phase transitions and damage spreading in a nonequilibrium lattice gas model with mixed dynamic rules abstract phase transitions and damage spreading for a lattice gas model with mixed driven lattice gas dlg glauber dynamics are studied by means of monte carlo simulations in order to control the number of sites updated according to the nonconservative glauber dynamics a parameter p 0 1 is defined in this way for p 0 the system corresponds to the dlg model with biased kawasaki conservative dynamics while for p 1 it corresponds to the ising model with glauber dynamics the results obtained show that the introduction of nonconservative dynamics dramatically affects the behavior of the dlg model leading to the existence of ising like phase transitions from fully occupied to disordered states the short time dynamics results suggest that this transition is second order for values of p 0 1 and p 0 6 and first order for 0 1 p 0 6 on the other hand damage always spreads within the investigated temperature range and reaches a saturation value d s a t that depends on the system size the temperature and p the value of d s a t in the thermodynamic limit is estimated by performing a finite size analysis for p 0 6 the results show a change in the behavior of d s a t with temperature similar to those reported for the pure p 0 dlg model however for p 0 6 the data remind us of the ising p 1 curves in each case a damage temperature t d p can be defined as the value where either d s a t reaches a maximum or it becomes nonzero this temperature is within error bars similar to the reported values of the temperatures that characterize the mentioned phase transitions

automatic image segmentation by dynamic region growth and multiresolution merging image segmentation is a fundamental task in many computer vision applications in this paper we propose a new unsupervised color image segmentation algorithm which exploits the information obtained from detecting edges in color images in the cie l a b color space to this effect by using a color gradient detection technique pixels without edges are clustered and labeled individually to identify some initial portion of the input image content elements that contain higher gradient densities are included by the dynamic generation of clusters as the algorithm progresses texture modeling is performed by color quantization and local entropy computation of the quantized image the obtained texture and color information along with a region growth map consisting of all fully grown regions are used to perform a unique multiresolution merging procedure to blend regions with similar characteristics experimental results obtained in comparison to published segmentation techniques demonstrate the performance advantages of the proposed method

damage spreading in confined geometries and the influence of boundary conditions a monte carlo study of the ising ferromagnet the spreading of damage in the ising ferromagnet in two dimensional confined geometries of size l m l m close to the critical temperature is studied by means of computer simulations imposing both periodic and open boundary conditions along the m direction the influence of the interfaces between domains of spins having opposite orientation on the spreading of damage can be studied analyzing the spatio temporal evolution of the damage it is found that such interfaces not only considerably speed up the spreading but also cause the enhancement of the damaged area of the sample these statements are based on the evaluation of relevant exponents which characterize the spatio temporal spreading of the damage

contour detection and hierarchical image segmentation this paper investigates two fundamental problems in computer vision contour detection and image segmentation we present state of the art algorithms for both of these tasks our contour detector combines multiple local cues into a globalization framework based on spectral clustering our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree in this manner we reduce the problem of image segmentation to that of contour detection extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms the automatically generated hierarchical segmentations can be interactively refined by user specified annotations computation at multiple image resolutions provides a means of coupling our system to recognition applications

optimal linear glauber model contrary to the actual nonlinear glauber model the linear glauber model lgm is exactly solvable although the detailed balance condition is not generally satisfied this motivates us to address the issue of writing the transition rate w j in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least the advantage of this work is that by studying the lgm analytically we will be able to anticipate how the kinetic properties of an arbitrary ising system depend on the temperature and the coupling constants the analytical expressions for the optimal values of the parameters involved in the linear w j are obtained using a simple moore penrose pseudoinverse matrix this approach is quite general in principle applicable to any system and can reproduce the exact results for one dimensional ising system in the continuum limit we get a linear time dependent ginzburg landau equation from the glauber s microscopic model of non conservative dynamics we analyze the critical and dynamic properties of the model and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach we will also show in this paper that the effect of magnetic field can easily be studied within our approach in particular we show that the inverse of relaxation time changes quadratically with weak magnetic field and that the fluctuation dissipation theorem is valid for our model

nonlocal growth equations a test case for dynamic renormalization group analysis abstract in this paper we discuss nonlocal growth equations such as the generalization of the kardar parisi zhang kpz equation that includes long range interactions also known as the nonlocal kardar parisi zhang nkpz equation and the nonlocal version of the molecular beam epitaxy nmbe equation we show that the steady state strong coupling solution for nonlocal models such as nkpz and nmbe can be obtained exactly in one dimension for some special cases using the fokker planck form of these equations the exact results we derive do not agree with previous results obtained by dynamic renormalization group drg analysis this discrepancy is important because drg is a common method used extensively to deal with nonlinear field equations while difficulties with this method for d 1 has been realized in the past it has been believed so far that drg is still safe in one dimension our result shows differently the reasons for the failure of drg to recover the exact one dimensional results are also discussed

damage spreading and dynamic stability of kinetic ising models we investigate how the time evolution of different kinetic ising models depends on the initial conditions of the dynamics to this end we consider the simultaneous evolution of two identical systems subjected to the same thermal noise we derive a master equation for the time evolution of a joint probability distribution of the two systems this equation is then solved within an effective field approach by analysing the fixed points of the master equation and their stability we identify regular and chaotic phases

perceptually uniform color spaces for color texture analysis an empirical evaluation rgb a nonuniform color space is almost universally accepted by the image processing community as the means for representing color on the other hand perceptually uniform spaces such as l a b as well as approximately uniform color spaces such as hsv exist in which measured color differences are proportional to the human perception of such differences this paper compares rgb with l a b and hsv in terms of their effectiveness in color texture analysis there has been a limited but increasing amount of work on the color aspects of textured images the results have shown that incorporating color into a texture analysis and recognition scheme can be very important and beneficial the presented methodology uses a family of gabor filters specially tuned to measure specific orientations and sizes within each color texture effectiveness is measured by the classification performance of each color space as well as by classifier independent measures experimental results are obtained with a variety of color texture images perceptually uniform spaces are shown to outperform rgb in many cases

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

self consistent expansion for the kardar parisi zhang equation with correlated noise a minor modification of the self consistent expansion sce for the kardar parisi zhang kpz system with uncorrelated noise is used to obtain the exponents in systems where the noise has spatial long range correlations for d dimensional systems with correlations of the form d stackrel ensuremath rightarrow r ensuremath r ensuremath t ensuremath t ensuremath 2d 0 stackrel ensuremath rightarrow r ensuremath r ensuremath 2 ensuremath rho ensuremath d ensuremath delta t ensuremath t ensuremath ensuremath rho g0 we find a lower critical dimension d 0 ensuremath rho 2 2 ensuremath rho above which a perturbative edwards wilkinson ew solution appears below the lower critical dimension two solutions exist each in a different distinct region of ensuremath rho for small ensuremath rho s the solution of kpz with uncorrelated noise is recovered for large ensuremath rho s a ensuremath rho dependent solution is found the existence of only one solution in each region of ensuremath rho is not a result of a competition between two solutions but a direct outcome of the sce equation

orientation of particle attachment and local isotropy in diffusion limited aggregation dla we simulate 50 off lattice diffusion limited aggregation dla clusters of one million particles each the probability distribution of the angle of attachment of arriving particles with respect to the local radial direction is obtained numerically for increasing cluster size n the distribution crosses over extremely accurately to a cosine with an amplitude which decreases towards zero as a power law in n from this specific viewpoint asymptotically large dla clusters are locally isotropic

time correlations in mode hopping of coupled oscillators we study the dynamics in a system of coupled oscillators when arnold tongues overlap by varying the initial conditions the deterministic system can be attracted to different limit cycles adding noise the mode hopping between different states become a dominating part of the dynamics we simplify the system through a poincare section and derive a 1d model to describe the dynamics we explain that for some parameter values of the external oscillator the time distribution of occupancy in a state is exponential and thus memoryless in the general case on the other hand it is a sum of exponential distributions characteristic of a system with time correlations

chaotic behavior and damage spreading in the glauber ising model a master equation approach we investigate the sensitivity of the time evolution of a kinetic ising model with glauber dynamics against the initial conditions to do so we apply the damage spreading method i e we study the simultaneous evolution of two identical systems subjected to the same thermal noise we derive a master equation for the joint probability distribution of the two systems we then solve this master equation within an effective field approximation which goes beyond the usual mean field approximation by retaining the fluctuations though in a quite simplistic manner the resulting effective field theory is applied to different physical situations it is used to analyze the fixed points of the master equation and their stability and to identify regular and chaotic phases of the glauber ising model we also discuss the relation of our results to directed percolation

hierarchical image segmentation based on iterative contraction and merging in this paper we propose a new framework for hierarchical image segmentation based on iterative contraction and merging in the proposed framework we treat the hierarchical image segmentation problem as a sequel of optimization problems with each optimization process being realized by a contraction and merging process to identify and merge the most similar data pairs at the current resolution at the beginning we perform pixel based contraction and merging to quickly combine image pixels into initial region elements with visually indistinguishable intra region color difference after that we iteratively perform region based contraction and merging to group adjacent regions into larger ones to progressively form a segmentation dendrogram for hierarchical segmentation comparing with the state of the art techniques the proposed algorithm can not only produce high quality segmentation results in a more efficient way but also keep a lot of boundary details in the segmentation results

efficient graph based image segmentation this paper addresses the problem of segmenting an image into regions we define a predicate for measuring the evidence for a boundary between two regions using a graph based representation of the image we then develop an efficient segmentation algorithm based on this predicate and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties we apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph and illustrate the results with both real and synthetic images the algorithm runs in time nearly linear in the number of graph edges and is also fast in practice an important characteristic of the method is its ability to preserve detail in low variability image regions while ignoring detail in high variability regions

complete devil s staircase fractal dimension and universality of mode locking structure in the circle map it is shown numerically that the stability intervals for limit cycles of the circle map form a complete devil s staircase at the onset of chaos the complementary set to the stability intervals is a cantor set of fractal dimension d 0 87 this exponent is found to be universal for a large class of functions

damage spreading in random field systems we investigate how a quenched random field influences the damage spreading transition in kinetic ising models to this end we generalize a recent master equation approach and derive an effective field theory for damage spreading in random field systems this theory is applied to the glauber ising model with a bimodal random field distribution we find that the random field influences the spreading transition by two different mechanisms with opposite effects first the random field favours the same particular direction of the spin variable at each site in both systems which reduces the damage second the random field suppresses the magnetization which in turn tends to increase the damage the competition between these two effects leads to a rich behaviour

anomalous dynamic scaling of the non local growth equations abstract the anomalous dynamic scaling behavior of the d 1 dimensional non local growth equations is investigated based on the scaling approach the growth equations studied include the non local kardar parisi zhang nkpz non local sun guo grant nsgg and non local lai das sarma villain nldv equations the anomalous scaling exponents in both the weak and strong coupling regions are obtained respectively our results show that non local interactions can affect anomalous scaling properties of surface fluctuations

time evolution of damage in the ising model the time evolution of the damage in the ising model with the heat bath and glauber dynamics has been investigated with the damage spreading method the damage density d t and the average distance r t of damaged sites from the origin have been measured numerically from the simulational data the scaling forms have been established as d t tx r t t1z and d t r t df and the corresponding exponents x z and df have been estimated

automatic image segmentation by dynamic region merging this paper addresses the automatic image segmentation problem in a region merging style with an initially oversegmented image in which many regions or superpixels with homogeneous color are detected an image segmentation is performed by iteratively merging the regions according to a statistical test there are two essential issues in a region merging algorithm order of merging and the stopping criterion in the proposed algorithm these two issues are solved by a novel predicate which is defined by the sequential probability ratio test and the minimal cost criterion starting from an oversegmented image neighboring regions are progressively merged if there is an evidence for merging according to this predicate we show that the merging order follows the principle of dynamic programming this formulates the image segmentation as an inference problem where the final segmentation is established based on the observed image we also prove that the produced segmentation satisfies certain global properties in addition a faster algorithm is developed to accelerate the region merging process which maintains a nearest neighbor graph in each iteration experiments on real natural images are conducted to demonstrate the performance of the proposed dynamic region merging algorithm

evolution by damage spreading in kauffman model in kauffman s boolean automata model on the square lattice the darwinian fitness of survival can be defined as the fraction of elements which do not change from one iteration to the next biological mutations are simulated by filpping one bit in the rule of one site selection of the fitter mutant then optimizes the whole lattice completely this optimization is particularly effective near the critical point of the transition to chaos but is in itself not a critical phenomenon also a two dimensional spin glass can be optimized in this way

nonlocal kardar parisi zhang equation with spatially correlated noise the effects of spatially correlated noise on a phenomenological equation equivalent to a nonlocal version of the kardar parisi zhang kpz equation are studied via the dynamic renormalization group drg techniques the correlated noise coupled with the long ranged nature of interactions prove the existence of different phases in different regimes giving rise to a range of roughness exponents defined by their corresponding critical dimensions finally self consistent mode analysis is employed to compare the non kpz exponents obtained as a result of the long range interactions with the drg results

uncertain destination dynamics certain dynamical systems exhibit a sensitivity to initial conditions in which the asymptotic state is selected from an infinite number of possible states the phase space of such systems is foliated with attractors each of which is associated with a particular set of initial conditions the associated uncertain destination dynamics can be analyzed by an appropriate reduction of the full system to a subsystem that explicitly yields the dynamics s1063 651x 99 09909 2 pacs number s 05 45 2a recent studies of high dimensional dynamical systems have revealed many new modes of complex evolution such as synchronization 1 on off intermittency 2 and fractal riddled and intermingled basins 3 many of these studies have raised fundamental questions concerning the relationship between model systems and the real systems they attempt to describe 4 in this paper we report on another gross complexity in the evolution of high dimensional systems for many dynamical systems governed by evolution equations of the form

natural image segmentation based on tree equipartition bayesian flooding and region merging we propose a general purpose image segmentation framework which involves feature extraction and classification in feature space followed by flooding and merging in spatial domain region growing is based on the computed local measurements and distances from the distribution of features describing the different classes using the properties of the label dependent distances spatial coherence is ensured since the image features are described globally the distribution of the features for the different classes are obtained by block wise unsupervised clustering based on the construction of the minimum spanning tree of the blocks grid using the mallows distance and the equipartition of the resulting tree the final clustering is obtained by using the k centroids algorithm with high probability and under topological constraints connected components of the maximum likelihood classification map are used to compute a map of initially labelled pixels an efficient flooding algorithm is introduced namely priority multi class flooding algorithm pmcfa that assign pixels to labels using bayesian dissimilarity criteria a new region merging method which incorporates boundary information is introduced for obtaining the final segmentation map therefore the merging stage is based on region features and edge localization segmentation results on the berkeley benchmark data set demonstrate the effectiveness of the proposed methods

effect of long range interactions in the conserved kardar parisi zhang equation the conserved kardar parisi zhang equation in the presence of long range nonlinear interactions is studied by the dynamic renormalization group method the long range effect produces new fixed points with continuously varying exponents and gives distinct phase transitions depending on both the long range interaction strength and the substrate dimension d the long range interaction makes the surface width less rough than that of the short range interaction in particular the surface becomes a smooth one with a negative roughness exponent at the physical dimension d 2

damage spreading and critical exponents for model a ising dynamics using damage spreading and heat bath dynamics we study the ising model in 2 and 3 dimensions with non conservative dynamics our algorithm differs in some important points from previous ones which makes it rather efficient we give estimates for the exponent z which seem to be the most precise published so far 2 172 0 006 for d 2 2 032 0 004 for d 3 we also give precise estimates of the exponent introduced by janssen et al z phys b 73 1989 539 and of analogous but in principle independent exponents we find surprisingly that some of the latter agree with and give an explanation for this

in an ising model with spin exchange dynamics damage always spreads we investigate the spreading of damage in ising models with kawasaki spin exchange dynamics which conserves the magnetization we first modify a recent master equation approach to account for dynamic rules involving more than a single site we then derive an effective field theory for damage spreading in ising models with kawasaki spin exchange dynamics and solve it for a two dimensional model on a honeycomb lattice in contrast to the cases of glauber or heat bath dynamics we find that the damage always spreads and never heals in the long time limit the average hamming distance approaches that of two uncorrelated systems these results are verified by monte carlo simulations

learning based hierarchical graph for unsupervised matting and foreground estimation automatically extracting foreground objects from a natural image remains a challenging task this paper presents a learning based hierarchical graph for unsupervised matting the proposed hierarchical framework progressively condenses image data from pixels into cells from cells into components and finally from components into matting layers first in the proposed framework a graph based contraction process is proposed to condense image pixels into cells in order to reduce the computational loads in the subsequent processes cells are further mapped into matting components using spectral clustering over a learning based graph the graph affinity is efficiently learnt from image patches of different resolutions and the inclusion of multiscale information can effectively improve the performance of spectral clustering in the final stage of the hierarchical scheme we propose a multilayer foreground estimation process to assemble matting components into a set of matting layers unlike conventional approaches which typically address binary foreground background partitioning the proposed method provides a set of multilayer interpretations for unsupervised matting experimental results show that the proposed approach can generate more consistent and accurate results as compared with state of the art techniques

on the perturbation expansion of the kpz equation we present a simple argument to show that the function of the d dimensional kpz equation d 2 is to all orders in perturbation theory given by beta g r d 2 g r 2 8 pi d 2 text gamma 2 d 2 g r 2 neither the dynamical exponent z nor the roughness exponent have any correction in any order of perturbation theory this shows that standard perturbation theory cannot attain the strong coupling regime and in addition breaks down at d 4 we also calculate a class of correlation functions exactly

are damage spreading transitions generically in the universality class of directed percolation we present numerical evidence for the fact that the damage spreading transition in the domany kinzel automaton found by martinset al is in the same universality class as directed percolation we conjecture that also other damage spreading transitions should be in this universality class unless they coincide with other transitions as in the ising model with glauber dynamics and provided the probability for a locally damaged state to become healed is not zero

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

time dependent thermodynamic properties of the ising model from damage spreading the relationship between damage spreading and static thermodynamic properties in the ising model developed by coniglioet al is here extended to include time dependent thermodynamic quantities we exploit this new result to measure the time dependent spin correlation function from damage spreading in the ising model with heat bath and glauber dynamics until now only static thermodynamic quantities have been correctly determined from damage spreading and even then only with heat bath dynamics we also show that there are significant differences between the kinetics of damage spreading as found in heat bath and glauber dynamics