate that message passing operations in such models are equivalent to some variant of matrix multiplication in the tropical semiring for which we offer an o n2 5 expected case solution

separating p and s waves in prestack 3d elastic seismograms using divergence and curl the reflected p and s waves in a prestack 3d three component elastic seismic section can be separated by taking the divergence and curl during finite difference extrapolation the elastic seismic data are downward extrapolated from the receiver locations into a homogeneous elastic computational model using the 3d elastic wave equation during downward extrapolation divergence a scalar and curl a three component vector of the wavefield are computed and recorded independently at a fixed depth as a one component seismogram and a three component seismogram respectively the p and s velocities in the elastic computational model are then split into two independent models the divergence seismogram containing p waves only is then upward extrapolated using the scalar wave equation through the p velocity model to the original receiver locations at the surface to obtain the separated p waves the x component y component and z component seismograms of the curl containing s waves only are upward ex

stability of switched systems a lie algebraic condition we present a sucient condition for asymptotic stability of a switched linear system in terms of the lie algebra generated by the individual matrices namely if this lie algebra is solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of linear systems satisfying this condition possesses a quadratic common lyapunov function we also discuss the implications of this result for switched nonlinear systems c 1999 elsevier science b v all rights reserved

sharing information for the all pairs shortest path problem we improve the time complexity of the all pairs shortest path apsp problem for special classes of directed graphs one is a nearly acyclic directed graph and the other is a directed graph with limited edge costs the common idea for speed up is information sharing by n single source shortest path sssp problems that are solved for apsp we measure the degree of acyclicity by the size r of a given set of feedback vertices if r is small the given graph can be considered to be nearly acyclic we consider this parameter r in addition to the traditional parameters of the number of vertices n and that of edges m in the first part we improve the existing time complexity of o mn r 3 for the all pairs shortest path problem to o mn rnlogn this complexity is equal to or better than the previous one for all values of r under a reasonable assumption of m n in the second part we deal with a directed graph with non negative integer edge costs bounded by c we show the all pairs shortest path apsp problem can be solved in o mn n 2log c n time with the data structure of cascading bucket system we use the traditional computational model such that comparison addition operations on distance data and random access with o logn bits can be done in o 1 time also the graph is not separated meaning m n 1

approximating the restricted 1 center in graphs abstract this paper studies the restricted vertex 1 center problem rv1cp and restricted absolute 1 center problem ra1cp in general undirected graphs with each edge having two weights cost and delay first we devise a simple fptas for rv1cp with o m n 3 1 log log n running time based on fptas proposed by lorenz and raz 1999 11 for computing end to end restricted shortest path rsp during the computation of the fptas for rv1cp we derive a rsp distance matrix next we discuss ra1cp in such graphs where the delay is a separable e g linear function of the cost on edge we investigate an important property that the fptas for rv1cp can find a 1 approximation of ra1cp when the rsp distance matrix has a saddle point in addition we show that it is harder to find an approximation of ra1cp when the matrix has no saddle point this paper develops a scaling algorithm with at most o m n 3 k log k log log n running time where k is a step size parameter and is a given positive number to find a 1 approximation of ra1cp

finding the hidden path time bounds for all pairs shortest paths the all pairs shortest paths problem in weighted graphs is investigated an algorithm the hidden paths algorithm that finds these paths in time o m n n 2 log n where m is the number of edges participating in shortest paths is presented the algorithm is a practical substitute for dijkstra s algorithm it is argued that m is likely to be small in practice since m o n log n with high probability for many probability distributions on edge weights an omega mn lower bound on the running time of any path comparison based algorithm for the all pairs shortest paths problem is also proved path comparison based algorithms form a natural class containing the hidden paths algorithm as well as the algorithms of e w dijkstra numer math 1 1959 pp 269 271 and r w floyd comm acm 5 1962 p 345 lastly generalized forms of the shortest paths problem are considered and it is shown that many of the standard shortest paths algorithms are effective in this more genera

some results on approximate 1 median selection in metric spaces a 1 median in a finite metric space is a point with the minimum average distance to all other points given a positive integer n and oracle access to a distance metric on 1 2 n we study the problem of finding a 1 median in particular we show the nonexistence of 1 deterministic o 1 approximation o n query algorithms 2 deterministic email protected 1 approximation o n 2 query algorithms for graph metrics 3 deterministic email protected 1 approximation o n 2 query algorithms and 4 monte carlo email protected 1 approximation o n query algorithms with an w 1 probability of success we also show a monte carlo email protected approximation o log 2 1 e e 3 query algorithm with a 1 o e probability of success where email protected 0 1

an invariance principle for nonlinear hybrid and impulsive dynamical systems in this paper we develop an invariance principle for dynamical systems possessing left continuous flows specifically we show that left continuity of the system trajectories in time for each fixed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi infinite interval are sufficient for establishing an invariance principle for hybrid and impulsive dynamical systems as a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems namely state dependent impulsive dynamical systems these results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems

generalizations of the projection methods with application to sor theory for hermitian positive semidefinite linear systems ann n complex matrixb is calledparacontracting if b 2 1 and 0 x n i b bx 2 x 2 we show that a productb b k b k 1 b1 ofk paracontracting matrices is semiconvergent and give upper bounds on the subdominant eigenvalue ofb in terms of the subdominant singular values of theb i s and in terms of the angles between certain subspaces our results here extend earlier results due to halperin and due to smith solomon and wagner we also determine necessary and sufficient conditions forn numbers in the interval 0 1 to form the spectrum of a product of two orthogonal projections and hence characterize the subdominant eigenvalue of such a product in the final part of the paper we apply the upper bounds mentioned earlier to provide an estimate on the subdominant eigenvalue of the sor iteration matrix associated with ann n hermitian positive semidefinite matrixa none of whose diagonal entries vanish

subcubic equivalences between path matrix and triangle problems we say an algorithm on n n matrices with integer entries in l m mr or n node graphs with edge weights from l m m is truly subcubic if it runs in o n3 poly log m time for some 0 we define a notion of subcubic reducibility and show that many important problems on graphs and matrices solvable in o n3 time are equivalent under subcubic reductions namely the following weighted problems either all have truly subcubic algorithms or none of them do the all pairs shortest paths problem on weighted digraphs apsp detecting if a weighted graph has a triangle of negative total edge weight listing up to n2 99 negative triangles in an edge weighted graph finding a minimum weight cycle in a graph of non negative edge weights the replacement paths problem on weighted digraphs finding the second shortest simple path between two nodes in a weighted digraph checking whether a given matrix defines a metric verifying the correctness of a matrix product over the min semiring finding a maximum subarray in a given matrix therefore if apsp cannot be solved in n3 e time for any e 0 then many other problems also need essentially cubic time in fact we show generic equivalences between matrix products over a large class of algebraic structures used in optimization verifying a matrix product over the same structure and corresponding triangle detection problems over the structure these equivalences simplify prior work on subcubic algorithms for all pairs path problems since it now suffices to give appropriate subcubic triangle detection algorithms other consequences of our work are new combinatorial approaches to boolean matrix multiplication over the or and semiring abbreviated as bmm we show that practical advances in triangle detection would imply practical bmm algorithms among other results building on our techniques we give two improved bmm algorithms a derandomization of the combinatorial bmm algorithm of bansal and williams focs 09 and an improved quantum algorithm for bmm

prestack gaussian beam depth migration kirchhoff migration is the most popular method of three dimensional prestack depth migration because of its flexibility and efficiency its effectiveness can become limited however when complex velocity structure causes multipathing of seismic energy an alternative is gaussian beam migration which is an extension of kirchhoff migration that overcomes many of the problems caused by multipathing unlike first arrival and most energetic arrival methods which retain only one traveltime this alternative method retains most arrivals by the superposition of gaussian beams this paper presents a prestack gaussian beam migration method that operates on common offset gathers the method is efficient because the computation of beam superposition isolates summations that do not depend on the seismic data and evaluates these integrals by considering their saddle points gaussian beam migration of the two dimensional marmousi test data set demonstrates the method s effectiveness for structural imaging in a case w

a strategy for nonlinear elastic inversion of seismic reflection data the problem of interpretation of seismic reflection data can be posed with sufficient generality using the concepts of inverse theory in its roughest formulation the inverse problem consists of obtaining the earth model for which the predicted data best fit the observed data if an adequate forward model is used this best model will give the best images of the earth s interior three parameters are needed for describing a perfectly elastic isotropic earth the density x and the lame parameters x and x or the density x and the p wave and s wave velocities x and x the choice of parameters is not neutral in the sense that although theoretically equivalent if they are not adequately chosen the numerical algorithms in the inversion can be inefficient in the long spatial wavelengths of the model adequate parameters are the p wave and s wave velocities while in the short spatial wavelengths p wave impedance s wave impedance and density are adequate the problem of inversion o

a shortest path algorithm with expected time o n 2 log n log n we present an algorithm which determines the shortest distances between all pairs of points in a nonnegatively weighted directed graph in average time o n 2 log n log n this algorithm which uses a search strategy similar to dantzig management sci 2 1960 pp 187 190 linear programming and extensions princeton univ press 1963 and spira siam j comput 2 1973 pp 28 32 executes in the stated time over quite general classes of probability distributions on such graphs

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

full waveform inversion with extrapolated low frequency data abstractthe availability of low frequency data is an important factor in the success of full waveform inversion fwi in the acoustic regime the low frequencies help determine the kinematically relevant low wavenumber components of the velocity model which are in turn needed to avoid convergence of fwi to spurious local minima however acquiring data less than 2 or 3 hz from the field is a challenging and expensive task we have explored the possibility of synthesizing the low frequencies computationally from high frequency data and used the resulting prediction of the missing data to seed the frequency sweep of fwi as a signal processing problem bandwidth extension is a very nonlinear and delicate operation in all but the simplest of scenarios it can only be expected to lead to plausible recovery of the low frequencies rather than their accurate reconstruction even so it still requires a high level interpretation of band limited seismic records into individual events each of which can be extr

linearized inversion of multioffset seismic reflection data in the ω k domain in the acoustic approximation the earth is described using only density and bulk modulus assuming smooth density variations reflections can be described using a single function the velocity of compressional waves if a reference model which is close enough to the actual earth is known the problem of estimating the medium velocity from the observed data can be linearized using a least squares formulation and working in the k domain the linearized inverse problem for a homogeneous reference medium can be solved by a noniterative algorithm which is economically competitive with prestack migration numerical tests with synthetic and real data demonstrate the feasibility and the numerical stability of the method the numerical results compare well with those obtained by migration of unstacked data although superior results will only be obtained when the physics of the problem including elastic versus acoustic effects three dimensional propagation and accurate source estimation will realistically b

a small gain theorem for switched interconnected nonlinear systems and its applications a small gain theorem for switched interconnected nonlinear systems is set up which provides a tool for analyzing the behavior of switched systems also a method exploiting an average dwell time and the small gain technique is proposed based on the small gain theorem this technical note investigates the problem of global stabilization of switched nonlinear systems in strict feedback form whose all zero dynamics are input to state stable iss or only some are iss and others are not a sufficient condition for the global stabilization problem under a class of switching signals with average dwell time is derived by constructing state feedback controllers for subsystems the result is also applied to a class of switched nonlinear network control systems

geometry of the limit sets of linear switched systems this paper is concerned with asymptotic stability properties of linear switched systems under the hypothesis that all the subsystems share a nonstrict quadratic lyapunov function we provide a large class of switching signals for which a large class of switched systems are asymptotically stable for this purpose we define what we call nonchaotic inputs which generalize the different notions of inputs with dwell time next we turn our attention to the behavior for possibly chaotic inputs finally we give a sufficient condition for a system composed of a pair of hurwitz matrices to be asymptotically stable for all inputs

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

target oriented wave equation least squares migration inversion with phase encoded hessian prestack depth migration produces blurred images resulting from limited acquisition apertures complexities in the velocity model and band limited characteristics of seismic waves this distortion can be partially corrected using the model space least squares migration inversion approach where a target oriented wave equation hessian operator is computed explicitly and then inverse filtering is applied iteratively to deblur or invert for the reflectivity however one difficulty is the cost of computing the explicit hessian operator which requires storing a large number of green s functions making it challenging for large scale applications a new method to compute the hessian operator for the wave equation based least squares migration inversion problem modifies the original explicit hessian formula enabling efficient computation of this operator an advantage is that the method eliminates disk storage of green s functions the modifications however also introduce undesired crosstalk artifacts two different phase encoding schemes plane wave phase encoding and random phase encoding suppress the crosstalk when the randomly phase encoded hessian operator is applied to the sigsbee2a synthetic data set an improved subsalt image with more balanced amplitudes is obtained

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

seismic modeling and imaging based upon spectral element and adjoint methods the overarching goal of exploration geophysics is to map or image geological structures seismic migration which attempts to map reflected and or refracted signals to their actual spatial origin plays a central role in imaging migration techniques are frequently based upon approximations to the seismic wave equation e g ray theory based kirchhoff migration or acoustic first arrival wavefield continuation methods

inversion of seismic reflection data in the acoustic approximation the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation the method is based on the generalized least squares criterion and it can handle errors in the data set and a priori information on the model multiply reflected energy is naturally taken into account as well as refracted energy or surface waves the inverse problem can be solved using an iterative algorithm which gives at each iteration updated values of bulk modulus density and time source function each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation backward in time of the data residuals the correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models this shows in particular that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data and commerc

interval observer design for continuous time switched systems under known switching and unknown inputs this paper deals with unknown input estimation for switched linear systems in an unknown but bounded error ubbe framework based on a known switching signal and under the fulfilment of the relati

a shortest path algorithm for real weighted undirected graphs we present a new scheme for computing shortest paths on real weighted undirected graphs in the fundamental comparison addition model in an efficient preprocessing phase our algorithm creates a linear size structure that facilitates single source shortest path computations in o m log alpha time where alpha alpha m n is the very slowly growing inverse ackermann function m the number of edges and n the number of vertices as special cases our algorithm implies new bounds on both the all pairs and single source shortest paths problems we solve the all pairs problem in o mn log alpha m n time and if the ratio between the maximum and minimum edge lengths is bounded by n log n o 1 we can solve the single source problem in o m n log log n time both these results are theoretical improvements over dijkstra s algorithm which was the previous best for real weighted undirected graphs our algorithm takes the hierarchy based approach invented by thorup

elastic wavefield separation based on the helmholtz decomposition abstractdivergence and curl operators used for the decomposition of p and s wave modes in elastic reverse time migration rtm change the amplitudes units and phases of extrapolated wavefields i separate the p and s waves in elastic media based on the helmholtz decomposition the decomposed wavefields based on this approach have the same amplitudes units and phases as the extrapolated wavefields to avoid expensive multidimensional integrals in the helmholtz decomposition i introduce a fast poisson solver to efficiently solve the vector poisson s equation this fast algorithm allows us to reduce computational complexity from o n2 to o n log n where n is the total number of grid points because the decomposed p and s waves are vector fields i use vector imaging conditions to construct pp ps ss and sp images several 2d numerical examples demonstrate that this approach allows us to accurately and efficiently decompose p and s waves in elastic media in addition elastic rtm images based

stabilizing switching signals for switched systems this article deals with stability of continuous time switched systems under constrained switching given a family of systems possibly containing unstable dynamics we characterize a new class of switching signals under which the switched system generated by it and the family of systems is globally asymptotically stable our characterization of such stabilizing switching signals involves the asymptotic frequency of switching the asymptotic fraction of activation of the constituent systems and the asymptotic densities of admissible transitions among them our techniques employ multiple lyapunov like functions and extend preceding results both in scope and applicability

all pairs shortest paths using bridging sets and rectangular matrix multiplication we present two new algorithms for solving the all pairs shortest paths apsp problem for weighted directed graphs both algorithms use fast matrix multiplication algorithms the first algorithm solves the apsp problem for weighted directed graphs in which the edge weights are integers of small absolute value in o n2 time where satisfies the equation 1 1 1 2 and 1 1 is the exponent of the multiplication of an n n matrix by an n n matrix currently the best available bounds on 1 1 obtained by coppersmith imply that 0 is an error parameter and w is the largest edge weight in the graph after the edge weights are scaled so that the smallest non zero edge weight in the graph is 1 it returns estimates of all the distances in the graph with a stretch of at most 1 e corresponding paths can also be found efficiently

phase correction in separating p and s waves in elastic data two dimensional elastic data containing reflected p waves and converted s wave generated by a p source may be separated using dilatation and rotation calculation sun 1999 the algorithm is a combination of elastic full wavefield extrapolation sun and mcmechan 1986 chang and mcmechan 1987 1994 and wave type separation using dilatation divergence and rotation curl calculations dellinger and etgen 1990 it includes 1 downward extrapolating the multicomponent elastic data in an elastic velocity model using the elastic wave equation 2 calculating the dilatation to represent pure p waves and calculating the rotation to represent pure s waves at some depth and 3 upward extrapolating the dilatation in a p velocity model and upward extrapolating the rotation in an s velocity model using the acoustic wave equation for each

uniform asymptotic stability of switched nonlinear time varying systems and detectability of reduced limiting control systems this paper is concerned with the study of both local and global uniform asymptotic stability for switched nonlinear time varying nltv systems through the detectability of output maps with this aim the notion of reduced limiting control systems for switched nltv systems whose switchings verify time state dependent constraints and the concept of weak zero state detectability for those reduced limiting systems are introduced necessary and sufficient conditions for the global uniform asymptotic stability of families of trajectories of the switched system are obtained in terms of this detectability property these sufficient conditions in conjunction with the existence of multiple weak lyapunov functions yield a criterion for the global uniform asymptotic stability of families of trajectories of the switched system this criterion can be seen as an extension of the classical krasovskii lasalle theorem an interesting feature of the results is that no dwell time assumptions are made moreover they can be used for establishing the global uniform asymptotic stability of the switched nltv system under arbitrary switchings the effectiveness of the proposed results is illustrated by means of various interesting examples including the stability analysis of a semiquasi z source inverter

on shortest paths in graphs with random weights we consider the shortest paths between all pairs of nodes in a directed or undirected complete graph with edge lengths which are uniformly and independently distributed in 0 1 we show that die longest of these paths is bounded by c log n n almost surely where c is a constant and n is the number of nodes our bound is the best possible up to a constant we apply this result to some well known problems and obtain several algorithmic improvements over existing results our results hold with obvious modifications to random as opposed to complete graphs and to any distribution of weights whose density is positive and bounded from below at a neighborhood of zero as a corollary of our proof we get a new result concerning the diameter of random graphs

derivation of forward and adjoint operators for least squares shot profile split step migration the forward and adjoint operators for shot profile least squares migration are derived the forward operator is demigration and the adjoint operator is migration the demigration operator is derived from the born approximation the process begins with a green s function that allows for a laterally varying migration velocity model using the split step approximation next the earth is divided into horizontal layers and within each layer the migration velocity model is made to be constant with respect to depth for a given layer 1 the source side wavefield is propagated down to its top using the background wavefield this gives a background wavefield incident at the layer s upper boundary 2 the layer s contribution to the scattered wavefield is computed using the born approximation to the scattered wavefield and the background wavefield 3 next its scattered wavefield is propagated back up to the measurement surface using again the background wavefield the measured wavefield is approximated by the sum of scattered wavefields from each layer in the derivation of the measured wavefield the shot profile migration geometry is used for each shot the resulting wavefield modeling operator takes the form of a fredholm integral equation of the first kind and this is used to write down its adjoint the shot profile migration operator this forward adjoint pair is used for shot profile least squares migration shot profile least squares migration is illustrated with two synthetic examples the first uses data collected over a four layer acoustic model and the second uses data from the sigsbee 2a model

least squares migration data domain versus image domain using point spread functions abstract conventional amplitude inversion assumes that the migrated image preserves relative amplitude information however illumination effects caused by complex geologic settings undersampled acquisition geometry and limited recording aperture pose a challenge to even the most advanced imaging algorithms in addition standard depth migration images can suffer from lack of resolution caused by wavelet stretch attenuation and suboptimal deghosting least squares migration lsm can mitigate many of these problems and produce better resolved migration images suitable for avo inversion however whether formulated in the data domain or the image domain lsm is an inversion algorithm and is sensitive to inaccuracies in the source wavelet velocity model data preprocessing and the propagator used practical considerations to mitigate these problems under nonideal conditions and cost reduction strategies differ between the data and image domain formulations the relative merits of each approach are ev

iterative asymptotic inversion in the acoustic approximation we propose an iterative method for the linearized prestack inversion of seismic profiles based on the asymptotic theory of wave propagation for this purpose we designed a very efficient technique for the downward continuation of an acoustic wavefield by ray methods the different ray quantities required for the computation of the asymptotic inverse operator are estimated at each diffracting point where we want to recover the earth image in the linearized inversion we use the background velocity model obtained by velocity analysis we determine the short wavelength components of the impedance distribution by linearized inversion of the seismograms observed at the surface of the model because the inverse operator is not exact and because the source and station distribution is limited the first iteration of our asymptotic inversion technique is not exact we improve the images by an iterative procedure since the background velocity does not change between iterations there is no need to retrace rays

prestack scalar reverse time depth migration of 3d elastic seismic data using two independent 3d scalar reverse time depth migrations we migrate the reflected p and s waves in a prestack 3d three component 3 c elastic seismic data volume generated with a p wave source in a 3d model and recorded at the top of the model reflected p and s waves are extracted by divergence a scalar and curl a 3 c vector calculations respectively during shallow downward extrapolation of the elastic seismic data the imaging time for the migrations of both the reflected p and p s converted waves at each point is the one way p wave traveltime from the source to that point the divergence the extracted p waves is reverse time extrapolated using a finite difference solution of the 3d scalar wave equation in a 3d p velocity modeland is imaged to obtain the migrated p image the curl the extracted s waves is first converted into a scalar s wavefield by taking the curl s absolute value as the absolute value of the scalar s wavefield and assigning a positive sign if the curl is counterc

average case complexity of the min sum matrix product problem we study the average case complexity of min sum product of matrices which is a fundamental operation that has many applications in computer science we focus on optimizing the number of algebraic operations i e operations involving real numbers used in the computation since such operations are usually expensive in various environments we present an algorithm that can compute the min sum product of two n n real matrices using only o n 2 algebraic operations given that the matrix elements are drawn independently and identically from some fixed probability distribution satisfying several constraints this improves the previously best known upper bound of o n 2 log n the class of probability distributions under which our algorithm works include many important and commonly used distributions such as uniform distributions exponential distributions folded normal distributions etc in order to evaluate the performance of the proposed algorithm we performed experiments to compare the running time of the proposed algorithm with algorithms in 1 the experimental results demonstrate that our algorithm achieves significant performance improvement over the previous algorithms

a converse lyapunov theorem for a class of dynamical systems which undergo switching the authors investigate the stability of a system in which the dynamics at any instant in time will follow one of a fixed set of vector fields they allow switching between members of the family of vector fields to be completely random the focus of this paper is to prove a converse lyapunov theorem for this class of systems

an extension of lasalle s invariance principle for switched systems in this paper we address invariance principles for a certain class of switched nonlinear systems we provide an extension of lasalle s invariance principle for these systems and state asymptotic stability criteria we also present some related results on the compactness of the trajectories of these switched systems

p sv wave propagation in heterogeneous media velocity stress finite difference method i present a finite difference method for modeling p sv wave propagation in heterogeneous media this is an extension of the method i previously proposed for modeling sh wave propagation by using velocity and stress in a discrete grid the two components of the velocity cannot be defined at the same node for a complete staggered grid the stability condition and the p wave phase velocity dispersion curve do not depend on the poisson s ratio while the s wave phase velocity dispersion curve behavior is rather insensitive to the poisson s ratio therefore the same code used for elastic media can be used for liquid media where s wave velocity goes to zero and no special treatment is needed for a liquid solid interface typical physical phenomena arising with p sv modeling such as surface waves are in agreement with analytical results the weathered layer and corner edge models show in seismograms the same converted phases obtained by previous authors this method gives stable results for step discontinuities as shown for a liquid layer above an elastic half space the head wave preserves the correct amplitude finally the corner edge model illustrates a more complex geometry for the liquid solid interface as the poisson s ratio v increases from 0 25 to 0 5 the shear converted phases are removed from seismograms and from the time section of the wave field

depth imaging with multiples depth imaging with multiples is a prestack depth migration method that uses multiples as the signal for more accurate boundary mapping and amplitude recovery the idea is partially related to model based multiple suppression techniques and reverse time depth migration conventional reverse time migration uses the two way wave equation for the backward wave propagation of recorded seismic traces and ray tracing or the eikonal equation for the forward traveltime computation the excitation time imaging principle consequently reverse time migration differs little from most other one way wave equation or ray tracing migration methods which expect only primary reflection events because it is almost impossible to attenuate multiples without degrading primaries there has been a compelling need to devise a tool to use multiples constructively in data processing rather than attempting to destroy them furthermore multiples and other nonreflecting wave types can enhance boundary imaging and amplitude recovery

efficient calculation of a partial derivative wavefield using reciprocity for seismic imaging and inversion linearized inversion of surface seismic data for a model of the earth s subsurface requires estimating the sensitivity of the seismic response to perturbations in the earth s subsurface this sensitivity or jacobian matrix is usually quite expensive to estimate for all but the simplest model parameterizations we exploit the numerical structure of the finite element method modern sparse matrix technology and source receiver reciprocity to develop an algorithm that explicitly calculates the jacobian matrix at only the cost of a forward model solution furthermore we show that we can achieve improved subsurface images using only one inversion iteration through proper scaling of the image by a diagonal approximation of the hessian matrix as predicted by the classical gauss newton method our method is applicable to the full suite of wave scattering problems amenable to finite element forward modeling we demonstrate our method through some simple 2 d synthetic examples

analyzing the stability of switched systems using common zeroing output systems this paper introduces the notion of common zeroing output systems czos to analyze the stability of switched systems the concept of czos allows one to verify weak zero state detectability it characterizes a common behavior of any individual subsystem when the output signal for each subsystem is approaching zero heuristically speaking it removes the effect of switching behavior and thus enables one to analyze stability properties in systems with complex switching signals with the help of czos the krasovskii lasalle theorem can be extended to switched nonlinear time varying systems with both arbitrary switching and more general restricted switching cases for switched nonlinear time invariant systems the needed detectability condition is further simplified leading to several new stability results particularly when a switched linear time invariant system is considered it is possible to generate a recursive method which combines a krasovskii lasalle result and a nested matrosov result to find a czos if it exists the power of the proposed czos is demonstrated by consensus problems in literature to obtain a stronger convergence result with weaker conditions

approximating the minimum cycle mean we consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight our contributions are twofold 1 first we show that the algorithmic question is reducible to the problem of a logarithmic number of min plus matrix multiplications of nxn matrices where n is the number of vertices of the graph 2 second when the weights are nonnegative we present the first 1 e approximation algorithm for the problem and the running time of our algorithm is o n wlog 3 nw e e where o n w is the time required for the classicnxn matrix multiplication and w is the maximum value of the weights with an additional o log nw e factor in space a cycle with approximately optimal weight can be computed within the same time bound

least squares wave equation migration for avp ava inversion we present an acoustic migration inversion algorithm that uses extended double square root wave equation migration and modeling operators to minimize a constrained least squares data misfit function least squares migration we employ an imaging principle that allows for the extraction of ray parameter domain common image gathers cigs from the propagated seismic wavefield the cigs exhibit amplitude variations as a function of half offset ray parameter avp closely related to the amplitude variation with reflection angle ava our least squares wave equation migration inversion is constrained by a smoothing regularization along the ray parameter this approach is based on the idea that rapid amplitude changes or discontinuities along the ray parameter axis result from noise incomplete wavefield sampling and numerical operator artifacts these discontinuities should therefore be penalized in the inversion the performance of the proposed algorithm is examined with two synthetic examples in the first

2d isotropic elastic gaussian beam migration for common shot multicomponent records gaussian beam migration is flexible and adaptable for imaging geologically complicated areas it avoids some limitations of traditional ray based migration approaches such as amplitude singularity in caustic zones and inability to image multiple arrivals previous studies on gaussian beam migration mainly focused on acoustic media we develop a 2d isotropic elastic gaussian beam migration scheme for common shot multicomponent records the proposed method extrapolates p and s mode wavefields simultaneously using the kirchhoff helmholtz integral solution of the isotropic elastodynamic equation we separate the extrapolated wavefields into compressional and shear modes using the helmholtz decomposition and then implement a modified dot product imaging condition this approach enables us to produce clear pp images and avoid polarity reversal issues for ps images in addition based on the theory of wavefield approximation in the effective vicinity of central rays we derive a formula to compute the propaga

an effective imaging condition for reverse time migration using wavefield decomposition reverse time migration rtm exhibits great superiority over other imaging algorithms in handling steeply dipping structures and complicated velocity models however low frequency high amplitude noises commonly seen in a typical rtm image have been one of the major concerns because they can seriously contaminate the signals in the image if they are not handled properly we propose a new imaging condition to effectively and efficiently eliminate these specific noises from the image the method works by first decomposing the source and receiver wavefields to their one way propagation components followed by applying a correlation based imaging condition to the appropriate combinations of the decomposed wavefields we first give the physical explanation of the principle of such noises in the conventional rtm image then we provide the detailed mathematical theory for the new imaging condition finally we propose an efficient scheme for its numerical implementation it replaces the computationally intensiv

all pairs shortest paths in o n 2 time with high probability we present an all pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from 0 1 is o n2 in expectation and with high probability this resolves a long standing open problem the algorithm is a variant of the dynamic all pairs shortest paths algorithm of demetrescu and italiano 2006 the analysis relies on a proof that the number of locally shortest paths in such randomly weighted graphs is o n2 in expectation and with high probability we also present a dynamic version of the algorithm that recomputes all shortest paths after a random edge update in o log2n expected time

accelerating extended least squares migration with weighted conjugate gradient iteration abstractleast squares migration lsm iteratively achieves a mean square best fit to seismic reflection data provided that a kinematically accurate velocity model is available the subsurface offset extension adds extra degrees of freedom to the model thereby allowing lsm to fit the data even in the event of significant velocity error this type of extension also implies additional computational expense per iteration from crosscorrelating source and receiver wavefields over the subsurface offset and therefore places a premium on rapid convergence we have accelerated the convergence of extended least squares migration by combining the conjugate gradient algorithm with weighted norms in range data and domain model spaces that render the extended born modeling operator approximately unitary we have developed numerical examples that demonstrate that the proposed algorithm dramatically reduces the number of iterations required to achieve a given level of fit or gradient reduction compared with conjuga

an invariance principle for nonlinear switched systems abstract in this paper we address the problem of extending lasalle invariance principle to switched system we prove an extension of the invariance principle relative to dwell time switched solutions and a second one relative to constrained switched systems

switched adaptive control of switched nonlinearly parameterized systems with unstable subsystems this paper investigates the problem of adaptive stabilization for a class of switched nonlinearly parameterized systems where the solvability of the adaptive stabilization problem for subsystems is unnecessary a new switched adaptive control technique for the problem studied is set up by exploiting the generalized multiple lyapunov functions method and the parameter separation technique different update laws are designed to reduce the conservativeness caused by adoption of a common update law for all subsystems also the proposed technique permits removal of a common restriction in which the parameterization in the switched systems is restricted to a linear parameterization as an application of the proposed design technique stabilization for a class of non triangular switched systems with nonlinear parameterization is achieved by design of adaptive controllers since no subsystem of such a switched system is assumed to be adaptively stabilizable the problem under study cannot be handled by the existing methods a two inverted pendulums as a practical example is also provided to demonstrate the effectiveness of the proposed design method

svd for multioffset linearized inversion resolution analysis in multicomponent acquisition acquisition of the full elastic response compressional and shear of the subsurface is an important technology in the seismic industry because of its potential to improve the quality of seismic data and to infer accurate information about rock properties fluid type and rock lithology in the framework of 3 d propagation in 1 d media we propose a computational tool to analyze the information about elastic parameters contained in the amplitudes of reflected waves with offset the approach is based on singular value decomposition svd analysis of the linearized elastic inversion problem and can be applied to any particular seismic data we applied this tool to examine the type of information in the model space that can be retrieved from sea bottom multicomponent measurements the results are compared with those obtained from conventional streamer acquisition techniques we also present multiparameter linearized inversion results obtained from synthetic data that illustrate the resolution of elastic parameters this approach allows us to investigate the reliability of the elastic parameters estimated for different offset ranges wave modes data types and noise levels involved in data space

wave field separation in two dimensional anisotropic media until recently the term elastic usually implied two dimensional 2 d and isotropic in this limited context the divergence and curl operators have found wide use as wave separation operators for example mora 1987 used them in his inversion method to allow separate correlation of p and s arrivals although the separation is buried in the math and not obvious clayton 1981 used them explicitly in several modeling and inversion methods devaney and oristaglio 1986 used closely related operators to separate p and s arrivals in elastic vsp data

adaptive fuzzy tracking control of switched uncertain nonlinear systems with unstable subsystems this paper is concerned with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems where the solvability of the fuzzy tracking control problem for subsystems is unnecessary fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a new adaptive fuzzy tracking control technique for the problem under study is set up based on the technique above we design a switching law and construct adaptive fuzzy controllers of subsystems explicitly by a recursive design algorithm to guarantee that all the signals in the resulting closed loop system remain bounded and the system output of the closed loop system converges to a small neighborhood of the reference signal multiple lyapunov functions are exploited to get out of the conservativeness caused by adoption of a common lyapunov function for all subsystems which is commonly required when applying the backstepping like recursive design scheme a mass spring damper system is provided to demonstrate the effectiveness of the proposed design method

isotropic angle domain elastic reverse time migration multicomponent data usually are not processed with specifically designed procedures but with procedures analogous to those used for single component data in isotropic media the vertical and horizontal components of the data commonly are taken as proxies for the p and s wave modes which are imaged independently with the acoustic wave equations this procedure works only if the vertical and horizontal components accurately represent p and s wave modes which generally is not true therefore multicomponent images constructed with this procedure exhibit artifacts caused by incorrect wave mode separation at the surface an alternative procedure for elastic imaging uses the full vector fields for wavefield reconstruction and imaging thewavefieldsarereconstructedusingthemulticomponentdata as a boundary condition for a numerical solution to the elastic wave equation the key component for wavefield migration is theimagingcondition whichevaluatesthematchbetweenwavefields reconstructed from sources and receivers for vector wave fields a simple component by component crosscorrelation between two wavefields leads to artifacts caused by crosstalk between the unseparated wave modes we can separate elastic wavefields after reconstruction in the subsurface and implement theimagingconditionascrosscorrelationofpurewavemodesinstead of the cartesian components of the displacement wavefield thisapproachleadstoimagesthatareeasiertointerpretbecause they describe reflectivity of specified wave modes at interfaces of physical properties as for imaging with acoustic wavefields the elastic imaging condition can be formulated conventionally crosscorrelation with zero lag in space and time and extendedtononzerospaceandtimelags theelasticimagesproduced by an extended imaging condition can be used for angle decomposition of primary pp or ss and converted ps or sp reflectivity angle gathers constructed with this procedure have applicationsformigrationvelocityanalysisandamplitude variation with angleanalysis

multidirectional vector based elastic reverse time migration and angle domain common image gathers with approximate wavefield decomposition of p and s waves abstractelastic reverse time migration e rtm has limitations when the migration velocities contain strong contrasts first the traditional scheme of p s wave mode separation is based on helmholtz s equations which ignore the conversion between p and s waves at the current separation time thus it contains an implicit assumption of the constant shear modulus and requires smoothing the heterogeneous model to approximately satisfy a locally constant condition second the vector based imaging condition needs to use the reflection image normal and it also cannot give the correct polarity of the pp image in all possible conditions third the angle domain common image gathers adcigs calculated using the poynting vectors pvs do not consider the wave interferences that happen at each reflector therefore smooth models are often used for e rtm we relax this condition by proposing an improved data flow that involves three new contributions the first contribution is an improved system of p s wave mode

amplitude and kinematic corrections of migrated images for nonunitary imaging operators obtaining migrated images with meaningful amplitudes is a challenging problem when the migration operator is not unitary one possible solution to this problem is iterative inversion however inversion is an expensive process that can be rather difficult to apply especially with 3d data in this paper i propose estimating migrated images similar to the least squares inverse images by approximating the inverse hessian thus avoiding the need for iterative inversion the inverse hessian is approximated with a bank of nonstationary matching filters these filters are not exact impulse responses and are limited in their ability to mimic the full effects of least squares inversion tests on two data sets show that this filtering approach gives results similar to iterative least squares inversion at a lower cost this technique is flexible enough to be applied to images migrated from zero offset or angle domain common image point gathers

sh wave propagation in heterogeneous media velocity stress finite difference method a new finite difference fd method is presented for modeling sh wave propagation in a generally heterogeneous medium this method uses both velocity and stress in a discrete grid density and shear modulus are similarly discretized avoiding any spatial smoothing therefore boundaries will be correctly modeled under an implicit formulation standard problems quarter plane propagation sedimentary basin propagation are studied to compare this method with other methods finally a more complex example a salt dome inside a two layered medium shows the effect of lateral propagation on seismograms recorded at the surface a corner wave always in phase with the incident wave and a head wave will appear which will pose severe problems of interpretation with the usual vertical migration methods

global stability results for switched systems based on weak lyapunov functions in this paper we study the stability of nonlinear and time varying switched systems under restricted switching we approach the problem by decomposing the system dynamics into a nominal like part and a perturbation like one most stability results for perturbed systems are based on the use of strong lyapunov functions i e functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state however switched systems under restricted switching may not admit strong lyapunov functions even when asymptotic stability is uniform over the set of switching signals considered the main contribution of the current paper consists in providing stability results that are based on the stability of the nominal like part of the system and require only a weak lyapunov function these results may have wider applicability than results based on strong lyapunov functions the results provided follow two lines first we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal like and the perturbation like parts of the system second we provide input to state stability iss results for the case when the nominal like part is switched linear time varying we provide two types of iss results standard iss that involves the essential supremum norm of the input and a modified iss that involves a power type norm

common polynomial lyapunov functions for linear switched systems in this paper we consider linear switched systems dot x t a u t x t x in r n u in u a u u in u compact and the problem of asymptotic stability for arbitrary switching functions uniform with respect to switching uas given a uas system it is always possible to build a common polynomial lyapunov function our main result is that the degree of that common polynomial lyapunov function is not uniformly bounded over all the uas systems this result answers a question raised by dayawansa and martin a generalization to a class of piecewise polynomial lyapunov functions is given

the convergence of general products of matrices and the weak ergodicity of markov chains abstract we determine a sufficient condition for the convergence to 0 of general products formed from a sequence of real or complex matrices our result is applied to obtain a condition for the weak ergodicity of an inhomogeneous markov chain we make some remarks comparing coefficients of ergodicity and we give a method for constructing these

more algorithms for all pairs shortest paths in weighted graphs in the first part of the paper we reexamine the all pairs shortest path apsp problem and present a new algorithm with running time o n 3 log 3 log n log 2n which improves all known algorithms for general real weighted dense graphs in the second part of the paper we use fast matrix multiplication to obtain truly subcubic apsp algorithms for a large class of geometrically weighted graphs where the weight of an edge is a function of the coordinates of its vertices for example for graphs embedded in euclidean space of a constant dimension d we obtain a time bound near o n 3 3 omega 2d 4 where omega 2 376 in two dimensions this is o n 2 922 our framework greatly extends the previously considered case of small integer weighted graphs and incidentally also yields the first truly subcubic result near o n 3 3 omega 4 o n 2 844 time for apsp in real vertex weighted graphs as well as an improved result near o n 3 omega 2 o n 2 688 time for the all pairs lightest shortest path problem for small integer weighted graphs

invariance principles for switching systems via hybrid systems techniques invariance principles and sufficient conditions for asymptotic stability for switching systems are given multiple lyapunov like functions are used and dwell time persistent dwell time and weak dwell time switching signals are considered the invariance principles are derived from general invariance principles for hybrid systems asymptotic stability is concluded under observability assumptions or common bounds on the lyapunov like functions

two dimensional nonlinear inversion of seismic waveforms numerical results the nonlinear problem of inversion of seismic waveforms can be set up using least squares methods the inverse problem is then reduced to the problem of minimizing a lp nonquadratic function in a space of many 104to106 variables using gradient methods leads to iterative algorithms each iteration implying a forward propagation generated by the actual sources a backward propagation generated by the data residuals acting as if they were sources and a correlation at each point of the space of the two fields thus obtained which gives the updated model the quality of the results of any inverse method depends heavily on the realism of the forward modeling finite difference schemes are a good choice relative to realism because although they are time consuming they give excellent results numerical tests performed with multioffset synthetic data from a two dimensional model prove the feasibility of the approach if only surface recorded reflections are used the high spatial frequency content of the

an all pairs shortest path algorithm with expected time o n 2 log n an algorithm is described that solves the all pairs shortest path problem for a nonnegatively weighted directed graph of n vertices in average time o n 2 log n the algorithm is a blend of two previous shortest path algorithms those of dantzig management sci 6 1960 pp 187 190 and spira siam j comput 2 1973 pp 28 32 bloniarz siam j comput 12 1983 pp 588 600 categorised a class of random graphs called endpoint independent graphs the new algorithm executes in the stated time on endpoint independent graphs and represents an asymptotic improvement over the o n 2 log n log n algorithm given by bloniarz for this class of random graphs

elastic least squares reverse time migration via linearized elastic full waveform inversion with pseudo hessian preconditioning abstracttime domain elastic least squares reverse time migration lsrtm is formulated as a linearized elastic full waveform inversion problem the elastic born approximation and elastic reverse time migration rtm operators are derived from the time domain continuous adjoint state method our approach defines p and s wave impedance perturbations as unknown elastic images our algorithm is obtained using continuous functional analysis in which the problem is discretized at the final stage optimize before discretize approach the discretized numerical versions of the elastic born operator and its adjoint elastic rtm operator pass the dot product test the conjugate gradient least squares method is used to solve the least squares migration quadratic optimization problem in other words the hessian operator for elastic lsrtm is implicitly inverted via a matrix free algorithm that only requires the action of forward and adjoint operators on vectors the diagonal of the pseudo hessian operator is used t

flexibly preconditioned extended least squares migration in shot record domain abstractwe have developed a method for accelerating the convergence of iterative least squares migration the algorithm uses a pseudodifferential scaling dip and spatially varying filter preconditioner together with a variant of conjugate gradient cg iteration with iterate dependent flexible preconditioning the migration is formulated without the image stack thus producing a shot dependent image volume that retains offset information useful for velocity updating and amplitude variation with offset analysis numerical experiments indicate that flexible preconditioning with pseudodifferential scaling not only attains considerably smaller data misfit and gradient error for a given computational effort but also produces higher resolution image volumes with more balanced amplitude and fewer artifacts than is achieved with a nonpreconditioned cg method

approximate distance oracles let g v e be an undirected weighted graph with vvv n and vev m let k 1 be an integer we show that g v e can be preprocessed in o kmn1 k expected time constructing a data structure of size o kn1p1 k such that any subsequent distance query can be answered approximately in o k time the approximate distance returned is of stretch at most 2k 1 that is the quotient obtained by dividing the estimated distance by the actual distance lies between 1 and 2k 1 a 1963 girth conjecture of erdos implies that n1p1 k space is needed in the worst case for any real stretch strictly smaller than 2kp1 the space requirement of our algorithm is therefore essentially optimal the most impressive feature of our data structure is its constant query time hence the name oracle previously data structures that used only o n1p1 k space had a query time of n1 k our algorithms are extremely simple and easy to implement efficiently they also provide faster constructions of sparse spanners of weighted graphs and improved tree covers and distance labelings of weighted or unweighted graphs