estimating pagerank on graph streams this article focuses on computations on large graphs e g the web graph where the edges of the graph are presented as a stream the objective in the streaming model is to use small amount of memory preferably sub linear in the number of nodes n and a smaller number of passes in the streaming model we show how to perform several graph computations including estimating the probability distribution after a random walk of length l the mixing time m and other related quantities such as the conductance of the graph by applying our algorithm for computing probability distribution on the web graph we can estimate the pagerank p of any node up to an additive error of se p e in o sm passes and o min n 1 esm 1 e m nsm 1 e sm space for any i 0 1 specifically for e e m n e m 1 2 we can compute the approximate pagerank values in o nm 1 4 space and o m3 4 passes in comparison a standard implementation of the pagerank algorithm will take o n space and o m passes we also give an approach to approximate the pagerank values in just o 1 passes although this requires o nm space

cooling schedules for optimal annealing a monte carlo optimization technique called simulated annealing is a descent algorithm modified by random ascent moves in order to escape local minima which are not global minima the level of randomization is determined by a control parameter t called temperature which tends to zero according to a deterministic cooling schedule we give a simple necessary and sufficient condition on the cooling schedule for the algorithm state to converge in probability to the set of globally minimum cost states in the special case that the cooling schedule has parametric form tt c log1 t the condition for convergence is that c be greater than or equal to the depth suitably defined of the deepest local minimum which is not a global minimum state

korteweg de vries surfaces abstract we consider 2 surfaces arising from the korteweg de vries kdv hierarchy and the kdv equation the surfaces corresponding to the kdv equation are in a three dimensional minkowski m 3 space they contain a family of quadratic weingarten and willmore like surfaces we show that some kdv surfaces can be obtained from a variational principle where the lagrange function is a polynomial function of the gaussian and mean curvatures we also give a method for constructing the surfaces explicitly i e finding their parameterizations or finding their position vectors

a new computational algorithm for functional inequality constrained optimization problems abstract in this note a computational algorithm is devised for solving a class of functional inequality constrained optimization problems based on a penalty function for illustration a numerical example is solved

modified korteweg de vries surfaces in this work we consider 2 surfaces in r3 arising from the modified korteweg de vries mkdv equation we give a method for constructing the position vector of the mkdv surface explicitly for a given solution of the mkdv equation mkdv surfaces contain willmore like and weingarten surfaces we show that some mkdv surfaces can be obtained from a variational principle where the lagrange function is a polynomial of the gaussian and mean curvatures

a generalized formula for integrable classes of surfaces in lie algebras we discuss relations between the approach of fokas and gelfand to immersions on lie algebras and the theory of soliton surfaces of sym we show that many results concerning immersions on lie algebras can be reduced to or interpreted within the soliton surfaces approach we present also some new results including a generalization of the fokas gelfand formula for integrable classes of surfaces in lie algebras and in particular in pseudo euclidean n dim spaces the generalized formula is used to formulate a method of constructing integrable classes of surfaces as an example we discuss the class of linear weingarten surfaces defined by the linear relationship between gaussian and mean curvatures we construct explicitly a one parameter family of linear weingarten surfaces parallel equidistant to a given pseudospherical surface

on the geometry of an integrable 2 1 dimensional sine gordon system it is recorded that darboux9s method of linking the classical lame system governing triply orthogonal systems of surfaces with an integrable 2 1 dimensional sine gordon equation may be extended and applied to the integrable two component generalization of the latter introduced by konopelchenko and rogers thus in a reinterpretation this 2 1 dimensional sine gordon system is shown to define particular integrable motions of surfaces

soliton surfaces associated with generalized symmetries of integrable equations in this paper based on the fokas et al approach fokas and gel fand 1996 commun math phys 177 203 20 fokas et al 2000 sel math 6 347 75 we provide a symmetry characterization of continuous deformations of soliton surfaces immersed in a lie algebra using the formalism of generalized vector fields their prolongation structure and links with the frechet derivatives we express the necessary and sufficient condition for the existence of such surfaces in terms of the invariance criterion for generalized symmetries and identify additional sufficient conditions which admit an explicit integration of the immersion functions of 2d surfaces in lie algebras we discuss in detail the su n valued immersion functions generated by conformal symmetries of the cpn 1 sigma model defined on either the minkowski or euclidean space we further show that the sufficient conditions for explicit integration of such immersion functions impose additional restrictions on the admissible conformal symmetries of the model defined on minkowski space on the other hand the sufficient conditions are identically satisfied for arbitrary conformal symmetries of finite action solutions of the cpn 1 sigma model defined on euclidean space

distributed random walks performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science including distributed computing in this article we focus on the problem of sampling random walks efficiently in a distributed network and its applications given bandwidth constraints the goal is to minimize the number of rounds required to obtain random walk samples all previous algorithms that compute a random walk sample of length e as a subroutine always do so naively that is in o e rounds the main contribution of this article is a fast distributed algorithm for performing random walks we present a sublinear time distributed algorithm for performing random walks whose time complexity is sublinear in the length of the walk our algorithm performs a random walk of length e in o ed rounds o hides polylog n factors where n is the number of nodes in the network with high probability on an undirected network where d is the diameter of the network for small diameter graphs this is a significant improvement over the naive o e bound furthermore our algorithm is optimal within a poly logarithmic factor as there exists a matching lower bound nanongkai et al 2011 we further extend our algorithms to efficiently perform k independent random walks in o ked k rounds we also show that our algorithm can be applied to speedup the more general metropolis hastings sampling our random walk algorithms can be used to speed up distributed algorithms in applications that use random walks as a subroutine we present two main applications first we give a fast distributed algorithm for computing a random spanning tree rst in an arbitrary undirected unweighted network which runs in o md rounds with high probability m is the number of edges our second application is a fast decentralized algorithm for estimating mixing time and related parameters of the underlying network our algorithm is fully decentralized and can serve as a building block in the design of topologically aware networks

new nonlinear evolution equations from surface theory we point out that the connection between surfaces in three dimensional flat space and the inverse scattering problem provides a systematic way for constructing new nonlinear evolution equations in particular we study the imbedding for guichard surfaces which gives rise to the calapso guichard equations generalizing the sine gordon sg equation further we investigate the geometry of surfaces and their imbedding which results in the korteweg devries kdv equation then by constructing a family of applicable surfaces we obtain a generalization of the kdv equation to a compressible fluid

intrinsic graph structure estimation using graph laplacian a graph is a mathematical representation of a set of variables where some pairs of the variables are connected by edges common examples of graphs are railroads the internet and neural networks it is both theoretically and practically important to estimate the intensity of direct connections between variables in this study a problem of estimating the intrinsic graph structure from observed data is considered the observed data in this study are a matrix with elements representing dependency between nodes in the graph the dependency represents more than direct connections because it includes influences of various paths for example each element of the observed matrix represents a co occurrence of events at two nodes or a correlation of variables corresponding to two nodes in this setting spurious correlations make the estimation of direct connection difficult to alleviate this difficulty a digraph laplacian is used for characterizing a graph a generative model of this observed matrix is proposed and a parameter estimation algorithm for the model is also introduced the notable advantage of the proposed method is its ability to deal with directed graphs while conventional graph structure estimation methods such as covariance selections are applicable only to undirected graphs the algorithm is experimentally shown to be able to identify the intrinsic graph structure

soliton surfaces and generalized symmetries of integrable systems in this paper we discuss some specific features of symmetries of integrable systems which can be used to construct the fokas gel fand formula for the immersion of 2d soliton surfaces associated with such systems in lie algebras we establish a sufficient condition for the applicability of this formula this condition requires the existence of two vector fields which generate a common symmetry of the initial system and its corresponding linear spectral problem this means that these two fields have to be group related and we determine an explicit form of this relation it provides a criterion for the selection of symmetries suitable for use in the fokas gel fand formula we include some examples illustrating its application

approximating the permanent a randomised approximation scheme for the permanent of a 0 1s presented the task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph the latter is accomplished by simulating a markov chain whose states are the matchings in the graph for a wide class of 0 1 matrices the approximation scheme is fully polynomial i e runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output this class includes all dense matrices those that contain sufficiently many 1 s and almost all sparse matrices in some reasonable probabilistic model for 0 1 matrices of given density for the approach sketched above to be computationally efficient the markov chain must be rapidly mixing informally it must converge in a short time to its stationary distribution a major portion of the paper is devoted to demonstrating that the matchings chain is rapidly mixing apparently the first such result for a markov chain with genuinely c

perturbation analysis for the design of flexible manufacturing system flow controllers dynamic allocation of stochastic capacity among competing activities in a just in time manufacturing environment is addressed by optimal flow control optimal policies are characterized by generally intractable bellman equations a near optimal controller design technique is proposed it provides an approximate numerical solution to the bellman equation a tight lower bound for the optimality gap of tractable near optimal controller designs and a building block for improved near optimal controller designs that rely on the decomposition of a multiple part type problem to smaller two or three part type problems computational experience is reported for two and three part type problems

two dimensional monomer dimer systems are computationally intractable the classic problem of counting monomer dimer arrangements on a two dimensional lattice is analyzed using techniques from theoretical computer science under a certain assumption made precise in the text it can be shown that the general problem is computationally intractable this negative result contrasts with the special case of a system with monomer density zero for which efficient solutions have been known for some time a second much easier result obtained under the same assumption is that the partition function of a three dimensional ising system is computationally intractable again the negative result contrasts with known efficient techniques for evaluating the partition function of a two dimensional system

deformation of surfaces integrable systems and chern simons theory a few years ago some of us devised a method to obtain integrable systems in 2 1 dimensions from the classical non abelian pure chern simons action via the reduction of the gauge connection in hermitian symmetric spaces in this article we show that the methods developed in studying classical non abelian pure chern simons actions can be naturally implemented by means of a geometrical interpretation of such systems the chern simons equation of motion turns out to be related to time evolving two dimensional surfaces in such a way that these deformations are both locally compatible with the gauss mainardi codazzi equations and completely integrable the properties of these relationships are investigated together with the most relevant consequences explicit examples of integrable surface deformations are displayed and discussed

on integrability of weingarten surfaces a forgotten class rediscovered by a systematic search a forgotten class of integrable surfaces is shown to disprove the finkel wu conjecture the associated integrable nonlinear partial differential equation possesses a zero curvature representation a third order symmetry and a nonlocal transformation to the sine gordon equation sin we leave open the problem of finding a backlund autotransformation and a recursion operator that would produce a local hierarchy

invariant submanifold flows given a lie group acting on a manifold our aim is to analyze the evolution of differential invariants under invariant submanifold flows the constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex applications to integrable soliton dynamics and to the evolution of differential invariant signatures used in equivalence problems and object recognition and symmetry detection in images are discussed

deformations of surfaces associated with integrable gauss mainardi codazzi equations using the formulation of the immersion of a two dimensional surface into the three dimensional euclidean space proposed recently a mapping from each symmetry of integrable equations to surfaces in r3 can be established we show that among these surfaces the sphere plays a unique role indeed under the rigid su 2 rotations all integrable equations are mapped to a sphere furthermore we prove that all compact surfaces generated by the infinitely many generalized symmetries of the sine gordon equation are homeomorphic to a sphere we also find some new weingarten surfaces arising from the deformations of the modified kurteweg de vries and of the nonlinear schrodinger equations surfaces can also be associated with the motion of curves we study curve motions on a sphere and we identify a new integrable equation characterizing such a motion for a particular choice of the curve velocity

on the construction of integrable surfaces on lie groups the problem of the immersion of a two dimensional surface into a three dimensional euclidean space can be formulated in terms of the immersion of surfaces in lie groups and lie algebras a general formalism for this problem is developed as well as an equivalent mauer cartan system of differential forms the particular case of the lie group su 2 is examined and it is shown to be useful for studying integrable surfaces some examples of such surfaces and their equations are presented at the end in particular the cases of constant mean curvature and of zero gaussian curvature

the time complexity of maximum matching by simulated annealing the random heuristic search algorithm called simulated annealing is considered for the problem of finding the maximum cardinality matching in a graph it is shown that neither a basic form of the algorithm nor any other algorithm in a fairly large related class of algorithms can find maximum cardinality matchings such that the average time required grows as a polynomial in the number of nodes of the graph in contrast it is also shown for arbitrary graphs that a degenerate form of the basic annealing algorithm obtained by letting temperature be a suitably chosen constant produces matchings with nearly maximum cardinality in polynomial average time

surfaces on lie groups on lie algebras and their integrability it is shown that the problem of the immersion of a 2 dimensional surface into a 3 dimensional euclidean space as well as then dimensional generalization of this problem is related to the problem of studying surfaces in lie groups and surfaces in lie algebras a particular case of the general formalism presented here implies that any surface can be characterized in terms of 2 2 matrices using an arbitrary parametrization it is also shown that this generality of parametrization is useful for studying integrable surfaces i e surfaces described by integrable equations in particular starting from a suitable lax pair i e a suitable integrable equation it is possible to construct explicitly large classes of integrable surfaces

stochastic dynamic job shops and hierarchical production planning this paper presents an asymptotic analysis of hierarchical production planning in a general manufacturing system consisting of a network of unreliable machines producing a variety of products the concept of a dynamic job shop is introduced by interpreting the system as a directed graph and the structure of the system dynamics is characterized for its use in the asymptotic analysis the optimal control problem for the system is a state constrained problem since the number of parts in any buffer between any two machines must remain nonnegative a limiting problem is introduced in which the stochastic machine capacities are replaced by corresponding equilibrium mean capacities as the rate of change in machine states approaches infinity the value function of the original problem is shown to converge to that of the limiting problem and the convergence rate is obtained furthermore near optimal controls for the original problem are constructed from near optimal controls of the limiting problem and an error estimate is obtained on the near optimality of the constructed controls

the korteweg de vries hierarchy as dynamics of closed curves in the plane the korteweg de vries modified korteweg de vries and harry dym hierarchies of integrable systems are shown to be equivalent to a hierarchy of chiral shape dynamics of closed curves in the plane these purely local dynamics conserve an infinite number of global geometric properties of the curves such as perimeter and enclosed area several techniques used to study these integrable systems are shown to have simple differential geometric interpretations connections with incompressible inviscid fluid flow in two dimensions are suggested

integrable equations arising from motions of plane curves the motion of plane curves in klein geometry is studied it is shown that the kdv harry dym sawada kotera burgers the defocusing mkdv hierarchies the camassa holm and the kaup kupershmidt equation naturally arise from the motions of plane curves in sl 2 sim 2 sa 2 and a 2 geometries these local and nonlocal dynamics conserve global geometric quantities of curves such as perimeter and enclosed area motions of curves in euclidean special linear and similarity geometries corresponding to the traveling wave solutions of the mkdv kdv and burgers equations are discussed