some experiments with simulated annealing for coloring graphs abstract methods of thermodynamical simulation have been used for several famous combinatorial optimization problems for graph coloring i e partition of the node set into as few independent sets as possible we describe a method of simulation such an approach is combined with other techniques for graph coloring experiments on random graphs show evidence that this combination gives better results than anyone of the original non combined methods

improving inductive logic programming by using simulated annealing in inductive logic programming ilp algorithms that are purely of the bottom up or top down type encounter several problems in practice since a majority of them are greedy ones these algorithms stop when finding clauses in local optima according to the quality measure used for evaluating the results moreover when learning clauses one by one the induced clauses become less and less interesting as the algorithm is progressing to cover few remaining examples in this paper we propose a simulated annealing framework to overcome these problems using a refinement operator we define neighborhood relations on clauses and on hypotheses i e sets of clauses with these relations and appropriate quality measures we show how to induce clauses in a coverage approach or to induce hypotheses directly by using simulated annealing algorithms we discuss the necessary conditions on the refinement operators and the evaluation measures to increase the effectiveness of the algorithm implementations included a parallelized version of the algorithm are described and experimentation results in terms of convergence of the method and in terms of accuracy are presented

regularity of the invariant measure and of the density of states in the one dimensional anderson model abstract let h 1 2 v on l2 z where v x x z are i i d r v s with common probability distribution let h t e itvd v let n e be the integrated density of states and let e be the invariant measure at energy e it is proven 1 1 let h be d times differentiable on 0 with bounded derivatives such that h j t 0 as t for j 0 1 d then i n e is a cd function ii if d 3 e is absolutely continuous for all e r and d e dx is of class c d 1 2 1 jointly in e and x 2 2 let h be differentiable on 0 with h j t o e b t for j 0 1 and some b 0 then d e dx is jointly analytic in e and x

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

diffusions for global optimizations we seek a global minimum of u 0 1 n to r the solution to d dt x t nabla u x t will find local minima the solution to dx t nabla u x t dt sqrt 2t dw t where w is standard n dimensional brownian motion and the boundaries are reflecting will concentrate near the global minima of u at least when temperature t is small the equilibrium distribution for x t is gibbs with density pi t x alpha exp u x t this suggests setting t t t downarrow 0 to find the global minima of u we give conditions on u x and t t such that the solution to dx t nabla u x t dt sqrt 2t dw t converges weakly to a distribution concentrated on the global minima of u

optimizing antenna array geometry for interference suppression the determination of an optimum antenna array geometry for suppressing interference is addressed an optimization problem is derived whose solution yields an optimum array geometry for a given interference environment a specific example is solved via the simulated annealing optimization algorithm and results are presented for arrays of varying configurations

a note on the analyticity of density of states we consider the d dimensional anderson model and we prove the density of states is locally analytic if the single site potential distribution is locally analytic and the disorder is large we employ the random walk expansion of resolvents and a simple complex function theory trick in particular we discuss the uniform distribution case and we obtain a sharper result using more precise computations the method can be also applied to prove the analyticity of the correlation functions

a class of self interacting processes with applications to games and reinforced random walks this paper studies a class of non markovian and nonhomogeneous stochastic processes on a finite state space relying on a recent paper by benaim hofbauer and sorin siam j control optim 44 2005 pp 328 348 it is shown that under certain assumptions the asymptotic behavior of occupation measures can be described in terms of a certain set valued deterministic dynamical system this provides a unified approach to simulated annealing type processes and permits the study of new models of vertex reinforced random walks and new models of learning in games such as markovian fictitious play

reinforcement learning with restrictions on the action set consider a two player normal form game repeated over time we introduce an adaptive learning procedure where the players only observe their own realized payoff at each stage we assume that agents do not know their own payoff function and have no information on the other player furthermore we assume that they have restrictions on their own actions such that at each stage their choice is limited to a subset of their action set we prove that the empirical distributions of play converge to the set of nash equilibria for zero sum and potential games and games where one player has two actions

a method of spatial reasoning based on qualitative trigonometry abstract due to the lack of exact quantitative information or the difficulty associated with obtaining or processing such information qualitative spatial knowledge representation and reasoning often become an essential means for solving spatial constraint problems as found in science and engineering this paper presents a computational approach to representing and reasoning about spatial constraints in two dimensional euclidean space where the a priori spatial information is not precisely expressed in quantitative terms the spatial quantities considered in this work are qualitative distances and qualitative orientation angles here we explicitly define the semantics of these quantities and thereafter formulate a representation of qualitative trigonometry qtrig the resulting qtrig formalism provides the necessary inference rules for qualitative spatial reasoning in the paper we illustrate how the qtrig relationships can be employed in generating qualitative spatial descriptions in two dimensional euclidean geometric problems and furthermore how the derived qualitative spatial descriptions can be used to guide a simulated annealing based exact quantitative value assignment finally we discuss an application of the proposed spatial reasoning method to the kinematic constraint analysis in computer aided pre parametric mechanism design

a note on the finite time behavior of simulated annealing simulated annealing has proven to be a very successful heuristic for various combinatorial optimization problems it is a randomized algorithm that attempts to find the global optimum with high probability by local exchanges in this paper we give a new proof of the convergence of simulated annealing by applying results about rapidly mixing markov chains with this proof technique it is possible to obtain better bounds for the finite time behavior of simulated annealing than previously known

on the fock space representation of functionals of the occupation field and their renormalization on fournit une representation du champ d occupation et de ses puissances renormalisees dans un bon espace de fock

analyticity of the density of states in the anderson model on the bethe lattice let h 1 2 v on l2 b whereb is the bethe lattice andv x xeb are i i d r v s with common probability distribution it is shown that for distributions sufficiently close to the cauchy distribution the density of states e is analytic in a strip about the real axis

synthesis of modular contiguously clustered linear arrays through a sparseness regularized solver an innovative methodology for the design of modular and contiguously clustered linear arrays is proposed the approach formulates the subarraying problem as a pattern matching one in which elementary modules taken from a user defined dictionary are combined to synthesize the final antenna layout by recasting such a synthesis problem within the compressive sensing framework an efficient solver is used to determine the array architecture starting from the a priori specification of the features e g the length of the admissible subarrays a set of representative numerical experiments is discussed to assess the advantages and drawbacks of the proposed algorithm also in comparison with some state of the art methods

a stochastic method for bayesian estimation of hidden markov random field models with application to a color model we propose a new stochastic algorithm for computing useful bayesian estimators of hidden markov random field hmrf models that we call exploration selection estimation ese procedure the algorithm is based on an optimization algorithm of o francois called the exploration selection e s algorithm the novelty consists of using the a posteriori distribution of the hmrf as exploration distribution in the e s algorithm the ese procedure computes the estimation of the likelihood parameters and the optimal number of region classes according to global constraints as well as the segmentation of the image in our formulation the total number of region classes is fixed but classes are allowed or disallowed dynamically this framework replaces the mechanism of the split and merge of regions that can be used in the context of image segmentation the procedure is applied to the estimation of a hmrf color model for images whose likelihood is based on multivariate distributions with each component following a beta distribution meanwhile a method for computing the maximum likelihood estimators of beta distributions is presented experimental results performed on 100 natural images are reported we also include a proof of convergence of the e s algorithm in the case of nonsymmetric exploration graphs

harmonic analysis on sl 2 r and smoothness of the density of states in the one dimensional anderson model we consider infinite jacobi matrices with ones off diagonal and independent identically distributed random variables with distributionf v dv on diagonal iff has compact support and lies in some sobolev spacel 1 then we prove that the integrated density of states k e isc ine

singularity of the density of states for one dimensional chains with random couplings we prove that the density of states for the tight binding model with off diagonal disorder under general conditions diverges forr 0 at least as sim frac 1 left e right ln left e right 4 this result is established through the study of the recurrence properties of an associated markov chain

cooling down levy flights let l t be a levy flights process with a stability index 0 2 and u be an external multi well potential a jump diffusion z satisfying a stochastic differential equation dz t u z t dt t dl t describes an evolution of a levy particle of an instant scale t in an external force field the scale is supposed to decrease polynomially fast i e t t for some 0 we discover two different decrease regimes if 1 fast cooling the levy particle gets trapped in one of the potential wells

smoothness of the integrated density of states on strips smoothness of the integrated density of states k e of random schrodinger operators i i d and non i i d cases on a discrete strip lattice is investigated it is proven that k e is c if only the potentials on the top surface of the strip have distributions with compactly supported densities in some fractional sobolev space the c result for the case of the anderson model i e all potentials having a distribution with compactly supported density in some sobolev space is also recovered

ergodicity in parametric nonstationary markov chains an application to simulated annealing methods a nonstationary markov chain is weakly ergodic if the dependence of the state distribution on the starting state vanishes as time tends to infinity a chain is strongly ergodic if it is weakly ergodic and converges in distribution in this paper we show that the two ergodicity concepts are equivalent for finite chains under rather general and widely verifiable conditions we discuss applications to probabilistic analyses of general search methods for combinatorial optimization problems simulated annealing

stochastic optimization on continuous domains with finite time guarantees by markov chain monte carlo methods we introduce bounds on the finite time performance of markov chain monte carlo mcmc algorithms in solving global stochastic optimization problems defined over continuous domains it is shown that mcmc algorithms with finite time guarantees can be developed with a proper choice of the target distribution and by studying their convergence in total variation norm this work is inspired by the concept of finite time learning with known accuracy and confidence developed in statistical learning theory

galois actions on blocks and classes of finite groups abstract we consider galois actions on blocks and conjugacy classes we extend some of the results valid in the case of complex conjugation we give some counterexamples where this extension is not possible

convergence to global minima for a class of diffusion processes abstract we prove that there exists a gain function t t t 0 such that the solution of the sde d x t t grad u x t d t t d b t settles down on the set of global minima of u in particular the existence of a gain function t t 0 so that yt satisfying d y t t grad u y t d t d b t converges to the set of the global minima of u is verified then we apply the results to the robbins monro and the kiefer wolfowitz procedures which are of particular interest in statistics

phase transition and landscape statistics of the number partitioning problem the phase transition in the number partitioning problem npp i e the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no solution is investigated by examining the energy landscape of this classic optimization problem this is achieved by coding the information about the minimum energy paths connecting pairs of minima into a tree structure termed a barrier tree the leaves and internal nodes of which represent respectively the minima and the lowest energy saddles connecting those minima here we apply several measures of shape balance and symmetry as well as of branch lengths barrier heights to the barrier trees that result from the landscape of the npp aiming at identifying traces of the easy hard transition we find that it is not possible to tell the easy regime from the hard one by visual inspection of the trees or by measuring the barrier heights only the difficulty measure given by the maximum value of the ratio between the barrier height and the energy surplus of local minima succeeded in detecting traces of the phase transition in the tree in addition we show that the barrier trees associated with the npp are very similar to random trees contrasting dramatically with trees associated with the p spin glass and random energy models we also examine critically a recent conjecture on the equivalence between the npp and a truncated random energy model

stochastic relaxation on partitions with connected components and its application to image segmentation we present a new method of segmentation in which images are segmented in partitions with connected components we give computationally inexpensive algorithms for probability simulation and simulated annealing on the space of partitions with connected components of a general graph in particular hastings algorithms 1970 and generalized metropolis algorithms are defined to avoid heavy computation to achieve segmentation we propose a hierarchical approach which at each step minimizes a cost function on the space of partitions with connected components of a graph the algorithm is applied to segment gray level color and textured images

extended states in the anderson model on the bethe lattice abstract we prove that the anderson hamiltonianh von the bethe lattice has extended states for small disorder more precisely given any closed intervalicontained in the interior of the spectrum of the laplacian on the bethe lattice we prove that for small disorderh has purely absolutely continuous spectrum iniwith probability one i e ac h i iand pp h i sc h i with probability one and its integrated density of states is continuously differentiable on the intervali

sharp asymptotics for fixation times in stochastic population genetics models at low mutation probabilities this article describes new models in population genetics that extend the neutral wright fisher model by including strong selection and mutation fixation times are studied in the limit of small mutation probabilities within the framework of markov chains with rare transitions the main result outlines the role of the discrete geometry of the fitness landscape and provides a mean for estimating the expected number of generations for an individual with better fitness value to appear some connections to evolutionary algorithms are discussed as well

some connections between excursion theory and the discrete schrodinger equation with random potentials we use here discrete excursion theory and the ray knight theorem in order to study questions concerning the analyticity of the density of states at low disorder as well as its smoothness properties in one dimension

nonstationary markov chains and convergence of the annealing algorithm we study the asymptotic behavior as timet of certain nonstationary markov chains and prove the convergence of the annealing algorithm in monte carlo simulations we find that in the limitt a nonstationary markov chain may exhibit phase transitions nonstationary markov chains in general and the annealing algorithm in particular lead to biased estimators for the expectation values of the process we compute the leading terms in the bias and the variance of the sample means estimator we find that the annealing algorithm converges if the temperaturet t goes to zero no faster thanc log t t0 ast with a computable constantc andt0 the initial time the bias and the variance of the sample means estimator in the annealing algorithm go to zero likeo t 1 e for some 0 e 1 with e 0 only in very special circumstances our results concerning the convergence of the annealing algorithm and the rate of convergence to zero of the bias and the variance of the sample means estimator provide a rigorous procedure for choosing the optimal annealing schedule this optimal choice reflects the competition between two physical effects a the adiabatic effect whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state and b the super cooling effect whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state s but may do so extremely slowly

simulated annealing via sobolev inequalities we use sobolev inequalities to study the simulated annealing algorithm this approach takes advantage of the local time reversibility of the process and yields the optimal freezing schedule as well as quantitative information about the rate at which the process is tending to its ground state

a hybrid approach to the synthesis of subarrayed monopulse linear arrays in this paper a hybrid approach for the synthesis of the ldquooptimalrdquo compromise between sum and difference patterns for subarrayed monopulse antennas is presented first the subarray configuration is determined by exploiting the knowledge of the optimum difference mode coefficients to reduce the dimension of the searching space in the second step the subarray weights are computed by means of a convex programming procedure which takes advantages from the convexity for a fixed clustering of the problem at hand a set of representative results is reported to assess the effectiveness of the proposed approach comparisons with state of the art techniques are also presented

a multi objective approach to subarrayed linear antenna arrays design based on memetic differential evolution in this paper we present a multi objective optimization approach to subarrayed linear antenna arrays design we define this problem as a bi objective one we consider two objective functions for directivity maximization and sidelobe level minimization memetic algorithms mas are hybrid algorithms that combine the benefits of a global search evolutionary algorithm ea with a local search method in this paper we introduce a new memetic multi objective evolutionary algorithm namely the memetic generalized differential evolution mgde3 this algorithm is a memetic extension of the popular generalized differential evolution gde3 algorithm another popular moea is the nondominated sorting genetic algorithm ii nsga ii mgde3 gde3 and nsga ii are applied to the synthesis of uniform and nonuniform subarrayed linear arrays providing an extensive set of solutions for each design case depending on the desired array characteristics the designer can select the most suitable solution the results of the proposed method are compared with those reported in the literature indicating the advantages and applicability of the multi objective approach

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

anderson localization for bernoulli and other singular potentials we prove exponential localization in the anderson model under very weak assumptions on the potential distribution in one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment in particular this solves the longstanding problem of localization for bernoulli potentials i e potentials that take only two values in dimensions greater than one we prove localization at high disorder for potentials with holder continuous distributions and for bounded potentials whose distribution is a convex combination of a holder continuous distribution with high disorder and an arbitrary distribution these include potentials with singular distributions we also show that for certain bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component

localization for one dimensional continuum bernoulli anderson models we use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional continuum anderson type models with singular distributions in particular the case of a bernoulli dis tribution is covered the operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms our main tools are the reflection and transmission coefficients for compactly supported single site perturbations of a periodic background which we use to verify the necessary hypotheses of multi scale analysis we show that non reflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs

a combined multistart annealing algorithm for continuous global optimization the application of simulated annealing to the global optimization of a function on a compact subset of rd is discussed for the langevin algorithm the class of convergent schedules depends on some a priori knowledge about the form of the function it is shown that this problem disappears by using the simplest annealing algorithm of jump type which can also be improved by performing local searches between two consecutive jump times the resulting algorithm is essentially a multistart technique controlled by an annealing schedule

supersymmetry and the parisi sourlas dimensional reduction a rigorous proof functional integrals that are formally related to the average correlation functions of a classical field theory in the presence of random external sources are given a rigorous meaning their dimensional reduction to the schwinger functions of the corresponding quantum field theory in two fewer dimensions is proven this is done by reexpressing those functional integrals as expectations of a supersymmetric field theory the parisi sourlas dimensional reduction of a supersymmetric field theory to a usual quantum field theory in two fewer dimensions is proven

diffusion for global optimization in r n we seek a global minimum of u mathbb r n to mathbb r the solution to d dt x t nabla u x t will find local minima using the idea of simulated annealing we consider th

an effective hybrid approach for the optimal synthesis of monopulse antennas the problem of synthesizing optimal sum and difference patterns subject to arbitrary sidelobe bounds by means of a simple feeding network is dealt with it is shown how a hybrid optimization procedure properly acting on both clustering into subarrays and excitations of these latter greatly improves performances of known feeding architectures with respect to existing procedures results of the proposed technique which significantly outperform existing methods renew the interest of these simple feeding architectures and emphasize the effectiveness of this kind of hybrid procedures exploiting the convexity of the problem with respect to a part of the unknowns

kotani theory for one dimensional stochastic jacobi matrices we consider families of operators h on l2 given by h u n u n 1 u n 1 v n u n wherev is a stationary bounded ergodic sequence we prove analogs of kotani s results including that for a e ac h is the essential closure of the set ofe where e the lyaponov index vanishes and the result that ifv is non deterministic then ac is empty

blocks inequivalent to their frobenius twists abstract let k be an algebraically closed field of characteristic p we give a general method for producing examples of blocks b of finite group algebras that are not morita equivalent as k algebras to the frobenius twist b p our method produces non nilpotent blocks having one simple module and elementary abelian defect group these also provide the first known examples of blocks where there is a perfect isotypy at the level of ordinary characters with all the signs positive but no derived equivalence between the blocks we do not know of any examples of blocks b that are not morita equivalent to the second frobenius twist b p 2

taylor patterns for discrete arrays the equivalent of a taylor pattern for continuous apertures is developed for discrete arrays this array factor can be realized exactly since it belongs to the appropriate class of patterns a method for determining the element excitations is also presented as an example the pattern and excitations are calculated for a 41 element array with bar n 6 and a 25 db design sidelobe level comparison is made with the patterns obtained by applying root matching and sampling of a continuous taylor aperture

instability of the anomalies in the one dimensional anderson model at weak disorder we study the asymptotic behavior of the invariant measure the lyapunov exponent and the density of states in the weak disorder limit in the case where the single site potential distribution is not centered and for the special energiese cos p q we also prove that in general the above quantities can be continuously extended to zero disorder as continuous functions in the disorder parameter for all energiese 1 1

new bounds for binary covering arrays using simulated annealing covering arrays cas are combinatorial structures specified as a matrix of n rows and k columns over an alphabet on v symbols such that for each set of t columns called the strength of the array every t tuple of symbols is covered recently they have been used to represent interaction test suites for software testing given that they provide economical sized test cases while still preserving important fault detection capabilities this paper introduces an improved implementation of a simulated annealing algorithm called isa for constructing cas of strengths three through six over a binary alphabet i e binary cas extensive experimentation is carried out using 127 well known benchmark instances for assessing its performance with respect to an existing simulated annealing implementation a greedy method and five state of the art algorithms the results show that our algorithm attains 104 new bounds and equals the best known solutions for the other 23 instances consuming reasonable computational time furthermore the implications of using these results as ingredients to recursive constructions are also analyzed

proposals for chunking and tabu search chunking grouping basic units of information to create higher level units is a critical aspect of human intelligence we identify special types of chunking to enhance tabu search memory structures producing improved problem solving ability and giving useful supporting information for decision makers tabu search as proposed by glover orsa journal on computing 1 3 1989 190 2 1 1990 4 has proven to be a very effective meta heuristic for hard optimization problems the search is typically based on a local improvement scheme that involves alteration of one or more attributes of fully specified solutions at each iteration in this paper we describe the use of and search for groupings of solution attributes although they are most natural in the context of the tabu search paradigm many of the proposals can also be employed in genetic algorithms and simulated annealing based algorithms chunking enables a number of search improvements including a general purpose metric for decision vectors the paper develops theory and proposals for learning about chunks and using them computational experience to date is summarized to support the contention that chunking can be an important part of effective optimization algorithms

synthesis of subarrayed monopluse arrays with contiguous elements using a de algorithm subarrayed monopulse linear and conformal circular arc arrays with low sidelobe sum and difference patterns are synthesized for the monopulse array with a subarray partition consisting of contiguous elements to reduce the cross points the synthesis problem is first formulated as a constrained optimization problem then by defining an appropriate fitness function to convert the problem into an unconstrained one the problem is efficiently solved by the differential evolution algorithm under successful parent selecting framework the numerical results of small and large monopulse linear arrays are reported by comparisons with the state of the art techniques at last synthesis of a monopulse conformal circular arc array is also investigated based on the same technique

asymptotic behavior of some linear differential systems abstract consider the following chasing game in r amongbparticles whose trajectories are governed by the following differential equations fori s 1 2 b f i t j i q ij t f j t f i t wherefi t is the position at timetof the particleiandqij t which measures the instantaneous rate that particleiis attracted toward particlej is given byqij t pij t u i j forj i the rate function t is positive with limt t 0 u i j 0 is the cost function indicating the level of difficulty fromitojand the nonnegative numberspijfori jreflect the neighborhood structure of the particles particles are attracted to one another but such attraction becomes weaker as time goes on a sufficient condition on t is given for allfi t converging to a common finite limit

generalized deterministic annealing we develop a general formalism for computing high quality low cost solutions to nonconvex combinatorial optimization problems expressible as distributed interacting local constraints for problems of this type generalized deterministic annealing gda avoids the performance related sacrifices of current techniques gda exploits the localized structure of such problems by assigning k state neurons to each optimization variable the neuron values correspond to the probability densities of k state local markov chains and may be updated serially or in parallel the markov model is derived from the markov model of simulated annealing sa although it is greatly simplified theorems are presented that firmly establish the convergence properties of gda as well as supplying practical guidelines for selecting the initial and final temperatures in the annealing process a benchmark image enhancement application is provided where the performance of gda is compared to other optimization methods the empirical data taken in conjunction with the formal analytical results suggest that gda enjoys significant performance advantages relative to current methods for combinatorial optimization

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

regularity of the density of states of random schrodinger operators in this paper we solve a long standing open problem for random schrodinger operators on l 2 mathbb r d with i i d single site random potentials we allow a large class of free operators including magnetic potential however our method of proof works only for the case when the random potentials satisfy a complete covering condition we require that the supports of the random potentials cover mathbb r d and the bump functions that appear in the random potentials form a partition of unity for such models we show that the density of states dos is m times differentiable in the part of the spectrum where exponential localization is valid if the single site distribution has compact support and has holder continuous m 1 st derivative the required holder continuity depends on the fractional moment bounds satisfied by appropriate operator kernels our proof of the random schrodinger operator case is an extensions of our proof for anderson type models on ell 2 mathbb g mathbb g a countable set with the property that the cardinality of the set of points at distance n from any fixed point grows at some rate in n alpha alpha 0 this condition rules out the bethe lattice where our method of proof works but the degree of smoothness also depends on the localization length a result we do not present here even for these models the random potentials need to satisfy a complete covering condition the anderson model on the lattice for which regularity results were known earlier also satisfies the complete covering condition

an effective approach for the optimal focusing of array fields subject to arbitrary upper bounds a new approach to the optimal focusing of array fields subject to arbitrary upper bounds is presented the approach formulates the problem as the minimization of a linear function in a convex set unlike other approaches this one guarantees the achievement of the global optimum by using local optimization techniques and can moreover deal with any convex constraint on the unknowns such as near field constraints optimization is performed by two ad hoc developed solution algorithms which exploit the geometrical characteristics of the problem at hand thus leading to extremely effective and computationally efficient numerical codes an extensive numerical analysis has been performed in all cases of linear planar and circular arc arrays the enhanced performance of the proposed technique with respect to the solution algorithms available in the literature fully confirms the effectiveness of the approach

simulated annealing for convex optimization we apply the method known as simulated annealing to the following problem in convex optimization minimize a linear function over an arbitrary convex set where the convex set is specified only by a membership oracle using distributions from the boltzmann gibbs family leads to an algorithm that needs only o n phases for instances in rn this gives an optimization algorithm that makes o n4 5 calls to the membership oracle in the worst case compared to the previous best guarantee of o n5 the benefits of using annealing here are surprising because such problems have no local minima that are not also global minima hence we conclude that one of the advantages of simulated annealing in addition to avoiding poor local minima is that in these problems it converges faster to the minima that it finds we also give a proof that under certain general conditions the boltzmann gibbs distributions are optimal for annealing on these convex problems

a limit theorem for a class of inhomogeneous markov processes pour un processus de markov xh irreductible et aperiodique avec un espace d etats fini et avec un taux de transition q ij t x t devient homogene dans le cas q ij t q ij et admet une loi limite qui est independante de x o le but de cet article est de demontrer qu un resultat similaire peut etre obtenu dans le cas de processus de markov non homogenes avec un certain type de taux de transition

a supersymmetric transfer matrix and differentiability of the density of states in the one dimensional anderson model let h v on 2 z where v x 9 xez are d r v s with common probability distribution v let h t e itvdv v and let k e be the integrated density of states it is proven i if h is n times differentiable with h j t 0 l t for some 0 7 0 l n then k e is a cn function in particular if v has compact support and h t 0 l h 1 with 0 then k e is c this allows v to be singular continuous ii lfh t 0 e a tl for some 0 then k e is analytic in a strip about the real axis the proof uses the supersymmetric replica trick to rewrite the averaged green s function as a two point function of a one dimensional supersymmetric field theory which is studied by the transfer matrix method

microwave imaging based on a markov random field model a new approach to microwave imaging of 2d inhomogeneous dielectric scatterers is presented the method is developed in the space domain and markov random fields are used to obtain a model of the distributions of dielectric features in the scattering region in this way a priori knowledge can be easily inserted in the imaging scheme this stochastic approach gives rise to a functional equation that can be minimized by using a simulated annealing algorithm an iterative scheme is derived that allows one to bypass the need for storing large matrices in the computer numerical simulation results confirming the capabilities and effectiveness of the proposed method are reported solutions have generally been obtained in few steps and seem better than those obtained by other imaging techniques in the space domain the capability of the algorithm to operate in a strongly noisy environment is also proved

holder continuity of the integrated density of states for quasi periodic schrodinger equations and averages of shifts of subharmonic functions in this paper we consider various regularity results for discrete quasiperiodic schr6dinger equations n l pn 1 v 9 nw on eon with analytic potential v we prove that on intervals of positivity for the lyapunov exponent the integrated density of states is holder continuous in the energy provided w has a typical continued fraction expansion the proof is based on certain sharp large deviation theorems for the norms of the monodromy matrices and the avalanche principle the latter refers to a mechanism that allows us to write the norm of a monodromy matrix as the product of the norms of many short blocks in the multi frequency case the integrated density of states is shown to have a modulus of continuity of the form exp log tl for some 0 a 1 but currently we do not obtain holder continuity in the case of more than one frequency we also present a mechanism for proving the positivity of the lyapunov exponent for large disorders for a general class of equations the only requirement for this approach is some weak form of a large deviation theorem for the lyapunov exponents in particular we obtain an independent proof of the herman sorets spencer theorem in the multi frequency case the approach in this paper is related to the recent nonperturbative proof of anderson localization in the quasi periodic case by j bourgain and m goldstein

a rigorous replica trick approach to anderson localization in one dimension leth v onl2 wherev x x are i i d r v s and letg l x y e i x hl e i 1 y whereh l denotes the operatorh restricted to l l 1 l with dirichlet boundary conditions we use a supersymmetric replica trick to prove that e g l 0 x e i eta 2 leqq k eta 2 exp m log eta sigma x for somem 0 0 k uniformly inl ande this estimate together with the usual necessary estimate on the density of states implies zero conductivity and gives exponential localization by the frohlich martinelli scoppola and spencer method

the density of states in the anderson model at weak disorder a renormalization group analysis of the hierarchical model we study the density of states in a hierarchical approximation of the anderson tight binding model at weak disorder using a renormalization group approach since the laplacian term in our model is hierarchical the renormalization group transformations act essentially on the local potential distribution and the energy technically we use the supersymmetric replica trick and study the averaged green s function starting with a gaussian distribution with small variance we find that the density of states is analytic as soon as the variance of the potential is turned on except possibly near the band edge where we can show this only for 2 which corresponds tod 4 moreover it is perturbatively close to the free one except near the eigenvalues of the hierarchical laplacian where it is given up to perturbative corrections by the rescaled potential distribution

on the density of states of schrodinger operators with a random potential using very recent results on ergodic theorems for superadditive processes on rd the authors prove the existence of the density of states for a wide class of random schrodinger operators in particular new non asymptotic estimates on the density of states are obtained and examples are discussed

ergodic properties of a model related to disordered quantum anharmonic crystals we introduce a model suggested by disordered anharmonic quantum crystals we then investigate in detail the ergodic properties exhibited by such a model

a bayesian approach to dynamic contours through stochastic sampling and simulated annealing in many applications of image analysis simply connected objects are to be located in noisy images during the last 5 6 years active contour models have become popular for finding the contours of such objects connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations these approaches do however have several disadvantages the numerical algorithms that are in use constrain the models that can be used furthermore in many cases only local minima can be achieved in this paper the author discusses a method for curve detection based on a fully bayesian approach a model for image contours which allows the number of nodes on the contours to vary is introduced iterative algorithms based on stochastic sampling is constructed which make it possible to simulate samples from the posterior distribution making estimates and uncertainty measures of specific quantities available further simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented in theory no restrictions on the models are made in practice however computational aspects must be taken into consideration when choosing the models much more general models than the one used for active contours may however be applied the approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain and show promising results

metropolis type annealing algorithms for global optimization in r d the convergence of a class of metropolis type markov chain annealing algorithms for global optimization of a smooth function u cdot on mathbb r d is established no prior information is assumed as to what bounded region contains a global minimum the analysis contained herein is based on writing the metropolis type algorithm in the form of a recursive stochastic algorithm x k 1 x k a k nabla u x k xi k b k w k where w k is a standard white gaussian sequence xi k are random variables and a k a k b k sqrt b sqrt k log log k for k large convergence results for x k are then applied from our previous work siam journal on control and optimization 29 1991 pp 999 1018 since the analysis of x k is based on the asymptotic behavior of the related langevin type markov diffusion annealing algorithm dy t nabla u y t dt c t dw t where w cdot is a standard wiener process and c t

a cost minimization approach to edge detection using simulated annealing the authors cast edge detection as a problem in cost minimization this is achieved by the formulation of a cost function that evaluates the quality of edge configurations the function is a linear sum of weighted cost factors the cost factors capture desirable characteristics of edges such as accuracy in localization thinness and continuity edges are detected by finding the edge configurations that minimize the cost function the authors give a mathematical description of edges and analyze the cost function in terms of the characteristics of the edges in minimum cost configurations through the analysis guidelines are provided on the choice of weights to achieve certain characteristics of the detected edges the cost function is minimized by the simulated annealing method a set of strategies is presented for generating candidate states and to devise a suitable temperature schedule

constrained nonlinear optimization approaches to color signal separation separating a color signal into illumination and surface reflectance components is a fundamental issue in color reproduction and constancy this can be carried out by minimizing the error in the least squares ls fit of the product of the illumination and the surface spectral reflectance to the actual color signal when taking in account the physical realizability constraints on the surface reflectance and illumination the feasible solutions to the nonlinear ls problem should satisfy a number of linear inequalities four distinct novel optimization algorithms are presented to employ these constraints to minimize the nonlinear ls fitting error the first approach which is based on ritter s superlinear convergent method luengerger 1980 provides a computationally superior algorithm to find the minimum solution to the nonlinear ls error problem subject to linear inequality constraints unfortunately this gradient like algorithm may sometimes be trapped at a local minimum or become unstable when the parameters involved in the algorithm are not tuned properly the remaining three methods are based on the stable and promising global minimizer called simulated annealing the annealing algorithm can always find the global minimum solution with probability one but its convergence is slow to tackle this a cost effective variable separable formulation based on the concept of golub and pereyra 1973 is adopted to reduce the nonlinear ls problem to be a small scale nonlinear ls problem the computational efficiency can be further improved when the original boltzman generating distribution of the classical annealing is replaced by the cauchy distribution

real 2 regular classes and 2 blocks abstract suppose that g is a finite group we show that every 2 block of g has a defect class which is real as a partial converse we show that if g has a real 2 regular class with defect group d and if n d d has no dihedral subgroup of order 8 then g has a real 2 block with defect group d more generally we show that every 2 block of g which is weakly regular relative to some normal subgroup n has a defect class which is real and contained in n we give several applications of these results and also investigate some consequences of the existence of non real 2 blocks

an innovative approach based on a tree searching algorithm for the optimal matching of independently optimum sum and difference excitations an innovative approach for the optimal matching of independently optimum sum and difference patterns through sub arrayed monopulse linear arrays is presented by exploiting the relationship between the independently optimal sum and difference excitations the set of possible solutions is considerably reduced and the synthesis problem is recast as the search of the best solution in a noncomplete binary tree towards this end a fast resolution algorithm that exploits the presence of elements more suitable to change subarray membership is presented the results of a set of numerical experiments are reported in order to validate the proposed approach pointing out its effectiveness also in comparison with state of the art optimal matching techniques

cluster analysis for the synthesis of subarrayed monopulse antennas the design of monopulse radar systems requires the synthesis of both a sum pattern and a difference pattern which is quite flexible and hard to be optimized for subarrayed antennas in this study innovative approaches to synthesize the optimal sum and difference patterns independently for subarrayed monopulse arrays are presented by exploiting the relationship of the subarray partition and optimal excitations the synthesis problem is formulated as the clustering of a set induced by the optimal excitations thus the optimal subarray partition is transformed to a clustering problem a clustering method is presented to solve the array synthesis with uniform excitation at element level furthermore an improved approach is proposed to synthesize low sidelobe patterns when compared with several classical approaches various numerical experiments validate the effectiveness and potentiality of the proposed methods

optimization of the difference patterns for monopulse antennas by a hybrid real integer coded differential evolution method the optimization of difference patterns of monopulse antennas is considered the synthesis problem is recast as an optimization problem by defining a suitable cost function in particular in this paper the cost function is based on constraints on the side lobe levels a subarray configuration is adopted and the excitations of the difference pattern are approximately determined the optimization problem is efficiently solved by a differential evolution algorithm which is able to contemporarily handle real and integer unknowns numerical results are reported concerning classical array configurations previously considered in the literature

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

analyticity of the density of states and replica method for random schrodinger operators on a lattice we analyze the density of states and some aspects of the replica method for anderson s tight binding model on a lattice of arbitrary dimension with diagonal disorder we give heuristic arguments for the conjectures that the classical value of the exponent of the localization length is 1 2 and that the upper critical dimension d c loc is bounded by 4 d c loc 6

the asymptotic evaluation of a class of path integrals ii the asymptotic behavior of a class of wiener like path integrals functions of the local time is determined these integrals are of interest in themselves and also arise very naturally in the theory of disordered systems we show that by making use of a grassman algebra i e a set of anticommuting variables the earlier treatment of this problem can be greatly simplified in particular the previous use of replica trick which involves a difficult to justify analytic continuation in the number of field components is thus avoided

anomalies in the one dimensional anderson model at weak disorder we show that at the special energiese 2cos p q the invariant measure the lyapunov exponent and the density of states can be extended to zero disorder as c functions in the disorder parameter in particular we obtain asymptotic series in the disorder parameter this gives a rigorous proof of the existence of the anomalies originally discovered by kappus and wegner and studied by derrida and gardner and by bovier and klein

markov chains with rare transitions and simulated annealing we consider approximate stationary markov chains in which the entries of the one step transition probability matrix are known to be of different orders of magnitude and whose structure that is the orders of magnitude of the transition probabilities does not change with time for such markov chains we present a method for generating order of magnitude estimates for the t step transition probabilities for any t we then notice that algorithms of the simulated annealing type may be represented by markov chains which are approximately stationary over fairly long time intervals using our results we obtain a characterization of the convergent cooling schedules for the most general class of algorithms of the simulated annealing type

defect groups conjugacy classes and the robinson map abstract we prove a generalization of the brauer nesbitt theorem we study the robinson map and relations between p regular conjugacy classes and block idempotents with common defect group we characterize defect classes and those class sums whose images under the brauer map are not nilpotent

on the density of state for the quantum percolation problem for the site dilution model on the hypercubic lattice zd d or 2 the authors examine the density of states for the tight binding hamiltonian projected onto the infinite cluster it is shown that with probability one the corresponding integrated density of states is discontinuous on a set of energies which is dense in the band this result is proved by constructing states supported on finite regions of the infinite cluster analogous to the kirkpatrick and eggarter zero energy molecular state

smoothness of the density of states in the anderson model at high disorder we prove smoothness of the density of states in the anderson model at high disorder for a class of potential distributions that include the uniform distribution