a network algorithm for performing fisher s exact test in r c contingency tables abstract an exact test of significance of the hypothesis that the row and column effects are independent in an r c contingency table can be executed in principle by generalizing fisher s exact treatment of the 2 2 contingency table each table in a conditional reference set of r c tables with fixed marginal sums is assigned a generalized hypergeometric probability the significance level is then computed by summing the probabilities of all tables that are no larger on the probability scale than the observed table however the computational effort required to generate all r c contingency tables with fixed marginal sums severely limits the use of fisher s exact test a novel technique that considerably extends the bounds of computational feasibility of the exact test is proposed here the problem is transformed into one of identifying all paths through a directed acyclic network that equal or exceed a fixed length some interesting new optimization theorems are developed in the process the numer

transient properties of a bistable kinetic model with correlations between additive and multiplicative noises mean first passage time the transient properties of a bistable system with correlations between additive and multiplicative noise terms are investigated the explicit expressions of the mean first passage time mfpt are obtained the numerical computations show that the mfpt of the system is affected by ensuremath lambda the strength of correlations between additive intensity ensuremath alpha and multiplicative intensity d noise terms for the case of perfectly correlated noises ensuremath lambda 1 the mfpt corresponding to ensuremath alpha ensuremath gtrsim d and ensuremath alpha d exhibits very different behaviors and the mfpt for ensuremath alpha d diverges to infinity textcopyright 1996 the american physical society

stochastic system with colored correlation between white noise and colored noise abstract a stochastic system with colored correlation between white noise and colored noise is investigated theoretically a general fokker planck equation of the system is derived by using a standard method we discuss a bistable system with colored correlation between additive white noise and multiplicative colored one it is found that the effects of the correlation time of multiplicative colored noise on the statistical properties of the bistable system are different from those of the correlation time of the correlation between additive white noise and multiplicative colored noise on the statistical properties of the bistable system

rate of quantum ergodicity in euclidean billiards for a large class of quantized ergodic flows the quantum ergodicity theorem states that almost all eigenfunctions become equidistributed in the semiclassical limit in this work we give a short introduction to the formulation of the quantum ergodicity theorem for general observables in terms of pseudodifferential operators and show that it is equivalent to the semiclassical eigenfunction hypothesis for the wigner function in the case of ergodic systems of great importance is the rate by which the quantum mechanical expectation values of an observable tend to their mean value this is studied numerically for three euclidean billiards stadium cosine and cardioid billiard using up to 6000 eigenfunctions we find that in configuration space the rate of quantum ergodicity is strongly influenced by localized eigenfunctions such as bouncing ball modes or scarred eigenfunctions we give a detailed discussion and explanation of these effects using a simple but powerful model for the rate of quantum ergodicity in momentum space we observe a slower decay we also study the suitably normalized fluctuations of the expectation values around their mean and find good agreement with a gaussian distribution

small delay approximation of stochastic delay differential equations delay differential equations evolve in an infinite dimensional phase space in this paper we consider the effect of external fluctuations noise on delay differential equations involving one variable thus leading to univariate stochastic delay differential equations sdde s for small delays a univariate nondelayed stochastic differential equation approximating such a sdde is presented another approximation complementary to the first is also obtained using an average of the sdde s drift term over the delayed dynamical variable which defines a conditional average drift this second approximation is characterized by the fact that the diffusion term is identical to that of the original sdde for small delays our approach yields a steady state probability density and a conditional average drift which are in close agreement with numerical simulations of the original sdde we illustrate this scheme with the delayed linear langevin equation and a stochastic version of the delayed logistic equation the technique can be used with any type of noise and is easily generalized to multiple delays s1063 651x 99 08304 x

polynomial time counting and sampling of two rowed contingency tables in this paper a markov chain for contingency tables with two rows is defined the chain is shown to be rapidly mixing using the path coupling method we prove an upper bound for the mixing time of the chain the upper bound is quadratic in the number of columns and linear in the logarithm of the table sum by considering a specific problem we prove a lower bound for the mixing time of the chain the lower bound is quadratic in the number of columns and linear in the logarithm of the number of columns a fully polynomial randomised approximation scheme for this problem is described

effect of non gaussian noise sources in a noise induced transition here we study a noise induced transition when the system is driven by a noise source taken as colored and non gaussian we show using both a theoretical approximation and numerical simulations that there is a shift of the transition as the noise departs from the gaussian behavior also we confirm the reentrance effect found for colored gaussian noise and show the behavior of the transition line in the phase like diagram as the noise departs from gaussianity in the large correlation time limit

a fast procedure for model search in multidimensional contingency tables summary a procedure to select the simplest acceptable models for a multidimensional contingency table is proposed it is based on two rules first that if a model is accepted then all models that include it are considered to be accepted and secondly that if a model is rejected then all its submodels are considered to be rejected two versions are described one for the class of graphical models and the other for the class of hierarchical log linear models application of both versions to a six dimensional table is illustrated the procedure can be regarded as an alternative to fitting all possible models made computationally feasible by application of the two rules it is a generalization of the procedure proposed by havr anek 1984 but is in many cases considerably faster

symbolic dynamics and periodic orbits for the cardioid billiard the periodic orbits of the strongly chaotic cardioid billiard are studied by introducing a binary symbolic dynamics the corresponding partition is mapped to a topologically well ordered symbol plane in the symbol plane the pruning front is obtained from orbits running either into or through the cusp we show that all periodic orbits correspond to maxima of the lagrangian and give a complete list up to code length 15 the symmetry reduction is done on the level of the symbol sequences and the periodic orbits are classified using symmetry lines we show that there exists an infinite number of families of periodic orbits accumulating in length and that all other families of geometrically short periodic orbits eventually get pruned all these orbits are related to finite orbits starting and ending in the cusp we obtain an analytical estimate of the kolmogorov sinai entropy and find a good agreement with the numerically calculated value and the one obtained by averaging periodic orbits furthermore the statistical properties of periodic orbits are investigated

colored multiplicative and additive non gaussian noise driven dynamical system mean first passage time abstract we have studied the barrier crossing dynamics in presence of non gaussian noises it has been observed that multiplicative colored non gaussian noise can induce resonant activation ra the conspicuous dependence of mean first passage time mfpt on correlation time 2 of additive colored noise having fixed variance have been analyzed beyond a critical value of 2 the mfpt increases for a given rate of increase of noise strength with 2 if the additive colored noise is non gaussian the mfpt first decreases with increase of the non gaussian parameter measures deviation from gaussian character of multiplicative colored noise followed by an increase exhibiting a minimum the appearance of the minimum critically depends on the additive noise

influence of strong noise on the decline and propagation of population in the delayed malthus verhulst model abstract the effects of strong noise on the decline and propagation processes of a population in the malthus verhulst model with time delay are investigated by a stochastic simulation time delays in two different processes are concurrent in ecosystems the simulation results indicate that the stability of the population is enhanced by the decreasing multiplicative noise intensity and the increasing delay time the replacement of old individuals with young ones is accelerated by an increasing multiplicative noise intensity an increasing additive noise intensity and a decreasing delay time an increasing multiplicative noise intensity will drive the population of species to fluctuate more largely

saturation of number variance in embedded random matrix ensembles we study fluctuation properties of embedded random matrix ensembles of noninteracting particles for ensemble of two noninteracting particle systems we find that unlike the spectra of classical random matrices correlation functions are nonstationary in the locally stationary region of spectra we study the number variance and the spacing distributions the spacing distributions follow the poisson statistics which is a key behavior of uncorrelated spectra the number variance varies linearly as in the poisson case for short correlation lengths but a kind of regularization occurs for large correlation lengths and the number variance approaches saturation values these results are known in the study of integrable systems but are being demonstrated for the first time in random matrix theory we conjecture that the interacting particle cases which exhibit the characteristics of classical random matrices for short correlation lengths will also show saturation effects for large correlation lengths

approximate fokker planck equation of system driven by multiplicative colored noises with colored cross correlation abstract using the hanggi ansatz to truncate the evolution equation for probability density an approximate fokker planck equation afpe is derived this afpe is valid for one dimensional general systems driven by two multiplicative colored noises 1 0 and 2 0 that are correlated in color 3 0 under the condition for 1 2 and 3 to satisfy some inequalities we apply this afpe to a symmetrical bistable potential system driven by a colored multiplicative noise and a white additive noise with white cross correlation to verify the validity of our analytical approximation the numerical simulations for this system is performed we discovered a new phenomenon that the symmetry of stationary probability density broken by the correlation between the noises can be gradually recovered as the noise self correlation time is increased

algebraic algorithms for sampling from conditional distributions we construct markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic examples include contingency tables logistic regression and spectral analysis of permutation data the algorithms involve computations in polynomial rings using grobner bases

bistable kinetic model driven by correlated noises steady state analysis a simple rule to obtain the fokker planck equation for a general one dimensional system driven by correlated gaussian white noises is proved by the functional method the fokker planck equation obtained in this paper is applied to the bistable kinetic model we find the following for the steady state 1 in the ensuremath alpha d parameter plane ensuremath alpha is the strength of the additive noise and d is the multiplicative noise strength the critical curve separating the unimodal and bimodal regions of the stationary probability distribution spd of the model is shown to be affected by ensuremath lambda the degree of correlation of the noises as ensuremath lambda is increased the area of the bimodal region in the ensuremath alpha d plane is contracted 2 when we take a point fixed in the ensuremath alpha d plane and increase ensuremath lambda the form of the spd changes from a bimodal to a unimodal structure 3 the positions of the extreme value of the spd of the model sensitively depend on the strength of the multiplicative noise and weakly depend on the additive noise strength 4 for ensuremath lambda 1 the case of perfectly correlated noises when the parameters ensuremath alpha and d take values in the neighborhood of the line ensuremath alpha d in the ensuremath alpha d plane the spd s corresponding to the points ensuremath alpha dg1 and ensuremath alpha d1 exhibit a very different shape of divergence therefore the ratio ensuremath alpha d 1 plays the role of a critical ratio

enhancement of stochastic resonance the role of non gaussian noises abstract we have analyzed the phenomenon of stochastic resonance in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation that enables us to get through the two state theory analytical expressions for the signal to noise ratio finding an enhancement of this quantity when the system departs from gaussian behavior this finding is supported by extensive numerical simulations we discuss the relation of these results to some experiments in sensory systems

stochastic resonance in time delayed bistable systems driven by weak periodic signal abstract we study theoretically a bistable system with time delayed feedback driven by a weak periodic force the effective potential function and the steady state probability density are derived the delay time and the strength of its feedback can change the shapes of the potential wells in the adiabatic approximation the signal to noise ratio snr of the system with a weak periodic force is obtained the time delayed feedback modulates the magnitude of snr by changing the shape of the potential and the effective strength of the signal the maximum of snr decreases with increasing the feedback intensity when is negative or positive the time delay can suppress or promote the stochastic resonance phenomenon

synchronization induced by periodic inputs in finite n unit bistable langevin models the augmented moment method we have studied the synchronization induced by periodic inputs applied to a finite n unit coupled bistable langevin model which is subjected to cross correlated additive and multiplicative noises the effects on the synchronization of the system size n the coupling strength and the cross correlation between additive and multiplicative noise have been investigated using the semi analytical augmented moment method amm which is a second order moment approximation for local and global variables h hasegawa phys rev e 67 2003 041903 a linear analysis of the stationary solution of the amm equations shows that the stability is improved degraded by positive negative couplings results of the nonlinear bistable langevin model are compared to those of the linear langevin model

response probability density functions of duffing van der pol vibro impact system under correlated gaussian white noise excitations abstract this paper aims to investigate the stationary probability density functions pdfs of a duffing van der pol vibro impact system excited by correlated gaussian white noise with the help of non smooth transformation the stationary pdfs are formulated analytically by the stochastic averaging of energy envelope the analytical results are verified by numerical simulation results stochastic bifurcations for different parameters are considered and several special pdf forms are observed in this paper the first form is the shape of the pdf of total energy can be similar to a crater which has a minimum and a maximum the second one is the shape of the joint pdf with three peaks that is to say the section of joint pdf has three maximum and two minimum in addition the influence of the degree of the correlation of gaussian white noises is explored

a moment approach to non gaussian colored noise abstract the langevin system subjected to non gaussian colored noise has been discussed by using the second order moment approach with two kinds of models for generating the noise we have derived the effective differential equation de for a variable x from which the stationary probability distribution p x has been calculated with the use of the fokker planck equation the result of p x calculated by the moment method is compared to several expressions obtained by different methods such as the universal colored noise approximation ucna jung and hanggi phys rev a 35 1987 4464 and the functional integral method it has been shown that our p x is in good agreement with that of direct simulations dss we have also discussed dynamical properties of the model with an external input solving des in the moment method

stochastic resonance nonperturbative calculation of power spectra and residence time distributions we examine the response of a finite temperature two state system to periodic driving using time dependent transition rate theory this system can exhibit the phenomenon of stochastic resonance where raising the temperature increases the signal to noise ratio of the response we obtain the power spectrum and the distribution of residence times nonperturbatively for any transition rates that are periodic in time given the drive period mathit t mathit s the power spectrum is the fourier transform of the sum of signal which is periodic in time with period mathit t mathit s and noise which is the product of an exponential and a function periodic with period mathit t mathit s the residence time distribution is the product of an exponential and a function that is periodic with period mathit t mathit s both the power spectrum and the residence time distribution can be calculated exactly given the dependence of the transition rates on the control parameter e g asymmetry or temperature we calculate the characteristics of stochastic resonance for a two state system with activated transition rates and for a quantum mechanical dissipative two level system

spectral fluctuations of billiards with mixed dynamics from time series to superstatistics a statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards one with mushroomlike shape and the other from the family of the limacon billiards is presented these billiards have mixed regular chaotic dynamics but different structures in their classical phase spaces the spectrum of each billiard is represented as a time series where the level order plays the role of time two most important findings follow from the time series analysis first the spectra can be characterized by two distinct relaxation lengths this is a prerequisite for the validity of the superstatistical approach which is based on the folding of two distribution functions second the shape of the resulting probability density function of the so called superstatistical parameter is reasonably approximated by an inverse chi2 distribution this distribution is used to compute nearest neighbor spacing distributions and compare them with those of the resonance frequencies of billiards with mixed dynamics within the framework of superstatistics the obtained spacing distribution is found to present a good description of the experimental ones and is of the same or even better quality as a number of other spacing distributions including the one from berry and robnik however in contrast to other approaches toward a theoretical description of spectral properties of systems with mixed dynamics superstatistics also provides a description of properties of the eigenfunctions in terms of a superstatistical generalization of the porter thomas distribution indeed the inverse chi2 parameter distribution is found suitable for the analysis of experimental resonance strengths in the limacon billiards within the framework of superstatistics

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

asymmetric bistable systems subject to periodic and stochastic forcing in the strongly nonlinear regime switching time distributions a detailed theoretical analysis of the dynamics of a sinusoidally driven noisy asymmetric bistable system is presented the results are valid for any two state system however the specific case of the duffing potential is considered in detail the dynamics are considered in the weak noise limit i e when the response of the system to the external periodic field is strongly nonlinear the system asymmetry is created by a nonzero dc component of the external force and manifests itself as an asymmetry between the mean switching times between the potential wells we obtain explicit analytic expressions for the whole hierarchy of switching time distributions including the residence time and return time distributions we also obtain expressions for the average residence times and describe how they depend on asymmetry together with an explicit expression for the difference between the residence times in the weak noise limit the results are presented in the context of using the switching dynamics to detect weak dc target signals

stochastic resonance in discrete kinetics with delay abstract multiplicative stochastic resonance in linear systems with delay is studied for the discrete case the overdamped linear system with symmetric multiplicative markovian dichotomous noise dn is considered the stability range of the solutions for different values of delay is analyzed the maximum of the signal to noise ratio is observed as a function of the noise intensity

effective markovian approximation for non gaussian noises a path integral approach abstract we have analyzed diffusion in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation to the initially non markovian problem such an approximation allows us to get analytical expressions for the mean first passage time that has been tested against extensive numerical simulations

internal fluctuations period doubling and chemical chaos the effects of internal molecular fluctuations on period doubling bifurcations and chaotic band merging are studied in a well stirred reactive chemical system where spatial degrees of freedom play no role the calculations are carried out using a stochastic model based on reactive lattice gas cellular automata molecular fluctuations arising from reactive collisions are incorporated in the model and the mass action rate equations are recovered in the mean field limit large system sizes can be studied and permit the investigation of the internal noise scaling structure in the periodic and chaotic regimes for the willamowski r ossler system the noise scaling exponent is consistent with that found for one dimensional quadratic maps subject to external noise the model provides a means to study small non equilibrium reacting systems where fluctuations may not be neglected

testing for independence in a two way table new interpretations of the chi square statistic the classical chi square test for independence in a two way contingency table often rejects the independence hypothesis at an extremely small significance level particularly when the sample size is large this paper proposes some alternative distributions to independence to help interpret the chi 2 statistic in such situations the uniform alternative in which every possible contingency table of the given dimension and sample size receives equal probability leads to the volume test as originally suggested in a regression context by h hotelling exponential family theory is used to generate a class of intermediate alternatives between independence and uniformity leading to a random effects model for contingency tables

on reducible nonlinear time delayed stochastic systems fluctuation dissipation relations transitions to bistability and secondary transitions to non stationarity we show the conditions under which nonlinear time delayed dynamical systems with multiplicative noise sources can be transformed into linear time delayed systems with additive noise sources we show that for such reducible systems analytical expressions for stationary distributions can be obtained we demonstrate that fluctuation dissipation relations of reducible systems become trivial and we show that reducible systems may exhibit delay and noise induced transitions to bistability and secondary transitions to non stationarity our general findings are exemplified for three models a gompertz model a hongler model and a model involving a 1 x 2 noise amplitude

stochastic system with coupling between non gaussian and gaussian noise terms a stochastic system with coupling between non gaussian and gaussian noise terms is investigated a general approximate fokker planck equation of the system is derived through a path integral approach for a bistable system the coupling between noise terms can induce the reentrance like phase transition while the parameter q of the departure from the gaussian noise can induce the first order like phase transition both the coupling and the parameter q can change the curve of the mean first passage time mfpt from monotonically decreasing function to a peak in the mfpt numerical simulations are carried out to check the approximate theoretical results reasonably good agreement is obtained

quantum surface of section method demonstration of semiclassical berry robnik energy level spacing distribution in a generic two dimensional hamiltonian system the recently developed quantum surface of section method is applied to a search for extremely high lying energy levels in a simple but generic hamiltonian system between integrability and chaos namely the semiseparable two dimensional oscillator using the stretch of 13445 consecutive levels with the sequential number around 1 8 107 eighteen million we have clearly demonstrated the validity of the semiclassical berry robnik level spacing distribution while at 1000 times smaller sequential quantum numbers we find the very persistent quasi universal phenomenon of power law level repulsion which is globally very well described by the phenomenological brody distribution this is the first statistically significant numerical confirmation of the berry robnik surmise in an autonomous two dimensional hamiltonian system

the study on a stochastic system with non gaussian noise and gaussian colored noise abstract in this paper a stochastic system with correlation between non gaussian noise and gaussian colored noise is investigated we carry out the functional methods to derive the approximate fokker planck equation and the expressions of stationary probability density function and mean first passage time are presented also we explore the effects of correlation between non gaussian and gaussian noise for the mean first passage time

distribution of resonance strengths in microwave billiards of mixed and chaotic dynamics a new measure for statistical properties of the wave function components of quantum systems the distribution of the product of two partial widths is introduced it is tested with data obtained in analog experiments with microwave billiards where the product of two partial widths equals the resonance strengths in the microwave spectra the billiards are from the family of the limacons one with chaotic and two with mixed classical dynamics for completely chaotic systems the partial widths generically obey a porter thomas distribution we show that in this case the distribution of their product equals a k0 distribution while we find deviations of the experimental strength distribution from the k0 distribution for the billiards with mixed dynamics the distributions agree perfectly for the chaotic billiard when taking into account the experimental threshold of detection in the theoretical description hence the strength distribution provides another stringent test for the connection between statistical properties of systems with classical chaotic dynamics and random matrix theory

three dimensional statistical data security problems suppose there is a three dimensional table of cross tabulated nonnegative integer statistics and suppose that all of the row column and file sums are revealed together with the values in some of the individual cells in the table the question arises as to whether as a consequence the values contained in some of the other suppressed cells can be deduced from the information revealed the corresponding problem in two dimensions has been comprehensively studied by gusfield siam j comput 17 1988 pp 552 571 who derived elegant polynomial time algorithms for the identification of any such compromised cells and for calculating the tightest bounds on the values contained in all cells that follow from the information revealed in this note it is shown by contrast that the three dimensional version of the problem is np complete it is also shown that if the suggested row column and file sums for an unknown three dimensional table are given with or without the values in some of the cells the problem of determining whether there exists any table with the given sums is np complete in the course of proving these results the np completeness of some constrained latin square construction problems which are of some interest in their own right is established

stochastic time delayed systems driven by correlated noises steady state analysis abstract in the present paper a class of stochastic time delayed systems driven by correlated gaussian white noises are considered novikov s theorem is used to derive delay fokker planck equations in the case of small time delays approximate stationary solutions are obtained as a special case the delay fokker planck equation and the approximate stationary probability density function is obtained for a bistable system numerical simulations show that the small delay approximation is a good approximation in the case of small delay furthermore the effects of the correlated noises and the feedback are investigated the critical curve separating the unimodal and bimodal regions of the stationary probability distribution is shown to be affected by the degree of the correlation of the noises and e the strength of the feedback both and e can change the curve of the stationary probability density function from a bimodal to a unimodal structure

behaviour of boundary functions for quantum billiards we study the behaviour of the normal derivative of eigenfunctions of the helmholtz equation inside billiards with dirichlet boundary condition these boundary functions are of particular importance because they uniquely determine the eigenfunctions inside the billiard and also other physical quantities of interest therefore they form a reduced representation of the quantum system analogous to the poincare section of the classical system for the normal derivatives we introduce an equivalent to the standard green function and derive an integral equation on the boundary based on this integral equation we compute the first two terms of the mean asymptotic behaviour of the boundary functions for large energies the first term is universal and independent of the shape of the billiard the second one is proportional to the curvature of the boundary the asymptotic behaviour is compared with numerical results for the stadium billiard different limacon billiards and the circle billiard and good agreement is found furthermore we derive an asymptotic completeness relation for the boundary functions

semiclassical trace formulas for noninteracting identical particles we extend the gutzwiller trace formula to systems of noninteracting identical particles the standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families the identical nature of the particles also introduces discrete permutational symmetries we exploit the formalism of creagh and littlejohn phys rev a 44 836 1991 who have studied semiclassical dynamics in the presence of continuous symmetries to derive many body trace formulas for the full and symmetry reduced densities of states numerical studies of the three particle cardioid billiard are used to explicitly illustrate and test the results of the theory

effects of time delay on transient behavior of a time delayed metastable system subjected to cross correlated noises abstract the effects of time delay on the transient properties of a time delayed metastable system subjected to cross correlated noises are studied by means of a stochastic simulation method it is found that i both additive noise and multiplicative noise can produce the noise enhanced stability nes effect ii the time delay induces critical behavior on the nes i e there is a critical value of the delay time c 1 2 2 above which the time delay increases the stability of the system enhanced by the additive noise and below which the nes effect induced by the additive noise disappears iii there exists another critical value of the delay time c 2 3 0 above which the time delay increases the stability of the system enhanced by the multiplicative noise and below which the time delay decreases it

delay fokker planck equations novikov s theorem and boltzmann distributions as small delay approximations we study time delayed stochastic systems that can be described by means of so called delay fokker planck equations using novikov s theorem we first show that the theory of delay fokker planck equations is on an equal footing with the theory of ordinary fokker planck equations subsequently we derive stationary distributions in the case of small time delays in the case of additive noise systems these distributions can be cast into the form of boltzmann distributions involving effective potential functions

the properties of the anti tumor model with coupling non gaussian noise and gaussian colored noise abstract the anti tumor model with correlation between multiplicative non gaussian noise and additive gaussian colored noise has been investigated in this paper the behaviors of the stationary probability distribution demonstrate that the multiplicative non gaussian noise plays a dual role in the development of tumor and an appropriate additive gaussian colored noise can lead to a minimum of the mean value of tumor cell population the mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states an increase in both the non gaussian noise intensity and the departure from the gaussian noise can accelerate the transition from the disease state to the healthy state on the contrary an increase in cross correlated degree will slow down the transition moreover the correlation time can enhance the stability of the disease state

effects of cross correlation on the relaxation time of a bistable system driven by cross correlated noise we study the effects of correlations between additive and multiplicative noise on relaxation time in a bistable system driven by cross correlated noise using the projection operator method we derived an analytic expression for the relaxation time t c of the system which is the function of additive ensuremath alpha and multiplicative d noise intensities correlation intensity ensuremath lambda of noise and correlation time ensuremath tau of noise after introducing a noise intensity ratio and a dimensionless parameter r d ensuremath alpha and then performing numerical computations we find the following i for the case of rl1 the relaxation time t c increases as r increases ii for the cases of rg 1 there is a one peak structure on the t c ensuremath r plot and the effects of cross correlated noise on the relaxation time are very notable iii for the case of rl1 t c almost does not change with both ensuremath lambda and ensuremath tau and for the cases of rg 1 t c decreases as ensuremath lambda increases however t c increases as ensuremath tau increases ensuremath lambda and ensuremath tau play opposite roles in t c i e ensuremath lambda enhances the fluctuation decay of dynamical variable and ensuremath tau slows down the fluctuation decay of dynamical variable

random generation of 2 2 2 j contingency tables we propose two markov chains for sampling m 1 dimensional contingency tables indexed by 1 2 m 1 2 n stationary distributions of our chains are the uniform distribution and a conditional multinomial distribution which is equivalent to the hypergeometric distribution if m 1 mixing times of our chains are bounded by n n 1 ln n 2me n n 1 ln dn e where d is the average of the values in the cells and e is a given error bound we use the path coupling method for estimating the mixing times of our chains and showed that our chains mix rapidly

new universal aspects of diffusion in strongly chaotic systems we study some new universal aspects of diffusion in chaotic systems especially those having very large lyapunov coefficients on the chaotic indecomposable topologically transitive component we do this by discretizing the chaotic component on the surface of section sos in a large number n of simplectically equally big cells in the sense of equal relative invariant ergodic measure normalized so that the total measure of the chaotic component is unity by iterating the transition of the chaotic orbit through the sos where j counts the number of iterations discrete time and assuming complete lack of correlation even between consecutive crossings which can be justified due to the very large lyapunov exponents we show the universal approach of the relative measure of the occupied cells denoted by to the asymptotic value of unity in the following way so that in the limit of big n we have for j n fixed the exponential law this analytic result is verified numerically in a variety of specific systems for a plane billiard robnik 1983 for a 3d billiard prosen 1997 for an ergodic logistic map tent map for a standard map k 400 and for the hydrogen atom in a strong magnetic field the agreement is almost perfect except in the latter two systems for some long time deviations on very small scales however for henon heiles system and for the standard map k 3 the deviations are noticeable though not very big only about 1 we have tested the random number generators press et al 1986 and confirmed that some are almost perfect ran0 and ran3 whilst two of them ran1 and ran2 exhibit big deviations

spectral statistics in the quantized cardioid billiard the spectral statistics of the strongly chaotic cardioid billiard is studied the analysis is based on the first 11 000 quantal energy levels for both odd and even symmetry it is found that the level spacing distribution is in good agreement with the gaussian orthogonal ensemble distribution of random matrix theory in the cases of the number variance and rigidity we observe agreement with the random matrix model for short range correlations only whereas for long range correlations both statistics saturate in agreement with semiclassical expectations furthermore the conjecture that for classically chaotic systems the normalized mode fluctuations have a universal gaussian distribution with unit variance is tested and found to be in very good agreement for both symmetry classes by means of the gutzwiller trace formula the trace of the cosine modulated heat kernel is studied since the billiard boundary is focusing there are conjugate points that give rise to zeros instead of exclusively at gaussian peaks at the locations of the periodic orbits

delay fokker planck equations perturbation theory and data analysis for nonlinear stochastic systems with time delays we study nonlinear stochastic systems with time delayed feedback using the concept of delay fokker planck equations introduced by guillouzic l heureux and longtin we derive an analytical expression for stationary distributions using first order perturbation theory we demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data in addition we show that the fokker planck perspective for stochastic systems with time delays is consistent with the so called extended phase space approach to time delayed systems

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators