qaplib a quadratic assignment problem library abstract after a short introduction into quadratic assignment problems we give a library of problem instances for the quadratic assignment problem the examples are listed y authors in alphabetical order

bounds for the quadratic assignment problem using the bundle method semidefinite programming sdp has recently turned out to be a very powerful tool for approximating some np hard problems the nature of the quadratic assignment problem qap suggests sdp as a way to derive tractable relaxations we recall some sdp relaxations of qap and solve them approximately using a dynamic version of the bundle method the computational results demonstrate the efficiency of the approach our bounds are currently among the strongest ones available for qap we investigate their potential for branch and bound settings by looking also at the bounds in the first levels of the branching tree

atiyah covering index theorem for riemannian foliations we use the symbol calculus for foliations developed in our previous paper to derive a cohomological formula for the connes chern character of the semi finite spectral triple the same proof works for the type i spectral triple of connes moscovici the cohomology classes of the two connes chern characters induce the same map on the image of the maximal baum connes map in k theory thereby proving an atiyah l 2 covering index theorem

ergodicity of the 2d navier stokes equations with degenerate stochastic forcing the stochastic 2d navier stokes equations on the torus driven by degenerate noise are studied we characterize the smallest closed invariant subspace for this model and show that the dynamics restricted to that subspace is ergodic in particular our results yield a purely geometric characterization of a class of noises for which the equation is ergodic in l 2 0 t 2 unlike previous works this class is independent of the viscosity and the strength of the noise the two main tools of our analysis are the asymptotic strong feller property introduced in this work and an approximate integration by parts formula the first when combined with a weak type of irreducibility is shown to ensure that the dynamics is ergodic the second is used to show that the first holds un

convex graph invariant relaxations for graph edit distance the edit distance between two graphs is a widely used measure of similarity that evaluates the smallest number of vertex and edge deletions insertions required to transform one graph to another it is np hard to compute in general and a large number of heuristics have been proposed for approximating this quantity with few exceptions these methods generally provide upper bounds on the edit distance between two graphs in this paper we propose a new family of computationally tractable convex relaxations for obtaining lower bounds on graph edit distance these relaxations can be tailored to the structural properties of the particular graphs via convex graph invariants specific examples that we highlight in this paper include constraints on the graph spectrum as well as tractable approximations of the stability number and the maximum cut values of graphs we prove under suitable conditions that our relaxations are tight i e exactly compute the graph edit distance when one of the graphs consists of few eigenvalues we also validate the utility of our framework on synthetic problems as well as real applications involving molecular structure comparison problems in chemistry

laws of large numbers for semimartingales with applications to stochastic regression strong laws of large numbers for matrix normalised vector valued local martingales are established the results are derived from strong laws for positive local submartingales and purely discontinuous local martingales and a borel cantelli type lemma for local martingales of finite variation the multivariate strong laws are applied to study strong consistency of estimates in stochastic linear regression models

stochastic integrators indexed by a multi dimensional parameter multi parameter stochastic integrators are described and classified according to directions of integrability sets of directions are distinguished precisely by the combinatorial dimension of corresponding fractional cartesian products the main theorem establishes existence of stochastic processes which are integrators in prescribed directions but not others

spectrum of ornstein uhlenbeck operators in lp spaces with respect to invariant measures abstract let a i j 1 n q ij d ij i j 1 n b ij x j d i be a possibly degenerate ornstein uhlenbeck operator in r n and assume that the associated markov semigroup has an invariant measure we compute the spectrum of a in l p for 1 p

estimating bounds for quadratic assignment problems associated with hamming and manhattan distance matrices based on semidefinite programming quadratic assignment problems qaps with a hamming distance matrix for a hypercube or a manhattan distance matrix for a rectangular grid arise frequently from communications and facility locations and are known to be among the hardest discrete optimization problems in this paper we consider the issue of how to obtain lower bounds for those two classes of qaps based on semidefinite programming sdp by exploiting the data structure of the distance matrix b we first show that for any permutation matrix x the matrix y alpha e xbx t is positive semidefinite where alpha is a properly chosen parameter depending only on the associated graph in the underlying qap and e ee t is a rank 1 matrix whose elements have value 1 this results in a natural way to approximate the original qaps via sdp relaxation based on the matrix splitting technique our new sdp relaxations have a smaller size compared with other sdp relaxations in the literature and can be solved efficiently by most open source sdp solvers experimental results show that for the underlying qaps of size up to n 200 strong bounds can be obtained effectively

ray holder continuity for fractional sobolev spaces in infinite dimensions and applications we prove holder continuity on rays in the direction of vectors in the generalized cameron martin space for functions in sobolev spaces in lp of fractional order 1 over infinite dimensional linear spaces the underlying measures are required to satisfy some easy standard structural assumptions only apart from wiener measure they include gibbs measures on a lattice and euclidean interacting quantum fields in infinite volume a number of applications e g to the two dimensional polymer measure are presented in particular irreducibility of the dirichlet form associated with the latter measure is proved without restrictions on the coupling constant

a two parameter maximal ergodic theorem with dependence let x 1 x 2 ldots and y 1 y 2 ldots be independent sequences of i i d u 0 1 random variables we characterize completely those borel functions f on lbrack 0 1 rbrack 2 for which the strong law of large numbers and the maximal ergodic theorem hold for the doubly indexed family 1 nm sum i leq n j leq m f x i y j

schramm loewner equations driven by symmetric stable processes we consider shape size and regularity of the hulls k t of the chordal schramm loewner evolution driven by a symmetric stable process we obtain derivative estimates show that the domains mathbb h setminus k t are holder domains prove that k t has hausdorff dimension 1 and show that the trace is right continuous with left limits almost surely

liouville theorems for non local operators abstract the paper characterizes some classes of pseudo differential operators for which there are or there are not non constant bounded harmonic functions non local perturbations of ornstein uhlenbeck operators and operators with dissipative coefficients are considered the methods used are probabilistic and based on the concept of absorption function and on a new extension of the bismut elworthy li formula the probabilistic interpretation of the liouville theorem by means of absorption functions for general markov processes is given as well

limit distributions of u statistics resampled by symmetric stable laws if y i and v i are independent random sequences such thaty i are i i d random variables belonging to the normal domain of attraction of a symmetric stable law 0 2 andv i are i i d random variables then the limit distributions of u statistics n 1 alpha sum limits 1 leqq i t ldots i d leqq n y i 1 ldots y i d f v i 1 ldots v i d coincide with the probability laws of multiple stochastic integralsx d f f t 1 t d dx t d with respect to a symmetric stable processx t

irreducibility and exponential mixing of some stochastic hydrodynamical systems driven by pure jump noise in this paper we derive several results related to the long time behavior of a class of stochastic semilinear evolution equations in a separable hilbert space h d mathfrak u t rm a mathfrak u t rm b mathfrak u t mathfrak u t dt dl t quad mathfrak u 0 x in rm h here a is a positive self adjoint operator and b is a bilinear map and the driving noise l is basically a d rm a 1 2 valued levy process satisfying several technical assumptions by using a density transformation theorem type for levy measure we first prove a support theorem and an irreducibility property of the ornstein uhlenbeck processes associated to the nonlinear stochastic problem second by exploiting the previous results we establish the irreducibility of the nonlinear problem provided that for a certain gamma in 0 1 4 b is continuous on d rm a gamma times d rm a gamma with values in d rm a 1 2 using a coupling argument the exponential ergodicity is also proved under the stronger assumption that b is continuous on rm h times rm h while the latter condition is only satisfied by the nonlinearities of goy and sabra shell models the assumption under which the irreducibility property holds is verified by several hydrodynamical systems such as the 2d navier stokes magnetohydrodynamics equations the 3d leray varvec alpha model the goy and sabra shell models

weighted sums of i i d random variables attracted to integrals of stable processes under the assumption of the convergence of partial sum processesz n t of i i d random variables to an stable levy processz t 0 2 the convergence of weighted sums f n u dz n u to f u dz u is studied the general convergence result is then applied to examine the domain of attraction of the fractional stable process

ergodicity for functional stochastic differential equations and applications abstract in this paper using the remote start or dissipative method we investigate ergodicity for several kinds of functional stochastic equations including functional stochastic differential equations sdes with variable delays neutral functional sdes functional sdes driven by jump processes and semi linear functional stochastic partial differential equations spdes using the ergodicity derived we then treat a couple of applications in stochastic approximation and optimization problems

stable bounded subsets of lα and sample unboundedness of symmetric stable processes let xt be the levy symmetric stable process with index 1 2 and let c be a convex symmetric subset of l 0 1 we prove that if c does not have compact closure then sup c 01 t dxt is infinite with probability one this extends a result of dudley in the case 2

implementation of a variance reduction based lower bound in a branch and bound algorithm for the quadratic assignment problem the efficient implementation of a branch and bound algorithm for the quadratic assignment problem qap incorporating the lower bound based on variance reduction of li pardalos ramakrishnan and resende 1994 is presented a new data structure for efficient implementation of branch and bound algorithms for the qap is introduced computational experiments with the branch and bound algorithm on different classes of qap test problems are reported the branch and bound algorithm using the new lower bounds is compared with the same algorithm utilizing the commonly applied gilmore lawler lower bound both implementations use a greedy randomized adaptive search procedure for obtaining initial upper bounds the algorithms report all optimal permutations optimal solutions for previously unsolved instances from the literature of dimensions n 16 and n 20 have been found with the new algorithm in addition the new algorithm has been tested on a class of large data variance problems requiring the examination of much fewer nodes of the branch and bound tree than the same algorithm using the gilmore lawler lower bound

ergodicity of stochastic magneto hydrodynamic equations driven by α stable noise abstract the current paper is devoted to the ergodicity of stochastic magneto hydrodynamic equations driven by stable noise with 3 2 2 by the maximal inequality for the stochastic stable convolution and vorticity transformation the well posedness of the mild solution for stochastic magneto hydrodynamic equation is established due to the discontinuous trajectories the existence and uniqueness of the invariant measure for stochastic magneto hydrodynamic equation are obtained by the strong feller property and the accessibility to zero instead of the irreducibility

on a p stable multiple integral ii we construct a multiple strictly p stable stochastic integral as a dunford type integral with respect to a l q valued vector measure 1qp 2

skew convolution semigroups and affine markov processes a general affine markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup we provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup the corresponding affine markov process is constructed as the strong solution of a system of stochastic equations with non lipschitz coefficients and poisson type integrals over some random sets based on this characterization it is proved that the affine process arises naturally in a limit theorem for the difference of a pair of reactant processes in a catalytic branching system with immigration

pseudodifferential operators on supermanifolds and the atiyah singer index theorem fermionic quantization or clifford algebra is combined with pseudodifferential operators to simplify the proof of the atiyah singer index theorem for the dirac operator on a spin manifold

absolutely continuous flows generated by sobolev class vector fields in finite and infinite dimensions abstract we prove the existence of the global flow ut generated by a vector field a from a sobolev class w1 1 on a finite or infinite dimensional space x with a measure provided is sufficiently smooth and that a a and a where a is the divergence with respect to are exponentially integrable in addition the measure is shown to be quasi invariant under ut in the case x r n and p dx where p w1 1loc r n is a locally uniformly positive probability density a sufficient condition is exp c a exp c a p p l1 for all c in the infinite dimensional case we get analogous results for measures differentiable along sufficiently many directions examples of measures which fit our framework important for applications are symmetric invariant measures of infinite dimensional diffusions and gibbs measures typically in both cases such measures are essentially non gaussian our result in infinite dimensions significantly extends previously studied cases where was a gaussian measure finally we study flows generated by vector fields whose values are not necessarily in the cameron martin space

analysis on wiener spaces ii differential forms abstract the author gives the notions of p forms and p forms and shows some properties of them in particular a vanishing theorem of de rham cohomology of poincare type also he shows the hypoellipticity of certain elliptic operators on wiener space and a theorem of poinare inequality type

a parametrix for the neumann problem on pseudoconvex domains of finite type abstract we construct a parametrix for the neumann problem on any pseudoconvex domain of finite type which reduces completely the study of isotropic lp sobolev and holder estimates to those for b and b we also establish the maximal nonisotropic estimates in the case of d q domains and provide a precise comparison of the bergman and szego projections and of the canonical solutions to with respect to these two operators the argument is substantially simpler than the known ones for the cases of strongly pseudoconvex domains and pseudoconvex domains of finite type in c 2

on equivalence of semidefinite relaxations for quadratic matrix programming we analyze two popular semidefinite programming relaxations for quadratically constrained quadratic programs with matrix variables these relaxations are based on vector lifting and on matrix lifting they are of different size and expense we prove under mild assumptions that these two relaxations provide equivalent bounds thus our results provide a theoretical guideline for how to choose a less expensive semidefinite programming relaxation and still obtain a strong bound the main technique used to show the equivalence and that allows for the simplified constraints is the recognition of a class of nonchordal sparse patterns that admit a smaller representation of the positive semidefinite constraint

two parameter strong laws and maximal inequalities for u statistics we provide necessary and sufficient conditions for two parameter convergence in the strong law of large numbers for u statistics we also obtain weak type 1 1 inequalities for one and two sample u statistics of order 2 which are in a sense best possible

lower bounds for the quadratic assignment problem based upon a dual formulation a new bounding procedure for the quadratic assignment problem qap is described which extends the hungarian method for the linear assignment problem lap to qaps operating on the four dimensional cost array of the qap objective function the qap is iteratively transformed in a series of equivalent qaps leading to an increasing sequence of lower bounds for the original problem to this end two classes of operations which transform the four dimensional cost array are defined these have the property that the values of the transformed objective function z are the corresponding values of the old objective function z shifted by some amount c in the case that all entries of the transformed cost array are nonnegative then c is a lower bound for the initial qap if moreover there exists a feasible solution u to the qap such that its value in the transformed problem is zero then c is the optimal value of z and u is an optimal solution for the original qap the transformations are iteratively applied until no significant increase in constant c as above is found resulting in the so called dual procedure dp several strategies are listed for appropriately determining c or equivalently transforming the cost array the goal is the modification of the elements in the cost array to obtain new equivalent problems that bring the qap closer to solution in some cases the qap is actually solved though solution is not guaranteed the close relationship between the dp and the linear programming formulation of adams and johnson is presented the dp attempts to solve adams and johnson s clp a continuous relaxation of a linearization of the qap this explains why the dp produces bounds close to the optimum values for clp calculated by johnson in her dissertation and by resende et al in their interior point algorithm for linear programming the benefit of using dp within a branch and bound algorithm is described then two versions of dp are tested on the nugent test instances from size 5 to size 30 as well as several other test instances from qaplib these compare favorably with earlier bounding methods

exponential ergodicity of stochastic burgers equations driven by α stable processes in this work we prove the strong feller property and the exponential ergodicity of stochastic burgers equations driven by 2 subordinated cylindrical brownian motions with 1 2 to prove the results we truncate the nonlinearity and use the derivative formula for sdes driven by stable noises established in zhang in stoch process appl 123 4 1213 1228 2013

on the multiple stable integral we prove that the n fold stochastic integral mathop smallint limits left 0 1 right n f left t 1 t n right dz left t 1 right dz left t n right with respect to a p stable levy process z t t 0 1 p 1 2 exists as a continuous linear mapping from the zygmund space l p log l n 1 of functions f 0 1 n to l q for any q p this strengthens the author s earlier result 15 the proof is based on an interpolation theorem due to bennett and rudnick 2

a note on estimates for stable integrals with drift let x be of the form x t t 0 b s dz s t 0 a s ds t 0 where z is a symmetric stable process of index a 6 1 2 with z 0 0 we obtain various l 2 estimates for the process x in particular for m n t 0 and any measurable nonnegative function we derive the inequality as an application of the obtained estimates we prove the existence of solutions for the stochastic equation dx t b x t dz t a x t dt for any initial value x 0 r

a new bound for the quadratic assignment problem based on convex quadratic programming we describe a new convex quadratic programming bound for the quadratic assignment problem qap the construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for qap the new bound dominates the well known projected eigenvalue bound and appears to be competitive with existing bounds in the trade off between bound quality and computational effort

levy gromov s isoperimetric inequality for an infinite dimensional diffusion generator we establish by simple semigroup arguments a levy gromov isoperimetric inequality for the invariant measure of an infinite dimensional diffusion generator of positive curvature with isoperimetric model the gaussian measure this produces in particular a new proof of the gaussian isoperimetric inequality this isoperimetric inequality strengthens the classical logarithmic sobolev inequality in this context a local version for the heat kernel measures is also proved which may then be extended into an isoperimetric inequality for the wiener measure on the paths of a riemannian manifold with bounded ricci curvature

self adjointness of some infinite dimensional elliptic operators and application to stochastic quantization we consider an operator k l in a hilbert space h where l is an ornstein uhlenbeck operator u w 1 4 h and is the invariant measure associated with l we show that k is essentially self adjoint in the space l 2 h where is the gibbs measure dx z 1 e 2u x dx an application to stochastic quantization is given

transversal dirac families in riemannian foliations we describe a family of differential operators parametrized by the transversal vector potentials of a riemannian foliation relative to the clifford algebra of the foliation this family is non elliptic but in certain ways behaves like a standard dirac family in the absolute case as a result of its elliptic like regularity properties the analytic and topological indices of this family are defined as elements of k theory in the parameter space we indicate how the cohomology of the parameter space is described via suitable maps to fredholm operators we outline the proof of a theorem of vafa witten type on uniform bounds for the eigenvalues of this family using a spectral flow argument a determinant operator is also defined with the appropriate zeta function regularization dependent on the codimension of the foliation with respect to a generalized coupled dirac yang mills system we indicate how chiral anomalies are located relative to the foliation

spectral gaps in wasserstein distances and the 2d stochastic navier stokes equations we develop a general method to prove the existence of spectral gaps for markov semigroups on banach spaces unlike most previous work the type of norm we consider for this analysis is neither a weighted supremum norm nor an lp type norm but involves the derivative of the observable as well and hence can be seen as a type of 1 wasserstein distance this turns out to be a suitable approach for infinite dimensional spaces where the usual harris or doeblin conditions which are geared toward total variation convergence often fail to hold in the first part of this paper we consider semigroups that have uniform behavior which one can view its the analog of doeblin s condition we then proceed to study situations where the behavior is not so uniform but the system has a suitable lyapunov structure leading to a type of harris condition we finally show that the latter condition is satisfied by the two dimensional stochastic navier stokes equations even in situations where the forcing is extremely de generate using the convergence result we show that the stochastic navier stokes equations invariant measures depend continuously on the viscosity and the structure of the forcing

matrix lifting semi definite programming for detection in multiple antenna systems this paper presents a computationally efficient decoder for multiple antenna systems the proposed algorithm can be used for any constellation qam or psk and any labeling method the decoder is based on matrix lifting semi definite programming sdp the strength of the proposed method lies in a new relaxation approach applied to the previous work by mobasher this results in a reduction of the number of variables from nk 1 nk 2 2 in the previous work by mobasher to 2n k 2 in the new method where n is twice the number of transmit antennas and k is the number of constellation points in each real dimension it is shown that this reduction in the number of variables results in a significant computational complexity reduction compared to the previous work by mobasher moreover the proposed method offers a better symbol error rate performance as compared to some known and recent sdp based quasi maximum likelihood detection methods reported in the literature

nonsymmetric ornstein uhlenbeck semigroups in banach spaces letebe a separable real banach space and letq l e e be positive and symmetric lets s t t 0be ac0 semigroup onewe study the relations between the reproducing kernel hilbert spaces associated with the operatorsqt t0 s s qs s ds under the assumption that these operators are the covariances of centered gaussian measures tone we also study equivalence t sfor different values of s and t and we calculate their radon nikodym derivatives

a branch and bound algorithm for the quadratic assignment problem based on the hungarian method this paper presents a new branch and bound algorithm for solving the quadratic assignment problem qap the algorithm is based on a dual procedure dp similar to the hungarian method for solving the linear assignment problem our dp solves the qap in certain cases i e for some small problems n 7 and for numerous larger problems 7 n 16 that arise as sub problems of a larger qap such as the nugent 20 the dp however does not guarantee a solution it is used in our algorithm to calculate lower bounds on solutions to the qap as a result of a number of recently developed improvements the dp produces lower bounds that are as tight as any which might be useful in a branch and bound algorithm these are produced relatively cheaply especially on larger problems experimental results show that the computational complexity of our algorithm is lower than known methods and that its actual runtime is significantly shorter than the best known algorithms for qaplib test instances of size 16 through 22 our method has the potential for being improved and therefore can be expected to aid in solving even larger problems

harnack and functional inequalities for generalized mehler semigroups abstract harnack inequalities are established for a class of generalized mehler semigroups which in particular imply upper bound estimates for the transition density moreover poincare and log sobolev inequalities are proved in terms of estimates for the square field operators furthermore under a condition well known in the gaussian case we prove that generalized mehler semigroups are strong feller the results are illustrated by concrete examples in particular we show that a generalized mehler semigroup with an stable part is not hyperbounded but exponentially ergodic and that the log sobolev constant obtained by our method in the special gaussian case can be sharper than the one following from the usual curvature condition moreover a harnack inequality is established for the generalized mehler semigroup associated with the dirichlet heat semigroup on 0 1 we also prove that this semigroup is not hyperbounded

stochastic partial differential equation driven by stable noise we construct a weak solution to the stochastic partial differential equation driven by a one sided stable noise without negative jumps we prove the weak existence of the solution for parameters the facts that for is not a lipschitz function and is not a gaussian noise require the development of new methods which we believe are of independent interest we also show that when the above equation gives an alternative description of super brownian motion with stable branching mechanism

stochastic integration with respect to cylindrical levy processes a cylindrical levy process does not enjoy a cylindrical version of the semimartingale decomposition which results in the need to develop a completely novel approach to stochastic integration in this work we introduce a stochastic integral for random integrands with respect to cylindrical levy processes in hilbert spaces the space of admissible integrands consists of caglad adapted stochastic processes with values in the space of hilbert schmidt operators neither the integrands nor the integrator is required to satisfy any moment or boundedness condition the integral process is characterised as an adapted hilbert space valued semimartingale with cadlag trajectories

finiteness and tenseness theorems for riemannian foliations we prove a finiteness theorem for the spectral sequence e i d i associated to a riemannian foliation inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i on a compact manifold m and to a flat vector bundle e over m with flat connection using this result we prove that every riemannian foliation on a compact manifold is tense in the sense of f w kamber and ph tondeur foliations and metrics progr math vol 32 1983 pp 103 152 we also show that the main tautness theorems for riemannian foliations on compact manifolds which were proved by several authors are immediate consequences of our results

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

characterizations of almost surely continuous p stable random fourier series and strongly stationary processes on etend le probleme de dudley fernique aux processus p stables fortement stationnaires 1 p 2

type ii non commutative geometry i dixmier trace in von neumann algebras abstract we define the notion of connes von neumann spectral triple and consider the associated index problem we compute the analytic chern connes character of such a generalized spectral triple and prove the corresponding local formula for its hochschild class this formula involves the dixmier trace for ii von neumann algebras in the case of foliations we identify this dixmier trace with the corresponding measured wodzicki residue

a computational study of graph partitioning letg n e be an edge weighted undirected graph the graph partitioning problem is the problem of partitioning the node setn intok disjoint subsets of specified sizes so as to minimize the total weight of the edges connecting nodes in distinct subsets of the partition we present a numerical study on the use of eigenvalue based techniques to find upper and lower bounds for this problem results for bisecting graphs with up to several thousand nodes are given and for small graphs some trisection results are presented we show that the techniques are very robust and consistently produce upper and lower bounds having a relative gap of typically a few percentage points

structural properties of semilinear spdes driven by cylindrical stable processes we consider a class of semilinear stochastic evolution equations driven by an additive cylindrical stable noise we investigate structural properties of the solutions like markov irreducibility stochastic continuity feller and strong feller properties and study integrability of trajectories the obtained results are applied to semilinear stochastic heat equations with dirichlet boundary conditions and bounded and lipschitz nonlinearities

generalized mehler semigroups and applications we construct and study generalized mehler semigroups p t t 0 and their associated markov processesm the construction methods for p t t 0 are based on some new purely functional analytic results implying in particular that any strongly continuous semigroup on a hilbert spaceh can be extended to some larger hilbert spacee with the embeddingh e being hilbert schmidt the same analytic extension results are applied to construct strong solutions to stochastic differential equations of typedx t c dw t ax t dt with possibly unbounded linear operatorsa andc onh on a suitably chosen larger spacee for gaussian generalized mehler semigroups p t t 0 with corresponding markov processm the associated non symmetric dirichlet forms ed e are explicitly calculated and a necessary and sufficient condition for path regularity ofm in terms of e d e is proved then using dirichlet form methods it is shown thatm weakly solves the above stochastic differential equation if the state spacee is chosen appropriately finally we discuss the differences between these two methods yielding strong resp weak solutions

symmetrization of nonsymmetric quadratic assignment problems and the hoffman wielandt inequality abstract a technique is proposed to transform a nonsymmetric quadratic assignment problem qap into an equivalent one consisting of complex hermitian matrices this technique provides several new hoffman wielandt type eigenvalue inequalities for general matrices and extends the eigenvalue bound for symmetric qaps to the general case

generalized ornstein uhlenbeck semigroups littlewood paley stein inequalities and the p a meyer equivalence of norms abstract let be a nondegenerate gaussian measure on a hilbert space h for an arbitrary selfadjoint nonnegative operator a we consider the semigroup e tl e ta on l p where stands for the second quantization operator we provide an explicit characterization of the domains of i l m 2 in l p in terms of gaussian sobolev spaces thus extending the p a meyer result on equivalence of norms the main tools are the littlewood paley stein inequalities which are proved under minimal assumptions by a purely analytic method following e stein 1970 topics in harmonic analysis princeton univ press princeton nj

hopf algebras cyclic cohomology and the transverse index theorem in this paper we solve a longstanding internal problem of noncommutative geometry namely the computation of the index of transversally elliptic operators on foliations we show that the computation of the local index formula for transversally hypoelliptic operators can be settled thanks to a very specific hopf algebra associated to each integer codimension this hopf algebra reduces transverse geometry to a universal geometry of affine nature the structure of this hopf algebra its relation with the lie algebra of formal vector fields as well as the computation of its cyclic cohomology are done in the present paper in which we also show that under a suitable unimodularity condition the cosimplicial space underlying the hochschild cohomology of a hopf algebra carries a highly nontrivial cyclic structure

hypercontraction principle and random multilinear forms we study a banach space valued random multilinear forms in independent real random variables extensively using the concept of hypercontractive maps between lq spaces we show that multilinear forms share with linear forms a lot of properties like comparability of lq l0 and almost sure convergence

on filtering equations in infinite dimensions abstract we consider a nonlinear filtering problem for a state processxin a hilbert spaceh given a finite dimensional observation processy we look for solutions of the corresponding filtering equations having densities with respect to a gaussian reference measure inh we derive the equations for the conditional densities and prove that they have solutions we can allow correlated noise in the state and observation equations provided additional assumptions hold

continuity and generators of dynamical semigroups for infinite bose systems abstract for a class of quasifree quantum dynamical semigroups on the algebra of the canonical commutation relations ccr we give sufficient conditions for these semigroups to extend to ultraweakly continuous semigroups of normal operators on the von neumann algebra associated with a representation of the ccr then the explicit form of the generators of the extended semigroups is calculated

a low dimensional semidefinite relaxation for the quadratic assignment problem the quadratic assignment problem qap is arguably one of the hardest np hard discrete optimization problems problems of dimension greater than 25 are still considered to be large scale current successful solution techniques use branch and bound methods which rely on obtaining strong and inexpensive bounds in this paper we introduce a new semidefinite programming sdp relaxation for generating bounds for the qap in the trace formulation we apply majorization to obtain a relaxation of the orthogonal similarity set of the quadratic part of the objective function this exploits the matrix structure of qap and results in a relaxation with much smaller dimension than other current sdp relaxations we compare the resulting bounds with several other computationally inexpensive bounds such as the convex quadratic programming relaxation qpb we find that our method provides stronger bounds on average and is adaptable for branch and bound methods

a new lower bound via projection for the quadratic assignment problem new lower bounds for the quadratic assignment problem qap are presented these bounds are based on the orthogonal relaxation of qap the additional improvement is obtained by making efficient use of a tractable representation of orthogonal matrices having constant row and column sums the new bound is easy to implement and often provides high quality bounds under an acceptable computational effort

central limit theorems and weak laws of large numbers in certain banach spaces for b a type 2 banach lattice we obtain a relationship between the central limit theorem in b and the weak law of large numbers for the sum of the squares of the random vectors in another banach lattice b 2 we then obtain some two sided estimates for e sn pwhich in lpspaces 1 p give n a s c for the weak law of large numbers as a consequence of these estimates we also solve the domain of attraction problem in lp p 2 several examples and counterexamples are provided

double stochastic integrals random quadratic forms and random series in orlicz spaces let x t t geq 0 be a process with independent symmetric and stationary increments and let xi i be i i d symmetric real random variables we provide a characterization of functions f s t s t geq 0 such that the double integral int int f s t dx s dx t exists a characterization of infinite matrices alpha ij such that the double series sum alpha ij xi i xi j converges a s and a characterization of orlicz space l psi valued sequences a i for which the series sum a i xi i converges a s in l psi the above three problems are closely related

global optimality conditions for quadratic optimization problems with binary constraints we consider nonconvex quadratic optimization problems with binary constraints our main result identifies a class of quadratic problems for which a given feasible point is global optimal we also establish a necessary global optimality condition these conditions are expressed in a simple way in terms of the problem s data we also study the relations between optimal solutions of the nonconvex binary quadratic problem versus the associated relaxed and convex problem defined over the l infty norm our approach uses elementary arguments based on convex duality

solving large quadratic assignment problems on computational grids the quadratic assignment problem qap is among the hardest combinatorial optimization problems some instances of size n 30 have remained unsolved for decades the solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computational platforms in this article we describe a novel approach to solve qaps using a state of the art branch and bound algorithm running on a federation of geographically distributed resources known as a computational grid solution of qaps of unprecedented complexity including the nug30 kra30b and tho30 instances is reported

on the cauchy problem for non local ornstein uhlenbeck operators abstract we study the cauchy problem involving non local ornstein uhlenbeck operators in finite and infinite dimensions we prove classical solvability without requiring that the levy measure corresponding to the large jumps part has a first finite moment moreover we determine a core of regular functions which is invariant for the associated transition markov semigroup such a core allows to characterize the marginal laws of the ornstein uhlenbeck stochastic process as unique solutions to fokker planck kolmogorov equations for measures

harnack inequalities for stochastic equations driven by levy noise abstract by using coupling argument and regularization approximations of the underlying subordinator dimension free harnack inequalities are established for a class of stochastic equations driven by a levy noise containing a subordinate brownian motion the harnack inequalities are new even for linear equations driven by levy noise and the gradient estimate implied by our log harnack inequality considerably generalizes some recent results on gradient estimates and coupling properties derived for levy processes or linear equations driven by levy noise the main results are also extended to semilinear stochastic equations in hilbert spaces

quadratic matrix programming we introduce and study a special class of nonconvex quadratic problems in which the objective and constraint functions have the form f boldmath x tr boldmath x t boldmath a boldmath x 2 tr boldmath b t boldmath x c boldmath x in real r n times r the latter formulation is termed quadratic matrix programming qmp of order r we construct a specially devised semidefinite relaxation sdr and dual for the qmp problem and show that under some mild conditions strong duality holds for qmp problems with at most r constraints using a result on the equivalence of two characterizations of the nonnegativity property of quadratic functions of the above form we are able to compare the constructed sdr and dual problems to other known sdrs and dual formulations of the problem an application to robust least squares problems is discussed

recent advances in the solution of quadratic assignment problems the quadratic assignment problem qap is notoriously difficult for exact solution methods in the past few years a number of long open qaps including those posed by steinberg 1961 nugent et al 1968 and krarup 1972 were solved to optimality for the first time the solution of these problems has utilized both new algorithms and novel computing structures we describe these developments as well as recent work which is likely to result in the solution of even more difficult instances

on the continuity of ornstein uhlenbeck processes in infinite dimensions existence and continuity of ornstein uhlenbeck processes in banach and hilbert spaces are investigated under various assumptions

multiple integration with respect to poisson and levy processes necessary and sufficient conditions are given for the existence of a multiple stochastic integral of the form fdx1 dxd where x1 xd are components of a positive or symmetric pure jump type levy process in d conditions are also given for a sequence of integrals of this type to converge in probability to zero or infinity or to be tight all arguments proceed via reduction to the special case of poisson integrals

strong solutions for the stochastic navier stokes equations on the 2d rotating sphere with stable levy noise abstract the navier stokes equation with rough data arises in many problems of fluid dynamics but mathematical analysis of such problems is notoriously difficult in this paper we consider a two dimensional fluid moving on the surface of a rotating sphere under the influence of an impulsive force that is very irregular in time more precisely we assume that the impulsive force is associated to a brownian motion subordinated by a stable subordinator then we prove the existence and uniqueness of a strong solution in pde sense to the stochastic navier stokes equations on the rotating 2 dimensional unit sphere perturbed by a stable levy noise this strong solution turns out to exist globally in time

traces of harmonic functions and a new path space for the free quantum field the infinite dimensional ornstein uhlenbeck process associated with the free field of quantum field theory on rd is reconstructed as the traces of random harmonic functions these harmonic functions are the solutions of a generalised dirichlet problem with a random schwartz distribution as boundary data a detailed analysis of the associated trace space which is a subspace of a scaled sobolev space of negative fractional order leads to a new path space for the free field as well as to a convenient regularisation method because of the particular form of the trace space it is possible to give an explicit formula for the transition function of the process furthermore the dependence of the path space on the dimension d is discussed and a formulation of our result in terms of abstract wiener spaces is given

quadratic assignment problems abstract this paper surveys quadratic assignment problems qap at first several applications of this problem class are described and mathematical formulations of qaps are given then some exact solution methods and good heuristics are outlined their computational behaviour is illustrated by numerical results further recent results on the asymptotic probabilistic behaviour of qaps are outlined

applications of parametric programming and eigenvalue maximization to the quadratic assignment problem we investigate new bounding strategies based on different relaxations of the quadratic assignment problem in particular we improve the lower bound found by using an eigenvalue decomposition of the quadratic part and by solving a linear program for the linear part the improvement is accomplished by applying a steepest ascent algorithm to the sum of the two bounds