homogenization limits and wigner transforms we present a theory for carrying out homogenization limits for quadratic functions called energy densities of solutions of initial value problems ivps with anti self adjoint spatial pseudo differential operators pdos the approach is based on the introduction of phase space wigner matrix measures that are calculated by solving kinetic equations involving the spectral properties of the pdo the weak limits of the energy densities are then obtained by taking moments of the wigner measure the very general theory is illustrated by typical examples like semi classical limits of schrodinger equations with or without a periodic potential the homogenization limit of the acoustic equation in a periodic medium and the classical limit of the dirac equation 1997 john wiley sons inc

adiabatic small noise fluctuations around anticipated synchronization a perspective from scalar master slave dynamics abstract in this paper we extract and highlight some essential ingredients and properties that characterize the phenomenon of anticipated synchronization when external additive noise sources perturb the master and slave dynamics our results rely on a minimal scalar setup able to exhibit the more fundamental aspects of this phenomenon where the fluctuations around the average dynamics are worked out in a small noise and adiabatic approximations allowing to describe their dynamics through linear delay langevin equations in this context we find necessary conditions that guarantee anticipated synchronization in the mean value fluctuations around this condition are studied through the stationary correlation of the delayed difference between the master and slave dynamics it is shown that external noise properties can be inferred by measuring this object conditions for minimizing the dynamical fluctuations around the anticipated synchronization in mean value are found a detailed analysis of the dependence on the characteristic parameters is presented

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

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

a small delay and correlation time limit of stochastic differential delay equations with state dependent colored noise we consider a general stochastic differential delay equation sdde with state dependent colored noises and derive its limit as the time delays and the correlation times of the noises go to zero the work is motivated by an experiment involving an electrical circuit with noisy delayed feedback an ornstein uhlenbeck process is used to model the colored noise the main methods used in the proof are a theorem about convergence of solutions of stochastic differential equations by kurtz and protter and a maximal inequality for sums of a stationary sequence of random variables by peligrad and utev

fokker planck equations for time delayed systems via markovian embedding for stochastic systems with discrete time delay the fokker planck equation fpe of the one time probability density function pdf does not provide a complete self contained probabilistic description it explicitly involves the two time pdf and represents in fact only the first member of an infinite hierarchy we here introduce a new approach to obtain a fokker planck description by using a markovian embedding technique and a subsequent limiting procedure on this way we find a closed complete fpe in an infinite dimensional space from which one can derive a hierarchy of fpes while the first member is the well known fpe for the one time pdf we obtain as second member a new representation of the equation for the two time pdf from a conceptual point of view our approach is simpler than earlier derivations and it yields interesting insight into both the physical meaning and the mathematical structure of delayed processes we further propose an approximation for the two time pdf which is a central quantity in the description of these non markovian systems as it directly gives the correlation between the present and the delayed state application to a prototypical bistable system reveals that this approximation captures the non trivial effects induced by the delay remarkably well despite its surprisingly simple form moreover it outperforms earlier approaches for the one time pdf in the regime of large delays

on the periodic wigner poisson fokker planck system abstract this paper is concerned with the existence and uniqueness analysis of global classical solutions of a diffusive quantum evolution equation with nonlinear coupling to the poisson equation the main technical difficulty in the existence proof is to show that the quantum fokker planck term is a semigroup generator in a weighted l 2 space the potential term is then a lipschitz perturbation of it

mixing and covering in the symmetric groups abstract we discuss mixing and covering theorems in the symmetric groups we present an example of a covering without mixing and study the conjugacy class 2 n 2 of symmetric group s n which demonstrates mixing without covering we derive some new character identities from the computation of 2 n 2 2 and also compute 2 n 2 3 filling a hole between theorems of j l brenner j austral math soc ser a 25 1978 210 214 and y dvir in products of conjugacy classes in groups lecture notes in math vol 1112 springer verlag new york berlin 1985 this computation also motivates a certain classification of 3 colored 3 regular graphs

diffusive corrections to asymptotics of a strong field quantum transport equation abstract the asymptotic analysis of a linear high field wigner bgk equation is developed by a modified chapman enskog procedure by an expansion of the unknown wigner function in powers of the knudsen number evolution equations are derived for the terms of zeroth and first order in in particular a quantum drift diffusion equation for the position density of electrons with an order correction on the field terms is obtained well posedness and regularity of the approximate problems are established and a rigorous proof that the difference between exact and asymptotic solutions is of order 2 uniformly in time and for arbitrary initial data is given

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

an operator splitting method for the wigner poisson problem the wigner poisson equation describes the quantum mechanical motion of electrons in a self consistent electrostatic field the equation consists of a transport term and a non linear pseudodifferential operator in this paper we analyze an operator splitting method for the linear wigner equation and the coupled wigner poisson problem for this semidiscretization in time consistency and nonlinear stability are established in an l2 framework we present a numerical example to illustrate the method

control of noise induced oscillations by delayed feedback abstract we propose a method to control noise induced motion based on using delayed feedback in the form of the difference between the delayed and the current states of the system the method is applied to two different types of systems namely a self oscillator near andronov hopf bifurcation and a threshold system in both cases we demonstrate that by variation of time delay one can effectively control coherence and timescales of stochastic oscillations the entrainment of the basic period of oscillations by time delay is discovered we give explanations of the phenomena observed and provide a theory for the system near bifurcation

effects of time delay on symmetric two species competition subject to noise noise and time delay act simultaneously on real ecological systems the lotka volterra model of symmetric two species competition with noise and time delay was investigated in this paper by means of stochastic simulation we find that i the time delay induces the densities of the two species to periodically oscillate synchronously ii the stationary probability distribution function of the two species densities exhibits a transition from multiple to single stability as the delay time increases iii the characteristic correlation time for the sum of the two species densities squared exhibits a nonmonotonic behavior as a function of delay time our results have the implication that the combination of noise and time delay could provide an efficient tool for understanding real ecological systems

a new stochastic gompertz diffusion process with threshold parameter computational aspects and applications abstract in this paper we propose a new homogeneous stochastic gompertz diffusion model with a threshold parameter this can be considered an extension of the homogeneous three parameter gompertz process with the addition of a fourth parameter from the corresponding kolmogorov equations and ito s stochastic differential equations we obtain the transition probability density function and the moments of this process specifically the trend functions the parameters are estimated by considering discrete sampling of the sample path of the model and by using maximum likelihood methodology estimation of the threshold parameter requires us to solve a non linear equation which is achieved by the newton raphson method simulated model data are considered and the methodology in question is applied to estimate the parameters the values obtained are compared with those used in the simulation finally the model is applied to model the evolution of the trend of the dynamic variable average monthly salary cost for all sectors and broken down construction industry services in spain for the period 1985 2005

path integral approach to quantum brownian motion abstract we apply the influence functional method of feynman and vernon to the study of brownian motion at arbitrary temperature by choosing a specific model for the dissipative interaction of the system of interest with its environment we are able to evaluate the influence functional in closed form and express it in terms of a few parameters such as the phenomenological viscosity coefficient we show that in the limit h 0 the results obtained from the influence functional formalism reduce to the classical fokker planck equation in the case of a simple harmonic oscillator with arbitrarily strong damping and at arbitrary temperature we obtain an explicit expression for the time evolution of the complete density matrix x x t when the system starts in a particular kind of pure state we compare our results with those of other approaches to the problem of dissipation in quantum mechanics

exact statistics for linear time delayed oscillators subjected to gaussian excitation abstract large classes of stochastic systems of interest to acoustics and vibrations have time delays the presence of these time delays hinders efforts to provide physical insight into the system behavior because of the difficulty of finding exact solutions this paper addresses this issue by presenting exact steady state solutions for the probability density functions pdf s for linear time delayed oscillators subjected to gaussian excitation of arbitrary correlation a key parameter influencing these pdf s is shown to be the ratio of mean generalized kinetic energy to the mean generalized potential energy in a single damped harmonic oscillator this ratio is unity which implies an equi partition of generalized energy time delays cause deviations in the equi partition of generalized energy which creates regions of preferential total phase and causes the amplitude pdf to shift from a rayleigh distribution to a hoyt distribution

characters of symmetric groups sharp bounds and applications we provide new estimates on character values of symmetric groups which hold for all characters and which are in some sense best possible it follows from our general bound that if a permutation s n has at most n o 1 cycles of length m then 1 1 m o 1 for all irreducible characters of s n this is a far reaching generalization of a result of fomin and lulov

fuchsian groups finite simple groups and representation varieties let be a fuchsian group of genus at least 2 at least 3 if is non oriented we study the spaces of homomorphisms from to finite simple groups g and derive a number of applications concerning random generation and representation varieties precise asymptotic estimates for hom g are given implying in particular that as the rank of g tends to infinity this is of the form g 1 o 1 where is the measure of we then prove that a randomly chosen homomorphism from to g is surjective with probability tending to 1 as g combining our results with lang weil estimates from algebraic geometry we obtain the dimensions of the representation varieties text hom gamma bar g where bar g is gl n k or a simple algebraic group over k an algebraically closed field of arbitrary characteristic a key ingredient of our approach is character theory involving the study of the zeta function g s 1 s where the sum is over all irreducible complex characters of g

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

upper bound on the characters of the symmetric groups let c be a conjugacy class in the symmetric group s n and be a partition of n let f be the degree of the irreducible representation s c the character of s at c and r c the normalized character c f we prove that there exist constants b 0 and 1 q 0 such that for n 4 for every conjugacy class c in s n and every irreducible representation s of s n r c max q 1 n 1 n b supp c where supp c is the number of non fixed digits under the action of a permutation in c 1 is the size of the largest part in and 1 is the number of parts in the proof is obtained by enumeration of rim hook tableaux the hook formula and probabilistic arguments combinatorial algebraic and statistical applications follow this result in particular we estimate the rate of mixing of random walks on the alternating groups with respect to conjugacy classes

an analysis of the wigner poisson problem with inflow boundary conditions abstract we present a study of the wigner poisson problem in a bounded spatial domain with non homogeneous and time dependent inflow boundary conditions this system of nonlinearly coupled equations is a mathematical model for quantum transport of charges in a semiconductor with external contacts we prove well posedness of the linearized n dimensional problem as well as existence and uniqueness of a global in time regular solution of the one dimensional nonlinear problem

theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback a network of leaky integrate and fire neurons with global inhibitory feedback and under the influence of spatially correlated noise is studied we calculate the spectral statistics of the network power spectrum of the population activity cross spectrum between spike trains of different neurons as well as of a single neuron power spectrum of spike train cross spectrum between external noise and spike train within the network as shown by comparison with numerical simulations our theory works well for arbitrary network size if the feedback is weak and the amount of external noise does not exceed that of the internal noise by means of our analytical results we discuss the quality of the correlation induced oscillation in a large network as a function of the transmission delay and the internal noise intensity it is shown that the strongest oscillation is obtained in a system with zero internal noise and adiabatically long delay i e the delay period is longer than any other time scale in the system for a neuron with a strong intrinsic frequency the oscillation becomes strongly anharmonic in the case of a long delay time we also discuss briefly the kind of synchrony introduced by the feedback induced oscillation

fokker planck description for a linear delayed langevin equation with additive gaussian noise we construct an equivalent probability description of linear multi delay langevin equations subject to additive gaussian white noise by exploiting the time convolutionless transform and a time variable transformation we are able to write a fokker planck equation fpe for the 1 time and for the 2 time probability distributions valid irrespective of the regime of stability of the langevin equations we solve exactly the derived fpes and analyze the aging dynamics by studying analytically the conditional probability distribution we discuss explicitly why the initially conditioned distribution is not sufficient to describe fully out a non markov process as both preparation and observation times have bearing on its dynamics as our analytic procedure can also be applied to linear langevin equations with memory kernels we compare the non markov dynamics of a one delay system with that of a generalized langevin equation with an exponential as well as a power law memory application to a generalization of the green kubo formula is also presented

stochastic order parameter equation of isometric force production revealed by drift diffusion estimates we address two questions that are central to understanding human motor control variability what kind of dynamical components contribute to motor control variability i e deterministic and or random ones and how are those components structured to this end we derive a stochastic order parameter equation for isometric force production from experimental data using drift diffusion estimates we show that the force variability increases with the required force output because of a decrease of deterministic stability and an accompanying increase of noise intensity a structural analysis reveals that the deterministic component consists of a linear control loop while the random component involves a noise source that scales with force output in addition we present evidence for the existence of a subject independent overall noise level of human isometric force production

analysis of a semidiscrete version of the wigner equation we introduce a semidiscretized version of the wigner equation discretization concerning the velocity variable we show that the corresponding discrete velocity problem is well posed and permits us to approach the solution of the continuous problem when the mesh size of the discretization vanishes the approximation shows spectral accuracy because the rate of convergence corresponds to the sobolev regularity of the solution of the continuous problem we also discuss the behavior of the solution with respect to the planck constant

representations of symmetric groups and free probability abstract we consider representations of symmetric groupssqfor largeq we give the asymptotic behaviour of the characters when the corresponding young diagrams rescaled by a factorq 1 2 converge to some prescribed shape this behaviour can be expressed in terms of the free cumulants for a probability measure associated with the limit shape of the diagram we also show that the basic operations of representation theory like taking tensor products restriction or induction have a limiting behavior which can be described using the free probability theory of d voiculescu

time dependent dissipation in nonlinear schrodinger systems a coupled nonlinear schrodinger poisson equation is considered which contains a time dependent dissipation function as a specific model of dissipation effects in nonlinear quantum transport theory and other areas the wigner poisson equation associated with this system is derived using conservation and quasiconservation laws and certain growth assumptions for the nonlinearities and the dissipation function global existence of solutions to the cauchy problem of the time dependent schrodinger poisson system is shown both for small attractive case or arbitrary data repulsive case

diameters of finite simple groups sharp bounds and applications let g be a finite simple group and let s be a normal subset of g we determine the diameter of the cayley graph r g s associated with g and s up to a multiplicative constant many applications follow for example we deduce that there is a constant c such that every element of g is a product of c involutions and we generalize this to elements of arbitrary order we also show that for any word w w xl xd there is a constant c c w such that for any simple group g on which w does not vanish every element of g is a product of c values of w from this we deduce that every verbal subgroup of a semisimple profinite group is closed other applications concern covering numbers expanders and random walks on finite simple groups

synchronization of noisy delayed feedback systems with delayed coupling synchronization of delayed coupled and stochastically perturbed systems with delayed nonlinear feedback is studied using as an example circular chains of three and four delayed coupled ikeda oscillators it is proved that in the case of multiplicative noise the exact synchronization in the mean occurs for sufficiently large coupling and an analytic estimate of the sufficient coupling is given the sufficiency condition is compared with numerical computations and typical effects of noise on the exact and some generalized types of synchronization are illustrated

the random k cycle walk on the symmetric group we study the random walk on the symmetric group s n generated by the conjugacy class of cycles of length k we show that the convergence to uniform measure of this walk has a cut off in total variation distance after frac n k log n steps uniformly in k o n as n rightarrow infty the analysis follows from a new asymptotic estimation of the characters of the symmetric group evaluated at cycles

controlling coherence of noisy and chaotic oscillators by a linear feedback abstract we analyze the dynamics of a noisy limit cycle oscillator coupled to a general passive linear system we analytically demonstrate that the phase diffusion constant which characterizes the coherence of the oscillations can be efficiently controlled theoretical analysis is performed in the framework of linear and gaussian approximations and is supported by numerical simulations we also demonstrate numerically the coherence control of a chaotic system

word maps conjugacy classes and a noncommutative waring type theorem let w w x xd 1 be a nontrivial group word we show that if g is a sufficiently large finite simple group then every element g e g can be expressed as a product of three values of w in g this improves many known results for powers commutators as well as a theorem on general words obtained in 19 the proof relies on probabilistic ideas algebraic geometry and character theory our methods which apply the zeta function g s x eirrg xo s giye rise to various additional results of independent interest including applications to conjectures of ore and thompson

influence of delayed time and colored noise in a bistable system subject to asymmetric dichotomous noise and colored noise the influence of delayed time and colored noise in a bistable system subject to asymmetric dichotomous noise and colored noise is studied applying small delay time approximation under the adiabatic limit condition the expression of the signal to noise ratio snr of the system is obtained it is found that the snr varies non monotonously with the delayed time and the correlation of the colored noise moreover the snr exhibits sr behavior when it is plotted as a function of the intensity and asymmetry of the dichotomous noise and as a function of the strength of the colored noise

augmented moment method for stochastic ensembles with delayed couplings ii fitzhugh nagumo model dynamics of fitzhugh nagumo fn neuron ensembles with time delayed couplings subject to white noises has been studied by using both direct simulations and a semianalytical augmented moment method amm which has been proposed in a preceding paper h hasegawa phys rev e 70 021911 2004 for n unit fn neuron ensembles amm transforms original 2n dimensional stochastic delay differential equations sddes to infinite dimensional deterministic des for means and correlation functions of local and global variables infinite order recursive des are terminated at the finite level m in the level m amm mathrm amm m yielding 8 m 1 dimensional deterministic des when a single spike is applied the oscillation may be induced if parameters of coupling strength delay noise intensity and or ensemble size are appropriate effects of these parameters on the emergence of the oscillation and on the synchronization in fn neuron ensembles have been studied the synchronization shows the fluctuation induced enhancement at the transition between nonoscillating and oscillating states results calculated by amm5 are in fairly good agreement with those obtained by direct simulations

the waring problem for finite simple groups the classical waring problem deals with expressing every natural number as a sum of g k k th powers recently there has been considerable interest in similar questions for non abelian groups and simple groups in particular here the k th power word can be replaced by an arbitrary group word w 6 1 and the goal is to express group elements as short products of

multivariate markov processes for stochastic systems with delays application to the stochastic gompertz model with delay using the method of steps we describe stochastic processes with delays in terms of markov diffusion processes thus multivariate langevin equations and fokker planck equations are derived for stochastic delay differential equations natural periodic and reflective boundary conditions are discussed both ito and stratonovich calculus are used in particular our fokker planck approach recovers the generalized delay fokker planck equation proposed by guillouzic et al the results obtained are applied to a model for population growth the gompertz model with delay and multiplicative white noise

measure preserving words are primitive a word w 2 fk the free group on k generators is called primitive if it belongs to some basis of fk associated with w and a finite group g is the word map w g g g defined on the direct product of k copies of g we call w measure preserving if given uniform measure on g g the image of this word map induces uniform measure on g for every finite group g it is easy to see that every primitive word is measure preserving and several authors have conjectured that the two properties are in fact equivalent here we prove this conjecture the main ingredients of the proof include random coverings of stallings graphs algebraic extensions of free groups and mobius inversions our methods yield the stronger result that a subgroup of fk is measure preserving iff it is a free factor as an interesting corollary of this result we resolve a question on the profinite topology of free groups and show that the primitive elements of fk form a closed set in this topology

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

surjective word maps and burnside s p aq b theorem we prove surjectivity of certain word maps on finite non abelian simple groups more precisely we prove the following if n is a product of two prime powers then the word map x y mapsto x ny n is surjective on every finite non abelian simple group if n is an odd integer then the word map x y z mapsto x ny nz n is surjective on every finite quasisimple group these generalize classical theorems of burnside and feit thompson we also prove asymptotic results about the surjectivity of the word map x y mapsto x ny n that depend on the number of prime factors of the integer n

stationary wigner equation with inflow boundary conditions will a symmetric potential yield a symmetric solution based on the well posedness of the stationary wigner equation with inflow boundary conditions given in a arnold h lange and p f zweifel j math phys 41 2000 pp 7167 7180 we prove without any additional prerequisite conditions that the solution of the wigner equation with inflow boundary conditions will be symmetric only if the potential is symmetric this improves the result in d taj l genovese and f rossi europhys lett 74 2006 pp 1060 1066 which depends on the convergence of the solution formulated in the neumann series by numerical studies we present the convergence of the numerical solution to the symmetric profile for three different numerical schemes this implies that the upwind schemes can also yield a symmetric numerical solution contrary to the argument given in d taj l genovese and f rossi europhys lett 74 2006 pp 1060 1066

pitchfork and hopf bifurcation thresholds in stochastic equations with delayed feedback the bifurcation diagram of a model stochastic differential equation with delayed feedback is presented we are motivated by recent research on stochastic effects in models of transcriptional gene regulation we start from the normal form for a pitchfork bifurcation and add multiplicative or parametric noise and linear delayed feedback the latter is sufficient to originate a hopf bifurcation in that region of parameters in which there is a sufficiently strong negative feedback we find a sharp bifurcation in parameter space and define the threshold as the point in which the stationary distribution function p x changes from a delta function at the trivial state x 0 to p x approximately x alpha at small x with alpha 1 exactly at threshold we find that the bifurcation threshold is shifted by fluctuations relative to the deterministic limit by an amount that scales linearly with the noise intensity analytic calculations of the bifurcation threshold are also presented in the limit of small delay tau 0 that compare quite favorably with the numerical solutions even for moderate values of tau

moment closure hierarchies for kinetic theories this paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory the first member of the hierarchy is the euler system which is based on maxwellian velocity distributions while the second member is based on nonisotropic gaussian velocity distributions the closure proceeds in two steps the first ensures that every member of the hierarchy is hyperbolic has an entropy and formally recovers the euler limit the second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct navier stokes behavior this is achieved through the introduction of a generalization of the bgk collision operator the simplest such system in three spatial dimensions is a 14 moment closure which also recovers the behavior of the grad 13 moment system when the velocity distributions lie near local maxwellians the closure procedure can be applied to a general class of kinetic theories

stochastic resonance in a tumor immune system subject to bounded noises and time delay abstract immunotherapy is one of the most recent approaches in cancer therapy a mathematical model of tumor immune interaction subject to a periodic immunotherapy treatment imitated by a periodic signal correlative and bounded stochastic fluctuations and time delays is investigated by numerical simulations for its signal power amplification spa within the tailored parameter regime the synchronous response of tumor growth to the immunotherapy stochastic resonance sr versus both the noises and delays is obtained the details are as follows i the peak values of spa versus the noise intensity a in the proliferation term of tumor cells decrease as the frequency of periodic signal increases i e an increase of the frequency restrains the sr ii an increase of the amplitude of periodic signal restrains the sr versus a but boosts up the sr versus the noise intensity b in the immune term iii there is an optimum cross correlated degree between the two bounded noises at which the system exhibits the strongest sr versus the delay time the reaction time of tumor cell population to their surrounding environment constraints iv upon increasing the delay time double sr versus the delay time the time taken by both the tumor antigen identification and tumor stimulated proliferation of effectors emerges these results may be helpful for an immunotherapy treatment for the sufferer

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

coherence of noisy oscillators with delayed feedback a theory ofe ect ofdelayed f on the coherence ofthe noisy self sustained oscillations is developed in the gaussian approximation a closed system ofequations is derived f the phase di usion constant and the mean frequency a comparison with numerics shows that the theory works well for weak feedback and strong noise c

functional characterization of linear delay langevin equations we present an exact functional characterization of linear delay langevin equations driven by any noise structure defined through its characteristic functional this method relies on the possibility of finding an explicitly analytical expression for each realization of the delayed stochastic process in terms of those of the driving noise general properties of the transient dissipative dynamics are analyzed the corresponding interplay with a color gaussian noise is presented as a full application of our functional method we study a model for population growth with non gaussian fluctuations the gompertz model driven by multiplicative white shot noise

delayed stochastic systems noise and time delay are two elements that are associated with many natural systems and often they are sources of complex behaviors understanding of this complexity is yet to be explored particularly when both elements are present as a step to gain insight into such complexity for a system with both noise and delay we investigate such delayed stochastic systems both in dynamical and probabilistic perspectives a langevin equation with delay and a random walk model whose transition probability depends on a fixed time interval past delayed random walk model are the subjects of in depth focus as well as considering relations between these two types of models we derive an approximate fokker planck equation for delayed stochastic systems and compare its solution with numerical results

character theory of symmetric groups subgroup growth of fuchsian groups and random walks we develop a number of statistical aspects of symmetric groups mostly dealing with the distribution of cycles in various subsets of sn asymptotic properties of ordinary characters of symmetric groups and estimates for the multiplicities of root number functions of these groups as main applications we present an estimate for the subgroup growth of an arbitrary fuchsian group a finiteness result for the number of fuchsian presentations of such a group resolving a long standing problem of roger lyndon as well as a proof of a well known conjecture of roichman concerning the mixing time of random walks on symmetric groups

a spectral method for the numerical simulation of quantum tunneling phenomena tunneling effects in solid state physics are frequently described via a quantum mechanical formulation based on the wigner distribution function in this paper a mixed finite difference spectral collocation method for the solution of the corresponding equation of motion is developed and analyzed numerical examples illustrating the convergence results are presented

on the three dimensional wigner poisson problem with inflow boundary conditions abstract we study the wigner poisson problem in a bounded spatial domain with non homogeneous and time dependent inflow boundary conditions this system is a quantum model of charge transport in a semiconductor device coupled with reservoirs in presence of a self consistent potential and of an external one we state a local in time well posedness result for the problem the main difficulty is proving in the three dimensional case that the non linear potential term is a lipschitz perturbation of the affine streaming operator in an appropriately weighted l 2 space

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

space time discretization of series expansion methods for the boltzmann transport equation the approximate solution of the boltzmann transport equation via galerkin type series expansion methods leads to a system of first order differential equations in space and time for the expansion coefficients this system is extremely stiff close to the fluid dynamical regime for small knudsen numbers and exhibits a mildly dispersive behavior due to the acceleration of waves by the external force the electric field in this paper a class of difference methods is presented and analyzed which represent a generalization of the well known scharfetter gummel exponential fitting approach for the drift diffusion equations it is shown that by using appropriate operator splitting methods for the time discretization one obtains stability properties which are only mildly dependent on the knudsen number and essentially independent of the size of the electric field

operator splitting methods applied to spectral discretizations of quantum transport equations the wigner poisson equation is the most successful basis for transient simulations of quantum effect semiconductor devices so far we present a full discretization of this nonlinear pseudo differential system using a mixed spectral collocation and operator splitting method convergence and nonlinear stability of the scheme are proven

on finitely generated profinite groups ii products in quasisimple groups we prove two results 1 there is an absolute constant d such that for any finite quasisimple group s given 2d arbitrary automorphisms of s every element of s is equal to a product of d twisted commutators defined by the given automorphisms 2 given a natural number q there exist c c q and m m q such that if s is a finite quasisimple group with s z s c j j 1 m are any automorphisms of s and qj j 1 m are any divisors of q then there exist inner automorphisms j of s such that s m s j j q j these results which rely on the classification of finite simple groups are needed to complete the proofs of the main theorems of part i

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

fuchsian groups coverings of riemann surfaces subgroup growth random quotients and random walks abstract fuchsian groups acting as isometries of the hyperbolic plane occur naturally in geometry combinatorial group theory and other contexts we use character theoretic and probabilistic methods to study the spaces of homomorphisms from fuchsian groups to symmetric groups we obtain a wide variety of applications ranging from counting branched coverings of riemann surfaces to subgroup growth and random finite quotients of fuchsian groups as well as random walks on symmetric groups in particular we show that in some sense almost all homomorphisms from a fuchsian group to alternating groups an are surjective and this implies higman s conjecture that every fuchsian group surjects onto all large enough alternating groups as a very special case we obtain a random hurwitz generation of an namely random generation by two elements of orders 2 and 3 whose product has order 7 we also establish the analogue of higman s conjecture for symmetric groups we apply these results to branched coverings of riemann surfaces showing that under some assumptions on the ramification types their monodromy group is almost always sn or an another application concerns subgroup growth we show that a fuchsian group has n o 1 index n subgroups where is the measure of and derive similar estimates for so called eisenstein numbers of coverings of riemann surfaces a final application concerns random walks on alternating and symmetric groups we give necessary and sufficient conditions for a collection of almost homogeneous conjugacy classes in an to have product equal to an almost uniformly pointwise our methods involve some new asymptotic results for degrees and values of irreducible characters of symmetric groups

commutator maps measure preservation and t systems let g be a finite simple group we show that the commutator map g g g is almost equidistributed as g 1 this somewhat surprising result has many applications it shows that a for a subset x g we have 1 x g 2 x g o 1 namely is almost measure preserving from this we deduce that almost all elements g 2 g can be expressed as commutators g x y where x y generate g this enables us to solve some open problems regarding t systems and the product replacement algorithm pra graph we show that the number of t systems in g with two generators tends to infinity as g 1 this settles a conjecture of guralnick and pak a similar result follows for the number of connected components of the pra graph of g with two generators some of our results apply for more general finite groups and more general word maps our methods are based on representation theory combining classical character theory with recent results on character degrees and values in finite simple groups in particular the so called witten zeta function g s p 2irr g 1 s plays a key role in the proofs

word maps and waring type problems waring s problem asks whether every natural number is a sum of g k fcth powers where g is a suitable function this was solved affirmatively by hubert in 1909 optimizing g k has been a central problem in additive number theory ever since see na for more detail and background recently there has been considerable interest in group theoretic analogues of this phenomenon where the aim is to present group elements as short products of certain special elements these special elements can be powers or commutators or values of a general word w or elements of a special conjugacy class in the group the motivation for this is sometimes topological let g be a topologically finitely generated pro p group using expressions of elements of the commutator subgroup g1 as bounded products of commutators serre showed that g is closed and deduced that every finite index subgroup of g is open a recent deep result of nikolov and segal nsi ns2 shows that this holds for every finitely generated profinite group again the core of the proof is presenting group elements as short products of values of certain words

quantum moment hydrodynamics and the entropy principle this paper presents how a non commutative version of the entropy extremalization principle allows to construct new quantum hydrodynamic models our starting point is the moment method which consists in integrating the quantum liouville equation with respect to momentum p against a given vector of monomials of p like in the classical case the so obtained moment system is not closed inspired from levermore s procedure in the classical case 26 we propose to close the moment system by a quantum wigner distribution function which minimizes the entropy subject to the constraint that its moments are given in contrast to the classical case the quantum entropy is defined globally and not locally as the trace of an operator therefore the relation between the moments and the lagrange multipliers of the constrained entropy minimization problem becomes nonlocal and the resulting moment system involves nonlocal operators instead of purely local ones in the classical case in the present paper we discuss some practical aspects and consequences of this nonlocal feature

stationary distributions of stochastic processes described by a linear neutral delay differential equation stationary distributions of processes are derived that involve a time delay and are defined by a linear stochastic neutral delay differential equation the distributions are gaussian distributions the variances of the gaussian distributions are either monotonically increasing or decreasing functions of the time delays the variances become infinite when fixed points of corresponding deterministic processes become unstable

quantum dynamical semigroups for diffusion models with hartree interaction we consider a class of evolution equations in lindblad form which model the dynamics of dissipative quantum mechanical systems with mean field interaction particularly this class includes the so called quantum fokker planck poisson model the existence and uniqueness of global in time mass preserving solutions is proved thus establishing the existence of a nonlinear conservative quantum dynamical semigroup the mathematical difficulties stem from combining an unbounded lindblad generator with the hartree nonlinearity

fibers of word maps and some applications every word w in the free group fd defines for each group g a word map also denoted w from gd to g we prove that for all w 1 there exists 0 such that for all finite simple groups g and all g g w 1 g o g d where the implicit constant depends only on w in particular the probability that w g1 gd 1 is at most g for some 0 and all large finite simple groups g this result is then applied in the context of subgroup growth and representation varieties

on finitely generated profinite groups i strong completeness and uniform bounds we prove that in every finitely generated profinite group every subgroup of finite index is open this implies that the topology on such groups is determined by the algebraic structure this is deduced from the main result about finite groups let w be a locally finite group word and d n then there exists f f w d such that in every d generator finite group g every element of the verbal subgroup w g is equal to a product of f w values an analogous theorem is proved for commutators this implies that in every finitely generated profinite group each term of the lower central series is closed the proofs rely on some properties of the finite simple groups to be established in part ii

upper bound on the characters of the symmetric groups for balanced young diagrams and a generalized frobenius formula we study asymptotics of an irreducible representation of the symmetric group sn corresponding to a balanced young diagram a young diagram with at most rows and columns for some fixed constant c in the limit as n tends to infinity we show that there exists a constant d which depends only on c with a property that where p denotes the length of a permutation the minimal number of factors necessary to write p as a product of transpositions our main tool is an analogue of the frobenius character formula which holds true not only for cycles but for arbitrary permutations

stationary solutions of linear stochastic delay differential equations applications to biological systems recently k uchler and mensch stochastics stochastics rep 40 23 1992 derived exact stationary probability densities for linear stochastic delay differential equations this paper presents an alternative derivation of these solutions by means of the fokker planck approach introduced by guillouzic phys rev e 59 3970 1999 61 4906 2000 applications of this approach which is argued to have greater generality are discussed in the context of stochastic models for population growth and tracking movements

numerical simulation of the quantum liouville poisson system abstract we simulate the one dimensional quantum liouville poisson system using the splitting scheme and the accompanying double fourier transformation in x and p space this code is used to study the quantum effects in the one dimensional electrostatic plasma i e the well known nonlinear landau damping and two stream instability problems

stochastic resonance in a bistable system subject to multi time delayed feedback and aperiodic signal we discuss in detail the effects of the multi time delayed feedback driven by an aperiodic signal on the output of a stochastic resonance sr system the effective potential function and dynamical probability density function pdf are derived to measure the performance of the sr system in the presence of a binary random signal the bit error rate ber defined by the dynamical pdf is employed as is commonly used in digital communications we find that the delay time strength of the feedback and number of time delayed terms can change the effective potential function and the effective amplitude of the signal and then affect the ber of the sr system the numerical simulations strongly support the theoretical results the goal of this investigation is to explore the effects of the multi time delayed feedback on sr and give a guidance to nonlinear systems in the application of information processing

the wignerpoisson x system in wiener algebra in this paper we concern over a class of the wignerpoisson x system introduced and developed by bao etal 2003 mauser 2001 and stimming 2005 respectively the model describes the quantum mechanical motion of particles under the influence of the nonlocal hartree potential and a local power term exchange potential the existence and uniqueness of local mild solution to the n dimensional n 1 3 cauchy problems are established on the space of some integrable functions whose inverse fourier transforms are also integrable