a stochastic continuation approach to piecewise constant reconstruction we address the problem of reconstructing a piecewise constant 3 d object from a few noisy 2 d line integral projections more generally the theory developed here readily applies to the recovery of an ideal n d signal n ges 1 from indirect measurements corrupted by noise stabilization of this ill conditioned inverse problem is achieved with the potts prior model which leads to a challenging optimization task to overcome this difficulty we introduce a new class of hybrid algorithms that combines simulated annealing with deterministic continuation we call this class of algorithms stochastic continuation sc we first prove that under mild assumptions sc inherits the finite time convergence properties of generalized simulated annealing then we show that sc can be successfully applied to our reconstruction problem in addition we look into the concave distortion acceleration method introduced for standard simulated annealing and we derive an explicit formula for choosing the free parameter of the cost function numerical experiments using both synthetic data and real radiographic testing data show that sc outperforms standard simulated annealing

on the essential features of metastability tunnelling time and critical configurations we consider metropolis markov chains with finite state space and transition probabilities of the form p eta eta q eta eta e beta h eta h eta for given energy function h and symmetric markov kernel q we propose a simple approach to determine the asymptotic behavior for large of the first hitting time to the ground state starting from a particular class of local minima for h called metastable states we separate the asymptotic behavior of the transition time from the determination of the tube of typical paths realizing the transition this approach turns out to be useful when the determination of the tube of typical paths is too difficult as for instance in the case of conservative dynamics we analyze the structure of the saddles introducing the notion of essentiality and describing essential saddles in terms of gates as an example we discuss the case of the 2d ising model in the degenerate case of integer tfrac 2j h

metastable behavior of stochastic dynamics a pathwise approach in this paper a new approach to metastability for stochastic dynamics is proposed the basic idea is to study the statistics of each path performing time averages along the evolution metastability would be characterized by the fact that the process of these time averages converges under a suitable rescaling to a measure valued markov jump process here this convergence is shown for the curie weiss mean field dynamics and also for a model with spatial structure harris contact process

the effect of imperfect boundary conditions on the collapse behavior of anisotropic shells abstract a rigorous solution is presented for the case of stiffened anisotropic shells with general imperfections under combined axial compression internal or external pressure and torsion donnell type equations are used to describe the behavior of the layered composite shell the stiffeners are represented by smeared theory and for the discrete end rings cohen s ring equations are used the circumferential dependence is eliminated by a truncated fourier series the resulting 2 point boundary value problem is solved numerically via the parallel shooting method the nonlinear collapse behavior is studied using different combinations of axisymmetric and asymmetric imperfections comparison with koiter type imperfection predictions display the range of validity of the asymptotic results it is shown that besides initial geometric imperfections also nonuniform harmonically varying boundary conditions can have severe degrading effect on the load carrying capacity of anisotropic shells

hitting time asymptotics for hard core interactions on grids we consider the hard core model with metropolis transition probabilities on finite grid graphs and investigate the asymptotic behavior of the first hitting time between its two maximum occupancy configurations in the low temperature regime in particular we show how the order of magnitude of this first hitting time depends on the grid sizes and on the boundary conditions by means of a novel combinatorial method our analysis also proves the asymptotic exponentiality of the scaled hitting time and yields the mixing time of the process in the low temperature limit as side result in order to derive these results we extended the model independent framework in manzo et al j stat phys 115 1 2 591 642 2004 for first hitting times to allow for a more general initial state and target subset

the convergence of stochastic algorithms solving flow shop scheduling abstract in the paper we apply logarithmic cooling schedules of simulated annealing based algorithms to flow shop scheduling in our problem setting the objective to minimize the overall completion time which is called the makespan we prove a lower bound for the number of steps that are sufficient to approach an optimum solution with a certain probability the result is related to the maximum escape depth from local minima of the underlying energy landscape in our approach we need n o log o 1 1 steps to be in an optimum solution with probability 1 where n denotes the total number of tasks the auxiliary computations are of polynomial complexity since the model cannot be approximated arbitrarily closely in the general case unless p np the approach can be used to obtain approximation algorithms that work well in the average case

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

critical droplets in metastable states of probabilistic cellular automata we consider the problem of metastability in a probabilistic cellular automaton pca with a parallel updating rule which is reversible with respect to a gibbs measure the dynamical rules contain two parameters beta and h which resemble but are not identical to the inverse temperature and external magnetic field in a ferromagnetic ising model in particular the phase diagram of the system has two stable phases when beta is large enough and h is zero and a unique phase when h is nonzero when the system evolves at small positive values of h from an initial state with all spins down the pca dynamics give rise to a transition from a metastable to a stable phase when a droplet of the favored phase inside the metastable phase reaches a critical size we give heuristic arguments to estimate the critical size in the limit of zero temperature beta to infty as well as estimates of the time required for the formation of such a droplet in a finite system monte carlo simulations give results in good agreement with the theoretical predictions

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

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

dynamical blume capel model competing metastable states at infinite volume this paper concerns the microscopic dynamical description of competing metastable states we study at infinite volume and very low temperature metastability and nucleation for kinetic blume capel model a ferromagnetic lattice model with spins taking three possible values 1 0 1 in a previous paper mo we considered a simplified irreversible nucleation growth model in the present paper we analyze the full blume capel model we choose a region u of the thermodynamic parameters such that everywhere in u b 1 all minuses corresponds to the highest in energy metastable state b 0 all zeroes corresponds to an intermediate metastable state and b 1 all pluses corresponds to the stable state we start from b 1 and look at a local observable like in mo we find that when crossing a special line in u there is a change in the mechanism of transition towards the stable state b 1 we pass from a situation 1 where the intermediate phase b 0 is really observable before the final transition with a permanence in b 0 typically much longer than the first hitting time to b 0 to the situation 2 where b 0 is not observable since the typical permanence in b 0 is much shorter than the first hitting time to b 0 and moreover large growing 0 droplets are almost full of 1 in their interior so that there are only relatively thin layers of zeroes between 1 and 1

behavior of droplets for a class of glauber dynamics at very low temperature we consider a class of glauber dynamics for the two dimensional nearest neighbor ferromagnetic ising model in which the rate with which each spin flips depends only on the increment in energy caused by its flip in a monotonic non increasing fashion

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

slow motion and metastability for a nonlocal evolution equation in this paper we consider a nonlocal evolution equation in one dimension which describes the dynamics of a ferromagnetic system in the mean field approximation in the presence of a small magnetic field it admits two stationary and homogeneous solutions representing the stable and metastable phases of the physical system we prove the existence of an invariant one dimensional manifold connecting the stable and metastable phases this is the unstable manifold of a distinguished spatially nonhomogeneous stationary solution called the critical droplet 4 10 we show that the points on the manifold are droplets longer or shorter than the critical one and that their motion is very slow in agreement with the theory of metastable patterns we also obtain a new proof of the existence of the critical droplet which is supplied with a local uniqueness result

stochastic local search for the feature set problem with applications to microarray data we prove a m o na time bound for finding minimum solutions smin of feature set problems where n is the total size of a given feature set problem smin m equals the number of non target features a is a relatively small constant and 1 is the confidence that the solution is of minimum length in terms of parameterized complexity of np complete problems our time bound differs from an fpt type bound by the factor mo for fixed the algorithm is applied to a prominent microarray dataset the classification of gene expression data related to acute myeloid leukaemia aml and acute lymphoblastic leukaemia all from the set of potentially significant features calculated by the algorithm we can identify three genes d88422 m92287 l09209 that produce zero errors on the test set by using a simple straightforward evaluation procedure performing the test on the single gene m84526 produces only one error

the energy transformation method for the metropolis algorithm compared with simulated annealing we present and analyze a new speed up technique for monte carlo optimization the iterated energy transformation algorithm where the metropolis algorithm is used repeatedly with more and more favourable energy functions derived from the original one by increasing transformations we show that this method allows a better speed up than simulated annealing when convergence speed is measured by the probability of failure of the algorithm after a large number of iterations we study also the limit of a large state space in the special case when the energy is made of a sum of independent terms we show that the convergence time of the i e t algorithm is polynomial in the size number of coordinates of the problem but with a worse exponent than for simulated annealing this indicates that the i e t algorithm is well suited for moderate size problems but not for too large ones the independent component case is a good model for the end of many optimization processes when at low temperature a neighbourhood of a local minimum is explored by small and far apart modifications of the current solution we show that in this case both global optimization methods simulated annealing and the i e t algorithm are less efficient than repeated local stochastic optimizations using the general concept of slow stochastic optimization algorithm we show that any slow global optimization scheme should be followed by a local one to perform the last approach to a minimum

sharp asymptotics for stochastic dynamics with parallel updating rule in this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule in particular we consider a finite volume probabilistic cellular automaton pca in a small external field at low temperature regime we are interested in the nucleation of the system i e the typical excursion from the metastable phase the configuration with all minuses to the stable phase the configuration with all pluses triggered by the formation of a critical droplet the main result of the paper is the sharp estimate of the nucleation time we show that the nucleation time divided by its average converges to an exponential random variable and that the rate of the exponential random variable is an exponential function of the inverse temperature times a prefactor that does not scale with our approach combines geometric and potential theoretic arguments

abrupt convergence and escape behavior for birth and death chains we link two phenomena concerning the asymptotical behavior of stochastic processes i abrupt convergence or cut off phenomenon and ii the escape behavior usually associated to exit from metastability the former is characterized by convergence at asymptotically deterministic times while the convergence times for the latter are exponentially distributed we compare and study both phenomena for discrete time birth and death chains on with drift towards zero in particular this includes energy driven evolutions with energy functions in the form of a single well under suitable drift hypotheses we show that there is both an abrupt convergence towards zero and escape behavior in the other direction furthermore as the evolutions are reversible the law of the final escape trajectory coincides with the time reverse of the law of cut off paths thus for evolutions defined by one dimensional energy wells with sufficiently steep walls cut off and escape behavior are related by time inversion

on the convergence rate of annealing processes for the class of inhomogeneous markov processes arising from simulated annealing it is shown that lim t to infty p x t i exp u i t t exists and is positive for each state i where t t is the temperature and u i is the energy level at i assuming that min u i 0 the method used is to consider the forward equations associated with such processes

asymptotical behaviour of several interacting annealing processes we prove that the optimal convergence speed exponent for parallel annealing based on periodically interacting multiple searches with time periodr is always worse than for independent multiple searches whenever the cost function has only one global minimum our proofs will be based on large deviation estimates coming from the theory of generalized simulated annealing g s a

renormalization group for markov chains and application to metastability in this paper we introduce a new renormalization group method for the study of the long time behavior of markov chains with finite state space and with transition probabilities exponentially small in an external parameter a general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two dimensional ising system at low temperature

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

karhunen loeve decomposition of random fields based on a hierarchical matrix approach summary the simulation of the behavior of structures with uncertain properties is a challenging issue because it requires suitable probabilistic models and adequate numerical tools nowadays it is possible to perform probabilistic investigations of the structural performance which take into account a space variant uncertainty characterization of the structures given a structural solver and the probabilistic models the reliability analysis of the structural response depends on the continuous random fields approximation which is carried out by means of a finite set of random variables the paper analyzes the main aspects of discretization in the case of 2d problems the combination of the well known karhunen loeve series expansion the finite element method and the hierarchical matrices approach is proposed in the paper copyright 2013 john wiley sons ltd

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

metastability for reversible probabilistic cellular automata with self interaction the problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the freidlin wentzel regime namely finite volume small magnetic field and small temperature the model is characterized by the existence of many fixed points and cyclic pairs of the zero temperature dynamics in which the system can be trapped in its way to the stable phase our strategy is based on recent powerful approaches not needing a complete description of the fixed points of the dynamics but relying on few model dependent results we compute the exit time in the sense of logarithmic equivalence and characterize the critical droplet that is necessarily visited by the system during its excursion from the metastable to the stable state we need to supply two model dependent inputs 1 the communication energy that is the minimal energy barrier that the system must overcome to reach the stable state starting from the metastable one 2 a recurrence property stating that for any configuration different from the metastable state there exists a path starting from such a configuration and reaching a lower energy state such that its maximal energy is lower than the communication energy

shapes of growing droplets a model of escape from a metastable phase nucleation from a metastable state is studied for an ising ferromagnet with nearest and next nearest neighbor interaction and at very low temperatures the typical escape path is shown to follow a sequence of configurations with a growing droplet of stable phase whose shape is determined by dynamical considerations and differs significantly from the equilibrium shape corresponding to the instantaneous volume

metastability and exponential approach to equilibrium for low temperature stochastic ising models we present a proof of the exponential convergence to equilibrium of single spin flip stochastic dynamics for the two dimensional ising ferromagnet in the low temperature case with not too small external magnetic fieldh uniformly in the volume and in the boundary conditions

uncertain buckling its past present and future an authoritative review on stochastic buckling of structures was written by amazigo some quarter century ago the present review summarizes some of the developments which took place since then a brief overview of the effect of uncertainty in the initial geometric imperfections elastic moduli applied forces and thickness variation is given for the benefit of the thoughtful reader the review is of critical nature

metastability and small eigenvalues in markov chains in this letter we announce rigorous results that elucidate the relation between metastable states and low lying eigenvalues in markov chains in a much more general setting and with considerably greater precision than has so far been available this includes a sharp uncertainty principle relating all low lying eigenvalues to mean times of metastable transitions a relation between the support of eigenfunctions and the attractor of a metastable state and sharp estimates of the convergence of the probability distribution of the metastable transition times to the exponential distribution

markov chains with exponentially small transition probabilities first exit problem from a general domain i the reversible case we consider general ergodic aperiodic markov chains with finite state space whose transition probabilities between pairs of different communicating states are exponentially small in a large parameter we extend previous results by m i freidlin and a d wentzell fw on the first exit problem from a general domainq in the present paper we analyze the case ofreversible markov chains the general case will be studied in a forthcoming paper we probe in a purely probabilistic way and without using the fw graphical technique some results on the first exit problem from a general domainq containing many attractors in particular we analyze the properties of special domains calledcycles and by using the new concept oftemporal entropy we obtain new results leading to a complete description of the typical tube of trajectories during the first excursion outsideq

nucleation and growth for the ising model in d dimensions at very low temperatures this work extends to dimension d 3 the main result of dehghanpour and schonmann we consider the stochastic ising model on zd evolving with the metropolis dynamics under a fixed small positive magnetic field h starting from the minus phase when the inverse temperature goes to the relaxation time of the system defined as the time when the plus phase has invaded the origin behaves like exp d the value d is equal to d 1d 1 1 d where i is the energy of the i dimensional critical droplet of the ising model at zero temperature and magnetic field h

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

on the investigation of shell buckling due to random geometrical imperfections implemented using karhunen loeve expansions for the accurate prediction of the collapse behaviour of thin cylindrical shells it is accepted that geometrical and other imperfections in material properties and loading have to be accounted for in the simulation there are different methods of incorporating imperfections depending on the availability of accurate imperfection data the current paper uses a spectral decomposition of geometrical uncertainty karhunen loeve expansions to specify the covariance of the required random field two methods are used first available experimentally measured imperfection fields are used as input for a principal component analysis based on pattern recognition literature thereby reducing the cost of the eigenanalysis second the covariance function is specified analytically and the resulting friedholm integral equation of the second kind is solved using a wavelet galerkin approach experimentally determined correlation lengths are used as input for the analytical covariance functions the above procedure enables the generation of imperfection fields for applications where the geometry is slightly modified from the original measured geometry for example 100 shells are perturbed with the resulting random fields obtained from both methods and the results in the form of temporal normal forces during buckling as simulated using ls dyna as well as the statistics of a monte carlo analysis of the 100 shells in each case are presented although numerically determined mean values of the limit load of the current and another numerical study differ from the experimental results due to the omission of imperfections other than geometrical the coefficients of variation are shown to be in close agreement copyright 2007 john wiley sons ltd

landscapes on spaces of trees combinatorial optimization problems defined on sets of phylogenetic trees are an important issue in computational biology for instance the problem of reconstructing a phylogeny using maximum likelihood or parsimony approaches the collection of possible phylogenetic trees is arranged as a so called robinson graph by means of the nearest neighborhood interchange move the coherent algebra and spectra of robinson graphs are discussed in some detail as their knowledge is important for an understanding of the landscape structure we consider simple model landscapes as well as landscapes arising from the maximum parsimony problem focusing on two complementary measures of ruggedness the amplitude spectrum arising from projecting the cost functions onto the eigenspaces of the underlying graph and the topology of local minima and their connecting saddle points

a relative shafarevich theorem suppose given a galois etale cover y x of proper non singular curves over an algebraically closed field k of prime characteristic p let h be its galois group and g any finite extension of h by a p group p we give necessary and sufficient conditions on g to be the galois group of an etale cover of x dominating y x

metastability in stochastic dynamics of disordered mean field models we study a class of markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures our main purpose is to give a precise relation between the metastable time scales in the problem to the properties of the rate functions of the corresponding gibbs measures we derive the analog of the wentzell freidlin theory in this case showing that any transition can be decomposed with probability exponentially close to one into a deterministic sequence of admissible transitions for these admissible transitions we give upper and lower bounds on the expected transition times that differ only by a constant factor the distributions of the rescaled transition times are shown to converge to the exponential distribution we exemplify our results in the context of the random field curie weiss model

normal subgroups of the algebraic fundamental group of affine curves in positive characteristic let 1 c be the algebraic fundamental group of a smooth connected affine curve defined over an algebraically closed field of characteristic p 0 of countable cardinality let n be a normal respectively characteristic subgroup of 1 c under the hypothesis that the quotient 1 c n admits an infinitely generated sylow p subgroup we prove that n is indeed isomorphic to a normal respectively characteristic subgroup of a free profinite group of countable cardinality as a consequence every proper open subgroup of n is a free profinite group of countable cardinality

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

metastability of the ising model on random regular graphs at zero temperature we study the metastability of the ferromagnetic ising model on a random r regular graph in the zero temperature limit we prove that in the presence of a small positive external field the time that it takes to go from the all minus state to the all plus state behaves like exp beta r 2 mathcal o sqrt r n when the inverse temperature beta rightarrow infty and the number of vertices n is large enough but fixed the proof is based on the so called pathwise approach and bounds on the isoperimetric number of random regular graphs