poisson approximations for the ising model a d dimensional ising model on a lattice torus is considered as the size n of the lattice tends to infinity a poisson approximation is given for the distribution of the number of copies in the lattice of any given local configuration provided the magnetic field a a n tends to and the pair potential b remains fixed using the stein chen method a bound is given for the total variation error in the ferromagnetic case

cluster expansion for abstract polymer models a new direct proof of convergence of cluster expansions for polymer contour models is given in an abstract setting it does not rely on kirkwood salsburg type equations or combinatorics of trees a distinctive feature is that at all steps the considered clusters contain every polymer at most once

detection of intensity bursts using hawkes processes an application to high frequency financial data given a stationary point process an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate it might signal a local nonstationarity or the presence of an external perturbation to the system in this paper we propose a procedure for the detection of intensity bursts within the hawkes process framework by using a model selection scheme we show that our procedure can be used to detect intensity bursts when both their occurrence time and their total number is unknown moreover the initial time of the burst can be determined with a precision given by the typical interevent time we apply our methodology to the midprice change in foreign exchange fx markets showing that these bursts are frequent and that only a relatively small fraction is associated with news arrival we show lead lag relations in intensity burst occurrence across different fx rates and we discuss their relation with price jumps

bootstrap and permutation tests of independence for point processes motivated by a neuroscience question about synchrony detection in spike train analysis we deal with the independence testing problem for point processes we introduce non parametric test statistics which are rescaled general u statistics whose corresponding critical values are constructed from bootstrap and randomization permutation approaches making as few assumptions as possible on the underlying distribution of the point processes we derive general consistency results for the bootstrap and for the permutation w r t to wasserstein s metric which induce weak convergence as well as convergence of second order moments the obtained bootstrap or permutation independence tests are thus proved to be asymptotically of the prescribed size and to be consistent against any reasonable alternative a simulation study is performed to illustrate the derived theoretical results and to compare the performance of our new tests with existing ones in the neuroscientific literature

finite cycle gibbs measures on permutations of mathbb z d we consider gibbs distributions on the set of permutations of mathbb z d associated to the hamiltonian h sigma sum x v sigma x x where sigma is a permutation and v mathbb z d rightarrow mathbb r is a strictly convex potential call finite cycle those permutations composed by finite cycles only we give conditions on v ensuring that for large enough temperature alpha 0 there exists a unique infinite volume ergodic gibbs measure mu alpha concentrating mass on finite cycle permutations this measure is equal to the thermodynamic limit of the specifications with identity boundary conditions we construct mu alpha as the unique invariant measure of a markov process on the set of finite cycle permutations that can be seen as a loss network a continuous time birth and death process of cycles interacting by exclusion an approach proposed by fernandez ferrari and garcia define tau v as the shift permutation tau v x x v in the gaussian case v vert cdot vert 2 we show that for each v in mathbb z d mu alpha v given by mu alpha v f mu alpha f tau v cdot is an ergodic gibbs measure equal to the thermodynamic limit of the specifications with tau v boundary conditions for a general potential v we prove the existence of gibbs measures mu alpha v when alpha is bigger than some v dependent value

a stochastic system with infinite interacting components to model the time evolution of the membrane potentials of a population of neurons we consider a new class of interacting particle systems with a countable number of interacting components the system represents the time evolution of the membrane potentials of an infinite set of interacting neurons we prove the existence and uniqueness of the process using a perfect simulation procedure we show that this algorithm is successful that is we show that the number of steps of the algorithm is almost surely finite we also construct a perfect simulation procedure for the coupling of a process with a finite number of neurons and the process with an infinite number of neurons as a consequence we obtain an upper bound for the error that we make when sampling from a finite set of neurons instead of the infinite set of neurons

non homogeneous polygonal markov fields in the plane graphical representations and geometry of higher order correlations we consider polygonal markov fields originally introduced by arak and surgailis probab theory relat fields 80 543 579 1989 our attention is focused on fields with nodes of order two which can be regarded as continuum ensembles of non intersecting contours in the plane sharing a number of features with the two dimensional ising model we introduce non homogeneous version of polygonal fields in anisotropic environment for these fields we provide a class of new graphical constructions and random dynamics these include a generalized dynamic representation generalized and defective disagreement loop dynamics as well as a generalized contour birth and death dynamics next we use these constructions as tools to obtain new exact results on the geometry of higher order correlations of polygonal markov fields in their consistent regime

robust synchronization of chaotic horizontal platform systems with phase difference this paper studies a robust synchronization of non autonomous chaotic systems with parameter mismatch in the synchronization scheme a linear state error feedback control is used to couple the master and slave horizontal platform systems excited by harmonic external forces between which there exists a phase mismatch a new definition of global synchronization with error bound is introduced using lyapunov s stability theory the sufficient synchronization criteria for the scheme are proven and the corresponding synchronization error bound is estimated the synchronization criteria are further optimized by optimally designing a quadratic lyapunov function to more precisely estimate the synchronization error bound the illustrative simulations verify the effectiveness of these criteria the estimated synchronization error bound is compared with numerical one in the examples

chaos and chaos synchronization of a symmetric gyro with linear plus cubic damping the dynamic behavior of a symmetric gyro with linear plus cubic damping which is subjected to a harmonic excitation is studied in this paper the liapunov direct method has been used to obtain the sufficient conditions of the stability of the equilibrium points of the system by applying numerical results time history phase diagrams poincare maps liapunov exponents and liapunov dimensions are presented to observe periodic and chaotic motions besides several control methods the delayed feedback control the addition of constant motor torque the addition of period force and adaptive control algorithm aca have been used to control chaos effectively finally attention is shifted to the synchronization of chaos in the two identical chaotic motions of symmetric gyros the results show that one can make two identical chaotic systems to synchronize through applying four different kinds of one way coupling furthermore the synchronization time is also examined

hitting times for independent random walks on ℤd we consider a system of asymmetric independent random walks on z d denoted by t t e r stationary under the product poisson measure v p of marginal density p 0 we fix a pattern a an increasing local event and denote by the hitting time of a by using a loss network representation of our system at small density we obtain a coupling between the laws of t conditioned on r t for all times t when d 3 this provides bounds on the rate of convergence of the law of t conditioned on r t toward its limiting probability measure as t tends to infinity we also treat the case where the initial measure is close to v without being product

properties of jeffreys mixture for markov sources we discuss the properties of jeffreys mixture for a markov model first we show that a modified jeffreys mixture asymptotically achieves the minimax coding regret for universal data compression where we do not put any restriction on data sequences moreover we give an approximation formula for the prediction probability of jeffreys mixture for a markov model by this formula it is revealed that the prediction probability by jeffreys mixture for the markov model with alphabet 0 1 is not of the form nx s ns where nx s is the number of occurrences of the symbol x following the context s 0 1 and ns n0 s n1 s moreover we propose a method to compute our minimax strategy which is a combination of a monte carlo method and the approximation formula where the former is used for earlier stages in the data while the latter is used for later stages

approximation complexity for piecewise monotone functions and real data abstract this paper investigates the relationship between approximation error and complexity a variety of complexity measures are used including the number of alternating strictly monotone segments computation time and for piecewise linear approximations the number of linear segments the results apply to piecewise monotone functions and to finite maps from reals to reals i e real data we provide a theoretical framework expressing the exact relationship between approximation error and the number of alternating strictly monotone segments we provide a linear time algorithm taking an error bound as input and returning a minimal segmentation of the approximated function s domain such that there exists an approximation alternatingly strictly monotone on the segments with error less than the given bound for real data we provide a suboptimal tradeoff between approximation error and number of linear segments in piecewise linear approximation the results are obtained by extending the theory of best piecewise monotone approximation to piecewise monotone functions and by application of a new concept scale dependent monotonicity

modified log sobolev inequality for a compact pure jump markov process with degenerate jumps we study the modified log sobolev inequality for a class of pure jump markov processes that describe the interactions between brain neurons as a result we obtain concentration properties for empirical approximations of the process in particular we focus on a finite and compact process with degenerate jumps inspired by the model introduced by galves and locherbach j stat phys 151 896 921 2013

synchronization multistability and basin crisis in coupled pendula abstract the synchronization dynamics of two linearly coupled pendula is studied in this paper based on the lyapunov stability theory and linear matrix inequality lmi some necessary and sufficient conditions for global asymptotic synchronization are derived from which an estimated threshold coupling k th for the on set of full synchronization is obtained the numerical value of k th determined from the average energies of the systems is in good agreement with theoretical analysis prior to the on set of synchronization the boundary crisis of the chaotic attractor is identified in the bistable states where two asymmetric periodic attractors co exist it is shown that the coupled pendula can attain multistable states via a new dynamical transition the basin crisis that occur prior to the on set of stable synchronization the essential feature of basin crisis is that the two co existing attractors are destroyed while new three or more co existing attractors of the same or different periodicity are created in addition the linear perturbation technique and the routh hurwitz criteria are employed to investigate the stability of steady states and clearly identify the different types of bifurcations likely to be encountered finally two parameter phase plots show various regions of chaos hyperchaos and periodicity

master slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control global chaos synchronization of two identical non autonomous horizontal platform systems coupled by linear state error feedback controller is investigated the sufficient criteria for global chaos synchronization are deduced based on the stability theory of linear time varied systems and lyapunov s direct method of which the criteria related to general coupling matrix are first proved and applied to derive the ones related to some special coupling matrices in the examples the coupling strengths are designed by the obtained criteria and the appearances of chaos synchronization are verified it is analytically and numerically examined that the synchronization criteria based on lyapunov s direct method are sharper than the criteria based on the stability theory of linear time varied systems

chaos synchronization and parameter identification for gyroscope system synchronization of chaos for a two degree of freedom heavy symmetric gyroscope system are studied in this paper because of the nonlinear terms of the system the system exhibits both regular and chaotic motions by lyapunov stability theory with control terms by adaptive control and by random optimization method the synchronization of two identical systems and tracking of the parameter of the systems are studied

chaos synchronization of a horizontal platform system chaos and chaos synchronization of the horizontal platform system are studied in this paper because of the non linear terms of the systems the systems exhibit both regular and chaotic motions by applying various numerical results such as phase portraits poincare maps time history and power spectrum analysis the behaviors of the periodic and chaos synchronization are presented the effects of the change of parameters in the system can be found in the bifurcation diagrams chaos synchronization of feedback methods in two coupled systems has been studied by lyapunov exponent and coupling strength besides phase effect of external excitations and the transient time in unidirectional synchronization also have been researched

universal lossless source coding with the burrows wheeler transform the burrows wheeler transform 1994 is a reversible sequence transformation used in a variety of practical lossless source coding algorithms in each the bwt is followed by a lossless source code that attempts to exploit the natural ordering of the bwt coefficients bwt based compression schemes are widely touted as low complexity algorithms giving lossless coding rates better than those of the ziv lempel codes commonly known as lz 77 and lz 78 and almost as good as those achieved by prediction by partial matching ppm algorithms to date the coding performance claims have been made primarily on the basis of experimental results this work gives a theoretical evaluation of bwt based coding the main results of this theoretical evaluation include 1 statistical characterizations of the bwt output on both finite strings and sequences of length n spl rarr spl infin 2 a variety of very simple new techniques for bwt based lossless source coding and 3 proofs of the universality and bounds on the rates of convergence of both new and existing bwt based codes for finite memory and stationary ergodic sources the end result is a theoretical justification and validation of the experimentally derived conclusions bwt based lossless source codes achieve universal lossless coding performance that converges to the optimal coding performance more quickly than the rate of convergence observed in ziv lempel style codes and for some bwt based codes within a constant factor of the optimal rate of convergence for finite memory sources

strong approximation of density estimators from weakly dependent observations by density estimators from independent observations we derive an approximation of a density estimator based on weakly dependent random vectors by a density estimator built from independent random vectors we construct on a sufficiently rich probability space such a pairing of the random variables of both experiments that the set of observations x 1 x n from the time series model is nearly the same as the set of observations y 1 y n from the i i d model with a high probability all sets of the form x 1 x n delta y 1 y n boolean and a 1 b 1 x x a d b d contain no more than o n 1 2 pi b i a i 1 log n elements respectively although this does not imply very much for parametric problems it has important implications in nonparametric statistics it yields a strong approximation of a kernel estimator of the stationary density by a kernel density estimator in the i i d model moreover it is shown that such a strong approximation is also valid for the standard bootstrap and the smoothed bootstrap using these results we derive simultaneous confidence bands as well as supremum type nonparametric tests based on reasoning for the i i d model

poissonian behavior of ising spin systems in an external field we apply the stein chen method for poisson approximation to spin half ising type models in positive external field which satisfy the fkg inequality in particular we show that provided the density of minus spins is low and can be expanded as a convergent power series in the activity fugacity variable the distribution of minus spins is approximately poisson the error of the approximation is inversely proportional to the number of lattice sites we obtain upper and lower bounds on the total variation distance between the exact distribution and its poisson approximation we illustrate these results by application to specific models including the mean field and nearest neighbor ferromagnetic ising models

poisson approximation for large contours in low temperature ising models we consider the contour representation of the infinite volume ising model at any fixed inverse temperature the solution of 0e 1 let be the infinite volume measure fix v zd 0 and a large n such that calling gn v the set of contours of length at least n intersecting v there are in average contours in gn v under we show that the total variation distance between the law of gn v under and a poisson process is bounded by a constant depending on and times e n the proof builds on the chen stein method as presented by arratia goldstein and gordon the control of the correlations is obtained through the loss network space time representation of contours due to fernandez ferrari and garcia

lossless near lossless and refinement coding of bilevel images we present general and unified algorithms for lossy lossless coding of bilevel images the compression is realized by applying arithmetic coding to conditional probabilities as in the current jbig standard the conditioning may be specified by a template for better compression the more general free tree may be used loss may be introduced in a preprocess on the encoding side to increase compression the primary algorithm is a rate distortion controlled greedy flipping of pixels though being general the algorithms are primarily aimed at material containing half toned images as a supplement to the specialized soft pattern matching techniques that work better for text template based refinement coding is applied for lossy to lossless refinement introducing only a small amount of loss in half toned test images compression is increased by up to a factor of four compared with jbig lossy lossless and refinement decoding speed and lossless encoding speed are less than a factor of two slower than jbig the de coding method is proposed as part of jbig2 an emerging international standard for lossless lossy compression of bilevel images

tight lower bounds for optimum code length corresp a new lower bound for the mean code length of all one to one codes for a random variable with n outcomes is derived the bound which is tight improves an earlier one due to leung yan cheong and cover another bound for one to one codes for binary information sources is derived

design and implementation of fuzzy sliding mode controllers for generalized projective synchronization of chaos horizontal platform systems this paper presents robust chattering free fuzzy sliding mode control fsmc as a way to achieve generalized projective synchronization gps of two horizontal chaos platform vibration systems with system uncertainty and external disturbance an appropriate sliding surface is acquired through an smc design such that the error state trajectories of a master slave system will reach such a sliding surface and approaches to the origin based on the lyapunov stability theory we address the design schemes of integration fuzzy sliding mode control where the reaching law is proposed by a set of linguistic rules and the control input is chattering free as a consequence the system is simulated and experimented to demonstrate that the error state tends to be stabilized and the chattering problem can be thus resolved implying that the slave horizontal platform system hps is gps with the master hps

master slave synchronization criteria for horizontal platform systems using time delay feedback control abstract this paper is concerned with master slave synchronization for two identical non autonomous horizontal platform systems by using time delay feedback control compared with some existing results on synchronization for horizontal platform systems the effect of the time delay in the feedback control on master slave synchronization is investigated applying a delay decomposition approach some delay dependent synchronization criteria are established and formulated in the form of linear matrix inequalities lmis sufficient conditions about the existence of a time delay feedback controller are derived by employing these newly obtained synchronization criteria the controller gains can be achieved by solving a set of lmis one simulation example is given to illustrate the effectiveness of synchronization criteria and the design method

dynamic adaptive partitioning for nonlinear time series summary we propose a dynamic adaptive partitioning scheme for nonparametric analysis of stationary nonlinear time series it yields estimates of the whole probability distribution of the underlying process we use information from past values to construct adaptive partitioning in a dynamic fashion which is then different from the more common static schemes in the regression set up the idea of dynamic partitioning is new we make it constructive by an approach based on quantisation of the data and adaptively modelling partition cells with a parsimonious markov chain the methodology is formulated in terms of a new model class the so called quantised variable length markov chains it is a new extension of finite valued variable length markov chains to processes with values in rd we discuss estimation explore asymptotic properties of the new method and give some numerical results which reflect the finite sample behaviour

optimal pruning with applications to tree structured source coding and modeling an algorithm introduced by l breiman et al 1984 in the context of classification and regression trees is reinterpreted and extended to cover a variety of applications in source coding and modeling in which trees are involved these include variable rate and minimum entropy tree structured vector quantization minimum expected cost decision trees variable order markov modeling optimum bit allocation and computer graphics and image processing using quadtrees a concentration on the first of these and a detailed analysis of variable rate tree structured vector quantization are provided it is found that variable rate tree structured vector quantization outperforms not only the fixed rate variety but also full search vector quantization the successive approximation character of variable rate tree structured vector quantization permits it to degrade gracefully if the rate is reduced at the encoder this has applications to the problem of buffer overflow

almost gibbsianness and parsimonious description of the decimated 2d ising model in this paper we complete and provide details for the existing characterizations of the decimation of the ising model on mathbb z 2 in the generalized gibbs context we first recall a few features of the dobrushin program of restoration of gibbsianness and present the construction of global specifications consistent with the extremal decimated measures we use them to prove that these renormalized measures are almost gibbsian at any temperature and to analyse in detail its convex set of dlr measures we also recall the weakly gibbsian description and complete it using a potential that admits a quenched correlation decay i e a well defined configuration dependent length beyond which this potential decays exponentially we use these results to incorporate these decimated measures in the new framework of parsimonious random fields that has been recently developed to investigate probability aspects related to neurosciences

average profile and limiting distribution for a phrase size in the lempel ziv parsing algorithm consider the parsing algorithm developed by lempel and ziv 1978 that partitions a sequence of length n into variable phrases blocks such that a new block is the shortest substring not seen in the past as a phrase in practice the following parameters are of interest number of phrases the size of a phrase the number of phrases of given size and so forth in this paper we focus on the size of a randomly selected phrase and the average number of phrases of a given size the so called average profile of phrase sizes these parameters can be efficiently analyzed through a digital search tree representation for a memoryless source with unequal probabilities of symbols generation the so called asymmetric bernoulli model we prove that the size of a typical phrase is asymptotically normally distributed with mean and variance explicitly computed in terms of digital search trees we prove the normal limiting distribution of the typical depth i e the length of a path from the root to a randomly selected node the latter finding is proved by a technique that belongs to the toolkit of the analytical analysis of algorithms and it seems to be novel in the context of data compression

infinite systems of interacting chains with memory of variable length a stochastic model for biological neural nets we consider a new class of non markovian processes with a countable number of interacting components at each time unit each component can take two values indicating if it has a spike or not at this precise moment the system evolves as follows for each component the probability of having a spike at the next time unit depends on the entire time evolution of the system after the last spike time of the component this class of systems extends in a non trivial way both the interacting particle systems which are markovian spitzer in adv math 5 246 290 1970 and the stochastic chains with memory of variable length which have finite state space rissanen in ieee trans inf theory 29 5 656 664 1983 these features make it suitable to describe the time evolution of biological neural systems we construct a stationary version of the process by using a probabilistic tool which is a kalikow type decomposition either in random environment or in space time this construction implies uniqueness of the stationary process finally we consider the case where the interactions between components are given by a critical directed erdos renyi type random graph with a large but finite number of components in this framework we obtain an explicit upper bound for the correlation between successive inter spike intervals which is compatible with previous empirical findings

cumulants of hawkes point processes we derive explicit closed form expressions for the cumulant densities of a multivariate self exciting hawkes point process generalizing a result of hawkes in his earlier work on the covariance density and bartlett spectrum of such processes to do this we represent the hawkes process in terms of a poisson cluster process and show how the cumulant density formulas can be derived by enumerating all possible family trees representing complex interactions between point events we also consider the problem of computing the integrated cumulants characterizing the average measure of correlated activity between events of different types and derive the relevant equations

on multirate optimality of jpeg2000 code stream arguably the most important and defining feature of the jpeg2000 image compression standard is its r d optimized code stream of multiple progressive layers this code stream is an interleaving of many scalable code streams of different sample blocks in this paper we reexamine the r d optimality of jpeg2000 scalable code streams under an expected multirate distortion measure emrd which is defined to be the average distortion weighted by a probability distribution of operational rates in a given range rather than for one or few fixed rates we prove that the jpeg2000 code stream constructed by embedded block coding of optimal truncation is almost optimal in the emrd sense for uniform rate distribution function even if the individual scalable code streams have nonconvex operational r d curves we also develop algorithms to optimize the jpeg2000 code stream for exponential and laplacian rate distribution functions while maintaining compatibility with the jpeg2000 standard both of our analytical and experimental results lend strong support to jpeg2000 as a near optimal scalable image codec in a fairly general setting

memory universal prediction of stationary random processes we consider the problem of one step ahead prediction of a real valued stationary strongly mixing random process xi sub i spl infin sup spl infin the best mean square predictor of x sub 0 is its conditional mean given the entire infinite past x sub i sub i spl infin sup 1 given a sequence of observations x sub 1 x sub 2 x sub n we propose estimators for the conditional mean based on sequences of parametric models of increasing memory and of increasing dimension for example neural networks and legendre polynomials the proposed estimators select both the model memory and the model dimension in a data driven fashion by minimizing certain complexity regularized least squares criteria when the underlying predictor function has a finite memory we establish that the proposed estimators are memory universal the proposed estimators which do not know the true memory deliver the same statistical performance rates of integrated mean squared error as that delivered by estimators that know the true memory furthermore when the underlying predictor function does not have a finite memory we establish that the estimator based on legendre polynomials is consistent

sieve bootstrap with variable length markov chains for stationary categorical time series a bootstrap for stationary categorical time series based on the method of sieves is studied here the data generating process is approximated by the so called variable length markov chain vlmc a flexible class of markov models that allows for parsimonious structure then the resampling is given by simulating from the fitted model it is shown that for a whole class of stationary categorical time series that is more general than vlmc the vlmc sieve has faster rate of convergence for variance estimation than the more general block bootstrap results are illustrated from a theoretical and empirical perspective for the latter a real data application about in homogeneity classification of a dna strand is also presented finally the vlmc sieve scheme enjoys an implementational advantage of using the plug in rule for bootstrapping a statistical procedure which generally is not the case for the block method

an alternate version of pirogov sinai theory a new approach to the pirogov sinai theory of phase transitions is developed not employing the contour models with a parameter the completeness of the phase diagram is proven

stability of nonlinear hawkes processes we address the problem of the convergence to equilibrium of a general class of point processes containing in particular the nonlinear mutually exciting point processes an extension of the linear hawkes processes and give general conditions guaranteeing the existence of a stationary version and the convergence to equilibrium of a nonstationary version both in distribution and in variation we also give a new proof of a result of kerstan concerning point processes with bounded intensity and general nonlinear dynamics satisfying a lipschitz condition

an o n algorithm for least squares quasi convex approximation this article is concerned with the approximation problem of fitting n data points by a quasi convex function using the least squares distance function an algorithm of o n worst case time complexity for computing a best fit is developed this problem arises in the context of curve fitting or statistical estimation

loss network representation of peierls contours we present a probabilistic approach for the study of systems with exclusions in the regime traditionally studied via cluster expansion methods in this paper we focus on its application for the gases of peierls contours found in the study of the ising model at low temperatures but most of the results are general we realize the equilibrium measure as the invariant measure of a loss network process whose existence is ensured by a subcriticality condition of a dominant branching process in this regime the approach yields besides existence and uniqueness of the measure properties such as exponential space convergence and mixing and a central limit theorem the loss network converges exponentially fast to the equilibrium measure without metastable traps this convergence is faster at low temperatures where it leads to the proof of an asymptotic poisson distribution of contours our results on the mixing properties of the measure are comparable to those obtained with duplicated variables expansion used to treat systems with disorder and coupled map lattices it works in a larger region of validity than usual cluster expansion formalisms and it is not tied to the analyticity of the pressure in fact it does not lead to any kind of expansion for the latter and the properties of the equilibrium measure are obtained without resorting to combinatorial or complexanalysis techniques

dynamics and synchronization of coupled self sustained electromechanical devices abstract the dynamics and synchronization of two coupled self excited devices are considered the stability and duration of the synchronization process between two coupled self sustained electrical oscillators described by the rayleigh duffing oscillator are first analyzed the properties of the hill equation and the whittaker method are used to derive the stability conditions of the synchronization process secondly the averaging method is used to find the amplitudes of the oscillatory states of the self sustained electromechanical device consisting of an electrical rayleigh duffing oscillator coupled magnetically to a linear mechanical oscillator the synchronization of two such coupled devices is discussed and the stability boundaries of the synchronization process are derived using the floquet theory and the hill s determinant good agreement is obtained between the analytical and numerical results

dobrushin kotecký shlosman theorem for polygonal markov fields in the plane we consider the so called length interacting arak surgailis polygonal markov fields with v shaped nodes a continuum and isometry invariant process in the plane sharing a number of properties with the two dimensional ising model for these polygonal fields we establish a low temperature phase separation theorem in the spirit of the dobrushin koteck shlosman theory with the corresponding wulff shape deteremined to be a disk due to the rotation invariant nature of the considered model as an important tool replacing the classical cluster expansion techniques and very well suited for our geometric setting we use a graphical construction built on contour birth and death process following the ideas of fernandez ferrari and garcia

universal modeling and coding the problems arising in the modeling and coding of strings for compression purposes are discussed the notion of an information source that simplifies and sharpens the traditional one is axiomatized and adaptive and nonadaptive models are defined with a measure of complexity assigned to the models a fundamental theorem is proved which states that models that use any kind of alphabet extension are inferior to the best models using no alphabet extensions at all a general class of so called first in first out fifo arithmetic codes is described which require no alphabet extension devices and which therefore can be used in conjunction with the best models because the coding parameters are the probabilities that define the model their design is easy and the application of the code is straightforward even with adaptively changing source models

chains with infinite connections uniqueness and markov representation if for a process xi n n infty infty the conditional distribution of n given the past does not depend on n for e g n 0 then the process may be called a chain with infinite connections under a well known continuity condition on this conditional distribution the process is shown to be distributed as an instantaneous function of a countable state markov chain also under a certain weaker continuity condition uniqueness of the distributions of the stationary chains is obtained

best quasi convex uniform approximation une fonction reelle bornee g sur 0 1 est quasiconvexe si on a g x max g s g t pour tous x s t tels que 0 s x s t 1 soit k l ensemble de ces fonctions quasiconvexes le probleme considere est celui de la meilleure approximation uniforme quasi convexe d une fonction continue f sur 0 1 c a d le probleme de trouver g k telle que f g inf f g g k

infinite dimensional srb measures we review the basic steps leading to the construction of a sinai ruelle bowen srb measure for an infinite lattice of weakly coupled expanding circle maps and we show that this measure has exponential decay of space time correlations first using the perron frobenius operator one connects the dynamical system of coupled maps on a d dimensional lattice to an equilibrium statistical mechanical model on a lattice of dimension d 1 this lattice model is for weakly coupled maps in a high temperature phase and we use a general but very elementary method to prove exponential decay of correlations at high temperatures

adaptive estimation for hawkes processes application to genome analysis the aim of this paper is to provide a new method for the detection of either favored or avoided distances between genomic events along dna sequences these events are modeled by a hawkes process the biological problem is actually complex enough to need a non asymptotic penalized model selection approach we provide a theoretical penalty that satisfies an oracle inequality even for quite complex families of models the consecutive theoretical estimator is

taming griffiths singularities infinite differentiability of quenched correlation functions we prove infinite differentiability of the magnetization and of all quenched correlation functions for disordered spin systems at high temperature or strong magnetic field in the presence of griffiths singularities we also show uniqueness of the gibbs state and exponential decay of truncated correlation functions with probability one our results are obtained through new simple modified high temperature or low activity expansions whose convergence can be displayed by elementary probabilistic arguments our results require no assumptions on the probability distributions of the random parameters except for the obvious one of no percolation of infinite couplings and in the strong field situation for the also obvious requirement that zero magnetic fields do not percolate

a universal data compression system a universal data compression algorithm is described which is capable of compressing long strings generated by a finitely generated source with a near optimum per symbol length without prior knowledge of the source this class of sources may be viewed as a generalization of markov sources to random fields moreover the algorithm does not require a working storage much larger than that needed to describe the source generating parameters

stochastically perturbed chains of variable memory in this paper we study inference for chains of variable order under two distinct contamination regimes consider a chain of variable memory on a finite alphabet containing zero at each instant of time an independent coin is flipped and if it turns head a contamination occurs in the first regime a zero is read independently of the value of the chain in the second regime the value of another chain of variable memory is observed instead of the original one our results state that the difference between the transition probabilities of the original process and the corresponding ones of the contaminated process may be bounded above uniformly moreover if the contamination probability is small enough using a version of the context algorithm we are able to recover the context tree of the original process through a contaminated sample

improved upper bounds for the contact process critical value the best known upper bound for the critical value c of the basic one dimensional contact process is 2 most techniques for finding bounds on critical values have the property that they can be modified in order to obtain improved bounds this seemed not to be the case for the approach which yielded c 2 for the basic contact process in this paper we propose a technique for generating better bounds in this context to illustrate its use we carry out the full program in one case with the conclusion that c 1 942

a unified approach to phase diagrams in field theory and statistical mechanics we construct the phase diagram of any system which admits a low temperature polymer or cluster expansion such an expansion turns the system into a hard core interacting contour model with small but not necessarily positive activities the method uses some of zahradnik s ideas z1 but applies equally well to systems with complex interactions we give two applications first to low temperaturep 2 models with complex couplings and second to a computation of asymptotics of partition functions in periodic volumes if the index of a supersymmetric field theory is known the second application would help determine the number of phases in infinite volume

cluster and virial expansions for the multi species tonks gas we consider a mixture of non overlapping rods of different lengths ell k moving in mathbb r or mathbb z our main result are necessary and sufficient convergence criteria for the expansion of the pressure in terms of the activities z k and the densities rho k this provides an explicit example against which to test known cluster expansion criteria and illustrates that for non negative interactions the virial expansion can converge in a domain much larger than the activity expansion in addition we give explicit formulas that generalize the well known relation between non overlapping rods and labelled rooted trees we also prove that for certain choices of the activities the system can undergo a condensation transition akin to that of the zero range process the key tool is a fixed point equation for the pressure

invariance under quasi isometries of subcritical and supercritical behavior in the boolean model of percolation in this work we study the poisson boolean model of percolation in locally compact polish metric spaces and we prove the invariance of subcritical and supercritical phases under mm quasi isometries more precisely we prove that if a metric space m is mm quasi isometric to another metric space n and the poisson boolean model in m exhibits any of the following a a subcritical phase b a supercritical phase or c a phase transition then respectively so does the poisson boolean model of percolation in n then we use these results in order to understand the phase transition phenomenon in a large family of metric spaces indeed we study the poisson boolean model of percolation in the context of riemannian manifolds in a large family of nilpotent lie groups and in cayley graphs also we prove the existence of a subcritical phase in gromov spaces with bounded growth at some scale

on the central limit theorem for stationary mixing random fields a simple proof of a central limit theorem for stationary random fields under mixing conditions is given generalizing some results obtained by more complicated methods e g bernstein s method

modeling cardiac pacemakers with relaxation oscillators abstract a modified van der pol oscillator model was designed in order to reproduce the time series of the action potential generated by a natural pacemaker of the heart i e the sa or the av node the main motivation was that the models published up to now were not altogether adequate for research on the heart based on either the classical van der pol oscillator or other nonlinear oscillators these models were interesting rather because of the physical phenomena that could be obtained chaos and synchronization however they were unable to simulate many important physiological features of true physiological action potentials we based our research on the experience of other groups which modeled neuronal oscillators there complex nonlinear oscillators were used whose most important feature was a certain topology of the phase space in our case we modified the phase space of the classical van der pol oscillator by adding two fixed points a saddle and a node in addition a damping term asymmetric with respect to the voltage was introduced introduction of these new features into the van der pol oscillator allowed to change the firing frequency of the pacemaker node without changing the length of the refractory period an important physiological detail we also show different ways of changing the pacemaker rhythm a comparison of the properties of the signal obtained from our model with the features of the action potentials measured by other groups is made

on lewis simulation method for point processes a simple and efficient method of simulation is discussed for point processes that are specified by their conditional intensities the method is based on the thinning algorithm which was introduced recently by lewis and shedler for the simulation of nonhomogeneous poisson processes algorithms are given for past dependent point processes containing multivariate processes the simulations are performed for some parametric conditional intensity functions and the accuracy of the simulated data is demonstrated by the likelihood ratio test and the minimum akaike information criterion aic procedure

chains of infinite order chains with memory of variable length and maps of the interval we show how to construct a topological markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order in particular we characterize the maps corresponding to stochastic chains with memory of variable length the problem treated here is the converse of the classical construction of the gibbs formalism for markov expanding maps of the interval

universal prediction of individual sequences the problem of predicting the next outcome of an individual binary sequence using finite memory is considered the finite state predictability of an infinite sequence is defined as the minimum fraction of prediction errors that can be made by any finite state fs predictor it is proven that this fs predictability can be achieved by universal sequential prediction schemes an efficient prediction procedure based on the incremental parsing procedure of the lempel ziv data compression algorithm is shown to achieve asymptotically the fs predictability some relations between compressibility and predictability are discussed and the predictability is proposed as an additional measure of the complexity of a sequence