on improved predictions for structural equilibrium path evaluations the paper describes how several procedures for higher order predictions have been introduced in order to improve the convergence speed in a general finite element program for non linear structural

tracing the equilibrium path beyond compound critical points a unified presentation of some popular continuation procedures used in the non linear finite element analysis of structural mechanics is introduced an extension of the elliptical constraint equation proposed by crisfield is given it is shown that in the proposed procedure real roots can always be obtained in solving the iterative change of the load parameter updated weighting factors are introduced in the constraint equation in order to get better convergence characteristics in the case when localized deformations occur for bifurcation points a modification of rheinboldt s branching procedure is presented post critical response after limit and bifurcation points is determined in some numerical examples

testing time reversibility without moment restrictions in this paper we propose a class of new tests for time reversibility it is shown that this test has an asymptotic normal distribution under the null hypothesis and non trivial power under local alternatives a novel feature of this test is that it does not have any moment restriction in contrast with other time reversibility and linearity tests our simulations also confirm that the proposed test is very robust when data do not possess proper moments an empirical study of stock market indices is also included to illustrate the usefulness of the new test

simultaneous parameter estimation and segmentation of gibbs random fields using simulated annealing an adaptive segmentation algorithm is developed which simultaneously estimates the parameters of the underlying gibbs random field grf and segments the noisy image corrupted by additive independent gaussian noise the algorithm which aims at obtaining the maximum a posteriori map segmentation is a simulated annealing algorithm that is interrupted at regular intervals for estimating the grf parameters maximum likelihood ml estimates of the parameters based on the current segmentation are used to obtain the next segmentation it is proven that the parameter estimates and the segmentations converge in distribution to the ml estimate of the parameters and the map segmentation with those parameter estimates respectively due to computational difficulties however only an approximate version of the algorithm is implemented the approximate algorithm is applied on several two and four region images with different noise levels and with first order and second order neighborhoods

entropy production and kullback leibler divergence between stationary trajectories of discrete systems the irreversibility of a stationary time series can be quantified using the kullback leibler divergence kld between the probability of observing the series and the probability of observing the time reversed series moreover this kld is a tool to estimate entropy production from stationary trajectories since it gives a lower bound to the entropy production of the physical process generating the series in this paper we introduce analytical and numerical techniques to estimate the kld between time series generated by several stochastic dynamics with a finite number of states we examine the accuracy of our estimators for a specific example a discrete flashing ratchet and investigate how close the kld is to the entropy production depending on the number of degrees of freedom of the system that are sampled in the trajectories

chaotic principle an experimental test abstract the chaotic hypothesis discussed in gallavotti and cohen 1995 is tested experimentally in a simple conduction model besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which as the forcing strength grows the attractor ceases to be an anosov system and becomes an axiom a attractor a first text of new predictions is also attempted

steady states invariant measures and response theory using the method of computer simulation we test the predictions of nonlinear response theory for classical systems subject to dissipative external fields we provide convincing numerical evidence that kawasaki methods agree with both the transient time correlation function predictions and with a direct measurement of the nonlinear response furthermore this numerical agreement is observed over a time scale which is sufficiently long for the response to have relaxed to within ensuremath sim 1 of its nonequilibrium steady state value this is in spite of the fact that in the steady state the n particle distribution function ultimately becomes fractal we discuss the normalization of the kawasaki distribution and derive a lagrangian form of the kawasaki response function and show that it is consistent with predictions that are obtained using a natural invariant measure for nonequilibrium steady states c 1995 the american physical society

causality response theory and the second law of thermodynamics we show that there is a close connection between the assumption of causality and the second law of thermodynamics we also show that for a class of classical reversible deterministic systems it is overwhelmingly improbable either to find causal steady states that violate the second law or anticausal states that satisfy the second law these arguments indicate that the existence of and the sign associated with the second law of thermodynamics is ultimately determined by causality our discussion employs a green kubo relation that we derive for an anticausal linear transport coefficient

new irreversibility measure and complexity analysis based on singular value decomposition abstract visibility graph algorithm is a powerful tool for visualization and analysis of complex dynamical system kullback leibler divergence kld based on the horizontal visibility graph algorithm has received largely extensive attention in the field of irreversibility analysis in this paper we will propose a new irreversibility measure built on the multi scale theory i e the kld based on singular value decomposition kld svd furthermore since matrix singular value can reflect the basic characteristics of the complex system we further bring forward the definition of shannon entropy with singular value decomposition se svd after considering that the shannon entropy has been well defined as a complexity measure in order to show the advantages of these two new measures in detecting the complexity of systems several simulation and real data experiments are chosen to examine the performance of them through these results we find that the average and variance of kld svd corresponding to each time series is less than that of the kld moreover kld svd s volatility is significantly weaker than kld s as there is a conceptual link between predictability and irreversibility we can argue that kld svd algorithm implies the higher predictability and lower confusion on the other hand se svd can do well in revealing the internal complexity of the different time series meanwhile it is useful to mention that se svd is robust against noise efficiently

derivatives of tangential stiffness matrices for equilibrium path descriptions the paper describes how several procedures based on expressions from analytical elastic stability theory are introduced as numerical tools in a general finite element program for geometrically non linear structural analysis especially is discussed how derivatives of the tangential stiffness matrix can be utilized in several contexts in the solution algorithm these include improved predictions for the step wise solution of equilibrium states identification of critical points and accurate descriptions of initial post bifurcation behaviour for two plane beam and bar elements formulations have been developed giving analytical expressions for these derivatives the corresponding numerical approximations needed in other element types are also discussed the paper discusses the relative efficiency of higher order predictions in relation to these different element types and different solution strategies some numerical examples showing different types of behaviour are analysed and discussed

post critical analysis of structures with a nonlinear pre buckling state in the presence of imperfections in the context of the geometrically nonlinear analysis of structures by continuation methods a technique for the determination of the imperfection sensitivity is carried out the technique is based on galerkin s reduction of equilibrium equations in the subspace of extrapolation branches emanating from the bifurcation points the pre and post critical behaviour in the neighbourhood of bifurcation points however is well approximated provided that extrapolations have a large convergence domain to this end an efficient asymptotic representation of the primary and secondary equilibrium paths and procedures that overcome the ill conditioning of the systems defined in the critical points is used here

some computational aspects of the stability analysis of nonlinear structures abstract the perturbation method and the continuation method are the two most popular techniques for the solution of finite element equations that describe instability phenomena this paper presents a summary of the principles involved and describes some trends in the development of these techniques

an orthogonal residual procedure for non linear finite element equations a general and robust solution procedure for non linear finite element equations with limit points is developed at each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state the method implements the physical condition that the orthogonal residual force will neither increase nor decrease the magnitude of the current displacement increment vector the orthogonality condition is formulated directly in terms of conjugate variables and therefore does not contain any scaling parameters passage of load and displacement limit points is discussed as well as the relation to line search minimum residual and arc length methods the method is illustrated by two examples

time reversibility from visibility graphs of nonstationary processes visibility algorithms are a family of methods to map time series into networks with the aim of describing the structure of time series and their underlying dynamical properties in graph theoretical terms here we explore some properties of both natural and horizontal visibility graphs associated to several nonstationary processes and we pay particular attention to their capacity to assess time irreversibility nonstationary signals are infinitely irreversible by definition independently of whether the process is markovian or producing entropy at a positive rate and thus the link between entropy production and time series irreversibility has only been explored in nonequilibrium stationary states here we show that the visibility formalism naturally induces a new working definition of time irreversibility which allows us to quantify several degrees of irreversibility for stationary and nonstationary series yielding finite values that can be used to efficiently assess the presence of memory and off equilibrium dynamics in nonstationary processes without the need to differentiate or detrend them we provide rigorous results complemented by extensive numerical simulations on several classes of stochastic processes

a characterization of horizontal visibility graphs and combinatorics on words abstract a horizontal visibility graph hvg is defined in association with an ordered set of non negative reals hvgs realize a methodology in the analysis of time series their degree distribution being a good discriminator between randomness and chaos luque et al b luque l lacasa f ballesteros j luque horizontal visibility graphs exact results for random time series phys rev e 80 2009 046103 we prove that a graph is an hvg if and only if it is outerplanar and has a hamilton path therefore an hvg is a noncrossing graph as defined in algebraic combinatorics flajolet and noy p flajolet m noy analytic combinatorics of noncrossing configurations discrete math 204 1999 203 229 our characterization of hvgs implies a linear time recognition algorithm treating ordered sets as words we characterize subfamilies of hvgs highlighting various connections with combinatorial statistics and introducing the notion of a visible pair with this technique we determine asymptotically the average number of edges of hvgs

unsupervised segmentation of textured images abstract in this paper a new unsupervised segmentation algorithm for textured images is developed the proposed algorithm utilizes the characteristic of the markov random fields mrf for modeling the contextual information embedded in image formation textured images are regarded as realizations of the stationary gaussian mrf on a two dimensional square lattice and are modeled by the conditional autoregressive car equations with a second order noncausal neighborhood a hypothesis test over two radially masked areas is involved in our algorithm to detect the location of boundaries the hypothesis assumes that these two areas belong to the same class of textures and car model parameters are estimated in a minimum mean square error mmse sense the hypothesis is tested by the analysis of variance anova like technique and if it is rejected a measure of dissimilarity is accumulated on the rejected area this approach produces potential edge maps from these maps the boundaries among various textures can be detected without microedges the performance of the proposed algorithm is demonstrated by some experiments using real textures as well as synthetic ones the experiments show that the proposed algorithm can produce satisfactory segmentation without any a priori information

test your surrogate data before you test for nonlinearity the schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis in particular we pinpoint some important caveats of the prominent algorithm of amplitude adjusted fourier transform surrogates aaft and compare it to the iterated aaft which is more consistent in representing the null hypothesis it turns out that in many applications with real data the inferences of nonlinearity after marginal rejection of the null hypothesis were premature and have to be reinvestigated taking into account the inaccuracies in the aaft algorithm mainly concerning the mismatching of the linear correlations in order to deal with such inaccuracies we propose the use of linear together with nonlinear polynomials as discriminating statistics the application of this setup to some well known real data sets cautions against the use of the aaft algorithm

note on two theorems in nonequilibrium statistical mechanics an attempt is made to clarify the difference between a theorem derived by evans and searles in 1994 on the statistics of trajectories in phase space and a theorem proved by the authors in 1995 on the statistics of fluctuations on phase space trajectory segments in a nonequilibrium stationary state

an improvement of the measurement of time series irreversibility with visibility graph approach abstract we propose a method to improve the measure of real valued time series irreversibility which contains two tools the directed horizontal visibility graph and the kullback leibler divergence the degree of time irreversibility is estimated by the kullback leibler divergence between the i n and o u t degree distributions presented in the associated visibility graph in our work we reframe the i n and o u t degree distributions by encoding them with different embedded dimensions used in calculating permutation entropy pe with this improved method we can not only estimate time series irreversibility efficiently but also detect time series irreversibility from multiple dimensions we verify the validity of our method and then estimate the amount of time irreversibility of series generated by chaotic maps as well as global stock markets over the period 2005 2015 the result shows that the amount of time irreversibility reaches the peak with embedded dimension d 3 under circumstances of experiment and financial markets

smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics this paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics we adopt a new point of view which has emerged progressively in recent years and which takes seriously into account the chaotic character of the microscopic time evolution the emphasis is on nonequilibrium steady states rather than the traditional approach to equilibrium point of view of boltzmann the nonequilibrium steady states in presence of a gaussian thermostat are described by srb measures in terms of these one can prove the gallavotti cohen fluctuation theorem one can also prove a general linear response formula and study its consequences which are not restricted to near equilibrium situations at equilibrium one recovers in particular the onsager reciprocity relations under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of dettmann and morriss the results just mentioned hold so far only for classical systems they do not involve large size i e they hold without a thermodynamic limit

irreversibility and fluctuation theorem in stationary time series the relative entropy between the joint probability distribution of backward and forward sequences is used to quantify time asymmetry or irreversibility for stationary time series the parallel with the thermodynamic theory of nonequilibrium steady states allows us to link the degree of asymmetry in the time signal with the distance from equilibrium and the lack of detailed balance among its states we study the statistics of time asymmetry in terms of the fluctuation theorem showing that this type of relationship derives from simple general symmetries valid for any stationary time series

two dimensional object detection in correlated noise abstract in this paper a procedure for the detection of two dimensional objects embedded in correlated noise is presented the procedure developed here is an extension of the dependent noise model of the recent work by chang and kurz object detection and experimental designs comput vision graphics image process 40 147 168 1987 the model for the dependent data is based on the two way analysis under the analysis of variance anova with fixed effects and known correlation matrix the detection is based on the test of homogeneity and heterogeneity properties of target and background arrays and the combination of both the global array for each data array f statistics are calculated and tested against tabulated thresholds for the case of objects with large size a reduced algorithm in the form of a contrast test statistic is proposed results of computer simulations carried out to evaluate the new algorithms are presented

time irreversibility of financial time series based on higher moments and multiscale kullback leibler divergence abstract irreversibility is an important property of time series in this paper we propose the higher moments and multiscale kullback leibler divergence to analyze time series irreversibility the higher moments kullback leibler divergence hmkld can amplify irreversibility and make the irreversibility variation more obvious therefore many time series whose irreversibility is hard to be found are also able to show the variations we employ simulated data and financial stock data to test and verify this method and find that hmkld of stock data is growing in the form of fluctuations as for multiscale kullback leibler divergence mkld it is very complex in the dynamic system so that exploring the law of simulation and stock system is difficult in conventional multiscale entropy method the coarse graining process is non overlapping however we apply a different coarse graining process and obtain a surprising discovery the result shows when the scales are 4 and 5 their entropy is nearly similar which demonstrates mkld is efficient to display characteristics of time series irreversibility

the koiter newton approach using von karman kinematics for buckling analyses of imperfection sensitive structures the koiter newton approach is a reduced basis method for nonlinear structural analyses the method combines koiter s approach as a predictor step and the newton arc length technique as a corrector step to trace the entire load displacement equilibrium path of a structure in a step by step manner this computationally highly efficient and accurate solution method has recently demonstrated a superior performance in nonlinear analyses compared to standard techniques in this paper we propose an extension to buckling imperfection sensitivity analyses exploiting the method s stability and reliability we present two different modeling techniques for imperfection loads that both profit from the koiter newton approach reducing the initial computation steps to a small fraction thereof we introduce von karman kinematics which neglect some nonlinear terms of the green strain displacement relations to further increase the computational efficiency of the analysis by an essential reduction of the computation effort required to obtain higher order derivatives of the strain energy using various numerical examples and benchmark tests we demonstrate the overall high quality and performance of the proposed method

multiscale multifractal time irreversibility analysis of stock markets abstract time irreversibility is one of the most important properties of nonstationary time series complex time series often demonstrate even multiscale time irreversibility such that not only the original but also coarse grained time series are asymmetric over a wide range of scales we study the multiscale time irreversibility of time series in this paper we develop a method called multiscale multifractal time irreversibility analysis mmra which allows us to extend the description of time irreversibility to include the dependence on the segment size and statistical moments we test the effectiveness of mmra in detecting multifractality and time irreversibility of time series generated from delayed henon map and binomial multifractal model then we employ our method to the time irreversibility analysis of stock markets in different regions we find that the emerging market has higher multifractality degree and time irreversibility compared with developed markets in this sense the mmra method may provide new angles in assessing the evolution stage of stock markets

entropy production for quantum markov semigroups an invariant state of a quantum markov semigroup is an equilibrium state if it satisfies a quantum detailed balance condition in this paper we introduce a notion of entropy production for faithful normal invariant states of a quantum markov semigroup on mathcal b mathsf h as a numerical index measuring how far they are from equilibrium the entropy production rate is defined as the derivative of the relative entropy of the one step forward and backward evolution in analogy with the classical probabilistic concept we prove an explicit trace formula expressing the entropy production rate in terms of the completely positive part of the generator of a norm continuous quantum markov semigroup showing that it turns out to be zero if and only if a standard quantum detailed balance condition holds

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

on the asymptotic convergence of the transient and steady state fluctuation theorems nonequilibrium molecular dynamics simulations are used to demonstrate the asymptotic convergence of the transient and steady state forms of the fluctuation theorem in the case of planar poiseuille flow we find that the transient form valid for all times converges to the steady state predictions on microscopic time scales further we find that the time of convergence for the two theorems coincides with the time required for satisfaction of the asymptotic steady state fluctuation theorem

finite element asymptotic analysis of slender elastic structures a simple approach an asymptotic method directly derived from koiter s theory and suitable for the solution of elastic buckling problems and its natural adaptation to a numerical solution by means of a finite element technique are presented here the order of the extrapolation of the equilibrium equations has been intentionally kept very low because attention has been entirely devoted to all those features theoretical definitions eigenproblem numerical techniques suitable fem implementation which make such an approach competitive with respect to the classic step by step methods for plane frames and 3d pin jointed trusses the performances of the algorithm numerical accuracy and computational cost are compared with those of riks are length method

the minimum description length principle for probability density estimation by regular histograms abstract the minimum description length principle is a general methodology for statistical modeling and inference that selects the best explanation for observed data as the one allowing the shortest description of them application of this principle to the important task of probability density estimation by histograms was previously proposed we review this approach and provide additional illustrative examples and an application to real world data with a presentation emphasizing intuition and concrete arguments we also consider alternative ways of measuring the description lengths that can be found to be more suited in this context we explicitly exhibit analyze and compare the complete forms of the description lengths with formulas involving the information entropy and redundancy of the data and not given elsewhere histogram estimation as performed here naturally extends to multidimensional data and offers for them flexible and optimal subquantization schemes the framework can be very useful for modeling and reduction of complexity of observed data based on a general principle from statistical information theory and placed within a unifying informational perspective

characterization and estimation of two dimensional arma models a class of finite order two dimensional autoregressive moving average arma is introduced that can represent any process with rational spectral density in this model the driving noise is correlated and need not be gaussian currently known classes of arma models or ar models are shown to be subsets of the above class the three definitions of markov property are discussed and the class of arma models are precisely stated which have the noncausal and semicausal markov property without imposing any specific boundary conditions next two approaches are considered to estimate the parameters of a model to fit a given image the first method uses only the empirical correlations and involves the solution of linear equations the second method is the likelihood approach since the exact likelihood function is difficult to compute we resort to approximations suggested by the toroidal models numerical experiments compare the quality of the two estimation schemes finally the problem of synthesizing a texture obeying an arma model is considered

divergence estimation of continuous distributions based on data dependent partitions we present a universal estimator of the divergence d p spl par q for two arbitrary continuous distributions p and q satisfying certain regularity conditions this algorithm which observes independent and identically distributed i i d samples from both p and q is based on the estimation of the radon nikodym derivative dp dq via a data dependent partition of the observation space strong convergence of this estimator is proved with an empirically equivalent segmentation of the space this basic estimator is further improved by adaptive partitioning schemes and by bias correction the application of the algorithms to data with memory is also investigated in the simulations we compare our estimators with the direct plug in estimator and estimators based on other partitioning approaches experimental results show that our methods achieve the best convergence performance in most of the tested cases

the large deviation principle and steady state fluctuation theorem for the entropy production rate of a stochastic process in magnetic fields fluctuation theorem is one of the major achievements in the field of nonequilibrium statistical mechanics during the past two decades there exist very few results for steady state fluctuation theorem of sample entropy production rate in terms of large deviation principle for diffusion processes due to the technical difficulties here we give a proof for the steady state fluctuation theorem of a diffusion process in magnetic fields with explicit expressions of the free energy function and rate function the proof is based on the karhunen loeve expansion of complex valued ornstein uhlenbeck process

testing time symmetry in time series using data compression dictionaries time symmetry often called statistical time reversibility in a dynamical process means that any segment of time series output has the same probability of occurrence in the process as its time reversal a technique based on symbolic dynamics is proposed to distinguish such symmetrical processes from asymmetrical ones given a time series observation of the otherwise unknown process because linear stochastic gaussian processes and static nonlinear transformations of them are statistically reversible but nonlinear dynamics such as dissipative chaos are usually statistically irreversible a test will separate large classes of hypotheses for the data a general purpose and robust statistical test procedure requires adapting to arbitrary dynamics which may have significant time correlation of undetermined form given a symbolization of the observed time series the technology behind adaptive dictionary data compression algorithms offers a suitable estimate of reversibility as well as a statistical likelihood test the data compression methods create approximately independent segments permitting a simple and direct null test without resampling or surrogate data we demonstrate the results on various time series reversible and irreversible systems

asymptotics of the entropy production rate for d dimensional ornstein uhlenbeck processes in the context of non equilibrium statistical physics the entropy production rate is an important concept to describe how far a specific state of a system is from its equilibrium state in this paper we establish a central limit theorem and a moderate deviation principle for the entropy production rate of d dimensional ornstein uhlenbeck processes by the techniques of functional inequalities such as poincare inequality and log sobolev inequality as an application we obtain a law of iterated logarithm for the entropy production rate

variational methods for time dependent classical many particle systems abstract a variational method for the classical liouville equation is introduced that facilitates the development of theories for non equilibrium classical systems the method is based on the introduction of a complex valued auxiliary quantity that is related to the classical position momentum probability density via a functional of is developed whose extrema imply that satisfies the liouville equation multiscale methods are used to develop trial functions to be optimized by the variational principle the present variational principle with multiscale trial functions can capture both the microscopic and the coarse grained descriptions thereby yielding theories that account for the two way exchange of information across multiple scales in space and time equations of the smoluchowski form for the coarse grained state probability density are obtained constraints on the initial state of the n particle probability density for which the aforementioned equation is closed and conserves probability are presented the methodology has applicability to a wide range of systems including macromolecular assemblies ionic liquids and nanoparticles

local kinetic interpretation of entropy production through reversed diffusion the time reversal of stochastic diffusion processes is revisited with emphasis on the physical meaning of the time reversed drift and the noise prescription in the case of multiplicative noise the local kinematics and mechanics of free diffusion are linked to the hydrodynamic description these properties also provide an interpretation of the pope ching formula for the steady state probability density function along with a geometric interpretation of the fluctuation dissipation relation finally the statistics of the local entropy production rate of diffusion are discussed in the light of local diffusion properties and a stochastic differential equation for entropy production is obtained using the girsanov theorem for reversed diffusion the results are illustrated for the ornstein uhlenbeck process

a local fluctuation theorem abstract a mechanism for the validity of a local version of the fluctuation theorem uniform in the system size is discussed for a reversible chain of weakly coupled anosov systems

simple parallel hierarchical and relaxation algorithms for segmenting noncausal markovian random fields the modeling and segmentation of images by mrf s markov random fields is treated these are two dimensional noncausal markovian stochastic processes two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of c mrf s the algorithms are designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology a doubly stochastic representation is used in image modeling here a gaussian mrf is used to model textures in visible light and infrared images and an autobinary or autoternary etc mrf to model a priori information about the local geometry of textured image regions for image segmentation the true texture class regions are treated either as a priori completely unknown or as a realization of a binary or ternary etc mrf in the former case image segmentation is realized as true maximum likelihood estimation in the latter case it is realized as true maximum a posteriori likelihood segmentation in addition to providing a mathematically correct means for introducing geometric structure the autobinary or ternary etc mrf can be used in a generative mode to generate image geometries and artificial images and such simulations constitute a very powerful tool for studying the effects of these models and the appropriate choice of model parameters the first segmentation algorithm is hierarchical and uses a pyramid like structure in new ways that exploit the mutual dependencies among disjoint pieces of a textured region

discussion about parameterization in the asymptotic numerical method application to nonlinear elastic shells abstract the asymptotic numerical method anm is a family of algorithms for path following problems based on the computation of truncated vectorial series with respect to a path parameter a b cochelin n damil m potier ferry methode asymptotique numerique hermes lavoisier paris 2007 in this paper we discuss and compare three concepts of parameterizations of the anm curves i e the definition of the path parameter a the first concept is based on the classical arc length parameterization e riks some computational aspects of the stability analysis of nonlinear structures computer methods in applied mechanics and engineering 47 1984 219 259 the second is based on the so called local parameterization w c rheinboldt j v burkadt a locally parameterized continuation acm transaction on mathematical software 9 1983 215 235 r seydel a tracing branches world of bifurcation online collection and tutorials of nonlinear phenomena http www bifurcation de 1999 j j gervais h sadiky a new steplength control for continuation with the asymptotic numerical method iam j numer anal 22 no 2 2000 207 229 and the third is based on a minimization condition of a rest s lopez an effective parametrization for asymptotic extrapolation computer methods in applied mechanics and engineering 189 2000 297 311 we demonstrate that the third concept is equivalent to a maximization condition of the anm step lengths to illustrate the performance of these proposed parameterizations we give some numerical comparisons on nonlinear elastic shell problems

context tree modeling of observed symbolic dynamics modern techniques invented for data compression provide efficient automated algorithms for the modeling of the observed symbolic dynamics we demonstrate the relationship between coding and modeling motivating the well known minimum description length mdl principle and give concrete demonstrations of the context tree weighting and context tree maximizing algorithms the predictive modeling technique obviates many of the technical difficulties traditionally associated with the correct mdl analyses these symbolic models representing the symbol generating process as a finite state automaton with probabilistic emission probabilities provide excellent and reliable entropy estimations the resimulations of estimated tree models satisfying the mdl model selection criterion are faithful to the original in a number of measures the modeling suggests that the automated context tree model construction could replace fixed order word lengths in many traditional forms of empirical symbolic analysis of the data we provide an explicit pseudocode for implementation of the context tree weighting and maximizing algorithms as well as for the conversion to an equivalent markov chain

econophysics financial time series from a statistical physics point of view in recent years physicists have started applying concepts and methods of statistical physics to study economic problems the word econophysics is sometimes used to refer to this work much recent work is focused on understanding the statistical properties of nancial time series one reason for this interest is that nancial markets are examples of complex interacting systems for which a huge amount of data exist and it is possible that nancial time series viewed from a dierent perspective might yield new results this article reviews the results of three recent phenomenological studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as eight orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by three orders of magnitude from 1 min up to approximately 10 d ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law and persist for several months iii correlations among dierent companies the third result bears on the application of random matrix theory to understand the correlations among price uctuations of any two dierent stocks from a study of the eigenvalue statistics of the cross correlation matrix constructed from price uctuations of the leading 1000 stocks we nd that the largest 1 of the eigenvalues and the corresponding eigenvectors show systematic deviations from the predictions for a random matrix whereas the rest of the eigenvalues conform to random matrix behavior suggesting that these 1 of the eigenvalues contain system specic information about correlated time evolution of dierent companies c 2000 published by elsevier science b v all rights reserved

equality governing nonequilibrium fluctuations and its information theory and thermodynamic interpretations the master equation is cast in the form of an equality involving the variation in the course of a transformation of a quantity playing the role of a generalized potential weighted with the probability of allowable transformations emanating from different initial states in the most general case this equality cannot be formulated entirely in terms of thermodynamic variables and state functions some conditions under which such a reduction becomes possible are identified and a comparison with fluctuation and work type relationships previously reported in the literature is carried out

entropy production fluctuations of finite markov chains for almost every trajectory segment over a finite time span of a finite markov chain with any given initial distribution the logarithm of the ratio of its probability to that of its time reversal converges exponentially to the entropy production rate of the markov chain the large deviation rate function has a symmetry of gallavotti cohen type which is called the fluctuation theorem moreover similar symmetries also hold for the rate functions of the joint distributions of general observables and the logarithmic probability ratio

time irreversibility and intrinsics revealing of series with complex network approach abstract in this work we analyze time series on the basis of the visibility graph algorithm that maps the original series into a graph by taking into account the all round information carried by the signals the time irreversibility and fractal behavior of series are evaluated from a complex network perspective and considered signals are further classified from different aspects the reliability of the proposed analysis is supported by numerical simulations on synthesized uncorrelated random noise short term correlated chaotic systems and long term correlated fractal processes and by the empirical analysis on daily closing prices of eleven worldwide stock indices obtained results suggest that finite size has a significant effect on the evaluation and that there might be no direct relation between the time irreversibility and long range correlation of series similarity and dissimilarity between stock indices are also indicated from respective regional and global perspectives showing the existence of multiple features of underlying systems

stochastic analysis of symmetry breaking bifurcations master equation approach the multivariate master equation for a general reaction diffusion system is solved perturbatively in the vicinity of a bifurcation point leading to symmetry breaking transitions the possibility to express the result through a brazovskii type of potential is examined and a comparison with the langevin analysis of walgraefet al adv chem phys 49 311 1982 is performed

topological properties of the limited penetrable horizontal visibility graph family the limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks in this work we extend this algorithm to create a directed limited penetrable horizontal visibility graph and an image limited penetrable horizontal visibility graph we define two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real value series we perform several numerical simulations to check the accuracy of our theoretical results finally we present an application of the directed limited penetrable horizontal visibility graph to measure real value time series irreversibility and an application of the image limited penetrable horizontal visibility graph that discriminates noise from chaos we also propose a method to measure the systematic risk using the image limited penetrable horizontal visibility graph and the empirical results show the effectiveness of our proposed algorithms

transition records of stationary markov chains in any markov chain with finite state space the distribution of transition records always belongs to the exponential family this observation is used to prove a fluctuation theorem and to show that the dynamical entropy of a stationary markov chain is linear in the number of steps three applications are discussed a known result about entropy production is reproduced a thermodynamic relation is derived for equilibrium systems with metropolis dynamics finally a link is made with recent results concerning a one dimensional polymer model

fluctuation theorems for entropy production and heat dissipation in periodically driven markov chains asymptotic fluctuation theorems are statements of a gallavotti cohen symmetry in the rate function of either the time averaged entropy production or heat dissipation of a process such theorems have been proved for various general classes of continuous time deterministic and stochastic processes but always under the assumption that the forces driving the system are time independent and often relying on the existence of a limiting ergodic distribution in this paper we extend the asymptotic fluctuation theorem for the first time to inhomogeneous continuous time processes without a stationary distribution considering specifically a finite state markov chain driven by periodic transition rates we find that for both entropy production and heat dissipation the usual gallavotti cohen symmetry of the rate function is generalized to an analogous relation between the rate functions of the original process and its corresponding backward process in which the trajectory and the driving protocol have been time reversed the effect is that spontaneous positive fluctuations in the long time average of each quantity in the forward process are exponentially more likely than spontaneous negative fluctuations in the backward process and vice versa revealing that the distributions of fluctuations in universes in which time moves forward and backward are related as an additional result the asymptotic time averaged entropy production is obtained as the integral of a periodic entropy production rate that generalizes the constant rate pertaining to homogeneous dynamics

a simple discrete model of brownian motors time periodic markov chains in this paper we consider periodically inhomogeneous markov chains which can be regarded as a simple version of physical model brownian motors we introduce for them the concepts of periodical reversibility detailed balance entropy production rate and circulation distribution we prove the equivalence of the following statements the time periodic markov chain is periodically reversible it is in detailed balance kolmogorov s cycle condition is satisfied its entropy production rate vanishes every circuit and its reversed circuit have the same circulation weight hence in our model of markov chains the directed transport phenomenon of brownian motors i e the existence of net circulation can occur only in nonequilibrium and irreversible systems moreover we verify the large deviation property and the gallavotti cohen fluctuation theorem of sample entropy production rates of the markov chain

hurst kolmogorov dynamics as a result of extremal entropy production abstract it is demonstrated that extremization of entropy production of stochastic representations of natural systems performed at asymptotic times zero or infinity results in constant derivative of entropy in logarithmic time and in turn in hurst kolmogorov processes the constraints used include preservation of the mean variance and lag 1 autocovariance at the observation time step and an inequality relationship between conditional and unconditional entropy production which is necessary to enable physical consistency an example with real world data illustrates the plausibility of the findings

fluctuation theorem for stochastic systems the fluctuation theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics it has been proved in a number of different ways for thermostatted deterministic nonequilibrium systems in the present paper we show that the fluctuation theorem is also valid for a class of stochastic nonequilibrium systems the theorem is therefore not reliant on the reversibility or the determinism of the underlying dynamics numerical tests verify the theoretical result

scaling behaviors in differently developed markets scaling properties of four di erent stock market indices are studied in terms of a generalized hurst exponent approach we nd that the deviations from pure brownian motion behavior are associated with the degrees of development of the markets and we observe strong di erentiations in the scaling properties of markets at di erent development stage c

on the work free energy relations in a driven isothermal system a historical and stochastic perspective equality relationships connecting the work performed in a non equilibrium driven process of an isothermal system with the difference of equilibrium thermodynamic potentials have been established by various authors since jarzynski s work of 1997 mostly based on a classical phase space description quantum considerations have been limited and stochastic derivations have been mainly ad hoc however such processes are better described by an ensemble in the a space for fluctuating state or mesoscopic variables going back to the probabilistic results of boltzmann and einstein and employing a few basic properties of generally non stationary markov processes these relationships follow almost naturally providing the initial and final states are in contact with the heat bath the essential point is that in the exponentiated work exp w the non equilibrium entropy functions of both initial and final states cancel out the results obtained are valid for any particle number n we note that the connection with the microscopic quantum statistical evolution must be considered in order to proceed in addition some aspects of irreversibility are briefly being discussed

symbolic approach for measuring temporal irreversibility we describe a symbolic approach for measuring temporal irreversibility in time series measurements temporal irreversibility is important because it excludes gaussian linear dynamics and static transformations of such dynamics from the set of possible generating processes a symbolic method for measuring temporal irreversibility is attractive because it is computationally efficient robust to noise and simplifies statistical analysis of confidence limits we propose a specific algorithm called false flipped symbols for establishing the presence of temporal irreversibility without the need for generating surrogate data besides characterizing experimental data our results are relevant to the question of selecting alternative models we illustrate our points with numerical model output and experimental measurements

element behavior in post critical plane frame analysis depending on the type of uni modal cuspoid catastrophe which governs the local behavior of a structure at a simple critical point correct prediction of the post critical path requires an accurat

a unified texture model based on a 2 d wold like decomposition a unified texture model that is applicable to a wide variety of texture types found in natural images is presented this model leads to the derivation of texture analysis and synthesis algorithms designed to estimate the texture parameters and to reconstruct the original texture field from these parameters the texture field is assumed to be a realization of a regular homogeneous random field which is characterized in general by a mixed spectral distribution the texture field is orthogonally decomposed into a purely indeterministic component and a deterministic component the deterministic component is further orthogonally decomposed into a harmonic component and a generalized evanescent component both analytical and experimental results show that the deterministic components should be parameterized separately from the purely indeterministic component the model is very efficient in terms of the number of parameters required to faithfully represent textures reconstructed textures are practically indistinguishable from the originals

edge detection in correlated noise using latin square masks abstract in this paper new classes of algorithms are developed for processing of two dimensional image data imbedded in correlated noise the algorithms are based on modifications of standard analysis of variance anova techniques involving latin square ls technique and ensuring their proper operation in dependent noise the ls technique enables us to analyse three effects including the gray level or diagonal effect instead of two based on the same data for two way designs though the theoretical development leading to the actual image processing procedure is laborious and complicated the actual procedure is simple robust and useful in real time applications the efficiency of all algorithms for processing image data corrupted by statistically dependent noise is verified by extensive monte carlo simulations

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

surrogate time series before we apply nonlinear techniques e g those inspired by chaos theory to dynamical phenomena occurring in nature it is necessary to first ask if the use of such advanced techniques is justified by the data while many processes in nature seem very unlikely a priori to be linear the possible nonlinear nature might not be evident in specific aspects of their dynamics the method of surrogate data has become a very popular tool to address such a question however while it was meant to provide a statistically rigorous foolproof framework some limitations and caveats have shown up in its practical use in this paper recent efforts to understand the caveats avoid the pitfalls and to overcome some of the limitations are reviewed and augmented by new material in particular we will discuss specific as well as more general approaches to constrained randomisation providing a full range of examples new algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains the main limitation which lies in the interpretability of the test results will be illustrated through instructive case studies we will also discuss some implementational aspects of the realisation of these methods in the tisean software package

the transient fluctuation theorem of sample entropy production for general stochastic processes the transient fluctuation theorem for stochastic processes was first put forward by d j searles and d j evans 1999 in the present paper it is rigorously proved that the transient fluctuation theorem tft of sample entropy production which is previously defined by jiang et al 2003 and reid et al 2005 and also called the general action functional up to boundary terms by lebowitz and spohn 1999 holds for general stochastic processes without the assumption of markovian homogeneous or stationary properties then the condition of our theorem is verified for various stochastic processes including homogeneous inhomogeneous markov chains and general diffusion processes among these cases the transient fluctuation theorems for inhomogeneous markov chains and general diffusion processes are rigorously derived for the first time

improved surrogate data for nonlinearity tests current tests for nonlinearity compare a time series to the null hypothesis of a gaussian linear stochastic process for this restricted null assumption random surrogates can be constructed which are constrained by the linear properties of the data we propose a more general null hypothesis allowing for nonlinear rescalings of a gaussian linear process we show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity an iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

an effective parametrization for asymptotic extrapolations abstract when considering the range of validity of asymptotic expansions the choice of the expansion parameter plays an essential role in effect with the exception of a posteriori adjustments of the expansion components the definition of this parameter is the only way of improving the approximation at a finite distance from the initial point good parametrization equations are usually obtained by norms that involve all variables of the problem or based on the nature of the mechanical phenomena here this equation is constructed following the criteria of reducing the residual error and at the same time exactly reproducing solutions that admit a polynomial second degree representation that choice is automatic in the analysis and improves the domain of accurate approximations an appropriate predictor corrector scheme was implemented to compare extrapolations obtained by this and several standard parametrizations the solution scheme was used to analyse geometrically nonlinear plane frame structures

chaotic hypothesis onsager reciprocity and fluctuation dissipation theorem it is shown that the chaoticity hypothesis recently introduced in statistical mechanics which is analogous to ruelle s principle for turbulence implies the onsager reciprocity and the fluctuation dissipation theorem in various reversible models for coexisting transport phenomena

entropy production and information gain in axiom a systems anosov systems are mathematical models for chaotic systems in statistical mechanics and fluid dynamics most of these systems enjoy the property of positive entropy production we introduce the concept of specific information gain or specific relative entropy h in anosov systems and prove that it is identical to the entropy production rate e p defined by ruelle and gallavotti in anosov systems from this point of view the entropy production rate e p characterizes the degree of macroscopic irreversibility of the system

on the definition of entropy production via examples we present a definition of entropy production rate for classes of deterministic and stochastic dynamics the point of departure is a gibbsian representation of the steady state path space measure for which the density is determined with respect to the time reversed process the gibbs formalism is used as a unifying algorithm capable of incorporating basic properties of entropy production in nonequilibrium systems our definition is motivated by recent work on the gallavotti cohen local fluctuation theorem and it is illustrated via a number of examples