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

randomized local search evolutionary algorithms and the minimum spanning tree problem randomized search heuristics among them randomized local search and evolutionary algorithms are applied to problems whose structure is not well understood as well as to problems in combinatorial optimization the analysis of these randomized search heuristics has been started for some well known problems and this approach is followed here for the minimum spanning tree problem after motivating this line of research it is shown that randomized search heuristics find minimum spanning trees in expected polynomial time without employing the global technique of greedy algorithms

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

global structure of self similar solutions in a semilinear parabolic equation abstract the aim of this paper is to investigate the structure of radial solutions for a semilinear elliptic equation u y u 2 u p 1 u p 1u 0 y rn which is related to forward self similar solutions of a semilinear parabolic equation vt v v p 1v t x 0 rn we study the existence uniqueness and parameter dependency of rapidly decaying solutions with a prescribed number of zeros

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

integer programs for logic constraint satisfaction abstract logic constraint satisfaction problems are in general np hard and a general deterministic polynomial time algorithm is not known since several logic constraint problems can be reduced in polynomial time to the satisfaction of a conjunctive normal form cnf sat this case is very important we present here a technique to transform a cnf sat problem in an integer optimization problem that can be solved by linear programming the size of the obtained integer program has a polynomial growth in comparison with the original problem size

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

global existence nonexistence and asymptotic behavior of solutions for the cauchy problem of semilinear heat equations abstract in this paper we study the cauchy problem of semilinear heat equations by introducing a family of potential wells we first prove the invariance of some sets and isolating solutions then we obtain a threshold result for the global existence and nonexistence of solutions finally we discuss the asymptotic behavior of the solution

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

structural stability for time periodic one dimensional parabolic equations denote q w x 0 l x r the nonlinear term f is assumed to satisfy the following conditions f l f q r is of class c f 2 f t l x u f t x u for all te w xe o l and uer define a self adjoint operator a in x l2 0 l by a t bxx for e d a h2 0 l a ha o l for each c1 e r let a be the fractional power of a and x d a be the fractional power space equipped with the graph norm ii 11 xn 1111 11x iia i ii x throughout this section we fix a c1 1 by the above assumptions f l f 2 for any u0 e x there exists a unique local in time classical solution u t x u t x of

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

pseudodifferential operator with a nonanalytic symbol on a half line we study the initial boundary value problem for the nonlinear pseudodifferential equations with nonanalytic symbol we study traditionally important problems of a theory of nonlinear partial differential equations such as global in time existence of solutions to the initial boundary value problem and the asymptotic behavior of solutions for large time

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

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

critical exponents for the blowup of solutions with sign changes in a semilinear parabolic equation ii abstract the blowup of solutions of the cauchy problem formula is studied let k be the set of functions on r which change sign k times it is shown that for p k 1 2 k 1 k 0 1 2 any solution with u 0 k blows up in finite time if 1 p p k whereas a global solution with u 0 k exists if p p k this is an extension of our previous result 17 in which a fast decay condition was imposed on initial data it is also shown in this paper that if u0 decays more slowly than x 2 p 1 as x then the solution blows up in finite time regardless of the number of sign changes

an extension of dickstein s small lambda theorem for finite time blowup abstract in this paper we prove for 1 p 1 1 n 1 l 1 r n with r n 0 and c 0 r n w 1 1 r n with r n 0 such that j that there exists 0 such that the solution u of the equation u t u u p 1 u with u 0 blows up in finite time for all 0 this extends a similar result of dickstein who treated the case r n 0 and 1 p 1 2 n

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

simulated annealing to cool or not abstract the optimization algorithm simulated annealing is considered presented is a class of problem instances and neighbor selection matrices for which no monotone decreasing temperature sequence is optimal with respect to certain natural performance criteria an algorithm called threshold random search is introduced and use is made of the fact that simulated annealing is a randomized version of threshold random search with deterministic thresholds

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

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

slow decay of solutions in a semilinear dissipative parabolic equation this paper is concerned with a cauchy problem p u t u x x u p 1 u in r x 0 u x 0 u 0 x in r where p 1 and u0 e l r a solution u of p is said to decay fast as t if limt tl p 1u x t 0 uniformly in r and to decay slowly as t otherwise we prove that if u0 x does not decay faster than x q with some q 0

asymptotic behavior of zeros of solutions for parabolic equations abstract let p 1 0 and l r l 1 r change its sign finite times this paper is concerned with a cauchy problem formula define the set of zeros of a solution u by z t x r u x t 0 for t 0 in the case of 0 we show that the set z t is contained in ct ct for large t 0 with some c 0 and that this order of t is best possible when 0 we also give estimates of z t for global solutions and prove that z t k k for all t 0 t with some k 0 for each blowup solution where t is the blowup time

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

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 new relaxation algorithm and passive sensor data association the static problem of associating measurements at a given time from three angle only sensors in the presence of clutter missed detections and an unknown number of targets is addressed the measurement target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition mathematically this formulation leads to a generalization of the 3 d assignment matching problem which is known to be np hard the solution to the optimization problem developed is a lagrangian relaxation technique that successively solves a series of generalized two dimensional 2 d assignment problems the algorithm is illustrated by several application examples

blow up of sign changing solutions for a one dimensional nonlinear diffusion equation abstract this paper is concerned with a spatially inhomogeneous semilinear diffusion equation on a bounded interval under the neumann or dirichlet boundary conditions assuming that the nonlinearity satisfies a rather general growth condition we consider the blow up and global existence of sign changing solutions it is shown that for some nonnegative integer k depending on the linearized operator at a trivial solution the solution blows up in finite time if an initial value changes its sign at most k times whereas there exist stationary solutions with more than k zeros the proof is based on the intersection number principle combined with a topological method

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

drift analysis and average time complexity of evolutionary algorithms the computational time complexity is an important topic in the theory of evolutionary algorithms eas this paper reports some new results on the average time complexity of eas based on drift analysis some useful drift conditions for deriving the time complexity of eas are studied including conditions under which an ea will take no more than polynomial time in problem size to solve a problem and conditions under which an ea will take at least exponential time in problem size to solve a problem the paper first presents the general results and then uses several problems as examples to illustrate how these general results can be applied to concrete problems in analyzing the average time complexity of eas while previous work only considered 1 1 eas without any crossover the eas considered in this paper are fairly general which use a finite population crossover mutation and selection 2001 elsevier science b v all rights reserved

growup of solutions for a semilinear heat equation with supercritical nonlinearity abstract we consider a cauchy problem for a semilinear heat equation p u t u u p in r n 0 u x 0 u 0 x 0 in r n let v be the radially symmetric singular steady state of p it is proved that if p n 2 n 1 n 4 2 n 1 and n 11 then for each nonnegative even integer n there exists a radially symmetric global solution u n of p with n intersections with v such that t a n u n t 1 as t for some a n 0 depending on n the exact value of a n is also given we show that a 0 is the optimal upper bound of growup rate for solutions below v

nonlinear evolution equations with a fractional derivative on a half line abstract we study the initial boundary value problem on a half line for the nonlinear evolution equations with a fractional derivative we study traditionally important problems of a theory of nonlinear partial differential equations such as global in time existence of solutions to the initial boundary value problem and the asymptotic behavior of solutions for large time

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

ergodic properties of microcanonical observables the problem of the existence of a strong stochasticity threshold in the fpu model is reconsidered using suitable microcanonical observables of thermodynamic nature like the temperature and the specific heat explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry measurements of the corresponding temporal autocorrelation functions locate the threshold at a finite value of the energy density which is independent of the number of degrees of freedom

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

critical exponents of fujita type for inhomogeneous parabolic equations and systems abstract we consider the large time behavior of sign changing solutions of inhomogeneous parabolic equations and systems for example for u t u u p w x in r n 0 t we show the following if n 3 and r n w x dx 0 and 1 p n n 2 then all solutions blow up in finite time while if p n n 2 there are both global and nonglobal solutions we show by example that global solutions exist for all p 1 and w satisfying r n w x dx n 1 2 and r n w x dx 0 no solution can exist for all time extensions of the above result to various geometries and some other problems are indicated

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

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

curvature torsion microcanonical density and stochastic transition we introduce geometrical indicators frenet serret curvature and torsion together with microcanonical density to give evidence to the stochastic transition of classical hamiltonian models fermi pasta ulam and lennard jones systems when the specific energy grows the transition is clearly detected through the breakdown of the harmonic like behaviour in combination with the vanishing of the dependence on the initial conditions this method of analysis presents both experimental and theoretical advantages it is fast and gives relatively sharp answers for the transition moreover a new insight is allowed on the deformations and the destruction of invariant surfaces in the ordered regime among the results it is noteworthy that going from 32 to 4096 degrees of freedom the stochastic transition depends only on the specific energy and not on the number of degrees of freedom

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

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

nearly separable behavior of fermi pasta ulam chains through the stochasticity threshold for the periodic fermi pasta ulam chain with quartic potential we prove the relation p k 2 t 1 k 2 q k 2 i e the proportionality already at early timest between averaged kinetic and harmonic energies of each mode the factor depends on the parameters of the model but not on the mode and the number of degrees of freedom it grows with the anharmonic strength from the value 0 of the harmonic limit virial theorem up to few units for the system much above the threshold in the stochastic regime the time necessary to reduce the fluctuations ink to a fixed percentage remains at least one order of magnitude smaller than the time necessary to reach a similar level of equipartition the persistence of such a behavior even above the stochasticity threshold clarifies a number of previous numerical results on the relaxation to equilibrium e g the existence of several time scales and the relevance of the harmonic frequency spectrum the difficulties in the numerical simulation of the thermodynamic limit are also discussed

blowup stability of solutions of the nonlinear heat equation with a large life span abstract we study the cauchy problem for the nonlinear heat equation u t u u p 1 u in r n the initial data is of the form u 0 where c 0 r n is fixed and 0 we first take 1 p p f where p f is the fujita critical exponent and c 0 r n l 1 r n with nonzero mean we show that u t blows up for small extending the h fujita blowup result for sign changing solutions next we consider 1 p p s where p s is the sobolev critical exponent and x decaying as x at infinity where p 1 2 we also prove that u t blows up when is small extending a result of t lee and w ni for both cases the solution enjoys some stable blowup properties for example there is single point blowup even if is not radial

asymptotic behavior and attractors for reaction diffusion equations in unbounded domains abstract in this paper we give general and flexible conditions for a reaction diffusion equation to be dissipative in an unbounded domain the functional setting is based on standard lebesgue and sobolev lebesgue spaces we show how the reaction and diffusion mechanisms have to work together to obtain the asymptotic compactness of solutions and therefore the existence of the compact attractor in particular cases our results allow us to improve some previous known results

the evolution to localized and front solutions in a non lipschitz reaction diffusion cauchy problem with trivial initial data abstract in this paper we establish the existence of spatially inhomogeneous classical self similar solutions to a non lipschitz semi linear parabolic cauchy problem with trivial initial data specifically we consider bounded solutions to an associated two dimensional non lipschitz non autonomous dynamical system for which we establish the existence of a two parameter family of homoclinic connections on the origin and a heteroclinic connection between two equilibrium points additionally we obtain bounds and estimates on the rate of convergence of the homoclinic connections to the origin

critical exponents for the decay rate of solutions in a semilinear parabolic equation this paper is concerned with the cauchy problem a solution u is said to decay fast if t 1 p 1 u rightarrow 0 as t rightarrow infty uniformly in r and is said to decay slowly otherwise for each nonnegative integer k let lambda k be the set of uniformly bounded functions on r which change sign k times and let p k 1 be defined by p k 1 2 k 1 it is shown that any nontrivial bounded solution with u 0 in lambda k decays slowly if 1 p p k whereas there exists a nontrivial fast decaying solution with u 0 in lambda k if p gep k

the zero set of a solution of a parabolic equation on etudie l ensemble nul d une solution u t x de l equation u t a x t u xx b x t u x c x t u sous des hypotheses tres generales sur les coefficients a b et c

variational problems related to self similar solutions of the heat equation on demontre la compacite de certains plongements de sobolev sous de bonnes conditions sur les poids k x exp x c 2 r n r on considere des methodes variationnelles pour la resolution d equations elliptiques

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

on two signed solutions to a second order semi linear parabolic partial differential equation with non lipschitz nonlinearity abstract in this paper we establish the existence of a 1 parameter family of spatially inhomogeneous radially symmetric classical self similar solutions to a cauchy problem for a semi linear parabolic pde with non lipschitz nonlinearity and trivial initial data specifically we establish well posedness for an associated initial value problem for a singular two dimensional non autonomous dynamical system with non lipschitz nonlinearity additionally we establish that solutions to the initial value problem converge algebraically to the origin and oscillate as

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

critical exponent for the bipolar blowup in a semilinear parabolic equation abstract the blowup of solutions of the initial boundary value problem formula is studied where is a cone inrn we say that a solutionuexhibits bipolar blowup if formula for somet 1 for the bipolar blowup in the following sense if 1 p then the bipolar blowup does not occur for any sufficiently small initial data the value ofp is expressed in terms of the dimensionnand the second dirichlet eigenvalue of the laplace beltrami operator on sn 1 in the case of r we definek polar blowup and determine critical exponents for thek polar blowup fork 1 2 3

global existence and blowup for sign changing solutions of the nonlinear heat equation abstract in this paper given 0 2 n we prove the existence of a function with the following properties the solution of the equation u t u u u on r n with the initial condition u 0 is global on the other hand the solution with the initial condition u 0 blows up in finite time if 0 is either sufficiently small or sufficiently large