low firing rates in a compartmental model neuron a nonlinear relationship is obtained between the membrane potential of a compartmental model neuron as a function of input stimulation this is used to show how shunting effects can lead to low output firing rates in associative memory networks

linearization of hyperbolic finite time processes abstract we adapt the notion of processes to introduce an abstract framework for dynamics in finite time i e on compact time sets for linear finite time processes a notion of hyperbolicity namely exponential monotonicity dichotomy emd is introduced thereby generalizing and unifying several existing approaches we present a spectral theory for linear processes in a coherent way based only on a logarithmic difference quotient in this abstract setting we introduce a new topology prove robustness of emd and provide exact perturbation bounds we suggest a new intrinsic approach for the investigation of linearizations of finite time processes including finite time analogues of the local un stable manifold theorem and theorem of linearized asymptotic stability as an application we discuss our results for ordinary differential equations on a compact time interval

a definition of spectrum for differential equations on finite time abstract hyperbolicity of an autonomous rest point is characterised by its linearization not having eigenvalues on the imaginary axis more generally hyperbolicity of any solution which exists for all times can be defined by means of lyapunov exponents or exponential dichotomies we go one step further and introduce a meaningful notion of hyperbolicity for linear systems which are defined for finite time only i e on a compact time interval hyperbolicity now describes the transient dynamics on that interval in this framework we provide a definition of finite time spectrum study its relations with classical concepts and prove an analogue of the sacker sell spectral theorem for a d dimensional system the spectrum is non empty and consists of at most d disjoint and often compact intervals an example illustrates that the corresponding spectral manifolds may not be unique which in turn leads to several challenging questions

the three dimensional dilute ising magnet the dilute ising model with a p 0 8 fraction of the sites occupied by spins is simulated on l3 systems for l up to 300 using a single cluster algorithm of wolff in the range of reduced temperature 0 002 t tc tc 0 03 the susceptibility appears to fit a simple power with an effective exponent eff 1 36

superparamagnetic segmentation by excitable neural systems magnetic modeling for clustering or segmentation purposes can either associate the image data to external quenched fields or to the interactions among a set of auxiliary variables the latter gives rise to superparamagnetic segmentation and is usually done with potts systems we have used the superparamagnetic clustering technique to segment images with the aid of different associated systems results using potts model are comparable to those obtained using excitable fitzhugh nagumo and morris lecar model neurons interactions between the associated system components are a function of the difference of luminosity on a gray scale of neighbor pixels and the difference of membrane potential

epidemic models and percolation the authors argue that local epidemic models with immunisation are in the same universality class as percolation cluster growth models and show that the static exponents are equal to all orders in the epsilon expansion they calculate the dynamic exponent nu t 1 1 28 epsilon o epsilon 2 and relate this to other exponents involving the chemical distance

bulk and surface critical behavior of the three dimensional ising model and conformal invariance using a continuous cluster monte carlo algorithm we investigate the critical three dimensional ising model in its anisotropic limit from the ratio of the magnetic correlations in the strong and the weak coupling directions we determine the length ratio relating the isotropic ising model and the anisotropic limit on this basis we simulate the critical ising model on a spherocylinder s2 x r1 i e a curved geometry obtained from a conformal mapping of the infinite space r3 from correlation lengths along the spherocylinder combined with the prediction of conformal invariance we estimate the magnetic and thermal scaling dimensions as x h 0 5182 6 and x t 1 419 7 respectively the behavior of the binder cumulant is also determined in the limit of an infinitely long spherocylinder next free boundary conditions are imposed on the equators of the spherocylinder and thus the geometry s1 x s x r1 is obtained the surface magnetic scaling dimension is estimated as x s h 1 263 5 the consistency of the aforementioned estimations and existing results confirms that the three dimensional ising model is conformally invariant further the precision of these results reveals that as in two dimensions conformal mappings provide a powerful tool to investigate critical phenomena with the continuous cluster algorithm we also perform simulations of systems inside a conventional solid cylinder the surface magnetic correlation length differs within the estimated error margin by a factor pi 2 from that along a half spherocylinder s1 x s x r1 with the same radius

field theoretic formulation of an epidemic process with immunisation the author describes a model of the spread of an epidemic on a lattice in which sites may be infected by their neighbours after which they recover and are subsequently immune it corresponds to a modification of the directed percolation problem and also to a growth model of clusters the model is analysed using a continuum field theory both within a self consistent approximation and using an epsilon expansion below six transverse dimensions

the multivariate skew normal distribution summary the paper extends earlier work on the so called skew normal distribution a family of distributions including the normal but with an extra parameter to regulate skewness the present work introduces a multivariate parametric family such that the marginal densities are scalar skew normal and studies its properties with special emphasis on the bivariate case

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

data clustering using a model granular magnet we present a new approach to clustering based on the physical properties of an inhomogeneous ferromagnet no assumption is made regarding the underlying distribution of the data we assign a potts spin to each data point and introduce an interaction between neighboring points whose strength is a decreasing function of the distance between the neighbors this magnetic system exhibits three phases at very low temperatures it is completely ordered all spins are aligned at very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered whereas different clusters remain uncorrelated this intermediate phase is identified by a jump in the order parameters the spin spin correlation function is used to partition the spins and the corresponding data points into clusters we demonstrate on three synthetic and three real data sets how the method works detailed comparison to the performance of other techniques clearly indicates the relative success of our method

critical slowing down in local dynamics simulations the author reports some universal and non universal aspects of the critical dynamics of the three dimensional ising model obtained in extensive monte carlo finite size simulations the author shows that the time dependence of the magnetization of finite lattices is composed of two kinds of fluctuations at the critical point i phase fluctuations from one metastable minimum of the free energy to the other dominating the long time behaviour of the magnetization ii critical fluctuations inside each minimum decaying on a comparatively short timescale both kinds of fluctuations show up the same critical exponent z 2 10 or 0 02 which is also in excellent agreement with the exponent z of energy fluctuations

system size dependence of the autocorrelation time for the swendsen wang ising model abstract we present monte carlo simulation results of the autocorrelation time for the swendsen wang method for the simulation of the ising model we have calculated the exponential and the integrated autocorrelation time at the critical point t c of the two dimensional ising model our results indicate that both autocorrelation times depend logarithmically on the linear system size l instead of a power law the simulations were carried out on the parallel computer of the condensed matter theory group at the university of mainz

monte carlo study of the ising model phase transition in terms of the percolation transition of physical clusters finite squarel l ising lattices with ferromagnetic nearest neighbor interaction are simulated using the swendsen wang cluster algorithm both thermal properties internal energyu specific heatc magnetization m susceptibility and percolation cluster properties relating to the physical clusters namely the fortuin kasteleyn clusters percolation probability p percolation susceptibility p cluster size distributionnl are evaluated paying particular attention to finite size effects it is shown that thermal properties can be expressed entirely in terms of cluster properties p being identical to m in the thermodynamic limit while finite size corrections differ in contrast p differs from even in the thermodynamic limit since a fluctuation in the size of the percolating net contributes to but not to p neartc the cluster size distribution has the scaling properties as hypothesized by earlier phenomenological theories we also present a generalization of the swendsen wang algorithm allowing one to cross over continuously to the glauber dynamics

self organized criticality in a forest fire model a forest fire model is introduced which contains a lightning probability f this leads to a self organized critical state in the limit f 0 provided that the time scales of free growth and burning down of forest clusters are separated we derive scaling laws and calculate all critical exponents the values of the critical exponents are confirmed by computer simulations for a two dimensional system there is evidence that the forest density in the critical state assumes its minimum possible value i e that energy dissipation is maximum

probabilistic non linear principal component analysis with gaussian process latent variable models summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure in this paper we provide an overview of some existing techniques for discovering such embeddings we then introduce a novel probabilistic interpretation of principal component analysis pca that we term dual probabilistic pca dppca the dppca model has the additional advantage that the linear mappings from the embedded space can easily be non linearised through gaussian processes we refer to this model as a gaussian process latent variable model gp lvm through analysis of the gp lvm objective function we relate the model to popular spectral techniques such as kernel pca and multidimensional scaling we then review a practical algorithm for gp lvms in the context of large data sets and develop it to also handle discrete valued data and missing attributes we demonstrate the model on a range of real world and artificially generated data sets

cluster monte carlo algorithms for random ising models abstract variations of the swendsen wang and wolff cluster flip algorithms are proposed to perform monte carlo simulations of ising models with random bonds and random fields including systems with frustration the new methods are tested by applying them to small lattices and comparing the results with exact data

renormalisation of random walks with memory the renormalisation of field theoretic models of the true self avoiding random walk is analysed for short range interactions the field theory is shown to be renormalisable only in a special case which corresponds to the problem of a random walk in a random environment and non renormalisable otherwise the long range version of the field theory is shown to be renormalisable in a larger region of the parameter space in the case which corresponds to the original long range true self avoiding random walk the renormalisation group analysis is carried out to two loop order anomalous dimensions of various composite operators are calculated and the crossover between scaling regimes described by short range and long range models is discussed

on a self organized critical forest fire model the author studies a forest fire model introduced in a paper by drossel and schwabl 1992 by means of simulations with high statistics and very close to the critical point in this way he can correct some statements made in that paper in particular he finds that the critical exponents are not the classical ones proposed by drossel and schwabl in spite of scaling laws with anomalous exponents the typical states of the system are not critical in the sense of being marginally stable locally

critical dynamics of the swendsen wang algorithm in the three dimensional ising model abstract the correlation times of the three dimensional ising model at the critical point for the swendsen wang dynamics are obtained up to a system size 893 strong corrections to scaling are present in the size dependences of the correlation times of the energy and the size of the largest cluster making the estimation of the true asymptotic dynamic critical exponent difficult when the largest cluster is not flipped the dynamic critical exponent zm defined by the magnetization correlations of the largest cluster is estimated to be 0 339 0 004

areas of attraction for nonautonomous differential equations on finite time intervals in this article new concepts of exponential attractivity for nonautonomous differential equations on a finite time interval are introduced due to nonuniqueness of finite time objects areas of attraction are studied rather than solutions which are attractive a sufficient and necessary condition for the existence of such areas is presented which makes use of a time varying riemannian metric several examples illustrate the theoretical results and definitions

a multiresolution stochastic level set method for mumford shah image segmentation the mumford shah model is one of the most successful image segmentation models however existing algorithms for the model are often very sensitive to the choice of the initial guess to make use of the model effectively it is essential to develop an algorithm which can compute a global or near global optimal solution efficiently while gradient descent based methods are well known to find a local minimum only even many stochastic methods do not provide a practical solution to this problem either in this paper we consider the computation of a global minimum of the multiphase piecewise constant mumford shah model we propose a hybrid approach which combines gradient based and stochastic optimization methods to resolve the problem of sensitivity to the initial guess at the heart of our algorithm is a well designed basin hopping scheme which uses global updates to escape from local traps in a way that is much more effective than standard stochastic methods in our experiments a very high quality solution is obtained within a few stochastic hops whereas the solutions obtained with simulated annealing are incomparable even after thousands of steps we also propose a multiresolution approach to reduce the computational cost and enhance the search for a global minimum furthermore we derived a simple but useful theoretical result relating solutions at different spatial resolutions

critical exponents of the sand pile models in two dimensions abstract we study three sand pile automaton models namely the critical height critical slope and the critical laplacian models in two dimensions in which the stability criterion of the sand columns depend on the zeroth first and the second derivatives of the sand height function we carried out simulations on system sizes up to 2048 2048 and up to 108 avalanches were generated the exponents of the critical height model were calculated by taking into account the strong corrections to scaling in order to determine the exponents of the critical laplacian model accurately we introduced a height restriction in the toppling criterion that maintains universality but accelerates convergence to the steady state by orders of magnitude we see clear scaling in the critical height and the critical laplacian models and find that they belong to different universality classes however we do not find any scaling in the critical slope model

damage spreading in the kawasaki ising model abstract we observe no phase transition in the damage spreading probability at the curie point of the 2d ising model with nearest neighbor spin exchange dynamics furthermore we report values of the growth exponent z close to unity implying speed of light transmission of information and values of the exponents describing the scaling behavior of the damage mass with time and distance close to two finally we discuss the spreading of damage in a one dimensional system

recursive sampling of random walks self avoiding walks in disordered media the author presents a new algorithm for simulating random walks which is simple versatile and efficient it uses recursive function calls and can be used to obtain unbiased samples with any given length distribution this makes it particularly useful in disordered geometries where the effective connectivity constant is not known a priori when applying it to self avoiding random walks on two dimensional media with quenched randomness he finds evidence for at least two new renormalization group fixed points

rigorous lower bound on the dynamic critical exponents of the swendsen wang algorithm we prove the rigorous lower bound z sw v for the dynamic critical exponent of the swendsen wang algorithm for two dimensional q state potts models with q 2 3 4 this implies z sw 0 2 5 1 we present numerical data indicating that z sw 0 55 0 03 0 89 0 05 for q 3 4 95 confidence limits statistical errors only the discrepancy for q 4 appears to be caused by multiplicative logarithmic corrections

geometrical properties of swendsen wang clusters abstract several geometrical properties of swendsen wang clusters are studied numerically for the 2d ising and 3 state potts models at the critical temperature the fractal dimensions of the total mass backbone elastic backbone shortest path and red bonds are determined the results agree with some theoretical predictions

graphical representations and cluster algorithms for critical points with fields a two replica graphical representation and associated cluster algorithm is described that is applicable to ferromagnetic ising systems with arbitrary fields critical points are associated with the percolation threshold of the graphical representation results from numerical simulations of the ising model in a staggered field are presented the dynamic exponent for the algorithm is measured to be less than 0 5

conformal invariance and simulations in curved geometries abstract conformal mappings serve as useful tools for the determination of universal properties of critical models typical applications are subject to a major restriction namely that the pertinent conformal mapping should lead to a geometry that can be investigated by means of numerical methods such as monte carlo simulations since conformal mappings of 3 d systems usually lead to curved geometries which are difficult to investigate numerically most applications have thus far been restricted to 2 d systems we present a solution of this problem for discrete spin models by taking the anisotropic or hamiltonian limit which renders one of the lattice directions continuous such that the dimensionality in effect reduces by one applications to the 3 d ising and percolation models confirm the predictions obtained from the assumption of conformal invariance and lead to accurate numerical results for the scaling dimensions

cascades and self organized criticality we generalize the model of self organized critical systems to cases where due to some internal degrees of freedom the local conservation law is violated this can be realized by taking a transfer ratio different from the critical one in a sand pile model global violation or allowing fluctuations around the critical ratio local violation in the first case the deviation from the critical ratior is a critical parameter and the characteristic avalanche size diverges as r in the second case the global conservation assures criticality however our numerical results indicate that the model is in a new universality class

cluster monte carlo algorithms abstract the swendsen wang and wolff monte carlo algorithms are described in some detail using the potts model as an example various generalizations are then reviewed and some applications are discussed two complete fortran programs for the algorithms are provided

crossover between field theories with short range and long range exchange or correlations the relation between scalar field theories with short range and long range exchange or correlations is studied it is shown to all orders in perturbation theory that the critical exponents of fields and composite operators are continuous functions of the parameters alpha xi characterising the decay rate of the long range exchange correlations with power like falloff 1 rd 2 2 alpha 1 rd 2 xi the scaling law d 2 xi v 2 where v is the correlation length exponent as well as the harris criteria 1970 are shown to be exact to all orders in perturbation theory a discrepancy between two widely used approaches to the crossover problem is pointed out

scaling properties of the cluster distribution of a critical nonequilibrium model abstract a geometric approach to critical fluctuations of a nonequilibrium model is reported the two dimensional majority vote model was investigated by monte carlo simulations on square lattices of various sizes and a detailed scaling analysis of cluster statistical and geometric properties was performed the cluster distribution exponents and fractal dimension were found to be the same as those of the two dimensional ising model this result which cannot be derived purely from the known bulk critical behaviour widens our knowledge about the range of validity of the ising universality class for nonequilibrium systems

renormalisation of the true self avoiding walk it is shown that the renormalisation of the true self avoiding walk of amit et al 1982 is its upper critical dimensionality two involves at least two possibly three coupling constants fixed points to first order in epsilon 2 d are identified and the asymptotic behaviour at d 2 is discussed

renormalisation of the long range true self avoiding walk the authors show that the true self avoiding walk with long range interactions leads to a renormalisable field theory they compute the characteristic exponent of the gyration radius up to first order in the difference between the upper critical dimension and space dimensionality and compare it with the estimates based on flory like arguments

a unified approach to finite time hyperbolicity which extends finite time lyapunov exponents a hyperbolicity notion for linear differential equations x a t x t t t is defined which unifies different existing notions like finite time lyapunov exponents haller 2001 13 shadden et al 2005 24 uniform or m hyperbolicity haller 2001 13 berger et al 2009 6 and t t t dichotomy rasmussen 2010 21 its relation to the dichotomy spectrum sacker and sell 1978 23 siegmund 2002 26 d hyperbolicity berger et al 2009 6 and real parts of the eigenvalues in case a is constant is described we prove a spectral theorem and provide an approximation result for the spectral intervals

non algebraic domain growth in random magnets a cell dynamical approach the authors develop a novel numerical approach based on a computationally efficient cell dynamical system cds model for studying the kinetics of ordering in systems described by a non conserved order parameter with quenched disorder evolving from unstable initial states they use this model to study the kinetics of domain growth in a coarse grained version of the random exchange ising model their numerical data strongly indicate quantitative agreement with the theoretically predicted asymptotic growth law over a limited range of disorder amplitudes they also compare their observations with those in laboratory experiments and make important predictions regarding dynamical scaling in these systems

length scales and power laws in the two dimensional forest fire model abstract we re examine a two dimensional forest fire model via monte carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two point correlation function of trees we check resp improve previously obtained values for other critical exponents and perform a first investigation of the critical behaviour of the slowest relaxational mode we also investigate the possibility of describing the critical point in terms of a distribution of the global density we find that some qualitative features such as a temporal oscillation and a power law of the cluster size distribution can nicely be obtained from such a model that discards the spatial structure

numerical studies of critical percolation in three dimensions presents results of high statistics simulations of the spreading of 3d percolation close to the critical point the main results are i a more precise estimate of the spreading resp chemical distance dimension ii a novel heuristic scaling theory for percolation near surfaces and iii more precise values for critical surface and edge exponents in addition the author verifies the very precise results of ziff and stell 1988 for the percolation thresholds and studies in detail corrections to scaling the latter is made possible by simulating bond and site percolation in a number of different geometries in addition in most cases one could measure more than one observable during each simulation which provided quite severe internal consistency constraints in some cases the author found quite important deviations from scaling which are not easily described by a single power or logarithmic correction term

boundary effects in the three dimensional ising model abstract simulations of the standard three dimensional ising model with a variety of boundary conditions for medium and large systems are compared with field theoretical predictions in particular setting boundary spins equal to zero is not the best approximation for the dirichtet boundary condition of zero magnetization at the boundary the simulations for the specific heat agree semiquantitatively with the field theory for periodic and dirichtet boundary conditions

ising model simulation in directed lattices and networks abstract on directed lattices with half as many neighbours as in the usual undirected lattices the ising model does not seem to show a spontaneous magnetisation at least for lower dimensions instead the decay time for flipping of the magnetisation follows an arrhenius law on the square and simple cubic lattice on directed barabasi albert networks with two and seven neighbours selected by each added site metropolis and glauber algorithms give similar results while for wolff cluster flipping the magnetisation decays exponentially with time

static and dynamic critical behavior of thin magnetic ising films this work presents a study of the effect of film thickness on the static and dynamic critical behavior of thin magnetic ising films monte carlo simulations using the wolff algorithm were performed to determine the static and dynamic critical exponents of the films a dimensionality crossover from 2d to 3d due to the finiteness of the films in the static and dynamic critical behavior was observed as the film thickness increases in addition a slight increase in the effective dimension deff and a considerable increase in the critical temperature tc were found small values for the dynamic critical exponents were obtained indicating that the wolff algorithm is a very efficient method for these magnetic systems

on a forest fire model with supposed self organized criticality we study a stochastic forest fire model introduced by p baket al as a model showing self organized criticality this model involves a growth parameterp and the criticality is supposed to show up in the limitp 0 by simulating the model on much larger lattices and with much smaller values ofp we find that the correlations with longest range do not show a nontrivial critical phenomenon in this limit though we cannot rule out percolation like critical behavior on a smaller but still divergent length scale in contrast the model shows nontrivialdeterministic evolution over time scales 1 p in the limitp 0

hierarchical monte carlo simulation of the ising model abstract we pursue schmidt s recent idea to generate ising spin configurations via a hierarchical monte carlo procedure the method is modified and improved and applied to the two dimensional ising model at criticality the system size dependence is investigated for a 32 32 lattice the autocorrelation functions of the energy and the squared magnetization decay faster than with the standard method by a factor in the range of 3 to 10 on the basis of a number of plausible hypotheses we construct a theoretical framework within which the hierarchical method can be understood

transient spectral theory stable and unstable cones and gershgorinʼs theorem for finite time differential equations abstract dynamical behaviour on a compact finite time interval is called monotone hyperbolic or m hyperbolic if there exists an invariant splitting consisting of solutions with monotonically decreasing and increasing norms respectively this finite time hyperbolicity notion depends on the norm for arbitrary norms we prove a spectral theorem based on m hyperbolicity and extend gershgorin s circle theorem to this type of finite time spectrum similarly to stable and unstable manifolds we characterize m hyperbolicity by means of existence of stable and unstable cones these cones can be explicitly computed for d hyperbolic systems with norms induced by symmetric positive definite matrices and also for row diagonally dominant systems with the sup norm thus providing sufficient and computable conditions for m hyperbolicity

single cluster monte carlo dynamics for the ising model we present an extensive study of a new monte carlo acceleration algorithm introduced by wolff for the ising model it differs from the swendsen wang algorithm by growing and flipping single clusters at a random seed in general it is more efficient than swendsen wang dynamics ford 2 giving zero critical slowing down in the upper critical dimension monte carlo simulations give dynamical critical exponentszw 0 33 0 05 and 0 44 0 10 ind 2 and 3 respectively and numbers consistent withzw 0 ind 4 and mean field theory we present scaling arguments which indicate that the wolff mechanism for decorrelation differs substantially from swendsen wang despite the apparent similarities of the two methods

robust bayesian inference via coarsening the standard approach to bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class however even a small violation of this assumption can ha

thermal operators in ising percolation we discuss a new cluster representation for the internal energy and the specific heat of the d dimensional ising model obtained by studying the percolation mapping of an ising model with an arbitrary set of antiferromagnetic links such a representation relates the thermal operators to the topological properties of the fortuin kasteleyn fk clusters of ising percolation and is a powerful tool to get new exact relations on the topological structure of fk clusters of the ising model defined on an arbitrary graph

optimization of monte carlo simulations abstract monte carlo simulations of phase transitions and critical phenomena are hampered by long relaxation times and large fluctuations the computational effort for the collection of data points in a simulation often varies from data point to data point by orders of magnitude the optimal investment of computing time at different data points is a priori not clear we propose a method to calculate distributions of statistical weight and computing time which minimize the error of the parameters to be determined the method is discussed for the example of a finite size simulation in statistical physics we calculate explicitly the optimal distributions for algebraic dependencies it is shown that the optimal distributions depend on d z x where d is the dimension of the system z is the dynamical critical exponent and x is the scaling exponent of the relative variance of the data depending on one may save 60 80 of the total computing time compared to distributions with equal relative weight

adaptive bayesian multivariate density estimation with dirichlet mixtures summary we show that rate adaptive multivariate density estimation can be performed using bayesian methods based on dirichlet mixtures of normal kernels with a prior distribution on the kernel s covariance matrix parameter we derive sufficient conditions on the prior specification that guarantee convergence to a true density at a rate that is minimax optimal for the smoothness class to which the true density belongs no prior knowledge of smoothness is assumed the sufficient conditions are shown to hold for the dirichlet location mixture of normals prior with a gaussian base measure and an inverse wishart prior on the covariance matrix parameter locally h older

simulations of lattice animals and trees the scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions using as microscopic models lattice animals and lattice trees on simple hypercubic lattices as a stochastic sampling method we use a biased sequential sampling algorithm with re sampling similar to the pruned enriched rosenbluth method perm used extensively for linear polymers essentially we start simulating percolation clusters either site or bond re weigh them according to the animal tree ensemble and prune or branch the further growth according to a heuristic fitness function in contrast to previous applications of perm this fitness function is not the weight with which the actual configuration would contribute to the partition sum but is closely related to it we obtain high statistics of animals with up to several thousand sites in all dimension 2 d 9 in addition to the partition sum number of different animals we estimate gyration radii and numbers of perimeter sites in all dimensions we verify the parisi sourlas prediction and we verify all exactly known critical exponents in dimensions 2 3 4 and 8 in addition we present the hitherto most precise estimates for growth constants in d 3 for clusters with one site attached to an attractive surface we verify for d 3 the superuniversality of the cross over exponent at the adsorption transition predicted by janssen and lyssy but not for d 2 there we find 0 480 4 instead of the conjectured 1 2 finally we discuss the collapse of animals and trees arguing that our present version of the algorithm is also efficient for some of the models studied in this context but showing that it is not very efficient for the classical model for collapsing animals

critical dynamics of cluster algorithms in the dilute ising model autocorrelation times for thermodynamic quantities att c are calculated from monte carlo simulations of the site diluted simple cubic ising model using the swendsen wang and wolff cluster algorithms our results show that for these algorithms the autocorrelation timesdecrease when reducing the concentration of magnetic sites from 100 down to 40 this is of crucial importance when estimating static properties of the model since the variances of these estimators increase with autocorrelation time the dynamical critical exponents are calculated for both algorithms observing pronounced finite size effects in the energy autocorrelation data for the algorithm of wolff we conclude that when applied to the dilute ising model cluster algorithms become even more effective than local algorithms for whichincreasing autocorrelation times are expected

self organized critical forest fire model a forest fire model is introduced which contains a lightning probability f this leads to a self organized critical state in the limit f ensuremath rightarrow 0 provided that the time scales of tree growth and burning down of forest clusters are separated we derive scaling laws and calculate all critical exponents the values of the critical exponents are confirmed by computer simulations for a two dimensional system we show that the forest density in the critical state assumes its minimum possible value i e that energy dissipation is maximum

behaviour of a newtonian particle in a random environment abstract we consider the behaviour of a newtonian particle in a quenched random environment within the perturbation theory the diffusion coefficient of the particle for dimensionality d 1 is obtained as d 5 0 m 2 d d 1 0 1 d 2 with 0 m being respectively the velocity and the mass 0 is the strength of the disorder describes the shape of the disorder correlator

cluster monte carlo simulation of the transverse ising model we formulate a cluster monte carlo method for the anisotropic limit of ising models on d 1 dimensional lattices which in effect are equivalent with d dimensional quantum transverse ising models using this technique we investigate the transverse ising models on the square triangular kagome honeycomb and simple cubic lattices the monte carlo data are analyzed by finite size scaling in each case we find as expected that the critical behavior fits well in the d 1 dimensional ising universality class for the transverse ising model on the square lattice we determine the binder cumulant of the classical counterpart for a range of aspect ratios between the system sizes in the third or classical direction and that in the other two directions matching this universal function with the case of the isotropic ising model yields the length ratio relating the isotropic ising model with the anisotropic limit the efficiency of the present algorithm is reflected by the precision of its results which improves significantly on earlier analyses

computer simulations of the forest fire model abstract we present results of simulations of the forest fire model proposed by p bak et al containing a tree growth rate p and fire spreading to nearest neighbors the space time structure of the fire and the scaling properties of the forest clusters show that the model cannot be critical in the limit p 0 instead we observe regular and quasideterministic spiral shaped fire fronts we present a deterministic forest fire model that helps understand the origin of these spirals

finding long cycles in graphs we analyze the problem of discovering long cycles inside a graph we propose and test two algorithms for this task the first one is based on recent advances in statistical mechanics and relies on a message passing procedure the second follows a more standard monte carlo markov chain strategy special attention is devoted to hamiltonian cycles of nonregular random graphs of minimal connectivity equal to 3

renormalisability and renormalisation of the true self avoiding random walks renormalisation of the recently proposed field theoretic model for the true self avoiding random walk is analysed apart from a special case which corresponds to the problem of a random walk in a random environment the model is shown to be non renormalisable in the case of short range interactions contrary to earlier conjectures the long range version of this field theoretic model is shown to be renormalisable in certain regions of the parameter space and renormalisation group analysis of the model is carried out to two loop order in the region corresponding to the true self avoiding random walk with long range repulsion in a different region of the parameter space the anomalous dimension of the diffusion coefficient is determined exactly in perturbation theory

non equilibrium critical relaxation of the wolff dynamics of the ising model abstract the non equilibrium critical relaxation of the single cluster dynamics is studied for the ferromagnetic ising model on the square and cubic lattices power law behavior is observed in the energy relaxation process starting from an all up spin configuration from this power decay the dynamical exponent z is estimated to be 0 50 0 05 and 1 3 0 1 for the square and cubic lattices respectively where the time is defined by the number of cluster flip trials if the time scale is normalized by cluster mass they are 0 25 0 05 and 0 3 0 1 respectively

critical behaviour of non equilibrium q state systems we present two classes of non equilibrium models with critical behaviour each model is characterized by an integer q 1 and is defined on configurations of q valued spins on regular lattices the definitions of the models are very similar to the updating rules in wolff s algorithm for the potts model but both classes break detailed balance except for q 2 and q infinity in the first case both models reduce to the ising model while one of them reduces to percolation more precisely to the general epidemic process for q infinity locations of the critical point and critical exponents are estimated in two dimensions

annealing markov chain monte carlo with applications to ancestral inference abstract markov chain monte carlo mcmc the metropolis hastings algorithm has been used for many statistical problems including bayesian inference likelihood inference and tests of significance though the method generally works well doubts about convergence often remain here we propose mcmc methods distantly related to simulated annealing our samplers mix rapidly enough to be usable for problems in which other methods would require eons of computing time they simulate realizations from a sequence of distributions allowing the distribution being simulated to vary randomly over time if the sequence of distributions is well chosen then the sampler will mix well and produce accurate answers for all the distributions even when there is only one distribution of interest these annealing like samplers may be the only known way to get a rapidly mixing sampler these methods are essential for attacking very hard problems which arise in areas such as statistical genetics we illustrate the methods wi

a new approach to critical exponents in phase transitions of spin systems abstract we investigate a method to obtain critical exponents using standard numerical simulation techniques for spin systems we show that by analyzing the inverse of the logarithmic derivative of the susceptibility with respect to temperature the accuracy in determining can be increased significantly the method is tested on the two and three dimensional ising models but this alternative approach is thought to be most useful for spin systems on non periodic structures like quasi crystals and fractal lattices where the finite size scaling method is difficult to apply

fast simulation of the ising model using cellular automata a totalistic ising cellular automaton ica is proposed which can reproduce the thermodynamics of the ising model the automaton rules are preset in the usual way but some random mixing of these existing rules is subsequently permitted the model employs a vectorized multispin coding algorithm to reach spin updating speeds comparable with the best metropolis monte carlo performances and is characterized by a nonlinear dynamical critical exponent whose value seems less than two