a fast bit vector algorithm for approximate string matching based on dynamic programming the approximate string matching problem is to find all locations at which a query of length m matches a substring of a text of length n with k or fewer differences simple and practical bit vector algorithms have been designed for this problem most notably the one used in agrep these algorithms compute a bit representation of the current state set of the k difference automaton for the query and asymptotically run in either o nm w or o nm log s w time where w is the word size of the machine e g 32 or 64 in practice and s is the size of the pattern alphabet here we present an algorithm of comparable simplicity that requires only o nm w time by virtue of computing a bit representation of the relocatable dynamic programming matrix for the problem thus the algorithm s performance is independent of k and it is found to be more efficient than the previous results for many choices of k and small m moreover because the algorithm is not dependent on k it can be used to rapidly compute blocks of the dynamic programming matrix as in the 4 russians algorithm of wu et al 1996 this gives rise to an o kn w expected time algorithm for the case where m may be arbitrarily large in practice this new algorithm that computes a region of the dynamic progr amming d p matrx w entries at a time using the basic algorithm as a subroutine is significantly faster than our previous 4 russians algorithm that computes the same region 4 or 5 entries at a time using table lookup this performance improvement yields a code that is either superior or competitive with all existing algorithms except for some filtration algorithms that are superior when k m is sufficiently small

robust backstepping control of a class of nonlinear systems using fuzzy logic abstract fuzzy logic fl controllers for the robust back stepping control of a class of nonlinear systems in both continuous and discrete time are presented control action is employed to achieve tracking performance for unknown nonlinear system novel parameter tuning algorithms are obtained that are similar to modification in the case of continuous time adaptive control uniform ultimate boundedness of the tracking error and the fuzzy parameter estimates are presented without using the persistency of excitation pe condition initialization of the fuzzy parameters is straightforward simulation results justify the theoretical conclusions

the limits of sinai s simple random walk in random environment we study the sample path asymptotics of a class of recurrent diffusion processes with random potentials including examples of sinai s simple random walk in random environment and brox s diffusion process with brownian potential the main results consist of several integral criteria which completely characterize all the possible levy classes therefore providing a very precise image of the almost sure asymptotic behaviors of these processes

fuzzy h_ infty filter design for a class of nonlinear discrete time systems with multiple time delays this paper studies the fuzzy hinfin filter design problem for signal estimation of nonlinear discrete time systems with multiple time delays and unknown bounded disturbances first the takagi sugeno t s fuzzy model is used to represent the state space model of nonlinear discrete time systems with time delays next we design a stable fuzzy hinfin filter based on the t s fuzzy model which guarantees asymptotic stability and a prescribed hinfin index for the filtering error system irrespective of the time delays and uncertain disturbances a sufficient condition for the existence of such a filter is established by using the linear matrix inequality lmi approach the proposed lmi problem can be efficiently solved with global convergence guarantee using convex optimization techniques such as the interior point algorithm simulation examples are provided to illustrate the design procedure of the present method

moderate deviation principles for stochastic differential equations with jumps moderate deviation principles for stochastic differential equations driven by a poisson random measure prm in finite and infinite dimensions are obtained proofs are based on a variational representation for expected values of positive functionals of a prm

robust observer design for ito stochastic time delay systems via sliding mode control this paper deals with the output feedback sliding mode control for ito stochastic time delay systems the system states are unmeasured and the uncertainties are unmatched a sliding mode control scheme is proposed based on the state estimates by utilizing a novel switching function the derivative of the switching function is ensured to be finite variation it is shown that the sliding mode in the estimation space can be attained in finite time the sufficient condition for the asymptotic stability in probability of the overall closed loop stochastic system is derived finally a simulation example is shown to illustrate the proposed method

direct adaptive fuzzy control for nonlinear systems with time varying delays this paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict feedback systems with time varying delays based on the razumikhin function approach a novel adaptive fuzzy controller is designed the proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed loop system remain bounded different from the existing adaptive fuzzy control methodology the fuzzy logic systems are used to model the desired but unknown control signals rather than the unknown nonlinear functions in the systems as a result the proposed adaptive controller has a simpler form and requires fewer adaptation parameters

robust h_ infty control for nonlinear stochastic systems a sliding mode approach this paper considers the sliding mode control for nonlinear stochastic systems modeled by ito stochastic differential equations it is noted that there exist state and exogenous disturbance dependent noise in the controlled systems by utilizing h infin disturbance attenuation technique a novel sliding mode control method is proposed such that the resultant system is asymptotically stable in probability with a prescribed h infin performance sufficient conditions for the solvability of these problems are derived via nonlinear hamilton jacobi hj type inequalities moreover it is shown that for a class of special nonlinear stochastic systems the h infin sliding mode control design can be obtained by solving linear matrix inequalities lmis finally a numerical simulation example is given

analysis of chattering in systems with second order sliding modes a systematic approach to the chattering analysis in systems with second order sliding modes is developed the neglected actuator dynamics is considered to be the main cause of chattering in real systems the magnitude of oscillations in nonlinear systems with unmodeled fast nonlinear actuators driven by second order sliding mode control generalized suboptimal 2 smc g so algorithms is evaluated sufficient conditions for the existence of orbitally stable periodic motions are found in terms of the properties of corresponding poincare maps for linear systems driven by 2 smc g so algorithms analysis tools based on the frequency domain methods are developed the first of these techniques is based on the describing function method and provides for a simple approximate approach to evaluate the frequency and the amplitude of possible periodic motions the second technique represents a modified tsypkin s method and provides for a relatively simple theoretically exact approach to evaluate the periodic motion parameters examples of analysis and simulation results are given throughout this paper

approximate boyer moore string matching the boyer moore idea applied in exact string matching is generalized to approximate string matching two versions of the problem are considered the k mismatches problem is to find all approximate occurrences of a pattern string length m in a text string length n with at most k mismatches the generalized boyer moore algorithm is shown under a mild independence assumption to solve the problem in expected time o kn 1 m k k c where c is the size of the alphabet a related algorithm is developed for the k differences problem where the task is to find all approximate occurrences of a pattern in a text with leqslant k differences insertions deletions changes experimental evaluation of the algorithms is reported showing that the new algorithms are often significantly faster than the old ones both algorithms are functionally equivalent with the horspool version of the boyer moore algorithm when k 0

adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems an adaptive fuzzy control approach is proposed for a class of multiple input multiple output mimo nonlinear systems with completely unknown nonaffine functions the mimo systems are composed of n subsystems and each of subsystems is in the nested lower triangular form it is difficult and complicated to control this class of systems due to the existence of unknown nonaffine functions and the couplings among the nested subsystems this difficulty is overcome by introducing some special type lyapunov functions and taking advantage of the mean value theorem the backstepping design method and the approximation property of the fuzzy systems the proposed control approach can guarantee that all the signals in the closed loop system are bounded a simulation experiment is utilized to verify the feasibility of the proposed approach

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

filtering and fault detection for nonlinear systems with polynomial approximation this paper is concerned with polynomial filtering and fault detection problems for a class of nonlinear systems subject to additive noises and faults the nonlinear functions are approximated with polynomials of a chosen degree different from the traditional methods the approximation errors are not discarded but formulated as low order polynomial terms with norm bounded coefficients the aim of the filtering problem is to design a least squares filter for the formulated nonlinear system with uncertain polynomials and an upper bound of the filtering error covariance is found and subsequently minimized at each time step the desired filter gain is obtained by recursively solving a set of riccati like matrix equations and the filter design algorithm is therefore applicable for online computation based on the established filter design scheme the fault detection problem is further investigated where the main focus is on the determination of the threshold on the residual due to the nonlinear and time varying nature of the system under consideration a novel threshold is determined that accounts for the noise intensity and the approximation errors and sufficient conditions are established to guarantee the fault detectability for the proposed fault detection scheme comparative simulations are exploited to illustrate that the proposed filtering strategy achieves better estimation accuracy than the conventional polynomial extended kalman filtering approach the effectiveness of the associated fault detection scheme is also demonstrated

new results on delay dependent robust stability criteria of uncertain fuzzy systems with state and input delays this paper focuses on the delay dependent stability analysis and stabilization for uncertain t s fuzzy control systems with state and input delays the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology in fact these techniques lead to more general and less conservative stability conditions that guarantee a wide stability region our delay dependent stability conditions thus obtained are given in terms of linear matrix inequalities lmis finally some examples are included to show that the proposed criteria improve the existing results significantly

fuzzy adaptive robust backstepping stabilization for siso nonlinear systems with unknown virtual control direction in this paper a direct fuzzy adaptive robust control approach is proposed for a class of siso nonlinear systems with completely unknown virtual control directions unknown nonlinearities unmodeled dynamics and dynamic disturbances in the backstepping recursive design fuzzy logic systems are employed to approximate the combined nonlinear uncertainties a dynamic signal and nussbaum gain technique are introduced into the control scheme to dominate the dynamic uncertainties and solve the unknown signs of virtual control directions respectively it is proved that the proposed robust fuzzy adaptive scheme can guarantee the all signals in the closed loop system are semi globally uniformly ultimately bounded the effectiveness of the proposed approach is illustrated via three examples

on slowdown and speedup of transient random walks in random environment we consider one dimensional random walks in random environment which are transient to the right our main interest is in the study of the sub ballistic regime where at time n the particle is typically at a distance of order o n from the origin kappa in 0 1 we investigate the probabilities of moderate deviations from this behaviour specifically we are interested in quenched and annealed probabilities of slowdown at time n the particle is at a distance of order o n nu 0 from the origin nu 0 in 0 kappa and speedup at time n the particle is at a distance of order n nu 1 from the origin nu 1 in kappa 1 for the current location of the particle and for the hitting times also we study probabilities of backtracking at time n the particle is located around n thus making an unusual excursion to the left for the slowdown our results are valid in the ballistic case as well

state observer based adaptive fuzzy output feedback control for a class of uncertain nonlinear systems this paper aims to develop state observer based adaptive fuzzy control techniques for controlling a class of uncertain nonlinear systems with bounded external disturbances an adaptive fuzzy observer is proposed to estimate the system state variables it is shown that the observation errors obtained from the observer are uniformly ultimately bounded applying the estimated system state for design of an output feedback controller the uniformly ultimate boundedness of the tracking errors for the resulting closed loop system can be guaranteed a typical robot arm system is employed in our simulation studies and the results demonstrate the usefulness and effectiveness of the proposed techniques for controlling nonlinear systems with bounded external disturbances

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

a sliding mode approach to stabilization of nonlinear markovian jump singularly perturbed systems this paper presents a sliding mode control smc method for a class of nonlinear markovian jump singularly perturbed systems mjspss the system is subject to parameter uncertainties and partly unknown transition probabilities to fully employ the model characteristics of such a hybrid system a novel integral type switching function is firstly designed by adopting the e dependent stochastic lyapunov function method sufficient conditions are presented to ensure the mean square asymptotic stability of the sliding mode dynamics a mode dependent fuzzy smc law is then synthesized to induce and maintain the sliding motion despite partly unknown transition probabilities and parameter uncertainties finally the developed method is applied to stabilize a modified series dc motor system

moderate deviations for diffusions with brownian potentials we present precise moderate deviation probabilities in both quenched and annealed settings for a recurrent diffusion process with a brownian potential our method relies on fine tools in stochastic calculus including kotani s lemma and lamperti s representation for exponential functionals in particular our result for quenched moderate deviations is in agreement with a recent theorem of comets and popov probab theory related fields 126 2003 571 609 who studied the corresponding problem for sinai s random walk in random environment

a new filtration method and a hybrid strategy for approximate string matching in this paper we propose a new filtration algorithm as well as a hybrid filtration strategy to efficiently solve the approximate string matching problem also called k differences problem which aims to find all the positions i s in a given text such that there exists a substring of the text ending at position i whose edit distance from a given pattern is less than or equal to a given error bound k our experimental results on simulated datasets of dna sequences show that our filtration algorithm has better performance on the efficiency to filter out those positions of the text at which the pattern does not occur approximately moreover our hybrid filtration strategy further improves the performance efficiency of our filtration algorithm greatly when the ratio of the error bound and the pattern size is about 0 2

robust adaptive critic control of nonlinear systems using fuzzy basis function networks an lmi approach abstract this paper proposes an adaptive critic tracking control design for a class of nonlinear systems using fuzzy basis function networks fbfns the key component of the adaptive critic controller is the fbfn which implements an associative learning network aln to approximate unknown nonlinear system functions and an adaptive critic network acn to generate the internal reinforcement learning signal to tune the aln another important component the reinforcement learning signal generator requires the solution of a linear matrix inequality lmi which should also be satisfied to ensure stability furthermore the robust control technique can easily reject the effects of the approximation errors of the fbfn and external disturbances unlike traditional adaptive critic controllers that learn from trial and error interactions the proposed on line tuning algorithm for aln and acn is derived from lyapunov theory thereby significantly shortening the learning time simulation results of a cart pole system demonstrate the effectiveness of the proposed fbfn based adaptive critic controller

analysis and design of integral sliding manifolds for systems with unmatched perturbations the robustness properties of integral sliding mode controllers are studied this note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal it is also shown that when the minimum is attained the resulting perturbation is not amplified this selection is particularly useful if integral sliding mode control is to be combined with other methods to further robustify against unmatched perturbations h sub spl infin is taken as a special case simulations support the general analysis and show the effectiveness of this particular combination

rates of convergence of diffusions with drifted brownian potentials we are interested in the asymptotic behaviour of a diffusion process with drifted brownian potential the model is a continuous time analogue to the random walk in random environment studied in the classical paper of kesten kozlov and spitzer we not only recover the convergence of the diffusion process which was previously established by kawazu and tanaka but also obtain all the possible convergence rates an interesting feature of our approach is that it shows a clear relationship between drifted brownian potentials and bessel processes

the most visited site of brownian motion and simple random walk let l t x be the local time at x for brownian motion and for each t let bar v t inf x underline underline 0 l t x vee l t x mathop sup limits y l t y the absolute value of the most visited site for brownian motion up to time t in this paper we prove that v t is transient and obtain upper and lower bounds for the rate of growth of v t the main tools used are the ray knight theorems and william s path decomposition of a diffusion an invariance principle is used to get analogous results for simple random walks we also obtain a law of the iterated logarithm for v t

a one dimensional diffusion process in a wiener medium we consider a one dimensional diffusion process in a random medium which is itself generated by a wiener process the asymptotic behaviour is investigated using the self similarity of the medium process the results are analogous to the lattice case

annealed tail estimates for a brownian motion in a drifted brownian potential we study brownian motion in a drifted brownian potential kawazu and tanaka j math soc japan 49 1997 189 211 exhibited two speed regimes for this process depending on the drift they supplemented these laws of large numbers by central limit theorems which were recently completed by hu shi and yor trans amer math soc 351 1999 3915 3934 using stochastic calculus we studied large deviations ann probab 29 2001 1173 1204 showing among other results that the rate function in the annealed setting that is after averaging over the potential has a flat piece in the ballistic regime in this paper we focus on this subexponential regime proving that the probability of deviating below the almost sure speed has a polynomial rate of decay and computing the exponent in this power law this provides the continuous time analogue of what dembo peres and zeitouni proved for the transient random walk in random environment comm math phys 181 1996 667 683 our method takes a completely different route making use of lamperti s representation together with an iteration scheme

robust integral sliding mode control for uncertain stochastic systems with time varying delay this paper is concerned with sliding mode control for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system an integral sliding surface is first constructed then by means of linear matrix inequalities lmis a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties the synthesized sliding mode controller guarantees the reachability of the specified sliding surface finally a simulation example is presented to illustrate the proposed method

sliding mode filter design for nonlinear polynomial systems with unmeasured states this paper addresses the mean square and mean module filtering problems for a nonlinear polynomial stochastic system with gaussian white noises the obtained solutions contain a sliding mode term signum of the innovations process it is shown that the designed sliding mode mean square filter generates the mean square estimate which has the same minimum estimation error variance as the estimate given by the conventional mean square polynomial filter basin et al 2008 8 although the gain matrices of both filters are different the designed sliding mode mean module filter generates the mean module estimate which yields a better value of the mean module criterion in comparison to the conventional mean square polynomial filter the theoretical result is complemented with an illustrative example verifying performance of the designed filters it is demonstrated that the estimates produced by the designed sliding mode mean square filter and the conventional mean square polynomial filter yield the same estimation error variance and there is an advantage in favor of the designed sliding mode mean module filter

limit law for transition probabilities and moderate deviations for sinai s random walk in random environment we consider a one dimensional random walk in random environment in the sinai s regime our main result is that logarithms of the transition probabilities after a suitable rescaling converge in distribution as time tends to infinity to some functional of the brownian motion we compute the law of this functional when the initial and final points agree also among other things we estimate the probability of being at time t at distance at least z from the initial position when z is larger than ln2t but still of logarithmic order in time

new delay dependent non fragile h observer based control for continuous time delay systems the problem of the delay dependent non fragile h observer based control for a class of continuous time delay systems is investigated in this paper the additive gain variations under consideration are contained in both the controller gain and obhsiunserver gain delay dependent criteria are derived to guarantee the stability of the non fragile h observer based control system using the lyapunov functional approach the controller and observer gains are given from the lmi feasible solutions based on the result of this paper the constraint of matrix equality is not necessary for designing the non fragile h observer based controls computer software matlab can be applied to solve all the proposed results finally a numerical example is illustrated to show the improvement of this paper

state estimation and sliding mode control for semi markovian jump systems with mismatched uncertainties this paper is concerned with the state estimation and sliding mode control problems for phase type semi markovian jump systems using a supplementary variable technique and a plant transformation a finite phase type semi markov process has been transformed into a finite markov chain which is called its associated markov chain as a result phase type semi markovian jump systems can be equivalently expressed as its associated markovian jump systems a sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated markovian jump systems satisfy the reaching condition moreover an observer based sliding mode control problem is investigated sufficient conditions are established for the solvability of the desired observer two numerical examples are presented to show the effectiveness of the proposed design techniques

large deviations for a brownian motion in a drifted brownian potential we derive a large deviation principle both quenched and annealed for a one dimensional diffusion process in a drifted brownian environment providing the continuous time analogue of what comets gantert and zeitouni recently establish for the random walk in random environment a key ingredient kotani s lemma allows us to compute the corresponding rate functions the results are more explicit than in the discrete time setting

robust control for a class of uncertain nonlinear systems adaptive fuzzy approach based on backstepping a robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances the controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique for each auxiliary system an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well it is shown that the resulting closed loop systems guarantee a satisfactory transient and asymptotic performance a simulation example is also presented to illustrate the design procedure and controller performance

h sliding mode control for uncertain neutral type stochastic systems with markovian jumping parameters this paper is devoted to the investigation of h sliding mode control smc for uncertain neutral stochastic systems with markovian jumping parameters and time varying delays a sliding surface functional is firstly constructed then the sliding mode control law is designed to guarantee the reachability of the sliding surface in a finite time interval the sufficient conditions for asymptotically stochastic stability of sliding mode dynamics with a given disturbance attenuation level are presented in terms of linear matrix inequalities lmis finally an example is provided to illustrate the efficiency of the proposed method

event triggered filtering and fault estimation for nonlinear systems with stochastic sensor saturations abstractthis paper is concerned with the filtering problem for a class of nonlinear systems with stochastic sensor saturations and event triggered measurement transmissions an event triggered transmission scheme is proposed with hope to ease the traffic burden and improve the energy efficiency the measurements are subject to randomly occurring sensor saturations governed by bernoulli distributed sequences special effort is made to obtain an upper bound of the filtering error covariance in the presence of linearisation errors stochastic sensor saturations as well as event triggered transmissions a filter is designed to minimise the obtained upper bound at each time step by solving two sets of riccati like matrix equations and thus the recursive algorithm is suitable for online computation sufficient conditions are established under which the filtering error is exponentially bounded in mean square the applicability of the presented method is demonstrated by dealing with the fault estimation problem

robust sliding mode control for uncertain time delay systems an lmi approach this note is devoted to robust sliding mode control for time delay systems with mismatched parametric uncertainties a delay independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities based on which the corresponding reaching motion controller is also developed the results are illustrated by an example

an observer based approach to controlling time delay chaotic systems via takagi sugeno fuzzy model this study presents a fuzzy model based control criterion for time delay chaotic systems with uncertainty the takagi sugeno t s fuzzy model is adopted for representing a chaotic system possessing a time delay a unified approach for designing a fuzzy observer which integrates parallel distributed compensation with an adaptive updating method is first discussed an observer based fuzzy control scheme is then developed to deal with stabilization and tracking problems based on lyapunov stability analysis sufficient conditions that ensure robust control performance of time delay chaotic systems are derived these conditions are represented in terms of linear matrix inequalities and adaptive updating laws finally the proposed approach is validated through numerical synchronization stabilization and model tracking control simulations

random walkers in one dimensional random environments exact renormalization group analysis sinai s model of diffusion in one dimension with random local bias is studied by a real space renormalization group which yields exact results at long times the effects of an additional small uniform bias force are also studied we obtain analytically the scaling form of the distribution of the position x t of a particle the probability of it not returning to the origin and the distributions of first passage times in an infinite sample as well as in the presence of a boundary and in a finite but large sample we compute the distribution of the meeting time of two particles in the same environment we also obtain a detailed analytic description of the thermally averaged trajectories by computing quantities such as the joint distribution of the number of returns and of the number of jumps forward these quantities obey multifractal scaling characterized by generalized persistence exponents ensuremath theta g which we compute in the presence of a small bias the number of returns to the origin becomes finite characterized by a universal scaling function which we obtain the full statistics of the distribution of successive times of return of thermally averaged trajectories is obtained as well as detailed analytical information about correlations between directions and times of successive jumps the two time distribution of the positions of a particle x t and x t ensuremath with tg t ensuremath is also computed exactly it is found to exhibit aging with several time regimes characterized by different behaviors in the unbiased case for t ensuremath t ensuremath ensuremath sim t ensuremath ensuremath alpha with ensuremath alpha g1 it exhibits a mathrm ln t mathrm ln t ensuremath scaling with a singularity at coinciding rescaled positions x t x t ensuremath this singularity is a novel feature and corresponds to particles that remain in a renormalized valley for closer times ensuremath alpha l1 the two time diffusion front exhibits a quasiequilibrium regime with a mathrm ln t ensuremath t ensuremath mathrm ln t ensuremath behavior which we compute the crossover to a t t ensuremath aging form in the presence of a small bias is also obtained analytically rare events corresponding to intermittent splitting of the thermal packet between separated wells which dominate some averaged observables are also characterized in detail connections with the green function of a one dimensional schr odinger problem and quantum spin chains are discussed