heat kernel estimates and riesz transforms on some riemannian covering manifolds consider a riemannian manifold m which is a galois covering of a compact manifold with nilpotent deck transformation group g for the laplace operator on m we prove a precise estimate for the gradient of the heat kernel and show that the riesz transforms are bounded in l p m 1 p we also obtain estimates for discrete oscillations of the heat kernel and boundedness of discrete riesz transform operators which are defined using the action of g on m

weighted poincare inequality and heat kernel estimates for finite range jump processes it is well known that there is a deep interplay between analysis and probability theory for example for a markovian infinitesimal generator mathcal l the transition density function p t x y of the markov process associated with mathcal l if it exists is the fundamental solution or heat kernel of mathcal l a fundamental problem in analysis and in probability theory is to obtain sharp estimates of p t x y in this paper we consider a class of non local integro differential operators mathcal l on mathbb r d of the form mathcal l u x lim limits varepsilon downarrow 0 int limits y in mathbb r d y x varepsilon u y u x j x y dy where displaystyle j x y frac c x y x y d alpha bf 1 x y leq kappa for some constant kappa 0 and a measurable symmetric function c x y that is bounded between two positive constants associated with such a non local operator mathcal l is an mathbb r d valued symmetric jump process of finite range with jumping kernel j x y we establish sharp two sided heat kernel estimate and derive parabolic harnack principle for them along the way some new heat kernel estimates are obtained for more general finite range jump processes that were studied in barlow et al in trans am math soc 2008 one of our key tools is a new form of weighted poincare inequality of fractional order which corresponds to the one established by jerison in duke math j 53 2 503 523 1986 for differential operators using meyer s construction of adding new jumps we also obtain various a priori estimates such as holder continuity estimates for parabolic functions of jump processes not necessarily of finite range where only a very mild integrability condition is assumed for large jumps to establish these results we employ methods from both probability theory and analysis extensively

two dimensional flr filter design using matrix dilation approach this paper develops an approach for the optimal design of two dimensional 2 d finite impulse response fir filters based on the minimization of a new performance index the approach gives analytical expressions for the optimal solution and offers a two parameter family of suboptimal filters it is shown that the conventional least square solutions is a member of this family the approach is based on a result in linear algebra and used in robust control theory known as the dilation equation an efficient numerical algorithm for solving the filter design problem using the dilation equation is proposed and some techniques for choosing the design parameters are discussed finally some examples are shown illustrating the flexibility of the design using the new approach

random walks on discrete groups of polynomial volume growth let mu be a probability measure with finite support on a discrete group gamma of polynomial volume growth the main purpose of this paper is to study the asymptotic behavior of the convolution powers mu n of mu if mu is centered then we prove upper and lower gaussian estimates we prove a central limit theorem and we give a generalization of the berry esseen theorem these results also extend to noncentered probability measures we study the associated riesz transform operators the main tool is a parabolic harnack inequality for centered probability measures which is proved by using ideas from homogenization theory and by adapting the method of krylov and safonov this inequality implies that the positive mu harmonic functions are constant finally we give a characterization of the mu harmonic functions which grow polynomially

constrained least squares design of 2 d fir filters we consider the design of 2 d linear phase finite impulse response fir filters according to the least squares ls error criterion subject to equality and or inequality constraints since we use a frequency domain formulation these constraints can be used to explicitly prescribe frequency dependent error tolerances the maximum minimum or fixed values of the frequency response at certain points and or regions our method combines lagrange multiplier and kuhn tucker theory to solve a much wider class of problems than do standard methods it allows arbitrary compromises between the ls and the equiripple design

a finite dimensional approximation of the effective diffusivity for a symmetric random walk in a random environment we consider a nearest neighbor symmetric random walk on a homogeneous ergodic random lattice z d the jump rates of the walk are independent identically bernoulli distributed random variables indexed by the bonds of the lattice a standard result from the homogenization theory see a de masi p a ferrari s goldstein w d wick an invariance principle for reversible markov processes applications to random walks in random environments j statist phys 55 3 4 1989 787 855 asserts that the scaled trajectory of the particle satisfies the functional central limit theorem the covariance matrix of the limiting normal distribution is called the effective diffusivity of the walk we use the duality structure corresponding to the product bernoulli measure to construct a numerical scheme that approximates this parameter when d 3 the estimates of the convergence rates are also provided

representations of nets of c algebras over s 1 in recent times a new kind of representations has been used to describe superselection sectors of the observable net over a curved spacetime taking into account the effects of the fundamental group of the spacetime using this notion of representation we prove that any net of c algebras over s 1 admits faithful representations and when the net is covariant under diff s 1 it admits representations covariant under any amenable subgroup of diff s 1

dimension free estimates for discrete riesz transforms on products of abelian groups let g be a lca group with a fixed g0 g spanning an infinite subgroup let j acting on l2 gn be translation by go in the jth coordinate the discrete derivatives j i j define a discrete laplacian l j 1n j j and discrete riesz transforms rj jl 12 we get dimension free estimates cp f lp gn j 1n rj f 2 rj f 212lp gn cp f lp gn for 2 p the right side inequality is false for 1 p 2 but we give the substitute we also consider the case where gpg0 is a cyclic group

heat kernel upper bounds for jump processes and the first exit time for all t 0 x m and f l2 m the function pt x y can be considered as the transition density of the associated markov processx xt t 0 and the question of estimating of pt x y which is the main subject of this paper is closely related to the properties of x the function pt x y is also referred to as a heat kernel and this terminology goes back to the classical gauss weierstrass heat kernel associated with the heat semigroup e t 0 in r n whose markov process is brownian motion a somewhat more general but still well treated case is when m d is a riemannian metric measure space that is m is a riemannian manifold

heat kernels and analyticity of non symmetric jump diffusion semigroups let d geqslant 1 and alpha in 0 2 consider the following non local and non symmetric levy type operator on mathbb r d begin aligned fancyscript l kappa alpha f x hbox p v int mathbb r d f x z f x frac kappa x z z d alpha mathord mathrm d z end aligned where 0 kappa 0 leqslant kappa x z leqslant kappa 1 kappa x z kappa x z and kappa x z kappa y z leqslant kappa 2 x y beta for some beta in 0 1 using levi s method we construct the fundamental solution also called heat kernel p kappa alpha t x y of fancyscript l kappa alpha and establish its sharp two sided estimates as well as its fractional derivative and gradient estimates we also show that p kappa alpha t x y is jointly holder continuous in t x the lower bound heat kernel estimate is obtained by using a probabilistic argument the fundamental solution of fancyscript l kappa alpha gives rise a feller process x mathbb p x x in mathbb r d on mathbb r d we determine the levy system of x and show that mathbb p x solves the martingale problem for fancyscript l kappa alpha c 2 b mathbb r d furthermore we show that the c 0 semigroup associated with fancyscript l kappa alpha is analytic in l p mathbb r d for every p in 1 infty a maximum principle for solutions of the parabolic equation partial t u fancyscript l kappa alpha u is also established as an application of the main result of this paper sharp two sided estimates for the transition density of the solution of mathord mathrm d x t a x t mathord mathrm d y t is derived where y is a rotationally symmetric stable process on mathbb r d and a x is a holder continuous d times d matrix valued function on mathbb r d that is uniformly elliptic and bounded

transition probabilities for symmetric jump processes we consider symmetric markov chains on the integer lattice in d dimensions where a 0 2 and the conductance between x and y is comparable to x y d we establish upper and lower bounds for the transition probabilities that are sharp up to constants

isoperimetric inequalities and markov chains soit a i j i j n la matrice stochastique d une chaine de markov reversible sur n 1 2 soit n 2 tel que f r c f d f c 0 n ou r 2n n 2 ou c 0 est independant de f et ou r indique la norme dans l r n d pour la mesure i i alors on a sup i j j 1 a i j 0 n 2

aleksandrov bakelman pucci type estimates for integro differential equations in this work we provide an aleksandrov bakelman pucci type estimate for a certain class of fully nonlinear elliptic integro differential equations the proof of which relies on an appropriate generalization of the convex envelope to a nonlocal fractional order setting and on the use of riesz potentials to interpret second derivatives as fractional order operators this result applies to a family of equations involving some nondegenerate kernels and as a consequence provides some new regularity results for previously untreated equations furthermore this result also gives a new comparison theorem for viscosity solutions of such equations which depends only on the l and ln norms of the right hand side in contrast to previous comparison results which utilize the continuity of the right hand side for their conclusions these results appear to be new even for the linear case of the relevant equations

meyers inequality and strong stability for stable like operators let 0 2 let e u u rd rd u y u x 2a x y x y d dydx be the dirichlet form for a stable like operator let u x rd u y u x 2a x y x y d dy 1 2 let l be the associated infinitesimal generator and suppose a x y is jointly measurable symmetric bounded and bounded below by a positive constant we prove that if u is the weak solution to lu h then u lp for some p 2 this is the analogue of an inequality of meyers for solutions to divergence form elliptic equations as an application we prove strong stability results for stable like operators if a is perturbed slightly we give explicit bounds on how much the semigroup and fundamental solution are perturbed

estimates of heat kernels for non local regular dirichlet forms in this paper we present new heat kernel upper bounds for a certain class of non local regular dirichlet forms on metric measure spaces including fractal spaces we use a new purely analytic method where one of the main tools is the parabolic maximum principle we deduce off diagonal upper bound of the heat kernel from the on diagonal one under the volume regularity hypothesis restriction of the jump kernel and the survival hypothesis as an application we obtain two sided estimates of heat kernels for non local regular dirichlet forms with finite effective resistance including settings with the walk dimension greater than 2

l sub 1 and l sub infinity minimization via a variant of karmarkar s algorithm simple iterative algorithms are presented for l sub 1 and l sub infinity minimization regression based on a variant of karmarkar s linear programming algorithm although these algorithms are based on entirely different theoretical principles to the popular irls iteratively reweighted least squares algorithm they have almost identical matrix operations also presented are the results of a monte carlo study comparing the numerical convergence properties of the karmarkar algorithm for l sub 1 minimization to those of an irls and a simplex algorithm the test problem involves l sub 1 estimation of ar autoregressive model parameters the karmarkar algorithm outperformed irls by achieving higher numerical accuracy in fewer iterations techniques for reducing the computational cost per iteration of the karmarkar l sub 1 algorithm are discussed

harnack inequalities for non local operators of variable order we consider harmonic functions with respect to the operator formula math under suitable conditions on n x h we establish a harnack inequality for functions that are nonnegative and harmonic in a domain the operator l is allowed to be anisotropic and of variable order

peak constrained least squares optimization we presented the basic concepts for peak constrained least squares pcls optimization in previous papers we present advanced pcls optimization concepts in this paper this paper discusses only a few of the many ways that pcls design problems can be formulated we believe that the pcls optimality criterion can be customized to fit virtually any practical application for example pcls optimization can readily be used to design equalizers in the prefilter equalizer or interpolated fir implementations of filters

random walks driven by low moment measures we study the decay of convolution powers of probability measures without second moment but satisfying some weaker finite moment condition for any locally compact unimodular group g and any positive function g 0 we introduce a function g which describes the fastest possible decay of n 2n e when is a symmetric continuous probability density such that is finite we estimate g for a variety of groups g and functions when is of the form with 0 0 a fixed increasing function and g 0 a natural word length measuring the distance to the identity element in g g can be thought of as a group invariant

the c0 x algebra of a net and index theory abstract given a connected and locally compact hausdorff space x with a good base k we assign in a functorial way a c 0 x algebra to any precosheaf of c algebras a defined over k afterwards we consider the representation theory and the kasparov k homology of a and interpret them in terms respectively of the representation theory and the k homology of the associated c 0 x algebra when a is an observable net over the spacetime x in the sense of algebraic quantum field theory this yields a geometric description of the recently discovered representations affected by the topology of x

which properties of a random sequence are dynamically sensitive consider a sequence of i i d random variables where each variable is refreshed i e replaced by an independent variable with the same law independently according to a poisson clock at any fixed time t the resulting sequence has the same law as at time 0 but there can be exceptional random times at which certain almost sure properties of the time 0 sequence are violated we prove that there are no such exceptional times for the law of large numbers and the law of the iterated logarithm so these laws are dynamically stable however there are times at which run lengths are exceptionally long that is run tests are dynamically sensitive we obtain a multifractal analysis of exceptional times for run lengths and for prediction in particular starting from an i i d sequence of unbiased random bits the random set of times t where log2 n bits among the first n bits can be predicted from their predecessors has hausdorff dimension 1 a s finally we consider simple random walk in the lattice zd and prove that transience is dynamically stable for d 5 and dynamically sensitive for d 3 4 moreover for d 3 4 the nonempty random set of exceptional times t where the walk is recurrent has hausdorff dimension 4 d 2 a s

on the parabolic harnack inequality for non local diffusion equations we settle the open question concerning the harnack inequality for globally positive solutions to non local in time diffusion equations by constructing a counter example for dimensions d ge beta where beta in 0 2 is the order of the equation with respect to the spatial variable the equation can be non local both in time and in space but for the counter example it is important that the equation has a fractional time derivative in this case the fundamental solution is singular at the origin for all times t 0 in dimensions d ge beta this underlines the markedly different behavior of time fractional diffusion compared to the purely space fractional case where a local harnack inequality is known the key observation is that the memory strongly affects the estimates in particular if the initial data u 0 in l q loc for q larger than the critical value tfrac d beta of the elliptic operator delta beta 2 a non local version of the harnack inequality is still valid as we show we also observe the critical dimension phenomenon already known from other contexts the diffusion behavior is substantially different in higher dimensions than d 1 provided beta 1 since we prove that the local harnack inequality holds if d beta

heat kernels for non symmetric diffusion operators with jumps abstract for d 2 we prove the existence and uniqueness of heat kernels to the following time dependent second order diffusion operator with jumps l t 1 2 i j 1 d a i j t x i j 2 i 1 d b i t x i l t where a a i j is a uniformly bounded elliptic and holder continuous matrix valued function b belongs to some suitable kato s class and l t is a non local stable type operator with bounded kernel moreover we establish sharp two sided estimates gradient estimate and fractional derivative estimate for the heat kernel under some mild conditions

geometry of the uniform spanning forest transitions in dimensions 4 8 12 the uniform spanning forest usf in d is the weak limit of random uniformly chosen spanning trees in n n d pemantle 11 proved that the usf consists a s of a single tree if and only if d 4 we prove that any two components of the usf in d are adjacent a s if 5 d 8 but not if d 9 more generally let n x y be the minimum number of edges outside the usf in a path joining x and y in d then max n x y x y in mathbb z d left lfloor d 1 4 right rfloor textrm a s

non local dirichlet forms and symmetric jump processes we consider the non local symmetric dirichlet form e f given by with f the closure with respect to e 1 of the set of c 1 functions on r d with compact support where e 1 f f e f f f rd f x 2 dx and where the jump kernel j satisfies for 0 2 x y 1 this assumption allows the corresponding jump process to have jump intensities whose sizes depend on the position of the process and the direction of the jump we prove upper and lower estimates on the heat kernel we construct a strong markov process corresponding to e f we prove a parabolic harnack inequality for non negative functions that solve the heat equation with respect to e finally we construct an example where the corresponding harmonic functions need not be continuous

harnack inequality for some classes of markov processes in this paper we establish a harnack inequality for nonnegative harmonic functions of some classes of markov processes with jumps

approaching criticality via the zero dissipation limit in the abelian avalanche model the discrete height abelian sandpile model was introduced by bak tang wiesenfeld and dhar as an example for the concept of self organized criticality when the model is modified to allow grains to disappear on each toppling it is called bulk dissipative we provide a detailed study of a continuous height version of the abelian sandpile model called the abelian avalanche model which allows an arbitrarily small amount of dissipation to take place on every toppling we prove that for non zero dissipation the infinite volume limit of the stationary measure of the abelian avalanche model exists and can be obtained via a weighted spanning tree measure we show that in the whole non zero dissipation regime the model is not critical i e spatial covariances of local observables decay exponentially we then study the zero dissipation limit and prove that the self organized critical model is recovered both for the stationary measure and for the dynamics we obtain rigorous bounds on toppling probabilities and introduce an exponent describing their scaling at criticality we rigorously establish the mean field value of this exponent for d 4

heat kernel estimates for jump processes of mixed types on metric measure spaces in this paper we investigate symmetric jump type processes on a class of metric measure spaces with jumping intensities comparable to radially symmetric functions on the spaces the class of metric measure spaces includes the alfors d regular sets which is a class of fractal sets that contains geometrically self similar sets a typical example of our jump type processes is the symmetric jump process with jumping intensity e c 0 x y x y int alpha 1 alpha 2 frac c alpha x y x y d alpha nu d alpha where is a probability measure on alpha 1 alpha 2 subset 0 2 c x y is a jointly measurable function that is symmetric in x y and is bounded between two positive constants and c 0 x y is a jointly measurable function that is symmetric in x y and is bounded between 1 and 2 where either 2 1 0 or 1 2 0 this example contains mixed symmetric stable processes on mathbb r n as well as mixed relativistic symmetric stable processes on mathbb r n we establish parabolic harnack principle and derive sharp two sided heat kernel estimate for such jump type processes

heat kernel estimates and parabolic harnack inequalities for symmetric dirichlet forms abstract in this paper we consider the following symmetric dirichlet forms on a metric measure space m d e f g e c f g m m f x f y g x g y j d x d y where e c is a strongly local symmetric bilinear form and j d x d y is a symmetric radon measure on m m under general volume doubling condition on m d and some mild assumptions on scaling functions we establish stability results for upper bounds of heat kernel resp two sided heat kernel estimates in terms of the jumping kernels the cut off sobolev inequalities and the faber krahn inequalities resp the poincare inequalities we also obtain characterizations of parabolic harnack inequalities our results apply to symmetric diffusions with jumps even when the underlying spaces have walk dimensions larger than 2

regularity results for stable like operators for 1 2 we consider operators of the form lf x rd f x h f x 1 h 1 f x h a x h h d dh and for 0 1 we consider the same operator but where the f term is omitted we prove under appropriate conditions on a x h that any solution u to lu f will be in c if f c

presheaves of superselection structures in curved spacetimes we show that superselection structures on curved spacetimes that are expected to describe quantum charges affected by the underlying geometry are categories of sections of presheaves of symmetric tensor categories when an embedding functor is given the superselection structure is a tannaka type dual of a locally constant group bundle which hence becomes a natural candidate for the role of the gauge group indeed we show that any locally constant group bundle with suitable structure group acts on a net of c algebras fulfilling normal commutation relations on an arbitrary spacetime we also give examples of gerbes of c algebras defined by wightman fields and constructed using projective representations of the fundamental group of the spacetime which we propose as solutions for the problem that existence and uniqueness of the embedding functor are not guaranteed

minorations pour les chaines de markov unidimensionnelles we prove a space time lower estimate for reversible random walks on graphs having linear growth this estimate complements a similar upper bound that follows from a work of hebisch and saloff coste

global heat kernel estimates for symmetric jump processes in this paper we study sharp heat kernel estimates for a large class of symmetric jump type processes in r d for all t 0 a prototype of the processes under consideration are symmetric jump processes on r d with jumping intensity

the liouville property and a conjecture of de giorgi we consider bounded entire solutions of the nonlinear pde u u u 3 0i n r d and prove that under certain monotonicity conditions these solutions must be constant on hyperplanes the proof uses a liouville theorem for harmonic functions associated with a nonuniformly elliptic divergence form operator c 2000 john wiley sons inc

a new light on nets of c algebras and their representations the present paper deals with the question of representability of nets of c algebras whose underlying poset indexing the net is not upward directed a particular class of nets called c net bundles is classified in terms of c dynamical systems having as group the fundamental group of the poset any net of c algebras has a canonical morphism into a c net bundle the enveloping net bundle which generalizes the notion of universal c algebra given by fredenhagen to nonsimply connected posets this allows a classification of nets in particular we call injective those nets such that the canonical morphism is faithful injectivity turns out to be equivalent to the existence of faithful representations we further relate injectivity to a generalized cech cocycle of the net and this allows us to give examples of nets exhausting the above classification

analysis on lie groups theorie locale diffusion de la chaleur sur des groupes de lie connexes la theorie globale les inegalites de sobolev bases graduees sur des corps lisses construction des bases graduees estimation locale du noyau diffusion de la chaleur demonstration de l inegalite de sobolev locale formes de dirichlet sur des groupes le semi groupe de convolution les conditions de sobolev modifiees

lower estimates of heat kernels for non local dirichlet forms on metric measure spaces abstract we are concerned with heat kernel estimates for a non local dirichlet form on an ahlfors regular metric measure space we use an analytic approach to obtain the full lower stable like estimate of the heat kernel from the near diagonal lower estimate combining with other known results we obtain certain equivalent conditions for two sided stable like estimates of the heat kernel the results can be simplified in certain cases for example when the dirichlet form admits an effective resistance

hr bounds for spectral multipliers on graphs we study the boundedness on the hardy spaces h p of spectral multiplier operators associated with the discrete laplacian on a weighted graph we assume that the graph satisfies the doubling volume property and a poincare inequality we prove that there is p 0 0 1 depending on the geometry of the graph such that if the multiplier satisfies a condition similar to the one we have in the classical hormander multiplier theorem then the corresponding operator is bounded on h p p p 0 1

characterization of sub gaussian heat kernel estimates on strongly recurrent graphs sub gaussian estimates for random walks are typical of fractal graphs we characterize them in the strongly recurrent case in terms of resistance estimates only without assuming elliptic harnack inequalities

disorder entropy and harmonic functions we study harmonic functions on random environments with particular emphasis on the case of the infinite cluster of supercritical percolation on z d we prove that the vector space of harmonic functions growing at most linearly is d 1 dimensional almost surely in particular there are no non constant sublinear harmonic functions thus implying the uniqueness of the corrector the main ingredient of the proof is a quantitative annealed version of the kaimanovich vershik entropy argument this also provides bounds on the derivative of the heat kernel simplifying and generalizing existing results the argument applies to many different environments even reversibility is not necessary we also mention several open problems and conjectures on the behavior of harmonic functions on stationary random graphs

symmetric stable laws and stable like jump diffusions asymptotic expansions are obtained for finite dimensional symmetric stable distributions they are used to prove the existence of continuous transition probability densities of stable and stable like jump diffusions and to construct local multiplicative asymptotics and global two sided estimates for these densities as a consequence the distribution of the first passage times for stable jump diffusions is estimated and the integral test for the limsup behaviour of their sample paths as t to 0 is provided 1991 mathematics subject classification 60e07 60g17 60j35 47d07

small time gaussian estimates of heat diffusion kernels ii the theory of large deviations la deuxieme partie d un article etudiant le noyau de chaleur d un operateur differentiel d ordre 2 sur une variete c

tree indexed random walks on groups and first passage percolation suppose that i i d random variables are attached to the edges of an infinite tree when the tree is large enough the partial sumss along some of its infinite paths will exhibit behavior atypical for an ordinary random walk this principle has appeared in works on branching random walks first passage percolation and rwre on trees we establish further quantitative versions of this principle which are applicable in these settings in particular different notions of speed for such a tree indexed walk correspond to different dimension notions for trees finally if the labeling variables take values in a group then properties of the group e g polynomial growth or a nontrivial poisson boundary are reflected in the sample path behavior of the resulting tree indexed walk

uniform spanning forests we study uniform spanning forest measures on infinite graphs which are weak limits of uniform spanning tree measures from finite subgraphs these limits can be taken with free fsf or wired wsf boundary conditions pemantle proved that the free and wired spanning forests coincide in z d and that they give a single tree iff d 4 in the present work we extend pemantle s alternative to general graphs and exhibit further connections of uniform spanning forests to random walks potential theory invariant percolation and amenability the uniform spanning forest model is related to random cluster models in statistical physics but because of the preceding connections its analysis can be carried further among our results are the following the fsf and wsf in a graph g coincide iff all harmonic dirichlet functions on g are constant the tail fields of the wsf and the fsf are trivial on any graph on any cayley graph that is not a finite extension of z all component trees of the wsf have one end this is new in z d for d 5 on any tree as well as on any graph with spectral radius less than 1 a s all components of the wsf are recurrent the basic topology of the free and the wired uniform spanning forest measures on lattices in hyperbolic space h d is analyzed a cayley graph is amenable iff for all e 0 the union of the wsf and bernoulli percolation with parameter e is connected harmonic measure from infinity is shown to exist on any recurrent proper planar graph with finite codegrees we also present numerous open problems and conjectures

a numerically stable dual method for solving strictly convex quadratic programs an efficient and numerically stable dual algorithm for positive definite quadratic programming is described which takes advantage of the fact that the unconstrained minimum of the objective function can be used as a starting point its implementation utilizes the cholesky and qr factorizations and procedures for updating them the performance of the dual algorithm is compared against that of primal algorithms when used to solve randomly generated test problems and quadratic programs generated in the course of solving nonlinear programming problems by a successive quadratic programming code the principal motivation for the development of the algorithm these computational results indicate that the dual algorithm is superior to primal algorithms when a primal feasible point is not readily available the algorithm is also compared theoretically to the modified simplex type dual methods of lemke and van de panne and whinston and it is illustrated by a numerical example

analyticity and discrete maximal regularity on lp spaces abstract in the first part of this paper we give the following interpolation result on the analyticity i e the property t i tn c n for all n n of an operator t on lp if t is powerbounded on lp and lq as well as analytic on lp then t is powerbounded and analytic on lr for all r strictly between p and q this is a discrete analogue of the well known corresponding result for analytic semigroups eta as recently shown by the author the analyticity of t is a necessary condition for the maximal regularity of the discrete time evolution equation un 1 tun fn for all n z u0 0 in the second part of this paper we establish the following two sufficient conditions for its maximal regularity t is a subpositive analytic contraction or t is an integral operator satisfying certain poisson bounds these results are discrete analogues of the corresponding results for the maximal regularity of the evolution equation u t au t f t for all t r u 0 0 due to lamberton weis coulhon and duong and hieber and pruss for the poisson bound result of coulhon and duong and hieber and pruss we give a slight improvement and a short proof

indistinguishability of trees in uniform spanning forests we prove that in both the free and the wired uniform spanning forest fusf and wusf of any unimodular random rooted network in particular of any cayley graph it is impossible to distinguish the connected components of the forest from each other by invariantly defined graph properties almost surely this confirms a conjecture of benjamini et al ann probab 29 1 1 65 2001 we also answer positively two additional questions of benjamini et al ann probab 29 1 1 65 2001 under the assumption of unimodularity we prove that on any unimodular random rooted network the fusf is either connected or has infinitely many connected components almost surely and if the fusf and wusf are distinct then every component of the fusf is transient and infinitely ended almost surely all of these results are new even for cayley graphs

heat kernel estimates for subordinate brownian motions in this article we study transition probabilities of a class of subordinate brownian motions under mild assumptions on the laplace exponent of the corresponding subordinator sharp two sided estimates of the transition probability are established this approach in particular covers subordinators with laplace exponents that vary regularly at infinity with index one e g log 1 1 or log 1 2 0 2 that correspond to subordinate brownian motions with scaling order that is not necessarily stricty between 0 and 2 these estimates are applied to estimate green function potential of subordinate brownian motion we also prove the equivalence of the lower scaling condition of the laplace exponent and the near diagonal upper estimate of the transition estimate

operateurs uniformement sous elliptiques sur les groupes de lie given a connected unimodular lie group g having polynomial volume growth and left invariant vector fields x1 xk which generate the lie algebra of g consider the operator la i j 1kxiaijxj where a g rk rk is a smooth symmetric matrix valued function which satisfies a 2 i j 1k aij x i j 1 2 x g rk for some 0 1 what we show is that the corresponding heat flow semigroup etla admits a kernel which satisfies two sided gaussian estimates in terms of the control distance determined by the xi s moreover the estimates can be made to depend on a only through we also prove harnack inequalities and holder regularity of solutions we end with a discussion of some other sub elliptic situations

matrix based algorithms for constrained least squares and minimax designs of 2 d linear phase fir filters the impulse response coefficients of a two dimensional 2 d finite impulse response fir filter are in a matrix form in nature conventional optimal design algorithms rearrange the filter s coefficient matrix into a vector and then solve for the coefficient vector using design algorithms for one dimensional 1 d fir filters some recent design algorithms have exploited the matrix nature of the 2 d filter s coefficients but not incorporated with any constraints and thus are not applicable to the design of 2 d filters with explicit magnitude constraints in this paper we develop some efficient algorithms exploiting the coefficients matrix nature for the constrained least squares cls and minimax designs of quadrantally symmetric 2 d linear phase fir filters both of which can be formulated as an optimization problem or converted into a sequence of subproblems with a positive definite quadratic cost and a finite number of linear constraints expressed in terms of the filter s coefficient matrix design examples and comparisons with several existing algorithms demonstrate the effectiveness and efficiency of the proposed algorithms

on a stochastic nonlinear equation arising from 1d integro differential scalar conservation laws abstract in this paper we study the initial problem for a stochastic nonlinear equation arising from 1d integro differential scalar conservation laws the equation is driven by levy space time white noise in the following form t a u x q u f u g u f t x for u t x 0 r u t x r where a is an integro differential operator associated with a symmetric nonlocal regular dirichlet form and f t x stands for a levy space time white noise the problem is interpreted as a stochastic integral equation of jump type involving certain convolution kernels existence of a unique local in time l 2 r valued solution is obtained

convex programming design of linear and nonlinear phase wideband blocking filters blocking filters are commonly used in array processing to excise targets from data when suitable target free training data is not available a drawback is the reduction of the effective size of the array by the order of the filter motivating a search for the smallest filter that meets the design specifications common linear phase approaches lead to convex optimization and efficient global solutions but can be inefficient when the phase of the blocking filter is unimportant although direct magnitude response optimization is nonconvex in general for narrowband linear arrays optimal magnitude blocking filters can be found using constrained optimization followed by spectral factorization this approach cannot be directly applied to wideband arrays as finite support spectral factors do not generally exist in higher dimensions instead a procedure is presented in which an approximate multidimensional spectral factor of an optimized spectral density is used as a target response in a second optimization stage linear and nonlinear phase solutions are found and compared for both narrowband and wideband notch filters with the nonlinear phase outperforming the linear phase in both notch width and passband error the various optimizations are performed using second order cone programming an efficient class of convex optimization

rate of escape of random walks on wreath products and related groups this article examines the rate of escape for a random walk on g z and proves laws of the iterated logarithm for both the inner and outer radius of escape the class of g for which these results hold includes finite g as well as groups of the form h z so the construction can be iterated laws of the iterated logarithm are also found for random walk on baumslag solitar groups and a discrete version of the sol geometry

dimension free lp estimates for single riesz transforms via an h joint functional calculus abstract by using an h joint functional calculus for strongly commuting operators we derive a scheme to deduce the l p boundedness of certain d dimensional riesz transforms from the l p boundedness of appropriate one dimensional riesz transforms moreover the l p bounds we obtain are independent of the dimension the scheme is applied to riesz transforms connected with orthogonal expansions and discrete riesz transforms on products of groups with polynomial growth

symmetric markov chains on ℤ with unbounded range we consider symmetric markov chains on z d where we do not assume that the conductance between two points must be zero if the points are far apart under a uniform second moment condition on the conductances we obtain upper bounds on the transition probabilities estimates for exit time probabilities and certain lower bounds on the transition probabilities we show that a uniform harnack inequality holds if an additional assumption is made but that without this assumption such an inequality need not hold we establish a central limit theorem giving conditions for a sequence of normalized symmetric markov chains to converge to a diffusion on d corresponding to an elliptic operator in divergence form

parabolic harnack inequality and heat kernel estimates for random walks with long range jumps we investigate the relationships between the parabolic harnack inequality heat kernel estimates some geometric conditions and some analytic conditions for random walks with long range jumps unlike the case of diffusion processes the parabolic harnack inequality does not in general imply the corresponding heat kernel estimates

stable iir notch filter design with optimal pole placement this paper presents a two stage approach for designing an infinite impulse response iir notch filter first the numerator of the transfer function of the iir notch filter is obtained by placing the zeros at the prescribed notch frequencies then the denominator polynomial is determined by using an iterative scheme in which the optimal pole placements are found by solving a standard quadratic programming problem for stability the pole radius in the single notch filter design is specified by the designer and in the multiple notch filter design the pole radius is constrained by using the implications of rouche s theorem examples are included to illustrate the effectiveness of the proposed techniques

the component graph of the uniform spanning forest transitions in dimensions 9 10 11 ldots 9 10 11 we prove that the uniform spanning forests of mathbb z d and mathbb z ell have qualitatively different connectivity properties whenever ell d ge 4 in particular we consider the graph formed by contracting each tree of the uniform spanning forest down to a single vertex which we call the component graph we introduce the notion of ubiquitous subgraphs and show that the set of ubiquitous subgraphs of the component graph changes whenever the dimension changes and is above 8 to separate dimensions 5 6 7 and 8 we prove a similar result concerning ubiquitous subhypergraphs in the component hypergraph our result sharpens a theorem of benjamini kesten peres and schramm who proved that the diameter of the component graph increases by one every time the dimension increases by four

quantum charges and spacetime topology the emergence of new superselection sectors a new form of superselection sectors of topological origin is developed by that it is meant a new investigation that includes several extensions of the traditional framework of doplicher haag and roberts in local quantum theories at first we generalize the notion of representations of nets of c algebras then we provide a brand new view on selection criteria by adopting one with a strong topological flavour we prove that it is coherent with the older point of view hence a clue to a genuine extension in this light we extend roberts cohomological analysis to the case where 1 cocycles bear non trivial unitary representations of the fundamental group of the spacetime equivalently of its cauchy surface in the case of global hyperbolicity a crucial tool is a notion of group von neumann algebras generated by the 1 cocycles evaluated on loops over fixed regions one proves that these group von neumann algebras are localized at the bounded region where loops start and end and to be factorial of finite type i all that amounts to a new invariant in a topological sense which can be defined as the dimension of the factor we prove that any 1 cocycle can be factorized into a part that contains only the charge content and another where only the topological information is stored this second part much resembles what in literature is known as geometric phases indeed by the very geometrical origin of the 1 cocycles that we discuss in the paper they are essential tools in the theory of net bundles and the topological part is related to their holonomy content at the end we prove the existence of net representations

random conductance models with stable like jumps heat kernel estimates and harnack inequalities abstract we establish two sided heat kernel estimates for random conductance models with non uniformly elliptic possibly degenerate stable like jumps on graphs these are long range counterparts of the well known two sided gaussian heat kernel estimates by m t barlow for nearest neighbor short range random walks on the supercritical percolation cluster unlike the cases of nearest neighbor conductance models we cannot use parabolic harnack inequalities since even elliptic harnack inequalities do not hold in the present setting as an application we establish the local limit theorem for the models