on a new class of completely integrable nonlinear wave equations i infinitely many conservation laws we point out a class of nonlinear wave equations which admit infinitely many conserved quantities these equations are characterized by a pair of exact one forms the implication that they are closed gives rise to equations the characteristics and riemann invariants of which are readily obtained the construction of the conservation laws requires the solution of a linear second order equation which can be reduced to canonical form using the riemann invariants the hodograph transformation results in a similar linear equation we discuss also the symplectic structure and backlund transformations associated with these equations

introduction to matrix analytic methods in stochastic modeling preface part i quasi birth and death processes 1 examples part ii the method of phases 2 ph distributions 3 markovian point processes part iii the matrix geometric distribution 4 birth and death processes 5 processes under a taboo 6 homogeneous qbds 7 stability condition part iv algorithms 8 algorithms for the rate matrix 9 spectral analysis 10 finite qbds 11 first passage times part v beyond simple qbds 12 nonhomogeneous qbds 13 processes skip free in one direction 14 tree processes 15 product form networks 16 nondenumerable states bibliography index

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

elliptic euler poisson darboux equation critical points and integrable systems the structure and properties of families of critical points for classes of functions obeying the elliptic euler poisson darboux equation e 1 2 1 2 are studied general variational and differential equations governing the dependence of critical points in variational deformation parameters are found explicit examples of the corresponding integrable quasi linear differential systems and hierarchies are presented there are the extended dispersionless toda nonlinear schrodinger hierarchies the inverse hierarchy and equations associated with the real analytic eisenstein series among them the specific bi hamiltonian structure of these equations is also discussed

the classical shallow water equations symplectic geometry the classical shallow water equations express the change with time of the height h and the velocity of a 1 dimensional fluid t x h x 0 h x h x 0 they possess an infinite number of integrals of motion due to benney 1973 and can be written in hamiltonian form relative to a symplectic structure introduced by manin 1978 the present paper deals with their complete integrability up to the advent of shocks this is proved in the small under an extra assumption satisfied by most height velocity pairs that hh only at isolated points

shape spectrum based view grouping and matching of 3d free form objects we address the problem of constructing view aspects of 3d free form objects for efficient matching during recognition we introduce a novel view representation based on shape spectrum features and propose a general and powerful technique for organizing multiple views of objects of complex shape and geometry into compact and homogeneous clusters our view grouping technique obviates the need for surface segmentation and edge detection experiments on 6 400 synthetically generated views of 20 free form objects and 100 real range images of 10 sculpted objects demonstrate the good performance of our shape spectrum based model view selection technique

adding nesting structure to words we propose the model of nested words for representation of data with both a linear ordering and a hierarchically nested matching of items examples of data with such dual linear hierarchical structure include executions of structured programs annotated linguistic data and html xml documents nested words generalize both words and ordered trees and allow both word and tree operations we define nested word automata finite state acceptors for nested words and show that the resulting class of regular languages of nested words has all the appealing theoretical properties that the classical regular word languages enjoys deterministic nested word automata are as expressive as their nondeterministic counterparts the class is closed under union intersection complementation concatenation kleene prefixes and language homomorphisms membership emptiness language inclusion and language equivalence are all decidable and definability in monadic second order logic corresponds exactly to finite state recognizability we also consider regular languages of infinite nested words and show that the closure properties mso characterization and decidability of decision problems carry over the linear encodings of nested words give the class of visibly pushdown languages of words and this class lies between balanced languages and deterministic context free languages we argue that for algorithmic verification of structured programs instead of viewing the program as a context free language over words one should view it as a regular language of nested words or equivalently a visibly pushdown language and this would allow model checking of many properties such as stack inspection pre post conditions that are not expressible in existing specification logics we also study the relationship between ordered trees and nested words and the corresponding automata while the analysis complexity of nested word automata is the same as that of classical tree automata they combine both bottom up and top down traversals and enjoy expressiveness and succinctness benefits over tree automata

population based algorithm portfolios with automated constituent algorithms selection abstract population based algorithm portfolios pap is an appealing framework for integrating different evolutionary algorithms eas to solve challenging numerical optimization problems particularly pap has shown significant advantages to single eas when a number of problems need to be solved simultaneously previous investigation on pap reveals that choosing appropriate constituent algorithms is crucial to the success of pap however no method has been developed for this purpose in this paper an extended version of pap namely pap based on estimated performance matrix epm pap is proposed epm pap is equipped with a novel constituent algorithms selection module which is based on the epm of each candidate eas empirical studies demonstrate that the epm based selection method can successfully identify appropriate constituent eas and thus epm pap outperformed all single eas considered in this work

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

extended symmetry analysis of an isothermal no slip drift flux model abstract we perform extended group analysis for a system of differential equations modeling an isothermal no slip drift flux the maximal lie invariance algebra of this system is proved to be infinite dimensional we also find the complete point symmetry group of this system including discrete symmetries using the megaideal based version of the algebraic method optimal lists of one and two dimensional subalgebras of the maximal lie invariance algebra in question are constructed and employed for obtaining reductions of the system under study since this system contains a subsystem of two equations that involves only two of three dependent variables we also perform group analysis of this subsystem the latter can be linearized by a composition of a fiber preserving point transformation with a two dimensional hodograph transformation to the klein gordon equation we also employ both the linearization and the generalized hodograph method for constructing the general solution of the entire system under study we find inter alia genuinely generalized symmetries for this system and present the connection between them and the lie symmetries of the subsystem we mentioned earlier hydrodynamic conservation laws and their generalizations are also constructed

an algebro geometric solution for a hamiltonian system with application to dispersive long wave equation by using an iterative algebraic method we derive from a spectral problem a hierarchy of nonlinear evolution equations associated with dispersive long wave equation it is shown that the hierarchy is integrable in liouville sense and possesses bi hamiltonian structure two commutators with zero curvature and lax representations for the hierarchy are constructed respectively by using two different systematic methods under a bargmann constraint the spectral is nonlinearized to a completely integrable finite dimensional hamiltonian system by introducing the abel jacobi coordinates an algebro geometric solution for the dispersive long wave equation is derived by resorting to the riemann theta function

reciprocal transformations of hamiltonian operators of hydrodynamic type nonlocal hamiltonian formalism for linearly degenerate systems reciprocal transformations of hamiltonian operators of hydrodynamic type are investigated the transformed operators are generally nonlocal possessing a number of remarkable algebraic and differential geometric properties we apply our results to linearly degenerate semi hamiltonian systems in riemann invariants a typical example being rti m 1nrm ri rxi i 1 2 n since all such systems are linearizable by appropriate generalized reciprocal transformations our formulas provide an infinity of mutually compatible nonlocal hamiltonian structures explicitly parametrized by n arbitrary functions of one variable

recursive markov chains stochastic grammars and monotone systems of nonlinear equations we define recursive markov chains rmcs a class of finitely presented denumerable markov chains and we study algorithms for their analysis informally an rmc consists of a collection of finite state markov chains with the ability to invoke each other in a potentially recursive manner rmcs offer a natural abstract model for probabilistic programs with procedures they generalize in a precise sense a number of well studied stochastic models including stochastic context free grammars scfg and multi type branching processes mt bp we focus on algorithms for reachability and termination analysis for rmcs what is the probability that an rmc started from a given state reaches another target state or that it terminatesq these probabilities are in general irrational and they arise as least fixed point solutions to certain monotone systems of nonlinear equations associated with rmcs we address both the qualitative problem of determining whether the probabilities are 0 1 or in between and the quantitative problems of comparing the probabilities with a given bound or approximating them to desired precision we show that all these problems can be solved in pspace using a decision procedure for the existential theory of reals we provide a more practical algorithm based on a decomposed version of multi variate newton s method and prove that it always converges monotonically to the desired probabilities we show this method applies more generally to any monotone polynomial system we obtain polynomial time algorithms for various special subclasses of rmcs among these for scfgs and mt bps equivalently for 1 exit rmcs the qualitative problem can be solved in p time for linearly recursive rmcs the probabilities are rational and can be computed exactly in p time we show that our pspace upper bounds cannot be substantially improved without a breakthrough on long standing open problems the square root sum problem and an arithmetic circuit decision problem that captures p time on the unit cost rational arithmetic ram model we show that these problems reduce to the qualitative problem and to the approximation problem to within any nontrivial error for termination probabilities of general rmcs and to the quantitative decision problem for termination extinction of scfgs mt bps

a hierarchy of nonlinear evolution equations its bi hamiltonian structure and finite dimensional integrable systems an isospectral problem and the associated hierarchy of nonlinear evolution equations is presented as a reduction a new generalized nonlinear schrodinger equation is obtained it is shown that the hierarchy possesses bi hamiltonian structure and is integrable in liouville sense moreover the eigenvalue problem can be nonlinearized as a finite dimensional completely integrable system under the bargmann constraint between the potentials and the eigenvalues

results on the propositional μ calculus abstract in this paper we define and study a propositional calculus l which consists essentially of propositional modal logic with a least fixpoint operator l is syntactically simpler yet strictly more expressive than propositional dynamic logic pdl for a restricted version we give an exponential time decision procedure small model property and complete deductive system theory subsuming the corresponding results for pdl

modularity of cycles and paths in graphs certain problems related to the length of cycles and paths modulo a given integer are studied linear time algorithms are presented that determine whether all cycles in an undirected graph are of length p mod q and whether all paths between two specified nodes are of length p mod q for fixed integers p q these results are compared to those for directed graphs

advances in metric embedding theory metric embedding plays an important role in a vast range of application areas such as computer vision computational biology machine learning networking statistics and mathematical psychology to name a few the mathematical theory of metric embedding is well studied in both pure and applied analysis and has more recently been a source of interest for computer scientists as well most of this work is focused on the development of bi lipschitz mappings between metric spaces in this paper we present new concepts in metric embeddings as well as new embedding methods for metric spaces we focus on finite metric spaces however some of the concepts and methods are applicable in other settings as well one of the main cornerstones in finite metric embedding theory is a celebrated theorem of bourgain which states that every finite metric space on n points embeds in euclidean space with o logn distortion bourgain s result is best possible when considering the worst case distortion over all pairs of points in the metric space yet it is natural to ask can an embedding do much better in terms of the average distortion indeed in most practical applications of metric embedding the main criteria for the quality of an embedding is its average distortion over all pairs in this paper we provide an embedding with constant average distortion for arbitrary metric spaces while maintaining the same worst case bound provided by bourgain s theorem in fact our embedding possesses a much stronger property we define the lq distortion of a uniformly distributed pair of points our embedding achieves the best possible lq distortion for all 1 q simultaneously the results are based on novel embedding methods which improve on previous methods in another important aspect the dimension of the host space the dimension of an embedding is of very high importance in particular in applications and much effort has been invested in analyzing it however no previous result improved the bound on the dimension which can be derived from bourgain s embedding our embedding methods achieve better dimension and in fact shed new light on another fundamental question in metric embedding which is whether the embedding dimension of a metric space is related to its intrinsic dimension i e whether the dimension in which it can be embedded in some real normed space is related to the intrinsic dimension which is reflected by the inherent geometry of the space measured by the space s doubling dimension the existence of such an embedding was conjectured by assouad 4 and was later posed as an open problem in several papers our embeddings give the first positive result of this type showing any finite metric space obtains a low distortion and constant average distortion embedding in euclidean space in dimension proportional to its doubling dimension underlying our results is a novel embedding method probabilistic metric decomposition techniques have played a central role in the field of finite metric embedding in recent years here we introduce a novel notion of probabilistic metric decompositions which comes particularly natural in the context of embedding our new methodology provides a unified approach to all known results on embedding of arbitrary finite metric spaces moreover as described above with some additional ideas they allow to get far stronger results the results presented in this paper5have been the basis for further developments both within the field of metric embedding and in other areas such as graph theory distributed computing and algorithms we present a comprehensive study of the notions and concepts introduced here and provide additional extensions related results and some examples of algorithmic applications

on the nature of the gardner transformation it is shown that every higher korteveg de vries equation can be included in a one parameter family of integrable equations

scaling symmetries conservation laws and action principles in one dimensional gas dynamics scaling symmetries of the planar one dimensional gas dynamic equations with adiabatic index are used to obtain lagrangian and eulerian conservation laws associated with the symmetries the known eulerian symmetry operators for the scaling symmetries are converted to the lagrangian form in which the eulerian spatial position of the fluid element is given in terms of the lagrangian fluid labels conditions for a linear combination of the three scaling symmetries to be a divergence or variational symmetry of the action are established the corresponding lagrangian and eulerian form of the conservation laws are determined by application of noether s theorem a nonlocal conservation law associated with the scaling symmetries is obtained by applying a nonlocal symmetry operator to the scaling symmetry conserved vector an action principle incorporating known conservation laws using lagrangian constraints is developed noether s theorem for the constrained action principle gives the same formulas for the conserved vector as the classical noether theorem except that the lie symmetry vector field now includes the effects of nonlocal potentials noether s theorem for the constrained action principle is used to obtain nonlocal conservation laws the scaling symmetry conservation laws only apply for special forms of the entropy of the gas

multi symplectic lagrangian one dimensional gas dynamics the equations of lagrangian ideal one dimensional compressible gas dynamics are written in a multi symplectic form using the lagrangian mass coordinate m and time t as independent variables and in which the eulerian position of the fluid element x x m t is one of the dependent variables this approach differs from the eulerian multi symplectic approach using clebsch variables lagrangian constraints are used to specify equations for xm xt and st consistent with the lagrangian map where s is the entropy of the gas we require st 0 corresponding to advection of the entropy s with the flow we show that the lagrangian hamiltonian equations are related to the de donder weyl multi momentum formulation the pullback conservation laws and the symplecticity conservation laws are discussed the pullback conservation laws correspond to invariance of the action with respect to translations in time energy conservation and translations in m in noether s theorem the conservation law due to m translatio

the complexity of mean payoff pushdown games two player games on graphs are central in many problems in formal verification and program analysis such as synthesis and verification of open systems in this work we consider solving recursive game graphs or pushdown game graphs that model the control flow of sequential programs with recursion while pushdown games have been studied before with qualitative objectives such as reachability and regular objectives in this work we study for the first time such games with the most well studied quantitative objective the mean payoff objective in pushdown games two types of strategies are relevant 1 global strategies which depend on the entire global history and 2 modular strategies which have only local memory and thus do not depend on the context of invocation but rather only on the history of the current invocation of the module our main results are as follows 1 one player pushdown games with mean payoff objectives under global strategies are decidable in polynomial time 2 two player pushdown games with mean payoff objectives under global strategies are undecidable 3 one player pushdown games with mean payoff objectives under modular strategies are np hard 4 two player pushdown games with mean payoff objectives under modular strategies can be solved in np i e both one player and two player pushdown games with mean payoff objectives under modular strategies are np complete we also establish the optimal strategy complexity by showing that global strategies for mean payoff objectives require infinite memory even in one player pushdown games and memoryless modular strategies are sufficient in two player pushdown games finally we also show that all the problems have the same complexity if the stack boundedness condition is added where along with the mean payoff objective the player must also ensure that the stack height is bounded

object recognition using shape from shading investigates whether surface topography information extracted from intensity images using a shape from shading sfs algorithm can be used for the purposes of 3d object recognition we consider how curvature and shape index information delivered by this algorithm can be used to recognize objects based on their surface topography we explore two contrasting object recognition strategies the first of these is based on a low level attribute summary and uses histograms of curvature and orientation measurements the second approach is based on the structural arrangement of constant shape index maximal patches and their associated region attributes we show that region curvedness and a string ordering of the regions according to size provides recognition accuracy of about 96 percent by polling various recognition schemes including a graph matching method we show that a recognition rate of 98 99 percent is achievable

reduction techniques for infinite dimensional hamiltonian systems some ideas and applications in the language of tensor analysis on differentiable manifolds we present a reduction method of integrability structures and apply it to recover some well known hierarchies of integrable nonlinear evolution equations

on an integrable hierarchy derived from the isentropic gas dynamics in this paper we study a new hierarchy of equations derived from the system of isentropic gas dynamics equations where the pressure is a nonlocal function of the density we show that the hierarchy of equations is integrable we construct the two compatible hamiltonian structures and show that the first structure has three distinct casimirs while the second has one the existence of casimirs allows us to extend the flows to local ones we construct an infinite series of commuting local hamiltonians as well as three infinite series related to the three casimirs of nonlocal charges we discuss the zero curvature formulation of the system where we obtain a simple expression for the nonlocal conserved charges which also clarifies the existence of the three series from a lie algebraic point of view we point out that the nonlocal hierarchy of hunter zheng equations can be obtained from our nonlocal flows when the dynamical variables are properly constrained

hamiltonian regularisation of shallow water equations with uneven bottom the regularisation of nonlinear hyperbolic conservation laws has been a problem of great importance for achieving uniqueness of weak solutions and also for accurate numerical simulations in a recent work the first two authors proposed a so called hamiltonian regularisation for nonlinear shallow water and isentropic euler equations the characteristic property of this method is that the regularisation of solutions is achieved without adding any artificial dissipation or dispersion the regularised system possesses a hamiltonian structure and thus formally preserves the corresponding energy functional in the present article we generalise this approach to shallow water waves over general possibly time dependent bottoms the proposed system is solved numerically with continuous galerkin method and its solutions are compared with the analogous solutions of the classical shallow water and dispersive serre green naghdi equations the numerical results confirm the absence of dispersive and dissipative effects in presence of bathymetry variations

better short seed quantum proof extractors we construct a strong extractor against quantum storage that works for every min entropy k has logarithmic seed length and outputs w k bits provided that the quantum adversary has at most bk qubits of memory for any b 12 the construction works by first condensing the source with minimal entropy loss and then applying an extractor that works well against quantum adversaries when the source is close to uniform we also obtain an improved construction of a strong quantum proof extractor in the high min entropy regime specifically we construct an extractor that uses a logarithmic seed length and extracts w n bits from any source over 0 1 n provided that the min entropy of the source conditioned on the quantum adversary s state is at least 1 b n for any b 12

canonical structures for dispersive waves in shallow water the canonical hamiltonian structure of the equations of fluid dynamics obtained in the boussinesq approximation are considered new variational formulations of these equations are proposed and it is found that as in the case of the kdv equation and the equations governing long waves in shallow water they are degenerate lagrangian systems therefore in order to cast these equations into canonical form it is again necessary to use dirac s theory of constraints it is found that there are primary and secondary constraints which are second class and it is possible to construct the hamiltonian in terms of canonical variables among the examples of boussinesq equations that are discussed are the equations of whitham broer kaup which kupershmidt has recently expressed in symmetric form and shown to admit tri hamiltonian structure

bi hamiltonian structures of d boussinesq and benney lax equations the dispersionless boussinesq and benney lax equations are equations of hydrodynamic type which can be obtained as reductions of the dispersionless kadomtsev petviashvili equation we find that for the three component reduction the dispersionless boussinesq and benney lax equations are the same up to a diffeomorphism this equivalence becomes manifest when the equations of motion are cast into the form of a triplet of conservation laws furthermore in this form we are able to recognize a non trivial scaling symmetry of these equations which plays an important role in the construction of their bi hamiltonian structure we exhibit a pair of compatible hamiltonian operators which belong to a restricted class of dubrovin and novikov operators appropriate to a system of conservation laws the recursion operator for this system generates three infinite sequences of conserved hamiltonians

efficient sampling of complex network with modified random walk strategies abstract we present two novel random walk strategies choosing seed node csn random walk and no retracing nr random walk different from the classical random walk sampling the csn and nr strategies focus on the influences of the seed node choice and path overlap respectively three random walk samplings are applied in the erdos renyi er barabasi albert ba watts strogatz ws and the weighted usair networks respectively then the major properties of sampled subnets such as sampling efficiency degree distributions average degree and average clustering coefficient are studied the similar conclusions can be reached with these three random walk strategies firstly the networks with small scales and simple structures are conducive to the sampling secondly the average degree and the average clustering coefficient of the sampled subnet tend to the corresponding values of original networks with limited steps and thirdly all the degree distributions of the subnets are slightly biased to the high degree side however the nr strategy performs better for the average clustering coefficient of the subnet in the real weighted usair networks some obvious characters like the larger clustering coefficient and the fluctuation of degree distribution are reproduced well by these random walk strategies

determinacy and optimal strategies in infinite state stochastic reachability games we consider perfect information reachability stochastic games for 2 players on countable graphs such a game is strongly determined if whenever we fix an inequality and a threshold p either player max has a strategy which forces the value of the game to satisfy p against any strategy of player min or min has a strategy which forces the opposite against any strategy of max one of our results shows that whenever one of the players has an optimal strategy in every state of a game then this game is strongly determined this significantly generalises e g recent results on finitely branching reachability games for strong determinacy our methods are substantially different based on which player has the optimal strategy because the roles of the players are not symmetric we also do not restrict the branching of the games and where we provide an extension of results for finitely branching games we had to overcome significant complications and employ new methods as well the other result is finding a subclass of stochastic games where player max has an optimal strategy in each state the subclass is defined by the property that if v is an accumulation point of the set of all values of a game then v 0 these results complement recent results classifying the existence of an optimal strategy for player min and our general strong determinacy theorem applies here as well we also apply our results for max in the context of recently studied one counter stochastic games this work extends a workshop version of this paper which appeared in gandalf 2011 in particular we prove a conjecture raised in that paper for the class of all reachability games

shape from shading level set propagation and viscosity solutions we present a new implementation of an algorithm aimed at recovering a 3d shape from its 2d gray level picture in order to reconstruct the shape of the object an almost arbitrarily initialized 3d function is propagated on a rectangular grid so that a level set of this function tracks the height contours of the shape the method imports techniques from differential geometry fluid dynamics and numerical analysis and provides an accurate shape from shading algorithm the method solves some topological problems and gracefully handles cases of non smooth surfaces that give rise to shocks in the propagating contours real and synthetic images of 3d profiles were submitted to the algorithm and the reconstructed surfaces are presented demonstrating the effectiveness of the proposed method

canonical formulation of shallow water waves the author introduces a new potential and use it with the velocity potential to construct a new variational principle for long surface waves in shallow water applying dirac s theory of constraints the author casts it into canonical form and obtain an explicit expression for the exact hamiltonian

bi hamiltonian structure of n component kodama equations the author presents a simple way of constructing the second hamiltonian operators for n component kodama equations using dimensional analysis he is led to an ansatz for the hamiltonian operator as well as the conserved quantities in terms of ratios of polynomials the coefficients of these polynomials are determined from the jacobi identities the resulting bi hamiltonian structure consists of generalization of cavalcante and mckean s work 1982 for n 2 and his earlier results for n 3 4

a coupled statistical model for face shape recovery from brightness images we focus on the problem of developing a coupled statistical model that can be used to recover facial shape from brightness images of faces we study three alternative representations for facial shape these are the surface height function the surface gradient and a fourier basis representation we jointly capture variations in intensity and the surface shape representations using a coupled statistical model the model is constructed by performing principal components analysis on sets of parameters describing the contents of the intensity images and the facial shape representations by fitting the coupled model to intensity data facial shape is implicitly recovered from the shape parameters experiments show that the coupled model is able to generate accurate shape from out of training sample intensity images

multi lagrangians for integrable systems we propose a general scheme to construct multiple lagrangians for completely integrable nonlinear evolution equations that admit multi hamiltonian structure the recursion operator plays a fundamental role in this construction we use a conserved quantity higher lower than the hamiltonian in the potential part of the new lagrangian and determine the corresponding kinetic terms by generating the appropriate momentum map this leads to some remarkable new developments we show that nonlinear evolutionary systems that admit n fold first order local hamiltonian structure can be cast into variational form with 2n 1 lagrangians which will be local functionals of clebsch potentials this number increases to 3n 2 when the miura transformation is invertible furthermore we construct a new lagrangian for polytropic gas dynamics in 1 1 dimensions which is a free local functional of the physical field variables namely density and velocity thus dispensing with the necessity of introducing clebsch potentials entirely this is a consequence of bi hamiltonian structure with a compatible pair of first and third order hamiltonian operators derived from sheftel s recursion operator

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

line pattern retrieval using relational histograms this paper presents a new compact shape representation for retrieving line patterns from large databases the basic idea is to exploit both geometric attributes and structural information to construct a shape histogram we realize this goal by computing the n nearest neighbor graph for the lines segments for each pattern the edges of the neighborhood graphs are used to gate contributions to a two dimensional pairwise geometric histogram shapes are indexed by searching for the line pattern that maximizes the cross correlation of the normalized histogram bin contents we evaluate the new method on a database containing over 2 500 line patterns each composed of hundreds of lines

an example of a miura map the shallow water wave equations the linear hamiltonian structure of modified shallow water wave equations goes to the non linear and second hamiltonian structure of the bi hamiltonian shallow water wave equations a similar situation must exist for gas dynamics according to a result of dubrovin and novikov 1983

boundary conditions and the first order conserved density for gas dynamics boundary conditions for gas dynamics are chosen to make the first order conserved density finitely integrable the action of the corresponding third order noetherian symmetry on the boundary condition is discussed a generalisation to first order diagonalised quasilinear systems is considered

on the complexity of nash equilibria and other fixed points we reexamine what it means to compute nash equilibria and more generally what it means to compute a fixed point of a given brouwer function and we investigate the complexity of the associated problems specifically we study the complexity of the following problem given a finite game gamma with 3 or more players and given epsilon 0 compute an approximation within epsilon of some actual nash equilibrium we show that approximation of an actual nash equilibrium even to within any nontrivial constant additive factor epsilon 1 2 in just one desired coordinate is at least as hard as the long standing square root sum problem as well as a more general arithmetic circuit decision problem that characterizes p time in a unit cost model of computation with arbitrary precision rational arithmetic thus placing the approximation problem in p or even np would resolve major open problems in the complexity of numerical computation we show similar results for market equilibria it is hard to estimate with any nontrivial accuracy the equilibrium prices in an exchange economy with a unique equilibrium where the economy is given by explicit algebraic formulas for the excess demand functions we define a class fixp which captures search problems that can be cast as fixed point computation problems for functions represented by algebraic circuits straight line programs over basis max min with rational constants we show that the exact or approximate computation of nash equilibria for 3 or more players is complete for fixp the price equilibrium problem for exchange economies with algebraic demand functions is another fixp complete problem we show that the piecewise linear fragment of fixp equals ppad many other problems in game theory economics and probability theory can be cast as fixed point problems for such algebraic functions we discuss several important such problems computing the value of shapley s stochastic games and the simpler games of condon extinction probabilities of branching processes probabilities of stochastic context free grammars and termination probabilities of recursive markov chains we show that for some of them the approximation or even exact computation problem can be placed in ppad while for others they are at least as hard as the square root sum and arithmetic circuit decision problems

new constraints on data closeness and needle map consistency for shape from shading this paper makes two contributions to the problem of needle map recovery using shape from shading first we provide a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint this not only improves the data closeness of the recovered needle map but also removes the necessity for extensive parameter tuning second we exploit the improved ease of control of the new shape from shading process to investigate various types of needle map consistency constraint the first set of constraints are based on needle map smoothness the second avenue of investigation is to use curvature information to impose topographic constraints third we explore ways in which the needle map is recovered so as to be consistent with the image gradient field in each case we explore a variety of robust error measures and consistency weighting schemes that can be used to impose the desired constraints on the recovered needle map we provide an experimental assessment of the new shape from shading framework on both real world images and synthetic images with known ground truth surface normals the main conclusion drawn from our analysis is that the data closeness constraint improves the efficiency of shape from shading and that both the topographic and gradient consistency constraints improve the fidelity of the recovered needle map

the µ calculus alternation hierarchy collapses over structures with restricted connectivity the alternation hierarchy of least and greatest fixpoint operators in the calculus is strict however the strictness of the hierarchy does not necessarily carry over when considering restricted classes of structures for instance over the class of infinite words the alternation free fragment of the calculus is already as expressive as the full logic our current understanding of when and why the calculus alternation hierarchy is and is not strict is limited this article makes progress in answering these questions by showing that the alternation hierarchy of the calculus collapses to the alternation free fragment over some classes of structures including infinite nested words and finite graphs with feedback vertex sets of a bounded size common to these classes is that the connectivity between the components in a structure from such a class is restricted in the sense that the removal of certain vertices from the structure s graph decomposes it into graphs in which all paths are of finite length the collapse results herein are obtained in an automata theoretic setting they subsume generalize and strengthen several prior results on the expressivity of the calculus over restricted classes of structures

on retrieving textured images from an image database abstract we discuss the problem of an image based query for retrieving images represented by sufficiently large regions of uniform textures from image data bases a distance measure to match the query image to the database content under possible orientation and scale differences between the textures of the same type is proposed the measure is based on comparing the gray level difference histograms collected in accord with the structure of multiple pairwise pixel interactions in the subimages to be matched the interaction structure is recovered with a proposed learning scheme for a markov random field image model with gibbs probability distribution texture rotation and scaling are handled to some extent by similar transformations of the interaction structures several results on experimental databases containing digitized textured images are presented

mathematics of dispersive water waves a commuting hierarchy of dispersive water wave equations makes a three hamiltonian system which belongs to a general class of nonstandard integrable systems whose theory is developed the modified water wave hierarchy is a bi hamiltonian system its modification bifurcates the water wave hierarchy and the hierarchies of the korteweg de vries and the modified korteweg de vries equations as well as the classical miura map are given new representations through various specializations of nonstandard systems

integrable evolution systems based on gerdjikov ivanov equations bi hamiltonian structure finite dimensional integrable systems and n fold darboux transformation a spectral problem and the associated gerdjikov ivanov gi hierarchy of nonlinear evolution equations is presented as a reduction the well known gi equation of derivative nonlinear schrodinger equations is obtained it is shown that the gi hierarchy is integrable in a liouville sense and possesses bi hamiltonian structure moreover the spectral problem can be nonlinearized as a finite dimensional completely integrable system under the bargmann constraint between the potentials and the eigenfunctions in particular an explicit n fold darboux transformation for the gi equation is constructed with the help of a gauge transformation of spectral problems and a reduction technique some explicit solitonlike solutions of the gi equation are given by applying its darboux transformation

language equivalence of probabilistic pushdown automata we study the language equivalence problem for probabilistic pushdown automata ppda and their subclasses we show that the problem is interreducible with the multiplicity equivalence problem for context free grammars the decidability of which has been open for several decades interreducibility also holds for ppda with one control state in contrast for the case of a one letter input alphabet we show that ppda language equivalence and hence multiplicity equivalence of context free grammars is in pspace and at least as hard as the polynomial identity testing problem

efficient analysis of probabilistic programs with an unbounded counter we show that a subclass of infinite state probabilistic programs that can be modeled by probabilistic one counter automata poc admits an efficient quantitative analysis we start by establishing a powerful link between poc and martingale theory which leads to fundamental observations about quantitative properties of runs in poc in particular we provide a divergence gap theorem which bounds a positive non termination probability in poc away from zero using these observations we show that the expected termination time can be approximated up to an arbitrarily small relative error in polynomial time and the same holds for the probability of all runs that satisfy a given regular property encoded by a deterministic rabin automaton

compatible poisson brackets of hydrodynamic type some general properties of compatible poisson brackets of hydrodynamic type are discussed in particular a an invariant differential geometric criterion of the compatibility based on the nijenhuis tensor which is slightly different from those existing in the literature b the lax pair with a spectral parameter governing compatible poisson brackets in the diagonalizable case c the connection of this problem with the class of surfaces in euclidean space which possess non trivial deformations preserving the weingarten operator

integrable generalizations of the two dimensional born infeld equation the born infeld equation in two dimensions is generalized to higher dimensions lorentz invariance is retained and the resulting system is completely integrable via linearization by legendre transformation this generalization retains homogeneity in second derivatives of the field

quasiclassical limit of coupled kdv equations riemann invariants and multi hamiltonian structure abstract we consider the quasiclassical limit of the first nontrivial flow in coupled kdv hierarchy written down in riemann invariants it assumes the extremely simple form r i k 1 n r k 2r i r x i i 1 n up to certain natural equivalence this turns out to be the only hydrodynamic system with n 1 compatible purely local hamiltonian structures

hamiltonian structures and conservation laws of the belov chaltikian lattice hierarchy a hierarchy of nonlinear differential difference equations associated with a 3 3 matrix spectral problem is proposed through discrete zero curvature equations one of the nontrivial equations in this hierarchy is the famous belov chaltikian lattice equation it is shown that the hierarchy possesses infinitely many conservation laws hamiltonian structures for this hierarchy are constructed with the aid of the trace identity

on a new class of completely integrable nonlinear wave equations ii multi hamiltonian structure the multi hamiltonian structure of a class of nonlinear wave equations governing the propagation of finite amplitude waves is discussed infinitely many conservation laws had earlier been obtained for these equations starting from a primary hamiltonian formulation of these equations the necessary and sufficient conditions for the existence of bi hamiltonian structure are obtained and it is shown that the second hamiltonian operator can be constructed solely through a knowledge of the first hamiltonian function the recursion operator which first appears at the level of bi hamiltonian structure gives rise to an infinite sequence of conserved hamiltonians it is found that in general there exist two different infinite sequences of conserved quantities for these equations the recursion relation defining higher hamiltonian structures enables one to obtain the necessary and sufficient conditions for the existence of the k 1 st hamiltonian operator which depends on the kth hamiltonian function the infinite sequence of conserved hamiltonians are common to all the higher hamiltonian structures the equations of gas dynamics are discussed as an illustration of this formalism and it is shown that in general they admit tri hamiltonian structure with two distinct infinite sets of conserved quantities the isothermal case of 1 is an exceptional one that requires separate treatment this corresponds to a specialization of the equations governing the expansion of plasma into vacuum which will be shown to be equivalent to poisson s equation in nonlinear acoustics

on hamiltonian perturbations of hyperbolic systems of conservation laws i quasi triviality of bi hamiltonian perturbations we study the general structure of formal perturbative solutions to the hamiltonian perturbations of spatially one dimensional systems of hyperbolic pdes vt v x 0 under certain genericity assumptions it is proved that any bi hamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the infinite jet space depending rationally on the derivatives the main tool is in constructing the so called quasimiura transformation of jet coordinates eliminating an arbitrary deformation of a semisimple bi hamiltonian structure of hydrodynamic type the quasi triviality theorem we also describe following 35 the invariants ofsuchbi hamiltonian structures with respect to the group of miura type transformations depending polynomially on the derivatives c

diagonalization and hamiltonian structures of hyperbolic systems a simple algorithm for casting two dimensional hyperbolic systems into the hamiltonian form is given first order conserved quantities are found and expressed in terms of eigenvalues it is shown that for some systems the dependence of the eigenvalues on the field variables can be used for classification

on the μ calculus over transitive and finite transitive frames we prove that the modal m calculus collapses to first order logic over the class of finite transitive frames the proof is obtained by using some byproducts of a new proof of the collapse of the m calculus to the alternation free fragment over the class of transitive frames moreover we prove that the modal m calculus is buchi and co buchi definable over the class of all models where in a strongly connected component vertexes are distinguishable by means of the propositions they satisfy

alternative bi hamiltonian structures for wdvv equations of associativity the wdvv equations of associativity in two dimensional topological field theory are completely integrable third order monge ampere equations which admit bi hamiltonian structure the time variable plays a distinguished role in the discussion of hamiltonian structure whereas in the theory of wdvv equations none of the independent variables merits such a distinction wdvv equations admit very different alternative hamiltonian structures under different possible choices of the time variable but all these various hamiltonian formulations can be brought together in the framework of the covariant theory of symplectic structure they can be identified as different components of the covariant witten zuckerman symplectic 2 form current density where a variational formulation of the wdvv equation that leads to the hamiltonian operator through the dirac bracket is available

on the combinatorial and algebraic complexity of quantifier elimination in this paper a new algorithm for performing quantifier elimination from first order formulas over real closed fields in given this algorithm improves the complexity of the asymptotically fastest algorithm for this problem known to this data a new feature of this algorithm is that the role of the algebraic part the dependence on the degrees of the imput polynomials and the combinatorial part the dependence on the number of polynomials are sparated another new feature is that the degrees of the polynomials in the equivalent quantifier free formula that is output are independent of the number of input polynomials as special cases of this algorithm new and improved algorithms for deciding a sentence in the first order theory over real closed fields and also for solving the existential problem in the first order theory over real closed fields are obtained

multi hamiltonian structure of the born infeld equation the multi hamiltonian structure conservation laws and higher order symmetries for the born infeld equation are exhibited a new transformation of the born infeld equation to the equations of a chaplygin gas is presented and explored the born infeld equation is distinguished among two dimensional hyperbolic systems by its wealth of such multi hamiltonian structures

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

multi hamiltonian structure of equations of hydrodynamic type the discussion of the hamiltonian structure of two component equations of hydrodynamic type is completed by presenting the hamiltonian operators for euler s equation governing the motion of plane sound waves of finite amplitude and another quasilinear second order wave equation there exists a doubly infinite family of conserved hamiltonians for the equations of gas dynamics that degenerate into one namely the benney sequence for shallow water waves infinite sequences of conserved quantities for these equations are also presented in the case of multicomponent equations of hydrodynamic type it is shown that kodama s generalization of the shallow water equations admits bi hamiltonian structure

coarse view synthesis using shape from shading this paper investigates the use of shape from shading for coarse view synthesis the aim of our study is to determine whether needle maps delivered by a new shape from shading sfs algorithm can be used as a compact object representation for the purposes of efficiently generating appearance manifolds specifically we aim to show that the needle maps can be used to generate novel object views under changing light source and viewer directions to this end we conduct two sets of experiments firstly we use the recovered needle maps to re illuminate objects under varying lighting directions here we show that a single input image can be used to construct relatively faithful re illuminations under radical illumination changes secondly we investigate how the needle map can be used to generate new object poses here we show that needle maps can be used for both view interpolation and view extrapolation

non polynomial conservation law densities generated by the symmetry operators in some hydrodynamical models a new extra series of conserved densities for the polytropic gas model and nonlinear elasticity equation is obtained without any reference to the recursion operator or to the lax operator formalism our method is based on the utilization of the symmetry operators and allows us to obtain the densities of arbitrary homogeneity dimensions the non polynomial densities with logarithmic behaviour are presented as an example special attention is paid to the singular case 1 for which we have found new non homogeneous solutions expressed in terms of the elementary functions

cosmos a representation scheme for 3d free form objects we address the problem of representing and recognizing 3d free form objects when 1 the object viewpoint is arbitrary 2 the objects may vary in shape and complexity and 3 no restrictive assumptions are made about the types of surfaces on the object we assume that a range image of a scene is available containing a view of a rigid 3d object without occlusion we propose a new and general surface representation scheme for recognizing objects with free form sculpted surfaces in this scheme an object is described concisely in terms of maximal surface patches of constant shape index the maximal patches that represent the object are mapped onto the unit sphere via their orientations and aggregated via shape spectral functions properties such as surface area curvedness and connectivity which are required to capture local and global information are also built into the representation the scheme yields a meaningful and rich description useful for object recognition a novel concept the shape spectrum of an object is also introduced within the framework of cosmos for object view grouping and matching we demonstrate the generality and the effectiveness of our scheme using real range images of complex objects

hamiltonian structure of real monge ampere equations the variational principle for the real homogeneous monge ampere equation in two dimensions is shown to contain three arbitrary functions of four variables there exist two different specializations of this variational principle where the lagrangian is degenerate and furthermore contains an arbitrary function of two variables the hamiltonian formulation of these degenerate lagrangian systems requires the use of dirac s theory of constraints as in the case of most completely integrable systems the constraints are second class and dirac brackets directly yield the hamiltonian operators thus the real homogeneous monge ampere equation in two dimensions admits two classes of infinitely many hamiltonian operators namely a family of local as well as another family non local hamiltonian operators and symplectic 2 forms which depend on arbitrary functions of two variables the simplest non local hamiltonian operator corresponds to the kac moody algebra of vector fields and functions on the unit circle hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair in the case of real monge ampere equations with constant right hand side this compatible pair is the only pair of hamiltonian operators that survives then the complete integrability of all these real monge ampere equations follows by magri s theorem some of the remarkable properties we have obtained for the hamiltonian structure of the real homogeneous monge ampere equation in two dimensions turn out to be generic to the real homogeneous monge ampere equation and the geodesic flow for the complex homogeneous monge ampere equation in arbitrary number of dimensions hence among all integrable nonlinear evolution equations in one space and one time dimension the real homogeneous monge ampere equation is distinguished as one that retains its character as an integrable system in multiple dimensions

a family of completely integrable multi hamiltonian systems explicitly related to some celebrated equations by introducing a spectral problem with an arbitrary parameter we derive a kaup newell type hierarchy of nonlinear evolution equations which is explicitly related to many important equations such as the kundu equation the kaup newell kn equation the chen lee liu cll equation the gerdjikov ivanov gi equation the burgers equation the modified korteweg devries mkdv equation and the sharma tasso olver equation it is shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure under the bargann constraint between the potentials and the eigenfunctions the spectral problem is nonlinearized as a finite dimensional completely integrable hamiltonian system the involutive representation of the solutions for the kaup newell type hierarchy is also presented in addition an n fold darboux transformation of the kundu equation is constructed with the help of its lax pairs and a reduction technique according to the darboux transformation the solutions of the ku

conservation laws for shallow water waves on a sloping beach shallow water waves are governed by a pair of nonlinear partial differential equations we transfer the associated homogeneous and nonhomogeneous systems corresponding to constant and sloping depth respectively to the hodograph plane where we find all the nonsimple wave solutions and construct infinitely many polynomial conversation laws we also establish correspondence between conservation laws and hodograph solutions as well as backlund transformations by using the linear nature of the problems on the hodograph plane

integrable hydrodynamic chains a new approach for derivation of benney type moment chains and integrable hydrodynamic type systems is presented new integrable hydrodynamic chains are constructed all their hydrodynamical reductions are described and integrated new 2 1 integrable hydrodynamic type systems are found

perfect fluid theory and its extensions we review the canonical theory for perfect fluids in euler s and lagrange s formulations the theory is related to a description of extended structures in higher dimensions internal symmetry and supersymmetry degrees of freedom are incorporated additional miscellaneous subjects that are covered include physical topics concerning quantization as well as mathematical issues of volume preserving diffeomorphisms and representations of chern simons terms vortex or magnetic helicity

improved mixing condition on the grid for counting and sampling independent sets the hard core model has received much attention in the past couple of decades as a lattice gas model with hard constraints in statistical physics a multicast model of calls in communication networks and as a weighted independent set problem in combinatorics probability and theoretical computer science in this model each independent set i in a graph g is weighted proportionally to i for a positive real parameter for large computing the partition function namely the normalizing constant which makes the weighting a probability distribution on a finite graph on graphs of maximum degree 3 is a well known computationally challenging problem more concretely let lambda c mathbb t delta denote the critical value for the so called uniqueness threshold of the hard core model on the infinite regular tree recent breakthrough results of weitz proceedings of the 38th annual acm symposium on theory of computing stoc pp 140 149 2006 and sly proceedings of the 51st annual ieee symposium on foundations of computer science focs pp 287 296 2010 have identified lambda c mathbb t delta as a threshold where the hardness of estimating the above partition function undergoes a computational transition we focus on the well studied particular case of the square lattice mathbb z 2 and provide a new lower bound for the uniqueness threshold in particular taking it well above lambda c mathbb t 4 our technique refines and builds on the tree of self avoiding walks approach of weitz resulting in a new technical sufficient criterion of wider applicability for establishing strong spatial mixing and hence uniqueness for the hard core model our new criterion achieves better bounds on strong spatial mixing when the graph has extra structure improving upon what can be achieved by just using the maximum degree applying our technique to mathbb z 2 we prove that strong spatial mixing holds for all 2 3882 improving upon the work of weitz that held for 27 16 1 6875 our results imply a fully polynomial deterministic approximation algorithm for estimating the partition function as well as rapid mixing of the associated glauber dynamics to sample from the hard core distribution